  With density functional theory we have performed molecular dynamics
simulations of ZrC which displayed spontaneous Frenkel pair formation at a
temperature of 3200 K, some 500 K below the melting point. To understand this
behaviour, 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 quasi-harmonic 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.
