Phase Diagrams

h. P. r. Frederikse

A phase is a structurally homogeneous portion of matter.

Regardless of the number of chemical constituents of a gas, there is

only one vapor phase. This is true also for the liquid form of a pure

substance, although a mixture of several liquid substances may ex-

ist as one or several phases, depending on the interactions among

the substances. On the other hand a pure solid may exist in several

phases at different temperatures and pressures because of differ-

ences in crystal structure (Reference 1). At the phase transition

temperature, T

tr

, the chemical composition of the solid remains

the same, but a change in the physical properties often will take

place. Such changes are found in ferroelectric crystals (example

BaTiO

3

) which develop a spontaneous polarization below T

tr

, in

superconductors (example Pb) which lose all electrical resistance

below the transition point, and in many other classes of solids.

In quite a few cases it is difficult to bring about the phase tran-

sition, and the high- (or low-) temperature phase persists in its

metastable form. Many liquids remain in the liquid state for short-

er or longer periods of time when cooled below the melting point

(supercooling). However, often the slightest disturbance will cause

solidification. Persistence of the high temperature phase in solid–

solid transitions is usually of much longer duration. An example of

this behavior is found in white tin; although gray tin is the thermo-

dynamically stable form below T

tr

(286.4 K), the metal remains in

its undercooled, white tin state all the way to T = 0 K, and crystals

of gray tin are very difficult to produce.

A phase diagram is a map that indicates the areas of stability

of the various phases as a function of external conditions (tem-

perature and pressure). Pure materials, such as mercury, helium,

water, and methyl alcohol are considered one-component systems

and they have unary phase diagrams. The equilibrium phases in

two-component systems are presented in binary phase diagrams.

Because many important materials consist of three, four, and more

components, many attempts have been made to deduce their mul-

ticomponent phase diagrams. However, the vast majority of sys-

tems with three or more components are very complex, and no

overall maps of the phase relationships have been worked out.

It has been shown during the last 20 to 25 years that very use-

ful partial phase diagrams of complex systems can be obtained by

means of thermodynamic modeling (References 2, 3). Especially

for complicated, multicomponent alloy systems the CALPHAD

method has proved to be a successful approach for producing

valuable portions of very intricate phase diagrams (Reference 4).

With this method thermodynamic descriptions of the free energy

functions of various phases are obtained that are consistent with

existing (binary) phase diagram information and other thermody-

namic data. Extrapolation methods are then used to extend the

thermodynamic functions into a ternary system. Comparison of

the results of this procedure with available experimental data is

then used to fine-tune the phase diagram and add ternary interac-

tion functions if necessary. In principle this approximation strat-

egy can be extended to four, five, and more component systems.

The nearly two dozen phase diagrams shown below present

the reader with examples of some important types of single and

multicomponent systems, especially for ceramics and metal alloys.

This makes it possible to draw attention to certain features like

the kinetic aspects of phase transitions (see Figure 22, which pres-

ents a time-temperature-transformation, or TTT, diagram for the

precipitation of α-phase particles from the β-phase in a Ti-Mo al-

loy; Reference 1, pp. 358–360). The general references listed below

and the references to individual figures contain phase diagrams for

many additional systems.

general references

1. Ralls, K. M., Courtney, T. H., and Wulff, J., Introduction to Materials

Science and Engineering, Chapters 16 and 17, John Wiley & Sons, New

York, 1976.

2. Kaufman, L., and Bernstein, H., Computer Calculation of Phase

Diagrams, Academic Press, New York, 1970.

3. Kattner, U. R., Boettinger, W. J. B., and Coriell, S. R., Z. Metallkd., 87,

9, 1996.

4. Dinsdale, A. T., Ed., CALPHAD, Vol. 1–20, Pergamon Press, Oxford,

1977–1996 and continuing.

5. Baker, H., Ed., ASM Handbook, Volume 3: Alloy Phase Diagrams,

ASM International, Materials Park, OH, 1992.

6. Massalski, T. B., Ed., Binary Alloy Phase Diagrams, Second Edition,

ASM International, Materials Park, OH, 1990.

