CHAPTER 10Kinetics—Heat

Treatment

The microstructure of a rapidly cooled “eutec-tic” soft solder (≈ 38 wt % Pb − 62 wt %Sn) consists of globules of lead-rich solid so-lution (dark) in a matrix of tin-rich solid solu-tion (white), 375X. The contrast to the slowly-cooled microstructure at the opening of Chap-ter 9 illustrates the effect of time on microstruc-tural development. (From ASM Handbook,Vol. 3: Alloy Phase Diagrams, ASM Interna-tional, Materials Park, Ohio, 1992.)

T

t

tx

(a) (b)

T

Tmp

Completion of reaction

Figure 10-1 Schematic illustration of the approach to equilibrium. (a) The time for solidi-fication to go to completion is a strong function of temperature, with the minimum timeoccurring for a temperature considerably below the melting point. (b) The temperature–time plane with “transformation curve.” We shall see later that the time axis is often plot-ted on a logarithmic scale.

Liquid

(a) (b)

(c) (d)

Solid

Crystalnucleus

Crystalgrowth

Figure 10-2 (a) On a microscopic scale, a solid precipitate in a liquid matrix. The pre-cipitation process is seen on the atomic scale as (b) a clustering of adjacent atoms toform (c) a crystalline nucleus followed by (d) the growth of the crystalline phase.

Net

ene

rgy

chan

ge

Net energy change

Surface energy addition

Volume energy reduction

rcr0

+

–

Figure 10-3 Classical nucleation theory involves an energy balancebetween the nucleus and its surrounding liquid. A nucleus (clus-ter of atoms) as shown in Figure 10–2(c) will be stable only iffurther growth reduces the net energy of the system. An ideallyspherical nucleus will be stable if its radius, r , is greater than acritical value, rc .

Contribution of diffusion (clustering of atoms)

Contribution of liquid phase instability

Net nucleation rate (= product of two dashed lines)

Nucleation rate, N (s–1)

Tm

Tem

pera

ture

, T

Figure 10-4 The rate of nucleation is a product of two curves that represent twoopposing factors (instability and diffusivity).

Overall transformation rate

Rate, (s–1)

Tm

Tem

pera

ture

, T

N

G

Figure 10-5 The overall transformation rate is the product of the nucleationrate N (from Figure 10–4) and the growth rate G (given by Equation 10.1).

Time, t (logarithmic scale)

Temperature, T

1 50 100 % completion of reaction

Curve shown in Figure 10-1

Tmp

Figure 10-6 A time–temperature–transformation diagram for the solidification reac-tion of Figure 10–1 with various percent completion curves illustrated.

Time, seconds0.10

100

200

300

400

500

600

700

727˚

800

˚C

1 10 102 103 104 105 0 0.77wt % C

Coarse pearlite

Fine pearlite

Bainite

1 sec 1 hour1 min 1 day

Figure 10-7 TTT diagram for eutectoid steel shown in relation to the Fe–Fe3C phasediagram (see Figure 9–39). This shows that, for certain transformation tempera-tures, bainite rather than pearlite is formed. In general, the transformed microstruc-ture is increasingly fine-grained as the transformation temperature is decreased. Nu-cleation rate increases and diffusivity decreases as temperature decreases. The solidcurve on the left represents the onset of transformation (∼ 1% completion). Thedashed curve represents 50% completion. The solid curve on the right representsthe effective (∼ 99%) completion of transformation. This convention is used insubsequent TTT diagrams. (TTT diagram after Atlas of Isothermal Transforma-tion and Cooling Transformation Diagrams, American Society for Metals, MetalsPark, Ohio, 1977.)

Temperature

Time (logarithmic scale)

Coarse pearlite

Figure 10-8 A slow cooling path that leads to coarse pearlite formation is superimposedon the TTT diagram for eutectoid steel. This type of thermal history was assumed,in general, throughout Chapter 9.

Figure 10-9 The microstructure of bainite involves extremely fineneedles of α-Fe and Fe3C, in contrast to the lamellar structureof pearlite (see Figure 9–2), 535×. (From Metals Handbook,8th Ed., Vol. 7: Atlas of Microstructures, American Societyfor Metals, Metals Park, Ohio, 1972.)

