STRUCTURAL CALCULATIONS OF OXIDE SURFACES AT FINITE-TEMPERATURE

An Einstein-like approximation for phonons is presented and used to estimate the free energy of ionic crystals at finite temperatures. The long-range Coulomb forces in these materials correlate the motion of the ions so that the local modes correspond to the vibrations of embedded layers. The thermal expansion of bulk oxides can be efficiently calculated using these modes and is found to be in good agreement with lengthier calculations that use the full phonon spectrum. The model can also be applied to defect structures with two-dimensional symmetry which are normally inaccessible to the harmonic approximation due to computational limitations. Results of calculations on a (100) rocksalt surface are presented. The local modes reflect the symmetry of the surface and are sensitive to variations of the ionic locations in the surface region. This model provides a reasonably accurate and efficient method of studying surface relaxation with temperature.