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| Content Provider | World Health Organization (WHO)-Global Index Medicus |
|---|---|
| Author | Baskaran, Arvind Ratsch, Christian Smereka, Peter |
| Description | Country affiliation: United States Author Affiliation: Baskaran A ( Department of Mathematics, University of California, Irvine, California 92697-3875, USA.); Ratsch C ( Department of Mathematics and Institute for Pure and Applied Mathematics, University of California, Los Angeles, California, USA.); Smereka P ( Department of Mathematics and Michigan Center for Theoretical Physics, University of Michigan, Ann Arbor, Michigan 48109, USA.) |
| Abstract | Some issues that arise when modeling elastic energy for binary alloys are discussed within the context of a Keating model and density-functional calculations. The Keating model is a simplified atomistic formulation based on modeling elastic interactions of a binary alloy with harmonic springs whose equilibrium length is species dependent. It is demonstrated that the continuum limit for the strain field are the usual equations of linear elasticity for alloys and that they correctly capture the coarse-grained behavior of the displacement field. In addition, it is established that Euler-Lagrange equation of the continuum limit of the elastic energy will yield the same strain field equation. This is the same energy functional that is often used to model elastic effects in binary alloys. However, a direct calculation of the elastic energy atomistic model reveals that the continuum expression for the elastic energy is both qualitatively and quantitatively incorrect. This is because it does not take atomistic scale compositional nonuniformity into account. Importantly, this result also shows that finely mixed alloys tend to have more elastic energy than segregated systems, which is the exact opposite of predictions made by some continuum theories. It is also shown that for strained thin films the traditionally used effective misfit for alloys systematically underestimate the strain energy. In some models, this drawback is handled by including an elastic contribution to the enthalpy of mixing, which is characterized in terms of the continuum concentration. The direct calculation of the atomistic model reveals that this approach suffers serious difficulties. It is demonstrated that elastic contribution to the enthalpy of mixing is nonisotropic and scale dependent. It is also shown that such effects are present in density-functional theory calculations for the Si-Ge system. This work demonstrates that it is critical to include the microscopic arrangements in any elastic model to achieve even qualitatively correct behavior. |
| File Format | HTM / HTML |
| ISSN | 24700045 |
| e-ISSN | 24700053 |
| Journal | Physical Review E |
| Issue Number | 6 |
| Volume Number | 92 |
| Language | English |
| Publisher | American Physical Society |
| Publisher Date | 2015-12-01 |
| Publisher Place | United States |
| Access Restriction | Open |
| Subject Keyword | Statistical and Nonlinear Physics many-body systems Condensed Matter Physics |
| Content Type | Text |
| Resource Type | Article |
| Subject | Statistics and Probability Statistical and Nonlinear Physics Condensed Matter Physics |
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