ALBERT

Notes: A computer program has been developed for the Rietveld analysis of time-of-flight neutron diffraction data taken on a high-resolution powder diffractometer, HRP, at the pulsed spallation neutron source, KENS. A new profile shape function is implemented which is optimized for a solid-methane moderator at 20 K. The program has several convenient features such as single-pass operation, multiphase capability, automatic successive refinements and constrained minimization. The results of Rietveld refinements of Si and α-Al2O3 show that the profile shape function fits neutron diffraction patterns taken on the HRP very well, and that very precise crystal-structure parameters can be obtained with this program.

Notes: The crystal symmetries of two precipitate phases, q1-AlFeSi (C-centred orthorhombic) and q2-AlFeSi (monoclinic), which were discovered in a dilute Al–Fe–Si alloy, have been determined with the use of convergent-beam electron diffraction (CBED). The space group of q1-AlFeSi is Cmmm and that of q2-AlFeSi is Pm.

Notes: A simple scheme is described for calculating weighted averages of multiple equivalent measurements using weights based on estimated normal probabilities.

Notes: The effectiveness of employing an elastically bent perfect Si (111) crystal as a monochromator for neutron-diffraction experiments is demonstrated on rocking curves presented for a flat perfect Si (220) crystal and a mosaic Fe (110) crystal, for two different collimations of the incident beam. For the sake of comparison equivalent rocking curves with a conventional mosaic Zn monochromator are also introduced. The experimental results obtained indicate that curved perfect-crystal monochromators may become a useful alternative to mosaic-crystal ones.

Notes: Intensity data were collected at room temperature from an extended-face crystal of AgI using Mo Kα radiation. Least-squares refinement indicates that the thermal motion of the Ag+ ions is large with a considerable anharmonic component. The wurtzite positional parameter, u, was found to be 0.3748(2). The proportion of point defects was determined to be no greater than 0.9%. The proportion of random staking faults was determined by two experimental techniques to be no greater than 2%.

Notes: The optical anisotropy of polycrystalline graphite layers formed after catalytic graphitization of single-crystal diamond surfaces has been studied as a function of crystallographic substrate orientation. It was found that the shapes and orientations of the two-dimensional indicatrices of the graphite coatings were in complete agreement with the two-dimensional point-group symmetry of the underlying diamond surfaces. This means the graphite crystallites have one or more preferential orientations imposed by the substrate.

Notes: The sensitivity of measurements of the lattice-parameter difference in monocrystalline heterostructures can be enhanced by use of an extremely asymmetrical diffraction geometry. If the angle of incidence is somewhat higher than the critical angle for total external reflection, the Bragg peak is shifted from the position calculated by kinematic theory. The amount of shift depends on the angle of incidence as well as on the mass density of the material used. For heteroepitaxic structures both the layer and the substrate peaks are shifted but by different amounts. Therefore it becomes possible to characterize layers of totally lattice-matched structures also.

Notes: The construction and performance of a small-angle X-ray camera equipped with a two-dimensional multiwire proportional chamber (two-dimensional MWPC) are described. The system has been used for studies of the structure of biological samples with a conventional rotating-anode X-ray source. The small-angle camera is of Franks type with two orthogonal platinum-coated bent optical flats placed in a helium-tight box. The specimen-to-detector distance is variable between 60 and 260 cm. The sensitive area of the two-dimensional MWPC is 256 × 256 mm with 256 × 256 resolution elements. The camera covers high angles up to about 5 Å, although diffraction line widths in this region are highly broadened owing to parallax. The electronic system comprises NIM modules, a hand-made module and a commercially available compact two-dimensional multichannel analyser (two-dimensional MCA). The two-dimensional MCA has a memory size of 256 × 256 channels (24 bits/channel). The estimated dead time of this system is approximately 5 μs, which permits a maximum count rate of 20 kHz at 10% loss. Diffraction patterns of a Langmuir–Blodgett film of arachidic acid and stacked purple membranes and a solution scattering of horse spleen apoferritin are demonstrated as examples.

