Ag-Ga

LatticeDiffusion Coefficient, D†

Phase Space Group1 Parameter1

(nm)DiffusingElement

Do

(m2/sec)

Q(kJ/mole)

2Ag

(550 –1228 K)

D10=5.5x10-6 Q1

0=171.1

Ag cubic

Fm m3−

a=0.4086 D20=1.51x10-3 Q2

0=226.7

2Ga

(873 - 1213 K)

D0=4.2x10-5 Q=162.19

ζ1 rhombo-

hedral3

P 3−

Ga

ortho-

rhombic

a=0.4523

b=0.7661 2Ga

D = 5.3x10-17

(282.8 K)

Cmca c=0.4524 D = 4.2x10-16

(302.7 K)

1 W.B. Pearson, A Handbook of Lattice Spacings and Structures of Metals and Alloys,

Vol. 2, Pergamon Press, 1967, pp. 80, 82, 101.2 E. A. Brandes and G.B. Brook, Smithells Metals Reference Book, 7th Ed., Butterworth-

Heinemann, 1992, pp. 13-9, 13-10, 13-15.3 Baren, M.R., “The Ag-Ga (Silver-Gallium) System,” Bull. Alloy Phase Diag., 18, No. 4,

1990, pp. 336.

† D = Do exp (-Q/kT) or [D = D1o exp(-Q1/kT) + D2o exp (-Q2/kT)]

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11/99 #61 11/99 #61

Ag-Ga Ag-O

The diagram is redrawn from Massalski (1), which is similar to that in Hansen (2), butwith higher oxygen solubility in the silver rich solid phase. Elliot (3) has reviewed thereferences on higher oxides of silver including AgO and Ag

2O, and also on an eutectic

between Ag and Ag2O at 500°C and 25.5 a/o O. Shunk (4) has reviewed the results

obtained for the crystal structures of AgO, Ag2O and AgO

2.

(1) Karakaya, I. and Thompson, W.T., in Binary Alloy phase Diagrams, 2nd

edition, edited by Massalski, T.B., ASM International, Materials Park, OH,1990; pp. 66-68.

(2) Hansen, M., Constitution of Binary Alloys, 2nd edition, McGraw Hill, 1958;pp. 37-38.

(3) Elliot, R.P.., Constitution of Binary Alloys First Supplement, McGraw Hill,1965; pp. 14-15.

(4) Shunk, A., Constitution of Binary Alloys Second Supplement, McGraw Hill,1969; pp. 6-7.

The diagram is redrawn from Baren (1), and is based mainly on the work ofHume-Rothery et al (2,3) and Predel et al (4). The system is characterized by aperitectic reaction at 611°C, an eutectoid reaction at 381°C and the z-z1 order-disorder reaction which occurs over a range of compositions on the Silver-richside.

(1) Baren, M.R., “The Ag-Ga (Silver-Gallium) System,” Bull. Alloy PhaseDiag., 18, No. 4, 1990; pp. 334-339.

(2) Hume-Rothery, W., and Andrews, K.W., “The Equilibrium Diagram of theSystem Silver-Gallium. I-The a-phase Region,” J.Inst. Met., 68, 1942; pp.133-143.

(3) Hume-Rothery, W., and Andrews, K.W., “The Equilibrium Diagram of theSystem Silver-Gallium,” Z. Metallkd., 60, 1958; pp. 661-662.

(4) Predel, B., and Stein, D.W., “The Enthalpies of Formation of BinaryCompounds of Gallium with Copper, Silver and Gold and an Analysis ofthe Thermodynamic Characteristics of 3/2 Electron Compounds,” Acta.Metall., 20, 1972; pp. 681-692.

