Showing papers in "Journal of Applied Crystallography in 1975"
TL;DR: In this article, a procedure for the determination of all reference intensities of interest simultaneously is presented, and the maximum standard deviation of the matrix-flushing method has been estimated to be 8% relative.
Abstract: A set of reference intensities, ki, are required for the quantitative interpretation of X-ray diffraction patterns of mixtures. Each ki was heretofore determined individually from binary mixtures of a one-to-one weight ratio. A procedure for the determination of all ki's of interest simultaneously is presented. The X-ray diffraction patterns of multicomponent mixtures usually contain overlapping peaks. This overlapping problem can be avoided by choosing an arbitrary reference material already present in the mixture and/or using the strongest resolved reflections directly. These concepts are substantiated by ten examples. The maximum standard deviation of the matrix-flushing method has been estimated to be 8% relative.
295 citations
TL;DR: In this article, a method for determining powder data from photographs is presented, where a microphotometer is used to measure the density in steps of 0.01° 2θ.
Abstract: A method is presented of determining powder data from photographs. With a microphotometer the density is measured in steps of 0.01° 2θ. These data are used by a computer program. With this program the background and the noise level are determined first. After the detection of the diffraction peaks, the peak positions and intensities are refined, a suitable model for the peak profile being used. A procedure is described for scaling of several photographs. The final results are illustrated with a comparison of 2θ values determined according to this method and the calculated values of the lattice refined with these data. The resulting data prove to be equivalent to the data obtained by conventional means. The computer program is written in FORTRAN IV.
207 citations
TL;DR: In this article, a main program for inspection and correction of the intensity data, and a number of subroutines covering specific operations are described, which can be called upon in any desired sequence.
Abstract: The program comprises a main program for inspection and correction of the intensity data, and a number of subroutines covering specific operations. These subroutines can be called upon in any desired sequence.
170 citations
TL;DR: A silicon powder standard reference material, SRM-640, has been prepared for use as a standard in powder diffractometry as discussed by the authors, which can be used to obtain accurate measurements of lattice parameters.
Abstract: A silicon powder Standard Reference Material, SRM-640, has been prepared for use as a standard in powder diffractometry. Powder diffraction measurements were performed with a tungsten internal standard and a high-angle goniometer. The measured a/λ is 3.525176. With λ(Cu Kα1 peak) taken as 1.5405981 A, a = 5.430880 (35) A, uncorrected for refraction. Comparison of a with values obtained with a single-crystal from one of the boules reveals a difference of 3 parts in 105. This difference suggests a subtle systematic error in powder diffractometry or a change in lattice spacing near crystal boundaries. Use of the SRM should permit individual measurements of lattice parameters to be made reproducible to near 1 part in 105 and an absolute accuracy of at least 3 parts in 105.
148 citations
TL;DR: The lattice constants of a diamond platelet and of large single, undoped, crystals of silicon and germanium have been determined from measurements of multiple diffraction patterns by the method described in Part I as discussed by the authors.
Abstract: The lattice constants of a diamond platelet and of large single, undoped, crystals of silicon and germanium have been determined from measurements of multiple diffraction patterns by the method described in Part I [Post (1975). J. Appl. Cryst. 8, 452–456]. The mean values, based on measurements of eight to twelve reflections, and their standard deviations are: diamond a = 3.566986 A, Aa/a = 2.6 × 10−6; silicon a = 5.430941 A, Aa/a = 2 × 10−6; germanium a = 5.657820 A, Δa/a = 1.6 × 10−6.
133 citations
TL;DR: In this paper, contamination-free TiNx was prepared and the lattice parameter (a0) -nitrogen content (x) relation determined and the result can be expressed as a0 = 4.1925 + 0.0467x (in A) in the range 0.605 ≤ x ≤ 0.999.
Abstract: Contamination-free TiNx was prepared and the lattice parameter (a0)–nitrogen content (x) relation determined. The result can be expressed as a0 = 4.1925 + 0.0467x (in A) in the range 0.605 ≤ x ≤ 0.999. Density measurement showed that no titanium vacancies existed in the lattice.
