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Showing papers in "Journal of Applied Crystallography in 1976"


Journal ArticleDOI
TL;DR: In this paper, a small-angle camera D11 has been used at the high-flux reactor in Grenoble to record the scattering of neutrons at different angles.
Abstract: The neutron small-angle scattering system at the high-flux reactor in Grenoble consists of three major parts: the supply of cold neutrons via bent neutron guides; the small-angle camera D11; and the data handling facilities. The camera D11 has an overall length of 80 m. The effective length of the camera is variable. The full length of the collimator before the fixed sample position can be reduced by movable neutron guides; the secondary flight path of 40 m full length contains detector sites in various positions. Thus, a large range of momentum transfers can be used with the same relative resolution. Scattering angles between 5 × 10−4 and 0.5 rad and neutron wavelengths from 0.2 to 2.0 nm are available. A large-area position-sensitive detector is used which allows simultaneous recording of intensities scattered at different angles; it is a multiwire proportional chamber. 3808 elements of 1 cm2 are arranged in a two-dimensional matrix.

341 citations


Journal ArticleDOI
TL;DR: In this article, a second harmonic analyzer has been constructed which can resolve space group ambiguities arising from Friedel's Law with a confidence level greater than 99% and is optimized for use with powdered crystalline samples.
Abstract: The existence of optical second harmonic generation has been shown to be a highly reliable and sensitive physical test for the detection of crystalline non-centrosymmetry. A second harmonic analyzer has been constructed which can resolve space group ambiguities arising from Friedel's Law with a confidence level greater than 99%. The system has been optimized for use with powdered crystalline samples so as to obviate the need for large single crystals and thus facilitates rapid determination of crystalline non-centrosymmetry. The present analyzer can routinely detect second harmonic generation at levels 1/1000 of that generated in a quartz standard, this is about an order of magnitude increase over previously reported systems. Data are reported on several materials including dibenzyldisulfide, and [(C6H5)3P]3CuBF4. The detection of structural phase transitions with the second harmonic analyzer is reported for BaTiO3, colemanite and phenanthrene. Second harmonic generation in the `cubic' phase of BaTiO3 promises to be a powerful tool for determining the dynamics of the ferroelectric phase transition. It is the most direct method for establishing the existence or nonexistence of microscopic polar regions well above the Curie point in a nominally centrosymmetric phase.

258 citations


Journal ArticleDOI
TL;DR: The Reference Intensity Ratio, I/Ic (c = corundum) as mentioned in this paper is a scale factor derived from the relative to the absolute/relative intensity scale of powder patterns.
Abstract: A scale factor γ, to convert from the relative to the absolute/relative intensity scale, is readily calculated during computer simulation of powder patterns. Previously used scale factors are related to γ. The Reference Intensity Ratio, I/Ic (c = corundum), is obtained from μ, ρ, and γ for the sample and for corundum. Comparing calculated and experimental I/Ic values confirms that microabsorption and primary extinction can be serious experimental aberrations possibly limiting the accuracy to several wt.% in quantitative analysis by powder diffraction.

217 citations


Journal ArticleDOI
TL;DR: In this paper, the hexagonal cell dimensions of 2H-MoS2 and WSe2 were measured over the temperature range 20 to 800 °C, with the linear thermal expansion coefficient of c being greater than that of a.
Abstract: The hexagonal cell dimensions a and c of 2H-MoS2, 2H-MoSe2 and 2H-WSe2 have been measured over the temperature range 20 to 800 °C. In all three compounds a and c increased non-linearly with temperature, the linear thermal expansion coefficient of c being greater than that of a. Above 500°C the compounds begin to decompose in vacuum.

141 citations


Journal ArticleDOI
TL;DR: In this article, a procedure for the digital processing of fiber diffraction patterns to yield a quasi-continuous map representing a central section through the cylindrically averaged intensity transform of the specimen is described.
Abstract: A procedure is described for the digital processing of fibre diffraction patterns to yield a quasi-continuous map representing a central section through the cylindrically averaged intensity transform of the specimen. No assumptions are required about the nature of the specimen other than that it has fibre-type symmetry. The specimen intensity transform can be used to obtain integrated intensities for discrete reflections from microcrystalline fibres that are potentially as accurate as those obtained from crystals. Improved procedures for extracting structure amplitudes from specimens with continuous layer lines are also described.

