The structure of directionally solidified GaSbCrSb eutectic alloy

The structure of directionally solidified GaSbCrSb eutectic alloy

METALLOGRAPHY 20:31 I-319 ( 19871 311 The Structure of Directionally Solidified GaSb-CrSb Eutectic Alloy YOSHIAKI UMEHARA AND SHIGEYASU KODA* The ...

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METALLOGRAPHY 20:31 I-319 ( 19871


The Structure of Directionally Solidified GaSb-CrSb Eutectic Alloy


The First Research Center of Technical Research and Development Institute, Japan Defence Agency, 2-2-1, Nakameguro, Meguroku, Tokyo 153, Japan

The eutectic alloy of GaSb-CrSb was directionally solidified at various rates to investigate the structural changes due to solidification conditions. The boundary energy between the GaSb and CrSb phases was determined from a dislocation model of the interface.

Introduction Continuing from our previous studies on directionally solidified eutectic alloys [1, 2], we now turn to the eutectic alloy GaSb-CrSb. An earlier study of this alloy by Mfiller et al. [3] used the normal horizontal freezing method. In the present study, we prepared the GaSb-CrSb eutectic by means of the Tammann-Bridgman method and have examined the subsequent microstructure.

Experimental Procedure The specimens of GaSb-CrSb eutectic were prepared from ultrapure Sb (99.9999%), Ga (99.9999%), and Cr (99.999%). The metals were sealed in vacuum, in amounts corresponding to the GaSb-CrSb eutectic composition, in a quartz tube. This composition [3], in wt.%, was 64.5%-Sb, 31.5%-Ga, and 4%-Cr (86.6%-GaSb and 13.4%-CrSb). The samples were then melted and withdrawn from the hot zone toward the lowertemperature zone for solidification at various rates. The apparatus is the same one used in previous experiments [1, 2], but the temperature of the * Emeritus Professor of Tohoku University. Present address: 4-28-10, Eifukucho, Suginamiku, Tokyo 163, Japan. © Elsevier Science Publishing Co., Inc., 1987 52 Vanderbilt Ave., New York, NY 10017



Y. Umehara and S. Koda

furnace was higher in the case of the GaSb-CrSb eutectic because of the elevated melting point (963 K). Ingots about 120 mm long were made. Subsequently, longitudinal and transverse specimens of all alloys were prepared for metallographic examination. The specimens were ground on "600" grade carborundum paper, polished with diamond paste, then etched (1 part of HF, 3 HNO3, and 5 CH3COOH) for 1-2 s to reveal the microstructure. The orientation relationship between the eutectic phases achieved by directional solidification was determined by x-ray diffraction, using the same technique as that described in the previous study [2].

Experimental Results The alloy specimens were polycrystalline and consisted of coarse columnar grains, about 2-4 mm in diameter, which were elongated in the solidification direction, as shown in Fig. 1. The microstructures of GaSb-CrSb eutectic are illustrated by Fig. 2, which shows both longitudinal and transverse sections at various solidification rates. The size of the CrSb rods was about 100-500 Ixm in length and about 1-4 I~m in diameter, decreasing with increasing solidification rate. The rodlike CrSb, when observed in transverse section, appeared

FIG. 1 Crystal of GaSb-CrSb composed of columnar grains. Diameter of ingot is 13 mm.

Directionally Solidified GaSb-CrSb Eutectic








Fxc. 2 The influence of solidification rate (7.25, 3.0, and 1.5 ~.m/s) on the microstructure of directionally grown GaSb-CrSb eutectic specimens. (a), (b), and (c) Transverse section, and (d), (e), and (f) longitudinal section.

rounded [Figs. 2(a), (b), and (c)]. The scanning electron micrographs of the transverse section are presented in Fig. 3 and confirm that the rods are chromium-rich and contain no gallium. Many investigators have studied the relationship between the rod spacing h and solidification rate R and found that, for the most part, the expression h2R = constant is valid. Similarly, in the present tests, the spacing h between the CrSb rods was found to be inversely proportional to R ~/2, and h2R equal to 1.52 x 10-16m3/s for GaSb-CrSb, as shown in Fig. 4. X-ray examination indicated that the (I 10) direction in the GaSb matrix phase was parallel to the growth direction. The rods of CrSb were aligned





Directionally Solidified GaSb-CrSb Eutectic



I O r~









t f

I" /






R -I/2 I






I 2

R / FIG. 4


/ 10 3 (m/s)


I 1

10 -6


-I/2 I 0.5


Variation of rod spacing with growth rate for GaSb-CrSb system.

parallel to each other in the growth direction and oriented in the (0001), direction. The preferred crystallographic orientation relationship observed between the GaSb and CrSb phases can be stated approximately as:

Growth direction: (110) GaSb // (0001) CrSb Crystallographic plane: {I 10} GaSb // {1120} or {1010} CrSb. Discussion

CrSb crystallizes in a Niccolite-type structure, with the chromium atoms in close-packed hexagonal layers, with interleaved close-packed layers of antimony nesting between three chromium atoms above and Fit3. 3 Scanning electron micrographs of the GaSb-CrSb eutectic alloy normal to the growth direction at a rate 1.5 ~m/s. (a) Secondary electron image, (b) G a - K a image and (c) Cr-Kc~ image.