96 citations
TL;DR: In this article, a lattice-imaging technique is applied in a study of the intimate structure of non-graphitizing PVDC C atoms heat treated in the range 803 to 2973
Abstract: A lattice-imaging technique is applied in a study of the intimate structure of non-graphitizing PVDC C atoms heat treated in the range 803 K to 2973 K. Fine detail in the resulting electron micrographs indicates that the bulk material consists of a high proportion of intertwined crystallites comprising turbostratically packed aggregates of graphitic basal planes. Schematic models are presented incorporating the electron-microscope observations of this particular geometrical arrangement of ribbon-shaped layer planes which is thought to be responsible for the inhibition of recrystallization, i.e. graphitization at elevated temperatures. Evidence is presented which indicates that the structural transformation in PVDC differs from that of other non-graphitizing C atoms recently investigated. There is discussion of the structural factors which give rise to this effect.
84 citations
TL;DR: In this article, the feasibility of using synchrotron radiation for X-ray diffraction topography has been investigated, and the authors showed that the instrumentation required is far simpler for synchoretron radiation than for conventional sources.
Abstract: With almost perfect silicon crystals and cleaved lithium fluoride crystals as extreme examples, the feasibility of using synchrotron radiation for X-ray diffraction topography has been investigated. In both spatial resolution and strain resolution the synchrotron source diffraction topographs are competitive with topographs obtained using conventional X-ray sources but exposure times are reduced from several hours per cm2 to one second per cm2 using standard recording techniques with Ilford nuclear emulsions. Contrary to (the author's) expectations, the instrumentation required is far simpler for synchrotron radiation than for conventional sources.
75 citations
TL;DR: In this paper, it is shown that it is necessary to use an angle-dependent doublet separation within a given profile when performing an α2 elimination in X-ray diffraction line profiles.
Abstract: It is shown that it is necessary to use an angle-dependent doublet separation within a given profile when performing an α2 elimination in X-ray diffraction line profiles. Two formulations for the doublet separation are suggested, which give better results than the doublet separation as obtained from a differentiation of Bragg's law. One formulation has the important advantage of being a constant on a sin θ scale; the other formulation may serve as the basis for a computerized monochromator.
71 citations
TL;DR: In this article, the average defect size was estimated to be about 2000 µm in a double-crystal spectrometer close to Bragg reflections of about 2′′ halfwidth and a very noticeable asymmetry was observed with much higher intensities at the high-angle tail of the Bragg reflection.
Abstract: X-ray diffuse scattering has been observed in silicon crystals containing oxygen clusters. The crystals were initially dislocation free and the clustering was produced by a heat treatment at 950°C for 5 h. Since defect sizes are relatively large, measurements were made in a double-crystal spectrometer close to Bragg reflections of about 2′′ halfwidth. From the angular dependence of the diffuse scattering we estimate the average defect size to be about 2000 A. In addition a very noticeable asymmetry in the diffuse scattering was observed with much higher intensities at the high-angle tail of the Bragg reflection. Very marked changes in the intensity of the anomalous transmission of X-rays in silicon have previously been observed following similar treatment. The defects responsible for the observed anomalous transmission and diffuse scattering effects have been characterized by X-ray topography and electron microscopy. The asymmetry of the diffuse scattering observed is consistent with the direct determination of the interstitial nature of the defects produced after clustering.
68 citations
TL;DR: For screenless X-ray intensity-data films the setting angles of the crystal can be derived directly from cut reflections on these films, which means errors which arise by the transition from setting photographs to the intensity photograph are avoided.
Abstract: For screenless X-ray intensity-data films the setting angles of the crystal can be derived directly from cut reflections on these films. By this means errors which arise by the transition from setting photographs to the intensity photograph are avoided, and the accuracy of the calculated setting angles is typically better than 3′. Setting photographs are only necessary for initial and approximate alignment of the crystal.
TL;DR: In this article, the shape relationship between observed α1 and α2 components is used as a basis for eliminating the α2 profile, which can be applied to an on-line computer-controlled diffractometer to produce real time Cu Kα2-free diffraction patterns.