7. Roth. R. S., Ed., Phase Diagrams for Ceramists, Vol. I (1964) to Volume

XI (1995), American Ceramic Society, Waterville, OH.

references to individual Phase Diagrams

Figure 1. Carbon: Reference 7, Vol. X (1994), Figure 8930. Reprinted

with permission.

Figure 2. Si-Ge : Ref. 5, p. 2.231. Reprinted with permission.

Figure 3. H

2

O (ice): See figure.

Figure 4. SiO

2

: Reference 7, Vol. XI (1995), Figure 9174. Reprinted with

permission.

Figure 5. Fe-O: Darken, L.S., and Gurry, R.W., J. Am. Chem. Soc., 68, 798,

1946. Reprinted with permission.

Figure 6. Ti-O: Reference 5, p. 2.324. Reprinted with permission.

Figure 7. BaO-TiO

2

: Reference 7, Vol. III (1975), Figure 4302. Reprinted

with permission.

Figure 8. MgO-Al

2

O

3

: Reference 7, Vol. XI (1995), Figure 9239. Reprinted

with permission.

Figure 9. Y

2

O

3

-ZrO

2

: Reference 7, Vol. XI (1995), Figure 9348. Reprinted

with permission.

Figure 10. Si-N-Al-O (Sialon): Reference 7, Vol. X (1994), Figure 8759.

Reprinted with permission.

Figure 11. PbO-ZrO

2

-TiO

2

(PZT): Reference 7, Vol. III (1975), Figure

4587. Reprinted with permission.

Figure 12. Al-Si-Ca-O: Reference 7 (1964), Vol. I, Figure 630. Reprinted

with permission.

Figure 13. Y-Ba-Cu-O: Whitler, J.D., and Roth, R.S., Phase Diagrams for

High T

c

Superconductors, Figure S-082, American Ceramic

Society, Waterville, OH, 1990. Reprinted with permission.

Figure 14. Al-Cu: Reference 5, p. 2.44. Reprinted with permission.

Figure 15. Fe-C: Ralls, K.M., Courtney, T.H., and Wulff, J., Introduction to

Materials Science and Engineering, Figure 16.13, John Wiley &

Sons, New York, 1976. Reprinted with permission.

Figure 16. Fe-Cr: Reference 5, p. 2.152. Reprinted with permission.

Figure 17. Cu-Sn: Reference 5, p. 2.178. Reprinted with permission.

Figure 18. Cu-Ni: Reference 5, p. 2.173. Reprinted with permission.

Figure 19. Pb-Sn (solder): Reference 5, p. 2.335. Reprinted with permis-

sion.

Figure 20. Cu-Zn (brass): Subramanian, P.R., Chakrabarti, D.J., and

Laughlin, D.E., Eds., Phase Diagrams of Binary Copper Alloys,

p. 487, ASM International, Materials Park, OH, 1994. Reprinted

with permission.

Figure 21. Co-Sm: Reference 5, p. 2.148. Reprinted with permission.

Figure 22. Ti-Mo: Reference 5, p. 2.296; Reference 1, p. 359. Reprinted

with permission.

Figure 23. Fe-Cr-Ni: Reference 5, Figure 48. Reprinted with permission.

12-181

200

150

100

50

0

0

Diamond

2000

4000

6000

Liquid

A

B

C

Graphite

T/K

P

/GP

a

Figure 1.

Phase diagram of carbon. (A) Martensitic transition: hex graphite → hex diamond. (B) Fast graphite-to-diamond transition. (C)

Fast diamond-to-graphite transition.

Figure 2.

Si-Ge system.

Composition,

Pearson

Space

Phase

mass % Si

symbol

group

(Ge,Si)

0 to 100

cF8

Fd3–m

High-pressure phases
GeII

–

tI4

I4

1

/amd

SiII

–

tI4

I4

1

/amd

12-182

Phase Diagrams

200

150

100

50

0

-50

-100

-150

Liquid

t /

° C

VI

VII

VIII

V

III

II

I

P /MPa

0 500 1000 1500 2000 2500 3000 3500

Figure 3.

Diagram of the principal phases of ice. Solid lines are measured boundaries between stable phases; dotted lines are extrapolated.

Ice IV is a metastable phase that exists in the region of ice V. Ice IX exists in the region below –100°C and pressures in the range 200–400 MPa.

