scholarly journals Mean Square Vibration Amplitudes in Zinc

1977 ◽  
Vol 30 (1) ◽  
pp. 105 ◽  
Author(s):  
DW Field
Keyword(s):  
Single Crystal ◽  
Debye Temperature ◽  
Mean Square ◽  
X Ray Diffraction ◽  
Zinc Single Crystal ◽  
X Ray ◽  
Structure Factors ◽  
Principal Directions ◽  
The Mean ◽  
Integrated Intensities

The structure factors of 98 independent reflections have been determined by measurement of the integrated intensities for X-ray diffraction from a zinc single crystal at 295 K. The mean square vibration amplitudes found for the two principal directions are' compared with 'other recent measurements. The X-ray Debye temperature determined from the data' is 207 � 3 K at 295 K.

Dynamic and Static Displacements of Atoms in B2-Phase of TiNi Alloy

2008 ◽  
Vol 59 ◽  
pp. 108-112
Author(s):  
Vyacheslav M. Gundyrev ◽  
Vitaly I. Zel'dovich
Keyword(s):  
Single Crystal ◽  
Crystal Lattice ◽  
Titanium Nickelide ◽  
Tini Alloy ◽  
Mean Square ◽  
Atomic Displacements ◽  
Structure Factors ◽  
The Mean ◽  
B2 Phase ◽  
Integrated Intensities

We measured integrated intensities of 26 reflections of the B2-phase of titanium nickelide single crystal and determined structure factors for these reflections. Based on the structure factors, mean squares of displacements of Ni and Ti atoms with respect to the crystal-lattice sites have been determined. After that we determined the mean squares of atomic displacements <u2>Ni and <u2>Ti in temperature range of existence of the B2-pase, at temperatures Т1=328 K and T2=376 K. We separated the mean squares of atomic displacements <u2>Ni and <u2>Ti into static and dynamic ones. The mean squares of dynamic displacements of Ni and Ti atoms are identical, but the mean square of static displacements is greater by a factor of 4.7 for Ni atoms than for Ti atoms. The Debye temperature calculated from the mean squares of displacements of Ni atoms is 360 K; that calculated for Ti atoms in a similar way is 390 K. The large value of complete atomic displacements in TiNi is due to static rather than dynamic displacements of atoms, mainly due to static displacements of nickel atoms.

Predicting some Effects of Lattice Vibrations on Proton Scattering Patterns

1970 ◽  
Vol 14 ◽  
pp. 1-10
Author(s):  
C. S. Barrett
Keyword(s):  
Temperature Factor ◽  
Lattice Vibrations ◽  
Proton Scattering ◽  
Mean Square ◽  
X Ray Diffraction ◽  
X Ray ◽  
Structure Factors ◽  
Integrated Intensity ◽  
The Mean ◽  
Thermal Vibrations

AbstractA method of predicting the approximate relative intensities of lines in proton blocking patterns recently proposed, which is based on summing the squares of structure factors for the various orders of reflection of a plane, is found to predict certain effects of lattice vibrations on the lines in some recently reported patterns. The mean square amplitude of vibration enters the calculations through a Debye-Waller temperature factor like that used in X-ray diffraction. When patterns are compared for groups of crystals that are nearly identical except for this temperature factor, the qualitative predictions by this method agree with the observations. If it is also arbitrarily assumed that the integrated intensity dip at a spot where lines intersect is approximated by summing the calculated Integrated intensity dips for all of the lines crossing at the spot, one has a simple and convenient method of predicting relative spot intensities. Such calculations have been successful in establishing the order of decreasing intensity for most of the spots along a given line, with several different kinds of crystals. This method also serves to predict qualitatively how prominent the spots appear relative to the lines, in general, in patterns of crystals that differ appreciably only in the amplitude of the thermal vibrations.

