Modeling of lattice parameter in the Ni-Al system
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9/27/04
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Modeling of Lattice Parameter in the Ni-Al System TAO WANG, JINGZHI ZHU, REBECCA A. MACKAY, LONG-QING CHEN, and ZI-KUI LIU Considering the effects of temperature and composition, a phenomenological description of lattice parameters in solid states was developed. The lattice parameter of the pure element is modeled under the assumption of a linear temperature dependence of thermal expansion, while the lattice parameters of substitutional solid-solution phases are treated similar to the Gibbs-energy modeling in the CALPHAD (CALculation of PHAse Diagram) approach. Using this model, the lattice parameters of the and phases in the Ni-Al system were analyzed and the model parameters were evaluated. The calculated lattice parameters and mismatches show good agreement with existing experimental data.
I. INTRODUCTION
THE lattice parameter and thermal expansion are two important material properties that are strongly correlated to many thermophysical properties. Because of their importance in both theoretical study and practical applications, a large number of studies have been done on this subject from many different points of view, using theoretical, experimental, and empirical approaches. The composition dependency of lattice parameters was modeled in various ways, such as elasticity theory, various potential approaches, and first-principle calculation, but none of them is very successful:[1] they are neither simple nor accurate enough. The most frequently used prediction of the lattice parameters across a solid solution was the linear relationship proposed by Vegard.[2] However, the investigations on metallic systems always show some deviations from Vegard’s law, because Vergard’s law is only valid when the electronic environment of both kinds of atoms is undisturbed by the formation of the solid solution, but, in reality, electrons in states just below the Fermi level can also participate in metallic bonding.[3] Due to the limited and scattered experimental data, the temperature effect on the lattice parameter is often overlooked, especially for multicomponent alloys. In many cases, such an effect is assumed to be small enough to be neglected or approximated by some arbitrary polynomials (the linear relationship is often suggested). However, such an assumption is seldom supported by the experimental results, except in a very narrow temperature region. In the present work, a simple phenomenological model is developed to describe the lattice parameters of solid-solution phases as a function of their composition and temperature. The temperature effect on the linear-expansion coefficient (L) of the pure element is considered first, and then the lattice parameters of pure elements are then calculated from the thermal expansion. The contribution from substitutional solute is treated using an approach similar to that used in TAO WANG, Ph.D. Student, JINGZHI ZHU, Postdoctoral Scholar, LONGQING CHEN, Professor, and ZI-KUI LIU, Associate Professor, are with the Department of Materials Science a
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