Ice X exists at pressures above 44 GPa. See Table 1 for the coordinates of the triple points, where liquid water is in equilibrium with two adjacent

solid phases.

Table 1. Crystal structure, Density, and Transition Temperatures for the Phases of ice

Crystal

Phase

system

Cell parameters

Z

n

ρ/g cm

-3

Triple points

Ih

Hexagonal

a = 4.513; c = 7352

4

4

0.93

I-III: –21.99°C, 209.9 MPa

Ic

Cubic

a = 6.35

8

4

0.94

II

Rhombohedral

a = 7.78; α = 113.1°

12

4

1.18

III

Tetragonal

a = 6.73; c = 6.83

12

4

1.15

III-V: –16.99°C, 350.1 MPa

IV

Rhombohedral

a = 7.60; α = 70.1°

16

4

1.27

V

Monoclinic

a = 9.22; b = 7.54,

28

4

1.24

V-VI: 0.16°C, 632.4 MPa

c = 10.35; β = 109.2°

VI

Tetragonal

a = 6.27; c = 5.79

10

4

1.31

VI-VII: 82°C, 2216 MPa

VII

Cubic

a = 3.41

2

8

1.56

VIII

Tetragonal

a = 4.80; c = 6.99

8

8

1.56

IX

Tetragonal

a = 6.73; c = 6.83

12

4

1.16

X

Cubic

a = 2.83

2

8

2.51

references

1. Wagner, W., Saul, A., and Pruss, A., J. Phys. Chem. Ref. Data, 23, 515,

1994.

2. Lerner, R.G. and Trigg, G.L., Eds., Encyclopedia of Physics, VCH

Publishers, New York, 1990.

3. Donnay, J.D.H. and Ondik, H.M, Crystal Data Determinative Tables,

Third Edition, Volume 2, Inorganic Compounds, Joint Committee on

Powder Diffraction Standards, Swarthmore, PA, 1973.

4. Hobbs, P.V., Ice Physics, Oxford University Press, Oxford, 1974.

5. Glasser, L., J. Chem. Edu., 81, 414, 2004.

Phase Diagrams

12-183

C

al

cu

la

te

d

2000

1500

1000

500

0 0

Coesite

20

40

60

80

100

120

P/kbar

t/°

C

Stishovite

Crist

Liq.

αQuartz

βQuartz

1300

°

34 kbars

M

Trid

1190

°

1.43 kbars

Figure 4.

SiO

2

system. Crist = cristobalite; Trid = tridymite.

0

1600

1400

1200

1000

800

600

400

Mass % Oxygen

°F

50

.2 .4 22

24

26

28

30

Q

L

3000

2600

2200

1800

1400

1000

52

54

56

58

60

Atom % Oxygen

Magnetite

+

hematite

Wustite

+

magnetite

Magnetite

+ oxygen

Liquid oxide

+ oxygen

Liquid oxide

+ magnetite

Liquid

oxide

Wustite

α-Iron +

magnetite

N J

I H

S

R

Y

Z

V

R´

G

C

A

B

Fe

3

O

3

Z´

Fe

3

O

4

FeO

α-Iron +

wustite

γ-Iron +

wustite

γ-Iron + liq. oxide

δ-Iron +

liq. oxide

Liq. iron +

Liq. oxide

Liq. iron

Liq. iron

Hematite + oxygen

Magnetit

e

t/°

C

..

..

..

..

Figure 5.

Fe-O system.

12-184

Phase Diagrams

Point

t/°C

% O

p

CO2

/p

CO

Point

t/°C

% O

p

CO2

/p

CO

p

O2

/atm

A

1539

Q

560

23.26

1.05

B

1528

0.16

0.209

R

1583

28.30

1

C

1528

22.60

0.209

R´

1583

28.07

1

G

1400

a

22.84

0.263

S

1424

27.64

16.2

H

1424

25.60

16.2

V

1597

27.64

0.0575

I

1424

25.31

16.2

Y

1457

28.36

1

J

1371

23.16

0.282

Z

1457

30.04

1

L

911

a

23.10

0.447

Z´

30.6

N

1371

22.91

0.282

a

Values for pure iron.

