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THE magnitude and sign of the lattice mismatch between the c (fcc) and the c¢ (L12) phases are important parameters affecting the microstructure evolution and creep strength of Ni-base superalloys. For example, the sign of the lattice mismatch dictates the orientation of the c¢ precipitates under an external stress field, and the magnitude of lattice mismatch has a strong effect on the morphology of the c¢ particles. Lattice parameter data are typically obtained experimentally by diffraction measurements (X-ray, neutron, etc.). They are usually scattered because of their sensitivity to the details of alloy processing.[1] Those uncertainties may sometimes even lead to a change in the sign of the lattice mismatch. Recently, we[1] proposed a phenomenological model to describe the lattice parameter of an alloy as a function of temperature and composition. In particular, it was applied to Ni-Al binary alloys, and a self-consistent lattice parameter database was constructed. The model parameters were evaluated using a large amount of experimental data. However, in general, the availability of experimental data on lattice parameters of alloys is very limited. Very often there are poor agreements among experimental data from different sources. As a result, extracting modeling parameters based on experimental data alone can be difficult. In the last decade, the quality of first-principles calculations of electronic and structural properties has improved considerably. For most cases, the reliable TAO WANG, Post Doctorate, LONG-QING CHEN, Professor, and ZI-KUI LIU, Professor, are with theDepartment of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802, USA . TAO WANG, Post Doctorate, is with the Department of Materials Science and Engineering, Iowa State University, Ames, IA 50011, USA . Contact e-mail: [email protected] Manuscript submitted June 27, 2006. Article published online April 11, 2007. 562—VOLUME 38A, MARCH 2007

formation energy of alloys and compounds and band structures can be calculated at 0 K. In this article, we use the first-principles approach to fundamentally understand local and macroscopic lattice distortions caused by various solute additions in the c phase of Nibase superalloys, and the purpose of this work is to establish a computational approach for predicting the effect of alloying elements on lattice parameters. Ten commonly used alloying elements in Ni-base alloys were chosen, namely, Al, Co, Cr, Hf, Mo, Nb, Re, Ru, Ta, Ti, and W. The goal is to predict the lattice parameter changes in fcc-Ni binary and multicomponent alloys as a function of temperature and composition. The results will be compared with available experimental measurements. II.

FIRST-PRINCIPLES CALCULATIONS

The first-principles calculations of the lattice parameter were performed using the Vienna ab initio simulation package VASP (version 4.6),[2] which allows one to minimize the total energy with respect to the volume and shape of the cell and the positions of atoms within the cell. In