Y. Umehara and S. Koda

three below. Likewise, each chromium atom rests on three antimony atoms, with three other antimony atoms above. All chromium atom layers have their atoms in rows parallel to the c-axis, whereas the antimony atom layers are staggered with repetition along the c-axis on the alternate layers [4]. The lattice constants of the CrSb crystal are a = 0.4108 nm and c = 0.5440 nm [5]. On the other hand, GaSb crystallizes in a Sphalerite-type structure. Here, every atom is surrounded tetrahedrally by four nearest neighbors of the opposite kind, and strong covalent electron bonds are formed between unlike neighbors. The lattice constant of the GaSb crystal is a = 0.60955 nm [6]. As mentioned above, two crystallographic relationships were observed. In the first case, the structure of the interface is defined by {110} GaSb corresponding to {1120} CrSb, and in the perpendicular direction, where {100} GaSb is parallel to {1010} CrSb. Also, the other case can be shown, wherein {110} GaSb//{10T0} CrSb and {100} GaSb // {1120} CrSb. The structure of the interface in one case is represented in Fig. 5, where {I 10} GaSb corresponds to {10]0} CrSb. The hatched planes indicate the other corresponding crystallographic planes. If the gallium atoms in the GaSb








<°°+°el> ,


Ga Cr

, ~







I oio}


Fro. 5 Geometry of the minimum energy phase-boundary between GaSb and CrSb: Crystallographic plane {110} of GaSb // {1120} of CrSb. Hatched planes indicate the other crystallographic planes.

Directionally Solidified GaSb-CrSb Eutectic


crystal are joined to antimony atoms in the CrSb crystal, as supposed in Figure 5, a small amount of misfit will be introduced at the interface because of the difference in the lattice spacing. As a result, the interface is not perfectly coherent but semicoherent. Therefore, the misfit at the interface has to be accommodated by introducing edge dislocations along both the growth and the transverse directions at the interface. The interface energy between the GaSb and the CrSb phases can be calculated from the strain energy E r of the network of interface dislocations which accommodate the difference in atomic alignment at this interface. It can be obtained from the following equation, from [1]:


G { blL~ blR~ "~ 4~r(1 -- v) _A/ILl ln-A-~tm + AltB1 In AltBlj ,


where the difference between the interatomic distances of antimony atoms in the GaSb and the CrSb crystals along the growth direction, Alum, will be given as [ Ln - LI [, and the difference along the transverse direction, AILsl, as [Bu - B~ ], and b will be given by L~ or BI. G is the shear modulus, v is Poisson's ratio. Taking G -- 4.33 × 10 ~° N/m 2 and v = 0.31 [7], the values were estimated for the interfacial energies of each case as shown in Table 1. The interfacial energy is lower in the case of {100} GaSb // {10]0} CrSb than in that of {110} GaSb//{1 IE0} CrSb, and it is also lower in the case of {100} GaSb//{I IE0} CrSb than in that of {110} GaSb // {10]0} CrSb. It seems that the {10]0} CrSb plane and the {11E0} CrSb plane are equally likely to occur in conjunction with the {100} GaSb plane, and thus the CrSb rods will appear rounded in transverse section as was noted in Figs. 2 and 3. If Jackson's theory [8] is assumed to be applicable to the present case, using the interfacial energy calculated from the dislocation model and the other solidification parameters, the diffusion coefficient between the TABLE 1 Calculated Values of Interface Energy



Altm (nm)

Interface energies (J/m2)






