Lattice Thermal Conductivity

摘要: The lattice thermal conductivity for monatomic crystals is discussed high temperatures, above and around the Debye temperature. While this problem cannot be treated in a suitable way by conventional methods calculating transport coefficients, it represents an excellent example of use correlation-function techniques. By splitting total anharmonic interatomic potential into its diagonal nondiagonal contributions, $V={V}_{\mathrm{d}}+{V}_{\mathrm{nd}}$, effect equilibrium nonequilibrium properties crystal on can studied separately. current-current correlation function calculated to second order $V$ single-phonon-lifetime approximation. ${V}_{\mathrm{nd}}$ only contributes approximation space-time-dependent part function, ${V}_{\mathrm{d}}$ as well space-time-independent part. latter contribution ${{V}_{\mathrm{d}}}^{0}$ temperature-dependent Hartree determines lattice. At constant pressure gives rise expansion system, which causes decrease frequency with increasing temperature, resulting depression below $\frac{1}{T}$ behavior. Even case volume, temperature dependence phonon This again behavior leads ${T}^{2}$ term resistivity region taking account entire anharmonicity lowest atomic displacements. Thus Peierls' expression rederived terms renormalized group velocity due ${{V}_{\mathrm{d}}}^{0}$, rather than pure harmonic potential. dissipative mechanism given $V$, cancels partially conductivity. For temperatures just $\frac{1}{T}(1+\ensuremath{\alpha}T)$. With reaches minimum, followed steep one approaches dynamical instability system.