Intergranular segregation and vibrational effects: A local analysis

Abstract

The segregation vibrational entropy is computed for the main sites of the $\Sigma =5\mathrm{}$ (310) 〈001〉 tilt grain boundary for the Cu(Ag) system described by N-body potentials. This is obtained by using the recursion method to evaluate the local density of vibrational states in the harmonic approximation on one hand and in the homogeneous and inhomogeneous quasiharmonic approximation on the other hand. Moreover the local harmonic method (or Einstein model) is also applied in order to determine the accuracy and range of applicability of this method. The results indicate that the segregation vibrational entropy is very inhomogeneous, being a large contribution to the segregation Gibbs free energy for a particular site of the grain boundary plane and being negligible for the other sites. The Einstein method leads to unreliable results, whereas the harmonic approximation significantly underestimates the segregation vibrational entropy, even at intermediate temperature.