Showing papers in "Journal of Applied Crystallography in 1973"
TL;DR: In this article, the mean square of the electron-density gradient, 〈|grad η|2〉 in isotropic structures is shown to be proportional to the fourth moment of the SAXS intensity distribution in reciprocal space ∫s4I(s)ds, as well as to the second derivative of the correlation function in the origin.
Abstract: The mean square of the electron-density gradient, 〈|grad η|2〉 in isotropic structures is shown to be proportional to the fourth moment of the SAXS intensity distribution in reciprocal space ∫s4I(s)ds, as well as to the second derivative of the correlation function in the origin. In the case of two-phase structures with unsharp phase boundaries, these relations may be used to find the thickness E of the transition regions. As was shown by Ruland [J. Appl. Cryst. (1971). 4, 70–73] E can also be determined by analysis of the intensity in the tail of the SAXS pattern. This approach is used here to investigate the effect of E on the one-dimensional correlation function. In the application of both methods, separation of the SAXS intensity from the continuous background of liquid scattering constitutes a critical step. A procedure in which the background is represented by a curve of the type a + bsn, where n is an even number, is found to work well for a number of polymers.
299 citations
TL;DR: In this article, a general procedure for determination of the crystallinity in polymers from the X-ray diffraction pattern was developed by modifying the method described by Ruland [Acta Cryst. (1961), 14, 1180-1185] on two points.
Abstract: A general procedure for determination of the crystallinity in polymers from the X-ray diffraction pattern was developed by modifying the method described by Ruland [Acta Cryst. (1961), 14, 1180–1185] on two points. One of these modifications furthermore permits substantial reduction of the required number of experimental data without a serious loss of accuracy being involved.
274 citations
TL;DR: In this paper, an X-ray diffraction analysis has been performed on superlattice crystals which were grown epitaxically by alternately depositing GaAs and GaAs 0.5P0.5 layers on a gallium arsenide substrate.
Abstract: An X-ray diffraction analysis has been performed on superlattice crystals which were grown epitaxically by alternately depositing GaAs and GaAs0.5P0.5 layers on a gallium arsenide substrate. The periodic change of compositions causes a one-dimensional periodic lattice distortion along the direction of growth. The periodic lattice distortion gives rise to satellite peaks close to the Bragg reflections of the sphalerite-type lattice of gallium arsenide. Two models are employed to calculate the X-ray diffraction intensities: in one the lattice distortion is described by two longitudinal phonons with frequency ω = 0, in the other a periodic step function is used. The X-ray diffraction data obtained on two samples show that the two alternating layers of different composition are coherent and, therefore, constitute one single-crystal with its unit cell large (g 100 A) along the growth direction. From the fit of the two models to the data one can determine the period and amplitude of the lattice distortion, the relative thickness of the two layers and the size of the domains which diffract coherently. These parameters are discussed in relation to the physical growth conditions.
167 citations
TL;DR: The program presented here performs an automatic indexing of powder patterns by means of a trial-and-error method that has been optimized and presents a good flexibility.
Abstract: The program presented here performs an automatic indexing of powder patterns by means of a trial-and-error method. It has been optimized and presents a good flexibility. It can account for various additional information, known a priori. In addition, extensive error computations are included in it, leading to a good reliability, even with some incidental errors. Moreover its input and printout have been implemented so that the program can be easily used even by non-specialists.
134 citations
TL;DR: In this article, the electron-microscope technique of lattice imaging can be used to observe the structure of materials directly, and examples of cases in which a direct correlation between image contrast and structural features has been established are given.
Abstract: The electron-microscope technique of lattice imaging can in favourable circumstances be used to observe the structure of materials directly. The technique is described, and examples of cases in which a direct correlation between image contrast and structural features has been established are given. Procedures for computing contrast in n-beam lattice images are outlined, and the important experimental parameters, thickness and orientation of the specimen, and spherical aberration and defocusing of the microscope objective, are discussed in some detail.
132 citations
TL;DR: In this paper, X-ray data is presented and analyzed for the semiconducting compound CuInSe2, prepared by zone levelling, and intensity calculations have been used in the evaluation of interatomic separation and bond angles.
Abstract: X-ray data is presented and analysed for the semiconducting compound CuInSe2, prepared by zone levelling. Values of a = 5.782 and c = 11.620 A, have been determined and intensity calculations have been used in the evaluation of interatomic separation and bond angles. Some aspects of stoichiometry, related to electrical characteristics, are discussed and it seems probable that the structure of the compound is modified by a small concentration of Se vacancies.