Notes: It is shown that a recurrence relation exists such that the resolution function and luminosity of an optical system consisting of any number of alternate collimators and reflecting crystals can be calculated analytically. Certain cases of practical interest in neutron and X-ray diffraction are evaluated explicitly using a Gaussian approximation for the transmission functions of the collimators, and for the mosaic spread distributions or reflection profiles of the crystals. It is shown that true absorption has a negligible effect on luminosity when the Darwin width of a reflection is of the order of the opening angle of the X-ray beam from a synchrotron source.

Notes: Absolute calibration forms a valuable diagnostic tool in small-angle neutron scattering (SANS) experiments, and allows the parameters of a given model to be restricted to the set which reproduces the observed intensity. Discrepancies between the observed and calculated intensities may arise from potential artifacts or even new physical processes and absolute calibration methods are useful in delineating these circumstances. General methods which are available for absolute scaling are discussed along with estimates of the degree of internal consistency which may be achieved between the various standards. In order to minimize the time devoted to calibration in a given experimental program, emphasis is placed on developing a set of precalibrated strongly scattering standards which may be run in the chosen experimental geometry. Comparison of such a set developed at the National Center for Small-Angle Scattering Research (Oak Ridge) with independent determinations by SANS users indicates consistency to within ± 5%.

Notes: Two easy-to-use indirect Fourier-transformation routines for the evaluation of slit-length-smeared SAXS curves of polystyrene in solution are demonstrated. For approximation of the SAXS curve, analytically transformable Gaussian and Lorentzian functions are chosen. The nonlinear least-squares fit is transformed to a linear one by specifying fixed non-linear coefficients. The fit is constrained by allowing only positive linear coefficients. The range over which nonlinear coefficients have to be specified can be easily obtained from the SAXS curve. An exact specification of this range is unnecessary for the fit. The method allows direct and clear control of the indirect Fourier transformation.

Notes: The double-null technique in conjunction with the conjugate-gradient algorithm gives an efficient method of regularizing protein structures. The double-null technique constrains planar groups by introducing two artificial atoms which are geometrically the apices of tetrahedra from three selected atoms in the planar group. The model-fitting procedure is simply concerned with reconciling information on (x, y, z) atomic coordinates with information on bond length, bond angle and planarity constraints. This can be done without treatment of hydrogen-bond, van der Waals or electrostatic interactions and consequently the minimization function is nearly quadratic. The equations which have to be solved have many unknowns but few coefficients and an effective iterative method can be used.

Notes: The powder data for p-chloroiodobenzene and p-bromochlorobenzene/p-chloroiodobenzene mixed crystals [pBCB]x[pCIB]1 − x at 293 K are reported; their stability at 293 K is given. The cell dimensions have been refined by least squares from accurate powder diffractometer data recorded at T = 293 (1) K (quartz as internal standard). Vertical diffractometer, graphite monochromator, Cu Kα1−Cu Kα2 correction so that λ = 1.54056 Å. They are all isomorphous, monoclinic, P21/a with Z = 2. a = 15.818(4), b = 5.912(2), c = 4.214(2) Å, β = 113.61(1)°, V = 361.1 Å3, Dx = 2.193 Mg m−3 for pCIB; JCPDS No. 37–2000. a = 15.210(5), b = 5.860(3), c = 4.091(2) Å, β = 112.64(2)°, V = 336.5 Å3, Dx = 1.936 Mg m−3 for [pBCB]0.90[pCIB]0.10; JCPDS No. 37–1989. a = 15.287(6), b = 5.870(3), c = 4.111(2) Å, β = 112.78(2)°, V = 340.1 Å3, Dx = 1.961 Mg m−3 for [pBCB]0.80[pCIB]0.20; JCPDS No. 37–1990. a = 15.360(5), b = 5.880(2), c = 4.126(1) Å, β = 112.87(2)°, V = 343.3 Å3, Dx = 1.988 Mg m−3 for [pBCB]0.70[pCIB]0.30; JCPDS No. 37–1991. a = 15.424(5), b = 5.889(3), c = 4.137(2) Å, β = 112.99(2)°, V = 346.0 Å3, Dx = 2.018 Mg m−3 for [pBCB]0.60[pCIB]0.40; JCPDS No. 37–1992. a = 15.493(4), b = 5.896(2), c = 4.155(2) Å, β = 113.09(2)°, V= 349.1 Å3, Dx = 2.045 Mg m−3 for [pBCB]0.50[pCIB]0.50; JCPDS No. 37–1993. a = 15.566(5), b = 5.901(3), c = 4.168(2) Å, β = 113.20(2)°, V = 351.9 Å3, Dx = 2.073 Mg m−3 for [pBCB]0.40[pCIB]0.60; JCPDS No. 37–1994. a = 15.623(5), b = 5.904(3), c = 4.178(3) Å, β = 113.26(2), V = 354.0 Å3, Dx = 2.105 Mg m−3 for [pBCB]0.30[pCIB]0.70; JCPDS No. 37–1995. a = 15.691(4), b = 5.913(3), c = 4.195(2)Å, β = 113.43(2)°, V = 357.1 Å3, Dx = 2.130 Mg m−3 for [pBCB]0.20[pCIB]0.80; JCPDS No. 37–1996. a = 15.759(4), b = 5.906(2), c = 4.204(2) Å, β = 113.55(2)°, V = 358.7 Å3, Dx = 2.164 Mg m−3 for [pBCB]0.10[pCIB]0.90; JCPDS No. 37–1999.