Abstract: The existence of the Kα2 lines in powder diffractograms has always obscured the interpretation of the diffraction patterns. Studies involving integrated intensity measurements, peak intensities and line broadening have been hampered owing to these extraneous lines. Crystal monochromators are ineffective for eliminating the Kα2 profile. This paper presents an algorithm which practically removes the Cu Kα2 profile. Previous procedures to remove the Kα2 line or resolve the Kα doublet assumed the shape of the α2 component to be identical to that of the a, component. The algorithm presented here uses the actual shape relationship between observed α1 and α2 components as a basis for elimination of the α2 profile. This algorithm has been applied to an on-line computer-controlled diffractometer to produce `real time' Cu Kα2-free diffraction patterns. The method is quite general and can be extended to remove the Kα2 lines of other radiations.
TL;DR: The cylindrical texture camera described in this paper employs a fiat specimen inclined to the incident X-ray beam, which, as in the above cases, is along the cylinder axis, and is capable of detecting and identifying very thin deposits and of characterizing the type of preferred orientation that may have occurred.
Abstract: X-ray diffraction cameras in which the diffraction pattern is recorded on a cylindrical photographic film coaxial with the incident beam have previously been used to make measurements of preferred orientations in polycrystalline materials by Kratky (1930), Wooster (1948), Mackay (1953) and Richards (1964). The diffraction cones of constant 20 intersect the recording film in straight lines. These may then be scanned with a linear densitometer to yield intensity distributions characteristic of the preferred orientation, allowing for the effects of X-ray absorption in the specimen. The uniaxial textures of continuously rotated drawn wires and graphite specimens, mounted normal to the camera axis, have been studied by Mackay (1953) and Richards (1964). The more complex moving-film method of Wooster (1948) has been used to plot the pole figures of rolled sheets. The cylindrical texture camera described here employs a fiat specimen inclined to the incident X-ray beam, which, as in the above cases, is along the cylinder axis. The camera is particularly applicable to the crystallographic examination of thin crystalline films deposited on flat substrates. It is capable of detecting and identifying very thin deposits and of characterizing the type of preferred orientation that may have occurred. For cases where orientation effects are not pronounced, consideration of the specimen absorption factors provides information about layer thickness and order of deposition when more than one layer is present.
TL;DR: A diffractometers control program is described which can be used without modification on all Picker Nuclear FACS-I diffractometer equipped with a DF-32 disk and provides a wide variety of preprogrammed data-collection options including an automatic crystal orientation checking algorithm which is described.
Abstract: A diffractometer control program is described which can be used without modification on all Picker Nuclear FACS-I diffractometer equipped with a DF-32 disk. The assembly language program provides a wide variety of preprogrammed data-collection options including an automatic crystal orientation checking algorithm which is described. The program is organized in semi-independent segments to facilitate modification and extension. Several laboratories currently use the program and documentation is available.
TL;DR: In this paper, the Fourier-transformed, long-range strain fields entering into the Huang diffuse scattering can be expressed in terms of the dipole force model, and in this work comparisons of calculations based on this model with measured scattering from spherical precipitates and dislocation loops in copper are reviewed.
Abstract: X-ray diffraction techniques provide powerful tools for the study of lattice defects in crystals. For the case of clustered defects, many of these techniques are based on the scattering properties of the strained regions surrounding the defects rather than on the scattering from the defects themselves. This is particularly true of Huang diffuse scattering, anomalous transmission, and lattice-parameter measurements; the interpretation of these measurements, therefore, relies on a detailed knowledge of the strains around the defects. The Fourier-transformed, long-range strain fields entering into the Huang diffuse scattering can be expressed in terms of the dipole force model, and in this work comparisons of calculations based on this model with measured scattering from spherical precipitates and dislocation loops in copper are reviewed. The use of integral diffuse scattering measurements, made with a two-axis diffractometer, are discussed in terms of a direct analysis of the defect systems in the form of defect concentrations and size distributions and this procedure is applied to the study of the effects of irradiation conditions and post-irradiation annealing on the defect distributions in neutron-irradiated copper. The relation of these diffuse scattering measurements to lattice parameter, anomalous transmission, electron microscopy and electrical resistivity measurement is also discussed.