94 citations
TL;DR: In this article, a procedure is described for obtaining the standard deviations in cell dimensions derived front powder patterns by Cohen's method of least squares, which applies to any crystal system and the error in the volume of the cell is evaluated.
Abstract: A procedure is described for obtaining the standard deviations in cell dimensions derived front powder patterns by Cohen's method of least squares. The analysis applies to any crystal system and the error in the volume of the cell is evaluated. The method is particularly suited to the study of minerals where isomorphous replacements give rise to small changes in lattice parameters. As an example, the cell dimensions and their errors are obtained for an iron–rich actinolite asbestos and the powder pattern is indexed.
74 citations
TL;DR: A doping-vehicle dependence of the relative substitution of Nd at the two non-equivalent Ca sites in fluorapatite has been verified as discussed by the authors, where detailed structure refinements based on especially reliable single-crystal X-ray diffraction data from undoped, Nd2O3-doped, and NdF3doped synthetic fluorapitite were used.
Abstract: A doping-vehicle dependence of the relative substitution of Nd at the two non-equivalent Ca sites in fluorapatite has been verified. By implication, similar differences may be expected for other rare-earth dopants in other apatites. Detailed structure refinements based on especially reliable single-crystal X-ray diffraction data from (i) undoped, (ii) Nd2O3-doped, and (iii) NdF3-doped synthetic fluorapatite were used. An analysis of ratios of site-occupancy factors, based on Nd3+-for-Ca2+ as the substitution model, led to the conclusions that (i) Nd substitutes at both Ca(l) and Ca(2) sites in approximately equal atomic fractions in the NdF3-doped material and (ii) Nd substitutes only at the Ca(2) site in the Nd2O3-doped material. These results correlate well with reports that neodymium-doped fluorapatite crystals prepared as solid-state laser hosts differ in spectra, growth rate, and laser quality with the source of dopant (NdF3 or Nd2O3).
62 citations
TL;DR: In this paper, precision lattice parameters of hexagonal germanium dioxide have been determined at various temperatures in the range 36 to 516 °C by the X-ray method.
Abstract: With a Unicam 19 cm high-temperature powder camera, precision lattice parameters of hexagonal germanium dioxide have been determined at various temperatures in the range 36 to 516 °C by the X-ray method. From these data the coefficients of thermal expansion have been evaluated by a graphical method. The temperature dependence of the coefficients of thermal expansion, || and , parallel and perpendicular to the principal axis respectively, are represented by the following equations:
where T is the numerical value of the temperature expressed in °C. The thermal expansion of hexagonal GeO2 has been compared with that of the isomorphous -quartz and the polymorphous tetragonal rutile-type GeO2.
53 citations
TL;DR: In this article, a simple two-dimensional model of crystal growth disorder is described, which assumes growth probability parameters which involve the interaction of a crystallizing molecule with neighbours in two crystal directions.
Abstract: A simple two-dimensional (2D) model of crystal-growth disorder is described. The model assumes growth probability parameters which involve the interaction of a crystallizing molecule with neighbours in two crystal directions. The disorder that results from this process is described mathematically and with the use of an optical simulation technique. It is found that the correlations between neighbours that result in the completed crystal are not simply related to the initial probabilities, but when a special linearity restriction is made the correlations can be used to retrieve these probabilities. The direction in which the crystal is grown is inherently different from other directions and this is evident in the diffuse diffraction patterns that are obtained from the model.
48 citations
TL;DR: In this article, a new X-ray diffraction method for the determination of crystallinity of polymers is reported, where a probability function is used to express the intensity distribution of an amorphous halo.
Abstract: A new X-ray diffraction method for the determination of crystallinity of polymers is reported. A probability function is used to express the intensity distribution of an amorphous halo. The intensity of the halo buried under any crystalline peak can be calculated by this function. An amorphous-standard-addition method was used to determine crystallinity. A linear relationship between intensity and concentration is derived theoretically and applied to polyethylene terephthalate. No previous chemical or structural information about the polymer is necessary for this method. Very good agreement between X-ray data and density measurements were obtained. This method is rapid, practical and suitable for routine analysis.