109 citations


Journal ArticleDOI
TL;DR: In this article, Schmidt, Weil and Brill proposed a method to estimate the total X-ray intensity as a function of h (h is the radial coordinate in reciprocal space), scattered by an isotropic system of particles of equal shapes but of different sizes R, can, under certain conditions, be expressed as an integral over the particle size distribution function D(R), multiplied by a common single-particle function, which can be calculated from the assumed particle shape.
Abstract: The total X-ray intensity as a function of h (h is the radial coordinate in reciprocal space), scattered by an isotropic system of particles of equal shapes but of different sizes R, can, under certain conditions, be expressed as an integral over the particle size distribution function D(R), multiplied by a common single-particle function of hR which can be calculated from the assumed particle shape. In the first method D(R) is calculated from this relation by the method of least squares, in which values of D at a limited number of particle sizes are the unknowns. To avoid oscillations in the D curve, constraints are imposed on the D values. The proper weight to be assigned to these constraints must be determined by trial and error. The method has been adapted to suit various assumptions and requirements as to the shape of the particles, the type of distribution function to be calculated, and experimental conditions (slit or pinhole focusing). The second method is essentially the one described by Schmidt, Weil & Brill [X-ray & Electron Methods of Analysis, pp. 86–100. (1968), New York: Plenum], which, however, is adapted to the use of slit-smeared intensities. Both methods may give rise to artefacts in the calculated distribution functions in the range of the smallest particle sizes, which are sensitive to the setting of the various parameters and to experimental errors. However, the position and shape of the main maxima can usually be determined quite well. The agreement between the results obtained by the two methods is satisfactory.

93 citations


Journal ArticleDOI
TL;DR: In this paper, a survey of techniques to monochromatize synchrotron X-radiation and eliminate harmonics in the most appropriate way is presented. But the theoretical estimates are compared with spectral intensity distribution measurements at DESY in Hamburg and found to be in good agreement.
Abstract: Some techniques are surveyed of how to monochromatize synchrotron X-radiation and to eliminate harmonics in the most appropriate way. The theoretical estimates are compared with spectral intensity distribution measurements at DESY in Hamburg and found to be in good agreement.

66 citations


Journal ArticleDOI
TL;DR: In electron diffraction patterns of nickel-rich β′-NiAl alloys, the appearance of diffuse intensity maxima between the reflexions of the B2 structure is explained by the formation of four possible variants of an ordered hexagonal superstructure corresponding to the Ni2Al composition.
Abstract: In electron diffraction patterns of nickel-rich β′-NiAl alloys, many anomalies are observed. One of these is the appearance of diffuse intensity maxima between the reflexions of the B2 structure. This is explained by the short-range ordering of the excess nickel atoms on the simple cubic sublattice occupied only by aluminum atoms in the stoichiometric, perfectly ordered NiAl alloy. After annealing Ni–37.5 at.% Al and Ni–37.75 at.% Al for one week at 300–400°C, the diffuse intensity maxima transformed into sharp superstructure reflexions. These reflexions are explained by the formation of the four possible variants of an ordered hexagonal superstructure corresponding to the Ni2Al composition (space group: P\bar 3m1, no. 164). This structure is closely related to the Ni2Al3 structure (same space group) formed by the ordering of vacancies on the nickel sublattice in aluminum-rich β′-NiAl alloys.

