Lattice dynamics studies of grain boundary structures: II. Thermodynamic functions

The change in the atomic vibrational frequency spectrum of an fcc crystal due to the presence of a grain boundary is obtained by lattice dynamics methods. The grain boundary is a 36.9° 〈100〉 symmetric tilt coincidence boundary. An orthorhombic computational cell of 58 atoms containing two such boundaries of opposite rotational sense is employed. The atomic interactions are simulated by a Morse potential developed by Cotterill and Doyama to fit aluminum. From the changes in frequency spectrum the excess thermodynamic functions of the grain boundary are calculated and compared with results from both experiment and the Einstein model. The general shift of frequencies toward lower values is probably due to the weaker binding of many atoms near the boundary, while there are some higher frequency states associated with a few more tightly bound atoms.