TL;DR: In this article, the authors compared the diffracting-zone model with the direct-image mosaic model, and showed that the direct image mosaic model gives a reasonably good prediction of image widths measured at half peak height, but the widths in different reflections are not selfconsistent; in particular, images in lower-order reflections are significantly wider than those predicted by the model.
Abstract: Detailed measurements have been made of dislocation image widths in X-ray topographs taken under conditions of low absorption (product of linear absorption coefficient and crystal thickness, μt = 0.15) with a silicon specimen and Mo Kα radiation. These have been compared with two theoretical models, the `diffracting-zone' model involving computation of misorientation gradient contours, and the direct-image `mosaic' model using calculations of effective misorientation contours. Neither model completely explains the image widths. The diffracting-zone model, though theoretically more attractive, gives a very poor correlation, probably because of (a) severe photographic limitations and (b) the uncertainty in the reconstruction of the intermediary image in translation topographs. For a given reflection the direct-image mosaic model gives a reasonably good prediction of image widths measured at half peak height. However, the widths in different reflections are not self-consistent; in particular, images in lower-order reflections are significantly wider than those predicted by the model. This implies that contributions from interbranch scattering (giving an intermediary image component) are more important in lower-order reflections, and that such contributions are proportional to the widths obtained from misorientation (rather than misorientation gradient) contours.
TL;DR: In this paper, the authors used energy-scanning diffraction rather than the traditional angle scanning diffraction, which is inherently faster and less beset with problems of experimental instability than are angular scanning methods.
Abstract: Quantitative liquid-structure analysis using energy-scanning diffraction rather than the traditional angle-scanning diffraction is introduced. In the experimental method, white radiation and a solid-state detector are employed. This new method is inherently faster and less beset with problems of experimental instability than are angular-scanning methods. However, many differences in analysis are introduced. In particular, measurement of the primary beam spectrum, the nature of the absorption and dispersion corrections, details of the polarization correction, the ranges of the atomic scattering factor and of the incoherent scattering term, and the mating of different scattering regimes all require special consideration. Application of the new instrumental method and the reconstructed analytical procedure to liquid mercury at room temperature has produced a result in agreement with other recent studies.
TL;DR: In this article, a short introduction to the theoretical relations between experimentally observed diffuse scattering results and the desired information about defects is given, under which diffuse scattered X-ray intensity from defects can be distinguished from other diffuse intensities (thermal diffuse scattering, Compton scattering).
Abstract: This review gives first a short introduction to the theoretical relations between experimentally observed diffuse scattering results and the desired information about defects. The situation is discussed under which diffuse scattered X-ray intensity from defects can be distinguished from other diffuse intensities (thermal diffuse scattering, Compton scattering). A typical experimental set-up is described to show what the requirements are in experimental resolution and how intensity distribution in reciprocal space can be measured most conveniently. A few typical experiments are discussed to demonstrate the physical potential of this method for studying impurities in metals and radiation-induced defects and defect clusters in ionic crystals. Special emphasis is given to the comparison of the experimental results with theoretical predictions; the intensity close to the Bragg peaks (Huang scattering) falls off as 1/g2, g being the distance from a reciprocal-lattice point G. The scattering intensity goes as G2. The intensity distribution in reciprocal space gives typical isointensity curves from which the symmetry of the double force tensor and its components can be deduced. Together with the measured shift of a Bragg peak, measurement of absolute scattering intensity gives a unique way of determining the defect concentration. Further away from the Bragg peaks (asymptotic scattering) the intensity is proportional to 1/g4 and shows characteristic oscillations.
TL;DR: In this paper, it was shown that fringes are observed in bright-field images of thin polycrystals (t≲ 40A), but they disappear in thicker samples and are not observed in any of the Polk-model images.
Abstract: Kinematical electron microscope images to be expected from the Polk continuous random-network model and from a polycrystalline cluster have been computed. Dark-field images of both models show qualitatively similar speckle patterns. Fringes are observed in bright-field images of thin polycrystals (t≲ 40A), but they disappear in thicker samples and are not observed in any of the Polk-model images. The experimental observation of fringes therefore cannot be explained by the current theory, possibly because it does not take account of the angular spread of illumination. Except perhaps in very thin specimens, it seems impossible at present to draw any reliable conclusions about the local atomic arrangement in amorphous materials by simple examination of electron micrographs.