Notes: Modifications to the restrained least-squares refinement program of Hendrickson & Konnert [Biomolecular Structure, Function, Conformation, and Evolution, edited by R. Srinivasan, pp. 43–57 (1980). Oxford: Pergamon Press] are described that result in dramatic acceleration of the refinement of protein structures. Proven fast-Fourier-transform-based algorithms for computing structure factors and least-squares matrix elements are incorporated that reduce up to a hundredfold the computation time required for a single cycle. The modified program is shown to give results comparable to refinement by conventional methods and has been successfully applied to the refinement of several protein crystal structures.

Notes: Symmetry-related van der Waals contacts and hydrogen bonds are stereochemical restraints which are often ignored in macromolecular structure refinement programs. PROTIN and PROLSQ have been modified to account for symmetry-related contacts. The derivatives calculated for an atom in its symmetry-transformed position need only be multiplied by the appropriate rotation matrix to be applied to the atom in its untransformed position. Therefore the code already present in PROLSQ for van der Waals contacts is readily adapted to account for symmetry-related contacts. The `cubing' algorithm, shown to be much faster than residue-by-residue center and radius methods for generating potential contacts, has been incorporated in PROTIN.

Notes: A least-squares algorithm to refine incommensurate structures in the framework of (3 + 1)-dimensional crystallographic symmetry is described in some detail. It is applicable to the cases of occupational and/or harmonic displacive modulation. Compact analytical expressions for the structure factor and its partial derivatives well suited for structure refinement by the least-squares method have been obtained. The efficiency of the algorithm is discussed.

Notes: Gd2Te3, Mr = 697.30, orthorhombic, Pnma, a = 12.009(9), b = 4.3012(6), c = 11.818(2) Å, V = 610.4(6) Å3, Z = 4, Dm = 7.384, Dx = 7.59 g cm−3, Mo Kα, λ = 0.71069 Å, μ = 357 cm−1, F(000) = 1136, room temperature, R = 0.033, 822 observed reflections. The redetermination confirms that Gd2Te3 is isostructural with Sb2S3 (stibnite). The reported solid-solution series Gd2Te3–Gd3Te4 does not exist. Gd–Te bond lengths vary from 3.104(1) to 3.240(3) Å and Gd is in sevenfold coordination. Gd2Te3 has a power factor S2/ρ = 0.6 × 10−6 V2 K−2 Ω−1 cm−1 at 1273 K. It is not suitable as a high-temperature thermoelectric material because it decomposes to GdTe which is metallic.

Notes: Single-crystal time-of-flight (TOF) neutron diffraction data have been collected for Cr3Si and MnF2 with the Argonne Intense Pulsed Neutron Source. The purpose of this study was to test the accuracy of the TOF technique by a comparison with results from recent γ-ray, X-ray and neutron diffraction experiments. The results show that for simple crystal structures the positional and thermal parameters obtained from TOF data approach those obtained by other diffraction methods.

