PROMETHEUS is a Fortran IV program system for investigation of anharmonic thermal vibrations in crystals, using elastic X-ray or neutron data. Three different anharmonictemperature-factor equations can be used, one of them up to sixth-order terms. The corresponding probability densities and mean effective atomic potentials can be calculated. Programs for correction of isotropic thermal diffuse scattering and of isotropic and anisotropic extinction are included. Fast averaging of symmetrically equivalent reflections combined with extended reflection statistics is possible. Calculations of Fourier syntheses and their errors and of Patterson functions can be carried out and the corresponding contour maps can be plotted.

Die Kristallstrukturen von LiAlCl4 (Raumgruppe P21/c) und von NaAlCl4 (Raumgruppe P212121) wurden als Funktion der Temperatur untersucht. Die Intensitäten der Bragg‐Reflexe wurden mit Einkristallen auf einem Vierkreisdiffraktometer gemessen und zwar für LiAlCl4 bei 293, 326 und 364 K und für NaAlCl4 bei 293, 353 und 393 K. Die Abstände in den AlCl4‐Tetraedern bleiben nahezu konstant, die LiCl‐ und NaCl‐Abstände vergrößern sich im Mittel um 0,025 Å/100 K. Eine Veränderung der Besetzungswahrscheinlichkeiten der Li‐ oder Na‐Positionen wurde nicht beobachtet. Die Richtungen der größten Schwingungsamplitude der Li‐ und Na‐Atome (etwa 0,30 Å bei 293 K) weisen auf Flächen ihrer Koordinationspolyeder.

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IntroductionBragg intensities of fl-PbF 2 (with the cubic fluorite structure) have been measured in the step-scan mode up to sin 0/2 = 1-17/k -1 at 295, 461 and 625 K by X-ray diffraction: a = 5.925(2), 5.952(2), 5.982 (4)A, respectively; R = 0.013 for 103 reflections, 0.015 for 103 reflections, 0.018 for 106 reflections, respectively. The intensities were used for the refinement of anharmonic temperature factors up to third order for F-and up to sixth order for Pb 2+. The temperature-factor formalism was based on the GramCharlier expansion. The probability density function (p.d.f.) of the F-and Pb 2+ ions were calculated from the coefficients of the anharmonic temperature factors. fl-PbF 2 crystallizes in the fluorite structure type. It exhibits a high F-conductivity at medium temperatures. Furthermore, the F-ions show pronounced anharmonic thermal vibrations along the body diagonals. Similar observations have been made for several other fluorides. The anharmonic part of the thermal motion of the F-ions have been partly described by so-called split atoms or by a third-order temperature coefficient. Anharmonic thermal vibrations and ionic conductivity are closely related to each other. A discussion of these effects and a literature survey are given by Koto, Schulz & Huggins (1981).Only harmonic temperature factors have been applied to the lead ions in all of these investigations. Owing to the high point symmetry of the Pb 2~ atomic position only an isotropic temperature factor is allowed for the harmonic model. If anharmonic thermal vibrations are considered, temperature factors (temperature tensors) of order four and six are allowed. The coefficients of these tensors can be determined by least-squares refinements of Bragg intensities. A discussion of the

Die Al‐C1‐Ab‐ Stände in den AlCl4‐Tetraedern von NaAlCl4 (RG: P2 1212,) und LiAlCl4 (RG: P21/c) bleiben zwischen 293 und 393 bzw. 364 Knahezu konstant, während sich die Li‐Clund Na‐C1‐Abstände im Mittel um 0.025 Ä/ 100 Kvergrößern.