evaluation of the surface reactivity of beta-titanium

Evaluation of the surfacereactivity of β-Titanium

Dissertation

zur

Erlangung des Grades

"Doktor der Naturwissenschaften"

an der Fakultät für Chemie und Biochemie

der Ruhr-Universität Bochum

vorgelegt von

Michael Teka Woldemedhin

geboren in Addis Abeba, Äthiopien

BochumDezember 2011

This doctoral study was carried out under the supervision of Prof. Dr. AchimWalter Hassel and Prof. Dr. Ing. Dierk Raabe in the group of Electrochemistryand Corrosion, Department of Interface Chemistry and Surface Engineering,Max Planck Institut für Eisenforschung, Düsseldorf, Germany in the frame of theInternational Max Planck Research School for Surface and Interface Engineer-ing in Advanced Materials (IMPRS-SurMat) and at the Institut für ChemischeTechnologie Anorganischer Stoffe (ICTAS), Johannes Kepler University, Linz,Austria in the period between April, 2008 and December, 2011.

1. Gutachter: Prof. Dr. Achim Walter Hassel2. Gutachter: Prof. Dr. Ing. Dierk Raabe2. Gutachter: Prof. Dr. Wolfgang Schuhmann

Acknowledgement

The lion share of my gratitude goes to Prof. Dr. Achim Walter Hassel andProf. Dr. Ing. Dierk Raabe for their supervision of my research in which theirconstant support, encouragement and complete freedom was always by my side.I would also like to thank Prof. Dr. Wolfgang Schuhmann for reviewing mydissertation.The Intenational Max Planck Research School for Surface and Interface Engi-neering in Advanced Materials (IMPRS-SurMat) is duely acknowledged for thedoctoral fellowship.I would take this opportunity to thank the administrative director of theIMPRS-SurMat school Dr. Rebekka Loschen and the SurMat staff Vanja Wüsterand Elke Gattermann for their support during my time as a SurMat student.The group members of the Electrochemistry and Corrosion group of the MaxPlanck Institut für Eisenforschung and the Institut für Chemische TechnologieAnorganischer Stoffe (ICTAS) at the Johannes Kepler University are also duelyacknowledged for their support and welcoming me to the group: Dr. AndreiIonut Mardare for passing on his knowledge about the fabrication of scanningdroplet cell and the scanning droplet setup, Dr. Daniel Sanders for the scientificdiscussions we had, Andrea Mingers for the technical support during my stayat MPIE, Karl Kellner for the fast provision of all the chemicals and for all thetechnical help I was in need for.Special thanks goes to the head of the mechanical workshop of the MPIE RalfSelbach and Peter Thyssen for the fabrication of the componenets of the scan-ning droplet cell.I thank my office mates Dr. Genesis Ankah, Dr. Daniel Sanders, Dr. YingChen, Stefanie Drensler, Christian Schnepf for all the laughter we had in thethree offices I sat during my PhD studies.I thank my friends Dr. Faycal Riad Hamou, Dr. Juan Zuo, Dr. Edmanuel Tor-res, Mulda Muldarisnur, Mauro Martin and Kemal Davut for the crazy laughsand good times we had.Friends back home and in far away places Samson Gebremedhin, Anteneh (Abu)Gashaw, Tesfa Solomon, Yohannes Tesfaye, Sefonias Mekonnen, Yonas (Pupi)Abera, Wondwossen Shewangizaw (Baby) thank you for the morale boost.

I would like to express my deepest gratitude for all the teachers and instructorsfrom my time in Misrak Dil school till the present day who shared their invalu-able knowledge and made me what I am today.My parents, TekaWoldemedhin and Enanu Alemu (Zeduye), and siblings Sirgut,Addis and Netsi (Mitaye) for your love and support which would have been im-possible to acomplish this. Love you all!!

Evaluation of the surface reactivityof β-Titanium

Dissertation

by

Michael Teka Woldemedhin

The secret is comprised in three words-Work, finish, publish.

Michael Faraday

Abstract

The surface reactivity of three Ti-Nb alloys is presented in this work. The threealloys are a β-type titanium alloy with a composition of Ti-30at.% Nb andtwo α+β-type titanium alloys with compositions Ti-10at.% Nb and Ti-20at.%Nb. The surface reactivity of these alloys is investigated by using two typesof electrochemical cells: double glass-walled electrochemical cell and a scanningdroplet cell.The double glass walled electrochemical cell is used to evaluate the surface re-activity of all the three alloys in an acetate buffer of pH 6.0. The reactivitystudies were carried out by anodizing a 0.3 cm2 sample surface exposed to theelectrolyte solution. The anodization process was carried out by using cyclicvoltammetry electrochemical technique in steps of 1 V so that the mechanismof oxide growth, reactions involved during oxide growth, oxide growth rate andkinetics behind the oxide growth were studied.Electrochemical impedance measuremets right after each anodic oxide growthenabled for the in situ characterization of the oxide/electrolyte interface. Thedielectric number of the respective oxides is thus determined from the capacitivereactance of these oxides obtained from the impedance measurements. More-over, the semiconducting properties of the mixed oxides of titanium and niobiumgrown on these alloys were assessed by using Mott-Schottky analysis where thetype of the semiconductor, charge carrier concentration and flat band potentialof the respective oxides were determined.Surface reactivity of the microstructures such as grain and grain boundarieswas approached by using scanning droplet cell in which the basic idea entailsbringing a small electrolyte droplet as small as 45 µm in diameter to the samplesurface so that localized electrochemical measurements can be carried out. Thelocal reactivity of individual grains and grain boundaries is related to the crys-tallographic orientation data obtained from an electropolished sample surfaceusing electron backscatter diffraction (EBSD) technique. From the anodizationand the subsequent electrochemical impedance measuremets, the oxide growthmechanism, formation factor and dielectric number of the oxides grown on dif-ferently oriented grains and grain boundaries were determined. Moreover, thesemiconducting properties of the oxide spots grown on these grains and grainboundaries were also studied using Mott-Schottky analysis to get a comprehen-sive picture of the surface reactivity of β-type Ti-30at.% Nb alloy.

Contents

1 Introduction 1

2 Theory 52.1 Electrochemical oxide layer formation on metals . . . . . . . . . 12

2.1.1 The electrochemical behaviour of metals . . . . . . . . . 122.1.2 The electrochemical behaviour of Ti and Nb . . . . . . . 16

3 Experimental 253.1 Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.1.1 Mechanical grinding and polishing . . . . . . . . . . . . . 253.1.2 Electropolishing . . . . . . . . . . . . . . . . . . . . . . . 26

3.2 Electrochemical characterization . . . . . . . . . . . . . . . . . . 293.2.1 Electrochemical cells . . . . . . . . . . . . . . . . . . . . 293.2.2 Cyclic voltammetry . . . . . . . . . . . . . . . . . . . . . 333.2.3 Electrochemical impedance spectroscopy . . . . . . . . . 363.2.4 Mott-Schottky Analysis . . . . . . . . . . . . . . . . . . 38

3.3 Electron Backscatter Diffraction (EBSD) . . . . . . . . . . . . . 413.3.1 Qualitative and quantitative representations of crystal ori-

entation in EBSD . . . . . . . . . . . . . . . . . . . . . . 433.4 Chemicals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4 Anodic oxides of Ti-30at.%Nb alloy 514.1 Anodic oxides grown in a conventional electrochemical cell . . . 53

4.1.1 Anodic oxide growth on Ti-30at.%Nb . . . . . . . . . . . 534.2 Microelectrochemistry of single grains of Ti-30at.%Nb . . . . . . 644.3 Microelectrochemistry at grain boundaries . . . . . . . . . . . . 73

5 Anodic oxides of (α+β)-type Ti-Nb alloys 835.1 Oxide growth on Ti-10 wt.% Nb and Ti-20 wt.% Nb . . . . . . . 865.2 Oxide characterization by electrochemial impedance spectroscopy 89

xiii

Contents

5.3 Mott- Schottky analysis of the oxides of (α+β)-type Ti-Nb alloys 98

6 Summary 103

Bibliography 107

List of Figures 121

List of Tables 127

Glossary 129

Index 133

Curriculum Vitae 138

xiv

1 Introduction

The quest for biomaterials which can be used in different parts of our body assurgical implants involved different kind of materials in the long run. Duringthis time the implantation technology employed three main material systems:316L stainless steel, cobalt-chromium based alloys and titanium and its alloys[1–3]. The alloys have been used from cranial plates, maxillofacial reconstruc-tion, dental implants, orthopedic fracture plates, joint replacement prosthesesto ablation catheters. The interface between the surgical implants and the sur-rounding biological environment when these implants are placed inside the bodyhave been of interest to the corrosion and material scientists. With this regardelectrochemistry have lend a big hand in studying the performance of such im-plant materials in biological environments. However, the biological environmentin a human body is not a hospitable environment for an implant as it containsa highly oxygenated saline electrolyte of pH of 7.4 at 37 0C. Moreover the pres-ence of aggresive chloride ions, ionic composition and protein concentration inbody fluids complicates the nascent understanding of biomedical corrosion evenfurther.The main prerequisite for a metallic material to be used as surgical implant isexcellent corrosion resistance and biocompatibility so that it exhibits no toxicityto the biological system. Titanium and its alloys fulfill these requirements toa greater extent than stainless steel and cobalt-chromium alloys. Ti-6Al-4V isone of the many titanium alloys used extensively as a biomaterial. However,these alloys have also some drawbacks reported due to the cytotoxicity of theAl and V. Developments in the field thus led to the introduction of alloys con-taining biocompatible elements instead of Al and V [4–7]. The stabilization ofthe high temperature phase of titanium with elements like niobium would resultin β-type titanium alloys which have superior properties over all the predecessorimplant materials for their excellent corrosion resistance, low modulus of elas-ticity and no cytotoxicity against osteoblastic cells. The corrosion resistanceis attributed to the spontaneous formation of a passive oxide film comprised

1

1 Introduction

mainly of titanium dioxide and plays an important role in the integration of theimplant with the surrounding tissue as it is the part which comes in contactwith the biological environment instead of the bare metal surface.The titanium dioxide is of main interest in the electronic industry as well forapplications in dynamic random access memory (DRAM) storage capacitors ormetal-oxide-semiconductor field-effect transistor (MOSFET) gate oxides besidesprotecting the substrate metal from corrosion [8].In this work the surface reactivity of β-type and (α+β)-type Ti-Nb alloys havebeen studied using different electrochemical cells. First, the surface reactivityof these alloys were investigated using a double glass-walled electrochemical cellwhich gives information about the overall reactivity of the surface of these alloysduring potential application. The applied electrochemical potential results inoxide growth on the surface of these alloys where the mechanism and kineticsof the growth was studied with the applied potential. Moreover, the electronicproperties of the oxides such as dielectric number, donor concentration and flatband potentials were determined from electrochemical impedance measurementscarried out right after oxide growth with and without application of a bias po-tential.Conventional electrochemical cells such as the double glass walled electrochem-ical cell expose part of the polycrystalline sample to the electrolyte on a cen-timeter scale. The results obtained with such techniques are a net contibutionfrom all the microstructural elements such as grains, grain boundaries etc. incontact with the electrolyte. The individual contributions of the single grainsand grain boundaries thus need microcells with small working electrode areain the micrometer range. For this reason the scanning droplet cell [9] is usedto investigate the local electrochemical response of the single grains and grainboundaries of Ti-Nb β-type titanium alloy. The scanning droplet cell is an mi-croelectrochemical cell which entails the idea of bringing a small drop of an elec-trolyte into contact with the sample surface forming a working electrode diam-eter down to 45 µm in this work. The wetted area (working electrode) containsreference and counter electrode, enabling to carry out all electrochemical tech-niques such as cyclic voltammetry, transients and electrochemical impedancemeasurements. The local electrochemical reactivity was studied in relation tothe crystallographic orientation of the substrate grains and grain boundaries.The crystallographic orientation of the polycrystalline sample was determinedby using electron backscatter diffraction (EBSD) technique in a scanning elec-

2

tron microscope.Thus this work encompasses an assessment of the macroscopic surface reactivityof β-type and (α+β)-type Ti-Nb alloys together with the electronic propertiesof the oxides on these alloys using a double glass walled electrochemical cell.Moreover, the local electrochemical reactivity of the single grains and grainboundaries of a β-type Ti-Nb alloy addresseed using the scanning droplet cellis also presented.

3

2 Theory

Named after the Greek mythological dieties Titans, the sons of the earth god-dess, titanium played and still plays an important role in the day to day activitiesof human beings. It is discovered in 1791 by a British geologist William Gregorin Cornwall, England [10]. It is placed in Group IVB of the periodic table ofelements with an electron configuration of [Ar] 3d2 4s2. The unfilled 3d subshellenables titanium to form solid solutions with most elements having a size factorwithin about 20 % and this fact has opened many alloying possiblities for ex-ploitation [11]. The main source for titanium is its oxide ore rutile. In the firststep of the extraction of titanium, the oxide ore is heated with chlorine in thepresence of coke to form gaseous TiCl4:

TiO2 (s) + (x+ y)C(s) + 2Cl2 (g) −→ TiCl4 (g) + xCO(g) + yCO2 (g)

The x and y represent variable quantities in which the ratio depends on thereaction temperature which lies in the range 850 to 1000 0C. Liquified TiCl4then undergoes metal displacement reaction when reduced with magnesium inKroll process or sodium in Hunter process in an argon atmosphere:

TiCl4 (l)+ 2Mg(l) −→ Ti(s)+2MgCl2 (l)TiCl4 (l)+ 4Na(l) −→ Ti(s)+ 4NaCl(l)

The titanium produced in the two processes is in the form of a highly porousmaterial called titanium sponge where the chloride salts of sodium or magnesiumare entrapped in the pores.Titanium and its alloys exist in different phases depending on temperature,pressure, cooling rate and alloy composition which will result in equilibriumand non-equilibrium phases. Whether equilibrium or non-equilibrium phasesare obtained depends heavily on the the time allowed to reach steady state

5

2 Theory

conditions by minimization of the Gibbs free energy for phase stability. Non-equilibrium phases with a high value of Gibbs free energy can be formed whenthe heating or cooling rate is high enough to cause a cooperative movementof atoms by shuffling or shear type displacive transformation which results ina homogeneous transformation from the body centered cubic lattice into thehexagonal crystal lattice over a given volume. The phase with higher Gibbs freeenergy can eventually transform to stable phases under favourable conditionsby lowering their Gibbs free energy. The most common equilibrium phasesof titanium and its alloys are α- and β-phase. The α-phase of titanium ischaracterized by hexagonal close packed hcp crystal structure. The hexagonalunit cell of titanium is shown in Fig. 2.1 where the lattice parameters a and chave values of 0.295 nm and 0.468 nm respectively at room temperature. Thec/a ratio is then 1.587 compared to the ideal value of 1.633 for the hexagonalclose packed unit cell.

Figure 2.1: The hexagonal close packed and body centered cubic unit cells of the α-and β-phase of titanium. (Figure taken from [12]).

The hexgonal close packed unit cell has three most densely packed latticeplanes; the (0002) basal plane, one of the three 1 0 1 0 which are calledprismatic planes and one of the six 1 0 1 1 planes called pyramidal planes.The three a1, a2 and a3 axes with indices <1 1 2 0> are the close packeddirections. Fig. 2.1 shows the body centered cubic bcc unit cell of the β-phase oftitanium indicating the 1 1 0 lattice plane together with the lattice parameterfor pure β titanium at 900 0C. The four <1 1 1> vectors are the most closepacked directions in the bcc unit cell (see section 3.3.1 for vector and planes) [12].

6

Figure 2.2: Schematic illustration of the effect of alloying elements on the phase di-agrams:(a) α stabilizing element (b) β eutectoid and (c) β isomorphous stabi-lizing elements where γ is an intermetallic compound and the β-transusis for pure titanium [13].

In Ti based alloys a very important effect of an alloying element pertains to themanner in which its addition affects the allotropic α- to β-phase transformationtemperature. For pure titanium the allotropic transformation between theα- and β-phase occurs at 882 0C. The effect of the alloying elements lies onraising or lowering the transformation temperature. Elements which raisethe transformation temperature or bring about little changes in it whendissolved in titanium are referred as α stabilizers. These elements are generallynon-transition metals or interstitial elements such as Al, B, Sc, Ga, La, Ge, C,O and N. On the other hand, elements like Nb, V, Mo, Hf, Ta, Mn, Cr, Fe,Cu, Au, Ag and W reduce the transformation temperature and stabilize thecubic crystal strucure and thus are referred to as β stabilizers. β stabilizingelements are usually transition elements and noble metals with unfilled orjust filled d-electron bands. The β stabilizing elements are further classifiedinto β isomorphous (Nb, V, Mo, Hf, Ta) and β eutectoid (Mn, Cr, Fe, Cu,Au, Ag, W) depending on whether or not a solid solution/eutectoid exists atsufficiently elevated temperature. Hydrogen is a β stabilizing element amongthe interstitial elements. In titanium alloys the single phase α and the singlephase β regions are separated by a two phase (α+β) region in the temperatureversus composition phase diagram. The width of this region increases withincreasing solute content. The single equilibrium α- to β-phase transformationtemperature associated with the elemental pure titanium is replaced by twoequilibrium temperatures in the case of an alloy: the α transus temperature,

7

2 Theory

below which the alloy contains only the α-phase, and the β-transus temper-ature, above which the alloy contains only the β-phase. At temperaturesbetween these two temperatures, both the α- and β-phases are present. Fig. 2.2shows a simple phase diagram where the effect of α and β stabilizing elementson the relative stabilities of the α- and β-phases is illustrated [11, 13].The main non-equilibrium phases in titanium alloys are α′ , α′′ and ω. The α′

is a metastable hexagonal martensitic phase that is formed as a result of a veryrapid rate of cooling from the high temperature β phase. The α′ martensiteis observed only in pure titanium, in alloys with low solute content and inalloys with high transformation temperature. However, the α′′ phase whichhas an orthorhombic crystal structure is formed by martensitic transformationof alloys with high solute content. Unlike the α′ martensite, application ofan external force can cause stress or strain induced α

′′ martensite besides therapid quenching. The martensitic transformation temperature for pure titaniumis around 850 0C and increases with increasing amount of α stabilizer anddecreases with increasing content of β stabilizing element in the alloy. The lastnon-equilibrium phase to be discussed here is the ω phase which could be oftwo types: athermal and isothermal ω phase. The transformation that involvesdecomposition of the β phase by suppressing the martensitic reaction whichresults in either α′ or α′′ upon quenching athermally results in an athermalω phase. Thus during the formation of the ω phase shuffling reaction takesplace instead of a martensitic shear transformation. The athermal ω phase hasa trigonal symmetry in heavily β stabilized alloys and a hexagonal symmetry(not hexagonal close packed) in leaner alloys [12]. The isothermal ω phase isformed during aging of alloys with high solute content in the temperature rangeof 100 to 500 0C and depends heavily on the hold time and the cooling ratewhere the volume fraction of the isothermal ω phase increases with increasinghold time and decreasing cooling rate [11]. The isothermal ω phase has thesame crystallographic symmetry as the athermal ω phase.Titanium alloys which contain α- stabilizing and/or β-stabilizing elements arebroadly classified into α-, (α+β)- and β-type alloys. The (α+β)-type alloysare further classified into near α and near β type alloys depending on theircomposition which will place them near the α/(α+β) or the (α+β)/β phaseboundaries, respectively. α-type titanium alloys consist of pure titanium andits alloys which consist of one or more α-stabilizing elements where the α-phaseis the predominant or the only phase present. (α+β)-type titanium alloys

8

however, consist a mixture of the α- and β-phases. These alloys thus consist ofone or more of the α- as well as β-stabilizing elements alloyed with titanium.In β-type titanium alloys, the β phase is stabilized by the addition of adequateamounts of β-stabilizing elements and can be retained at room temperature[14].Owing to the high corrosion resistance coupled with its exceptional highstrength to weight ratio, titanium and its alloys have found wide spreadapplications in different sectors of application materials since their commercicalinception in the early 1950’s. From that time onwards titanium and itsalloys were used in aerospace applications such as jet engines and air frameswhere high temperature performance, creep resistance and superior strengthare needed together with a relatively light weight. In jet engines wide chordtitanium fan blades increase efficiency by reducing noise. Moreover, the use oftitanium and its alloys in place of steel and nickel alloys for landing gear andnacelle applications proved to reduce weight and improve aircraft efficiency.Titanium has been proven by the power industry to be the most reliable surfacecondenser tubing material because of the corrosion resistance that titaniumexhibit to all the processes happening during condenser operation which was aproblem when other metals with less corrosion resistance were used resulting ina damage or a threat to the operational efficiency.Besides having excellent corrosion resistance and high strength to weight ratio,titanium and its alloys have to fulfill additional requirements when intendedto be used as a biomaterial for load bearing surgical implants such as hipand knee prostheses. The excellent corrosion resistance of titanium and itsalloys in aqueous environment is due to the spontaneous formation of a passiveoxide film which mainly consists of titanium dioxide. The physilogical andelectrochemical properties of the passive oxide film and its stability in biologicalenvironments for a very long time plays a decisive role for the biocompatibilityof titanium surgical implants. The passive oxide film which is normally a fewnanometer thick is very stable in vitro [15–17]. However, the surface reactivityof titanium implants in vivo showed a marked difference because the passivefilm formed on such kind implants can reach a thickness beyond the nanometerrange after some years inside the human body. During this time not only isthe thickness of the oxide changes but also the composition of the oxide will bechanged due to incorporation of mineral ions from the surrounding biologicalenvironment [15, 18, 19].

