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Instructor: Dr. Xueyan Wu (吴雪艳)

Materials Lab 1(MT344) –

X-ray Diffractometer Operation and Data Analysis

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Goals

• To give students a practical introduction into the use

of X-ray diffractometer and data collection.

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Hot-Cathode X-Ray Tube

How are X-rays produced?

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Two sharp peaks

Right: Kα, X-rays produced by transitions from the n=2 to n=1 levels.

Left: Kβ , X-rays produced by transitions from the n=3 to n=1 levels.

Characteristic X-ray

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Schematic diagram of an X-ray diffractometer; T= x-ray source, S= specimen, C= detector, and O= the axis around which the specimen and detector rotate. 2θ: diffraction angle.

As the counter moves at

constant angular velocity, a

recorder automatically plots

the diffracted bean intensity,

which is monitored by the

counter, as a function of 2θ.

X-ray Diffractometer

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Filter: to filter Kβ, a suitable material is placed between the X-ray

tube and the specimen . Filter materials should be chosen according to target materials . In general, the filter element has an atomic number which is 1 or 2 smaller than the target element.

ZT< 40: ＺF = ＺT-1

ZT ≥ 40: ＺF = ＺT-2T: target; F: filter

Widely-used Target and according FilterTarget Atom

No.Kα

Wavelength(nm)

Kẞ Wavelength

(nm)

FilterFilter Atom

No.λk

Cr

Fe

Co

Ni

Cu

Mo

Ag

24

26

27

28

29

42

47

0.22909

0.19373

0.17902

0.16591

0.15418

0.07107

0.05609

0.20848

0.17565

0.16207

0.15001

0.13922

0.06323

0.04970

V

Mn

Fe

Co

Ni

Zr

Rh

23

25

26

27

28

40

45

0.22690

0.18694

0.17429

0.16072

0.14869

0.06888

0.05338

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Suppose that the incident X-rays are reflected specularly fromparallel planes of atoms in the crystal

The value of θ can be used to determine on which crystallographic planethe diffraction takes place. The relative intensities of the diffracted beamsare determined by the composition of the material.

The path difference betweenbeams should be an integer of thewavelength to have constructiveinterference:

λθ nd =sin2

The Bragg Law

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DV : volume weighted crystallite size;

K :Scherrer constant describing the

shape of the crystal (typical values fall in

the range 0.87 - 1; K=0.9 corresponds to

"spherical crystals);

λ : X-ray wavelength;

B = integral breadth of a reflection (in

radians) located at 2θ. B can be assumed

to take a Lorentzian distribution;

B : 1⁄2 π × FWHM.

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Positions, intensities and profile characteristics of Braggpeaks in an X-ray diffraction (XRD) can provide information of:

atomic structure • lattice constant• atom position

microstructure• crystallite size• microstrain• preferred orientation

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Thank you!

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Course DescriptionWhat are X-rays and How to Produce Them?

X-rays: energies ranging 100 eV to 100 KeVwavelength ranging around 0.01~10 nm

Kinds of waves in the electromagnetic spectrum

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X-ray diffraction (XRD) is a method of analyzing thediffraction pattern of a material by X-ray diffraction, obtainingthe composition of the material, the structure or morphology ofthe atom or molecule inside the material.

What is XRD

2.2.Device for measurement

Goniometer(量角仪）—————change the incidence angle

Counter （计数器）——————collect the phonons released by X-ray

Monochromator(单色仪）———— filter the light

2. Theory2.3.Factors influencing the final choice

Factors Reasons

Target materialsBackground won't be too strong

Mainly chosed by atomic number

Filters Determined by the target material

Slits Ensure the X-ray in place

Scanning range 2° to 90°(normal condition)

Scanning speed 2°/min or 4°/min

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Course DescriptionXRD: X-ray Diffraction

Application:1. To identify unknown crystalline materials

2. To characterize crystalline materials

3. To determine unit cell dimensions

4. To measure sample purity

5. To determine crystal structures using Rietveld refinement.

6. To determine of modal amounts of minerals (quantitative

analysis)

7. ……

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• The intensity of diffracted X-rays is continuously recorded as

the sample and detector rotate through their respective

angles.

• A peak in intensity occurs when the mineral contains lattice

planes with d-spacings appropriate to diffract X-rays at that

value of θ.

• Results are commonly presented as peak positions at 2θ and

X-ray counts(intensity) in the form of a table or an x-y

plot(shown in next slide page)

Data Collection

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XRD pattern of α-iron polycrystal(cubic)

2. Theory2.4.Phase Analysis

Qualitative phase analysis:1.obtain X-ray diffraction spectrum2.calculate planar spacing d&arrange them with according intensity I3.compare the results with standard PDF

Quantitative analysis:Acquire te fraction of different components in the material

Figure 4 Powder Diffraction File of SiO2

PDF for SiO2

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Determination of an unknown• The d-spacing of each peak is obtained by solution of the Bragg

equation for the appropriate value of λ.

• Automated search-match routines can be applied to compare

the ds with those of known materials, a systematic procedure

is used by ordering the d-spacings in terms of their intensity

beginning with the most intense peak.

• Principle : Each minerals has a unique set of d-spacings.

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Determination of an unknown• Sources: 1) the International Centre for Diffraction Data(the

Powder Diffraction File, PDF)

2) American Mineralogist Crystal Structure Database

• Note: 1) Phases as little as 1-3% sample weight can be

identified

2) Samples must be crystalline.

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References:•“Fundamentals Of Material Science and Engineering”,

4th Edition, Chapter 3, William D. Callister, JR. David G.

Rethwisch.

•“Elements of X-ray Diffraction”, Cullity and Stock

•“Introduction to X-ray Powder Diffractometry”, Jenkins

and Snyder

•“Fundamentalls fo Powder Diffraction and Structural

Characterization of Materials”, Pecharsky and Vitalij