Temperature

Time (logarithmic scale)

Coarse pearlite

Coarse pearlite remains upon cooling

Figure 10-10 The interpretation of TTT diagrams requires considerationof the thermal history “path.” For example, coarse pearlite, once formed,remains stable upon cooling. The finer-grain structures are less stablebecause of the energy associated with the grain boundary area. (Bycontrast, phase diagrams represent equilibrium and identify stable phasesindependent of the path used to reach a given state point.)

Time, seconds0.1

0

100

200

300

400

500

600

700

727˚

800

˚C

1 10 102 103 104 105 0 0.77wt % C

Coarse pearlite

Fine pearlite

Bainite

1 sec

M90

M50

Ms

1 hour1 min 1 day

Figure 10-11 A more complete TTT diagram for eutectoid steel than was givenin Figure 10–7. The various stages of the time-independent (or diffusion-less) martensitic transformation are shown as horizontal lines. Ms repre-sents the start, M50 50% transformation, and M90 90% transformation. Onehundred percent transformation to martensite is not complete until a finaltemperature (Mf ) of −46◦C.

a0

a

c

a0|! 2

(a) (b)

Figure 10-12 For steels, the martensitic transformation involves the sudden reorientation of C and Fe atoms fromthe fcc solid solution of γ -Fe (austenite) to a body-centered tetragonal (bct) solid solution (martensite). In (a),the bct unit cell is shown relative to the fcc lattice by the 〈100〉α axes. In (b), the bct unit cell is shown before (left)and after (right) the transformation. The open circles represent iron atoms. The solid circle represents an inter-stitially dissolved carbon atom. This illustration of the martensitic transformation was first presented by Bain in1924, and while subsequent study has refined the details of the transformation mechanism, this remains a usefuland popular schematic. (After J. W. Christian, in Principles of Heat Treatment of Steel, G. Krauss, Ed., Ameri-can Society for Metals, Metals Park, Ohio, 1980.)

Figure 10-13 Acicular, or needlelike, microstructure of martensite 1000×. (FromMetals Handbook, 8th Ed., Vol. 7: Atlas of Microstructures, American So-ciety for Metals, Metals Park, Ohio, 1972.)

Time, seconds

Continuous coolingtransformation

Isothermaltransformation

Rapid cooling rate

Moderate cooling rate

Slow cooling rate

1

2

1

2

3

3

0.10

100

200

300

400

500

600

700

727˚

800

˚C

1 10 102 103 104 105

1 sec 1 hour 1 day1 min

M90

M50

Ms

Figure 10-14 A continuous cooling transformation (CCT) diagram is shown superimposedon the isothermal transformation diagram of Figure 10–11. The general effect of contin-uous cooling is to shift the transformation curves downward and toward the right. (AfterAtlas of Isothermal Transformation and Cooling Transformation Diagrams, AmericanSociety for Metals, Metals Park, Ohio, 1977.)

Time, seconds0.1

0

100

200

300

400

500

600

700

727˚

880˚

Ms

M50

M90

800

900

˚C

1 10 102 103 104 105 0 1.13wt % C

1 sec 1 min 1 hour 1 day

Figure 10-15 TTT diagram for a hypereutectoid composition (1.13 wt % C) comparedto the Fe–Fe3C phase diagram. Microstructural development for the slow coolingof this alloy was shown in Figure 9–40. (TTT diagram after Atlas of IsothermalTransformation and Cooling Transformation Diagrams, American Society for Met-als, Metals Park, Ohio, 1977.)

Time, seconds0.1

100

200

300

400

500

600

700

727˚

770˚800

900

˚C

1 10 102 103 104 105 0 0.5wt % C

1 sec 1 min

Ms

M50

M90

1 hour 1 day

Figure 10-16 TTT diagram for a hypoeutectoid composition (0.5 wt % C)compared to the Fe–Fe3C phase diagram. Microstructural developmentfor the slow cooling of this alloy was shown in Figure 9–41. By compar-ing Figures 10–11, 10–15, and 10–16, one will note that the martensitictransformation occurs at decreasing temperatures with increasing car-bon content in the region of the eutectoid composition. (TTT diagramsafter Atlas of Isothermal Transformation and Cooling TransformationDiagrams, American Society for Metals, Metals Park, Ohio, 1977.)

