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An analytical treatment of decomposition of the phonon thermal conductivity of a crystal with a monatomic unit cell is developed on the basis of a twostage decay of the heat current autocorrelation function observed in molecular dynamics simulations. It is demonstrated that the contributions from the acoustic short-and long-range phonon modes to the total phonon thermal conductivity can be presented in the form of simple kinetic formulas, consisting of products of the heat capacity and the average relaxation time of the considered phonon modes as well as the square of the average phonon velocity. On the basis of molecular dynamics calculations of the heat current autocorrelation function, this treatment allows for a self-consistent numerical evaluation of the aforementioned variables. In addition, the presented analysis allows, within the Debye approximation, for the identification of the temperature range where classical molecular dynamics simulations can be employed for the prediction of phonon thermal transport properties. As a case example, Cu is considered. IntroductionIt is well known that the thermodynamic and transport properties of a crystal lattice can be generally described using the concept of phonons (lattice vibrations or lattice waves) [1][2][3]. For example, the temperature dependence of the lattice heat capacity can be well accounted for within the harmonic approximation of the lattice vibrations by the Debye model [1]. In particular, the Debye model, in accordance with experiment, predicts that at high temperatures T [ T D (T D ¼ hx D =k B is the Debye temperature, x D is the Debye frequency -the highest allowed phonon frequency in the crystal, ℏ is the Planck constant divided by 2π, and k B is the Boltzmann constant), the lattice heat capacity can be approximated by the classical value C % 3Nk B =V (N is the number of atoms in the crystal volume V), which is known as Dulong and Petit value; whilst at low temperatures T \T D the lattice heat capacity starts to decrease (following C ∼ T 3 law at T ( T D ) which is a reflection of quantum effects on the phonon population [1].

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The phonon-mediated contribution to the thermal transport properties of liquid NiAl alloy is investigated in detail over a wide temperature range. The calculations are performed in the framework of equilibrium molecular dynamics making use of the Green-Kubo formalism and one of the most reliable embedded-atom method potentials for the intermetallic alloy. The phononmediated contribution to the thermal conductivity of the liquid alloy is calculated at equilibrium as well as for the steady state. The relative magnitude of the thermal conductivity decrease induced by the transition to the steady state is estimated to be less than 2% below 2000 K and less than 1% at 3000 and 4000 K. It is also found that the phonon-mediated contribution to the thermal conductivity of the liquid alloy can be accurately estimated (well within 1%) on the basis of an approximation which invokes the straightforwardly accessible microscopic expression for the total heat flux without demanding calculations of the partial enthalpies needed for the precise evolution of the reduced heat flux (pure heat conduction). On the basis of these calculations, the correspondence between the experimentally observed and modelled kinetics of solidification due to a difference in thermal conductivity is discussed.

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