J O U R N A L O F M A T E R I A L S S C I E N C E 6 (1971) 4 8 - 5 3

Structure of Liquid Cadmium-Antimony Alloys R. K U M A R , C. S. S I V A R A M A K R I S H N A N

National Metallurgical Laboratory, Jamshedpur, India The structure of liquid Cd-Sb alloys was determined with the help of the Kumar-Samarin technique of centrifuging liquid metals. Alloys containing 7, 29, 50, 57 and 79 at. % Sb were examined in the range 350 to 650 ~ C. It shows that (i) all alloys except in the vicinity of equi-atomic composition, consist of a colloidal dispersion of compound clusters in a random monatomic matrix, and (ii) the cluster size depends on composition with minima occurring at the two eutectic compositions. The volume fraction of clusters and their heat of formation were determined. The composition of the compound cluster was deduced as Cd,oSb30. Concentration gradient was not established in the equi-atomic alloy during centrifuging. The investigation shows that residual structure can exist far into the liquid state and is not confined to liquids of stoichiometric compound compositions.

I. Introduction In a number of binary metallic liquid systems of the simple eutectic type, Kumar and Sivaramakrishnan [1-4] have demonstrated that a dispersion of clusters of like atoms (solute-solute or solvent-solvent) exists colloidally in random, monatomic environment of solute and solvent atoms. The formation of clusters in liquid alloys indicates that, despite the mutual solubility in the liquid state, the preferential interaction between like atoms in a solid solution is not entirely destroyed on melting. In binary alloy systems involving intermetallic compounds in the solid state, the strong interaction between unlike atoms, which results in compound formation in the solid state, is again not suddenly destroyed on melting, but clusters of short range order persist significantly in the liquid state. X-ray, electrical resistivity and thermodynamic observations relative to the liquid state indicate that the degree of short range order varies with composition, with a maximum usually occurring in the liquid alloy of intermetallic compound composition. As the temperature is raised in the liquid state in both types of systems, the extent of clusters of either like or unlike atoms decreases and randomisation of solute and solvent atoms is promoted. The existence of clusters of short-range order in AI-Cu liquid alloys up to 2 5 ~ Cu was demonstrated by Kumar and Singh [5], by the 48

Kumar-Samarin technique which established concentration gradients on centrifuging liquid alloys due to the difference in the densities of clusters and monatomic liquid atoms. They deduced the composition of the clusters from thermodynamic arguments involving their size and volume fraction and the viscosity of the liquid and found them to be copper rich [6]. In their centrifuge, Kumar and Singh could not study the behaviour of the copper-rich AI-Cu alloys because of the corrosive action of the liquids on the stainless steel crucibles at temperatures above the liquidus line. If the concept of short range order is valid, centrifuging the alloys corresponding to the composition of the cluster in liquid state would not establish any concentration gradient. The Cd-Sb system was chosen because it has strong interaction between Cd and Sb atoms and has been extensively investigated in the liquid state by conventional techniques. It forms both stable and metastable compounds [7] when liquid alloys are cooled at normal rates. In addition to the stable CdSb compound melting at 456 to 459 ~ C, the formation of another compound Cd4Sb3 melting at about the same temperature is also reported, but CdSb is only ordinarily shown in their binary equilibrium diagram. The metastable Cd-Sb system, however, shows the formation of an additional intermetallic compound Cd 3Sb2melting at 420 ~ 9 1971 Chapman and Hall Ltd.

STRUCTURE OF LIQUID C A D M I U M - A N T I M O N Y ALLOYS

Geffken et al [8] concluded that the inflections in the plots of partial molar entropy versus composition in the temperature range 420 to 500 ~ C at about 57 at. % Cd (Cd4Sba) are due to the existence of strong short-range order in the liquid state, which decreases as the temperature is raised and the solution simultaneously tends towards randomisation. The resistivity composition curves of liquid alloys also show two maxima at compositions corresponding to the formation of CdSb and CdsSb2 in the solid state. Since the electrical resistivity of liquid metals provides information regarding interatomic interactions and their effects upon structures these results were interpreted in terms of complex short range ordering behaviour which changes rapidly with increasing temperature [9]. Similarly, the alloy CdSb has maximum viscosity in liquid state [10]. It, therefore, appears that strong interaction between Cd and Sb atoms persists in the liquid state in the composition range 40 to 50 at. % Sb. 2. E x p e r i m e n t a l

40g, 5 0 0 ~

x

f

O-- 15 min

"~" ~

1.9oi

A - - 3 0 rain

e~

r~-90 rain

"" "-. ~ "

"~...