9

2 Theory

The additional requirements involve properties like high fatigue resistance, lowmodulus of elasticity and low toxicity to name a few. In this regard β-typetitanium alloys have proven to be superior over the conventional titanium and(α+β)-type titanium alloys. Alloying of titanium with biocompatible elementssuch as Nb, Ta, Zr and Mo to stabilize the bcc β phase will result in β-typetitanium alloys which will fulfill the additional requirements mentioned aboveto be used as a biomaterial. Experimental investigation on such kind of alloysrevealed that these alloys do not show any toxicity against osteoblastic cells,excellent corrosion resistance and good mechanical properties compared to thepredecessor titanium biomaterials. Cytotoxicity is the main problem for otheralloys which have been used as a biomaterial. Among these alloys the mostwidely used titanium surgical implant Ti-6Al-4V exhibited high cytotoxicitydue to the realease of Al and V which may cause neurological disorders andalergic reactions [4, 20]. The other alloys which have been used as biomaterialwere Ti-Ni alloys as orthodontic archwire, endodonthic file and cardiovascularstent due to their shape memory effect and superelasticity. However, the use ofsuch kind of alloys is hampered by their corrosion properties in the human bodydue to the release of metal ions and the risk of Ni induced hypersensitivity [21].The mechanical properties advantage is imparted by the low modulus ofelasticity that β-type titanium alloys have compared to the α-, (α+β)-typetitanium alloys and other biomaterials. The modulus of elasticity of some of thealloys used as biomaterials such as pure titanium (105 GPa), Ti-6Al-4V (110GPa), 316L stainless steel (200 GPa) and Co-Cr-Mo (210 GPa) is 4 to 7 timeshigher than the human cortical bone which has a modulus of elasticity around30 GPa. By using β-type titanium alloys which has a modulus of elasticityaround 60 GPa the disparity observed in the modulus of elasticity between thehuman bone and the surgical implant can be reduced significantly. The modulusof elasticity is of particular relevance because an important requirement ofa bone replacing surgical implant is to have a modulus of elasticity value asclose as possible to that of the surrounding bone tissue. The principle behindthis is the stress shielding effect. Since bone is a living material subjected tomechanical load emanating from the weight it carries and the motion it creates.A mismatch in elasticity observed when an elastically much stiffer surgicalimplant is placed in place of a bone in the human skeleton system createsuneven distribution of the physiological load. Such uneven distribution in themechanical load shields the bone from the mechanical load that surrounds

10

the surgical implant. The shielding of the bone from the physiological loadresults in resorption of the bone which will lead to undesirable effects such asa decrease in bone density, mineralization state and health. The subsequenteffect would be tissue resorption which increases the danger of formation andmigration of wear debris at the bone/implant interface via body fluid transport.Thus, stress shielding and the subsequent tissue resorption may eventuallyresult in contact loosening, premature implant failure and/or infections inducedby debris transport from the bone/implant system to other parts of the bodyvia biological fluids [22].

Figure 2.3: The Ti-Nb phase diagram [23].

Among these β type titanium alloys the Ti-Nb system have drawn considerableattention as a biomaterial due to the biocompatibility nature, excellent corro-sion resistance, low elastic modulus and better shape memory effect [24–29].The shape memory effect in Ti-Nb alloys results from reversible transformationbetween the α′′ martensitic phase and the austenitic β phase. Quenching ofbinary Ti-Nb alloys results in a metastable α′ martensitic phase which has thesame hcp structure as the pure unalloyed titanium with the lattice parametersa ≈ 0.295 nm and c ≈ 0.468 nm, for Nb concentration upto 12 wt.%. Beyondthis concentration, the α′ hcp undergoes rhombic distortion which would resultin an orthorhombic crystal structure with lattice parameters of a ≈ 0.313 nm,

11

2 Theory

b ≈ 0.482 nm and c ≈ 0.282 nm of the α′′ martensite phase. A hexagonalmetastable ω phase with a ≈ 0.465 nm and c ≈ 0.282 nm also appears in the βmatrix where the bcc structure has a ≈ 0.331 nm during quenching. Quenchingof Ti-Nb alloys where the Nb content is above 42 wt.% tends to transform intosingle β phase [29–37]. The phase diagram of the Ti with Nb which is one ofthe β isomorphous stabilizing elements is shown in Fig. 2.3.

2.1 Electrochemical oxide layer formation onmetals

2.1.1 The electrochemical behaviour of metals

Exposure of most metals to an aqueous electrolyte makes a corrosion cell con-taining an anodic site where oxidation of the metal will occur and a cathodic sitewhere either reduction of dissolved oxygen or evolution of hydrogen gas takesplace as given in the following reactions:

M −→ M z+(aq) + ze –

2H+ + 2 e− −→ H2

O2 + 4H+ + 4 e −→ 2H2O

The anodic reaction results in a dissolution of the metal as metallic ions inthe electrolyte or the conversion of these ions into insoluble corrosion products.This destroys the metal and is referred to as corrosion. The active dissolutionof the metal can be hampered if the anodic reaction involved a spontaneousformation of a dense oxide film having limited conductivity as given in thefollowing reaction:

M + z2H2O −→ MO z

2+ zH+ + ze –

The formation of such kind of oxide film with low conductivity will passivatethe substrate metal from further electrochemical reactions. The passive oxidefilm can be stabilized or dissolved by various kinds of reactions which involveion transfer reaction (ITR), electron transfer reaction (ETR) or a combination

12

2.1 Electrochemical oxide layer formation on metals

Figure 2.4: Schematic diagram of the processes taking place at the oxide film oftitanium [38, 39].

of the two. The schematic diagram of the reactions taking place at passivatedtitanium is shown in Fig. 2.4.

The passivation reaction given above involves two half ion transfer reactions:

M −→ M z+(ox) + ze –

which take place at the metal/oxide interface and:

H2O −→ OH –ox + H+

at the oxide/electrolyte interface. The subsequent process involves migrationof cations and/or anions within the oxide. The electrochemical reactions might

13

2 Theory

be steady state reactions which take place at constant oxide film thickness orinstationary processes involving oxide growth, corrosion or oxide reduction ormodification. For example, if the only reactions taking place at constant oxidefilm thickness involve the above two half reactions and an ion transfer reaction:

M z+(ox) −→ M z+

(aq)

the net reaction would be the active corrosion of the metal which falls to asteady state reaction since the reaction takes place at constant film thickness.In contrast, reaction which involve redox reaction:

MO y2

+ ( (z−y)2 )H2O −→ MO z

2+ (z−y)H+ + (z−y)e –

or hydration of the oxide:

MO z2

+ z2H2O −→ M(OH)z

are examples of instationary processes. Moreover, the oxide might undergoreduction into the metal or other soluble product as shown in the followingreactions:

MO z2

+ zH+ + ze – −→ M + z2H2O

MO z2

+ zH+ + (z−y)e – −→ M y+ + z2H2O

The current measured under electrochemical conditions however is the totalcurrent from all the half reactions taking place in the metal/oxide/electrolytesystem shown in Fig. 2.4 and the capacitive charging (iC) and is given by:

i = iox + iredox + icorr + iC (2.1)

where iox is the oxide formation current, iredox is the current for redox reactionsinvolving hydrogen or oxygen evolution, icorr is corrosion current and iC is dueto capacitive charging.

Among the reaction involved in a metal/oxide/electrolyte system, the elec-tron transfer reactions are of particular interest in corrosion and electrochemicaltechnology as the formation, reduction and modification of oxide films involvessuch kind of reactions. For electron transfer reaction to take place the oxide film

14


must exhibit electronic conductivity. Electron transfer reactions are consideredas elastic (isoenergetic) exchange of electrons between occupied and empty en-ergy states in the oxide and electrolyte, respectively. Unlike metals where theelectron transfer takes place at the Fermi level, electron transfer reactions inoxide films take place at higher or lower energy states as shown schematicallyfor different systems in Fig. 2.5.

Figure 2.5: Schematic diagram of the different mechanisms of electron exchange be-tween redox systems:(a) H2 evolution on stable oxide (TiO2, Nb2O5)(b) Reduction before hydrogen evolution (PtO, Bi2O3)(c) Oxidation before oxygen evolution (Cu2O)[38, 39].

Electron transfer reaction can take place via the conduction band or valenceband or between the metal and the electrolyte. The ETR via the conductionband takes place at the oxide surface via the edge of the conduction band or bydirect or resonance tunneling to the conduction band of the oxide. The ETRvia the valence band at the surface with following tunnel process to the metalor via hole diffusion to the valence band. The ETR between the metal and theelectrolyte takes place by resonance or direct tunneling [38]. The later happensfor suffiently thin oxide films (≤ 2-3 nm) so that electrons can be exchangedbetween the metal and the electrolyte. When the oxide film is too thick forelectron tunneling to take place, the intrinsic electronic properties of the oxidefilm dictate the kinetics of the electron transfer at the oxide film/electrolyteinterface. The electronic properties of the oxide films can vary greatly fromone oxide to the other. The energetics of the valence and conduction bandsof different oxides relative to the vacuum level is given in Fig. 2.6. Thus the

15

2 Theory

mechanism of the ETR depends on the band structure of the oxide, the filmthickness and the electrode potential.

Figure 2.6: Band energetics of the different oxides. (Figure taken from [38]).

2.1.2 The electrochemical behaviour of Ti and Nb

Titanium and niobium, the two metals involved in this work, are not corrosionresistant in the same way as gold and other noble metals are. The corrosionresistance of these two metals relies on the formation of a strongly protectiveoxide film that prevents the bare metal from further reaction. The oxide filmis formed spontaneously as it is evident from the negative value of the Gibbsenergy of formation of the corresponding oxides in water and oxygen as shownin the following reactions. The Gibbs energy values were calculated consideringatmospheric conditions having a relative humidity of 80 %, T = 298 K, pO2 =21.28 kPa, pH2O = 2.57 kPa and pH2 = 6.24 ×10−37 Pa [40–42].

Ti + O2 −−−− TiO2 ∆G = -885.6 kJ mol−1

Ti + 4H2O −−−− TiO2 + 4H2 ∆G = -884.6 kJ mol−1

2Nb + 52O2 −−−− Nb2O5 ∆G = -1768.4 kJ mol−1

2Nb + 5H2O −−−− Nb2O5 + 5H2 ∆G = -1766.8 kJ mol−1

An understanding of the corrosion behaviour of titanium and niobium andthe thermodynamic stability of the corresdponding oxides of the two metals

16


can be obtained from their Pourbaix diagrams. Fig. 2.7 and 2.8 represent thePourbaix diagram of titanium and niobium respectively at 25 oC. The Pourbaixdiagram of titanium is established by considering the anhydrous oxides Ti2O3

and rutile TiO2. The reactions and the corresponding equations for the relativestability of the titanium and niobium and their oxides the following equationswere considered:

Ti + H2O −−−− TiO +2H+ + 2 e – E = -1.306 - 0.0591 pH2TiO + H2O −−−− Ti2O3 +2H+ + 2 e – E = -1.123 - 0.0591 pHTi2O3 + H2O −−−− 2TiO2+2H+ + 2 e – E = -0.556 - 0.0591 pHNb + H2O −−−− NbO +2H+ + 2 e – E = -0.733 - 0.0591 pHNbO + H2O −−−− NbO2 +2H+ + 2 e – E = -0.625 - 0.0591 pH2NbO2+ H2O −−−− Nb2O5+2H+ + 2 e – E = -0.289 - 0.0591 pH

The following reactions and the corresponding equations are for the corrosionand solubility of titanium:

Ti 2+ + H2O −−−− TiO + 2H+ log[Ti2+] = 10.91 - 2pHTi −−−− Ti 2+ + 2 e – E = -1.63 + 0.0295log[Ti2+]

2Ti 2+ + 3H2O −−−− Ti2O3 + 6H+ + 2 e – E = -0.478 - 0.1773pH - 0.0591log[Ti2+]Ti 2+ + 2H2O −−−− TiO2 + 4H+ + 2 e – E= -0.502 - 0.1182pH - 0.0295log[Ti2+]

Figure 2.7: Pourbaix diagram of titanium in water at 25 oC [43].

17

2 Theory

Figure 2.8: Pourbaix diagram of niobium in water at 25 oC [43].

From Fig. 2.7 and 2.8 it is seen that both titanium and niobium apear to be basemetals as their domain of thermodyamic stability does not have any portion incommon with the domain of the thermodynamic stability of water and lies atpotentials well below the potential which correspond to the stability of water.Titanium monoxide (TiO) is unstable in the presence of water and dissolves re-sulting in the evolution of hydrogen in the presence of acidic solutions free fromoxidizing agent. Likewise, titanous oxide (Ti2O3) dissolves in acidic solutionsforming titanous ion (Ti3+). In some cases the dissolution is accompanied bythe reduction of the acid. Moreover, the Pourbaix diagram of titanium showsthat the domain of stability of rutile TiO2 cover the domain stability of waterwhich shows that TiO2 is thermodynamically stable in water or aqueous solu-tions. Thus the TiO2 is the most stable of the oxides of titanium which is thereason behind the protection of titanium from further electrochemical reactiononce it is formed spontaneously on the surface. Similarly, niobium monoxide(NbO) and niobium dioxide (NbO2) are thermodynamically unstable in aqueoussolutions of any pH as the domain of stability of the two oxides lies below theline which corresponds to the equilibrium of the reaction of the reduction ofwater to hydrogen at atmospheric pressure. These oxides become oxidized tohigher oxides when they react with water resulting in the evolution of hydrogen.Niobium pentoxide (Nb2O5) is the thermodynamically stable oxide of niobiumin water, non-complexing acid, alkaline and neutral solutions as its domain ofstability covers the entire domain of stability of water.

18


High field model

Oxide formation on valve metals like Ti and Nb follows the high field mech-anism where the development and the concept of the model will be discussedthroughly in this subsection. Valve metals bear the name because they do notpass current in both directions (current rectification). The current rectificationcan be explained for the cathodic and anodic current where the cathodic cur-rent is almost zero and anodic current is recorded when the potential appliedexceeds the oxide formation potential of the oxide film present on the surface ofthe metal. The anodic oxide formation on valve metals is governed by the highfield equation [44] :

i = i0 exp(βE) (2.2)

where i is the oxide formation current, i0 and β are material dependent constantsand E is the electric field strength inside the oxide. An ideal valve metal canbe described by the following points:

• The metal surface is covered by a 2-5 nm thick native oxide from air orelectrolyte passivation

• Anodization increases the oxide thickness

• The oxide layer is not reduced by cathodic current

• The oxide has a small ionic conductivity in steady state conditions or atpotential lower than the oxide formation potential of the oxide alreadypresent on the surface of the metal

Al, Bi, W, Ti, Nb, Ta, Hf and Zr are examples of typical valve metals.Güntherschulze and Betz [45] forwarded the first oxide formation models in1934 from their work on the anodization of Al and Ta where they reported thedependence of the oxide formation current i on the electric field strength E asgiven in eqn. (2.2). Verwey [46] reported the oxide formation involved cationsreleased from the metal electrode which jump from one interstitial position to thenext because of the high electric field strength present within the oxide. the nextcontribution comes from Mott and Cabrera [47–49] where their model assumesthe movement of cations by a thermally activated field assisted ion hoppingmechanism like Verwey suggested. The combination of the theories and modelsproposed by Guntherschulze, Betz, Verwey, Mott and Cabrera is referred to asthe high field model. The model is based on the ion hopping mechanism where

19

2 Theory

ions positioned at regular sites or interstitial positions hop along a distance a tovacancies and interstitial positions located in their neighbourhood as shown inFig. 2.9. The hopping distance a is typically a lattice parameter. The high fieldmodel neglects the quantum effect associated with the ion hopping mechanismdue to the high mass of the ions. Thus the model will be discussed soley fromthe mechanistic view point. In order for the hopping of ions to undergo anapplication of an activation energy A would be necessary.

Figure 2.9: Figure taken from [42] showing the ion hopping between two adjacentlattice planes within the oxide film.

Figure 2.10: A plot showing the effect of the electric field strength on the activationenergy of hopping ions.

The derivation of the high field equation starts by assuming to lattice planesseparated by a distance a at x and x+a positions as shown in Fig. 2.9. Thenumber of moles of mobile species in 1 cm2 of the lattice planes placed at xand x+a respectively is designated by nx and na+x. Thus the amount of ions

20


exchanged in a certain time interval can be written as the difference betweenthe transfer rates of the ions to the left and to the right:

dndt = dn→

dt −dn←dt = nxP→ − nx+aP← (2.3)

where P is the transition probability given by the relation:

P = ν exp(− A

RT ) (2.4)

where ν is the attempt frequency where the ion is treated as a harmonic oscilla-tor, R is the gas constant and T is absolute temperature. The activation energyfor ion hopping in both directions is equal in the abscence of an electric fieldas shown in the symmetrical activation energy curve of Fig. 2.10. However, theactivation energy for the ion hopping in opposite directions become differentwhen an electric field is applied. This results in a change in the shape of theactivation energy curve as shown in Fig. 2.10. Thus in the presence of an elec-tric field the activation energy depends on the ion hopping direction. It needs asmaller activation energy when the electric field supports the ion hopping andhigher in the opposite direction. The activation energy for the forward andreverse directions is thus given by:

A→ = A− αazFE (2.5)

A← = A+ (1− α)azFE (2.6)

where α is the transfer coefficient which explains the symmetry of the activationenergy barrier, z is the charge number of the mobile species and F is the Faradayconstant. Introducing the ion concentration c as:

c = n

a(2.7)

and the concentration at the position x+a can be calculated from the concen-tration gradient dc/dx as:

cx+a = cx + dcdxa (2.8)

Inserting the corresponding terms of eqn. (2.7) and (2.8) in eqn. (2.3):

dndt = acxP→ − acx+aP← = acxP→ − a

(cx + dc

dxa)P← (2.9)

21

2 Theory

Inserting the corresponding transition probability terms of eqn. (2.4) ineqn. (2.9) yields:

dndt = aν

[cxexp

(−A→RT

)−(cx + dc

dxa)exp

(−A←RT

)](2.10)

Substituting the corresponding relation of the activation energy for the forwardand reverse hopping:

dndt = aν exp

(− A

RT

) [cx exp

(αazFERT

)−(cx + dc

dxa)exp

(−(1− α)azFE

RT

)](2.11)

In the absence of an electric field (E=0) eqn. (2.11) reduces to:

dndt = a2ν exp

(− A

RT

) dcdx (2.12)

Eqn. (2.12) corresponds to Fick’s first law of diffusion where the diffusion fluxis driven by concentration gradient (dc/dx) in the direction from the higherconcentration to the lower direction where the diffusion coefficient D is givenby:

D = a2ν exp(− A

RT

)(2.13)

However, when an electric field is applied the ion transport is assisted by the fieldand the effects from diffusion due to concentration gradient will be supressed.Thus the case becomes electrochemical in nature where the dn/dt term willbe replaced by current density i and the charge number z by mobile chargeconcentration σ given in Coulomb per unit volume as:

i = zFdndt (2.14)

σ = czF (2.15)

In the absence of diffusion eqn. (2.11) can be rewritten as:

i = aνσ exp(− A

RT

)exp

(αazFERT

)[1− exp

(−azFERT

)](2.16)

The current density i depends linearly on the electric field strength and alsothe applied potential like Ohm’s law as far as the thickness d remains constant

22


for low values of the electric field strength and eqn. (2.16) thus reduces to eqn.(2.17) if azFE/RT < 1:

i = aνσ exp(− A

RT

)αazFERT (2.17)

In the case where the electric field strength is high enough to make ion transferin the opposite direction to what is assumed to be in eqn. (2.3) where the effectfrom diffusion is supressed then eqn. (2.16) can be rewritten as:

i = aνσ exp(− A

RT

)exp

(αazFERT

)(2.18)

Eqn. (2.18) is equivalent to the experimentally determined high field equationeqn. (2.2) which relates the current with the electric field during anodic oxidegrowth on valve metals [50] where:

i0 = νPσ exp(− A

RT

)(2.19)

β = αazFRT (2.20)

Taking the natural logarithm of eqn. (2.2) will modify it to a Tafel equationwhere the material dependent constant β can be determined from the slope ofthe Tafel plot assuming constant layer thickness d:

ln i = ln i0 + βE (2.21)

The ion hopping mechanism assumes the ion transfer between the lattice planesin Fig. 2.10a to take place regardless of the position where the lattice planesare located within the metal/oxide/electrolyte system. The planes might rep-resent either the metal/oxide interface or the oxide/electrolyte interface orplanes located in random position with the oxide film. Experiments fulfillingeqn. (2.2) cannot determine where the rate determining step is located withinthe metal/oxide/electrolyte system. Previous arguments as to the location ofthe rate determining step is located is proposed by different authors. Güther-schulze and Betz [45] proposed for the rate determining step to be located withinthe oxide, Mott and Cabrera [49] assumed it to be at the metal/oxide inter-face and Fehlner and Mott [51] assumed to be at the oxide/gas interface inmetal/oxide/oxygen gas system. However, transient experiments indicate the

23

2 Theory

rate determining movement of ions is located within the oxide and also the valid-ity of eqn. (2.2). This infers that the processes taking place at the metal/oxide,oxide/electrolyte or oxide/gas interface are not rate determining step. Secondly,the oxide is homogeneous and hence the electric field strength within the oxide isconstant. The constant field strength thus can be calculated from the potentialdrop ∆E within the oxide and the layer thickness:

E = ∆Ed

(2.22)

Thus eqn. (2.2) can also be rewritten as [44]:

i = i0 exp(βE) = i0 exp(β∆Ed

) (2.23)

24

3 Experimental

3.1 Sample preparation

The first crucial step in studying the surface reactivity of a material involvespreparation of a sample surface following certain procedures that will ultimatelyresult in the true microstructure of the surface. The microstructure of the sur-face of Ti alloys in this work is revealed by Electron Backscattered Diffraction(EBSD) (explained in detail in section 3.3). The EBSD technique relies heavilyon the information obtained from the very top surface of crystalline samples.Thus sample surfaces must be as defect free as possible to obtain good results.The most critical defects for EBSD are roughness, deformation of crystal struc-ture through mechanical damage, surface contamination, surface relief, residualstrains, etc. [52]. The sample preparation techniques and procedures followedin this work are described in the following subsections.

