Intensities Of X-ray Reflections Research Articles

Temperature dependence of X-ray reflection intensity from an absorbing perfect crystal near an absorption edge

The temperature effect of X-ray integrated reflection intensities is discussed theoretically in the energy region near the absorption edge of Ga in GaAs perfect crystal. From the calculation based on the dynamical theory of diffraction, it is concluded that the integrated intensity of {\bar 5}{\bar 5}{\bar 5} in the Bragg case shows a complicated temperature effect depending on the change of the anomalous scattering factor across the absorption edge. Calculated results are compared with a preliminary measurement which shows a qualitative agreement with the theory.

Increase of X-ray reflection intensities and profile widths at the low- to high-V3O5 phase transition state

An unexpected increase in peak intensity and profile half width has been observed in an X-ray diffraction experiment for many reflections from a crystal of V3O5 kept at its phase transition temperature. One explanation of the phenomena is that the ‘mosaic structure’ of the crystal is altered in the phase transition state, resulting in decreased extinction and increased profile widths. The results presented here are interesting spin off products of crystallographic studies of the mixed-valency oxide V3O5. The semiconductor low-V3O5 transforms in a first order transition at 155 °C into high-V3O5, which is a ‘poor metal’1. The transformation is instantaneous and reversible and implies that an ordered distribution of V(III) and V(IV) atoms is replaced by an only partially ordered distribution, the changes in the atomic positions being fairly small (≲0.1). These facts are based on the results of accurate X-ray crystal structure determinations of the two modifications at 25 °C (ref. 2) and 185 °C (ref. 3) respectively. We started diffraction measurements of V3O5 at or near the phase transition temperature tT, using the good temperature-control facility of the available non-ambient-temperature equipment4.

Polyoma Virion and Capsid Crystal Structures

X-ray diffraction shows that complete virus particles and empty capsids crystallize isomorphously. The surface morphology of the protein coat, as revealed by electron microscopy, is the dominant structural feature determining the intensity of x-ray reflections to a resolution of approximately 30 angstroms. The structure and variability of the viral chromatin core can now be analyzed by comparison of electron density maps.

Relationship Between New Structural Data on Clinoptilolite and Its Behaviour in Ion-Exchange and Heating

Abstract Low degrees of removal of K in ion-exchange as well as alterations of relative intensities of (0k0) X-ray reflections under heating have been found for clinoptilolite. These observations are in good accord with the newly provided structural data of clinoptilolite

An examination of five preferred orientation functions

Five functions for describing the preferred orientation of graphite-like materials were examined. Their relative behavior for various degrees of orientation were compared, particularly with respect to the ease of discriminating among them experimentally. The results obtained when data were fitted by a non-linear least squares method were used for a practical comparison. It was found that a constant term is required to allow for base line effects and some unoriented material. For careful evaluation of functions it is necessary to assume that the angle for maximum X-ray reflection intensity was set with some error. Among the five functions compared, the Bragg function fitted the comparison data best. However, if zero slope is required 90° away from the reference axis, this function is ineligible. In that case the Bacon and Ergun functions were equally good. Systematic trends in some of the data were related to sample preparation. The standard deviation for measuring the orientation parameter by fitting a function in this manner was from 0.4 to 3%.

The effect of grain size of the sample on the determination of the temperature and lattice defects factor by X-ray diffraction

The influence of the particle effect on the distortion of the temperature and lattice defects coefficcient 2M as determined from integrated intensities of X-ray reflections was investigated on three samples of tungsten carbide powders of various grain size. This distortion towards lower measured values can be considerable and for very coarse powder samples it can lead even to negative values of the coefficient 2M if its values are determined in the usual way, i.e. irrespective of the particle effect.

On the criterion of equal intensities in a high-precision Laue method for crystal orientation

The influence of the crystal surface orientation on the intensities of X-ray reflexions in Laue patterns is investigated in the kinematical approximation as well as in the framework of the dynamical theory. The results are used to discuss the limitation of the criterion of equal intensities in a high-precision method for crystal orientation.

An x-ray and Raman study of the diffuse transition in SrCl 2

The temperature dependence of X-ray scattering and Raman scattering in SrCl 2 to temperatures above the region of the diffuse transition is reported. The lattice parameter increases quite smoothly with increasing temperature; however the intensity of certain X-ray reflections changes drastically at temperatures above the transition region. The frequency of the Raman active vibrational mode decreases with increasing temperature. At high temperatures a background appears in the Raman spectrum which is attributed to Cl sublattice disorder.