Notes: A new method is proposed for the study of the structure and arrangement of components in multi-component particles. In this method the difference between the scattering curve of a solution containing two types of structurally identical particles differing only in degree of deuteration and the scattering curve of a solution containing particles of a third type deuterated to an intermediate degree is considered. This difference scattering curve is distinguished only by a numerical multiplier from the `vacuum' scattering curve of the particle in which the scattering density is equal to the difference between the scattering densities of particles of the first and second types. This means that components protonated (deuterated) to the same degree within particles of the three types considered do not contribute to the difference scattering curve and, consequently, are `invisible' to neutrons. The difference scattering curve depends neither on the solvent isotopic content nor on interparticle interference and particle association. Possible applications of the method to a study of the structure of macromolecules in solution are discussed.

Notes: Growth imperfections in (Ga1−xAlxAs)n1–(GaAs)n2/ GaAs superlattices, grown on GaAs(001) substrates, have been investigated by X-ray diffraction techniques coupling image and rocking-curve recording. The use of a synchrotron radiation source has enabled topographic images formed with very weak superlattice reflections to be obtained. The intensity distribution across the sample surface observed in such images has revealed two different types of superlattice defects: either overall gradients of both the average composition and period or islands showing different composition and period from the surrounding material. Since these parameters control the optoelectronic properties and particularly the gap value it is of primary importance to grow homogeneous samples and to have a technique able to detect inhomogeneities such as the ones described in the present work.

Notes: The wavelength dependence of the neutron absorption cross section of hydrogen in [ReH3(C2H4)2{P(i-Pr)2Ph}2] was investigated by recording the decrease in Bragg peak intensity from a standard NaC1 crystal caused by attenuation of the incident beam by the Re sample. Data were collected on the Single Crystal Diffractometer (SCD) at the Intense Pulsed Neutron Source (IPNS, Argonne National Laboratory) which enabled concurrent measurements at a selection of wavelengths using the time-of-flight technique.

Notes: X-ray data have been collected from crystals of bovine pancreatic ribonuclease A at temperatures of 220K and below, by use of a nitrogen-gas cold stream and a computer-controlled diffractometer. One data set, collected from a crystal mounted in the traditional manner in a quartz capillary tube, showed radiation damage of 21% after 14.6 days of exposure to Cu Kα radiation at 160K. Another crystal, mounted on a glass fiber by use of uncured epoxy cement, showed only a 3% decay of the intensity standards after 28.3 days of exposure to the same radiation and at similar temperatures.

Notes: New X-ray powder diffraction data for 9,10-dihydroanthracene, C14H12, have been obtained from crystals prepared at 273 K by slow evaporation of acetone solution. Chemical analysis gives a purity better than 99.8% for this compound which crystallizes in the monoclinic space group P21. The cell parameters were determined by employing single-crystal diffraction methods (Bragg and precession patterns) and refined from accurate powder diffractometer data recorded at T = 293(1)K with quartz monochromator, Cu Kα radiation, λ = 1.54178 Å, and Si as external standard. The cell constants are a = 7.72 (1), b = 6.25 (1), c = 10.82 (1) Å and β = 108.3(1)°; V = 495 (2) Å3, Z = 2, Dm = 1.19 (2) and Dx = 1.21 Mg m−3. The JCPDS Diffraction File No. is 37-1987.

Notes: High-resolution synchrotron powder X-ray data have been used to solve the structures of I2O4 and Al2Y4O9 by profile decomposition into individual structure amplitudes, followed by application of standard Patterson and direct methods. The data were obtained from a series of spectra recorded with a small linear position-sensitive detector, and some of the errors arising from this approach are discussed. The final structures were obtained by Rietveld refinement, and Rp values for the profile intensities are 10.9 and 9.2% for Al2Y4O9 and I2O4 respectively. For Al2Y4O9 good agreement was found with the known isomorphous compound Al2Eu4O9, while I2O4 data were compared with high-resolution neutron powder data. This analysis, together with other recently reported studies, shows that structure determination from powder data will be feasible even for rather complicated structures.

