Atomic displacements in binary alloys

Molecular dynamics calculations are used to model the thermal and static displacements in copper and copper-gold alloys. Adjusted embedded atom potentials that give very accurate atomic sizes for the pure metals are used. The agreement with experiments supports the argument that this is a reliable approach for predicting displacements, and will be useful in interpreting experimental data on atomic displacements in metals and alloys. The positions of the atoms in a binary alloy at temperature $T$ at all times $t$,${\rm {\bf R}}_i \left( t \right)$, can be found using molecular dynamics (MD)\footnote{D. C. Rapaport, \textit{The Art of Molecular Dynamics Simulation}, \textbf{2}nd edition (Cambridge University Press, Cambridge, U. K., 2004)} if the forces on the atoms are known. It is still necessary to use supercells, but they can contain thousands of atoms. The set of ${\rm {\bf R}}_i \left( t \right)$ contains all the information about both static and thermal displacements. Of course, MD is a classical theory, and the only quantum mechanical effects appear in the construction of the forces.