54 citations


Journal ArticleDOI
TL;DR: In this paper, a triple-Laue-case (LLL) interferometer was used to calculate the intensity profiles for the case of zero absorption, which in practice is predominantly encountered with thermal neutrons.
Abstract: Amplitude and intensity distributions within the outgoing beams of the triple-Laue-case (LLL) interferometer have been calculated for the case of zero absorption, which in practice is predominantly encountered with thermal neutrons. The type-1 wavefield with antinodes on the atomic sites, which with X-rays is quite frequently anomalously attenuated in the lattice, is here fully taken into account together with the type-2 wavefield of anomalous low absorption. After the combined diffraction by beam splitter, mirror, and analyser crystal of the interferometer for an incident plane wave has been solved, the solution for an incident spherical wave is developed by Fourier expansion, by a similar method to that first given by Kato [Acta Cryst. (1961), 14, 526–532] for just one diffracting crystal plate. In order to optimize the interferometer geometry spatial intensity profiles as functions of the geometric dimensions of the interferometer and of the phase shift between the interfering beams are calculated. The influence of deviations from the ideal geometry is investigated. Deviations of the order of the extinction length can result in a drastic reduction of interference contrast. Very good energy-converging and contrast properties are found if tM = 2tS= 2tA where tM, tS, tA are the thicknesses of mirror, beam splitter, and analyser respectively. The calculated intensity profiles are in agreement with preliminary experimental profiles obtained recently with a silicon interferometer at the HFR in Grenoble.

50 citations


Journal ArticleDOI
TL;DR: An upper limit for the volume of unit cells which can be verified by the de Wolff figure of merit is given as a function of the errors in observed d spacings in this paper.
Abstract: An upper limit for the volume of unit cells which can be verified by the de Wolff figure of merit [Wolff, P. M. de, J. Appl.Cryst. (1968). 1, 108–113] is given as a function of the errors in observed d spacings. In the use of the de Wolff figure of merit the requirement of information about the errors of measurement is emphasized. A number of examples are given where the unit cells that are found cannot be accepted as true, because of the lack of accuracy in the published data.

48 citations


Journal ArticleDOI
TL;DR: In this paper, the unit cell parameters for LnPO4 (Ln = La, Ce, Pr, Nd, Sm, Eu, Gd, Tb and Dy) have been determined from Guinier photographs, and are plotted against effective ionic radii of the lanthanides.
Abstract: Monoclinic unit-cell parameters for LnPO4 (Ln = La, Ce, Pr, Nd, Sm, Eu, Gd, Tb and Dy) have been redetermined from Guinier photographs, and are plotted against effective ionic radii of the lanthanides. Full powder-diffraction data are given for LaPO4 and GdPO4.

Journal ArticleDOI
TL;DR: In this article, a fast Fortran program written in Fortran is presented to calculate the unit-cell dimensions of triclinic and orthorhombic lattices.
Abstract: A fast computer program written in Fortran is presented. It calculates with a trial-and-error method the unit-cell dimensions from the d values obtained from powder patterns. The special techniques used in this program to keep the computation time short are described. The program itself is designed primarily for triclinic and orthorhombic lattices. Monoclinic lattices are treated like triclinic ones: for tetragonal, hexagonal and rhombohedral structures orthorhombic cells can be calculated.

Journal ArticleDOI
TL;DR: In this paper, an algorithm was developed and implemented to determine automatically the indices and other reciprocal-lattice information from the positions of a dozen or so arbitrary reflections on a four-circle diffractometer.
Abstract: An algorithm has been developed and implemented to determine automatically the indices and other reciprocal-lattice information from the positions of a dozen or so arbitrary reflections on a four-circle diffractometer. Output includes the indices, reduced cell dimensions, and the reduced cell scalars for Bravais lattice determination. Illustrations of the use of the indexing procedure both with the four-circle diffractometer and with precession camera techniques are given. A comparison to some other autoindexing procedures is also given.

Journal ArticleDOI
TL;DR: In this paper, the temperature dependence of the axial lattice spacings of a pure BaTiO3 crystal, grown from a ''top-seeded'' TiO2-rich melt, is presented for the four phases.
Abstract: The temperature dependence of the axial lattice spacings of a pure BaTiO3 crystal, grown from a `top-seeded' TiO2-rich melt, is presented for the four phases. This behaviour is compared with that of a crystal grown using a potassium fluoride flux. The lower ferroelectric paraelectric transition temperature and the smaller lattice parameter discontinuities exhibited by the latter crystal are attributed to the incorporation of impurities from the flux.