Notes: The program package UNISOFT has been developed for lattice-dynamical calculations. Phonon dispersion curves can be calculated for any crystal structure with up to 20 atoms per primitive cell. The interaction between each individual pair of atoms can be modelled by one or more interaction types such as longitudinal and transverse springs (Born–von Karman model), Born–Mayer potential, Lennard-Jones potential, van der Waals potential, Coulomb potential, shell model. In addition to the model calculation part, UNISOFT contains several auxiliary programs dealing with group-theoretical analysis, neighbourhood analysis, plot of the phonon dispersion, calculation of partial derivatives, check of rotational invariance, calculation of local electrical fields and gradients, calculation of phonon intensities. In combination with a spectrometer for inelastic neutron scattering, UNISOFT provides a tool for the optimization of experiments as well as for a first interpretation of the results.

Notes: A computer program has been written for the purpose of standardizing crystal structure data according to rules formulated by Parthé & Gelato [Acta Cryst. (1984). A40, 169–183]. From input consisting of space-group symbol, unit-cell parameters and positional coordinates of the atoms, a reordered and renumbered list of standardized atom coordinates is obtained. The space group is now in the standard setting and the cell is reduced if applicable. The origin and the orientation of the coordinate system have been chosen in such a way as to minimize the standardization parameter Γ. A second standardization parameter, based on the position of the centre of gravity of the atoms in the asymmetric unit, is introduced. The Wyckoff sequence, obtained from the standardized structure data, can be used to recognize structures which are isopointal. An example of the application of STRUCTURE TIDY is given.

Notes: Ternary fluorides LnMoF7 have been synthesized by solid-state reactions between MoF4 and LnF3 for yttrium and all lanthanides except dysprosium. These compounds are all monoclinic, space group P21; they are isotypic with the LnZrF7 and LnNbF7 compounds. Unit-cell parameters for the 14 compounds are: LaMoF7: a = 6.3952(4), b = 5.6285(4), c = 8.4351(5) Å, β = 102.695(6)°, V = 296.2(5) Å3, Z = 2, Dx = 4.12 Mg m−3; CeMoF7: a = 6.3275(5), b = 5.6657(5), c = 8.4122(7) Å, β = 102.985(7)°, V = 293.9(5) Å3, Z = 2, Dx = 4.17 Mg m−3; PrMoF7: a = 6.3155(5), b = 5.6599(7), c = 8.4167(6) Å, β = 102.946(6)°, V = 293.2(5) Å3, Z = 2, Dx = 4.19 Mg m−3; NdMoF7: a = 6.1152(4), b = 5.6983(4), c = 8.2914(5) Å, β = 103.201(6)°, V = 281.3(5) Å3, Z = 2, Dx = 4.41 Mg m−3; SmMoF7: a = 6.0686(4), b = 5.6503(6), c = 8.2261(5) Å, β = 103.246(5)°, V = 274.6(4) Å3, Z = 2, Dx = 4.59 Mg m−3; EuMoF7: a = 6.0337(5), b = 5.6311(4), c = 8.1953(5) Å, β = 103.420(6)°, V = 270.8(4) Å3, Z = 2, Dm = 4.63, Dx = 4.67 Mg m−3; GdMoF7: a = 6.0138(4), b = 5.6241(5), c = 8.1726(5) Å, β = 103.371 (7)°, V = 268.9(5) Å3, Z = 2, Dx = 4.77 Mg m−3; TbMoF7: a = 6.0081(5), b = 5.6621(5), c = 8.1868(5) Å, β = 103.685(7)°, V = 270.6(5) Å3, Z = 2, Dx = 4.76 Mg m−3; HoMoF7: a = 5.9801(4), b = 5.6456(5), c = 8.1282(5) Å, β = 103.465(6)°, V = 266.9(4) Å3, Z = 2, Dx = 4.90 Mg m−3; ErMoF7: a = 5.9293(5), b = 5.5732(5), c = 8.0831(5) Å, β = 103.540(7)°, V = 259.7(5) Å3, Z = 2, Dm = 5.01, Dx = 5.07 Mg m−3; TmMoF7: a = 5.9309(4), b = 5.5976(5), c = 8.1096(4) Å, β = 104.056(5)°, V = 261.2(4) Å3, Z = 2, Dx = 5.06 Mg m−3; YbMoF7: a = 5.8950(4), b = 5.5448(4), c = 8.0199(5) Å, β = 103.552(6)°, V = 254.9(4) Å3, Z = 2, Dx = 5.24 Mg m−3; LuMoF7: a = 5.8593(5), b = 5.5172(5), c = 8.0423(6) Å, β = 103.752(8)°, V = 252.5(6) Å3, Z = 2, Dx = 5.31 Mg m−3; YMoF7: a = 5.9397(4), b = 5.5945(5), c = 8.1108(5) Å, β = 103.643(6), V = 262.0(4) Å3, Z = 2, Dx = 4.03 Mg m−3. The variation of unit-cell data is in agreement with the lanthanidic contraction and the tetrad effect. Powder diffraction data have been obtained at 293 K with a Philips PW1050/25 counter diffractometer; Ni-filtered Cu Kα radiation ({\bar \lambda = 1.5418 Å). The JCPDS Diffraction File Nos. are: LaMoF7 38–1498; CeMoF7 38–1497; PrMoF7 38–1496; NdMoF7 38–1495; SmMoF7 38–1494; EuMoF7 38–1493; GdMoF7 38–1492; TbMoF7 38–1491; HoMoF7 38–1490; ErMoF7 38–1489; TmMoF7 38–1488; YbMoF7 38–1487; LuMoF7 38–1486; YMoF7 38–1485.