TL;DR: In this paper, the Debye-Scherrer X-ray diffraction technique was used to determine the lattice parameters and the linear coefficient of thermal expansion of f.c. β-Cu2−xSe (1.86 ≥ 2−x ≥ 1.72).
Abstract: The lattice parameters and the linear coefficient of the lattice thermal expansion of f.c.c. β-Cu2−xSe (1.86 ≥ 2−x ≥ 1.72) were determined by means of the Debye–Scherrer X-ray diffraction technique in the temperature range 25–336°C. The concentration and temperature dependence of the coefficient of thermal expansion are discussed. In addition the equilibrium phase diagram of the Cu–Se system in the region of a non-stoichiometric Cu2−xSe compound (2.00 ≥2−x ≥1.72) was redetermined, with special consideration of the homogeneity range of the f.c.c. β-Cu2−xSe, and compared with previously published results.
TL;DR: In this article, a model for the modification of the pair interaction energy between the atoms of a binary alloy due to the electron-ion interaction as modified by the electronelectron interaction, is developed to lowest order.
Abstract: The formalism for the modification of the pair interaction energy between the atoms of a binary alloy due to the electron-ion interaction as modified by the electron-electron interaction, is developed to lowest order. In a manner analogous to the treatment of Krivoglaz it is shown how the fluctuationdependent part of the alloy pair energy contains a contribution from e(q), the dielectric function for the alloy, which in turn reflects singularities at e(2kr), where kF is the Fermi wave vector. The strength of these singularities and their contribution to the diffuse scattering of radiation is discussed and recent experimental observations of several groups on 'imaging' the Fermi surface in this manner are presented.
TL;DR: In this article, the anisotropic structural evolution of ferrocene has been studied using X-ray powder diagrams in the range 15 to 295'k, by means of a prototype diffractometer and a high-efficiency cryostat.
Abstract: About fifty X-ray powder diagrams were recorded in the range 15 to 295 K, by means of a prototype diffractometer and a high-efficiency cryostat, so that a very precise study of the anisotropic structural evolution of ferrocene could be made. The cell parameters and volume have been computed. These parameters present a discontinuity at 164 K; the cell is triclinic below and monoclinic above this temperature. The transition is first order. The principal thermal expansion coefficients have been computed and their evolution, in terms of temperature, has been related to the anisotropic change of the intermolecular contacts in the crystal. Assumptions about the mechanism of transition and about the ferrocene configuration in the ordered phase are expressed.
TL;DR: In this article, an indirect method for the analysis of the outer atomic layers of thin films is proposed, in which the copper and silver layers typically proceed from an epitaxic growth on the gold (111) planes.
Abstract: From theoretical simulations, an indirect method entitled `sandwich stacking' has already been suggested for the analysis of the outer atomic layers of thin films. By means of a new suitable deposit (with the same material and the same thickness as the substrate) these outer foreign layers, if any, are embedded within a homogeneous film. When such stackings are analysed by X-rays at grazing reflexion (either specular or diffuse), a change in the interference-pattern contrast appears and provides a quantitative determination of the height distribution of foreign atoms. In this paper, the method is applied first to silver films exposed for a time at room temperature and secondly to multilayer films of the types Au–Cu–Au and Au–Ag–Au, in which the copper and silver layers typically proceed from an epitaxic growth on the gold (111) planes. In such an investigation the roughness of the various interfaces in the stacking must be taken into account and therefore a roughness model has been tested for X-ray specular reflexion from glass substrates (float-glass as delivered, or borosilicate crown glass optically polished) and also from gold or silver films evaporated on a glass substrate in an ultra-high vacuum.
TL;DR: In this paper, the root mean square deviation of the scattering density was 0.35 × 1010 cm−2 with respect to the mean value of 3.15 × 1.15 cm −2, and the mean saturation of native ferritin with iron was estimated to about 0.6.