3.1.1 Mechanical grinding and polishing

Silicon carbide, aluminum oxide, emery, diamond and boron carbide are someof the many grinding and polishing abrasives that can be used for grinding andpolishing of sample surfaces in metallography. Graded abrasive is bonded toa paper or cloth in a variety of forms, for example, as sheets, belts or discsof varying size. Alternatively, loose abrasive particles can be applied to a lapfor grinding. Each abrasive size and type produces different scratch and de-formation depth on different samples. Silicon carbide is the most widely usedabrasive used in metallographic laboratories due to its hardness (Mohs 9.5),cost and excellent cutting characteristics. The surface of the Ti-Nb alloys weresuccesively ground with silicon carbide papers, starting with a coarse abrasive of220 grit and then progressing through to finer abrasives of 2500 and 4000 grit in

25

3 Experimental

the presence of flowing water. The water helps to minimize the heat produceddue to friction between the sample surface and the abrasive which might havean effect in altering the microstructure of the sample surface. Moreover, thewater helps to reduce metal entrapment between abrasive particles (clogging)and avoids smearing and burnishing and thereby increase the cutting efficienyby exposing more of the abrasive to the sample surface[53, 54].The next step after grinding is polishing. Polishing involves sprinkling or spray-ing of polishing abrasives on to a polishing disc which can be made of differentkind of clothing to produce a flat and reasonably scratch free surface with highreflectivity. Polishing can also be classified as coarse or fine. Coarse polishinguses abrasive size in the range of 30-3 µm, while fine polishing involves abrasiveswith a size of 1 µm and below. Coarse polishing is usually done using diamondpaste or aerosol together with a lubricant and final polishing mostly employsabrasives like aluminum oxide, magnesium oxide and colloidal suspension of sil-icon oxide[54, 55].The Ti-Nb sample surfaces which were ground with 2500 and 4000 grit siliconcarbide papers were then polished with 40 nm silicon oxide abrasive (Struers)on a nylon cloth disc (Struers) to remove the damage from the grinding processand thereby getting a smooth surface with less deformation to the crystal struc-ture of the sample surface. One fraction by volume of 30 % hydrogen peroxideis added to five parts of colloidal silica solution for polishing of the α + β typeTi-Nb alloys for better results. The last seconds of the polishing procedure weredone in the presence of a running water to clean the sample surface from silicaresiduals.

3.1.2 Electropolishing

Electropolishing is an electrochemical sample preparation technique to obtaina sample surface smooth enough and free from lattice deformations and hencereveals the true microstructure of the sample surface. Such kind of surface isattained by removal of the outer most surface of a metal/alloy in an electrolytesolution under controlled current, voltage, electrolyte temperature and stirringrate of the electrolyte. The electrolyte composition is selected based on theelectrochemical activty of the metal/alloy components and on the solubility ofthe salts of the metal or components of the alloy [56]. Fundamental aspectsof electropolishing were reviewed by Landolt [57]. Electropolishing of titanium

26

3.1 Sample preparation

and other valve metals can be carried out in an acidic media containing fluorideor perchlorate ions, a typical example being concentrated acetic acid-perchloricacid solution [58, 59]. The use of such kind of electrolytes, however, posed asafety hazard. A common feature of the electrolytes used for electropolishingis the presence of aggressive ions in order to facilitate the attack of the passiveoxide films and a relatively low water content. The presence of a high amountof water increases the chemical stability of the passive film on titanium andvalve metals in general and thus prevents electropolishing.

Figure 3.1: Schematic diagram of mass transport mechanisms involving:(a) anodically formed metal ions Maq - salt film mechanism(b) acceptor anion A or(c) H2O as transport limiting species. MAy is a complex ion and Csat issaturation concentration [57].

Electropolishing usually involves anodic dissolution at a limiting current and ismass transport controlled process. The mechanism of electropolishing can beexplained by either of the two theories: salt film and acceptor mechanism. Insalt film mechanism, at the limiting current a thin salt film is present on the an-ode and the rate of the reaction depends on the rate at which the metal ions are

27

3 Experimental

transported away from the sample surface into the bulk of the electrolyte. Theacceptor mechanism instead assumes diffusion limited transport of an acceptor(water or complexing agent) necessary for the solvation [60, 61]. Fig. 3.1 showsthe schematic representation of the transport mechanisms involved where in allcases mass transport being the rate determining step.A perchlorate ion free electrolyte such as sulfuric acid-methanol solution havebeen reported for electropolishing of titanium and its alloys [62, 63]. Effectivepolishing of titanium and its alloys was obtained in a 3 M sulfuric acid- methanolsolution using 8 V applied potential. Mass transport controlled limiting currentplateaus were observed for sulfuric acid concentration in the range of 2 - 4 M.In this work as well a 3 M methanolic sulfuric acid solution was used for elec-tropolishing all the Ti-Nb alloys. The electropolishing experiments were donepotentiostatically at 8 V using a DC power supply, a platinum sheet as cathodein an electrolyte stirred with a magnetic stirrer at 100 rpm and temperaturerange of 251 - 263 K. For achieving the desired electrolyte temperature andkeeping it constant through out the experiment two types of cryostats (LAUDARC 20-CP and JULABO FT 901) were used.Ultrasonic baths were used in order to effectively clean the sample surfaces

from leftovers of the sample preparation procedures. Ultrasonic cleaning resultsfrom cavitation, a phenomenon that occurs in many liquids. When an ultrasonicwave passes through a liquid it produces fluctuations in hydrostatic pressure. Anacoustic wave consists of an alternating pressure front that moves at a particularvelocity in the liquid. In an ultrasonic cleaner, a standing wave is produced as aresult of reflections, leading to a stationary wave front. However, the alternatingpressure phase persists. Most liquids exhibit an amplitude threshold level abovewhich cavitation occurs. The frequency and amplitude of the acoustic wave andcleaning medium all influence cleaning action[53]. All the samples were cleanedin an ultrasonic bath of ethanol and distilled water to remove remainings ofthe sample preparation procedures from the samples surface. Finally, the sam-ple surface was rinsed with ethanol and dried with compressed nitrogen gas tocomplete the sample surface preparation.

28

3.2 Electrochemical characterization


3.2.1 Electrochemical cells

Double glass-walled electrochemical cell

A double glass walled electrochemical cell with seven outlets as shown in Fig.3.2was used for carrying out the electrochemical measurements. From the sevenoutlets two of them were used to insert the gas inlet used for purging the elec-trolyte with an inert gas like argon or nitrogen to drive the dissolved oxygenout from the electrolyte and a gas outlet. A gold plate of 2 cm2 area counterelectrode and Ag/AgCl/3 M KCl (Metrohm) reference electrode placed insidea luggin capillary were inserted through the other two inlets. The sample forthe experiment is placed in a sample holder made of teflon exposing an areaof 0.3 cm2 to the electrolyte. It is inserted through the centraal inlet into theelectrochemical cell. The electrochemical cell has also two inlets besides theseven outlets which can be connected to cryostat to keep the temperature ofthe electrolyte inside the electrochemical cell constant by circulating a coolingsolution between the glass walls.

Figure 3.2: Picture of the double glass-walled electrochemical cell.

29

3 Experimental

Scanning droplet cell

Conventional electrochemical cells like the double glass walled cell explainedabove are well suited for a relatively big working electrode area. Many effortswere made in the past in reducing the working electrode area using differenttechniques. Of these attempts the first main effort involves the usage of ultra-microelectrodes with different geometries and critical dimension in the microm-eter range for voltammetric and polarographic measurements [64, 65]. Otherapproaches included covering the sample surface partially with insulating film[64–67] or completely with photoresist materials and produce the microelec-trodes by using a radiation source [68, 69]. However the usage of such kind ofmasks might result in undesirable effects like surface modification of the sampleunder consideration. The effort to minimize the working electrode area laterinvolved different probe techniques such as scanning microelectrodes [70, 71]especially the scanning electrochemical microscope [72–76], ion sensitive cap-illary electrodes [77] scanning tunnel microscope (STM) [78, 79] and Kelvinprobe [80, 81]. The probe techniques showed impressive resolution to analyzestructured surfaces, but lack the wide spectrum of the conventional macroscopicmethods [82].The limitations mentioned above for the different microelectrodes is overcomedby positioning a tiny electrolyte droplet at the tip of a capillary based microcelland making a contact with the sample surface with it. The wetted area from thecontact of the tiny droplet with the sample surface defines the working electrodearea. The droplet formed between the capillary tip and sample surface is heldby its own surface tension. The droplet can also be moved across the sample sur-face and thus referred Scanning Droplet Cell (SDC) [9, 83]. The SDC containsreference and counter electrodes which completes the three electrode configu-ration. By using SDC a complete range of electrochemical techniques such ascyclic voltammetry, transients and impedance measurements can be performed.Schematic drawing of the SDC used in this work is shown in Fig. 3.3a. The basicidea entails pumping a small amount of electrolyte through the electrolyte inletin the acrylic block and bringing it at the tip of the outer capillary to makeelectrical contact with the sample when the tip of the cell is pressed against thesample surface. The tip of the outer capillary made of borosilicate glass withouter diameter of 2.5 mm and inner diameter of 1.5 mm was first pulled usinga capillary puller (PC-10, Narishige) and ground with a microgrinder (EG-400,Narishige) to achieve the desired diameter for the capillary tip.

30


Figure 3.3: (a) Schematic diagram of scanning droplet cell(b) Picture of scanning droplet cell setup.

31

3 Experimental

The tip of the capillary is then dipped in silicone and blown with compressed ni-trogen gas to form the silicone gasket at the rim of the capillary tip. The siliconegasket helps to seal off the electrolyte from contact with the atmosphere andthereby preventing the evaporation of the electrolyte. In addition the changein the wetted area when a potential is applied resulting from the change inthe contact angle due to electrocapillarity effects can be prevented and therebydefining the working electrode area precisely [82]. The scanning droplet cell isthen fixed to a force sensor ( KD45 2N, ME-Messsysteme) which helps to applya precise amount of force through the capillary tip on the sample surface. Theapplied force should be small enough to guarantee only a small elastic defor-mation to the silicone gasket. A constant force of 3 mN was applied throughout all of the experiments so that the crucial part in microelectrochemistry, theworking electrode area will be highly reproducible. The reproducibilty of theworking electrode area is demonstrated in detail for anodic oxide spots grownon Hafnium thin film by Maradare et al.[84]. The other end of the force sensoris connected to a computer controlled 3D scanner for spatial movement of thecell tip across the sample surface. The position of the cell tip in relation to thesample surface is controlled by two cameras; a top camera to control the posi-tion of the tip in the sample surface and grazing view to determine the heightof the tip in relation to the sample surface.A precise amount of electrolyte is pumped through the electrolyte inlet with

a resolution of 50 pl/step using a computer controlled microsyringe pump (Mi-cro 4, World precision instruments) actuating a 100 µl syringe. A microrefer-ence electrode AuHg/Hg2(CH3COO)2/CH3COONa placed inside the scanningdroplet cell through one of the openings at the top of the cell and brought asclose as possible to the outer capillary tip to decrease potential drop between thereference electrode tip and the working electrode. The microreference electrodeis prepared by two step electrodeposition of mercury followed by acetate salt ona very pure (99.999 %) 100 µm thick gold wire. The result is mercury acetatesalt on the surface of an amalgamated gold wire. The wire together with thedeposited salt is placed inside of a flexible microfiller (World precision instru-ments) with an outer diameter of 350 µm and inner diameter of 250 µm. Thespace between the wire and the capillary is filled by sucking from a hot solu-tion of NaCH3COO and agar with a syringe. Solidification of the agar at roomtemperature helps to preserve the NaCH3COO salt solution inside the capillary[85]. The three electrode configuration is completed by inserting a 100 µm in

32


diameter gold wire wound around the reference electrode and brought out of thecell for electrical contact through the inlet on the left side of the acrylic blockas shown in Fig. 3.3b. A tungsten wire pressed against the sample surface wasused to serve as an electrical contact for the working electrode.The SDC have been used since its introduction for different kinds of micro-electrochemical measurements. It was used in microbiology for determining themembrane potential in living cells [86]. In material science research it has beenused to study the local electrochemical response of single grains of technicallyrelevant samples [87–90], for microelectrochemical lithography [91] and com-binatorial electrochemistry of binary and ternary alloys [42, 92–96]. The SDCwas used in this work as well to study the local electrochemical response of Ti-Nb alloys in relation to the crystallographic orientation of the microstructuresselected for the measurements.

3.2.2 Cyclic voltammetry

Cyclic voltammetry is one of the voltammetric techniques that developed afterthe discovery of polarography by the Czech scientist Jaroslav Heyrovsky in 1922and received 1959 Nobel prize in chemistry for his contribution. The techniqueinvolves varying the potential applied to the working electrode in an electro-chemical cell at a certain scan rate towards a certain potential and reversing thescan of potential towards the starting potential while measuring the current inthe mean time. The task of applying a potential to an electrochemical cell atthe certain scan rate and measuring the current in the mean time is done byusing a potentiostat.

The basic circuit components of a potentiostat connected to an electrochemi-cal cell is shown in Fig. 3.4a. A potentiostat measures the potential differencebetween the working electrode and reference electrode, applies current throughthe counter electrode and measures the current by measuring the voltage acrossthe serial resistor Rm. The applied current passes through the electrolyte andpolarizes the working electrode exactly so that the voltage between the refernceand working electrode is as close as possible to the voltage of the input sourceEin. This is achieved by the operational amplifier (OPA). The OPA continouslyadjusts its output voltage Eout to control current passsing through the elec-trochemical cell so that the input feedback potential Er is equal to the inputpotential Ein. Fig. 3.4b shows the electrochemical cell and the serial resistor

33

3 Experimental

Figure 3.4: (a) Basic components of a three-electrode potentiostat connected to anelectrochemical cell(b) Circuit of the potentiostat after the electrochemical cell and thecurrent measuring circuit were replaced by two impedances Z1 and Z2.

Rm replaced by two impedances (explained in section 3.2.3) Z1 and Z2. Z1 isthe impedance which includes the serial resistor Rm in series with the interfa-cial impedance of the counter electrode and the electrolyte solution resistancebetween the counter electrode and reference electrode and Z2 includes the inter-facial impedance of the working electrode in series with the electrolyte resistancebetween the reference and working electrode. Based on the function of the OPAwhich includes the amplification of the potential difference between the non-inverting and inverting inputs of the OPA:

Eout = A (Ein − Er) (3.1)

where A is the amplification factor of the OPA. The current passing throughthe reference electrode is zero or negligible because it is connected to a resistor

34


Rr. This helps to protect the OPA from being destroyed by static high voltageshocks when the input is open. Thus the current passing through the cell Ic isgiven by:

Ic = EoutZ1 + Z2

= ErZ2

(3.2)

Solving for Er:Er = Z2

Z1 + Z2Eout = αEout (3.3)

where α is the feedback factor.

α = Z2

Z1 + Z2(3.4)

Inserting eqn. (3.1) in eqn. (3.3) and rearranging yields:

ErEin

= αA

1 + αA(3.5)

When αA 1, eqn. (3.5) becomes:

Er = Ein (3.6)

Eqn. (3.6) shows how the OPA works to keep the voltage between the referenceelectrode and working electrode as close as possible to the voltage of the inputsource Ein.In this work a PAR Potentiostat/ Galvanostat Model 283 (Princeton AppliedResearch) potentiostat was used to grow anodic oxides on Ti-Nb alloys usingcyclic voltammetry as an electrochemical technique. The oxides were grown bysweeping the potential at a rate of 100 mV s−1 starting from 0 V to 8 V with 1V step in eight cycles as shown in Fig. 3.5.A potentiostat can also be used to apply a constant potential to the workingelectrode for a certain time. Such kind of experiments are referred to as poten-tiostatic. The above potentiostat was used also to grow anodic oxides on Ti-Nballoys potentiostatically at 3 V for 1000 s for Mott-Schottky analysis (See sec-tion 3.2.4). The oxide growth on Ti-Nb alloys were carried out in an acetatebuffer of pH 6.0 at room temperature.

35

3 Experimental

Figure 3.5: Excitation signals for successive cyclic voltammetric sweeps.

3.2.3 Electrochemical impedance spectroscopy

The opposition of components of an electrical circuit to the passage of an al-ternating current (AC) at a given frequency is regarded as impedance. Theterm electrochemical impedance spectroscopy (EIS) is used when dealing withthe impedance of an electrochemical system. EIS measurement is carried out byapplying an AC voltage to an electrochemical system and measuring the currentpassing through the system. Mathematically, the AC voltage E and current Ican be written as[97]:

E(t) = E0 exp (iωt) (3.7)I(t) = I0 exp (i(ωt− φ)) (3.8)

where E0 and I0 are amplitudes of the AC voltage and current respectively, φis the phase shift between the AC current and voltage, t is time, ω is the radialfrequency expressed in radians per second and related to frequency f as:

ω = 2πf (3.9)

Analogous to Ohm’s law the impedance (Z) can be written as:

Z = E(t)I(t) = E0exp(iωt)

I0exp(i(ωt− φ)) = E0

I0expiφ (3.10)

36


Euler’s equation is given by:

eiφ = cosφ+ isinφ (3.11)

Thus the impedance relation in eqn. (3.10) can be rewritten as:

Z = E0

I0(cos φ+ isin φ) = Z

′ + iZ ′′ (3.12)

where Z′ and Z′′ are the real and imaginary part of the impedance Z. Eqn (3.12)is a complex number which can be represented vectorially as:

Figure 3.6: Vectorial representation of impedance.

EIS experiments employ frequency response analyzer (FRA) to impose a smallamplitude AC signal to the working electrode of an electrochemical cell. TheFRA analyzes the current measured at the counter electrode by comparing itwith the applied signal to determine the impedance at a certain frequency. AnImpedance/gain-phase analyzer (Solartron SI 1260) and FRA (NF ElectronicInstruments, S 5720C) were used in this work for electrochemical impedancemeasurements. The EIS measurements were carried out right after each oxidegrowth in a wide frequeny range (100 kHz - 10 mHz) with a perturbation ACvoltage of 10 mV. Besides EIS measurements were also carried out with theapplication of a bias voltage to assess the semiconducting properties of theoxides using Mott-Schottky analysis (See section 3.2.4).

37

3 Experimental

3.2.4 Mott-Schottky Analysis

The qualitative and quantitative information regarding the semiconductingproperties of a material can be revealed by Mott-Schottky analysis [98, 99]. Theconcept could be explained easily by considering an ideal interface between asemiconductor electrode and an electrolyte. In order for the semiconductor andthe electrolyte be in equilibrium, the Fermi level of the semiconductor must beon the same energy level as to the redox potential of the electrolyte. If these twoenergy levels are not equal there will be an exchange of charge between the semi-conductor electrode and the electrolyte solution until equilibrium is attained.Space charge region extending 1-1000 nm into the electrode is formed due to theexcess charge. For an n-type semiconductor, electrons will be transferred fromthe electrode to the electrolyte because the Fermi level is high in energy thanthe redox potential of the electrolyte. This results in a positive charge for thespace charge region leading to the bending of the band edge upwards as shownin Fig. 3.7. From Fig. 3.7 it is obvious that the concentration of the elec-

Figure 3.7: Semiconductor/electrolyte interface.

trons in the space charge region varies with the potential difference between thesemiconductor electrode (working electrode) and the reference electrode whichdictates the energy level of the electrolyte. It is worth mentioning at this point

38


that there are two double layers at the semiconductor/electrolyte interface: thespace charge and the Helmholtz double layer. The later is formed due to accu-mulation of nonadsorbed counter ions at the interface. The capacitance of thespace charge region Csc is much smaller than the Helmholtz capacitance CH (i.eCsc CH) hence the potential drop in the Helmholtz layer ∆EH is constant andany possible change in the applied potential between the semiconductor and thereference electrode is directly observed in the potential drop in the space chargeregion ∆Esc. Thus the potential in the bulk of the semiconductor E can bewritten as:

E = ∆Esc + Efb (3.13)

where Efb is the flat band potential, the potential where there is no net transferof charge and hence no band bending as shown in Fig 3.8b. Any potentialpositive or negative of the flat band potential results in band bending as shownin Fig 3.8 a & c for an n-type semiconductor.

Figure 3.8: Effect of applied potential (E) on the band edges in the interior of ann-type semiconductor: (a) E > Efb, (b) E = Efb and (c) E < Efb [98].

