Intrinsic thermal-resistive process of crystals: Umklapp processes at low and high temperatures

Three-phonon umklapp processes are considered as the main intrinsic thermal-resistive processes in the crystals. The splitting umklapp processes are considered as the important process in thermal-resistive processes at low and high temperatures. Based upon a two-dimensional model, the simplest possible model is constructed for umklapp process. Real computational expressions are provided using the data of a phonon-dispersion relation of the direction of the principal reciprocal-lattice vectors and the given lattice characteristics. To test the model, the calculations are compared with the existing data of the purest crystals of LiF and NaF.