Abstract: From the dependence of zero-angle scattering of polydisperse solutions on the scattering density of the solvent, information about the mean scattering density and the width of the scattering density distribution of different dissolved molecules can be obtained. This method has been tried with a commercial solution of native ferritin. The root-mean-square deviation of the scattering density was 0.35 × 1010 cm−2 with respect to the mean value of 3.15 × 1010 cm−2. From these data the mean saturation of native ferritin with iron is estimated to about 0.6 and the root-mean-square fluctuation of the iron contents of different ferritin molecules to about 0.4. The neutron scattering curves agree with the results from X-ray small-angle scattering.
TL;DR: The ambiguity in indexing of powder patterns is geometrical rather than accidental as mentioned in this paper, in which different lattices give calculated powder patterns with the identical number of distinct lines in identical 20 angular positions, but the number of planes contributing to each reflection may differ.
Abstract: There are cases in which different lattices give calculated powder patterns with the identical number of distinct lines in identical 20 angular positions. The number of planes (hkl) contributing to each reflection may differ, however. The lattices having this property are related to each other by transformation matrices with simple rational elements. The resulting ambiguity in indexing of powder patterns is, in these cases, geometrical rather than accidental.
TL;DR: In this article, single crystals belonging to a new modification of GeSe2 have been prepared by several methods and the measured density is 4.35±0.040 cm−3.
Abstract: Single crystals belonging to a new modification of GeSe2 have been prepared by several methods. This new form appears orthorhombic with parameters a = 7.037±0.30, b = 11.826±0.010, c = 16.821± 0.040 A and z = 16. The measured density is 4.35±0.040 g cm−3. The space group has not yet been determined because cutting thin X-ray samples from large as-grown crystals induces considerable cleavage.
TL;DR: In this paper, a matrix-inversion method for complete separation of diffuse X-ray scattering from a binary system AB is suggested for those cases in which the approximate equality of the Debye-Waller factors (DWF) of the individual atomic species indicates that some terms of the scattering equation may be neglected.
Abstract: The assumptions in the Borie & Sparks [Acta Cryst. (1971). A27, 198–201] procedure for the separation of order- and displacement-dependent components of diffuse X-ray scattering from a binary system AB are examined with the use of the concentration deviation (spin-like) notation. The more limiting assumption, that the structure-factor ratio η = (mAfA + mBfB)/(fA−fB) is constant in reciprocal space, is shown to produce an incomplete separation for normal variations in η. A matrix-inversion method for completing the separation is suggested for those cases in which the approximate equality of the Debye–Waller factors (DWF) of the individual atomic species indicates that some terms of the scattering equation may be neglected. The extension suggested by Ramesh & Ramaseshan [Acta Cryst. (1971). A27, 569–572] that anomalous dispersion induced changes in η could be used to separate the atomic static displacement properties of the various atomic pairs is shown to require a change in η greater than the variation of η across the reciprocal-space volume. Some difficulties of obtaining such a change are pointed out.
TL;DR: In this paper, a model with two kinds of stacking faults was proposed to explain quantitatively X-ray powder diffraction patterns of disordered kaolinites, where the first defect consists of random translations which limit coherent scattering regions in all hk directions except h = k = 0.
Abstract: By the use of a model with two kinds of stacking faults it is possible to explain quantitatively X-ray powder diffraction patterns of disordered kaolinites. The first kind of defect consists of random translations which limit coherent scattering regions in all hk directions except h = k = 0. The second kind consists of shifts between layers of ± nb/3 (n integer) which limit coherent scattering only in hk directions with k ≠ 3n. The comparison of calculated patterns with experimental (02,11) and (20,13) bands gives the proportions of different kinds of layer displacements in two disordered kaolinites.
TL;DR: The thermal expansion of cyclopentadienylthallium, TlC5H5, was determined in the range 78 to 295 K using X-ray powder diffractometry.
Abstract: The thermal expansion of cyclopentadienylthallium, TlC5H5, was determined in the range 78 to 295 K, using X-ray powder diffractometry. Expansion is very anisotropic: α1 = 125 ± 12, α2 = 97 ± 5, α3 = 0 ± 4 (all 10−6 K−1). Directions and ratio of the two greatest expansion coefficients: α1 and α2, are explained by considering the shortest distances Tl+–Tl|+ in this ionic structure.