2200

2000

1800

1600

1400

1200

1000

800

600

400

70

Atomic Percent Oxygen

Ti

2

O

t/°

C

60

50

40

30

20

10

0

~1885

°C

Mass Percent Oxygen

Ti

40

30

20

10

0

L

(

αTi)

(

βTi)

βTiO

γTiO

1670

°C

1720

°C

1842

°C 1870°C

~1250

°C

940

°C

882

°C

Ti

3

O

Ti

3

O

2

α

Ti

O

βTi

1-x

O

αTi

1-x

O

βT

i

2

O

3

TiO

2

(rutile)

higher Magneli phases

Ti

n

O

2n-1

Figure 6.

Ti-O system.

Composition,

Pearson

Space

Phase

mass % O

symbol

group

(βTi)

0 to 3

cI2

Im

¯

3m

(αTi)

0 to 13.5

hP2

P63/mmc

Ti

3

O

~8 to ~13

hP~16

P

¯

3c

Ti

2

O

~10 to 14.4

hP3

P

¯

3m1

γTiO

15.2 to 29.4

cF8

Fm

¯

3m

Ti

3

O

2

~18

hP~5

P6/mmm

βTiO

~24 to ~29.4

c**

–

αTiO

~25.0

mC16

A2/m or B*/*

βTi

1–x

O

~29.5

oI12

I222

αTi

1–x

O

~29.5

tI18

I4/m

βTi

2

O

3

33.2 to 33.6

hR30

R

¯

3c

αTi

2

O

3

33.2 to 33.6

hR30

R

¯

3c

βTi

3

O

5

35.8

m**

–

αTi

3

O

5

35.8

mC32

C2/m

α´Ti

3

O

5

35.8

mC32

Cc

γTi

4

O

7

36.9

aP44

P

¯

1

βTi

4

O

7

36.9

aP44

P

¯

1

αTi4O

7

36.9

aP44

P

¯

1

γTi

5

O

9

37.6

aP28

P

¯

1

βTi

6

O

11

38.0

aC68

A

¯

1

Ti

7

O

13

38.3

aP40

P

¯

1

Ti

8

O

15

38.5

aC92

A

¯

1

Ti

9

O

17

38.7

aP52

P

¯

1

Rutile TiO

2

40.1

tP6

P4

2

/mnm

Metastable phases

Anatase

–

tI12

I4

1

/amd

Brookite

–

oP24

Pbca

High-pressure phases

TiO

2

-II

–

oP12

Pbcn

TiO

2

-III

–

hP~48

–

Phase Diagrams

12-185

1600

1500

1400

1300

1200

60

70

80

90

100

Mol %

BaO

TiO

2

t/

°C

Liquid

1428

°

~1300

°

~1320

°

~1330

°

~1357

°

TiO

2

+ Liq.

TiO

2

+ BaTi

4

O

9

TiO

2

+ Ba

2

Ti

9

O

20

Ba

2

Ti

9

O

20

Ba

Ti

4

O

9

Ba

4

Ti

13

O

30

Ba

6

Ti

17

O

40

BaTiO

3

+

Ba

6

Ti

17

O

40

BaTiO

3

+

Liq.

Figure 7.

BaO-TiO

2

system.

2800

2600

2400

2200

2000

1800

1600

1400

70

Spinel s s

+ Liquid

Mol %

Al

2

O

3

t/°

C

60

50

40

30

20

10

0

Periclase s s

+ Liquid

1995°

Periclase ss + Spinel ss

~1500°

Periclase + Spinel

2105°

Spinel

ss

Periclase

ss

MgO

Figure 8.

MgO-Al

2

O

3

system.

12-186

Phase Diagrams

t/°

C

2800

2400

2000

1600

1200

800

400

0

20

40

60

80

100

ZrO

2

0

Y

2

O

3

Mol %

6:1

ss

Y

ss

H

ss

Liquid

C

ss

Y

ss

+ H

ss

C

ss

+ Y

ss

Tet

ss

+ C

ss

Tet

ss

Mon

ss

Mon

ss

+ C

ss

4:3 + 1:6

ss

1700

°C

1375

°

C

ss

+ Liq.