Isomorphous replacement in electron diffraction of wet crystals of rat hemoglobin

1983 ◽  
Vol 41 ◽  
pp. 446-447
Author(s):  
William F. Tivol ◽  
Murray Vernon King ◽  
D. F. Parsons
Keyword(s):  
Electron Diffraction ◽  
Heavy Atom ◽  
Isomorphous Substitution ◽  
X Ray Diffraction ◽  
Salt Solutions ◽  
X Ray ◽  
Isomorphous Replacement ◽  
Structure Factors ◽  
Diffraction Structure ◽  
The Mean

Feasibility of isomorphous substitution in electron diffraction is supported by a calculation of the mean alteration of the electron-diffraction structure factors for hemoglobin crystals caused by substituting two mercury atoms per molecule, following Green, Ingram & Perutz, but with allowance for the proportionality of f to Z3/4 for electron diffraction. This yields a mean net change in F of 12.5%, as contrasted with 22.8% for x-ray diffraction.Use of the hydration chamber in electron diffraction opens prospects for examining many proteins that yield only very thin crystals not suitable for x-ray diffraction. Examination in the wet state avoids treatments that could cause translocation of the heavy-atom labels or distortion of the crystal. Combined with low-fluence techniques, it enables study of the protein in a state as close to native as possible.We have undertaken a study of crystals of rat hemoglobin by electron diffraction in the wet state. Rat hemoglobin offers a certain advantage for hydration-chamber work over other hemoglobins in that it can be crystallized from distilled water instead of salt solutions.

scholarly journals Integration techniques for surface X-ray diffraction data obtained with a two-dimensional detector

2014 ◽  
Vol 47 (1) ◽  
pp. 365-377 ◽  
Author(s):  
Jakub Drnec ◽  
Tao Zhou ◽  
Stelian Pintea ◽  
Willem Onderwaater ◽  
Elias Vlieg ◽  
...  
Keyword(s):  
Reciprocal Space ◽  
Two Dimensional ◽  
X Ray Diffraction ◽  
Integration Methods ◽  
X Ray ◽  
Structure Factors ◽  
Integration Techniques ◽  
Intensity Map ◽  
Integrated Intensities ◽  
Surface Diffraction

This article proposes two integration methods to determine the structure factors along a surface diffraction rod measured with a two-dimensional detector. The first method applies the classic way of calculating integrated intensities in angular space. This is adapted to work efficiently with two-dimensional data. The second method is based on integration in reciprocal space. An intensity map is created by converting the detected intensity pixel by pixel to the reciprocal space. The integration is then performed directly on this map. A theoretical framework, as well as a comparison between the two integration methods, is provided.

(Ph4P)2 Mn2Br6 und (Ph3PCH2Ph)2Mn2I6 (Ph = C6H5) / (Ph4P)2Mn2Br6 and (Ph 3PCH2Ph)2Mn2I6 (Ph = C6H5

1988 ◽  
Vol 43 (2) ◽  
pp. 171-174 ◽  
Author(s):  
Siegfried Pohl ◽  
Wolfgang Saak ◽  
Peter Stolz
Keyword(s):  
Single Crystal ◽  
Diffraction Data ◽  
Unit Cell ◽  
Formula Unit ◽  
X Ray Diffraction ◽  
Triclinic Space Group ◽  
X Ray ◽  
Bond Lengths ◽  
The Mean ◽  
The Difference

(Ph4P)2Mn2Br6 (1) and (Ph3PCH2Ph)2Mn2I6 (2) were prepared from the reaction of manganese dihalide with the corresponding phosphonium halide in CH2Cl2.The structures of 1 and 2 were determined from single crystal X-ray diffraction data.Both compounds crystallize in the triclinic space group P 1 with one formula unit per unit cell.1:a = 998.1(1), b = 1005.7(1), c = 1313.3(2) pm, α = 108.51(1), β = 94.25(1), γ = 100.36(1)°.2: a = 1058.6(2), b = 1236.3(2), c = 1248.4(3) pm, α = 63.53(1), β = 74.15(1), γ = 74.65(1)°.The structures of 1 and 2 exhibit discrete, dimeric anions formed by the fusion of two identical tetrahedral-like units with a common halogen-halogen edge. The mean Mn-Hal bond lengths were found to be 251.8 pm (Mn-Br) and 272.2 pm (Mn-I). The difference between the bridging and terminal Mn-Hal bond lengths is about 12-13 pm in both compounds

