Path-integral approach to anharmonic vibration of solids and solid interfaces

The temperature dependence of EXAFS (extended X-ray absorption fine structure) cumulants was investigated for bulk Cu and a thin film of Cu by means of the path-integral effective classical potential method. By using the semi-empirical embedded-atom method as a potential, agreement between the experiments and calculations is found to be excellent for bulk Cu. In the thin Cu(111) film, anisotropic anharmonic vibration was clearly observed; the out-of-plane vibration is much more enhanced and more anharmonic than the lateral vibration. The results are semiquantitatively consistent with the previous experimental data on Cu(111)/graphite. Such a vibrational enhancement should be the driving force for the roughening transition and/or the surface pre-melting at higher temperature. The practical usefulness of the path-integral effective classical potential method combined with the embedded-atom method is demonstrated.