TL;DR: In this paper, an X-ray camera has been constructed for rapid three-dimensional data collection from macromolecular crystals by means of a series of contiguous small-angle oscillation photographs without layer-line screens.
Abstract: An X-ray camera has been constructed for rapid three-dimensional data collection from macromolecular crystals by means of a series of contiguous small-angle oscillation photographs without layer-line screens. The use of the camera, the microdensitometry of the film and the correction and processing of data are discussed.
TL;DR: In this paper, the authors used the Pendellosung fringe patterns obtained from Laue transmitting crystals with full-spectrum incident radiation to determine crystal structure factors with high precision, and the characteristics of the neutron wave packet became available from the experimental studies.
Abstract: Neutron diffraction studies of perfect, non-absorbing crystals have been used to explore aspects of dynamical diffraction theory. The Pendellosung fringe patterns obtained from Laue transmitting crystals with full-spectrum incident radiation have been used to determine crystal structure factors with high precision. It has been established that spherical wave theory is called for, and small crystal curvature must be allowed for, in the interpretation of the fringe patterns. Novel information about the characteristics of the neutron wave packet becomes available from the experimental studies.
TL;DR: In this paper, it is shown that the ions give rise to a considerable disturbance of the solvent structure, in fact the ''order range'' in the solutions appears to be shorter than in pure water.
Abstract: Alkali halide aqueous solutions (LiCl, LiBr, NaCl, NaBr) have been investigated by X-ray diffraction in order to clarify the structural features of these systems (the existence of ordered local structures, their stability, geometry, etc.). The cation–H2O interaction is particularly evident for the Li+ ions, for which a well resolved peak at 2.1 A is apparent in the correlation function. It is shown that the ions give rise to a considerable disturbance of the solvent structure, in fact the `order range' in the solutions appears to be shorter than in pure water. The high coordination numbers of the Cl− and Br− ions could be due to close packing of solvent molecules or hydrated cations around the anions.
Abstract: X-ray and neutron-diffraction techniques have been used to ascertain the structures of vanadium deuterides with compositions between V2D and V4D3 over a temperature range 5–425 °K. The β phase, V2D, has a monoclinic crystal structure at room temperature with a≃c = 4.46; b = 3.00 A, β = 95.5°. The deuterium atoms prefer octahedral interstitial sites. Near 425 °K this phase transforms to a b.c.c. phase, and the deuterium atoms prefer tetrahedral sites. The b.c.c. phase of V4D3 has been designated α′ and transforms to α′′ at about 220 °K. This transition is an ordering of deuterium as shown by additional neutron-diffraction peaks. This α′′ structure can be indexed with a≃c≃4.46; b≃3.00 A; β = 90°. Below 160 °K an additional neutron peak appears at 2θ = 12° which indicates a doubling of the b lattice parameter. This transformation to α′′′ phase involves further ordering. The metal sublattice in α′ and α′′′ is very near b.c.c. Therefore, the neutron patterns do not allow a determination of octahedral or tetrahedral site occupancy. The exact crystal structure cannot be determined. The V–D system is not completely analogous to the V–H system and some of the differences are discussed.
TL;DR: In this paper, the geometrical and physical aberrations affecting the positions and breadths of diffraction maxima as determined by the energy distribution of photons diffracted through a fixed angle and analyzed by a solid-state detector differ in many points of detail from those determined by an angular distribution of photon of fixed energy analysed by a conventional diffractometer.
Abstract: The geometrical and physical aberrations affecting the positions and breadths of diffraction maxima as determined by the energy distribution of photons diffracted through a fixed angle and analysed by a solid-state detector differ in many points of detail from those determined by the angular distribution of photons of fixed energy analysed by a conventional diffractometer. The main differences are investigated and the accuracy of spacing measurements is discussed. There is no simple analogue of the extrapolation method of reducing errors in spacing measurements.
TL;DR: In this article, the TlGaSe2 was grown by solidification from melts and the space group a = 7.60, c = 31.36, β = 90°20′, is P21/m.
Abstract: Crystals of TlGaSe2 were grown by solidification from melts. The space group a = 7.60, c = 31.36 A, β = 90°20′, is P21/m.
TL;DR: In this article, a new technique is presented for the automatic determination of peak positions, intensities and widths from complex numerically recorded X-ray powder diagrams using standard powders.