{110} GaSb // {1120} CrSb {100} GaSb // {1070} CrSb

0.43101 0.1130 0.43101 0.1130

0.60955 0.43101

0.1020 0.0202

1.66 1.06

{110} GaSb // {101_0} CrSb (100} GaSb // {1120} CrSb

0.43101 0.43101

0.60955 0.43101

0.1988 0.2805

1.87 1.36

0.1130 0.1130


Y. Umehara and S. Koda

GaSb and CrSb phases in the melt can be calculated from the equation

h2R = 4(1 + ~)~/2CoM

- + - L ~ -m,


= constant,


where Co is the total amount of eutectic composition, ma and mp are the respective slopes of the liquidus curve near the eutectic point (assuming a = CrSb and 13 = GaSb), L is the latent heat of fusion, TE is the melting temperature, ~ is the volume ratio of the two phases, M is a value calculated from the volume ratio, and cr~ is the phase-boundary energy of a-liquid and 13-liquid interfaces and is assumed to be equal to the abovementioned interfacial energy. The following values have been used for the calculation: Co = 1 mol fraction, m,~ = 490 K/mol fraction, m~ = 110 K/mol fraction, (TE/L)~ = 1.03 × 1 0 - 6 m 3 K / j [9], ~ = 8.15, M = 0.040 [8], cr~ = 1.49 J/m 2 and h2R = 1.52 × 10- ~6 m 3 / s . Assuming that the value of (Te/L)~ for CrSb is identical to that for AuSn, and that L (for AuSn) is 14.2 × 10 3 J/tool [10], (TE/L)~ is calculated to be 1.20 × 10 - 6 m3K/J. The diffusion coefficient D of CrSb in molten G a S b - C r S b eutectic alloy was thus estimated to be 1.7 × 10 - 9 m2/s, a value similar to those observed in other liquid metals ( ~ 1 0 - 9 m2/s) [11].

Conclusions A eutectic alloy of G a S b - C r S b was directionally solidified at various rates of solidification to investigate the structural changes during solidification. The results are as follows: 1. The spacing k of CrSb rods was found to be inversely proportional to R ~/2, where R is the rate of solidification, and k2R was 1.52 × 10- ~6 m3/s. 2. The alloy specimens consisted of polycrystalline columnar grains that were elongated in the solidification direction. The crystallographic orientation relationship between the GaSb and CrSb phases was determined by x-ray diffraction. Preferred relationships were observed and can be stated approximately as follows: Growth direction: (110) GaSb // (0001) CrSb Crystallographic plane: {1 I0} GaSb // {1120}, or {1010} CrSb 3. The interfacial energies between the GaSb and CrSb phases were calculated from a dislocation model by considering the mismatch at the interface to be equal to 1.06-1.66 J/m 2. 4. Assuming that the crystal growth follows Jackson's model, and also

Directionally Solidified GaSb-CrSb Eutectic


using the above-mentioned phase-boundary energy, the diffusion coefficient of CrSb in molten GaSb-CrSb eutectic alloy was calculated to be equal to 1.7 × 10 - 9 m2/s.

The authors thank Mr. T. Masald, Senior Scientist of the EMPA Section, Analytical Center of Shimazu Seisakusho Ltd. for his kind assistance with the electron microprobe x-ray analyses. References 1. Y. Umehara and S. Koda, Structure and phase-boundary energies of the directionally solidified InSb-MnSb, InSb-NiSb, InSb-FeSb, and InSb-CrSb eutectic alloy, MetalIography 7:313-331 (1974). 2. Y. Umehara and S. Koda, Structure of the directionally solidified InSb-Sb eutectic alloy, Metallography in press. (1987) 3. A. Miiller und M. Wilhelm, 13ber den gerichteten einbau von shwermetallphasen in AmBV-verbindungen, die eutectika GraSb-CrSb, GaSb-FeGa~.3, GaSb-CoGa].3, InAs-CrAs und InAs-FeAs, J. Phys. Chem. Solids 26:2029-2035 (1965). 4. L. G. Berry and B. Mason, Mineralogy, Freeman, San Francisco (1959), p. 317. 5. B. T. M. Willis, Crystal structure and antiferromagnetism of CrSb, Acta Cryst. 6:425426 (1953). 6. G. Gieseck and H. Pister, Prhzisionbestimmung der gitterkonstanten von AmBV-verbindungen, Acta Cryst. 11:369-371 (1958). 7. H. B. Huntington, The elastic constants of crystals, Solid State Phys. 7:213-351 (1958). 8. K. A. Jackson and J. D. Hunt, Lamellar and rod eutectic growth, Trans. Met. Soc. AIME 236:1129-1142 (1966). 9. B. D. Lichter and P. Sommelet, Thermal properties of AraB v compounds-l: high-temperature heat contents and heats of fusion of InSb, GaSb, and AISb, Trans. Met. Soc. AIME 245:99-105 (1969). 10. S. Misra, B. W. Howlett, and M. B. Bever, On the thermodynamic properties of the intermediate phases in the system Au-Sn, Trans. Met. Soc. AIME 233:749-754 (1965). 11. A. Moore and R. Elliot, The Solidification of Metals, ISI, London (1967), p. 68.

Received July 1986; accepted December 1986.