Spontaneous Frenkel pair formation in zirconium carbide

With density functional theory we have performed molecular dynamics simulations of ZrC, which displayed spontaneous carbon Frenkel pair formation at a temperature of 3200 K, some 500 degrees below the melting point. To understand this behavior, rarely seen in equilibrium simulations, we quenched and examined a set of lattices containing a Frenkel pair. Five metastable structures were found, and their formation energies and electronic properties were studied. Their thermal generation was found to be facilitated by a reduction of between 0.7 and 1.5 eV in formation energy due to thermal expansion of the lattice. With input from a quasiharmonic description of the defect-free energy of formation, an ideal solution model was used to estimate lower bounds on their concentration as a function of temperature and stoichiometry. At 3000 K (0.81 of the melting temperature) their concentration was estimated to be 1.2% per mole in a stoichiometric crystal, and 0.3% per mole in a crystal with 10% per mole of constitutional vacancies. Their contribution to heat capacity, thermal expansion, and bulk modulus was estimated.