MITSUKO ONODA, MASANOBU SAEKI AND ISAO KAWADA 957 easier than that of the fully occupied Ti layer. It is probable that the stacking faults which occur at a low temperature such as 683 K are due only to the slide between the sandwiches, and the experimental data shown in Fig. 1 should be interpreted appropriately on the basis of the extended model.Experimental patterns which suggest the occurrence of stacking faults are often observed for the various temperatures and compositions in the Ti-S system. The method of analysis of the structure with stacking faults described above may be effectively used for considering the phase-relation problem in this system. The effect of dynamic deformation on the Debye-Waller factor of silicon and, to a slightly lesser extent, the other three elements, is investigated. The Debye-Waller factor for the shells only in the the shell models is calculated. The effect introduced by dynamic deformation whereby the Debye-Waller B value varies with scattering vector K is evaluated. Finally, the anisotropic Debye-Waller factor components for the bond charges are calculated for all four elements. It is found that the bond charges in the bond-charge model and the shells in the shell model vibrate substantially less than the main atomic cores. It is concluded that if the models are at all realistic then the effects of dynamic deformation on the Debye-Waller factors of these elements should be seriously considered.

Equations of motion are derived for a shell model in which the shells are allowed to deform. Dispersion curves are then calculated for NaF, NaCl, NaBr, and Nal from measured dielectric, infrared, and elastic constants. A comparison with published phonon frequencies shows that a simple model with radial deformation gives some improvement over a rigid-shell model. A rather more general treatment with increased radial deformation produces even better curves. However, the LO (0,0,1) zone-boundary phonons are not well represented by either model. The eigenvectors from the rigid-shell model and from the best deformableshell models are then used to work out the ionic form-factor changes in NaCl when (0,0,??) phonon states are excited, and the corresponding changes in the x-ray one-phonon cross sections along the (0,0,1) axis are obtained. It is found that the rigid-shell model gives small variations in the cross sections resulting from the displacements of the shells, and that the radial deformations give additional changes. The models predict the occurrence of asymmetries in x-ray scattering, but the intensity differences are an order of magnitude less than the effects which have been observed. Further calculations with the inclusion of deformation of the inner electrons are required.

Measurements of x-ray diffuse scattering by phonons in three alkali halides show that the usual scattering theory which assumes rigid ions is not adequate. The generalization of the theory to account for the deformation of the ions is given, and leads, in the case of x-ray scattering, to intensities consistent with those observed. The new terms in the scattering are due to the x-ray Raman effect. The measurements indicate that for NaCl a change of about 2% in the scattering factor of the negative ion occurs for a 0.1 A change in the distance of its nearest-neighbor ion. It is shown that the core-shell displacements of the shell model are too small to explain the observed magnitude of the deformation, and that changes in the radial charge density of an ion are required.

Uranium dioxide is an antiferromagnetic below 30.8 "K. It has been suggested that there may be a displacement of the uranium ions associated with the magnetic phase transition. X-ray measurements show that provided the antiferromagnetic domains are sufficiently large (severa! hundred A ) a possible uranium movement in the (loo> directions is less than 0.0076 A.Urandioxid ist unterhalb 30,s K antiferroniagnetisch. Es wurde vermutet, da13 mit dem magnetischen Phasenubergang eine Verschiebung des Uranions verknupft ist. Rontgenitntersuchungen zeigen, dag unter Voraussetzung genugend groBer antiferromagnetiseber Domanen (einige hundert A) die in (100)-Richtung mogliche Bewegung des Urans kleiiier als 0,0076 A ist. T a b l e 2 Data Tabulation _ _ _ __ X-ray reflection Bragg angle 0 Debye Waller factor exp ( Form factor fr, X-ray wavelength 1 Absorption coeff. p Crystal to receiving slit r Height of receiving slit t Width of receiving slit PI ~ ~--MU) 110 1 210 ll"36' 1 18'31' 0.995 0.987 [6] 80.0 1 73.0 1.542 . t 25.0 crn 0.65 cm 0.50 cm 0.67

Measurements of the absolute intensity of the x-ray thermal scattering from sodium fluoride crystals have been made at a representative set of positions in reciprocal space. The distribution of scattered intensity can be interpreted to give the ionic form factor dependence on neighbouring ionic positions during thermal motion. The simplest interpretation is a fractional change of the form factor of a negative ion with relative displacement of a nearest-neighbour positive ion, increasing with the magnitude of the scattering vector K. The measurements also give transverse and longitudinal phonon dispersion curves for the [1,0,0], [1,1,0] and [1,1,1] directions. The errors in the frequencies are small except for a few higher-frequency phonons. The slopes of the dispersion curves at low wave vectors suggest that the differences between the first- and zero-sound velocities are less than 3%.