Journal ArticleDOI
TL;DR: In this article, a new type of thermal neutron polarizing monochromator, consisting of alternate thin layers of iron and germanium, has been constructed and tested Bragg reflection from such artificial ''crystals' in the fully magnetized state yields a highly polarized beam with high reflecting efficiency (~084) for the reflected spin state.
Abstract: A new type of thermal neutron polarizing monochromator, consisting of alternate thin layers of iron and germanium, has been constructed and tested Bragg reflection from such artificial `crystals' in the fully magnetized state yields a highly polarized beam with high reflecting efficiency (~084) for the reflected spin state These multilayer monochromators have the additional advantage that higher orders in the reflected beam are almost completely suppressed Since d spacings are typically large (~100 A), they produce a broader wavelength distribution than conventional single-crystal polarizing monochromators Nevertheless, there are many applications where wavelength resolution is of secondary importance and the large gain in intensity (~40-fold) over conventional polarizing crystals can be a considerable advantage Multilayers can also be used to advantage in combination with good monochromating crystals such as pyrolytic graphite or beryllium to produce polarized beams of high intensity and good wavelength resolution

Journal ArticleDOI
TL;DR: In this paper, a double-diffractometric method for X-ray topography revealing the smallest crystal defects in as-grown silicon by a relatively low display is described, and a low-resolution display is used to display the defects.
Abstract: A double-diffractometric method for X-ray topography revealing the smallest crystal defects in as-grown silicon by a relatively low display is described.

Journal ArticleDOI
TL;DR: In this paper, it was shown that the neglect of higher-order terms in the logarithmic series expansion introduces larger errors at small values of the strain than the cosine series while at larger values the dominance is less pronounced.
Abstract: The Warren–Averbach analysis for the separation of particle size and strain involves a cosine and a logarithmic power series expansion. It is shown that the neglect of higher-order terms in the logarithmic series expansion introduces larger errors at small values of the strain than the cosine series while at larger values the dominance is less pronounced. Furthermore it is shown that the power series expansion for the logarithm is superfluous and as a result the Warren–Averbach analysis can be improved. In common practice the differences between the improved method and the original one can easily be 10% for particle-size Fourier coefficients and 30% for mean square strain values.

Journal ArticleDOI
TL;DR: In this article, the crystal data of three compounds in the system SeO2-CuO have been determined from X-ray single-crystal and powder studies, and powder diffraction data are given for all three compounds.
Abstract: Crystal data of three compounds in the system SeO2–CuO have been determined from X-ray single-crystal and powder studies. CuSe2O5 is monoclinic, space group Cc or C2/c, with a = 12.254 (5), b = 4.858 (3), c = 7.960 (3) A, β = 110.7 (1)°, Z = 4. CuSeO3 is monoclinic, space group P21/c, with a = 7.718 (2), b = 8.266 (3), c = 10.529 (3), β = 127.2 (2)°, Z = 8. Cu2SeO4 is cubic, space group P213 or P4232, with a = 8.928 (3) A, Z = 8. Powder diffraction data are given for all three compounds.

Journal ArticleDOI
TL;DR: In this article, X-ray scattering functions of liquid water at 4°, 25° and 50°C have been measured in a transmission arrangement with a plane-parallel liquid sample.
Abstract: X-ray scattering functions of liquid water at 4°, 25° and 50°C have been measured in a `θ–θ' transmission arrangement with a plane-parallel liquid sample. Reduced intensities and RDF's have been calculated with an improved data reduction procedure. The results have been compared with those of previous authors.

Journal ArticleDOI
TL;DR: Amorphous films of AgCu and CuMg2, approximately 3000-A in thickness, were prepared by co-evaporation of Ag and Cu, and Cu and Mg, respectively, onto 25 μm thick Be sheets, held at liquid nitrogen temperature as discussed by the authors.
Abstract: Amorphous films of AgCu and CuMg2, approximately 3000 A in thickness, were prepared by co-evaporation of Ag and Cu, and Cu and Mg, respectively, onto 25 μm thick Be sheets, held at liquid nitrogen temperature. Mo Kα X-rays were used as a radiation probe to determine the structure of the films, at room temperature, and of the liquid alloys of Cu with 50 at.% Ag and with 0 and 67 at.% Mg at 50°C above the liquidus temperature. With the transmission technique, the interference functions (or structure factors) I(K) were determined in the range of K = 4π sin θ/λ between 0.8 A−1 and 12.5 A−1, and then Fourier transformed to obtain the radial distribution functions (RDF). The I(K) and RDF of the amorphous AgCu and CuMg2 films were compared with those of the liquid Ag–Cu and Cu–Mg alloys, respectively. It was found that the structures of the amorphous and liquid Ag–Cu alloys were similar with a more well defined short-range order occurring in the solid alloys, whose I(K) exhibited the well known shoulder on the second peak. The I(K) and RDF of the amorphous CuMg2 and the liquid Cu–Mg alloys cannot be explained by a common structure, although I(K) showed a small premaximum below the first main peak in both the amorphous and liquid alloys, a feature observed in many liquid Mg alloys.