0

200

400

800

600

(Ag)

1000

0 100908010 20 30 40 50 60 70

0

Tem

pe

ratu

re ˚

C

Atomic Percent Gallium

Weight Percent Gallium

Ag

L

Ga

(Ga)

10 20 30 40 50 60 70 80 90 100

22

27

26˚C

300˚C

611˚C

29.7741˚C

961.93˚C

425˚C

381˚C

ζ'

ζ

900

1000

939˚C

961.93˚C

1100

1200

1300

0 0.5 1 1.5 2 2.5

0

Tem

pera

ture

˚C

Atomic Percent Oxygen

Weight Percent Oxygen

Ag

L L + G

0.30.20.1

(Ag) (Ag) + G

Cu-Ga

LatticeDiffusion Coefficient, D†

Phase Space Group1 Parameter1

(nm)DiffusingElement

Do

(m2/sec)

Q(kJ/mole)

Cu cubic a=0.36147

2Cu(573- 1334K)

D10=1.3x10-5 Q1

0=197.8

Fm m3− D2

0=4.5x10-4 Q20=237.4

β cubicIm3m

a=0.29671

γ cubic

P m4 3−

γ1 cubic

P m4 3−

a=0.87296at 31 a/o Ga

γ2 cubic

P m4 3−

a=0.87315at 31 a/o Ga

γ3 cubic

P m4 3−

a=0.86922at 31 a/o Ga

ζ hexagonal

P63/mmc

a=0.26007

c=0.42433at 22 a/o Ga

υ tetragonal3

P4/mmm

Gaortho-

rhombica=0.4523b=0.7661 2Ga

D = 5.3x10-17

(282.8 K)

Cmca c=0.4524 D = 4.2x10-16

(302.7 K)

1 W.B. Pearson, A Handbook of Lattice Spacings and Structures of Metals and Alloys,

Vol. 2, Pergamon Press, 1967, pp. 81, 82, 222, 223.2 E. A. Brandes and G.B. Brook, Smithells Metals Reference Book, 7th Ed., Butterworth-

Heinemann, 1992, pp. 13-9, 13-10.3 Subramanian, P.R., and Laughlin, D.E., in Binary Alloy phase Diagrams, 2nd edition,

edited by Massalski, T.B., ASM International, Materials Park, OH, 1990, pp. 1410- 1412.

† D = D0 exp (-Q/ kT) or [D = D10 exp (-Q1

0/ kT) + D20 exp (-Q2

0/ kT)]

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11/99 #61 11/99 #61

Cr-O

The diagram is redrawn from Okamoto (1), and is the phase diagram calcu-lated based on a thermodynamic model by Kowalski et al (2), which agreeswith experimental results. The role of other oxides of chromium such as CrO

2,

Cr5O

12, Cr

6O

15, and CrO

3 in the phase diagram have not been determined.

(1) Okamato, H., “Cr-O (Chromium-Oxygen),” in J. Ph. Equil.,18, No.4, 1997;pp. 402

(2) Kowalski, M., and Spencer, P.J., Calphad, 19, 1995; pp. 229-239.

Cu-Ga

The diagram is redrawn from Massalski (1), which is similar to that presentedin Hansen (2), with modifications to the z phase field, based on results of Kittlet al (3).

(1) Subramanian, P.R., and Laughlin, D.E., in Binary Alloy phase Diagrams,2nd edition, edited by Massalski, T.B., ASM International, Materials Park,OH, 1990; pp. 1410-1412.

(2) Hansen, M., Constitution of Binary Alloys, 2nd edition, McGraw Hill, 1958;p. 582-584.

(3) Kittl, J.E., and Massalski, T.B., J.Inst. Met., 93, 1964; pp. 182-188.

600

800

1000

1200

1400

1600

1800

2200

2400

2600

2800

3000

2000

3200

100 20 30 40 50 60 70 80 90 100

0

Tem

pe

ratu

re ˚

C

Atomic Percent Oxygen

Weight Percent Oxygen

Cr

L1

G

L2

O

5 6010 20 30 40 50 70 80 90100

Cr 3

O4

Cr 2

O3

1455˚C

(Cr)

0

100

200

300

400

500

600

700

800

900

1000

1100

100 20 30 40 50 60 70 80 90 100

0

254˚C

468˚C~38.1

~37.6

~34.7

485˚C

645˚C

29.5

30.9

20.623.7

836˚C

620˚C616

490˚C

27.45

~73.6

29.6˚C~100

29.7741˚C

~76

~42.6

322˚C

~96

16.8 21.3

(Cu)

Tem

pe

ratu

re ˚

C

Atomic Percent Gallium

Weight Percent Gallium

Cu

L

Ga

7050 60 80 9010 20 30 40 100

γ

β

γ2

γ3

γ1

ζ

ζ'

915˚C

1084.87˚C

(Ga)

υ