Abstract: A new technique is presented for the automatic determination of peak positions, intensities and widths from complex numerically recorded X-ray powder diagrams. The method uses standard powders for the determination of the actual repartition of incoming radiations and the determination of the apparatus function (aberrations, calibration etc.). The first trials give results the accuracy of which is much better than one could except from manual determinations.
TL;DR: In this article, the effect of the double-scattering process on X-ray intensity diffracted by an amorphous sample is studied in the case of θ-2θ diffractometric techniques with monochromator, by transmission and reflexion.
Abstract: The effect of the double-scattering process on X-ray intensity diffracted by an amorphous sample is studied in the case of θ–2θ diffractometric techniques with monochromator, by transmission and reflexion; the small-angle X-ray scattering method is taken into account. An experimental application shows the amount of the correction in the case of transmission.
TL;DR: In this article, it was shown that a precision of about 0.01% is attainable without much difficulty by the use of a suitable Soller-slit system and a suitable scattering angle.
Abstract: According to the papers so far published about diffractometers with energy-dispersive detectors, the precision of a measured lattice spacing has been estimated to be about 0.05% at best. In the present paper, it is shown that a precision of about 0.01% is attainable without much difficulty by the use of a suitable Soller-slit system and a suitable scattering angle. This was demonstrated on an Al powder sample. It has been concluded that the limitation of precision is in the electronics rather than in the detector, when the necessary conditions are realised in the present improved system.
TL;DR: In this paper, high-temperature X-ray diffraction methods have been used to determine unit-cell parameters of two boron carbide compositions from 12° to about 940°C.
Abstract: High-temperature X-ray diffraction methods have been used to determine unit-cell parameters of two boron carbide compositions from 12° to about 940°C. One composition was at the carbon-rich end of the phase field (i.e. B4C), the second at the boron-rich end (5 at. % C by chemical analysis). The lattice expansion of both substances was isotropic in the temperature range studied. The mean linear thermal expansion coefficient for the carbon-rich composition is 5.65 x 10−6°C−1, while that of the boron-rich composition is 5"87 x 10−6°C−1.
TL;DR: In the Na2O-Ca3Al2O6 solid-solution series at room temperature, three crystalline forms (cubic, orthorhombic OI and OII) have been obtained by quenching as mentioned in this paper.
Abstract: Three crystalline forms (cubic, orthorhombic I and orthorhombic II) exist in the Na2O–Ca3Al2O6 solid-solution series at room temperature. A tetragonal form may be obtained by quenching. All the phases have lattices extremely close to the cubic form. The cubic and tetragonal varieties show no polymorphic transformations. The orthorhombic OI and OII phases become tetragonal at high temperature. There is complete agreement between the transition points revealed by X-ray diffraction and microscopy. However, only the order–disorder OII→T transition is observed by μDTA.
TL;DR: In this paper, powder X-ray diffraction patterns were obtained for the series of synthesized compounds RCo2Ge2 with R = La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, and Y.
Abstract: Powder X-ray diffraction patterns were obtained for the series of synthesized compounds RCo2Ge2 with R = La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, and Y. The compounds have been indexed on the basis of a tetragonal unit cell with two formula units per cell. Except for YbCo2Ge2 the series shows the expected lanthanide contraction.
TL;DR: In this article, the lattice constants are reported for an isotypic series of hexagonal (P63/m)M(OH)3 compounds where M = La, Sm, Eu, Gd, Tb, Dy, Ho, Y, Er and Tm.
Abstract: Lattice constants are reported for an isotypic series of hexagonal (P63/m)M(OH)3 compounds where M = La, Sm, Eu, Gd, Tb, Dy, Ho, Y and Er. A stability field plot (V1/3 vs. ionic radii) is linear, an indication of the internal consistency and accuracy of these constants. Plots of a and c vs. ionic radii are also linear and plots of a vs. c and a, c and V1/3 vs. Z yield smooth regular curves contrary to several earlier investigations. The new results compare reasonably well with the recent results of Christensen [Acta Chem. Stand. (1966). 20, 896–899] and Christensen, Hazell & Nilsson [Acta Chem. Stand. (1967). 21,481–492] for Ce. Tb, Dy, Ho, Y, Er and Tm.
TL;DR: Errors in separating diffuse scattering resulting from local order from that from static and dynamic displacements have been examined; the Borie-Sparks symmetry procedure was employed, which includes second-order terms in the displacements as mentioned in this paper.
