Mean Field Study Of Point Defects In B2-NiAl
Point defects control many properties of technological importance in intermetallic compounds such as atomic diffusion, creep, hardness, mechanical properties and sintering. Farther, since intermetallic compounds are characterized by long range atomic order, the point defects in these compounds can be qualitatively different from those in pure metals and disordered alloys. In the present study, we have chosen β-NiAl for our point defect studies since it is a potential candidate for high temperature applications and a model system for the study of basic phenomena in ordered alloys. We have used a mean field formulation for studying point defect concentrations. The outline of the formulation is as follows: We divide the rigid, body centred cubic lattice into two interpenetrating cubic sublattices called α and j3 which are made up of the cube corners and body centres respectively. We write a generic free energy function (G) that involves the temperature T and the six sublattice occupancies viz., the A (Ni), B (Al) and vacancies (V) on the two sublattices α andβ. We use the constraints on the number of α and β sublattice sites viz., the number of α sublattice sites is equal to the number of β sublattice sites, to write G as a function of four of the six sublattice occupancies and T. We define three auxiliary parameters η1, η2 and η3 which correspond to the vacancy concentration, the differential B species population on the two sublatices (the chemical or atomic order), and the differential vacancy population on the two sublattices, respectively. We then rewrite G as a function of T, xB and ηi. The G can now be minimized with respect to the three auxiliary variables so that we recover the free energy (G) as a function of XB and T only. The formulation requires as inputs the Ni-Ni, Al-Al, Ni-Al, Ni-V and Al-V interaction energies in the nn and nnn shells. We have obtained the Ni-Ni, Al-Al and Ni-Al interaction energies from the effective pair potentials reported in the literature. For the Ni-V and Al-V interaction energies we have used a bond breaking model in which we have assumed that the Ni-V and Al-V interaction energies in the nnn shell to be zero. Using the above interaction parameters in our mean field formulation we have determined the concentrations of various types of point defects in β-NiAL We have specifically chosen the temperature range of 800 - 2000 K and the composition range of 45 - 55 atomic% Al. Our results can be summarised as follows: 1.The predominant defect in the stoichiometric alloy is a combination of an Ni-antisite defect and two vacancies on the Ni sublattice. 2.The Al-rich alloys of composition (50 + ∆) atomic% contain 2∆% vacancies;since the alloys are almost perfectly ordered, these vacancies predominantly occupy the Ni sublattice. Similarly, the Ni-rich alloys of composition (50 — ∆)atomic% contain ∆% Ni antisites. 3.Both the vacancies on the Ni sublattice (in Al-rich alloys) and Ni-antisites (in Ni-rich alloys) show negligible temperature dependence, and hence owe their origin to the off-stoichiometry. 4.In all the alloys, the Al-antisites have the lowest concentration (of the order 10-6 even at 2000 K) and the concentration of the vacancies on the β sublattice is the next lowest. Thus, our results support the view that β-NiAl is a triple defect B2 and, if we consider constitutional vacancies as those which have a little or no temperature dependence, there exist constitutional vacancies in Al-rich β-NiAl. This conclusion is in agreement with some of the experimental results. However, it must be pointed out that there is considerable disagreement among experimental results from different groups.