Temperature

Time (logarithmic scale)

Tempering temperature

Thermal history for center of part being heat-treated

Thermal history for surface of part being heat-treated

Tempered martensiteMartensite

Transformation

Ms

Mf

Figure 10-17 Tempering is a thermal history [T = f n(t)] in which marten-site, formed by quenching austenite, is reheated. The resulting temperedmartensite consists of the equilibrium phase of α-Fe and Fe3C but in a mi-crostructure different from both pearlite and bainite (note Figure 10–18).(After Metals Handbook, 8th Ed., Vol. 2, American Society for Metals,Metals Park, Ohio, 1964. It should be noted that the TTT diagram is, forsimplicity, that of eutectoid steel. As a practical matter, tempering is gener-ally done in steels with slower diffusional reactions permitting less severequenches.)

Figure 10-18 The microstructure of tempered martensite, althoughan equilibrium mixture of α-Fe and Fe3C, differs from thosefor pearlite (Figure 9–2) and bainite (Figure 10–9), 825×. Thisparticular microstructure is for a 0.50 wt % C steel comparablewith that described for Figure 10–16. (From Metals Handbook,8th Ed., Vol. 7: Atlas of Microstructures, American Society forMetals, Metals Park, Ohio, 1972.)

Temperature

Time (logarithmic scale)

Tempering temperature

Surface

Center

Tempered martensiteMartensite

Transformation

Figure 10-19 In martempering, the quench is stopped just above Ms. Slow cool-ing through the martensitic transformation range reduces stresses associ-ated with the crystallographic change. The final reheat step is equivalent tothat in conventional tempering. (After Metals Handbook, 8th Ed., Vol. 2,American Society for Metals, Metals Park, Ohio, 1964.)

Temperature

Time (logarithmic scale)

Surface

Center

Bainite

Transformation

Figure 10-20 As with martempering, austempering avoids the distortion andcracking associated with quenching through the martensitic transforma-tion range. In this case, the alloy is held long enough just above Ms to al-low full transformation to bainite. (After Metals Handbook, 8th Ed., Vol.2, American Society for Metals, Metals Park, Ohio, 1964.)

(a)

(b)(c)

t

DT

tTDQuench rate =

Water spray

Specimen

Figure 10-21 Schematic illustration of the Jominy end-quenchtest for hardenability. (After W. T. Lankford et al., Eds.,The Making, Shaping, and Treating of Steel, 10th Ed., UnitedStates Steel, Pittsburgh, Pa., 1985. Copyright 1985 by UnitedStates Steel Corporation.)

0 10 20 30

1

2111000

2

5

10

20

50

100

200

500

2

40

Distance from quenched end, Dqe(Jominy distance)

Distance from quenched end, inches

Coo

ling

rate

at 7

00˚C

, C

/sec

50 mm

1

2

1

4

1

8

Figure 10-22 The cooling rate for the Jominy bar (see Figure 10–21) varies alongits length. This curve applies to virtually all carbon and low-alloy steels. (Af-ter L. H. Van Vlack, Elements of Materials Science and Engineering, 4th Ed.,Addison-Wesley Publishing Co., Inc., Reading, Mass., 1980.)

Distance from quenched end – sixteenths of an inch

Roc

kwel

l har

dnes

s C

sca

le

0

60

55

50

45

40

35

30

25

20

15

10

5

4 8 1220 6 10 14 18 22 26 3016 20 24 28 32

Figure 10-23 Variation in hardness along a typical Jominy bar. (From W. T.Lankford et al., Eds., The Making, Shaping, and Treating of Steel, 10thEd., United States Steel, Pittsburgh, Pa., 1985. Copyright 1985 by UnitedStates Steel Corporation.)

