A method is presented whereby the amplitude coefficients of molecular normal modes of vibration are treated as independent variables in the treatment of thermal effects in X-ray diffraction, and applied to the bovine pancreatic trypsin inhibitor, form II (P212121, a = 74.1, b = 23.4, c = 28.9 A). It is shown that the description of molecular motion furnished by 892 isotropic temperature factors may be largely reproduced using only 19 molecular thermal parameters from which anisotropic temperature factors may be synthesised for every atom. The method shows that motions and/or disorders external to each molecule are the largest single source of apparent motion, and that the internal motions are comparable to those predicted by Levitt, Sander & Stern [J. Mol. Biol. (1985). 181, 423-427] at 300 K.

On the use of normal modes in thermal parameter refinement: theory and application to the bovine pancreatic trypsin inhibitor

UO2(C2H3O2)2·2H2O reacts with AX or A(C2H3O2 or ClO4) (where A = Li, Na, K; X = Cl, Br) and crown ethers in HCl or HBr aqueous solutions to give the sandwich-type compounds [K(18-crown-6)]2[UO2Cl4] (1), [K(18-crown-6)]2[UO2Br4] (2), [Na(15-crown-5)]2[UO2Cl4] (3), [Na(15-crown-5)]2[UO2Br4] (4), [Li(12-crown-4)]2[UO2Cl4] (5), and [Li(12-crown-4)]2[UO2Br4] (6). The compounds have been characterized by single-crystal X-ray diffraction, powder diffraction, elemental analysis, IR, and Raman spectroscopy. The [UO2X4]2- ions coordinate to two [A(crown)]+ cations through the four halides only (2), through two halides only (3), through the two uranyl oxygens and two halides (3, 4), or through the two uranyl oxygen atoms only (5, 6). Raman spectra reveal νU-O values that correlate with expected trends. The structural trends are discussed within the context of classical principles of hard−soft acid−base theory.

Coordination Trends in Alkali Metal Crown Ether Uranyl Halide Complexes: The Series [A(Crown)]2[UO2X4] Where A = Li, Na, K and X = Cl, Br

The physical properties of mixed crystals of alkali halides are reviewed. The properties considered are experimentally determined quantities like the lattice constants, the compressibility, the elastic constants, thermal expansion, specific heats, Debye-Waller factors, dielectric constant, refractive index, IR spectra and Raman spectra and also some calculated solid-state parameters like Debye temperatures and lattice energies. A critical analysis of composition dependence shows four groups designated as follows: Type A, properties which vary linearly with composition; Type B, properties which vary slightly non-linearly with composition; Type C, properties which depend highly non-linearly on composition with the values for mixed crystals exceeding the values for end members; and Type D, properties which are peculiar to the mixed crystals and are not shown by the parent crystals. Most of the physical properties belong to Types A or B. Variation of Type C is shown only by properties affected by differences in ion size like the Debye-Waller factor and the microhardness. Properties which are symmetry-dependent like the first-order Raman spectrum and the IR spectra are of Type D. Attention is drawn to areas where further work is needed.

Physical properties of mixed crystals of alkali halides

The reactions of UO(3) with acidic aqueous chloride solutions resulted in the formation of two new polymeric U(VI) compounds. Single crystals of Cs(2)[(UO(2))(3)Cl(2)(IO(3))(OH)O(2)].2H(2)O (1) were formed under hydrothermal conditions with HIO(3) and CsCl, and Li(H(2)O)(2)[(UO(2))(2)Cl(3)(O)(H(2)O)] (2) was obtained from acidic LiCl solutions under ambient temperature and pressure. Both compounds contain pentagonal bipyramidal coordination of the uranyl dication, UO(2)(2+). The structure of 1 consists of infinite [(UO(2))(3)Cl(2)(IO(3))(mu(3)-OH)(mu(3)-O)(2)](2-) ribbons that run down the b axis that are formed from edge-sharing pentagonal bipyramidal [UO(6)Cl] and [UO(5)Cl(2)] units. The Cs(+) cations separate the chains from one another and form long ionic contacts with terminal oxygen atoms from iodate ligands, uranyl oxygen atoms, water molecules, and chloride anions. In 2, edge-sharing [UO(3)Cl(4)] and [UO(5)Cl(2)] units build up tetranuclear [(UO(2))(4)(mu-Cl)(6)(mu(3)-O)(2)(H(2)O)(2)](2-) anions that are bridged by chloride to form one-dimensional chains. These chains are connected in a complex network of hydrogen bonds and interactions of uranyl oxygen atoms with Li(+) cations. Crystal data: 1, orthorhombic, space group Pnma, a = 8.2762(4) A, b = 12.4809(6) A, c = 17.1297(8) A, Z = 4; 2, triclinic, space group P1, a = 8.110(1) A, b = 8.621(1) A, c = 8.740(1) A, Z = 2.