1325

°± 25°

(28%)

1650

°± 50°

C

ss

+ 6:1

(55%)

C

ss

+ 4:3

(95.5%)

490

°

Zr

3

Y

4

O

12

Figure 9.

Y

2

O

3

-ZrO

2

system. C

ss

= cubic ZrO

2

ss (fluorite-type ss); Y

ss

= cubic Y

2

O

3

ss; Tet

ss

= tetragonal ZrO

2

ss; Mon

ss

= monoclinic ZrO

2

ss; H

ss

= hexagonal Y

2

O

3

ss; 3:4 = Zr

3

Y

4

O

12

; 1:6 = ZrY

6

O

11

ss.

Phase Diagrams

12-187

Mol %

60

40

20

0

Si

3

N

4

80

100

4(AIN)

100

80

60

40

20

0

Si

2

ON

2

O´

Mol

%

Liquid

X

1700

°C

ALON

ss

β´

8H

15

R

12

H

21

R

27

R

2H

δ

3(SiO

2

)

2(Al

2

O

3

)

Al

6

Si

4

O

13 ss

Figure 10.

3(SiO

2

)-Si

3

N

4

-4(AlN)-2(Al

2

O

3

) system. “Behavior” diagram at 1700°C. The labels 8H, 15R, 12H, 21R, 27R, 2H

δ

indicate defect

AlN polytypes. β´ = 3-sialon (Si

6–x

Al

x

O

x

N

8–x

); O´ = sialon of Si

2

ON

2

type; X = SiAlO

2

N (“nitrogen mullite”). ALON ss = aluminum oxynitride ss

extending from approximately Al

7

O

9

N to Al

3

O

3

N.

40

60

80

TiO

2

(86%)

(8%)

ZrO

2

TiZrO

4

Mol %

PbO

1100

°C

(PZ-PT)ss(orth)

PbZrO

3

PbTiO

3

(PT-PZ)ss(tet)

(PT-PZ)ss(rhom)

Liq. + (PT-PZ)ss

Zss + (PT-PZ)ss

Zss + ZT + (PT-PZ)ss

Tss + ZT + (PT-PZ)ss

ZT

+ (P

T-PZ)

ss

Ts

s + (PT

-PZ)ss

Figure 11.

PbO-ZrO

2

-TiO

2

(PZT) system, subsolidus at 1100°C. P = PbO; T = TiO

2

; Z = ZrO

2

.

12-188

Phase Diagrams

Figure 12.

CaO-Al

2

O

3

-SiO

2

system (temperatures in °C).

Crystalline Phases

Notation

Oxide formula

Cristobalite

Tridymite

}

SiO

2

Pseudowollastonite

CaO·SiO

2

Rankinite

3CaO·2SiO

2

Lime

CaO

Corundum

Al

2

O

3

Mullite

3Al

2

O

3

·2SiO

2

Anorthite

CaO·Al

2

O

3

·2SiO

2

Gehlenite

2CaO·Al

2

O

3

·SiO

2

Temperatures up to approximately 1550°C are on the

Geophysical Laboratory Scale; those above 1550°C are on

the 1948 International Scale.

Phase Diagrams

12-189

BaO(BaCO

3

)

1:2:1

2:1:3

~4:1:2

~5:1:3

20

40

60

80

100

CuO

0

1/2(Y

2

O

3

)

b

1

Mol %

Y

2

Cu

2

O

3

a

2

a

1

Ba

4

Y

2

O

7

c

1

Ba

2

Y

2

O

5

Ba

3

Y

4

O

9

BaY

2

O

4

BaCuO

2

Ba

2

CuO

3

b

2

P

ss

c

2

Figure 13.

BaO-Y

2

O

3

-CuO system. 2:1:3 = Ba

2

YCu

3

O

7–x

; 1:2:1 = BaY

2

CuO

5

; 4:1:2 = Ba

4

YCu

2

O

7.5+x

; and 5:1:3 = Ba

5

YCu

3

O

9.5 + x

. The supercon-

ducting 2:1:3 phase was prepared using barium peroxide.

t/°

C

1100

1000

900

800

700

600

500

400

300

100

0

10

20

30

40

50

60

70

80

90

Mass Percent Copper

Al

Cu

100

20

30

40

50

60

70 80 90

0

10

Atomic Percent Copper

(Cu)

L

660.452

°C

548.2

°C

567

°C

(Al)

θ

η

2

ζ

1

ζ

2

γ

1

ε

1

γ

0

β

0

β

ε

2

η

1

δ

α

2

1084.87

°

Figure 14.