A program for the calculation of X-ray reflection intensities, Part 2

The current work presents an exhaustively study on cooling rate-dependent yield behavior of Cu50Zr50 (at%) and Ni56Nb44metallic glass (MG) wires fabricated by a melt-extraction technique. After tension test, based on the measurement of the fracture angle, the yield behavior of the MG wires with different diameters is analyzed. Based on the Mohr-Columb criterion, the cohesion strength of the MG wires is evaluated. According to the free volume model, the cohesion strength of the MG wires is quantitatively predicted. The correlation between the yield behavior and the quantity of free volume in the glassy phase is elucidated.

On the cation distribution in the spinel systemyMg2TiO4−(1−y)MgFe2O4

The cation distribution and the oxygen parameter for the system Mg1+y Fe2(1−y) Ti y O4 have been determined using the intensities of X-ray reflections. Results are given for slowly cooled and quanched samples. An explanation is proposed to account for the behaviour of the lattice parameter and the oxygen parameter.

Study of the effect of the size distribution of the long periods in polymers on the width and intensity of the low angle X-ray reflections, by the light modelling method

The effect of the size distribution of the long periods in orientated polymers on the intensity and diffractional width of the low angle X-ray reflections has been studied by the method of light modelling. The results are in good qualitative and quantitative agreement with the results of calculations made previously.

The distribution of nickel ions among octahedral and tetrahedral sites in NiAl 2O 4MgAl 2O 4 solid solutions

The cation distribution in NiAl 2O 4 and in the solid solutions Ni x Mg 1− x Al 2O 4 with x ranging from 0.01 to 0.55 has been studied by X-ray analysis, magnetic susceptibility and reflectance spectroscopy. The relative X-ray intensities of various reflections for each compound were measured and compared with intensities calculated for various models of cation distribution. Lattice parameters, magnetic moments of Ni 2+, and the position of nickel absorption bands have also been measured. The results show that all specimens have a predominantly octahedral distribution for their nickel ions, and that there is a small change towards a random distribution when the quenching temperature is increased from 1273 to 1673°K. Both X-ray and magnetic results show that the fraction, α, of Ni 2+ ions on tetrahedral sites varies with nickel content. For samples quenched from 1273°K, NiAl 2O 4 is 78% inverse, but between x = 1.0 and x = 0.25 the value of α decreases from 0.22 towards 0.1. Thus, the fraction of nickel on octahedral sites in the solid solutions is higher than in NiAl 2O 4. The effect is linked with an increase in Dq for the Ni 2+ ion. Below x = 0.25, there is tentative evidence that α may increase. In nickel-dilute solutions the matrix as a whole is nearly normal, and it is suggested that Madelung energy may then be more effective in counteracting the octahedral stabilization of nickel. The same trend is observed in the specimens quenched from 1673°K.

X-ray study of anharmonicity in AuGa2

Au${\mathrm{Ga}}_{2}$ has been studied extensively in recent years because of its rather surprising temperature-dependent Knight shift and magnetic susceptibility. To gain some information on its vibrational properties we have measured the temperature dependence of the integrated x-ray intensities of various Bragg reflections from 300 to 625\ifmmode^\circ\else\textdegree\fi{}K. We have detected the anharmonic anisotropic Ga atom vibration. The ratio of the anharmonic to harmonic potential coefficients for the Ga atom is about half that of other ionic fluorite compounds. The vibrational mean-square amplitudes of Au and Ga are found to be equal to within experimental error, while in other fluorite compounds these relative amplitudes differ by 50%. The temperature dependence of the x-ray intensities was found to be anomalously large. To fit the data a conventional quasiharmonic treatment would require a Gruneisen parameter ${\ensuremath{\gamma}}^{\ensuremath{'}}=4.6$ which is more than twice the value expected from measured expansion coefficients, specific heat, and bulk modulus. We show that this large value of ${\ensuremath{\gamma}}^{\ensuremath{'}}$ is most likely associated with the ${C}_{11}\ensuremath{-}{C}_{12}$ shear modulus which appears to be both volume and temperature dependent. This temperature dependence is shown to be consistent with the thermal depopulation of the high density of states just below ${\ensuremath{\epsilon}}_{F}$ and is consistent with the high-temperature Knight-shift behavior.