Journal ArticleDOI
TL;DR: In the ZRD-SEARCH-MATCH program as mentioned in this paper, the file of standards is restricted to the 298 most frequently encountered phases, and a single index file based on the most intense reflection is used.
Abstract: Four major improvements have been made in the ZRD–SEARCH–MATCH program [Frevel (1965), Anal. Chem. 37, 471–482]; namely, (1) restriction of the file of standards to the 298 most frequently encountered phases, (2) utilization of a single index file based on the most intense reflection, (3) incorporation of a novel search function, and (4) revision of the quantitative matching of powder patterns.

Journal ArticleDOI
TL;DR: The crystal structure of Cs2HfCl6 was determined to be cubic, Fm3m, similar to K2PtCl6, with parameters: a 0 = 1042±001 1 A, and u = 0247±000 3 Powder diffraction data on which the determination was based as discussed by the authors.
Abstract: The crystal structure of Cs2HfCl6 was determined to be cubic, Fm3m, similar to K2PtCl6, with parameters: a0 = 1042±001 A, and u = 0247±0003 Powder diffraction data on which the determination was based are given

Journal ArticleDOI
TL;DR: In this article, a method of calculating the profile of the X-ray diffraction bands (for a powder) for partially disordered kaolinites containing rotational stacking faults is described.
Abstract: This work describes a method of calculating the profile of the X-ray diffraction bands (for a powder) for partially disordered kaolinites containing rotational stacking faults. The profiles of the bands have been calculated for stackings containing ±2π/3 rotational faults. These faults are such that two first neighbouring layers (i) are translated as in a perfect kaolinite but additionally rotated by +2π/3 or −2π/3; (ii) are disposed strictly as in dickite, or (iii) start with the enantiomorphic kaolinite structure. Among the different models envisaged, only the model with faults of the first type mentioned above seems to agree with the experimental profiles of the different natural kaolinites.

Journal ArticleDOI
TL;DR: In this paper, the temperature dependence of the cell parameters and the principal thermal expansion coefficients presents anomalies (below 240 K) which are due to the existence of an order-disorder transition in the range 240-170K.
Abstract: About forty X-ray powder diagrams were recorded, in the range 5 to 295 K, with a prototype diffractometer and a high-efficiency cryostat. The temperature dependence of the cell parameters and the principal thermal expansion coefficients presents anomalies (below 240 K) which are due to the existence of an order–disorder transition in the range 240–170K. There is a correlation between the temperature dependence of the thermal expansion coefficients αhkl and the asymmetric broadening of corresponding peaks. The existence of domains and frontier zones and the important reorganization of the molecular packing, in the ordered phase, explain the asymmetrical broadening of peaks. The nickelocene molecular configuration is probably eclipsed (D5h) in the ordered phase.

Journal ArticleDOI
TL;DR: In this article, the authors reported the appearance of singularity in the equal-thickness fringes at the outcrop of a dislocation in silicon observed with a plane-wave of X-rays and proposed a method of determining directly the magnitude and sense of the Burgers vector from the number of the extra half lines of the fringes.
Abstract: This note reports on the observation of the appearance of singularity in the equal-thickness fringes at the outcrop of a dislocation in silicon observed with a plane-wave of X-rays and proposes a method of determining directly the magnitude and sense of the Burgers vector from the number of the extra half lines of the fringes.