39

3 Experimental

With the assumption of constant charge density within the space charge region,Poisson’s equation is given by:

d2Edx2 = eND

εrε0(3.14)

where e is the electronic charge, ND is the donor concentration in the spacecharge region, εr is the relative permitivity of the semiconductor and ε0 is thevacuum permitivity. Integrating eqn. (3.14) twice yields;

∆Esc = eND

2εrε0(dsc)2 (3.15)

where dsc is the width of the space charge region. Eq. (3.15) is obtained assum-ing the electric field at x0 and the potential in the bulk of the semiconductor iszero. The width of the space charge region can be written as:

dsc = εrε0

Csc(3.16)

where Csc is the capacitance of the space charge region. Inserting eqn. (3.13) andeqn. (3.16) in eqn. (3.15) and rearranging yields the Mott-Schottky equation;

C−2sc = 2

eNDεrε0(E − Efb) (3.17)

A linear region in a Mott-Schottky plot (C−2sc vs. E) gives information as to the

type of the semiconductor, charge carrier density and flat band potential. Thesign of the slope of the linear region indicates the type of the semiconductor;positive slope indicates an n-type and negative slope a p-type. The value ofthe slope ( 2

eNDεrε0) gives the charge carrier concentration. The intercept of the

potential axis with the extrapolation of the linear region gives the flat bandpotential. In this work Mott-Schottky analysis were carried out on an oxidegrown potentiostatically at 3 V for 1000 s in an acetate buffer of pH = 6.0on Ti-Nb alloys. Electrochemical impedance spectroscopy measurements werecarried out by applying bias potential to follow the variation of the capacitanceof the space charge region with the applied potential.

40

3.3 Electron Backscatter Diffraction (EBSD)


Electron backscattered diffraction is a vital technique in microstructure researchwhich provides information regarding crystallographic orientation, phase identi-fication, grain size measurement, strain measurements etc. In EBSD acceleratedelectrons of the primary beam of a scanning electron microscope (SEM) are di-rected onto the surface of a crystalline sample tilted at 700 from horizontal asshown in Fig. 3.9.

Figure 3.9: Schematic diagram of a typical EBSD system.

Upon hitting the sample surface, the primary electrons are diffusely and elasti-cally scattered through large angles within the sample; so that electrons divergefrom a point source just below the sample surface and impinge upon crystalplanes in all directions. Part of the scatterd electrons which are incident on setof lattice planes and satisfying Bragg’s law (eqn. 3.18 ) undergo elastic scatter-ing to form Kossel cones for every diffraction lattice plane as shown in Fig. 3.11.Two diffraction cones, one from diffraction from the upper side and the otherfrom the lower side of of the crystal planes are formed for each set of crystalplanes[100].

nλ = 2dsinθ (3.18)

41

3 Experimental

Figure 3.10: Schematic diagram for Bragg diffraction [101].

where n is an integer, λ is the wavelength of the electrons, d is the interplanarspacing of the scattered atoms and θ is the angle of incidence. When thesecones are intercepted by the phosphor screen the result are Kikuchi bands ofthe electron backscatter pattern (EBSP).

Figure 3.11: Formation of the Kikuchi lines from a tilted sample [102].

The collected EBSP is then indexed for determinination of the crystal orien-tation of the part of the sample from where the pattern is obtained. Indexingis a process which involves detecting the bands, determining the angle betweenthe bands and determining the phase. Once the bands are detected, the crystalorientation and phase can be determined from the angles between the bands in

42


EBSP as these angles represent the angles between the diffracting lattice planes.Fig. 3.12 a & b shows the EBSP of Ti-30at.% Nb alloy before and after index-ing.EBSD experiments can be carried out either in manual or automatic mode. Inmanual mode, specific points on the sample surface where crystal orientation in-formation is needed are selected by the operator, whereas in an automatic modethe electron beam is scanned over the sample surface to collect and index EBSPat each grid point and obtain crystal orientation of a wider area of the sample.A plot of the orientation at each grid point will give the crystal orientation map.

Figure 3.12: (a) An example of EBSP and(b) Indexed EBSP of Ti-30at.% Nb β-type Ti alloy.

3.3.1 Qualitative and quantitative representations of crystalorientation in EBSD

Direction vectors and planes

Direction vectors in real lattice, where a, b and c are base vectors as shown inFig. 3.13 is given by:

r = ua+ vb+ wc = [uvw] (3.19)

Likewise the vector representation of a crystal plane or set of planes can be doneusing Miller indices (h k l). Miller indices were developed by William Miller andfollows the simple rules:

• Determine the intercepts of the plane with the crystallographic axes.

43

3 Experimental

Figure 3.13: Base vectors and direction vectors in real lattice.

• Take the reciprocals of the intercepts

• change the fractions to integers by multiplying the fractions with the leastcommmon multiplier of the denominators of the fractions

• reduce to lowest terms

i.e (hkl) =(m

u′

m

v′

m

w′

)(3.20)

where u′ , v′ , w′ are intercepts of the planes with the axes a, b and c respectivelyand m is the number used to change the fractions to integers. If all members ofa symmetry family are meant then the notation <u v w> and hkl are usedfor vectors and crystal planes respectively.

Figure 3.14: Miller indices for low index planes of a cubic crystal.

Description of crystallographic orientation

An example of a relationship between sample coordinate system (ND,TD andRD) and the crystal coordinate system of a cubic unit cell is shown in Fig. 3.15.

44


Figure 3.15: Relationship between sample coordinate system and crystal coordinatesystem ([100], [010], [001]) [102].

The orientation is defined as the rotation that transforms the sample coordinatesystem onto the cystal coordinate system. Mathematically,

C = S.R (3.21)

where C and S are the crystal and sample coordinate systems respectively andR is the orientation given by the square matrix:

R =

cosα1 cosβ1 cosγ1



=

R11 R12 R13

R21 R22 R23

R31 R32 R33

(3.22)

where α2, β2 and γ2 are the angles between [010] and RD, TD and ND respec-tively and likewise α3, β3 and γ3 are the angles between [001] and RD, TD andND respectively [102–104]. Crystal orientation is commonly described by theuse of pole figures, inverse pole figures, Euler space and metallurgical description((h k l)<u v w>).

Pole figures Pole figure is a plot of crystal orientations of a given plane normal(pole) with respect to the sample axes and constructed by means of stereographicprojection. Stereographic projection involves projection of points on the surfaceof a sphere onto its equatorial plane as shown in Fig. 3.16a. Point P′ is the

45

3 Experimental

intersection of the normal to the crystal plane placed at the center of the spherewith the surface of the sphere. The intersection point P of the line joining thesouth pole S and P′ with the equatorial plane is the projection point and thusthe pole figure for the crystal plane under consideration. Spatial arrangementof the poles in pole figure are characterized by angles α (00 ≤ α ≤ 900) andβ (00 ≤ β ≤ 3600) and give the crystallogrpahic orientation of the crystal underconsideration as shown in Fig. 3.16b.

Figure 3.16: (a) Streographic projection of the normal to a crystal plane hkl onto the equatorial plane(b) Pole figure as described by the two angles α and β.

46


Inverse pole figure In inverse pole figure the orientation of the sample co-ordinate system is projected into crystal coordiante system unlike pole figureand thus the name "inverse" is used. Thus the reference system in inverse polefigures is the crystal coordinate system C, and the orientation is defined by theaxes of the sample coordinate system S. Because of crystal symmetry a completeinverse pole figure usually consists of many areas where the same information isrepeated. Fig. 3.17a shows the inverse pole figure for a cubic system where thereare 24 symmetric sections. Thus practically only the well known unit triangleshown in Fig. 3.17b which is 1/24th of the complete inverse pole figure is used.Inverse pole uses a basic Red-Green-Blue (RGB) color mode where full red,green and blue are assigned to grains whose <100>, <110> or <111> axes,respectively are parallel to the projection direction of the inverse pole figure.The other orientations are colored by the RGB mixture of the primary colors[105].

Figure 3.17: (a) Complete inverse pole figure(b) Unit triangle of the inverse pole figure for a cubic system.

Euler space Euler space is another method for expressing the crystal orienta-tion using Euler angles. Euler angles represent three angles involved in succesiverotation of a crystal which helps to transform the sample coordinate system ontocrystal coordinate system and thereby defining the crystal orientation. Euler

47

3 Experimental

angles as defined by Bunge [106, 107] are shown in Fig. 3.18a and follows thesequence:

a) φ1 about normal direction (ND), transforming the transverse direction(TD) and rolling direction (RD) into TD′ and RD′ respectively;

b) Φ about RD′ ;

c) φ2 about ND′′ in its new orientation

where φ1, Φ and φ2 are the Euler angles that will coincide the sample and crystalcoordinate systems and satisfy the relations:

00 ≤ φ1 ≤ 3600, 00 ≤ Φ ≤ 1800, 00 ≤ φ2 ≤ 3600 (3.23)

Figure 3.18: (a) Euler angles(b) Representation of orientation in Euler space [108].

48

3.4 Chemicals

Using the Euler angles the orientation can be expressed as a point in a three-dimensional coordinate system whose axes are the Euler angles as shown in Fig.3.18b. The resulting three-dimensional coordinate system is called Euler space.

Goss orientation - (h k l)<u v w> A more intutive description of orientationis given by Goss orientation. In Goss orientation, the orientation is described bythe crystal plane (h k l) parallel to the ND plane of the sample and the vectordirection <u v w> parallel to the RD of the sample.

Figure 3.19: Schematic illustration of Goss orientation.

3.4 Chemicals

Reagent grade chemicals purchased from VWR international were used withoutany modifications throughout this work:

• CH3COONa . 3H2O• CH3COONa• CH3COOH• H2SO4 (95-97%)• CH3OH• C2H5OH• Hg2(NO3)2

• Agar• H2O2 (30%)

Deionized water produced in the laboratory with a water purification system wasused for preparing of aqueous solutions and for rinsing the sample surfaces.

49

4 Anodic oxides of Ti-30at.%Nballoy

Owing to the excellent corrosion resistance combined with their light weightcharacteristics and high strength Ti and its alloys have found wide spread ap-plications in aerospace, chemical industries, power plants, medical prostheses[109, 110], military [111] and sporting goods [112] in a relatively short timesince their inception in the early 1950s. Based on their crystal structures Tialloys are categorized into α-, (α + β)- and β-type alloys.The β-type Ti alloys which are characterized by body centered cubic crystalstructure excel the other classes of Ti alloys for applications as biomaterialdue to their nontoxicity against osteoblastic cells, high corrosion resistance andimproved mechanical properties due to solid solution and second phase strength-ening while preserving the light weight characteristics of titanium [22, 113, 114].The main advantage in using β-type Ti alloys is seen in the favourable mechan-ical properties. For crystallographic reasons, the body centered cubic crystalstructure shows higher symmetry as compared to the α-type Ti alloys whichare characterized by a hexagonal close packed crystal structure resulting in anisotropic mechanical behaviour. Moreover, β-type Ti alloys have low modu-lus of elasticity which makes them premium choices for load bearing surgicalimplants where the aim consists of providing surgical implant materials withstiffness similar to that of the human bone. This strategy lowered the loadshielding effect which in the conventional α-type Ti alloys results in bone decayfollowed by abrasion, infection and eventual implant failure [22]. The excellentcorrosion resistance is attributed to the spontaneous formation of a dense andpassive thin oxide film on the surface which protects the material underneatheffeciently from deterioration despite the high affinity of Ti for oxygen [115, 116].This dense passive oxide layer which consists of TiO2 has a thickness of 1.3-5.4nm [39] has a low electronic conductivity [117], great thermodynamical stabil-ity [118] and low ion formation tendency in aqueous environments [119, 120]

51

4 Anodic oxides of Ti-30at.%Nb alloy

which is responsible for the observed corrosion resistance of Ti alloys. Besides,the passive oxide layer has a high relative permitivity value which makes it aninteresting material for electronic application such as dynamic random accessmemory (DRAM) storage capacitors or metal-oxide-semiconductor field effecttransistor (MOSFET) gate oxides [8].Ti-30at.%Nb alloy has also found applications in hydrogen storage devices wherethe hydrogen forms a solid solution with Ti-30at.%Nb alloy. The hydrogen dif-fusion coeffcient which depends strongly on the hydrogen content where its de-pendence on temperature follows the Arrhenius type behaviour in samples withhydrogen content between 0.03 and 0.37 H/M (Hydrogen/Metal atoms ratio) atdifferent temperatures. The diffusion coefficient at room temperature decreasesbetween 0 and 0.1 H/M, but has a significantly higher value for 0.37 H/M. Thedecrease of the diffusion coefficient upto 0.1 H/M can be related to the mutualblocking of Ti4 sites by hydrogen. These sites are prefentially occupied at lowhydrogen contents. The increase at 0.37 H/M is attributed to the occupationof Ti3Nb sites which have a lower activation energy for hydrogen diffusion incomparison to the Ti4 sites [121].Despite their potential application, only few papers addressed the passivity andelectronic properties of the oxides grown on Ti-Nb alloys. Semoboshi et al. [122]studied the structural and dielectric properties of anodic oxide films on Ti-Nballoys with Ti contents in the alloy ranging from 0 to 15 at.%. They reportedthat the oxide films contained amorphous and partly crystalline niobium and ti-tanium oxides. The increase of titanium content in the alloy lead to an increasein the amount of titanium oxide in the mixed oxide film. The growing content oftitanium oxide in the oxide increases the capacitance of the mixed oxide film dueto the higher dielectric number of the titanium oxide up to a composition of 3at.%Ti in the substrate alloy. Further increase in Ti content in the alloy beyond3 at.% decreases the capacitance due to the formation of a thicker oxide filmwhich suppresses the effect of the higher dielectric number of titanium oxide.Mardare et al. [95] reported the high-throughput growth and characterizationof anodic oxides on the surface of Ti-Nb thin film libraries where issues like thepassivity of the surface and electrical properties of the anodic oxides grown werediscussed for a large spread of alloys.Ti-30at.% Nb alloy is one of the β-type Ti alloys which draw considerable atten-tion for potential applications as a biomaterial [29]. Theory-guided bottom-updesign of Ti-30at.%Nb alloy as a biomaterial is reported by Raabe et al. [22]

52

4.1 Anodic oxides grown in a conventional electrochemical cell

using parameter free density funtional theory calculations. The study of the pas-sivity of Ti-30at.%Nb β-Ti alloy surface and characterization of the electronicproperties of the mixed oxide grown on this alloy by electrochemical impedancespectroscopy will be discussed thoroughly in this chapter.

4.1 Anodic oxides grown in a conventionalelectrochemical cell

The investigation of the mechanism involved and the kinetics behind the growthof thin anodic films on valve metals and their characterization have great sig-nificance from the scientific and technlogical point of view. Valve metals have agreat affinity to oxygen and when placed in an aqueous electrolyte solution reactwith water or oxygen to form an oxide on the surface of the metal. The oxideformed is a barrier to the flow of charge carriers like ions and electrons whichresults in reducing or stopping further oxidation of the base metal. Applicationof an anodic potential to the valve metal increases the thickness of the oxidedue to the migration of the metal cations and oxygen anions in opposite direc-tions to form oxides at the metal/oxide and oxide/electrolyte interface whichis determined by the final potential. In this section the growth mechanism,kinetics of anodic thin oxide films on Ti-30at.%Nb β-type Ti alloy and theircharacterization by electrochemical impedance spectroscopy is presented.

4.1.1 Anodic oxide growth on Ti-30at.%Nb

Anodic oxide films were grown on the surface of Ti-30at.%Nb alloy using adouble glass walled cell (see section 3.2.1) by using cyclic voltammetry electro-chemical technique (see section 3.2.2). Oxide formation using cyclic voltam-merty technique gives information about the influence of applied potential onoxide formation current, reversibility/irreversiblity of oxide formation and thethickness of the oxide from the charge consumed to grow the oxides. The anodicoxides were grown on the sample surface in an acetate buffer of pH = 6.0. Thepotential was swept at a rate of 100 mV s−1 starting from 0 V and reversalpotentials varying in increments of 1 V up to a maximum potential of 8 V wereused. Fig. 4.1 shows the successive cyclic voltammograms recorded during an-odic oxide growth due to the appled potential. A sharp overshoot in current

53


Figure 4.1: Cyclic voltammograms from the anodic oxide growth on Ti-30at.% Nbin an acetate buffer of pH=6.0.

density is observed in the first cycle. The observed overshoot is the consequenceof the delay in the oxide formation due to the build up of mobile ionic spacecharge regions as explained by the extended high field model [44]. The observedovershoot in current differs significantly from what has been predicted by thehigh field model. Such kind of deviations from the high field model for thegrowth of anodic oxide films on valve metals were first published by Günther-schulze and Betz [123] on Al and later on other valve metals like Ta and Nbby Vermilyea [124]. Based on the extended high field model the migration ofcounter ions, cations of Ti and Nb emanating from the metal/oxide interfaceand oxygen anions from the oxide/electroyte interface, in opposite direction willresult in overlapping of the opposite charge clouds at a certain position in theoxide. The complete overlap of these oppositely charged clouds is noted by theovershoot in current as it is shown in the first cycle of the voltammograms inFig. 4.1. Moreover, the overlapping will result also in the interaction of theseopposite charge clouds. Their interaction delays the arrival time of the counterions at the two interfaces where the new oxide is formed and hence results ina delay in the oxide formation. Fig. 4.2 shows a schematic representation of

54


oxide growth according to high field model for two counter ions having equaltransport numbers.In the subsequent cycles the overshoot current is less pronounced as the thicker

Figure 4.2: Schematic representation of oxide growth at the metal/oxide and ox-ide/electrolyte interface for counter ions with transport number 0.5.

oxide that is formed by the increased applied potential results in a slower elec-tric field strength for the same scan rate. From the fourth cycle onwards theovershoot in current is not observed anymore and instead a current plateau isrecorded till the upper oxide formation potential. During the reverse cathodicsweep of potential, the current falls rapidly towards zero. In the subsequentcycle the anodic current stays to the minimum until it surpasses the formationpotential of the previously grown oxide. The observed current plateau signifiesthat the sole process involved is an ion transfer reaction resulting in the thicken-ing of the oxide at a constant rate for every potential applied. No side reactionssuch as electron transfer reactions which would ultimately result in an oxygenevolution reaction were observed unlike the conventional Ti where an onset ofoxygen evolution was reported in the potential region of 2-4 V [125–129]. Thegrowth of anodic oxides becomes more and more retarded as the applied po-tential is increased as the retardation of the migrating ions is dominating thekinetics of the oxide growth. The kinetic delay is evident from the smearedout increase in the current density at higher applied potentials. Moreover the

55


kinetic delay in oxide formation is observed from the inreasing gap between thefalling cathodic curve and the subsequent anodic curve as exhibited in Fig. 4.1.The next step in the study of growth and charaterization of anodic oxide filmson valve metals is the determination of the oxide thickness d. The thickness ofoxide films depends on the substrate metal or alloy. It ranges from monomolec-ular oxide films on noble metals like Pt and Au to thicker films in micrometerrange in valve metals. The thickness of homogeneous films can be determinedby chemical, electrochemical and spectroscopic techniques [38]. Using Faraday’slaw the relation for the oxide thickness can be written from the analysis of thecoulometric data as:

d = MQ

zrFρ(4.1)

Figure 4.3: A plot of the charge consumed to grow the oxides as a function of appliedpotential.

where M is the molecular weight, Q charge density, z the number of exchangedelectrons per formula unit, r the roughness factor a ratio between the true andgeometrical area is assumed to be equal to one for an electropolished surface andρ the density of the oxide [39]. The density of the mixed oxide of Ti & Nb wascalculated based on the assumption that the composition of the mixed oxide isequivalent to the substrate alloy composition. A value of 4.22 & 4.36 g cm−3

was taken for the densities of the pure TiO2 and Nb2O5 respectively [42]. The

56


thickness of the oxide film is determined by the applied potential for oxidegrowth governed by the high field model:

d = k(E − Eox) (4.2)

where k is formation factor, E applied potential and Eox is the equlibriumpotential of the oxide electrode. Combining eqn. (4.1) & eqn. (4.2) and solvingfor the charge density Q yields:

Q = AE +B (4.3)

where A = zrFρkM

and B = − zrFρkEox

M. Eqn.(4.3) is a slope-intercept equation for

a line where a plot of the charge density as a function of the applied potentialwill give the formation factor k from the slope as shown in Fig. 4.3. Based onthe slope from Fig. 4.3 the formation factor k was calculated to be 2.4 nm V−1

for Ti-30at.%Nb. The reciprocal of the formation factor gives the film formationfield strength Eform:

Eform = 1k

(4.4)

The electrified interface formed when a metal electrode covered with its oxidecomes in contact with an electrolyte solution can be represented by an equivalentcircuit diagram shown in Fig. 4.4 where the contribution from the resistance andcapacitance of surface states is neglected. From Fig. 4.4 RMe/OX and Cm repre-

Figure 4.4: Equivalent circuit for a metal covered with an oxide in contact withan electrolyte solution where the contribution from the resistance andcapacitance of surface states is neglected.

sent the resistance and capacitance of the metal/oxide interface, ROX and COX

represent the resistance and capacitance of the oxide respectively which are con-nected in series with the RC combination for the Helmholtz double layer whereRCT is the charge transfer resistance of the interface and CH is the capacitance

57


of the Helmholtz double layer. The serial resistor RS is for the uncompensatedelectrolyte resistance. Thus the equivalent capacitance can be written as:

1C

= 1Cm

+ 1COX

+ 1CH

(4.5)

Eqn. (4.5) can be simplified into eqn. (4.6) taking the approximation that CH

COX and Cm COX into account.