Notes: Reflection electron microscopy (REM) in ultra-high vacuum (UHV) conditions is reviewed. UHV-REM can characterize surface structures of monolayer levels such as steps, domains of reconstructed surface structures and their boundaries and these capabilities are used to observe surface dynamic processes such as phase transitions of reconstructed surface structures and adsorbate structures and adsorption processes, oxidations, sublimations and ion-sputtering and annealing. The method is compared with other surface-imaging techniques.

Notes: General formulae allowing estimation of the unit-cell volume are derived. They are valid for all Bravais lattices. The precision of the estimation is discussed. The examples illustrate the application of the method.

Notes: The optimization method of indexing powder diffraction patterns based on minimizing the suitable criterion function within a required range of unit-cell parameters is presented. The features of the method are discussed. A computer program is described which performs the optimization in two steps: systematic search and Powell method. The results are refined by the least-squares method. The actual version indexes patterns of orthorhombic or higher symmetry.

Notes: A design is given for a powder diffractometer on a synchrotron source. A reasonable balance between resolution and luminosity is achieved by making the effective mosaic spread parameters of the monochromator and analyser crystal equal to the vertical divergence of the synchrotron beam. A monochromator with a Bragg angle of 60° should be used. Care is necessary in preparing specimens for data collection to avoid the hazards of particle-size broadening on one hand and extinction on the other. The conclusions are compared with recent experimental work.

Notes: The recursive method of Schmidt & Fedorov [J. Appl. Cryst. (1978). 11, 411–416] allows for calculation of the correction function g(t) for slit-height smearing in terms of the slit transmission function f(t). In this method, if the primitive function g(t) = g0(t) is known for the interval 0 ≤ t ≤ t0, then g(t) = gn(t) can be calculated recursively, for the intervals n½t0 ≤ t ≤ (n + 1)½t0. A general method is presented for calculating g0(t) in powers of t. To illustrate the utility of our method, three numerical examples are examined, indicating rapid convergence to a level of accuracy of 1 in 106.

Notes: An X-ray partial diffuse intensity equation has been explicitly expressed as a function of ordering energies between different atomic species by referring to the description of the interatomic correlation function of de Fontaine [J. Phys. Chem. Solids (1973), 34, 1285–1304]. The expression suggests the appearance of a negative partial intensity. As an interesting example of its application, the calculation of the partial intensity for the disordered Cu2NiZn ternary alloy by means of the derived equation in terms of the ordering energies obtained theoretically by de Rooy, van Royen, Bronsveld & de Hosson [Acta Metall. (1980), 28, 1339–1347] is shown to lead to a distribution of diffuse scattering very similar to that given by experimental observations [Hashimoto, Iwasaki, Ohshima, Harada, Sakata & Terauchi (1985). J. Phys. Soc. Jpn, 54, 3796–3807].