"-.

7Og, 4 5 0 ~

e--lh a--3h A--4h

~&.

x-- 4 h

185

sa

~ 1"80

40g~ 4 5 0 ~

d

1-85 ~ ' ~ . . . .

"~

1"80

O

--. -.

1.O 2'0 3"0 4'0 5.0 6.0 DISTANCE FROM FARTHER END OF CRUCIBLE (r

Figure 2 Chemical I'95

analysis of Cd-29 at. ~/o Sb alloys.

.~

70 g, 500~

1-90 --~.

Details of the experimental techniques and methods of statistical analysis of the results have been described earlier [1, 2]. Alloys containing 7, 29, 50, 57 and 79 at. % Sb were investigated in the temperature range 350 to 650 ~ C at two 2.0

1.95

--.

El'-

~'~-

1"85

9Ol.80 O ~ ~

"~70s176

1'90~.

""-.~

1"95 1'85 1"90

I

I

I

"

~

~

"

" .,.

I

7Og, 350~

1.80 l O

i I I "" ~ I 10 20 30 40 50 60 DISTANCE FROM FARTHER END OF CRUCIBLE (r

1"95

Figure 3 Chemical Uo1.90

I

2.0

I

1

I

4Og, 350~

A

1"95

1'90

i

I

I

I

40s176

1"95

1.90

I E I I O 1.O 2.0 3.0 4.0 5.0 DISTANCE FROM FARTHER END OF CRUCIBLE (crn)

Figure 1 Chemical

analysis data of Cd-7 at. ~/o Sb alloys,

analysis of Cd-29

at. ~/o Sb alloys.

centrifugal speeds which developed forces 40 and 70 times gravitational acceleration. Samples of about 60 g each of the alloys were centrifuged in graphite crucibles for various times and at different temperatures. The experimental conditions are summarised in table I. If the preferential solid state interaction between Cd and Sb atoms persists in the liquid state as well, Cd-Sb compound clusters will migrate to the inner end of the crucible and this will result in the setting up of concentration gradients. 2.1. Cluster Size

In figs. 1-5 best fitting lines are drawn on the basis of a least square analysis in each case. The 49

R. KUMAR,

1'70 40g,

1"68 "~"~ I'66 ~- x -

500~

o- 15min ~,- 3 0 rain ~._ ~-9Omin " ' " "---,,-" " " " ~.K . ~ x - 4 h

1'72

C. S. SIVARAMAKRISHNAN

409,

650~

El

1"70

|

t,.

o

~a 1.62

&

1'68

~1.6o

,

l

~- - -

,

tO 70 g, 500~ 0 1"68 "~"-- ..m 1 ' 6 6 ~ ' ~ "

I

1"66

I

I

70 g,650~

~ El

9~ |

z,

~

"~

"~ 1"72 U

~"

~.~o

|

o -:-'>-4:

z~

1.60 1 I I I ~ O 1"O 2'0 3-0 4'0 5'0 DISTANCE FROM FARTHER END OF CRUCIBLE (cm)

Figure 4 Chemical analysis data of Cd-57 at. ~/o Sb alleys. 1.50 ~

1.68

o-th

7Og, 6OO~

h

o

u 1.70 0 O

~x o

B

~

o

[3

~El

I

,

0

.-3.

I'70

1"68 1"30

"fi

" ~ "~ ~A ~ " ~ , , . o~

70 9 , 5 O O ~ I i I I 0 I'0 2'0 3'0 4'0 5'0 DISTANCE F R O M F A R T H E R E N D O F CRUCIBLE (cm) 1"66

1.20

I

o Q

I 7 0 g, 6 5 0 ~

I

f

Figure 6 Chemical analysis of Cd-50 at. % Sb alloy showing no correlation.

