Point defects in NiGa

S c r i p t a ME]'AI.LIH~GTCA

Vol. 11, pp. 1159-I163, 1977 P r i n t e d in the United States

Pergamon Press, Inc.

POINT DEFECTS IN NiGa

K. Ho*, M. A. Quader**, F. Lin* and R. A. Dodd*** *Respectively Graduate Student in Materials Science **Research Associate ***Professor of Metallurgical Engineering, College of Engineering University of Wisconsin Madison, Wisconsin 53706

{Received October 18, 1977)

Introduction Point defects in the B2 phase NiGa, both constitutional and thermal, have been the subject of several investigations(l-4). The existence of high concentrations of thermal vacancies in the range 8OO-9OO°C (-0.75 Tm) is firmly established(2), but the compositional dependency of the constitutional vacancy concentration is less certain. The l a t t i c e parameter and density measurements of Seybolt and Westbrook(1) were somewhat inconclusive, but suggested, reasonably enough, that the characteristics of NiGa paralleled those of NiAl(5-11). That is to say that nickel antistructure atoms were the dominant defect in Ni(l+x) Ga(l-x), but that constitutional nickel vacancies for~d in N i ( l - x ) Ga(l+x) in a concentration necessary to give the required alloy composition. The more recent l a t t i c e parameter and density data of Donaldson and Rawlings(3) was interpreted to indicate the existence of constitutional nickel vacancies on both sides of stoichiometry, but, unfortunately, both investigations referred to above(l,3) reported pycnometric densities determined on bulk specimens. One of the present authors has emphasized the undesirability of using bulk material due to unavoidable solidification microporosity(lO,12,13), and certainly the s o l i d i f i c a t i o n range of NiGa is not negligible, being -8O°C for the stoichiometric alloy, and lesser and greater than this respectively for Ni-rich and Ga-rich alloys(14). Experimental Four alloys of nominal composition 49a/o Ga 51a/o Ni, 50a/o Ga 50a/o Ni, 51a/o Ga 49a/o Ni, 52.5a/o Ga 47.5a/o Ni were arc-melted and, after re-melting several times to promote homogeneity, were annealed for 7 days at 80O°C in argon. Chemical analyses of the resulting ingots gave 51.1, 49.8, 48.9 and 47.3a/o Ni. Samples for l a t t i c e parameter determination were crushed, sieved, and slowly cooled from 8OO°C in evacuated Vycor capsules. Samples for dilatometry were cut with a diamond wheel, hand-lapped, and f i n a l l y annealed as above. Dilatometric measurements were made using a Leitz Bollenrath-type dilatometer, and a l l l a t t i c e parameters, ambient and high temperature, were measured with a Unicam 19 cm. high temperature powder camera. Thermal Vacancies The plots of a l / l and aa/a vs temperature are shown in Figure l , al and aa referring to length and l a t t i c e parameter changes respectively. The deviation of the dilatometric and x-ray values at 400-500°C corresponds to the formation of an appreciable concentration of thermal vacancies, and the data can be analyzed to give the vacancy concentrations vs temperature(15). The results are given in Table l together with e a r l i e r data obtained by Wasilewski et al also using the Simmons-Balluffi analysis(2). The agreement between the data is very satisfactory. Constitutional Vacancies The l a t t i c e parameters (-21°C) determined in this investigation were: o

0

47.5a/o Ni, a = 2.8873 A; 49a/o Ni, a = 2.8942 ~; 5Oa/o Ni, a 2.8952 A; 51a/o Ni, a 2.8955 A;