Notes: A novel type of X-ray diffraction pattern results when a layer-disordered crystal is photographed by X-ray precession using the stacking direction as the precession axis and no layer-line screen. The 10l, 20l, 21l and symmetry-equivalent rows of diffuse scattering of layer-disordered wurtzite (ZnS-2H) are represented by compound loops superimposed on the zero-level hk0 diffraction pattern. Closed loops result because the reciprocal-lattice rows associated with diffuse scattering remain in contact with the sphere of reflection during the precession cycle. Formulae for dimensional parameters of the compound loops of diffuse scattering are derived from the sphere-of-reflection construction.

Notes: The distribution of carbon among octahedral and tetrahedral interstices of the f.c.c. iron-alloy lattice has been measured by neutron diffraction on a poly crystalline rod of an FeMn alloy containing 5.4 at.% carbon, quenched from 1373 K. The integrated intensities of six reflections have been collected for several sample positions in order to reduce the effect of preferred orientation in the sample. The fraction of carbon atoms occupying octahedral interstices has been found to be 0.9 (1). In analogy with previous work on spinels a thermodynamic relation has been deduced which allows the difference of nonthermal internal energy between the two sites to be calculated from measured occupancy.

Notes: The unit-cell parameters of the mixed-valence oxide V3O5 have been studied as functions of pressure from 0.3 up to 7.5 GPa in a single-crystal experiment involving measurements at 21 different pressure values. A diamond-anvil high-pressure (h.p.) cell of new construction [Malinowski (1987). Submitted to J. Appl. Cryst.] mounted on a four-circle X-ray diffractometer was used. At Pt = 6.25(9) GPa a phase transition was observed at room temperature. This is analogous to the semiconductor-metal transition observed at Tt = 428 K and normal pressure, which implies a change in the ordering of the metal-atom valencies. The linear Eulerian strain tensor for the transition has been calculated. The bulk modulus K has been determined for the low-pressure (l.p.) as well as for the h.p. phase: Kl.p.(0.3–5.5 GPa) = 269(3), Kh.p.(6.3–7.5 GPa) = 175(11) GPa. Certain anomalies in the cell-parameter values in a small pressure interval around the phase transition indicate a preparation in the crystal structure for the transition in both the l.p. and the h.p. phase.

Notes: The variation of diffuse scattered intensities with scattering angle due to resolution effects is described by different Lorentz factors depending on the dimensionality of the disorder (e.g. diffuse streaks or planes) and the type of scan. Intensities are calculated by folding the cross section of the diffuse scattering with the resolution function of the instrument. For the most general results existing calculations of the resolution function are extended to include (i) a characteristic line spectrum used together with a monochromator, (ii) a possible mis-set of the monochromator (e.g. between Kα1 and Kα2) and (iii) a perpendicular arrangement of the scattering planes at the monochromator and at the sample. Both a Gaussian and a slightly simplified rectangular approximation have been applied. Explicit formulae are derived for sharp diffuse streaks and planes for a point measurement as well as integrated intensities. Since the evaluation of point measurements requires exact knowledge of the instrumental divergences and, moreover, there are differences between the two approximations, it is strongly recommended that integrated intensities be used, preferably from scans perpendicular to the streak or plane.

Notes: The use of the fine structure of X-ray rocking curves for the characterization of the abruptness of heterointerfaces is presented for the particular example of Ga1−xAlxAs/GaAs heterojunctions. The sensitivity of the method is discussed in detail for the 400 reflection with two different wavelengths (1.2378 and 1.5410 Å). It is shown that the conclusions can be extended to other reflections and wavelengths provided that the ratio χhi/χhr depending on both the absorption and the strength of the reflection is kept below 10−1.

Notes: A fast simple and non-destructive method is described to provide qualitative structural information for flat-plate crystals and epitaxically grown films. The technique, based upon the Buerger precession camera, produces an easy-to-interpret photograph of the reciprocal space of all the components at once: substrate, film or buffer layer, and/or superlattice. A wide variety of technologically important examples are used to illustrate the technique: a mixture of CdTe phases on (001) Si, an aluminium layer on a (001) Si substrate, (001) Ge epitaxic layers on (001) Si substrates, three combinations of possible orientations of CdTe epitaxic layers on various substrate types, CdTe/ZnTe and other II–VI superlattices on GaAs substrates. In addition, the precession pictures readily reveal the common [111] face-centered cubic twin fault, or stacking disorder, seen in bulk growth methods. This finding may have severe consequences for the electronic mobility and the feasibility of devices fabricated from these composite systems.