Hitachiite, Pb5Bi2Te2S6, a new mineral from the Hitachi mine, Ibaraki Prefecture, Japan

2019 ◽  
Vol 83 (5) ◽  
pp. 733-739 ◽  
Author(s):  
Takahiro Kuribayashi ◽  
Toshiro Nagase ◽  
Tatsuo Nozaki ◽  
Junichiro Ishibashi ◽  
Kazuhiko Shimada ◽  
...  
Keyword(s):  
Single Crystal ◽  
New Mineral ◽  
Chemical Formula ◽  
X Ray Diffraction ◽  
Calculated Density ◽  
X Ray ◽  
Diffraction Peaks ◽  
The Mean ◽  
Ibaraki Prefecture ◽  
Symmetry Space

AbstractHitachiite, Pb5Bi2Te2S6, is a new mineral discovered in the Hitachi mine, located in the Ibaraki Prefecture of Japan. The mean of 21 electron microprobe analyses gave: Pb 52.01, Bi 23.06, Fe 0.69, Sb 0.17, Te 13.74, S 9.71, Se 0.54, total 100.04 wt.%. The empirical chemical formula based on 15 apfu is (Pb4.75Fe0.23)Σ4.98(Bi2.09Sb0.03)Σ2.12Te2.04(S5.73Se0.13)Σ5.86, ideally Pb5Bi2Te2S6. Synchrotron single-crystal X-ray diffraction experiments indicated that hitachiite has trigonal symmetry, space group P${\bar 3}$m1, with a = 4.2200(13) Å, c = 27.02(4) Å and Z = 1. The four strongest diffraction peaks shown in the powder X-ray pattern [d, Å (I)(hkl)] are: 3.541(35)(012), 3.391(59)(013), 3.039(100)(015) and 2.114(56)(110). The calculated density (Dcalc) for the empirical chemical formula is 7.54 g/cm3.The crystal structure of hitachiite has been refined using synchrotron single-crystal X-ray diffraction data, to R = 7.38% and is based on ABC-type stacking of 15 layers (five Pb, two Bi, two Te, and six S layers) along the [001] direction, and with each layer ideally containing only one kind of atom. The stacking sequence is described as Te–Bi–S–Pb–S–Pb–S–Pb–S–Pb–S–Pb–S–Bi–Te. The discovery of hitachiite implies that the minerals of the Bi2Te2S–PbS join might form a homologous series of Bi2Te2S·nPbS.

Variable-temperature single-crystal X-ray diffraction study of tetragonal and cubic perovskite-type barium titanate phases

2016 ◽  
Vol 72 (1) ◽  
pp. 151-159 ◽  
Author(s):  
Tomotaka Nakatani ◽  
Akira Yoshiasa ◽  
Akihiko Nakatsuka ◽  
Tatsuya Hiratoko ◽  
Tsutomu Mashimo ◽  
...  
Keyword(s):  
Single Crystal ◽  
Diffraction Study ◽  
Variable Temperature ◽  
Cubic Phase ◽  
X Ray Diffraction ◽  
Temperature Dependent ◽  
X Ray ◽  
M Phase ◽  
The Mean ◽  
Perovskite Type

A variable-temperature single-crystal X-ray diffraction study of a synthetic BaTiO3perovskite has been performed over the temperature range 298–778 K. A transition from a tetragonal (P4mm) to a cubic (Pm \overline 3 m) phase has been revealed near 413 K. In the non-centrosymmetricP4mmsymmetry group, both Ti and O atoms are displaced along thec-axis in opposite directions with regard to the Ba position fixed at the origin, so that Ti4+and Ba2+cations occupy off-center positions in the TiO6and BaO12polyhedra, respectively. Smooth temperature-dependent changes of the atomic coordinates become discontinuous with the phase transition. Our observations imply that the cations remain off-center even in the high-temperature cubic phase. The temperature dependence of the mean-square displacements of Ti in the cubic phase includes a significant static component which means that Ti atoms are statistically distributed in the off-center positions.

