Thermodynamic properties and stability of grain boundaries in metals based on the universal equation of state at negative pressure

Abstract

Adopting a free volume approach at negative pressure of the universal equation of state, the thermodynamic properties of unrelaxed grain boundaries are determined for f.c.c., b.c.c. and h.c.p. metals including the excess energy, excess enthalpy, the bulk modulus, the Grüneisen parameter and consequently, the excess entropy and Gibbs free energy. A mechanical instability of a grain boundary is predicted based on the Gibbs stability criteria at an excess volume of about 0.45, corresponding to a scaled atomic separation of 0.7. The calculations suggest that grain boundaries with an excess volume close to this mechanical instability condition are entropy stabilized and can become more stable than boundaries with small excess volume at elevated temperatures. Taking the entropy of sublimation as an upper limit of the grain boundary entropy in order to prevent an entropy catastrophe, this state is separated by the single crystal state at elevated temperatures by an energy barrier on the order of 1 eV.