Roc

kwel

l har

dnes

s C

sca

le

4340

9840

4140

8640

5140

010

15

20

25

30

35

40

45

50

55

60

65

4 82 6 10 14 18 22 26 3012 16 20 24 28 32

Distance from quenched end—sixteenths of an inch

Figure 10-24 Hardenability curves for various steels with the same carbon con-tent (0.40 wt %) and various alloy contents. The codes designating the alloycompositions are defined in Table 11.1. (From W. T. Lankford et al., Eds.,The Making, Shaping, and Treating of Steel, 10th Ed., United States Steel,Pittsburgh, Pa., 1985. Copyright 1985 by United States Steel Corporation.)

Slow cool

Timewt % Al

10090 95

700˚C

600

500

400

300

200

100

0

Figure 10-25 Coarse precipitates form at grain boundaries in an Al–Cu (4.5 wt%) alloy when slowly cooled from the single-phase (κ ) region of the phasediagram to the two-phase (θ + κ ) region. These isolated precipitates do littleto affect alloy hardness.

taging

Fine dispersion ofprecipitates within grains(retained upon cooling)

Timewt % Al

10090 95

700˚C

600

500

400

300

200

100

0

Solution treatment

Quench

Figure 10-26 By quenching and then reheating an Al–Cu (4.5 wt %) alloy, a fine dispersion of precipi-tates forms within the κ grains. These precipitates are effective in hindering dislocation motion and,consequently, increasing alloy hardness (and strength). This is known as precipitation hardening, orage hardening.

Coarse precipitateswithin grains

Temperature

Time

(a)

Hardness(arbitrary units)

taging (hours)

(b)

0.01 0.1 1 10 100 1000

taging

Figure 10-27 (a) By extending the reheat step, precipitates coalesce and becomeless effective in hardening the alloy. The result is referred to as “overaging.”(b) The variation in hardness with the length of the reheat step (“aging time”).

Figure 10-28 Schematic illustration of the crystalline ge-ometry of a Guinier–Preston (G.P.) zone. This struc-ture is most effective for precipitation hardening, andis the structure developed at the hardness maximumin Figure 10–27b. Note the coherent interfaces length-wise along the precipitate. The precipitate is approxi-mately 15 nm × 150 nm. (From H. W. Hayden, W. G.Moffatt, and J. Wulff, The Structure and Propertiesof Materials, Vol. 3: Mechanical Behavior, John Wi-ley & Sons, Inc., New York, 1965.)

(b)

(a)

Figure 10-29 Examples of cold-working operations: (a) cold-rolling of a baror sheet and (b) cold-drawing a wire. Note in these schematic illustrationsthat the reduction in area caused by the cold-working operation is associ-ated with a preferred orientation of the grain structure.

(a) (b) (c)

(d) (e)

Figure 10-30 Annealing can involve the complete recrystallization and subsequentgrain growth of a cold-worked microstructure. (a) A cold-worked brass (de-formed through rollers such that the cross-sectional area of the part was reducedby one-third). (b) After 3 s at 580◦C, new grains appear. (c) After 4 s at 580◦C,many more new grains are present. (d) After 8 s at 580◦C, complete recrystal-lization has occurred. (e) After 1 h at 580◦C, substantial grain growth has oc-curred. The driving force for this is the reduction of high-energy grain bound-aries. The predominant reduction in hardness for this overall process had oc-curred by step (d). All micrographs at magnification of 75×. (Courtesy of J. E.Burke, General Electric Company, Schenectady, N.Y.)

200120

110

100

90

800 200 400100 300 500 700600 800

400 600 800

Temperature, ˚F

Har

dnes

s, H

RH

Temperature, ˚C

1000 1200

C26000

1400

Figure 10-31 The sharp drop in hardness identifies the recrystallization tem-perature as ∼ 290◦C for the alloy C26000, “cartridge brass.” (From Met-als Handbook, 9th Ed., Vol. 4, American Society for Metals, Metals Park,Ohio, 1981.)