1C≈ 1COX

= d

εrε0(4.6)

where d is the oxide thickness, εr and ε0 are the relative permitivity of theoxide and vacuum permitivity respectively. Thus the equivalent circuit diagramshown in Fig. 4.4 reduces to an RC combination of the oxide in series with theelectrolyte resistance. This simplified equivalent circuit is used in the followingsection to discuss the oxide/electrolyte interface. Electrochemical impedancespectroscopy measurements at such kind of systems will enable to characterizethe oxide/electrolyte interface and thus determination of numerical values forthe circuit elements involved at the interface is possible.

EIS measurements were carried out by applying a small AC voltage of 10 mVwhich is superimposed to the electrode potential right after each oxide growth bycyclic voltammetry technique on the Ti-30at.%Nb sample in the frequency rangeof 100 kHz to 10 mHz in an acetate buffer of pH = 6.0. The resulting currentand its phase shift were then measured as a function of frequency. The Bodeplot representation for the impedance spectra after each oxide growth on Ti-30at.%Nb sample is shown in Fig. 4.5 a & b. At higher frequencies the capactivereactance of the oxide capacitor COX is very small thus the oxide resistor isshort circuited. The phase shift at high frequencies is close to zero, showingthat the impedance is dominated by a response from the solution resistancewhich is around 100 Ω cm2. Conversely at lower frequencies current passagethough the oxide capacitor becomes impossible and the impedance will be acontribution from the resistance of the oxide and electolyte. Since ROX RS, at lower frequencies the total impedance can be taken to be the oxideresistance. The oxide resistance is not shown in Fig. (4.5) since the phase shiftat the lowest frequency measured (10 mHz) is in the range -200 to -600. Anear capacitive behaviour is observed with a phase shift close to -900 in theintermediate frequency range (10 - 100 Hz). The impedance in this region is

58


Figure 4.5: Bode plot representation of the EIS data of Ti-30 at.% Nb during suc-cessive oxide growth.

almost only a contribution from the capacitive reactance which increases withthe applied potential due to the oxide thickening as shown in Fig. 4.5a. Thecapacitive reactance from the impedance measurements are related to the oxidecapacitance as:

χc = 12πfC (4.7)

where χc is the capacitive reactance, f the frequency where the phase shiftreaches the maximum and C is the capacitance [130]. The capacitance is alsorelated to the oxide parameters and can be rewritten by combining eqn. (4.2)and (4.6) as:

1C

= k

εrε0(E − Eox) (4.8)

59


Figure 4.6: Reciprocal of oxide capacitance versus the applied potential.

A plot of the inverse capacitance as a function of applied potential as shownin Fig. 4.6 will thus give the relative permitivity of the oxide from its slopebased on the formation factor of the oxide (2.4 nm V−1) determined above. Therelative permitivity of the mixed oxide grown on Ti-30at.%Nb is calculated tobe 42.4. This value is close to the relative permitivity of an adsorbed watermolecule one indication of the high biocompatibility nature of this alloy.

Figure 4.7: Schematic drawing of the equivalent circuit used to simulate the ox-ide/electrolyte interface.

The best fit for all the impedance spectras was obtained by replacing the ca-pacitor of the oxide in the equivalent circuit shown in Fig. 4.4 with a constant

60


Figure 4.8: Bode plot for some of the experimental and fitted curves of the spectra.Symbols represent the experimental data and solid lines fitted lines.

phase element (CPE) as shown in Fig. 4.7. The impedance of a CPE is givenby:

Z(ω) = 1Q

(iω)−n (4.9)

where i is complex number, -1≤ n ≤ 1 and Q is a constant. The value of n tellswhether the CPE acts like an inductor, resistor or capacitor . When n = -1 theCPE acts as an inductor, n = 0 pure resistor and n = 1 perfect capacitor [97].The values of n obtained from fitting the experimental curves with the equiv-alent circuit shown in Fig. 4.7 are in the range of 0.92 - 0.97 indicating howmuch the CPE is close to being like an ideal capacitor. Fig. 4.8 a & b shows theexperimental and fitted curves obtained using this circuit model. Better fitting

61


is obtained in whole frequency range for the impedance spectra of oxides grownwith lower potentials, but deviation from the experimental curve is seen in thelower frequency range as the oxide is thickening at higher potentials.The semiconducting properties of the mixed oxides of titanium and niobiumgrown on the Ti-30at.%Nb were assessed by using Mott-Schottky analysis (seesection 3.2.4). It involves the determination of the apparent capacitance as afunction of applied bias potential under depletion condition based on the Mott-Schottky equation (eqn. 3.17). Electrochemical impedance measurements werecarried out at different bias potentials starting from 1.5 V and increasing thebias potential to -0.6 V in steps of 100 mV on an oxide grown potentiostaticallyat 3 V for 1000 s. The frequency range selected for the measurements is 10 kHzto 100 mHz with an AC perturbation voltage of 10 mV. Variation of the capac-itance of the space charge region which is calculated from the imaginary partof the impedance and the frequency where the phase shift reaches a maximumvalue versus the applied bias potential is given in Fig. 4.9 in what is calleda Mott-Schottky plot. A linear region with a positive slope, indicating n-typesemiconducting behaviour, is observed in the potential region of -0.4 - 0 V. Thedonor concentration and flat band potential are calculated, respectively, fromthe slope and intercept of the line fitted for this linear region with the potentialaxis where Csc = 0 as shown in Fig. (4.9). The Mott-Schottky evaluation yieldsdonor density of 8.2 ×1017 cm−3 and Efb equal to -0.47 V. The two values arelower than those reported Mardare et al. [95] for thin film samples of the samecomposition. The calculation in Mott-Schottky analysis were carried out basedon two assumptions. First there are two capacitances to consider, the capaci-tance of the space charge region in series with the Helmholtz double layer. Thecapacitance of the Helmholtz double layer is much greater than the capacitanceof the space charge region, thus the contribution of the capacitance of the doublelayer to the equivalent capacitance is neglected. Therefore the capacitance cal-culated is assumed to be a mere contribution from the capacitance of the spacecharge region. Secondly the equivalent circuit involves a series combination of aresistor and a capacitor for the space charge region.The passivity of Ti-30at.%Nb β-Ti alloy and the electronic properties of the ox-ide grown on this sample were discussed in this section using cyclic voltammetryand electrochemical impedance measurements. The oxide parameters such asformation factor, dielectric number, donor concentration and flat band potentialwere determined. The formation factor and the dielctric number of the oxide is

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Figure 4.9: Mott-Schottky plot for the potentiostatically grown oxide on the surfaceof Ti-30 at.% Nb alloy.

in close agreement to the corresponding values of 2.2 nm V−1 and 44 determinedby Mardare et al. [95] for the same composition from the Ti-Nb thin film library.However, the donor concentration of 2.5 ×1019 cm−3 determined by Mardare etal. [95] is about 1.5 orders of magnitude bigger than than the value determinedfor a bulk sample in this work. Likewise, the flat band potential is about 1.17 Vmore anodic to the value determined in this work. The comparison is howevermade to a thin film library of Ti-Nb where the size of the microstructure el-ements such as grain size is around 30 nm where the bulk sample involved inthis work has an average grain size of 400 µm. Such differences in size of themicrostructure elements together with defect or grain boundary concentrationsmight result in anodic oxide films with different electronic properties as shownin the donor concentration and flat band potential.

Fig. 4.10 shows optical micrograph of the surface of the Ti-30 at.% Nb takenafter the anodic oxide growth with cyclic voltammetry and the successive EISmeasurements. The picture shows some of the microstructures such as grain andgrain boundaries exposed to the acetate buffer electrolyte solution. Thus theresults discussed so far are a net contribution of all the microstructures in the an-odic oxide formation. Individual contributions from such kind of polycrystallinesamples cannot be addressed with the use of conventional electrochemical cells

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Figure 4.10: Optical micrograph of the surface of Ti-30at.%Nb after anodic oxidegrowth.

such as the double glass walled cell used in the above experiments and henceneeds the application of microcells to get an insight into the local electrochem-ical response. The local electrochemical response of Ti-30at.%Nb in relation tothe crystallographic orientation of the microstructure elements of the alloy wereaddressed using scanning droplet cell and discussed in detail in the followingsections 4.2 and 4.3.

4.2 Microelectrochemistry of single grains ofTi-30at.%Nb

The characterization of thin films fomed on the surface of a substrate are inthe domains of electrochemical measurements as it is explained in the abovesection 4.1. Because of the low resolution, only macroscopically averagedelectrochemical responses can only be obtained from measurements involvingconventional electrochemical cells. Therefore, important phenomena whichdepend on the texture of a polycrystalline material are hardly investigated.Electrochemical measurements aimed at determining the local electronicproperties of thin oxide films gives valuable information for catalysis, opticalfilms, microelectronics and corrosion [131].In the past efforts to determine the influence of local crystallographic orientationof polycrystalline substrates on the electrochemical response involved single

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4.2 Microelectrochemistry of single grains of Ti-30at.%Nb

crystals. However, such approaches have drawbacks because of microstructuraldifferences existing between single crystals and polycrystalline material. Singlecrystals are free from impurities with atomically flat surfaces. Besides effectof microstructural defects such as disclocations, grain boundaries, twins andinclusions which are part of polycrystalline materials cannot be answered.Another obstacle in studying texture effect of polycrystalline materials on thelocal electrochemical response was lack of suitable technique with sufficientresolution. With this regard several attempts were made in the past to addressthis issue. A break through was made ten years ago by Hassel and Lohrengelwith the introduction of the scanning droplet cell that laid the corner stone forspatially resolved surface electrochemistry [9].The scanning droplet cell was used in this work for doing microelectrochemicalmeasurements on individual grains of a technically relevant polycrystalllineTi-30at.% Nb β-Ti alloy. An opening of 100 µm in diameter of the tip ofouter capillary of the SDC enables to make separate microelectrochemicalmeasurements with in a single grain. Detailed description on how to producethe components of the scanning droplet cell and its set up is described insection 3.2.1.The local electrochemical response of technically relevant samples has beeninvestigated by using differrent microlectrochemical cells including the scanningdroplet cell. Such kind of experiments were carried out on Au [87], Ta [132], Ti[88, 126, 129, 133–137], Zn [90], Zr [132, 137, 138], FeAlCr light weight ferriticsteels [89], Fe [139, 140] and other metals [141]. Localized electrochemicalmeasurements on these alloys provided information regarding the reactivity andorientation dependent oxide parameters such as oxide thickness, conductivity,density, optical parameters and dielectric numbers [140]. In addition the localcrystal orientation can have also an effect on the crystallinity of the oxidegrown on differently oriented grains. Such effect is reported by Schweinsberget al. [138] on the single grains of Zr where well ordered, crystalline oxide filmswith a sharply defined epitaxy relation to the substrate were reported on allgrains of Zr except the grains with (0001) orientation.The surface of the Ti-30at%Nb sample was ground with silicon carbide papertill 2500 grit, polished with silica slurry on a linen cloth to a mirror finish. Thesample surface preparation is finalized by electropolishing potentiostaticallyat 8 V in a water free 3 M methanolic sulfuric acid solution maintained at-22 0C [63]. After each procedure the sample surface is cleaned in ultrasonic

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bath with ethanol and rinsed with distilled water to remove left overs from thesample preparation procedures. The electropolishing procedure helps to get adeformation free surface so that the true microstructure of the surface of theTi-30at.% Nb alloy is revealed.

Figure 4.11: (a) Inverse pole map with the legend showing the relative positions ofthe grains with the low index planes and(b) Image quality from the EBSD scan on the surface of Ti-30 at.% Nbsample.

Previous studies of the effect of crystallographic orientation on the local elec-trochemical response involved anisotropy microellipsometry (AME) to get crys-tallographic data. However, AME gives only one of the Euler angles Φ foranisotropic materials like Ti and Zr with hexagonal lattice which makes theanalysis of isotropic materials with cubic lattice impossible. In contrast, EBSD(see section 3.3) analysis reveals all the three Euler angles for all kinds of crys-talline samples. The texture of the Ti-30at.%Nb sample surface is thus re-vealed by EBSD using a field emission scanning electron microscope model1550 VP (Leo,UK) equipped with an EBSD detector from TSL immediately

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after the eletroplishing procedure and before the microelectrochemical measure-ments were carried out. An accelaration voltage of 20 kV, aperture 120 µm,700 tilt angle and stepsize of 8 µm were used for orientation mapping. Fig.4.11a & b show the inverse pole figure map and image quality from the EBSDmeasurements on the Ti-30at.% Nb surface. The black cross at the very top leftcorner in the EBSD maps is a cross made on the surface by scratching it witha tungsten needle to serve as a reference point in locating the individual grainsfrom the EBSD map on the sample surface. The numbers indicate the grainswhere microelectrochemical measurements were carried out and they are placedin the EBSD legend to show their relative orientation in relation to the lowerindices of (001), (101) & (111) as shown in Fig. 4.11.The effect of crystallographic orientation of the substrate on the local elec-

trochemical behaviour was studied by growing anodic oxide spots using cyclicvoltammetry technique on the single grains of a polycrystalline Ti-30at.% Nballoy. The cyclic voltammetric meaurements are carried out starting from 0 Vand going to 8 V in steps of 1 V by sweeping the potential at a rate of 100mV s−1 as explained in section 3.2.2 in an acetate buffer of pH=6.0.

Figure 4.12: Cyclic voltammograms from the single grains of the Ti-30 at.% Nb.

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A series of selected cyclic voltammograms recorded from the microelectrochem-ical measurements carried out on the single grains of the Ti-30at.% Nb samplemarked with numbers on the EBSD map Fig. 4.11 are shown in Fig. 4.12. Onlygrain number 9 and 10 with vicinal (101) and (001) respective orientations shownotable current densities in mA cm−2 range with no current rectification dueto the insuffient field strength in the first cycle of potential sweep up to 1 V.This is mainly attributed to the difference in the thickness of the native oxidelayers on the different grains of the sample. This difference in the intial ox-ide thickness can be observed from the small but noticable differences in thehalf-wave potentials for the different grains in the second cycle. The observeddifference in the half-wave potentials is attributed to difference in the surfacepacking density and roughness of the single grains which is a consequence ofthe difference in the orientations of the different grains. In the second cyclemany of the grains exhibited a sharp increase in current densities, the so calledovershoot, which broadens in the subsequent cycle. The observed overshoot asexplained in section 4.1 is a consequence of a delay in the oxide growth dueto the build of a space charge region as explained by the extended high fieldmodel [44]. No overshoot in current was observed in all of the grains startingfrom the fourth cycle onwards. Rather a constant current plateau, indicatingthe absence of any side reactions such as oxygen evolution, was observed cor-responding to the thickening of the oxide layer at a constant rate according tothe high field mechanism [44]. The absence of oxygen evolution is in contrastto the results reported for conventional titanium with hexagonal close packedstructure by J. W. Schultze and co-workers [126, 134]. The kinetics of the oxidegrowth becomes slower and slower as the applied potential is increased, evi-dent from the smeared out increase in the oxide formation current as seen inthe last cycles of the voltammograms in Fig. 4.12 for all grains. Besides, theincreased gap towards higher formation potentials between the falling cathodiccurve and the subsequent anodic curve is also another evidence for the kineticdelay in the oxide formation. Moreover, the current densities from the differentgrains have different values infering that the reactivity of the grains depends onthe crystallographic orientation. The integration of the area under each cyclicvoltammogram gives the charge density consumed to grow the anodic oxidespots. A plot the charge density as a function of applied potential is given is inFig. 4.13.

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Figure 4.13: Plot of charge consumed to grow the oxides on the single grains ofTi-30 at.% Nb as a function of applied potential.

A linear correlation was obtained between the charge density and the appliedpotential for all grains. This implies that the process was Faradaic andexclusive ionic conductivity disables the electron transfer reaction which wouldultimately result in side reactions such as oxygen evolution on the electrodesurface. The oxide formation factor can thus be calculated from the slope ofthe linear fit of such plot based on eqn. (4.3). Fig. 4.13 shows different slopeswhich will give different formation factor values as shown in Table 4.2 for thedifferent grains with different crystallographic orientation.After each anodic oxide growth by cyclic voltammetry the electronic propertiesof the oxides were investigated by electrochemical impedance spectroscopy ina frequency range of 20 kHz till 100 mHz with an AC perturbation voltageof 10 mV by using the scanning droplet cell. The dielectric number of theoxides were determined from the slope of a plot of the inverse capacitance as afunction of potential based on eqn. (4.8) as shown in Fig. 4.14. The values ofthe calculated dielectric numbers for the anodic oxides is listed in Table 4.2.

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Figure 4.14: Inverse capacitance of the anodic oxides on different grains of Ti-30at.%Nb versus the potential applied to grow the oxides.

The semiconducting properties of the oxides were also assessed by using Mott-Schottky analysis. The measurements were done in each of the single grainswhere the above microelectrochemical measurements were carried out. For thispurpose the scanning droplet cell tip is moved to another position inside thesingle grain to grow anodic oxides potentiostatically at 3 V for 1000 s in anacetate buffer of pH = 6.0. After the oxide growth electrochemical impedancemeasurements were carried out this time at a fixed frequency and by sweepingthe potential from 0.5 V to -1 V at steps of 50 mV. The frequency used forthe Mott-Schottky analysis for each grain was taken from the above impedancemeasurements where the phase shift reaches maximum. The capacitance of thespace charge region given in the ordinate of Fig. 4.15 is calculated from themagnitude of the impedance based on eqn.(4.7). All the oxides grown in thedifferent grains selected showed an n-type semiconducting property as shownfrom the positive slope of the linear region of the Mott-schottky plot in Fig. 4.15.The slope of the linear fit for this linear region gives the donor concentrationbased on eqn. (3.17) and its intercept with the abscissa gives the flat bandpotential which are tabulated for all the grains in Table 4.2.

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Figure 4.15: Mott-Schottky plots for the oxides grown on the differently orientedgrains of the Ti-30at.% Nb sample.

The values of the oxide parameters determined from the above meaurements onindividual grains is listed in Table 4.2 together with their respective orientations.The values show variation with crystallographic orientation of the grains. Theobserved difference in the oxide parameters can be approached by classifyingthe grains into two groups: low indexed (grain 7, 9 and 10) and high indexedgrains (grain 2, 3 and 6). For the low indexed grains the current density andhence the formation factor k follows the inequality grain 9 < grain 10 < grain7 with respective orientations of (16 1 23), (3 2 15) and (2 2 3) which couldbe approximated to the low index planes of (101), (001) and (111) respectively.Considering the atomic density of these planes in Table (4.1) gives an insightfor rationalizing the observed difference in the oxide parameters. Grain 7 with avicinal orientation of (111) has the highest current density owing to the higheratomic surface density compared to grain 9 and 10. But the participation ofthe second layer of atoms in forming the oxide should not be side lined as theselayers of atoms are approximately 0.235 and 0.165 nm away from the top layerfor grain 9 and 10 respectively. This helps to explain the observed higher currentdensity of grain 10 compared to grain 9 despite the fact that the atomic surfacedensity of grain 9 is higher than grain 10. Moreover the surface energy γ for the

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low indexed planes of body centered (bcc) metals is in the order γ(110) < γ(100)

< γ(111)[142–144] which is in line with the observed inequality for the currentdensity for the low indexed planes fo the Ti-30at.%Nb sample.

Plane Ap/ 10−15 cm2 Na/Plane

Sd/ 1015 cm2

(100) 1.10 1 0.91(101) 1.56 2 1.28(111) 0.96 1.75 1.83

Table 4.1: Properties of the low index planes of bcc Ti unit cell where Ap, Na andSd are plane area, number of atoms and surface density respectively.

High index grains 2, 3 and 6 with orientations of (4 2 5), (0 1 3) and (3 2 7) re-spectively result in higher current densitites as compared to the low index grains.High index grains have open-structure surfaces with high density of atomic stepsand kinks. Moreover the surface energies of high index planes is higher than lowindex planes for bcc transition metals [143]. Thus the open-structure surfaceand high surface energy of high index grains is the underlying reason for theobserved higher current density and formation factors in these grains. The onlyanomaly which cannot be explained by the reasons mentioned above is the cur-rent density of grain 8. Grain 8 with a crystal orientation (1 3 19) which can beapproximated to the low index plane (001) resulted in a current density compa-rable to the high index grains but higher than the low index grains 7, 9 and 10.Besides the half-wave potential for grain 8 is also higher than the other grainsindicating the oxide formation starts later in this grain.The compositons of the oxides grown on the different grains might be differentfrom the substrate compositions. Such kind of differences were reported fromMardare et al.[95] for oxides grown on composition spread thin films of Ti andNb where the TiO2 content on the surface of the mixed oxides on such kind ofthin film samples is bigger than the corresponding compositions of the metal inthe substrate. But the Nb2O5 concentration in the mixed oxide is less than theNb compostion in the substrate. Composition differences might arise from thedifference in the transport number of Ti and Nb. Moreover the mixed oxidesmight also contain the different suboxides of the constituent elements. Differ-ence in the compositions of the oxides on different grains of the Ti-30at.% Nbsample plus the presence/absence of suboxides of Ti and Nb in the mixed ox-ides will result in oxides having different dielectric number values which would

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4.3 Microelectrochemistry at grain boundaries

affect the calculated donor concentrations from the Mott-Schottky analysis onthe individual grains. Depth profile or angle resolved X-ray photoelectron spec-troscopy should reveal whether or not there is a preferential transport of cationsduring anodization.