Al-Cu system.

12-190

Phase Diagrams

Composition,

Pearson

Space

Phase

wt % Cu

symbol

group

(Al)

0 to 5.65

cF4

Fm

¯

3m

θ

52.5 to 53.7

tI12

I4/mcm

η

1

70.0 to 72.2

oP16 or oC16

Pban or Cmmm

η

2

70.0 to 72.1

mC20

C2/m

ζ

1

74.4 to 77.8

hP42

P6/mmm

ζ

2

74.4 to 75.2

(a)

–

ε

1

77.5 to 79.4

(b)

–

ε

2

72.2 to 78.7

hP4

P63/mmc

δ

77.4 to 78.3

(c)

R

¯

3m

γ

0

77.8 to 84

(d)

–

γ

1

79.7 to 84

cP52

P

¯

43m

β

0

83.1 to 84.7

(d)

–

β

85.0 to 91.5

cI2

Im

¯

3m

α

2

88.5 to 89

(e)

–

(Cu)

90.6 to 100

cF4

Fm

¯

3m

Metastable phases

θ´

–

tP6

–

β´

–

cF16

Fm

¯

3m

Al

3

Cu

2

61 to 70

hp5

P

¯

3m1

(a) Monoclinic? (b) Cubic? (c) Rhombohedral. (d) Unknown. (e) D0

22

-type long-period

superlattice.

2000

1500

1000

500

0 0

4.2

Atomic Percent Carbon

20

t/°

C

(

αFe), ferrite

2

4

6

8

10

12

10

0

30

L

L + C(graphite)

Mass Percent Carbon

(

γFe),

austenite

2.1

0.65

740

°C

1153

°C

(

δFe)

1394

°C

912

°C

Figure 15.

Fe-C system.

Composition,

Pearson

Space

Phase

mass % C

symbol

group

(δFe)

0 to 0.09

cI2

Im

¯

3m

(γFe)

0 to 2.1

cF4

Fm

¯

3m

(αFe)

0 to 0.021

cI2

Im

¯

3m

(C)

100

hP4

P6

3

/mmc

Metastable/high-pressure phases

(εFe)

0

hP2

P6

3

/mmc

Martensite

< 2.1

tI4

I4/mmm

Fe

4

C

5.1

cP5

P

¯

43m

Fe

3

C (θ)

6.7

oP16

Pnma

Fe

5

C

2

(χ)

7.9

mC28

C2/c

Fe

7

C

3

8.4

hP20

P6

3

mc

Fe

7

C

3

8.4

oP40

Pnma

Fe

2

C (η)

9.7

oP6

Pnnm

Fe

2

C (ε)

9.7

hP*

P6

3

22

Fe

2

C

9.7

hP*

P

¯

3m1

(C)

100

cF8

Fd

¯

3m

Phase Diagrams

12-191

1900

1700

1500

1300

1100

900

700

500

300

0

Atomic Percent Chromium

t/°

C

Mass Percent Chromium

10

20

30

40

50

60

70

80

90

100

0

10

20

30

40

50

60

70

80

90

100

L

(Cr)

F

r

13.4

1513

°C

19.8

830

°C

σ

47.2

T

C

1394

°C

1538

°C

912

°C

11.2

6.5

846

°C

(

αFe,δFe)

(

γFe)

45

1863

°C

770

°C

Figure 16.

Fe-Cr system.

