A fast computer program written in Fortran is presented. It calculates with a trial-and-error method the unit-cell dimensions from the d values obtained from powder patterns. The special techniques used in this program to keep the computation time short are described. The program itself is designed primarily for triclinic and orthorhombic lattices. Monoclinic lattices are treated like triclinic ones: for tetragonal, hexagonal and rhombohedral structures orthorhombic cells can be calculated.
A method for finding the unit cells from the d values of powder patterns of monoclinic substances is described. An appropriate computer program based on this method is developed and combined with an already existing program [Kohlbeck & H6rl, J. Appl. Cryst. (1976), 9, 28-33] which has treated monoclinic cells as triclinic. In this way, calculation times are obtainable for monoclinic cells approximately five times shorter than those obtained with the previous program alone.
There has been considerable theoretical interest in the effect of boundaries on lattice vibrations of monatomic and diatomic crystals/"^ Free boundaries cause two distinct types of surface modes in diatomic crystals, which are in some respects similar to the localized modes of crystals containing defects. The first type has acoustical character and is analogous to the Rayleigh waves in continua. The second type is derived from the optical branch and has no analog in continua.In comparison with the theoretical efforts, only little experimental work has been performed on this subject. Comparative measurements of the Debye-Waller factor^>^ and the specific heat*^'^ of bulk samples and microcrystals of a few metals and simple compounds were the only experiments which could be found in the literature. To the authors' knowledge no attempts have ever been made either to gain information about the dependence of the frequency spectra on the grain size of the substances by inelastic neutron scattering or to detect optical surface modes by infrared techniques.In the following, inelastic neutron-scattering experiments will be reported which were performed on crystalline samples of magnesium oxide with various grain sizes in order to get information about the change of the frequency spectrum due to surface effects. From experimental as well as theoretical points of view, magnesium oxide was chosen as a sample material. It exhibits mainly heteropolar character of binding, a high Debye temperature, and a high neutron-scattering cross section. Furthermore, there exist convenient techniques to produce microcrystals in several ways.In the experiments described below, a set of four different MgO samples was used whose properties are summarized in Table I. The samples were examined by electron-microscope as well as x-ray methods. The inelastic neutron-scattering spectra were taken on a conventional rotating-crystal spectrometer^'^° at an angle of 100° with a primary neutron energy of 22.2 meV. The samples were heated during the scattering experiments up to a temperature of 800°K in order to make negligible the contribution of adsorbed gases and water vapor. The thicknesses of the samples were chosen in such a way that the transmissions were kept between 88 and 94%, so that multiple scattering did not have to be considered.The phonon frequency distributions were derived from the scattering data by means of the incoherent approximation using the formulas given by Sjolander^^ and Marshall and Stuart.^ In the computations, second-order down-scattering overlap, multiphonon events, detector efficiency, and instrumental resolution were taken into account.The applicability of the incoherent approx-Table I. Sample properties. Sample designation MgO-10% MgO-5 % MgO-1%
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