Grain No. (hkl) [uvw] k/ nm V−1 εr ND/ 1018 cm−3 Efb/ V2 (4 2 5) [3 3 1] 2.61 66.9 14 -0.343 (0 1 3) [13 3 1] 2.44 74.5 9.8 -0.356 (3 2,7) [19 10 11] 2.58 65.3 23.9 -0.377 (2 2 3) [7 1 5] 2.52 62.2 21.1 -0.418 (1 3 19) [10 3 1] 2.45 55.6 16.6 -0.369 (16 1 23) [3 2 2] 2.25 59.4 14.1 -0.4510 (3 2 15) [5 0 1] 2.51 62.9 8.31 -0.32

Table 4.2: Formation factor k, dielectric number εr, donor concentration ND and flatband potential Efb calculated for the different grains of Ti-30at.% Nb.


The microstructure of metals and alloys consists not only of grains but also grainboundaries. Grain boundary is an important element of the microstructure ofa polycrystalline sample where grains of different orientations form an interfacewhich affects the physical and chemical properties such as intergranular fracture,segregation and corrosion [145]. Such kind of local mismatch in orientation canform an interface with unique local surface properties regarding atomic structureand energy. As a result surface properties which might be affected by grain ori-entation, vacancies and other defects may show different properties at the grainboundaries. Solute segregation, precipitation, embrittlement and intergranularcorrosion can be resulting processes to name only a few [146]. Intergranular cor-rosion is a localized process where corrosion occurs along the grain boundariesor in the area immediately adjacent to the grain boundaries while the grains inthe bulk of the material remain largely unaffected. It is usually associated withsegregation of elements or the formation of a compound at the grain boundary.Corrosion can then occur by a prefential attack of the grain boundary or theregion in the immediate vicinity that has lost an element necessary for the cor-rosion resistance thus making the grain boundary region more anodic comparedto the bulk of the sample. The preferential attack occurs in narrow path along

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the grain boundary. In severe cases of intergranular corrosion the entire grainsmight be dislodged which will affect the mechanical properties of the metal oralloy under consideration. Thus a comprehensive picture about the corrosionresistance and the passivation behaviour of a material can only be obtainedwithout sidelining the effect the grain boundaries might have in dictating theoverall electrochemical response. The passivity and electronic properties of themixed oxide grown on macroscopic surfaces of the Ti-30at.%Nb alloy were ex-plained in section 4.1 above where no side reactions were observed during oxidegrowth and the oxide proved to be a perfect dielectric material. Furthermorethe dependence of the local electrochemical response of the single grains of Ti-30at.%Nb alloy on the crystallographic orientation was studied using scanningdroplet cell. The single grains also exhibited excellent passivity with oxide for-mation being the sole process in which the oxide thickness is increasing withapplied potential. No oxygen evolution was noticed in any of the grains of Ti-30at.%Nb, a behaviour different from the conventional α-Ti alloys. However theoxide parameters such as oxide formation factor, dielectric number and donorconcentration depend on the crystallographic orientation of the substrate grainson which the microelectrochemical measurements were carried out (see section4.2).The concept of determining the local electrochemical response in relation tothe crystallographic orientation of the substrate was extended to the grainboundaries of Ti-30at.%Nb β-type Ti alloy and will be discussed in this section.The crystallographic orientation of the grains involved at the grain boundariesselected were determined by EBSD. The EBSD analysis was carried out infield emission scanning electron microscope (Zeiss 150XB) having an additionalEBSD unit.The sample surface preparation of the Ti-30at.%Nb alloy is finalizedby electropolishing potentiostatically at 8 V in a 3 M methanolic sulphuric acidsolution at -22 0C (see section 3.1.2) to get a surface free from deformation forgood EBSD results. An acceleration electron beam of 20 keV was focused on asmall area of the sample surface tilted 700 from the horizontal. Fig. 4.16 showsthe results from the EBSD scan where the scratch with a shape of a cross atthe very right bottom corner serves as a reference point to address specific grainboundaries. The numbers shown in the EBSD maps are the grains involved atthe grain boundary selected for the microelectrochemical measurements. Thegrain boundary angle is also determined and are color coded where each colorrepresents a certain range as shown in the legend of Fig. 4.16c.

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Figure 4.16: EBSD maps; (a) inverse pole plot, (b) image quality and (c) color codedgrain boundaries of Ti-30at.% Nb alloy.

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Figure 4.17: Optical micrograph of oxide spots at a grain boundary of Ti-30at.%Nb sample.

Oxide spots were grown at different grain boundaries varying in grain boundaryangles and crystallographic orientation combinations of Ti-30at.%Nb sample byusing the scanning droplet cell to study the local electrochemical response asshown in Fig. 4.17. The oxides were grown by scanning the potential at a rate of100 mV s−1 from 0 V in steps of 1 V till 8 V using cyclic voltammetry techniquein an acetate buffer of pH 6.0.

Figure 4.18: Cyclic voltammograms from grain boundaries of Ti-30at.% Nb sample.

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The successive cyclic voltammograms obtained from the local electrochemicalmeasurements carried out at the grain boundaries of the Ti-30at.%Nb sampleis shown in Fig. 4.18. All the grain boundaries showed very small current den-sity for the first cycle of the potential scan due to the thickness of the nativeoxide covering the surface after air passivation. Significant increase in currentis observed starting from the second cycle onwards. An overshoot in currentis observed in the second cycle which broadens and later disappears after thethird cycle due to a delay in the oxide growth following the development of aspace charge as explained by the extended high field model [44]. Grain boundary12-13 showed a much smaller current density 150 µA cm−2 in the second cyclecompared to the other grains boundaries. This difference might be attributedto the difference in native oxide thickness between grain 12 and grain 13 withvicinal orientation of (001) and (101) respectively, which results in the forma-tion of oxide in either of the grains only. Native oxide thickness differences werealso noticed from previous work on the single grains of the sample as explainedin the above section 4.2. A current plateau is observed for all grain boundariesin the intermediate potential region which shows the sole process involved is iontransfer reaction resulting in oxide thickening at a constant rate. A delay in thekinetics of the oxide growth is observed from the smeared out increase in thecurrent as the potential is increased. The kinetic delay is also evident from theincreased gap between two successive cathodic and anodic curves as the appliedpotential increases. The formation factor, inversely proportional to the electricfield strength during oxide growth, calculated based on eqn. (4.1) is given inTable 4.3.Electrochemical impedance measurements were carried out with an AC per-

turbation voltage of 10 mV in a frequency range of 100 kHz to 100 mHz rightafter each anodic potential sweep to study the electronic properties of the oxidesgrown. The capacitance of the oxide determined based on eqn. (4.8) is plottedas a function of the applied potential to determine the dielectric number of theanodic oxides grown at different grain boundaries of Ti-30at.%Nb sample asshown in Fig. 4.19. The linear relationship between inverse capacitance of theoxide and the applied potential as shown in Fig. 4.19 proofs that the anodic ox-ide formed at the grain boundaries of Ti-30at.%Nb act as a dielectric material.Moreover, the value of the slope for each oxide spot is different which indicatesthat the relative permitivity values of these oxides is different as shown in Table4.3.

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Figure 4.19: Plot of inverse capacitance versus applied potential from the differentgrain boundaries of Ti-30at.% Nb sample.

Moreover, just like in the previous sections the semiconducting properties of theoxides grown at the grain boundary of Ti-30at.%Nb are determined by usingMott-Schottky analysis on oxide grown potentiostatically at 3 V for 1000 s in anacetate buffer of pH 6.0. Electrochemical impedance measurements were thencarried out at a fixed frequency and sweeping the applied bias potential at stepsof 50 mV to follow the variation of the capacitance of the space charge regionwith the applied bias potential. The frequecy is selected from the impedancemeasurements carried out in another spot at the grain boundary where thephase shift reaches maximum. A linear region of the Mott-Schottky plot forthe different grain boundaries studied is shown in Fig. 4.20 where the positiveslope indicates an n-type semiconducting property for all the oxides from thedifferent grain boundaries. However the value of the slope of the linear fit whichcorresponds to the donor concentration based on the Mott-Schottky equation isdifferent. The values of the oxide parameters including the donor concentrationand the flat band potential from all the above microelectrochemical measure-ments for some of the grain boundaries together with the corresponding grainboundary angles is listed in Table 4.3.

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Figure 4.20: Mott-Schottky plot for the oxides grown potentiostatically at the grainboundaries of Ti-30at.% Nb alloy.

As shown in Table 4.3 the oxide parameters determined for each grain bound-ary show variations. The formation factor k values reaching a value around 3nm V−1. The observed differences might be due to the additional surface areaexposed to the electrolyte due to the difference in topography of the various

Grain boundary θ k/ nm V−1 εr ND/ 1018 cm−3 Efb/ V8-9 5.7 2.76 77.9 5.7 -0.236-8 23.5 2.46 53.5 14.6 -0.255-10 23.9 2.62 53.8 12.0 -0.2713-14 31.2 3.09 100.9 10.5 -0.2413-15 42.4 3.06 101.7 66.6 -0.2212-13 44.8 3.00 99.7 8.1 -0.2611-12 44.9 2.76 79.9 10.4 -0.249-10 46.8 2.55 70.3 12.3 -0.2515-16 46.9 2.70 78.2 11.8 -0.2710-11 59.8 2.78 78.5 8.3 -0.24

Table 4.3: Summary of the oxide parameters calculated for the oxides grown ondifferent grain boundaries of Ti-30at.% Nb alloy where θ is the misorien-tation angle.

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grain boundaries. The topographies of the grain boundaries were determinedby AFM measurements (AFM, Asylum Research MFP3D) in non-contact modeusing a microcantilever with a force constant of 2 Nm−1 and a commercial silicontip (Olympus). Three types of grain boundaries were encounterd; wall, trenchand step-like examples of which are given as AFM topographies in Fig. 4.21.

Figure 4.21: AFM micrograph after oxide growth of grain boundary: (a) 8-9 (wall-type), (b) 13-15 (trench-type) and 15-16(step-type) of Ti-30at.% Nbsample.

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Moreover the variation in grain boundary energy with the misorientationangle induces differences in reactivity towards oxide formation among thegrain boundaries. Like the formation factor the dielectric number and donorconcentration varies with the grain boundaries. Presence of impurities in thegrain boundary region might result in oxides having impurities/compounds ofimpurities besides the expected oxides of titanium and niobium. Incorporationof the impurities might change the dielectric number of the oxide and the freeelectron density concentration as can be seen in Table 4.3 for the different grainboundaries of the Ti-30at.%Nb alloy.

Figure 4.22: A series of anodic oxide spots grown at the grain boundary 14-24 ofTi-30at.%Nb using scanning droplet cell.

It is worth mentioning at this point about the position where the tip of thescanning droplet cell lies during anodic oxide formation at the grain boundary.Fig. 4.22 shows a series of oxide spots grown across the grain boundary 14-24with a scanning doplet cell having 75 µm in diameter for the working electrodearea. As it is shown in the Fig. 4.22 the oxide spots are positioned asymmet-rically across the grain boundary. Asymmetrical position of the oxide growthmight have the effect on the local electrochemical response because of the dif-ference in the area of the oxide spot lying in the grains involved at the grainboundary. In such cases of asymmetrical oxide growth at a grain boundarymight give a result in which the local electrochemical response is dominated bythe contribution from the grain covered by the bigger area of the oxide spot.Moreover, the oxide spots were grown in area which consists some parts fromthe two grains making the grain boundary and the grain boundary itself. Theeffect that individual grain orientation have on the local reactivity and oxideproperties were discussed thoroughly in section 4.2. In order to get the local

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electrochemical response of a certain grain boundary the opening of the capil-lary tip of the scanning droplet cell must be minimized as much as possible sothat only the contribution from the grain boundary can be obtained. In thiswork at the grain boundaries a working electrode diameter of 45 µm was usedto avoid as much as possible the effects from the grains involved at the grainboundary under consideration as shown in Fig. 4.17.

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5 Anodic oxides of (α+β)-typeTi-Nb alloys

The study of the surface reactivity of Ti-Nb alloys which is explained in the pre-vious chapter for Ti-30 at.% Nb alloy β-type Ti alloy is extended to (α+β)-typeTi-Nb alloys and will be discussed thoroughly in this chapter. Two alloys of Tiand Nb with specific compositions of Ti-10 wt.% Nb and Ti-20 wt.% Nb wereselected for the electrochemical characterization. The electrochemical charac-terization is done using cyclic voltammetry to grow anodic oxides on the twoalloys where issues of passivity, mechanism and kinetics of anodic oxide growthon the two alloys were addressed. The electronic properties of these anodic ox-ides and the interface they form with the aqueous electrolyte was studied byusing electrochemical impedance spectroscopy. Moreover, the semiconductingproperty of the oxides was assessed by using Mott-Schottky analysis.The study of the surface reactivity starts with preparation of a sample surfacegood enough for the aimed measurements. To obtain a good surface, series ofmechanical and electrochemical preparation technics were involved. The me-chanical preparation starts with grinding the surface of the two alloys with acoarse abrasive of 220 grit silicon carbide and progressing to the finer abrasivesof 2500 and 4000 grit in the presence of water. The effect of running water onthe grinding process is explained in section 3.1.1. The second stage of samplepreparation is polishing which combines mechanical and chemical removal of thedamaged surface from a certain material. The two Ti-Nb alloys were polishedwith a silica suspension on a nylon cloth disc to get a smooth surface with lessdeformation to the crystal structures of the samples surface. One fraction byvolume of 30 % H2O2 is added to five parts of the silica suspension for polishingthe Ti-Nb alloys for better results. The last seconds of the polishing proce-dure were carried out in the presence of running water to clean the samples’surface from silica residuals. The last procedure in sample surface preparationis electropolishing. Electropolishing is done potentiostatically at 8 V in a 3 M

83

5 Anodic oxides of (α+β)-type Ti-Nb alloys

methanolic sulfuric acid solution kept at -22 0C [63]. The samples’ surface iscleaned in an ultrasonic bath of ethanol and water, rinsed with ethanol anddried with compressed nitrogen gas after each procedure to remove left oversfrom the sample surface preparation procedures. Electropolishing will removeall the damage done to the surface of the two alloys from mechanical grindingand polishing resulting in the true microstructure of the samples’ surface. Fig.5.1 a & b shows optical micrograph of Ti-10 wt.% Nb and Ti-20 wt.% Nb alloysrespectively after sample preparation prior to any potential application.

Figure 5.1: Optical micrograph of the surface of (a) Ti-10 wt.% Nb and(b) Ti-20 wt.% Nb after sample preparation.

To get an insight into the microstructure of the Ti-Nb alloys and thereby con-firming that the samples’ surface is free of deformation EBSD scans were carriedout on the two alloys in a field emission scanning electron microscope with anacceleration voltage of 20 kV and step size of 150 nm for orientation mapping.The EBSD scans confirm that the sample surface procedures result in surfacesfree from deformation that is the basis to get the EBSD maps shown in Fig.5.2 a-d. From the EBSD maps the component phases of the two alloys can berevealed where the two alloys are made of a mixture of hexagonal close packedand body centered cubic crystal structures confirming that the two alloys are(α+β)-type Ti-Nb alloys as is expected from the phase diagram for the Ti-Nbsystem. The optical micrograph shows that the two Ti-Nb alloys consist of largegrains. But inside these large grains there are subgrains with sizes in the orderof 10 µm made up of hexagonal and body centered cubic crystal structures as itis revealed from the EBSD measurements as shown in Fig. 5.2. Similar needlelike subgrains were also reported earlier for Ti-Nb alloys within a single grain[112, 147]. The observed needle-like subgrains might be metastable martensiticstructures of α′ and α′′ . The α′ martensitic phase has a hexagonal close packed

84

structure like the α-Ti with a ≈ 0.295 nm and c ≈ 0.468 nm for Nb contentup to 12 wt.%. Beyond this composition for the Nb content the α′-Ti will un-dergo a rhombic distortion resulting in the α′′-Ti martensite structure with a ≈0.313 nm, b ≈ 0.482 nm and c ≈ 0.463 nm [29]. The α′′ martensite structure isnot noticed in the two Ti-Nb alloys especially in the Ti-20wt%Nb alloy even ifin the literature it was reported that such kind of martensite structures mightappear for Nb concentrations beyond 12 wt% as it is confirmed from the EBSDscans on the two samples.

Figure 5.2: (a) & (c) Inverse pole figure of Ti-10wt.% Nb and Ti-20wt.% Nb respec-tively(b) & (d) Image quality map of Ti-10wt.% Nb and Ti-20wt.% Nb re-spectively.

85


5.1 Oxide growth on Ti-10 wt.% Nb and Ti-20wt.% Nb

Cyclic voltammetry is the electrochemical technique used to grow anodic oxideson Ti-10 wt.% Nb and Ti-20 wt.% Nb alloys in a double glass walled electro-chemical cell (see section 3.2.1). The applied potential starting from 0 V andincreasing in steps of 1 V to 8 V was scanned at a rate of 100 mV s−1 on asample immersed in an acetate buffer of pH 6.0 so that the mechanism of theoxide growth and the kinetics involved during oxide growth can be studied. Thesuccessive cyclic voltammograms recorded during the oxide growth for the twoTi-Nb alloys are shown in Fig. 5.3.

Figure 5.3: Cyclic voltammograms from the anodization of Ti-10 wt.% Nb and Ti-20wt.% Nb.

A sharp overshoot in current density is observed in the first cycle for the twoalloys which broadens and later disappears after the second cycle onwards.The observed overshoot resulted from the complete overlap of oppositelycharged ion clouds of metal ions of the sustrate alloys and oxide anions duringfield assisted migration of the ions to the oxide/electrolyte and metal/oxide

86

5.1 Oxide growth on Ti-10 wt.% Nb and Ti-20 wt.% Nb

interfaces respectively as explained by the extended high field model [44]. Theformation of this space charge region during the overlap of the ions leads toa retardation in the migration and arrival of the ions at the two interfaceswhere the new oxide is formed. Thus the overshoot is a sign of the delay inthe kinetics of the oxide formation. In the intermediate potential regions theovershoot is no more observed, rather a current plateau is observed until theupper oxide formation potential. The current plateau indicates the absence ofany side electron transfer reactions which would result in oxygen evolution andthe sole reaction involved is an ion transfer reaction resulting in the constantthickening of the oxide according to the high field mechanism [44]. During thereverse cathodic sweep after reaching the upper oxide formation potential, thecurrent falls rapidly towards zero. In the subsequent anodic sweep the currentstays to the minimum until it surpasses the oxide formation potential of thepreviously grown oxide due to current rectification of the anodic oxides likethe oxides of other valve metals. As the applied potential is increased themigration of the oppositely charged ions towards the two interfaces dominatesthe kinetics of the oxide formation resulting in delayed oxide formation evidentfrom the smeared out increase in the current density as shown towards the lastcycles of the cyclic voltammograms. The retardation in the kinetics of the oxideformation can also be observed from the increasing gap between the cathodiccurve and the anodic curve of the subsequent cycle. An optical micrograph ofthe boundary between the surface where anodic oxide growth takes place bypotential application which has a golden colour and the native oxide is shownin Fig. 5.4 for the two Ti-Nb alloys.

Figure 5.4: Optical micrograph of the boundary between the oxidized (goldencolour) and the unoxidized surface of (a) Ti-10 wt.% Nb and (b) Ti-20 wt.% Nb alloy.

87


The area under each cycle in the cyclic voltammogram is proportional to thecharge density consumed to grow the respective oxides. Based on eqn.(4.1) &(4.2) which relate the charge density with the oxide thickness and to the ap-plied potential, the formation factor k is calculated from the slope of the plot ofcharge density versus potential. Fig. 5.5 shows the plot of the charge density Qconsumed to grow the anodic oxides on the respective Ti-Nb alloys versus thepotential applied to grow the oxides. A linear correlation is observed betweenthe charge density and the applied potential for both of the Ti-Nb alloys. Thisimplies that the oxide growth process was Faradaic and exclusive ionic conduc-tivity results in the continuous growth of the oxide with no electron transferreaction. A value of 2.45 and 2.49 nm V−1 was calculated from the slope ofFig. 5.5 as the formation factor values for Ti-10 wt.% Nb and Ti-20 wt.% Nballoy respectively. The oxide formation factor k calculated for the two alloyscorrespond to an electric field strength of 4×106 V cm−1 based on eqn. (4.4)which gives the reciprocal relation between the oxide formation factor and fieldstrength.

Figure 5.5: Plot of the charge density used to grow the oxides versus applied poten-tial.

88

5.2 Oxide characterization by electrochemial impedance spectroscopy

5.2 Oxide characterization by electrochemialimpedance spectroscopy

Electrochemical impedance spectroscopy is a powerful technique in probing theoxide/electrolyte interface. With this regard electrochemical impedance mea-surements were carried out to study the interface of the oxides of Ti-10 wt.%Nb and Ti-20 wt.% Nb have with the acetate buffer electrolyte. The electro-chemical impedance measurements were carried out before applying potentialin a frequency range of 50 kHz to 10 mHz with an AC perturbation voltageof 10 mV to study the oxide/electrolyte interface of the native oxide which isformed from the air passivation of the Ti-Nb alloys. Successive electrochemi-cal impedance measurements were carried out right after each oxide growth bycyclic voltammetry to study the interface between the previously formed oxideand the electrolyte. Bode plot representation of the impedance spectra recordedfor the oxides on the two Ti-Nb alloys, Ti-10 wt.% Nb and Ti-20 wt.% Nb, areshown in Fig. 5.6 & 5.7 respectively.