~. 1.40 s

913o

%

120

I

~ ' ~

I 40g,600~

l

r

"\ o

1.50

1"40 1"30 1'20

o

I I I o O 1"O 2'0 3"0 4"0 5"0 DISTANCE FROM FARTHER END OF CRUCIBLE (cm) 1"10

Figure 5 Chemical analysis data of Cd-79 at.

~/o S b alloys.

statistical parameters are also recorded in table I along with their confidence ranges on the concentration gradients for 80 to 95 % probability. These calculations show that, in general, the correlation between the logarithm of concentration and the distance is justified by rigorous statistical analysis. Table I also shows that correlation could not be established in the 50 at. % Sb alloy; the data are plotted in fig. 6. It can, 50

therefore, be concluded that the liquid alloy of equi-atomic composition consists essentially of CdxSby molecules. The cluster radii recorded in table I[ were calculated as was done earlier by the sedimentation equilibrium equation, using published values [10] of densities of Cd-Sb alloys. Values of the cluster radii are reproduced in table IIL These results show that the liquids corresponding to the two eutectic compositions have clusters of smaller sizes. The cluster size increases on the antimony-rich sides of both the eutectics. When the composition dependences of viscosity and cluster size are relatively evaluated, see fig. 7, it is noted that the viscosity plateau is in the region where short range order predominates in the liquid state and is not confined to the stoichiometric (equiatomic) compound composition. Increasing centrifugal force has practically no effect on the cluster size. 3. V o l u m e

F r a c t i o n of C l u s t e r s

If the deviation of the plot of viscosity against temperature from the usual Arrhenius type of expression,

STRUCTURE OF L I Q U I D C A D M I U M - A N T I M O N Y ALLOYS TABLE I

Statistics

Composition at. ~ S b

CentriTemperature Concentrafugal ~C tion force • g gradient

Correlation coefficient

No. of observations

Confidence range on conProbability centration gradient ( • level

40

7

of

0.00241 0.00021 0.00317 0.00055

1.0000 1.0000 1.0000 1.0000

12 12 12 9

100 100 100 100

450 500 450 500

0.01651 0.08037 0.02987 0.01740

0.8170 1.0000 0.8900 0.7620

6 13 12 10

95 100 99 98

70

650 500 650

0.00023 0.00002 0.00096

0.0129 0.0022 0.2500

12 12 12

90 90 90

40 70

500 500

0.00887 0.00741

1.0000 0.1095

13 16

100 90

40 70

650 600 650

0.06398 0.06136 0.06065

0.3129 0.9070 0.9101

7 9 16

90 99 99

40 70

50

57

79

system

350 450 350 450

70

29

the experimental data of Cadmium-Antimony

40

80

90

95

--

0.006

--

--

---

0.005 0.004

--

"~ Correlation is very p o o r indicating that no C d - C d , J S b - S b clusters are possible.

0.004

-0.054 0.011 0.306

*100~confidence.

TABLE

II Cluster size in Cadmium-Antimony alloys

Composition at. ~ Sb

Centrifugal force • g

Temperature ~

Statistical slope

Calculated values of cluster size A, at m e a n m i n i m u m and m a x i m u m slopes Cd

Sb

CdSb

40

350 450

0.00241 0.00021

20 10

---

18 8

70

350 450

0.00317 0.00051

18 12

---

16 9

40

450

0.01651

35

500

0.08037

58

450

0.02897

35

42 30

--

500

0.01740

29

31 27

--

40

500 650

0.00002 0.00023

---

---

---

70

650

0.00096

--

--

--

40 70

500 500

0.00887 0.00741

---

50 35

60 32

48 60

56 32

40

650

0.06398

--

98

118 61

156

167 102

600

0.06136

--

74

144

650

0.06065

--

76

88 58 82 71

172 80 160 110

7

48 9

45

---

44 10

65

29 70

54

58 41

39

36 32

50

57

79 70

130

51

R. K U M A R , C. S, S I V A R A M A K R I S H N A N T A B L E III Densities of Liquid Cadmium-Antimony and their Binary Alloys Temperature ~

:c

D e n s i t y g/cc

350 450 500 600 650

~

Cd

Sb

7 % Sb . . . .

