Elastic properties and stacking fault energies of Cr 2 Ta Suklyun Hong*, C.L. Fu, M.H. Yoo Metals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6114, USA Dedicated to Dr. Gerhard Sautho on the occasion of his 60th birthday Received 22 March 1999; accepted 25 March 1999 Abstract The elastic moduli, stacking fault and twin boundary energies of C15 Cr 2 Ta are calculated by ®rst-principles local-density-func- tional approach. Similarly to the case of Cr 2 Nb, Cr 2 Ta is characterized by a low twin boundary energy (33 mJ/m 2 ). On the other hand, the intrinsic and extrinsic stacking fault energies are found to be 88 and 83 mJ/m 2 , respectively. Using the results of elastic constants and stacking fault energies, we predict the equilibrium separation between Shockley partials. The results of Cr 2 Ta are compared with those of Cr 2 Nb. # 1999 Elsevier Science Ltd. All rights reserved. Keywords: A. Laves phase; B. Elastic properties 1. Introduction Cr 2 Ta is one of Laves phase compounds, which have attractive properties such as high-melting temperature, low density, and high oxidation resistance for structural applications. Mainly due to low temperature brittleness, this potential has not been well exploited. To understand the brittle fracture behavior and deformation mechanism, we need to know some basic properties such as elastic constants and stacking fault energies (SFEs),  SF , since these are important factors that control deformation processes such as dislocation dissociation, cross-slip, and twin formation. In this paper, we present the theoretical predictions of elastic moduli, and stacking fault and twin boundary energies of Cr 2 Ta. Using the results of elastic constants and stacking fault energies, we also predict the equili- brium separation between Shockley partials. These results of Cr 2 Ta are compared with those of Cr 2 Nb, which was studied in our previous papers [1,2]. 2. Elastic properties Total-energy calculations for C15 Cr 2 Ta were per- formed using the full-potential linearized augmented plane-wave (FLAPW) method within the local-density approximation. The FLAPW method solves the local- density-functional equations without any shape approximation to the potential or charge density. The atomic positions were relaxed by calculating Hellmann± Feynman forces acting on the atoms. The theoretical lattice constant 6.809 A Ê of C15 Cr 2 Ta was obtained, which is in good agreement with the experimental lattice constant 6.985 A Ê [3]. Next, we cal- culated the elastic constants. Similarly as in Ref. [1], three independent elastic constants (C 11 ; C 12 , and C 44 ) are determined from three relations of the energy den- sity U: (i) U  C 11  C 12  e 2 for e 1 e 2  e, (ii) U  C 11  C 12  e 2 for e 1  e 2  e, and (iii) U  1 2 C 44 e 2 for e 6  e, where e i 's are the strain components, by ®tting the calculated values to third-order polynomials. The results are shown in Table 1: C 11 and C 44 of Cr 2 Ta are larger than those of Cr 2 Nb, while C 12 is rather close to that of Cr 2 Nb. The dierence in the elastic constants at theoretical and experimental volumes is due to the lat- tice anharmonicity. In order to compare the elastic moduli of polycrystals, we calculate bulk, shear and Young's moduli of C15 Cr 2 Ta. To our knowledge, there has been no published experimental measurements on the elastic moduli. Table 2 shows the Hill's averages of elastic moduli of Cr 2 Ta, along with those of Cr 2 Nb. The Hill's average is the arithmetic mean of the Voigt average and Reuss average [1]. The elastic moduli of Cr 2 Ta are larger than those of Cr 2 Nb, which is consistent with the fact that Cr 2 Ta (2020  C [4]) has a higher melting point than Cr 2 Nb (1730  C [5]). 0966-9795/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S0966-9795(99)00039-4 Intermetallics 7 (1999) 1169±1172 * Corresponding author; present address: Department of Physics, Sejong University, Seoul, Korea.