Pb

Melting temperature, K

Rec

ryst

alliz

atio

n te

mpe

ratu

re, K

Rec

ryst

alliz

atio

n te

mpe

ratu

re, ˚

C

0

1000

2000

20000 4000

15000

WTa

BeNi

FeAs

Pt

ZuAu

AsAl

MgCd

Sn

TiPt

CuZu

Pb

Au

Mo1000

500

0

Melting temp.1

2

Melting temp.1

3

Figure 10-32 Recrystallization temperature versus melting points for variousmetals. This plot is a graphic demonstration of the rule of thumb that atomicmobility is sufficient to affect mechanical properties above approximately 1

3to 1

2Tm on an absolute temperature scale. (From L. H. Van Vlack, Elementsof Materials Science and Engineering, 3rd Ed., Addison-Wesley PublishingCo., Inc., Reading, Mass, 1975.)

Temperature, ˚C

00

100

Har

dnes

s, B

HN

200

100

65 Cu–35 Zn

60% cold work

40% cold work

20% cold work

200 300 400

Figure 10-33 For this cold-worked brass alloy, the recrystallization temperature dropsslightly with increasing degrees of cold work. (From L. H. Van Vlack, Elementsof Materials Science and Engineering, 4th Ed., Addison-Wesley Publishing Co.,Inc., Reading, Mass. 1980.)

Tensile strength

Ductility

Annealing temperature (˚C)

Newgrains

Cold workedand recovered

grains

Recovery Recrystallization Grain growth

600 60

50

40

30

20

500

Tens

ile s

tren

gth

(MP

a)G

ain

size

(m

m)

Duc

tilit

y (%

EL

)

400

0.040

0.030

0.020

0.010

300

100 200 300 400 500 600 700

Figure 10-34 Schematic illustration of the effect of annealing temperature on thestrength and ductility of a brass alloy shows that most of the softening of thealloy occurs during the recrystallization stage. (After G. Sachs and K. R. VanHorn, Practical Metallurgy: Applied Physical Metallurgy and the IndustrialProcessing of Ferrous and Nonferrous Metals and Alloys, American Societyfor Metals, Cleveland, Ohio, 1940.)

0.5

0.4

0.3

0.2

0.1

0

2.00

2.50

3.33

5.00

10.020.0

–60 –40 –20 0 20

Rat

e, h

r–1

Tim

e, h

r

Temperature, ˚C

∞

Figure 10-35 Rate of crystallization of rubber as a function of temperature. (From L.A. Wood, in H. Mark and G. S. Whitby, Eds., Advances in Colloid Science, Vol. 2,Wiley Interscience, New York, 1946, pp. 57–95.)

Figure 10-36 TTT diagram for (a) thefractional crystallization (10−4 vol%) of a simple glass of compositionNa2O · 2SiO2 and (b) the fractionalcrystallization (10−1 vol%) of a glassof composition CaO·Al2O3·2SiO2.[Part (a) from G. S. Meiling and D.R. Uhlmann, Phys. Chem. Glasses8, 62 (1967) and part (b) from H.Yinnon and D. R. Uhlmann, in Glass:Science and Technology, Vol. 1, D.R. Uhlmann and N. J. Kreidl, Eds.,Academic Press, New York, 1983,pp. 1–47.]

100

200

300

4001 10 102 103 104 105 106 107 108

Und

erco

olin

g (K

)

Time (sec)

Tmelt1550

950

1050

1150

1250

1350

1450

850105104103102

Tem

pera

ture

(˚C

)

Time (sec)

(a)

(b)

Glass formation

CrystallizationMelting

Forming

Nucleation

Growth

T

t

Figure 10-37 Typical thermal history for producing a glass ceramic by the controlled nu-cleation and growth of crystalline grains.

Figure 10-38 Transmission electron micrograph of monoclinic zirconiashowing a microstructure characteristic of a martensitic transforma-tion. Included in the evidence are twins labeled T. See Figure 4–15for an atomic-scale schematic of a twin boundary and Figure 10–13for the microstructure of martensitic steel. (Courtesy of Arthur H.Heuer)

Figure 10-39 An illustration of the sintering mech-anism for shrinkage of a powder compact isthe diffusion of atoms away from the grainboundary to the pore, thereby “filling in” thepore. Each grain in the microstructure wasoriginally a separate powder particle in theinitial compact.

Figure 10-40 Grain growth hinders the densifi-cation of a powder compact. The diffusionpath from grain boundary to pore (now iso-lated within a large grain) is prohibitively long.