Composition,

Pearson

Space

Phase

mass % Cr

symbol

group

(aFe, Cr)

0 to 100

cI2

Im

¯

3m

(γFe)

0 to 11.2

cF4

Fm

¯

3m

σ

42.7 to 48.2

tP30

P4

2

/mnm

t/°

C

1200

1100

1000

900

800

700

600

500

400

300

200

100

100

0

10

20

30

40

50

60

70

80

90

Mass Percent Tin

Cu

Sn

Atomic Percent Tin

100

0

10

20

30

40

50

60

70

80 90

L

58.6

640

°C

676

°C

755

°C

25.6

30.6

796

°C

13.5

(Cu)

582

°C

59

415

°C

189

°C 60.3

60.9

227

°C

186

°C

92.4

99.3

231.9681

°C

η

ε

γ

ζ

δ

β

22

586

°C

24.6

520

°C

15.8

27.0

~350

°C

32.55

11

1.3

η´

(Sn)

1084.87

°C

Figure 17.

Cu-Sn system.

12-192

Phase Diagrams

Phase

Composition, mass % Sn

Pearson symbol

Space group

α

0 to 15.8

cF4

Fm

¯

3m

β

22.0 to 27.0

cI2

Im

¯

3m

γ

25.5 to 41.5

cF16

Fm

¯

3m

δ

32 to 33

cF416

F

¯

43m

ζ

32.2 to 35.2

hP26

P6

3

ε

27.7 to 39.5

oC80

Cmcm

η

59.0 to 60.9

hP4

P6

3

/mmc

η´

44.8 to 60.9

(a)

–

(βSn)

~100

tI4

I4

1

/amd

(αSn)

100

cF8

Fd

¯

3m

(a) Hexagonal; superlattice based on NiAs-type structure.

Figure 18.

Cu-Ni system.

Composition,

mass % Ni

Pearson

symbol

Space

group

Phase

(Cu, Ni) (above 354.5°C)

0 to 100

cF4

Fm3–m

Phase Diagrams

12-193

350

300

250

200

150

100

50

0

0

Atomic Percent Tin

t/°

C

Mass Percent Tin

10

20

30

40

50

60

70

80

90

100

L

61.9

97.8

183

°C

18.3

(Pb)

327.502

°C

0

10

20

30

40

50

60

70

80

90

100

231.9681

°C

(

βSn)

Pb

Sn

Figure 19.

Pb-Sn system.

Composition,

mass % Sn

Pearson

symbol

Space

group

Phase
(Pb)

0 to 18.3

cF4

Fm

¯

3m

(βSn)

97.8 to 100

tI4

I4

1

/amd

(αSn)

100

cF8

Fd

¯

3m

High-pressure phases
ε(a)

52 to 74

hP1

P6/mmm

ε´(b)

52

hP2

P6

3

/mmc

(a) From phase diagram calculated at 2500 MPa. (b) This phase was claimed for alloys at 350°C and 5500 MPa.

12-194

Phase Diagrams

t/°

C

1100

1000

900

800

700

600

500

400

300

200

100

100

0

10

20

30

40

50

60

70

80

90

Atomic Percent Zinc

Cu

Zn

100

20

30

40

50

60

70

80

90

0

10

Mass Percent Zinc

L

D

36.8

A

36.1

C

55.8

G

31.9

B

902

38.27

E

454

°C

44.8

F

X

468

48.2 Y

57

β

γ

ε

α or (Cu)

β´

H

834

°C

59.1

69.2

L

700

°C

N

79.8

Q

87.9

98.25

419.58

°C

425

°C

η or (Zn)

560

°C

70

R

73.5 T

88

U

97.17

V

W

598

°C

78

78

76 P

S

M 72.45

δ

O

1064.62

°C

Figure 20.

Cu-Zn system.

Composition,

mass % Zn

Pearson

symbol

Space

group

Phase
α or (Cu)

0 to 38.95

cF4

Fm

¯

3m

β

36.8 to 56.5

cI2

Im

¯

3m

β´

45.5 to 50.7

cP2

Pm

¯

3m

γ

57.7 to 70.6

cI52

I

¯

43m

δ

73.02 to 76.5

hP3

P

¯

6

ε

78.5 to 88.3

hP2

P6

3

/mmc

η or (Zn)

97.25 to 100

hP2

P6

3

/mmc

Phase Diagrams

12-195

t/°

C

1600

1400

1200

1000

800

600

400

200

0

0

10

20

30

40

50

60

70

80

90

Mass Percent Samarium

Co

100

Sm

Atomic Percent Samarium

100

0

10

20

30

40

50

60 70 80 90

L

1074

°C

922

°C

734

°C

595

°C

695

°C

605

~93

~82

575

°C

(

γSm)

(

βSm)

(

αSm)

Co

4

Sm

9

CoSm

3

Co

3

Sm

1074

°C

1200

°C

1240

°C

1260

°C

Co

3

Sm

1100

°C

1325

°C

(

αCo)

(

εCo)

Co

5-

x

Sm

α

Co

17

Sm

2

α

Co

7

Sm

2

βCo

17

Sm

2

βCo

7

Sm

2

α→β

Co

19

Sm

5

Co

5+

x

Sm

1495

°C

Figure 21.