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POINT DEFECTS IN NiGa

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The values are in good agreement with those of Seybolt and Westbrook(1), and the combined data were used to calculate the theoretical densities in Figure 2. Other l a t t i c e parameter data were presented only in graphical form(3), so that precise values at specific compositions are d i f f i cult to derive. The theoretical densities were calculated on the assumption that Ni-rich alloys contain only antistructure defects, but two curves were drawn for Ga-rich alloys, one representing f u l l site occupancy (antistructure defects only) and the other a NiAl type defect model. The pycnometric densities due to Seybolt and Westbrook(1) are also shown, and the shape of this curve suggests that NiGa might well contain antistructure defects and vacant nickel sites in Ni-rich and Ga-rich compositions respectively. The fact that the pycnometric density curve lies below the theoretical curve may be partly due to microporosity in the bulk samples used for pycnometric densities. However, that portion of the theoretical density curve which is based on the assumption of a NiAl type defect structure is in error, possibly to a considerable extent. This is because the usual assumption that x-ray l a t t i c e parameters are insensitive to vacancies is inappropriate in this particular case. As can be seen in Figure l , the slope of Aa/a is affected much more by thermal vacancies than is that of A l / l , and the concomitant relaxation around a vacant l a t t i c e site leads to uncertainty about the vacancy volume. Clearly, the constitutional vacancy concentration cannot be determined from pycnometric densities unless the vacancy volume is known. In passing, i t should be remarked that NiGa and NiAl are dissimilar in the above respect. This can best be seen via l a t t i c e parameters of quenched powders; the parameter of NiGa is grossly reduced by quenched-in thermal vacancies while that of NiAl is affected very slightly(16). I t follows that simple calculations of constitutional vacancy concentrations from pycnometric densities are meaningful for NiAl but not for NiGa. I t is for this reason that density measurements did not form part of the present study. Despite these d i f f i c u l t i e s in analyzing data, the qualitative evidence does not support the view of Donaldson and Rawlings(3) who postulate the existence of constitutional nickel vacancies in Ni-rich as well as Ga-rich alloys. The same authors calculated a theoretical curve of l a t t i c e parameter vs composition based on their density-derived defect model (nickel vacancies at a l l compositions) which agreed with their determined parameters. However, i t has already been noted that densities determined on bulk specimens are suspect, and in any event, an agreement between theoretical and determined l a t t i c e parameters is possible on the basis of a different defect model. For instance, i f only antistructure defects are assumed in Nirich alloys, the observed variation of l a t t i c e parameter withocomposition gives ~he following calculated nickel and gallium atomic diameters, DNi = 2.5265 A and DGa = 2.4875 A. I f the vacancy diameter is assumed to be given by Dv = 0.95 DNi (vacancy volume -86% atomic volume) the theoretical l a t t i c e parameter for vacancy - defective Ni(l-x) Ga(l+x) f i t s the experimental curve quite closely (Figure 3). Discussion A theoretical model due to Neumann, Chang and Lee(4) permits calculation of the vacancy concentration in B2 phases exhibiting t r i p l e defects, e.g. NiGa, from a c t i v i t y data. Such a calculation giving the compositional dependence of total vacancy concentration in NiGa at various temperatures is shown in Figure 4a. The t h ~ v a c a n c y concentrations (present study) are shown in the same diagram. I f , as suggested, constitutional nickel vacancies form only in Ni (_i x) Ga(l+x) to give. the required alloy composition, the concentration of these must be added to the concentration of thermal vacancies to give the equivalent of the theoretical curve due to Neumann et al(16). This result is shown in Figure 4b and the agreement between the curves is quite reasonable. I f the constitutional vacancy concentration according to Donaldson and Rawlings(3) (equation l of their paper) is subtracted from the thermodynamically derived total vacancy concentration (Neumann et a l ) , the difference (ostensibly thermal vacancies) is in poor agreement with the experimentally determined thermal vacancy concentrations reported by the present authors. This gives further indication that the defect structure of NiGa probably parallels that of NiAI.

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POINT DEFECTS

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TABLE 1 Thermal Vacancy Concentrations in NiGa

50a/o Ni

51a/o Ni

47.5a/o Ni

49a/o Ni

2.07x10-3

l .80xlO-3 5.19xi0 -3

2.70xl 0-3

600°C

7.71xlO-3

3.12xlO-3

700°C

5.5xlO-3

9.39xi0 -3

l . 19xl 0-2

8.28xi O-3

8.73xi0-3

I. 30xl 0-2

I. 56xi 0-2

l .15xlO-2

l.lOxlO-2

l .59xi0 -2

l .95xi0 -2

1.45xi0 -2

47a/o Ni 500°

800°C 900°C

*0.38xi0 -2

53a/o Ni

O.6xlO-3

*O.81xlO-2

* l . 3Oxl0-2 *Wasilewski et al(2); remalni ng data refers to present work. References 1.

A. U. Seybolt and J. H. Westbrook, Acta Met., 12, 449, (1964).

2.

R. J. Wasilewski, S. R. Butler and J. E. Hanlon, J. Appl. Phys., 19, 9, 4234, (1968). A. T. Donaldson and R. D. Rawlings, Acta Met., 24, 811, (1976).

3. 5.

J. P. Neumann, Y. A. Chang and C. M. Lee, Acta Met, 24, 593, (1976). A. J. Bradley and A. Taylor, Proc. Royal Soc., 159, (1937).

6. 7.

A. J. Bradley and A. Taylor, Phil. Mag., 23, 1049, (1937). A. J. Bradley and A. Taylor, Proc. Royal Soc. [A], 166, 353, (1938).

8.

M. J. Cooper, Phil. Mag., 8, 805, (1963).

9.

L. N. Guseva, Dokl. Akad. Nauk, SSSR, 77, 415, (1951).

lO.

R. A. Dodd and W. J. Helfrich, Acta Met., I I (8), 982, (1963). A. Taylor and N. J. Doyle, J. Appl. Cryst., 5, 201, (1972).

4.

11. 13.

R. A. Dodd and W. J. Helfrich, Trans. Met. Soc. AIME, 224 (4), 757, (1962). R. A. Dodd and W. J. Helfrich, Acta Met., 12 (5), 667, (1964).

14.

E. Hellner, Zeit. Metallk., 41, 480, (1950).

12.

15.

R. O. Simmons and R. W. B a l l u f f i , Phys. Rev., 125, 862, (1962).

16.

M. A. Quader and R. A. Dodd, unpublished research. Acknowledgement

The authors are pleased to acknowledge the support of the National Science Foundation through grant No. DMR 76-10175.

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POINT DEFF,CTS

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12

Vol.

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POINT DEFECTS

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Measured Lattice Parameters vs Calculated Parameters Based on Antistructure Defects in Ni(l+x) Ga(l_x% and Nickel Vacancies in

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FIG. 2 Parameter-derived Densities vs Pycnometric Densities of NiGa

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FIG. 4 Comparison of Thermodynamically Derived Vacancy Concentrations (Neumann et al) with Thermal Vacancy Concentrations (present study) in (a) and Thermal plus Constitutional Defects in (b).