29 % Sb

50 % Sb

57 % s b ~

79 % Sb

8.22 7.85 7.82 7.72 7.67

6.68 6.68 6.68 6.50 6.41

7.80 7.62 ----

-7.30 7.18 ---

7.25 6.95 6.88 6.64 6.52

--6.80 ---

---6.62 6.55

TABLE IV Heat of formation of cluster in Cd-80 at. ~/o Sb alloy Temperature ~K

Viscosity (millipoise)

873 923

~i

Vsi

19.23 15.28

18.03 14.93

~ v o l u m e fractio n of clusters

lnKx

2.0 0.9

4.7053 3.6848

H e a t of f o r m a t i o n cal/g m o l e

H e a t of f o r m a t i o n Kcal/g atom Cd4oSbao

33

4.708

~/ = ~/0 exp (E/RT), is attributed to the existence of clusters in liquid metals, their volume fraction can be calculated [11 ] from the Einstein equation relating the viscosity of a colloidal solution to the volume fraction of the clusters: 7]i/7]si ~- l + 0~r -I- ]~r

where ~t = actual value of viscosity in millipoise, ~?st = value the viscosity would have if the Arrhenius expression is extrapolated to temperature Ti, r ~ volume fraction of suspended particle per millilitre at temperature T~, and a, fi = constants equal to 2.5 and 7 respectively. Values of actual and extrapolated viscosity of Cd-80 at. ~ Sb alloy from the experimental observations of Fisher and Phillips [10], recorded in table IV, were used to calculate the volume fraction of the clusters at 873 and 923 ~ K. Following Ubbelohde i11 ] and assuming that associations or dissociation of clusters obeys mass-action equations and involves no volume change, the equilibrium constant (Kx) between monomeric and clustered atoms may be calculated if the number of atoms, g, in the cluster is known from the following relationship: Kx=

[g(1 -- r g r162 + g(1 - Cj)]g-1

for the reaction (Cd4Sb3)g ~ g[4Cd + 3Sb]. Values of Kx are also recorded in table IV. The heat of cluster formation was calculated with the help of Van't Hoff's equation: 52

/n ~Xl -- R where A H is the heat of dissociation or aggregation of the cluster per g reel; the data yield a value of 33 Kcal/g mol, or 4.86 Kcal/g atom of the alloy for AH. But the thermodynamically determined value of the heat of formation [ 12] of 1 g atom of the alloy having a composition near Cd4Sb3, is 0.47 Kcal. The derived value can be reconciled with the thermodynamic value if it is assumed that the chemical composition of the cluster is around the pseudo-molecule Cd~0Sb3o (0.486 Kcal/g atom of the alloy). In view of the strong interaction between Cd and Sb atoms around Cd~Sb3 composition, a region o f pronounced short range order is indicated in fig. 7. 4. Discussion In order to appreciate the structure of liquid metallic solutions, Darken [13] introduced the concepts of stability and excess stability to define the properties of the system. Stability is defined as the second derivative of the molal free energy witfi reel fraction where the free energy change of any process by which the solution is broken down into two solutions is proportional to the stability function d2F/dN~2 identical with d2F/dN12 where F represents the molal free energy of the system. The stability of an ideal solution is RT/(NIN2) and the quantity

d2F dN22

RT (N~N~)

is designated as the excess stability. These

STRUCTURE

20 ~

OF L I Q U I D C A D M I U M - A N T I M O N Y

~

>-

ca <

/

the excess stability. R e d u c e d resistivity was defined as equal to (pexp - p1N1 - p2N2) where pe,,p, pl a n d P2 are the resistivities o f the alloy a n d o f the p u r e c o m p o n e n t s respectively. T h e y a t t r i b u t e d this c o r r e s p o n d e n c e between resistivity a n d excess stability to the lack o f availability o f electrons caused by the stabilisation o f t h a t p a r t i c u l a r c o m p o s i t i o n by electron bonds.

