  The impact of dispersion relations, anisotropy, and Brillouin zone structure
on intrinsic phonon scattering rates has been assessed within the harmonic
approximation-perturbation theory approach for lattice dynamics. Anisotropic
nonlinear elastic continuum has been considered with various levels of
representation of phonon dispersion and Brillouin zone shape, and with
Gr\"uneisen parameter used as an average measure of crystal anharmonicity. In
addition, thermal conductivity prediction of different models for the treatment
of the off-diagonal elements of phonon collision operator are compared. For a
model system, argon, with a relatively high anisotropy ratio, the results show
that accounting for anisotropy is critical for accurate determination of
available phase space for 3-phonon scattering and scattering rates. Moreover,
widely spread approximations such as isotropic continuum and Single Mode
Relaxation Time are found unreliable, even for cubic systems. The success of
these approximations is demonstrated to be a direct result of error
cancellations. By benchmarking against our iterative solution of Boltzmann
Transport Equation, which achieves excellent agreement with experimental
thermal conductivity data for solid argon (2-80 K), we show the essential
importance of considering coupling terms of phonon scattering kernel at phonon
mode level, and not in a statistical average sense as, for example, Callaway
model does. Moreover, our results manifest the role played by coherent phonon
scattering near the melting temperature, in agreement with molecular dynamics
findings, which serves as an evidence for the crossover between heat diffusion
mediated by particle-like phonons (incoherent scattering) and wave-like heat
propagation due to phonon coherent scattering. Furthermore, sensitivity of
conductivity prediction to phonon spectrum is revealed to change over
temperature.
