New Technique for AB Initio Atomistic Potentials and Application to Thermal Expansion of Ni/Cr Alloys
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NEW TECHNIQUE FOR AB INITIO ATOMISTIC POTENTIALS AND APPLICATION TO THERMAL EXPANSION OF Ni/Cr ALLOYS J. Mei, B.R. Cooper, Y.G. Hao, S.P. Lir, and F.L. VanScoy* West Virginia University, Department of Physics, Morgantown, WV 26506. *West Virginia University, Department of Computer Science, Morgantown, WV 26506.
ABSTRACT A scheme of developing ab initio many body potentials based on total energy calculations within density functional theory (DFT) is presented and demonstrated for transition metal alloys. An ab initio interatomic potential for Ni/Cr alloys is constructed with no input from experimental data. Molecular dynamics simulations have been performed to study thermal expansions. The coefficient of thermal expansion (CTE) has been calculated over a wide range of temperature, and good agreement is obtained between theory and experiment.
INTRODUCTION Nickel-based alloys have been extensively used in modern industries as high temperature structural materials. Thermal and mechanical properties of these materials are key factors of their high performance. Theoretical studies of thermal expansion of transition metal alloys have both basic scientific interest and strong industrial relevance, e.g. with regard to thermal compatibility at the interface between an alloy and its protective oxide scale or between an alloy matrix and a support in a composite. In this paper we will present a straightforward scheme for constructing interatomic potentials for transition metal systems starting from the generalized pseudopotential theory (GPT)[1]. The potential fitting is entirely based on total energy calculations within density functional theory (DFT)[2] using a spin polarized, full-potential linear combination of muffin-tin orbitals (LMTO) method[3]. A classical MD simulation has been performed on Ni/Cr alloys with fcc structure to study thermal expansion properties.
THE METHOD According to the Generalized Pseudopotential Theory (GPT)[l], we can write the total potential energy of a N particle system in the form
U = E(Q,{pn}) +
E V2(ra, rij{ P2}
1-
v3(ri,ri,rk,{p3})+"
(1)
where the prime in each summation denotes the exclusion of terms where two indices are equal. fl is the volume of the system and v,, is the n-body potential. {Pn}, {P2} and {P3} represent a set of adjustable parameters which are system dependent. This form is a complete representation of general interatomic potentials if all the n-body terms are properly included. However, it becomes extremely complicated going beyond 4-body term in practical calculations. Most applications stop only at the second or thii-d term in the above expansion. We first discuss the energy expansion for a pure metal, stopping at the second term, which we have applied to Ni/Cr fcc systems. Then we will discuss how one can fit an angle dependent potential by going to the third term of Eq.(1). Within the two term expansion, the total potential energy per unit cell, i, can be writen as
Mat. Res. Soc. Symp. Proc. Vol. 291. 01993 Materials Research Society
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where e(w) is the
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