The thermal diffuse scattering (TDS) of X-rays in the anharmonic one-phonon and harmonic two-phonon approximations is considered. The complete expression for the one-phonon intensity of X-rays is derived by perturbation theory and presented for a polyatomic crystal in the high-temperature limit. The method of evaluating the corrections of the X-rays intensities for the thermal diffuse scattering is given and the importance taking into account the anharmonic effects in the one-phonon scattering for KZnF,, CsCl, and YBa,Cu,O, crystals at room temperature is discussed. Anharmonic TDS-effects achieve considerable magnitudes for soft (acoustic) anharmonic crystals as CsCI.PaCCMOTpeHO TenJIOBOe AH@@y3HOe PaCCeXHAe PeHTreHOBCKHX JIyYeg B aHrapMOHHYeCKOM OnHO-(POHOHHOM I4 rapMOHHYeCKOM ABYX(POHOHH0M n p~6 n~~e~n f l x .c IIOMOUIbK) TeOpUU BO3MYlLleHHG

The effect of anharmonic atomic vibrations on the elastic scattering of X-rays by a crystal is treated by time-independent perturbation theory. The complete expression for the anharmonic temperature factor (TF) in the high-temperature limit is presented for atoms in general positions. The phonon-phonon interactions in an anharmonic crystal may be identified with X-ray diffraction data by using various temperature and scattering vector q dependencies of different anharmonic contri-butions to the TF. The expression for the intensity of elastic scattering by an anharmonic crystal contains an additional factor -the anharmonic cross-term. This term has to be taken into account for obtaining the unbiased thermal parameters of fourth order in | q | from X-ray diffraction data.