Interactions of Point and Extended Defects in Structural Intermetallics: Real-Space Lmto-Recursion Calculations
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sents the bulk material, and then boundary conditions relevant to the problem are simulated. For the embedded region, the effects of the electron density redistribution is described selfconsistently in the framework of the local density approximation and local charge neutrality within the atomic spheres of varying size is achieved. The perturbation of the remaining part of the cluster is taken into account approximately due to changes of structure constants under lattice deformations, but with LMTO potential parameters taken to be fixed as in the bulk. In the present work, all calculations were carried out in a basis of s, p and d states, for which, respectively, 10, 20 and 30 pairs of recursion coefficients were calculated. The procedure of Beer and Pettifor [7] was exploited for the correct termination of continued fractions. The second order Hamiltonian and exchange-correlation potential of von Barth and Hedin were used. RESULTS The precision of our implementation of the real space TB-LMTO-REC method and the self-consistency procedure employed was checked by calculating the equilibrium volume of pure NiA1. We found that the equilibrium lattice constant (a=2.824 A) is in good agreement both with experiment (2.887 A•)and with results of band structure methods (FP-LMTO a=2.839 A,[2], FLAPW a=2.810 A[8]). A 2% underestimation of the equilibrium lattice constant is typical for methods using the local-density approximation. We also found that the variations of recursion scheme parameters (cluster size from 1000 to 10000 atoms, length of continued fractions from 20 to 50, presence or absence of periodic boundary conditions) lead to less than 0.5 mRy changes in the self-consistent total energy, and do not change the position of theoretical equilibrium volumes. 0.4
'~ "- FLM•TO,'' S~supercell (12.5%)
' '
0.2-
0.04
single Impurity&.T-MORC X
-0.2-
"lTiV C•r Mn
ae N•i
Figure 1: Preferred site energies for TM impurities in NiA1 calculated by FLMTO and TB-LMTO-REC methods in supercell and single impurity approaches.
To better understand the mechanisms of solution strengthening in ordered alloys, the information regarding the crystallographic site occupancy of the ternary element is required. To verify the applicability of the method for preferred site energy evaluation, we calculated its values for transition metals (TM) from Ti to Ni modeled with a small 16-atom supercell, as was done previously by Medvedeva, et.al. [9] by the FLMTO method, which corresponds to a 12.5% impurity concentration. These supercells form a cubic cluster of 2000 atoms with periodic boundary conditions. The preferred site energy is determined as the difference between the total energies of supercells with additions in both sublattices and of pure Ni and Al metals in their structural forms having the lowest total energy. The results are presented in Fig. 1 in comparison with results of [9]. One can see the very good agreement between real space and band super-
cell results. According to our calculations, the site preference for Ti, V and Cr
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