Co-Sm system.

Composition,

mass % Sm

Pearson

symbol

Space

group

Phase
(αCo)

0 to ~3.7

cF4

Fm

¯

3m

(εCo)

~0

hP2

P6

3

/mmc

βCo

17

Sm

2

~23.0

hP38

P6

3

/mmc

αCo

17

Sm

2

~23.0

hR19

R

¯

3m

hP8

P6/mmm

Co

5 + x

Sm

~33 to 34

–

–

Co

5 - x

Sm

~34 to 35

–

–

Co

19

Sm

5

~40.1

hR24

R

¯

3m

hP48

P6

3

/mmc

αCo

7

Sm

2

~42.1

hR18

R

¯

3m

βCo

7

Sm

2

~42.1

hP36

P6

3

/mmc

Co

3

Sm

46

hR12

R

¯

3m

Co

2

Sm

56.0

hR4

R

¯

3m

cF24

Fd

¯

3m

Co

4

Sm

9

~85.1

o**

–

CoSm

3

88

oP16

Pnma

(γSm)

~100

cI2

Im

¯

3m

(βSm)

~100

hP2

P6

3

/mmc

(αSm)

~100

hR3

R

¯

3m

Other reported phases
Co

5

Sm

~33.8

hP6

P6/mmm

Co

2

Sm

5

~86.4

mC28

C2/c

12-196

Phase Diagrams

2600

2400

2200

2000

1800

1600

1400

1200

1000

800

600

400

0

Atomic Percent Molybdenum

t/°

C

Mass Percent Molybdenum

10

20

30

40

50

60

70

80

90 100

0

10

20

30

40

50

60

70

80

90

100

L

(

βTi,Mo)

Ti

Mo

~695

°C

~650

°C

882

°C

1670

°C

(

αTi)

~21

2623

°

Figure 22.

Ti-Mo system.

Composition,

mass % Mo

Pearson

symbol

Space

group

Phase
(βTi, Mo)

0 to 100

cI2

Im3–m

(αTi)

0 to 0.8

hP2

P6

3

/mmc

α´

(a)

hP2

P6

3

/mmc

α˝

(a)

oC4

Cmcm

ω

(a)

hP3

P6/mmm

(a) Metastable.

Sta

rt

Finis

h

800

700

600

500

400

0.1

t/°

C

1.0

10

100

1000

Time in Minutes

β + α´

M

S

β + α´

β

t

o

(

β + α)

eqm

Experimental time–temperature–transformation (TTT) diagram for Ti-Mo. The start and finish times of the isothermal precipitation reaction vary

with temperature as a result of the temperature dependence of the nucleation and growth processes. Precipitation is complete, at any temperature,

when the equilibrium fraction of α is established in accordance with the lever rule. The solid horizontal line represents the athermal (or nonthermally

activated) martensitic transformation that occurs when the β phase is quenched.

Phase Diagrams

12-197

10

Mass Percent Nickel

20

30

40

50

60

70

80

90

90

80

70

60

50

40

30

20

10

90

80

70

60

50

40

30

20

10

Mass Percent Ch

romium

Mass

Percent Iron

(Cr) + (

γFe,Ni)

(

γFe,Ni)

σ + (γFe,Ni)

(Cr) +

(γFe,Ni)

(Cr)

σ

(Cr) +

σ

Fe

Ni

Cr

18-8 Stainless steel

Figure 23.

The isothermal section at 900°C (1652°F) of the iron-chromium-nickel ternary phase diagram, showing the nominal composition

of 18-8 stainless steel.

12-198

Phase Diagrams