Journal ArticleDOI
TL;DR: In this paper, the Burgers vectors of dislocations in a Czochralski-grown LiNbO3 crystal were determined by using Lang X-ray diffraction topography.
Abstract: The Burgers vectors of dislocations in a Czochralski-grown LiNbO3 crystal have been determined by using Lang X-ray diffraction topography. Dislocations with Burgers vectors of both ⅙〈2\bar 201〉 and ⅓〈\bar 1101〉 types (in hexagonal indices) are observed. The direction of the two Burgers vectors is thus identified to be along the line from one Nb (or Li) to the nearest Nb (or Li), and along the line from one Nb (or Li) to the second neighbours respectively.

Journal ArticleDOI
TL;DR: In this paper, Bergman et al. determined the absolute polarity of single crystals of α-Cu(IO3)2 and Nd(IO 3)3 using point-charge and dipole models.
Abstract: The absolute polarity of single crystals of α-Cu(IO3)2 and Nd(IO3)3.H2O, determined by anomalous X-ray scattering techniques, has been related to the sense of the piezoelectric d22 and pyroelectric p2 coefficients in these monoclinic crystals. The absolute sense of d22 in both cases is predictable from a consideration of the behavior of the spontaneous polarization Ps under stress. Ps was calculated on the basis of a simple point-charge and dipole model. The positive sense of p2 in α-Cu(IO3)2 and Nd(IO3)3.H2O (each with magnitudes of about 2 x 10−5Cm−2deg−1: the secondary pyroelectric coefficients are probably nearly an order of magnitude smaller) allows the inference that |Ps| increases with increasing temperature. The absolute sense of d33 in hexagonal LiIO3, determined by Morosin [Private communication (1972) quoted as Ref. 25 of Bergman, J. G. & Crane, G. R. (1974). J. Chem. Phys. 60, 2470–2474] is similarly predictable from the calculated Ps. Turner's [J. Appl. Cryst. (1976). 9, 52] measurement of p3 in LiIO3 combined with Ps also leads to the inference of increasing |Ps| with temperature.

Journal ArticleDOI
TL;DR: In this article, a channel plate was used for taking X-ray diffraction topographs, and the spatial resolution of the plate was found to be at least better than 37μm.
Abstract: A channel plate has been used for taking X-ray diffraction topographs. A topograph of a Si crystal on a fluorescent screen has been recorded by an optical camera. The spatial resolution of the plate has been found to be at least better than 37 μm. The time for the optical recording of a topograph on this plate proved to be about 102 times shorter than that required by standard topography. The sensitivity of the plate has also been measured for Cr Kα radiation.

Journal ArticleDOI
TL;DR: In this paper, a rapid-identification file for crystalline materials is being prepared from the Crystal Data file, where each cell is represented in its reduced form, which is unique, primitive, and based on the three shortest noncoplanar vectors of the lattice.
Abstract: A rapid-identification file for crystalline materials is being prepared from the Crystal Data file. In this new file, each cell is represented in its reduced form, which is unique, primitive, and based on the three shortest noncoplanar vectors of the lattice. Unknown materials can be rapidly matched with the same or related crystals in the file. To identify an unknown crystalline material, a primitive cell is first determined experimentally, then it is reduced and checked against the file for a match. Even if the cell of the unknown lattice is not primitive, identification is still possible by calculating appropriate derivative lattices, reducing them, and then checking the file.

Journal ArticleDOI
TL;DR: In this article, a vertical float zoner combined with thermal imaging is uniquely suited to investigation of high-temperature noncontaminating melts by X-ray diffraction, where radiation from a halogen lamp is focused on the sintered-powder rods by means of the gold-plated internal surface of an ellipsoidal shell.
Abstract: A vertical float zoner combined with thermal imaging is uniquely suited to investigation of high-temperature noncontaminating melts by X-ray diffraction. Radiation from a halogen lamp is focused on the sintered-powder rods by means of the gold-plated internal surface of an ellipsoidal shell. This image furnace can easily be mounted on a conventional horizontal type of powder diffractometer, provides atmosphere control, and permits rapid heating and cooling. A temperature of 1700°C can readily be reached. The presence of a gap for the passage of X-rays solves the problem of X-ray absorption by window materials, and sufficient lateral length of the gap allows X-ray measurement over a wide diffraction range.