WIAS Preprint No. 1131, (2006)

Determination of stiffness and higher gradient coefficients by means of the embedded atom method: An approach for binary alloys



Authors

  • Böhme, Thomas
  • Dreyer, Wolfgang
  • Müller, Wolfgang H.

2010 Mathematics Subject Classification

  • 74A15 74N05 74N25 82B20 82B26

Keywords

  • atomic potentials, crystals, elastic constants, higher gradient coefficients, phase diagram, diffusion, phase transformation, phase field theories

Abstract

For a quantitative theoretical description of phase separation and coarsening reliable data of stiffness constants and the so called Higher Gradient Coefficients (HGCs) are required. For that reason pair potentials of the Lennard-Jones type were used in [1] to provide a theoretical tool for their quantitative determination. Following up on this work these quantities are now calculated by means of the Embedded-Atom Method (EAM), a recently developed approach to describe interatomic potentials in metals. This is done, first, to achieve a better agreement between predicted and experimentally observed stiffness data as well as to avoid artifacts, such as the Cauchy paradox, and, second, to increase the trustworthiness of the HGCs for which experimental data are rarely available. After an introduction to the fundamentals of EAM it is outlined how it can be used for calculating stiffness constants and HGCs. In particular, Johnson's modification of EAM for nearest neighbor interactions [3] is applied to present explicit numerical results for a case study alloy, Ag-Cu, which has a ``simple" face-centered-cubic crystal structure and where it is comparatively easy to obtain all the required analysis data from the literature and to experimentally compare the predictions of mechanical data.

Appeared in

  • Contin. Mech. Thermodyn., 18 (2007) pp. 411--441.

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