Aqueous reactions of U(VI) at high chloride concentrations: syntheses and structures of new uranyl chloride polymers.

The Debye-Waller factors of polycrystalline As, Sb and Bi, obtained by neutron diffraction in the temperature range of 5K up to almost the melting point, are compared with lattice dynamics model calculations and results from X-ray and Mossbauer effect measurements. Within experimental accuracy the thermal motions appear to be isotropic and almost harmonic except for Bi at high temperatures. Moreover, the temperature dependence of the lattice constants and the positional parameter z were determined.

https://iopscience.iop.org/article/10.1088/0022-3719/11/6/011/pdf

Debye-Waller factor and thermal expansion of arsenic, antimony and bismuth

Accurate measurements were made to determine the Debye temperature and Debye-Waller factors for powder ZnTe by the method of elastic neutron diffraction, using a triple-axis neutron spectrometer. Measurements were made with neutrons of wavelength 1.17 A and corrections were made for the thermal diffuse scattering. The values of the Debye-Waller factors are BZn = 1.26 (5) and BTe = 0.74 (5) A2. The mass-weighted mean value \bar B is 0.91 (5) A2 which corresponds to a Debye temperature Θ = 198 (5)K. The results are in good agreement with the values determined by Cooper, Rouse & Fuess [Acta Cryst. (1973), A29, 44-56] using single-crystal neutron diffraction techniques.

Debye–Waller factors and Debye temperature of ZnTe

The temperature factor of silicon has been determined by the powder neutron diffraction technique employing a double-axis neutron diffractometer. A neutron wavelength of 1.184 A was used in the experiment. The sample used was a fine powder of silicon of purity 99.999%. The correction to the observed intensities due to thermal diffuse scattering (TDS) was not applied as the neutron velocity of 3.34 km s-1 (corresponding to neutron wavelength of 1.184 A) is less than the minimum velocity of sound in this crystal. The B value obtained from these experiments was found to be 0.45 (2) A, corresponding to a mean-square vibrational amplitude of 0.017 (2) A2 and to a Debye temperature of 531 (11) K at the sample temperature of 284 K at which the experiment was performed.

Temperature factor of silicon by powder neutron diffraction

The neutron diffraction pattern of powdered KCl has been measured using the triple-axis spectrometer both in the double-axis and the triple-axis modes. The thermal diffuse scattering (TDS) correction, which is very important in the double-axis pattern, is essentially eliminated in the triple-axis mode. Theoretical calculations are presented which give the relative TDS correction for the two cases by calculating the energy distribution of TDS. The Debye-Waller coefficient B using the triple-axis data is found to be (2.17 ± 0.16 A2), which is in agreement with the TDS-corrected values of other workers.

Debye–Waller coefficient of KCl by the powder neutron diffraction method

The Debye-Waller parameter B of KBr has been determined by triple-axis neutron diffraction with a powder sample. Calculations have also been made to find the contributions of TDS to the diffraction peaks obtained by this technique and they were found to be negligible as expected. The B value thus found is 2.33 ± 0.09 A2.

Q. H. Khan

Papers

Debye–Waller factors and Debye temperature of ZnTe

Temperature factor of silicon by powder neutron diffraction

Debye–Waller coefficient of KCl by the powder neutron diffraction method

The Debye-Waller factor of KBr by powder elastic neutron diffraction

Concentration Dependence of the Debye Temperature for the KxRb1−xF System