At high frequencies (> 10 kHz) a constant value of impedance 18 ±1.1Ω cm2 andthe phase shift close to zero indicates a pure resistive behaviour which is a solecontribution from the electrolyte resistance. As the frequency is decreasing andreaching the intermediate frequency range, the impedance increases with theapplied potential proving that the oxide is thickening with the applied potentialfor both of the alloys. The phase shift recorded from the native oxide prior to anypotential application showed a one time constant with a value around -800 indi-cating a capacitive bahaviour for both of the Ti-Nb alloys. However, the phaseshift recorded after the application of potential on the two alloys is different. Aclear two time constant behaviour is observed from the impedance spectra onthe Ti-10 wt.% Nb alloy especially after an oxide growth with 1 V and 2 V. Fig.5.8 shows the equivalent circuits proposed to fit the impedance spectras of Ti-10wt.% Nb alloy. Fig. 5.8a is the equivalent circuit for the impedance spectra ofthe native oxide of Ti-10 wt% Nb which consists of resistance of the oxide R1

connected in parallel to constant phase element of the oxide CPE connectedto a serial resistance Rs of the electrolyte. The equivalent circuit proposed forthe oxides of Ti-10 wt.% Nb alloy after potential application however, consistsof a series connection of resistor connected parallel to CPE, resistor connectedparallel to a pure capacitor and electrolyte resistance Rs indicating that thereare two distinct layers of oxides with different electrical properties.

89



90



91


However, the phase shift for the Ti-20 wt.% Nb alloy showed only one time

Figure 5.8: Equivalent circuits used to fit the impedance spectra: (a) for the nativeoxide and (b) for the anodic oxides of Ti-10 wt.% Nb after potentialapplication.

constant for all of the nine impedance spectras. The phase shift reached a valuearound -860 indicating a near capacitive behaviour of the oxides of this alloy.The equivalent circuit used to fit the impedance spectras from the Ti-20 wt.%Nb alloy is shown in Fig. 5.9.A constant phase element is used instead of a pure capacitor for fitting purposes.The impedance of a constant phase element is given in eqn. (4.9). The value ofn tells how much the constant phase elements used in the equivalent circuits forthe two Ti-Nb alloys is close to an ideal capacitor. The value of n is in the rangeof 0.90-0.93 and 0.94-0.97 for the constant phase elements used in the proposedequivalent circuits for Ti-10 wt.% Nb and Ti-20 wt.% Nb alloys respectively.These values indicate how much the oxides of the two alloys especially the ox-ides of Ti-20 wt.% Nb are close to being an ideal capacitor which has n = 1.The experimental and fitted curves for some of the impedance spectras from thetwo alloys Ti-10 wt.% Nb and Ti-20 wt.% Nb are shown in Fig. 5.10 & 5.11respectively.

92


Figure 5.9: Equivalent circuit used to fit the impedance spectra of Ti-20 wt.% Nb.

Figure 5.10: Bode plot representation for some of the experimental and fitted curvesof the EIS spectra for the anodic oxides of Ti-10 at.% Nb. Symbolsrepresent the experimental data and solid lines fitted curves.

93


Figure 5.11: Bode plot representation for some of the experimental and fitted curvesof the EIS spectra for the anodic oxides of Ti-20 at.% Nb. Symbolsrepresent the experimental data and solid lines fitted curves.

One of the important attributes of the oxides of valve metals is their high dielec-tric number for applications in the electronic industry. The dielectric numberof these oxides can be determined from the impedance in the intermediate fre-quency range. The impedance in this region is almost a sole contribution of thecapacitive reactance of the oxide. The capacitive reactance is related to the ca-pacitance of the oxide as it is given in eqn. (4.7). The capacitance of oxide C0x iscalculated from the total electrode capacitance C by taking into consideration

94


the capacitance of the Helmholtz double layer CH . Since the two capacitors arein series the equivalent capacitance is written as:

1C

= 1Cox

+ 1CH

(5.1)

A value of 20 µF cm−2 [130, 148] commonly used in the literature for theHelmholtz layer capacitance is taken to calculate the oxide capacitance. Theinverse of the capacitance of the oxide is related to the applied potential ac-cording to eqn. (4.8). Based on eqn. (4.8) the slope from the plot of the inversecapacitance of the oxide as a function of applied potential given in Fig. 5.12will give the relative permittivity values of the respective oxides based on theformation factor k determined for the two alloys in section 5.1. Valuea of 48and 50.5 were determined for the relative permittivity of the mixed oxides ofTi-10 wt.% Nb and Ti-20 wt.% Nb respectively.

Figure 5.12: Plot of the inverse capacitance of the anodic oxides verus the potentialapplied to grow the oxides.

The value of the circuit elements from the equivalent circuits proposed for theoxides of the two Ti-Nb alloys Ti-10 wt.% Nb and Ti-20 wt.% Nb are tabulated

95


in Table 5.1 and 5.2 respectively. The equivalent circuit proposed for Ti-10wt.% Nb may have different physical meanings. It is generally used to modelsubsequent structures or processes. One example is a bilayer structure of ox-ides consisting of two different oxides or hydroxides with significantly differentresistive and capacitive properties. These differences are necessary to yield asufficiently different time constant so that it becomes visible in the impedancespectra meaning in the frequency range studied. Sometimes this behaviour isalso found for single oxide layers which are not completely blocking. In thiscase a charge transfer is still possible through electronic tunneling or electronicconduction resulting in a so called charge transfer resistance which forms atime constant with the Helmholtz capacity. A time constant τ can be generallycalculated from the following equation:

τ = R.C (5.2)

Since the latter one is typically in the range of 20 µF cm−2 as mentioned abovethe time constant is observed when the resistance is in the range from 50 kΩcm2 to 50 MΩ cm2 because this frequency results in a frequency f which resultsfrom f = 1/τ .The equivalent circuit proposed for the oxides of Ti-10 wt.% Nb alloy was pro-posed in the literature for oxides of titanium and its alloys having a bilayerstructure comprising of a barrier compact oxide layer underneath a porous ox-ide layer for different kind of electrolytes used [109, 149–152]. However, thiswork is done in an acetate buffer where the formation of a porous type oxidestructure is excluded. The observed two time constant however can be explainedby taking into consideration the formation of suboxides of the constituent el-ements of the alloy. Titanium and niobium are transition elements which canform different oxides and suboxides with different physical properties due to thevariable valencies they exhibit. Among these suboxides niobium monoxide NbOis a conductor [153, 154]. The formation of NbO will increase the electricalconductivity of the whole oxide which is exhibited by R2 value of 2.06 & 2.63kΩ cm2 for the oxides grown at 1 V and 2 V respectively as shown in Table5.1 for Ti-10 wt.% Nb alloy. The value of R2 increases drastically from 2.63kΩ cm2 to 51.87 kΩ cm2 up on moving from the oxide grown at 2 V to 3 V.The oxidation of the NbO to higher oxidation states to form Nb2O5 results in adecrease of the conductivity and thereby increasing the resistance as shown inthe value of R2. Similar observations were reported by Milosev et al. [155] from

96


the characterization of the passive film formed on a Ti-6Al-7Nb (α+β)-type Tialloy by electrochemical impedance spectroscopy and XPS measurements. Thepresence of suboxides of niobium were confirmed by XPS measurements and thevalue of the resistor in the proposed equivalent circuit increased drastically forpotentials ≥3 V similar to the change in R2 observed for this alloy as well.

E/ V R1/ MΩ cm2 CPE1 n R2/ kΩ cm2 C1/ µF cm−2 Rs/ Ω cm2

0 0.07 19.83 0.93 - - 17.831 1.20 18.73 0.91 2.06 55.14 18.552 1.71 12.83 0.92 2.63 27.56 18.463 2.01 10.49 0.91 51.87 16.88 18.134 1.94 8.98 0.91 54.06 11.45 18.255 2.13 7.87 0.91 58.99 8.34 18.576 2.32 7.09 0.91 68.30 6.65 18.567 2.28 6.47 0.90 81.03 5.64 18.558 2.35 5.69 0.90 75.58 5.12 18.57

Table 5.1: The values of the circuit elements from the proposed equivalent circuit ofthe oxide on Ti-10 wt.% Nb alloy. CPE1 is given by µΩ−1 sn cm−2.

E/ V R1/ MΩ cm2 CPE1/ µΩ−1 sn cm−2 n Rs/ Ω cm2

0 0.09 18.18 0.97 16.901 3.28 12.98 0.97 17.412 9.91 8.47 0.97 17.573 6.93 5.77 0.96 17.824 5.7 4.96 0.96 17.815 5.29 3.71 0.95 18.796 5.05 3.66 0.95 18.557 5.39 3.32 0.94 17.718 6.09 2.98 0.94 17.67

Table 5.2: The values of the circuit elements from the proposed equivalent circuit ofthe oxide on Ti-20 wt.% Nb alloy.

Another important parameter in the study of oxide growth and characterizationis the determination of the native oxide thickness d0. The thickness of thenative oxide on both alloys prior to any potential application is determined fromthe first impedance spectra using eqn. (4.6) based on the relative permitivityvalue of the respective oxides determined above. The native oxide thickenessis determined to be 0.88 & 0.62 nm respectively for Ti-10 wt.% Nb and Ti-20

97


wt.% Nb alloys. It must be emphasized, here that this numerical results expressthe average thickness of the amorphous metal-cation oxygen-anion film, sincethis thickness is already in the range of a few ionic radii. The difference in thenative oxide thickness between the two Ti-Nb alloys might be the underlyingreason for the observed current density difference in the first two cycles in thecyclic voltammogram as shown in Fig. 5.3. Ti-10wt.%Nb which forms a thickernative oxide than Ti-20wt.%Nb has a lower current density as compared toTi-20wt.%Nb. From this initial thickness the oxide thickenss on both alloyscontinue to grow with the applied potential.

5.3 Mott- Schottky analysis of the oxides of(α+β)-type Ti-Nb alloys

Mott-Schottky analysis was employed to study the semiconducting propertyof the mixed anodic oxides grown on Ti-10 wt.% Nb and Ti-20 wt.% Nballoys. From the Mott-Schottky analysis the type of semiconductor, chargecarrier concentration and flat band potentials were determined based on eqn.(3.17). The analysis was carried out on an oxide potentiostatically grown at3 V for 1000 s in an acetate buffer of pH 6.0 on both alloys. Electrochemicalimpedance measurements were carried out after the oxide growth at fixedfrequency by sweeping the bias potential from 1.5 V to -0.5 V in steps of 50mV. The variation of the capacitance of the space charge region versus theapplied bias potential for the mixed oxides of titanium and niobium on thetwo alloys is shown in the Mott-Schottky plot of Fig. 5.13. A linear region,0.25 V to -0.25 V, with a positive slope for the two alloys indicates an n-typesemiconducting property. The donor concentration and the flat band potentialof the respective oxides is calculated from the slope and intercept of the linefitted for this linear region with the potential axis as shown in Fig. 5.13.From the Mott-schottky analysis a donor concentration of 7.5 ×1018 cm−3

and 2.4 ×1019 cm−3 were determined for Ti-10 wt.% Nb and Ti-20 wt.% Nballoy respectively based on the relative permittivity values of the respectiveoxides determined in the above section. Likewise, the flatband potentialswere -0.15 V and -0.18 V respectively for Ti-10 wt.% Nb and Ti-20 wt.%Nb alloys. The oxides of Ti-20 wt.% Nb alloy has a donor concentration

98

5.3 Mott- Schottky analysis of the oxides of (α+β)-type Ti-Nb alloys

around half orders of magnitude higher than that of Ti-10 wt.% Nb alloywhereas the flat band potentials are almost eqivalent. Question arises whetherthe substrate composition with a doubled concentration in niobium can beresponsible for this behaviour. It must be taken into account that the transportnumbers of the two constituting elementsts may be significantly different.This could be part of a future work to study forexample by a surface analyti-cal method such as XPS how the compositional structure of the oxide looks like.

Figure 5.13: Mott-Schottky plots of the oxides of Ti-10 wt.% Nb and Ti-20 wt.%Nb.

Based on the results from the Mott-Schottky analysis a discussion of the di-mension of the space charge layer of the semiconductor is of interest. The spacecharge layer can be described in terms of the Debye length, which is the lengthover which the potential drops to a value of 1/e and is given by:

LD = 1e

(εrε0kT

2ND

) 12

(5.3)

where e is electronic charge, k Boltzmann constant, T absolute temperature andND donor concentration [156]. The value of the donor concentration ND for the

99


respective oxides is taken from the Mott-Schottky analysis carried out on thetwo alloys as explained in detail above. Thus a Debye length of 2.13 and 1.22 nmwere calculated for the oxides of Ti-10 wt.% Nb and Ti-20 wt.% Nb respectively.The Debye length of the oxide of Ti-10 wt.% Nb alloy is almost twice that ofTi-20 wt.% Nb alloy. Fig. 5.14 shows the plot of the ratio between the oxidethickness and the Debye length LD with the applied potential. The Debyelength is the distance in a semiconductor over which local electric field affectsdistribution of free charge carriers and decreases with increasing concentrationof free charge carriers as it is given in eqn (5.3). The thickness of the spacecharge layer is typically said to be four times that of the Debye layer owing tothe fact that this corresponds to a potential drop to 1/4e which correspondsnumerically to a drop by a factor of nearly 100. Looking at Fig. 5.14 it can beseen that this is the case for an oxide formation of 2 V vs. SHE for Ti-20 wt.%Nb alloy where as this value is reached for the Ti-10wt.% Nb alloy only at apotential of 3.5 V vs. SHE.

Figure 5.14: Plotof the ratio of the oxide thickness d and Debye length LD versusthe potential applied to grow the oxides.

The surface reactivity of the two (α+β)-type Ti-Nb alloys discussed above isdone with a conventional electrochemical cell where the results were a net con-

100

5.3 Mott- Schottky analysis of the oxides of (α+β)-type Ti-Nb alloys

tribution from the two phases, α- and β-phases, of the Ti-Nb system. Moreover,the two phases consist of grains which have different crystallographic orienta-tion. The two Ti-Nb samples would give an interesting substrate to work on forlocalized electrochemical measurements using the scanning droplet cell as theywould provide different combinations of microstructural elements in one. Suchkind of localized electrochemical measurements would enable to address the localelectrochemical response of the α and β rich grains in relation to the crystallo-graphic information that could be obtained from EBSD. In addition, localizedelectrochemical measurements at the grain boundaries of such samples wouldeven give different combinations of phase and crystallographic orientation sincethe grain boundaries might be between α-α, β-β or α-β grains.

101

6 Summary

The surface reactivity of two type of titanium alloys namely: the β-type and(α+β)-type Ti-Nb alloys with specific compositions of Ti-30 at.% Nb, Ti-20wt.% Nb and Ti-10 wt.% Nb alloys were evaluated using the double glass-walledelectrochemical cell and the scanning droplet cell.The double glass-walled cell exposed 0.3 cm2 area of the sample to the elec-trolyte. From this exposed area the surface reactivity of the polycrystallinesample was investigated where important information in surface reactivity suchas oxide growth mechanism, thickness of the oxide and kinetics of the oxidegrowth were studied. The anodic oxide growth on all the samples takes placeaccording to the high field mechanism where ions of opposite charge emanatingfrom the metal/oxide interface and the oxide/electrolyte interface are hopping inopposite directions as a result of the applied potential to grow oxides at the twointerfaces mentioned. In all of the titanium alloys studied in this work the solereaction taking place was an ion transfer reaction which resulted in the thick-ening of the oxide with the applied potential evident from the current plateausrecorded in the cyclic voltammograms for each oxide growth on the alloys. Thecurrent plateaus also infer the absence of any side reactions due to electrontransfer reactions such as oxygen evolution on any of the alloys. Had there beenan oxygen evolution reaction the current density would show a sudden increasein the 2-3 V region in the cyclic voltammograms like the conventional pure ti-tanium reported earlier in literature. The dielectric number of the mixed oxidesgrown on these alloys are of particular interest in the electronic industry. The ca-pacitive reactance of the oxides determined from the elctrochemical impedancemeasurements carried out enabled for the determination of the correspondingdielectric numbers of the oxide. Moreover, the semiconducting properties of theoxides on each of the alloys were assessed using Mott-Schottky analysis. Fromthe Mott-Schottky analysis information as to the type of the semiconductor, thecharge carrier concentration and flat band potential were obtained.The surface reactivity studies were then miniaturized to small areas inside a

103

6 Summary

single grain or accross a grain boundary to get information about the local elec-trochemistry of the substrate grain or grain boundary. Miniaturized workingelectrode area in electrochemistry is possible only with microcells. The scanningdroplet cell is used in this work for the single grain and grain boundary electro-chemical measurements. The scanning droplet cell brings a small droplet of anelectrolyte to the surface of the substrate. The wetted area defines the workingelectrode area. The desired working electrode area was achieved by pulling acapillary with capillary puller and grinding the tip with a microgrinder to thedesired tip diameter. The tip of the capillary was then dipped in a silicone togive a flexible edge to the capillary tip which was pressed against the samplesurface to seal off the droplet from the outside environment. This guarantees theabsence of electrolyte evaporation in addition to the wetted area change when apotential is applied due to the electrocapillarity effects and thus helps to definethe working electrode area precisely.The localized electrochemical measurements were carried out on the single grainsand grain boundaries of Ti-30at.% Nb β-type titanium alloy. The local reactivityresults were then correlated with the crystallographic orientaion data obtainedfrom the electron backscatter diffraction (EBSD) measurements. The local re-activity was studied by growing anodic oxide spots within a single grain andacross a grain boundary to study the reactions involved, the mechanism of an-odic oxide growth and the kinetics of the growth like the experiments carriedout using the double glass-walled electrochemical cell. The local oxide spotgrowth followed the high field mechanism and the reactions involved only iontransfer reaction similar to the experiments of oxide growth with the conven-tional double glass-walled cell in all of the single grains and grain boundariesstudied. Electrochemical impedance measurements carried out right after the ox-ide growth enabled to study the oxide/electrolyte interface in a wide frequencyrange. From the impedance measurements the corresponding value of the di-electric number of the oxides grown on the single grains and grain boundarieswere determined from the capacitive reactance. The semiconducting behaviourof the oxides were assessed locally using Mott-Schottky analysis which involvedelectrochemical impedance measurements carried out with the application of abias potential so that the change in the space charge capacitance with the ap-plied bias potential can be followed.The Ti-30at.% Nb β-type alloy showed excellent passivity be it at macroscopicsurface or at single grains and grain boundary level. Even the grain bound-

104

aries which bring together grains having different orientations at different grainboundary angles showed a passivity marked with a current plateau. The grainboundaries involved have three main topographies determined from the atomicforce microscopy (AFM) scans: wall-type, trench-type and step-like.From the localized electrochemical measurements on Ti-30at.% Nb β-type al-loy orientaion dependent electrochemistry was observed where oxide parameterssuch as the formation factor, dielectric number and donor concentration are dif-ferent for oxides grown on grains having different orientation. The variationof the oxide parameters showed a trend with the atomic surface density andthe surface energy of the respective grains. However, determination of the oxidecompositions, the transport number of the cations, the crystallinity or amor-phous structure of the oxides from each of the single grains might give moreinsight to explain the observed anisotropy in the oxide parameters.In this work, the surface reactivity of the three Ti-Nb alloys have been studiedusing two types of electrochemical cells where all the alloys showed excellentpassivity cementing the promise that this alloys provide for biomaterial applica-tions. The localized electrochemical measurements gave a close look at the localreactivity and the variation of the oxide parameters determined with the grainorientation. This work can thus serve as a platform for further investigationon these alloys and other materials to study explicitly the driving force behindthe observed oxide parameter anisotropy. With this regard depth profiles or an-gle resolved X-ray photoelectron spectroscopy should reveal whether or not apreferential transport of cations during anodization yields a normal compositiongradient.