A program for the calculation of x-ray reflection intensities

Title of program: FIREFLY II Catalogue number: AAQB Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland (see application form in this issue) Computer: ICL 4–70; Installation: U.K.A.E.A., Risley, U.K. Operating system: 7J Programming language used: FORTRAN IV High speed storage required: 138K bytes. No. of bits in a byte: 8 Is the program overlaid? No No. of magnetic tapes required: 1 What other peripherals are used? Card-reader, line-printer No. of cards in combined program and test deck: 2680 Card punching code: EBCDIC

Investigation of changes in the intensity of small-angle X-ray reflection from oriented fibres resulting from grafting to it another polymer as a new method of evaluating the density of intra-fibrillar amorphous regions

Investigation of changes in the intensity of small-angle X-ray reflection from oriented fibres resulting from grafting to it another polymer as a new method of evaluating the density of intra-fibrillar amorphous regions

Dependence of press-formability of aluminum sheets on crystallographic textures of sheets and cast slabs

Aluminum sheets having different textures were prepared from the castings, of which the crystallographic orientations were three dimensionally controlled by means of unidirectional growth of growth twin, columnar and equiaxed crystals. The sheet texture and the initial orientation of the casting significantly affected the Lankford value, the earing and the limited drawing ratio.(1) The initial orientations transform into the rolling textures, {110} , {112} and n {123} or their mixture.The {110} rolling texture transforms into the {110} recrystallization texture and the {112} or the n {123} into the {001} .(2) The earing correlates with the texture. The coexistence of two types of textures results in the 45° earing. The {001} and the {110} texture produce the 0°-90° earing. (3) A hyperbolic correlation exists between the X-ray reflection intensity of (200) planes and the Lankford value.(4) Positive and linear correlations are found between the earing and the planar anisotropy and between the deep-drawability and the normal anisotropy.It is suggested that press-formability depends on the final orientations, particularly the population of (200) planes which are further governed by the initial orientations of casting. The Lankford value is an effective parameter representing drawability.

X-ray topographic observation of 180° domains in ferroelectric Pb 5Ge 3O 11 single crystals

Antiparallel domains of ferroelectric Pb 5Ge 3O 11 single crystals were observed by the X-ray topographic method using {00,10} reflections. Reflected X-ray intensity from (00,10) plane or the positive end of P s appeared stronger than that from (00,ovbar|1ovbar|0) plane or the negative end of P s. These experimental results agree with the tendency of the calculated structure factors of | F(00,10) | and | F(00,ovbar|1ovbar|0) |.

X-ray investigation of recovery and aging in low-alloy sheet molybdenum

1. We measured the intensity of x-ray reflections as a function of annealing time at 13000 for grains with different orientations in samples of sheet molybdenum. 2. Grains with RP (111) have a higher rate of recovery and growth of regions of perfect lattice than grains with RP (001). 3. Carbides are precipitated in RP (111) grains earlier and in a shorter time than in RP (001) grains, which agrees with data on the cold hardening and growth rates of these grains. 4. The x-ray analysis showed that recrystallization of RP (111) grains occurs earlier.

Present problems and future opportunities in precise intensity measurements with single-crystal X-ray diffractometers

Considerable progress is foreseen toward the precise determination of integrated X-ray reflection intensities from small single crystals. High on the list of presently-limiting problems are multiple reflection, extinction, thermal diffuse scattering, unnecessary other background, counting statistics, effective integration and specimen change. Specific recommendations for equipment design and use are made which will partially alleviate each of them. Opportunities for better utilization of existing equipment through improved strategies for data collection and employment of small on-line computers are pointed out.

Investigation of the atomic vibration amplitudes in two alloys: silver-copper and gold-copper

The paper gives an account of the determination of the atomic vibration amplitudes in two alloys: silver-copper (409 at.% Cu) and gold-copper (AuCu3). It is found that the introduction of copper to the extent of 409 at.% into pure silver does not alter the inter-atomic binding forces of the silver atoms appreciably whereas the binding energy of the copper atom in the alloy is reduced to about 75% of its value in pure copper. Curves are given showing how the atomic root-mean-square displacement varies with temperature for copper in pure copper and in the alloy and for silver in pure silver and in the alloy. The second part of the paper is devoted to the determination of the characteristic temperature of the atom of `mean mass' in the gold-copper alloy AuCu3, and the study of the parallelism which exists in the changes with temperature that occur in the reflected X-ray intensity, the atomic r.m.s. displacement and the specific heat. The values of both the specific heat and the reflected X-ray intensity are governed by the extent of the atomic vibration. Increase of specific heat corresponds to a drop in the value of the characteristic temperature and a corresponding increase in the atomic r.m.s. displacement. Curves in the paper give information concerning the disappearance of long-range and short-range order amongst the atoms as the temperature is raised.