Phase Diagram of Ni-Pt from Linear Muffin-Tin Orbitals Total Energy Calculations

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PHASE DIAGRAM OF Ni-Pt FROM LINEAR MUFFIN-TIN ORBITALS TOTAL ENERGY CALCULATIONS C. AMADOR, W. R. L. LAMBRECHT and B. SEGALL Case Western Reserve University, Physics Department, Cleveland, OH 44106-7079

ABSTRACT Progress in the calculation of the phase diagram of the Ni-Pt compounds from "first-principles" is reported. Our procedure consists of: (1) calculating total energies for ordered structures as a function of volume and including internal relaxations by means of the linear muffin-tin orbitals method within the atomic sphere approximation; (2) mapping these results onto an Ising model with effective interaction parameters; and (3) calculating the phase diagram by means of the cluster variation method. We identify the elastic energy related to the difference in the Ni and Pt lattice constant as one of the major problems in this system and discuss the convergence of the cluster expansion of the energy. INTRODUCTION The multiple scattering theory based linear muffin-tin orbitals (LMTO) method [1] combined with the density functional theory [2] in the local density approximation (LDA) allows for fast and accurate calculation of the band-structure and total energy of a periodic solid. The relative ease of carrying out these calculations for a large number of structures opens the possibility of calculating thermodynamic properties such as the temperature-composition phase diagram of an alloy. The other fact that makes this approach a realistic possibility is the existence of accurate solutions of the statistical mechanical Ising model for an ordered lattice, namely the cluster variation method (CVM) of Kikuchi [3]. The success of the CVM in reproducing observed phase diagrams can be seen in the metallic Ni-Pt alloy. The use of three empirically adjusted interaction parameters (for two, three, and four bodies) resulted in close agreement with the observed portion of the phase diagram [4]. The question is, however, whether these parameters can be obtained from first-pinciples calculations. The connection between the calculated energies of formation, AE', for a structure o and the effective n-body interaction parameters, J,, needed in the Ising model is given by the cluster expansion formula [5]

Z

00

AEa = E,(Va) -

zaEA(VA)

-

4E"(VB) =

,

(1)

n0O

where IT' are the structure dependent correlation coefficients. The specialization of Eq. (1) to the particular set of five fcc structures consisting of the pure elements, the 1:3 and 3:1 compounds in the L1 2 crystal structure and the 1:1 compound in the L1 0 structure has become known as the Connolly-Williams (CW) method [6]. COMPUTATIONAL DETAILS The total energies were calculated using the LMTO method in the atomic sphere approximation (ASA) including the combined correction term [1]. The real space calculation of the structure constants in the tight-binding representation of the LMTO are calculated in a relatively large cluster containing -,60 neighbors in order to ensure adequate convergence. This was found to be important, in particular for the energies of the