Single crystal X-ray studies of cation-deficient magnetite

1997 ◽  
Vol 212 (6) ◽  
Author(s):  
H. Okudera
Keyword(s):  
Single Crystal ◽  
Cation Vacancy ◽  
Site Preference ◽  
Mean Square ◽  
X Ray Diffraction ◽  
X Ray ◽  
Cation Deficiency ◽  
Octahedral Cation ◽  
Synthetic Magnetite ◽  
Cation Sites

AbstractSite preference of cation vacancy and the effect of cation deficiency on the structure parameters have been investigated for synthetic magnetite specimens by means of the single-crystal X-ray diffraction methods. The cation vacancies are selectively formed at the octahedral cation sites even in the specimen quenched from 1793 K. The effects of cation deficiency are found as increase of atomic mean square displacements and decrease of anisotropy in thermal motions of the octahedral site cations.

The crystal structure of galeite, Na15(SO4)5F4Cl

1975 ◽  
Vol 40 (312) ◽  
pp. 357-361 ◽  
Author(s):  
L. Fanfani ◽  
A. Nunzi ◽  
P. F. Zanazzi ◽  
A. R. Zanzari
Keyword(s):  
Crystal Structure ◽  
Single Crystal ◽  
Least Squares ◽  
Diffraction Data ◽  
Three Dimensional ◽  
Thermal Parameters ◽  
X Ray Diffraction ◽  
Cell Content ◽  
X Ray ◽  
Structure Factors

SummaryThe crystal structure of galeite from Searles Lake (California) has been determined by means of X-ray diffraction data on a single crystal. A possible structure was derived from that of schairerite on the basis of chemical and lattice analogies and was confirmed by comparison of the observed diffractometric structure factors with the calculated ones. The refinement was performed by least-squares methods employing isotropic thermal parameters and assuming that atoms related by translational pseudosymmetry exhibit equal thermal parameters. The final R value is 0·09. The cell content is 3[Na15(SO4)5F4Cl]; the space group is P31m The lattice dimensions are a 12·197(4)Å, c 13·955(10) Å The marked subcell has P3m1 symmetry and a 7·042Å, c 13·955 Å. The crystal structure of galeite consists of a three-dimensional framework, formed by coordination octahedra around Na+ ions, including tetrahedral holes with sulphur atoms at the centres. The three-dimensional framework can be considered built up by five octahedral sheets (seven sheets can be recognized in schairerite and six in sulphohalite). The very close analogies occurring in the structures of galeite and schairerite are discussed.

An energy-dispersive X-ray diffraction study of mean-square atom displacements in highly oriented pyrolytic graphite

1986 ◽  
Vol 19 (3) ◽  
pp. 200-201 ◽  
Author(s):  
T. H. Metzger
Keyword(s):  
Pyrolytic Graphite ◽  
Energy Dispersive ◽  
Mean Square ◽  
Highly Oriented Pyrolytic Graphite ◽  
X Ray Diffraction ◽  
Thermal Diffuse Scattering ◽  
X Ray ◽  
Integrated Intensity ◽  
The Mean ◽  
Thermal Diffuse

The measurement of the mean-square thermal displacement 〈u 2〉 of carbon atoms in highly oriented pyrolytic graphite (HOPG) in the hexagonal c direction is reported. Energy-dispersive X-ray diffraction (EDXD) has been used to study the integrated intensity of all Bragg reflections 004 through 0′0′14 as a function of temperature. It is demonstrated that the correction of the Bragg intensities due to thermal diffuse scattering contributions is very important for HOPG, when EDXD is used. The Debye temperature ΘD = 554 (30) K is obtained.

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