105

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120

List of Figures

2.1 The hexagonal close packed and body centered cubic unit cells ofthe α- and β-phase of titanium. (Figure taken from [12]). . . . . 6

2.2 Schematic illustration of the effect of alloying elements on thephase diagrams: (a) α stabilizing element (b) β eutectoid and (c)β isomorphous stabilizing elements where γ is an intermetalliccompound and the β-transus is for pure titanium [13]. . . . . . . 7

2.3 The Ti-Nb phase diagram [23]. . . . . . . . . . . . . . . . . . . . 112.4 Schematic diagram of the processes taking place at the oxide film

of titanium [38, 39]. . . . . . . . . . . . . . . . . . . . . . . . . . 132.5 Schematic diagram of the different mechanisms of electron ex-

change between redox systems: (a) H2 evolution on stable oxide(TiO2, Nb2O5) (b) Reduction before hydrogen evolution (PtO,Bi2O3) (c) Oxidation before oxygen evolution (Cu2O)[38, 39]. . . 15

2.6 Band energetics of the different oxides. (Figure taken from [38]). 162.7 Pourbaix diagram of titanium in water at 25 oC [43]. . . . . . . 172.8 Pourbaix diagram of niobium in water at 25 oC [43]. . . . . . . . 182.9 Figure taken from [42] showing the ion hopping between two ad-

jacent lattice planes within the oxide film. . . . . . . . . . . . . 202.10 A plot showing the effect of the electric field strength on the

activation energy of hopping ions. . . . . . . . . . . . . . . . . . 20

3.1 Schematic diagram of mass transport mechanisms involving: (a)anodically formed metal ions Maq - salt film mechanism (b) ac-ceptor anion A or (c) H2O as transport limiting species. MAy isa complex ion and Csat is saturation concentration [57]. . . . . . 27

3.2 Picture of the double glass-walled electrochemical cell. . . . . . 293.3 (a) Schematic diagram of scanning droplet cell (b) Picture of

scanning droplet cell setup. . . . . . . . . . . . . . . . . . . . . . 31

121

List of Figures

3.4 (a) Basic components of a three-electrode potentiostat connectedto an electrochemical cell (b) Circuit of the potentiostat afterthe electrochemical cell and the current measuring circuit werereplaced by two impedances Z1 and Z2. . . . . . . . . . . . . . . 34

3.5 Excitation signals for successive cyclic voltammetric sweeps. . . 363.6 Vectorial representation of impedance. . . . . . . . . . . . . . . 373.7 Semiconductor/electrolyte interface. . . . . . . . . . . . . . . . . 383.8 Effect of applied potential (E) on the band edges in the interior

of an n-type semiconductor: (a) E > Efb, (b) E = Efb and (c)E < Efb [98]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.9 Schematic diagram of a typical EBSD system. . . . . . . . . . . 413.10 Schematic diagram for Bragg diffraction [101]. . . . . . . . . . . 423.11 Formation of the Kikuchi lines from a tilted sample [102]. . . . . 423.12 (a) An example of EBSP and (b) Indexed EBSP of Ti-30at.% Nb

β-type Ti alloy. . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.13 Base vectors and direction vectors in real lattice. . . . . . . . . . 443.14 Miller indices for low index planes of a cubic crystal. . . . . . . 443.15 Relationship between sample coordinate system and crystal co-

ordinate system ([100], [010], [001]) [102]. . . . . . . . . . . . . . 453.16 (a) Streographic projection of the normal to a crystal plane hkl

on to the equatorial plane (b) Pole figure as described by the twoangles α and β. . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

3.17 (a) Complete inverse pole figure (b) Unit triangle of the inversepole figure for a cubic system. . . . . . . . . . . . . . . . . . . . 47

3.18 (a) Euler angles (b) Representation of orientation in Euler space[108]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.19 Schematic illustration of Goss orientation. . . . . . . . . . . . . 49

4.1 Cyclic voltammograms from the anodic oxide growth on Ti-30at.% Nb in an acetate buffer of pH=6.0. . . . . . . . . . . . . 54

4.2 Schematic representation of oxide growth at the metal/oxide andoxide/electrolyte interface for counter ions with transport number0.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.3 A plot of the charge consumed to grow the oxides as a functionof applied potential. . . . . . . . . . . . . . . . . . . . . . . . . . 56

122

List of Figures

4.4 Equivalent circuit for a metal covered with an oxide in contactwith an electrolyte solution where the contribution from the re-sistance and capacitance of surface states is neglected. . . . . . . 57

4.5 Bode plot representation of the EIS data of Ti-30 at.% Nb duringsuccessive oxide growth. . . . . . . . . . . . . . . . . . . . . . . 59

4.6 Reciprocal of oxide capacitance versus the applied potential. . . 604.7 Schematic drawing of the equivalent circuit used to simulate the

oxide/electrolyte interface. . . . . . . . . . . . . . . . . . . . . . 614.8 Bode plot for some of the experimental and fitted curves of the

spectra. Symbols represent the experimental data and solid linesfitted lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.9 Mott-Schottky plot for the potentiostatically grown oxide on thesurface of Ti-30 at.% Nb alloy. . . . . . . . . . . . . . . . . . . . 63

4.10 Optical micrograph of the surface of Ti-30at.%Nb after anodicoxide growth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

4.11 (a) Inverse pole map with the legend showing the relative po-sitions of the grains with the low index planes and (b) Imagequality from the EBSD scan on the surface of Ti-30 at.% Nbsample. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.12 Cyclic voltammograms from the single grains of the Ti-30 at.% Nb. 674.13 Plot of charge consumed to grow the oxides on the single grains

of Ti-30 at.% Nb as a function of applied potential. . . . . . . . 694.14 Inverse capacitance of the anodic oxides on different grains of

Ti-30at.% Nb versus the potential applied to grow the oxides. . 704.15 Mott-Schottky plots for the oxides grown on the differently ori-

ented grains of the Ti-30at.% Nb sample. . . . . . . . . . . . . . 714.16 EBSD maps; (a) inverse pole plot, (b) image quality and (c) color

coded grain boundaries of Ti-30at.% Nb alloy. . . . . . . . . . . 754.17 Optical micrograph of oxide spots at a grain boundary of Ti-

30at.% Nb sample. . . . . . . . . . . . . . . . . . . . . . . . . . 764.18 Cyclic voltammograms from grain boundaries of Ti-30at.% Nb

sample. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 764.19 Plot of inverse capacitance versus applied potential from the dif-

ferent grain boundaries of Ti-30at.% Nb sample. . . . . . . . . . 784.20 Mott-Schottky plot for the oxides grown potentiostatically at the

grain boundaries of Ti-30at.% Nb alloy. . . . . . . . . . . . . . . 79

123

List of Figures

4.21 AFM micrograph after oxide growth of grain boundary: (a) 8-9(wall-type), (b) 13-15 (trench-type) and 15-16(step-type) of Ti-30at.% Nb sample. . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.22 A series of anodic oxide spots grown at the grain boundary 14-24of Ti-30at.%Nb using scanning droplet cell. . . . . . . . . . . . . 81

5.1 Optical micrograph of the surface of (a) Ti-10 wt.% Nb and (b)Ti-20 wt.% Nb after sample preparation. . . . . . . . . . . . . . 84

5.2 (a) & (c) Inverse pole figure of Ti-10wt.% Nb and Ti-20wt.% Nbrespectively (b) & (d) Image quality map of Ti-10wt.% Nb andTi-20wt.% Nb respectively. . . . . . . . . . . . . . . . . . . . . . 85

5.3 Cyclic voltammograms from the anodization of Ti-10 wt.% Nband Ti-20 wt.% Nb. . . . . . . . . . . . . . . . . . . . . . . . . . 86

5.4 Optical micrograph of the boundary between the oxidized (goldencolour) and the unoxidized surface of (a) Ti-10 wt.% Nb and (b)Ti-20 wt.% Nb alloy. . . . . . . . . . . . . . . . . . . . . . . . . 87

5.5 Plot of the charge density used to grow the oxides versus appliedpotential. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88



5.8 Equivalent circuits used to fit the impedance spectra: (a) for thenative oxide and (b) for the anodic oxides of Ti-10 wt.% Nb afterpotential application. . . . . . . . . . . . . . . . . . . . . . . . . 92

5.9 Equivalent circuit used to fit the impedance spectra of Ti-20 wt.%Nb. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

5.10 Bode plot representation for some of the experimental and fittedcurves of the EIS spectra for the anodic oxides of Ti-10 at.%Nb. Symbols represent the experimental data and solid lines fittedcurves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

5.11 Bode plot representation for some of the experimental and fittedcurves of the EIS spectra for the anodic oxides of Ti-20 at.%Nb. Symbols represent the experimental data and solid lines fittedcurves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

5.12 Plot of the inverse capacitance of the anodic oxides verus thepotential applied to grow the oxides. . . . . . . . . . . . . . . . 95

124

List of Figures

5.13 Mott-Schottky plots of the oxides of Ti-10 wt.% Nb and Ti-20wt.% Nb. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

5.14 Plotof the ratio of the oxide thickness d and Debye length LDversus the potential applied to grow the oxides. . . . . . . . . . 100

125

List of Tables

4.1 Properties of the low index planes of bcc Ti unit cell where Ap,Na and Sd are plane area, number of atoms and surface densityrespectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

4.2 Formation factor k, dielectric number εr, donor concentration ND

and flat band potential Efb calculated for the different grains ofTi-30at.% Nb. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.3 Summary of the oxide parameters calculated for the oxides grownon different grain boundaries of Ti-30at.% Nb alloy where θ is themisorientation angle. . . . . . . . . . . . . . . . . . . . . . . . . 79

5.1 The values of the circuit elements from the proposed equivalentcircuit of the oxide on Ti-10 wt.% Nb alloy. CPE1 is given byµΩ−1 sn cm−2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

5.2 The values of the circuit elements from the proposed equivalentcircuit of the oxide on Ti-20 wt.% Nb alloy. . . . . . . . . . . . 97

127

Glossary

A . . . . . . . . . . . . . . . . . activation energyE0 . . . . . . . . . . . . . . . . amplitude of the AC voltageI0 . . . . . . . . . . . . . . . . amplitude of the AC currentT . . . . . . . . . . . . . . . . . absolute temperatureE . . . . . . . . . . . . . . . . . AC voltageI . . . . . . . . . . . . . . . . . AC currentA . . . . . . . . . . . . . . . . . amplification factorAFM . . . . . . . . . . . . . atomic force microscopyAME . . . . . . . . . . . . . anisotropy microellipsometryAC . . . . . . . . . . . . . . . alternating currentα . . . . . . . . . . . . . . . . . alpha phaseν . . . . . . . . . . . . . . . . . attempt frequencyθ . . . . . . . . . . . . . . . . . angle of incidencebcc . . . . . . . . . . . . . . . body centered cubick . . . . . . . . . . . . . . . . . Boltzmann constant, 1.3806503 ×10−23 J K−1

β . . . . . . . . . . . . . . . . . beta phaseC . . . . . . . . . . . . . . . . . capacitanceC . . . . . . . . . . . . . . . . . crystal coordinate system, capacitanceIc . . . . . . . . . . . . . . . . . current passing through an electrochemical celliC . . . . . . . . . . . . . . . . current due to capacitive chargingicorr . . . . . . . . . . . . . . corrosion currentiredox . . . . . . . . . . . . . current for redox reactionsz . . . . . . . . . . . . . . . . . charge number of the mobile speciesQ . . . . . . . . . . . . . . . . charge densityCPE . . . . . . . . . . . . . . constant phase element

129

Glossary

χc . . . . . . . . . . . . . . . . capacitive reactanceD . . . . . . . . . . . . . . . . diffusion coefficientND . . . . . . . . . . . . . . . donor concentrationLD . . . . . . . . . . . . . . . Debye lengthDC . . . . . . . . . . . . . . . direct currentDRAM . . . . . . . . . . . dynamic random access memoryρ . . . . . . . . . . . . . . . . . densityφ1 Φ φ2 . . . . . . . . . . . Euler anglesE . . . . . . . . . . . . . . . . . electric field strengthEox . . . . . . . . . . . . . . . equilibrium potentiale . . . . . . . . . . . . . . . . . elementary charge, 1.60217646 ×10−19 CEBSD . . . . . . . . . . . . electron backscatter diffractionEBSP . . . . . . . . . . . . electron backscatter patternEIS . . . . . . . . . . . . . . . electrochemical impedance spectroscopyETR . . . . . . . . . . . . . electron transfer reactionEfb . . . . . . . . . . . . . . . flat band potentialEform . . . . . . . . . . . . . film formation field strengthf . . . . . . . . . . . . . . . . . frequencyk . . . . . . . . . . . . . . . . . formation factorF . . . . . . . . . . . . . . . . . Faraday constant, 96485.3415 C mol−1

FRA . . . . . . . . . . . . . frequency response analyzerα . . . . . . . . . . . . . . . . . feedback factorR . . . . . . . . . . . . . . . . . gas constant, 8.3144621 J K−1mol−1

CH . . . . . . . . . . . . . . . Helmholtz capacitancehcp . . . . . . . . . . . . . . . hexagonal close packedc . . . . . . . . . . . . . . . . . ion concentrationd . . . . . . . . . . . . . . . . . interplanar spacingEr . . . . . . . . . . . . . . . . input feedback potentialEin . . . . . . . . . . . . . . . input voltagen . . . . . . . . . . . . . . . . . integerZ . . . . . . . . . . . . . . . . . impedance

130

Glossary

ITR . . . . . . . . . . . . . . ion transfer reactiona . . . . . . . . . . . . . . . . . jump distancei0 . . . . . . . . . . . . . . . . . material dependent constantM . . . . . . . . . . . . . . . . molecular weightMOSFET . . . . . . . . . metal-oxide-semiconductor field-effect transistorα

′ . . . . . . . . . . . . . . . . martensite phaseα

′′ . . . . . . . . . . . . . . . . martensite phaseβ . . . . . . . . . . . . . . . . . material dependent constantσ . . . . . . . . . . . . . . . . . mobile charge concentrationd0 . . . . . . . . . . . . . . . . native oxide thicknessz . . . . . . . . . . . . . . . . . number of exchanged electrons per formula unitND . . . . . . . . . . . . . . . normal directionω . . . . . . . . . . . . . . . . . omega phaseEout . . . . . . . . . . . . . . output voltageiox . . . . . . . . . . . . . . . . oxide formation currentOPA . . . . . . . . . . . . . . operational amplifier∆EH . . . . . . . . . . . . . potential drop in the Helmholtz layer∆Esc . . . . . . . . . . . . . potential drop in the space charge regionx . . . . . . . . . . . . . . . . . positionω . . . . . . . . . . . . . . . . . radial frequencyr . . . . . . . . . . . . . . . . . roughness factorRC . . . . . . . . . . . . . . . resistor-capacitor connectionRD . . . . . . . . . . . . . . . rolling directionεr . . . . . . . . . . . . . . . . . relative permitivityCsc . . . . . . . . . . . . . . . space charge capacitanceRm . . . . . . . . . . . . . . . serial resistorS . . . . . . . . . . . . . . . . . sample coordinate systemSDC . . . . . . . . . . . . . . scanning droplet cellSEM . . . . . . . . . . . . . scanning electron microscopeSTM . . . . . . . . . . . . . scanning tunnel microscopeγ . . . . . . . . . . . . . . . . . surface energy

131

Glossary

d . . . . . . . . . . . . . . . . . thicknessi . . . . . . . . . . . . . . . . . . total currentP . . . . . . . . . . . . . . . . . transition probability3D . . . . . . . . . . . . . . . three dimensionalt . . . . . . . . . . . . . . . . . timeTD . . . . . . . . . . . . . . . transverse directionα . . . . . . . . . . . . . . . . . transfer coefficientε0 . . . . . . . . . . . . . . . . . vacuum permitivitydsc . . . . . . . . . . . . . . . . width of the space charge regionλ . . . . . . . . . . . . . . . . . wavelengthXPS . . . . . . . . . . . . . . X-ray photoelectron spectroscopy

132

Index

α stabilizer, 7α transus, 7β eutectoid, 7β isomorphous, 7β stabilizer, 7β transus, 8

acceptor mechanism, 28activation energy, 20anisotropy microellipsometry, 66anodic oxide, 51atomic force microscopy, 80

Bode plot, 58Bragg’s law, 41

capacitive charging, 14capacitive reactance, 59capacitor, 60charge transfer resistance, 57constant phase element, 60corrosion, 12corrosion current, 14counter electrode, 29cryostat, 28crystal coordinate system, 45crystallographic axis, 43crystallographic orientation, 2, 41cyclic voltammetry, 33

Debye length, 100direct tunneling, 15donor concentration, 40double glass-walled electrochemical

cell, 29dynamic random access memory, 52

electrochemical impedance spec-troscopy, 36

electrolyte resistance, 58electron backscatter diffraction, 2,

41electron backscatter pattern, 42Electron Backscattered Diffraction,

25electron transfer reaction, 12electronic charge, 40electropolishing, 26equivalent capacitance, 58equivalent circuit, 57equlibrium potential, 57Euler angle, 47Euler space, 47Euler’s equation, 37

Faraday’s law, 56Fermi level, 15, 38Fick’s first law of diffusion, 22film formation field strength , 57

133

Index

flat band potential, 39force sensor, 32formation factor, 57frequency response analyzer, 37

Goss orientation, 49grain, 64grain boundary, 73grain boundary angle, 74

half-wave potential, 68Helmholtz double layer, 39, 57high field equation, 19high field model, 19Hunter process, 5

impedance, 36in vitro, 9in vivo, 9inductor, 60intergranular corrosion, 73interplanar spacing, 42inverse pole figure, 47ion hopping mechanism, 19, 23ion sensitive capillary electrode, 30ion transfer reaction, 12

Kelvin probe, 30Kikuchi bands, 42Kossel cones, 41Kroll process, 5

martensite, 8martensitic transformation, 8metal-oxide-semiconductor field ef-

fect transistor, 52microreference electrode, 32Miller index, 43modulus of elasticity, 10, 51

Mott-Schottky Analysis, 38Mott-Schottky plot, 40, 61

native oxide, 97

operational amplifier, 33osteoblastic cells, 51oxide formation current, 14

phase shift, 36, 58phosphor screen, 42Poisson’s equation, 40pole figure, 45polycrystalline material, 65potentiostat, 33Pourbaix diagram, 17

reference electrode, 29relative permitivity, 40resistor, 60resonance tunneling, 15

salt film mechanism, 27sample coordinate system, 45scanning droplet cell, 3, 30scanning electrochemical micro-

scope, 30scanning electron microscope, 3, 41scanning microelectrode, 30scanning tunnel microscope, 30shape memory effect, 11single crystal, 65space charge region, 38stereographic projection, 45surface energy, 71surface packing density, 68

Tafel equation, 23transition probability, 21

134

Index

vacuum permitivity, 40valve metal, 19

working electrode, 30

135

Curriculum VitaeName: Michael Teka Woldemedhin

Date and Place of Birth: May 20, 1981, Addis Ababa, Ethiopia

Nationality: Ethiopian

Educational background:

10.1998 - 07.2002 B Ed. in ChemistryBahir Dar UniveristyDepartment of ChemistryBahir Dar, Ethiopia

04.2003 - 02.2004 Student pilotCommercial pilot license for multi-engineand instrument ratingEthiopian Airlines Pilot Training SchoolAddis Ababa, Ethiopia

10.2004 - 08.2006 M Sc. in ChemistryAddis Ababa UniversityDepartment of ChemistryAddis Ababa, Ethiopia

04.2008 - 03.2011 PhD student, in the frame of IMPRS-SurMatInternational Max-Planck Research School for Surfaceand Interface Engineering in Advanced MaterialsMax-Planck-Institut für Eisenforschung,Düsseldorf, Germany&Institute of Chemical Technology of Inorganic MaterialsJohannes Kepler University, Linz, AustriaFaculty for Chemistry and Biochemistry,Ruhr-UniversitätBochum, Germany

Publications

Research/Teaching Experience:

08.2002 - 03.2003 High school chemistry teacherLucy AcademyAddis Ababa, Ethiopia

08.2006 - 03.2008 LecturerHawassa UniversityFaculty of Natural SciencesDepartment of Applied ChemistryHawassa, Ethiopia

10.2009 until now LecturerInstitute of Chemical technology ofInorganic MaterialsJohannes Kepler UniversityLinz, Austria

Some of the results in this thesis were previously publicized in scientific confer-ences and journals:

Articles

• M. T. Woldemedhin, D. Raabe, A.W. Hassel"Anodic oxides on beta type Nb-Ti alloy and their characterization by electro-chemical impedance spectroscopy"Physica Status Solidi A 207 (2010) 812-816

• M. T. Woldemedhin, D. Raabe, A.W. Hassel"Grain boundary electrochemistry of β-type Nb-Ti alloy by a scanning dropletcell"Physica Status Solidi A 208 (2011) 1246-1251

• M. T. Woldemedhin, D. Raabe, A.W. Hassel"Microelectrochemical measurements on single grains of polycrystalline Ti-30at.% Nb β-Titanium alloy using scanning droplet cell"submitted

• M. T. Woldemedhin, D. Raabe, A.W. Hassel"Characterization of thin anodic oxides of Ti-Nb alloys by electrochemicalimpedance spectroscopy"submitted

139

Publications

Oral Presentations

• M. T. Woldemedhin, D. Raabe, A.W. Hassel"Microelectrochemical measurements on single grains of polycrystalline Ti-30at.% Nb β-Titanium alloy using scanning droplet cell", Electrochemistry 2010- From microscopic understanding to global impactBochum, Germany, 13-15 September 2010

• M. T. Woldemedhin, D. Raabe, A.W. Hassel"Microelectrochemistry of Ti-Nb β-Titanium alloy", 10th International sysmpo-siumon passivity of metals and semiconductors - Passivity 10Florianopolis, Brazil, 10-14 April 2011

• M. T. Woldemedhin, D. Raabe, A.W. Hassel"Microelectrochemistry of Ti-Nb β-Titanium alloy", 62nd Annual Meeting of theInternational Society of ElectrochemistryNiigata, Japan, 11-16 September 2011

Poster Presentations

• M. T. Woldemedhin, D. Raabe, A.W. Hassel"Surface reactivity of β-Ti alloys", SurMat International Research School Sym-posiumBochum, Germany, 15-16 July 2008

• M. T. Woldemedhin, D. Raabe, A.W. Hassel"Characterization of anodic oxides on Ti-30at.% Nb β"-Ti alloy, Engineering ofFunctional Interfaces EnFI 2009Hasselt, Belgium, 18-19 June 2009, with short oral presentation

• M. T. Woldemedhin, D. Raabe, A.W. Hassel"Anodic oxides grown on Ti-30at.% Nb β-Ti alloy and its characterizationby electrochemical impedance spectroscopy", Electrochem09 - 50th CorrosionsysmposiumManchester, England, 16-17 September 2009

• M. T. Woldemedhin, D. Raabe, A.W. Hassel"Microelectrochemical investigations on single grains of polycrystalline Ti-30at.% Nb β-type titanium alloy using scanning droplet cell", Engineering ofFunctional Interfaces EnFI 2010Marburg, Germany, 15-16 July 2010, with short oral presentation

• M. T. Woldemedhin, D. Raabe, A.W. Hassel"Thin oxide films on Ti-Nb alloys and the characterization by electrochemicalimpedance spectroscopy", Engineering of Functional Interfaces EnFI 2011Linz, Austria, 19-20 July 2011, with short oral presentation

140

evaluation of the surface reactivity of beta-titanium

Documents