I

[email protected]

u, /

t20

I

\ \\

z .<

~ I

//~\

~

ALLOYS

/

\ ~

\s

,a

5. Conclusion

/

\

o

o

RANGE OF

281

PREDOMINATING

I

_~2,~

SHORT

/

I RANGE

2

I ORDER xh /1~

_--~24 ~22 (

.~

)

/

/x /

/I

-140

/CLUSTER[ SIZE I

4Og /

u

o<: Ld

N

The investigation has shown t h a t the s t r o n g C d - S b interaction o f solid state is r e t a i n e d in the liquid state a n d t h a t liquid alloys o f c o m p o s i t i o n s o t h e r t h a n a r o u n d the equi-atomic, consist o f a colloidal dispersion o f p s e u d o - c o m p o u n d clusters a m o n g s t m o n a t o m i c atoms. The size o f the clusters is a f u n c t i o n o f c o m p o s i t i o n a n d temperature.

709 -130 ~

Acknowledgement

~2o

8~

/'--

/

~o ~ /

600

L

References

oU 550 bJ

~+- /

~soo

~+L

u~ 450 o_

57

~ 400 P 350 32I 30O

ct+L ~ ~ ~-~

250 "

3 ~+P

F

The a u t h o r s wish to t h a n k P r o f e s s o r V. A. Altekar, Director, National Metallurgical Labo r a t o r y , J a m s h e d p u r for his interest a n d permission to p u b l i s h this paper.

Y-~

~+7 l I

.

.

Cd 10 20 30 40 50 60 70 80 90 Sb ATOMIC PERCENTAGE ANTIMONY

Figure 7 Viscosity,

cluster size, reducing electrical resistivity and stabilities versus composition of Cd Sb liquid alloys.

functions are p l o t t e d in fig. 7 for the C d - S b system. T h e excess stability a p p r o a c h e s a cons t a n t value in each terminal region, b u t exhibits a m a r k e d positive p e a k in the central region. D a r k e n o b s e r v e d t h a t such p e a k s usually occur a t o r n e a r the composition(s) a n t i c i p a t e d f r o m a c o n s i d e r a t i o n o f classical valencies o f c o m p o n ents, or at the c o m p o s i t i o n o f i n t e r m e d i a t e solidstate phases. Excess stability can be t h o u g h t o f as a n i n d i c a t i o n o f the extent to which the electrons are tied up in bonding. T o m l i n s o n a n d Lichter [14] observed t h a t the m a x i m u m in the r e d u c e d resistivity versus c o m p o s i t i o n curve for the C d - S b system c o r r e s p o n d s to the m a x i m u m in

1. R. KUMAR, Trans. Indian Inst. Metals 18 (1965) 131. 2. R. KUMAR and c. s. SIVARAMAKRISI-INAN, jr. Mater. Sci. 4 (1969) 377. 3. Idem, ibid 4 (1969) 383. 4. Idem, ibid 4 (1969) 1008. 5. R. KUMAR and M. SINGH, Tram. Indian Inst. Metals 19 (1966) 117-121. 6. R. K U M A R , M. S I N G H , and r s. S I V A R A M A K R I S H NAN, Trans. Met. Soc. A I M E 239 (1969) 1219. 7. M. HANSEN and K. ANDERKO, "Constitution of Binary Alloys" (McGraw-Hill Book Co., New York, 1958) p. 437. 8. R. GEFFKEN~ K. L. K O M A R E K , and E. M I L L E R , Trans. Met. Soe. A I M E 239 (l 967) 1151. 9. E. M I N N E R , J. PACES~ and K. L. KOMAREK, Trans. Met. Soc. A I M E 2 3 0 (1964) 1557. 10. H. J. fiSHER and A. PHILLIPS, ibid200 (1954) 1060. 11. E. M C H A U G H L I N a n d A. R. U B B E L O H D E , Trans.

Faraday Soc. 56 (1960) 988. 12. HULTGREN et al, "Selected Values of Thermodynamic Properties of Metals and Alloys" (John Wiley & Sons, Inc.) p. 621. 13. L. S. DAR~:EN, Trans. Met. Soc. A I M E 239 (1967) 80. 14. J. L. TOMLINSON and B. o. L I C H T E R , Met. Zrans A I M E 1 (1970) 305.

Received 27 July and accepted 18 September 1970.

53