Abstract: Errors in separating diffuse scattering resulting from local order from that from static and dynamic displacements have been examined; the Borie–Sparks symmetry procedure was employed, which includes second-order terms in the displacements. The largest source of error when X-rays are employed is the variation in the ratio of scattering factors across the volume measured in reciprocal space. Large errors in the Warren local-order parameters result for clustering systems with displacement terms of the same order as the local-order parameters (or larger), but not if the size terms are smaller. For systems with local order the errors in these parameters are small. Uncertainties in the size terms are always appreciable. Other errors that were considered are: higher-order terms, extrapolation under Bragg peaks, errors in Compton scattering, background and surface roughness, and uncertainties in composition or polarization resulting from a monochromator.
TL;DR: In this article, a method is proposed which can be used for an analysis of small-angle X-ray scattering curves exhibited by solid polymers with lamellar structure, and the analysis is performed directly, i.e. without the use of model calculations.
Abstract: A method is proposed which can be used for an analysis of small-angle X-ray scattering curves exhibited by solid polymers with lamellar structure. The scattering curve is considered to be determined by the positions and the structure of the `amorphous' boundary layers around the lamellar interfaces. The analysis is performed directly, i.e. without the use of model calculations. Application of the method results in giving values for the mean L and the range of fluctuation, δL, of the lamellar thickness, the electron-density defect κ per square unit of the lamellar interface, and the second moment σ2 of the electron-density profile of the boundary layer.
TL;DR: In this article, a comparison of the Raman spectra of single crystals with those made using their powder reveals the following differences: (1) the intensity of Raman lines decreases with grain size.
Abstract: A comparison of the Raman spectra of single crystals with those made using their powder reveals the following differences: (1) The intensity of the Raman lines decreases with grain size. (2) The breadth of the lines increases with grain size. (3) The spectra of powder specimens show additional lines. The decrease in the intensity is mainly due to surface scattering, whereas the broadening of the lines can be caused by two different factors: (a) In the case of polar crystals different spectra overlap because of different orientations of the grains. (b) Additional interactions with `surface modes' of the individual crystals, which may also show a dispersion depending on the shape of the grains. Na2WO4 with its higher symmetry and the weakly polar SiO2 show the decrease in intensity, while the examples showing the interactions with `surface modes', are quartz and platy crystals of SiC. Anomalous broadening can be demonstrated using strongly polar KIO3. The results of this study have been applied to determining the effect of such lamellar structures, as in labradorites, on Raman lines.
TL;DR: A low-temperature device for use in the X-ray structural study of proteins has been designed and tested as mentioned in this paper, which is easy to construct, portable, inexpensive to operate and extremely reliable in operation.
Abstract: A low-temperature device for use in the X-ray structural study of proteins has been designed and tested. It is easy to construct, portable, inexpensive to operate and extremely reliable in operation.
TL;DR: In this article, a structural model based on analysis of the subcell of a 7.5μ thick β-Ta film with very high preferred orientation has been studied with both the Gandolfi and precession cameras.
Abstract: A 7.5μ thick β-Ta film with very high preferred orientation has been studied with both the Gandolfi and precession cameras. A hexagonal subcell with a = 2.831, c = 5.337 A has been found. The smallest hexagonal cell that accounts for all the observed spacings contains 144 subcells with a = 34 A. A structural model is proposed based on analysis of the subcell. It suggests that there are domains in the form of hexagonal prisms about 1000 A or more in height and about 250 A in diameter. The domains are divided into 12 coherently diffracting prismatic zones with impurity species, principally Ar and H2, incorporated into the zone boundaries. The structure within a zone is related to the simple h.c.p. structure. The domains are stacked together side by side, normal to the plane of the film, to form layers. Many layers in turn may be added together to form the complete film.
TL;DR: In this article, the angular separation between two neighbouring orders of reflection which may correspond to different wavelengths is recorded and a least-squares refinement is performed after taking into account the angular dependence of systematic aberrations.
Abstract: A method is described for precise unit-cell dimension measurements based on the accurate recording of the angular separation between two neighbouring orders of reflection which may correspond to different wavelengths. A number of pairs of reflections at high diffraction angles are used and a least-squares refinement is performed after taking into account the angular dependence of systematic aberrations. The method has been tested on Ge and several selenides (InSe, In2Se3, GaSe) and the accuracy of the results is discussed.