Notes: X-ray rocking-curve analysis is applied to the detection of artifacts in multilayer epitactic growth of III–V ternary compounds by metal–organic vapour-phase epitaxy (MOVPE). Transient spikes in the composition result in unwanted additional thin layers whose presence disturbs the interference pattern expected from the designed heterostructures, thus modifying the oscillating part of the reflection profile. X-ray methods and secondary-ion mass spectroscopy (SIMS) lead to descriptions of the actual layer stacking in good agreement with each other.

Notes: A simple numerical method has been developed to correct for absorption and decay effects in the intensities measured by area-detector X-ray diffractometers. Application of this method improves not only the internal consistency of symmetry-equivalent reflections, but also the agreement between the two independent data sets.

Notes: A system for collecting and measuring X-ray diffraction data from protein crystals has been developed for a multiwire area detector. Computer programs run concurrently on two microcomputers, which collect and reduce detector data to integrated intensities. The self-contained system consists of an X-ray area detector, a rotation/oscillation camera, and two microcomputers connected by a high-speed Ethernet network. One microcomputer is dedicated to operation of the detector, control of the camera, and storage of the raw data. The second microcomputer automatically integrates the data as they are collected and allows the user to monitor the quality of data as they are processed. The integration programs are written in Fortran 77 and have been designed to be portable. Additional programs for crystal alignment, detector and camera control, and graphics are written in the C programming language. A description of the system, some characteristics of the detector, and the results of data collection are presented.

Notes: Compact expressions are given for first and second derivatives necessary for inclusion of the Becker–Coppens isotropic extinction model in a least-squares procedure. Derivatives with respect to a scale factor, a structural parameter, and the two extinction parameters g and ρ are considered, for refinements on |F| and |F|2.

Notes: The method is designed to be used with a batch-processing computer system and will determine the integrated intensities of the spots on an X-ray diffraction photograph of an oriented fibre of a partially crystalline synthetic polymer. It is necessary to assume that the spot boundary is elliptical, that the intensity distribution along any line through the centre of this ellipse is Gaussian, and that the background intensity variation is linear over the region of a spot; these are justified experimentally, although, in the radial direction, the choice of a Gaussian intensity distribution is probably theoretically unsound. The computational procedures correct for minor differences between users in the choice of input parameters and reject bad choices. The method was applied to determine the intensities of the 30 visible spots in the diffraction photograph of oriented poly(trimethyleneterephthalate) which were used in a subsequent structure refinement. successful integrations were obtained for 22 spots, the failures being (1) pairs of similar intensity just resolved by eye, (2) better resolved pairs of which one member is stronger than the other, or (3) very weak. Statistical tests indicated very much better internal consistency of data than is usually obtained with these materials, and enabled a rational weighting scheme to be used in the structure refinement. The R factor of 7.9% obtained is unusually low, indicating much improved accuracy over earlier methods.

Notes: The Lorentz–polarization factor (1 + cos22 θ)/sin2 θ cos θ for the integrated intensity of a diffraction line is different from the Lorentz–polarization factor (1 + cos2 2θ)/sin2 θ for a diffraction-line profile; nevertheless, in most of the literature it is being used to correct diffraction-line profiles. The errors introduced in the peak shape and position by use of the Lorentz–polarization factor (1 + cos2 2θ)/sin2 θ cos θ are discussed.

Notes: A matrix formulation is given of the numerical procedures for the iterative method of X-ray diffraction phase analysis [Fiala (1980). Anal. Chem. 52, 1300–1304; Fiala (1982). Cryst. Res. Technol. 17, 643–650].

Notes: A full-symmetry Patterson search method is presented that performs a molecular coarse rotation search in vector space and orientation refinement using the σ function. The oriented molecule is positioned using the fast translation function τ0, which is based on the automated interpretation of τ projections using the sum function. This strategy reduces the number of Patterson-function values to be stored in the rotation search, and the use of the τ0 function minimizes the required time for the development of all probable rotation search solutions. The application of this method to five representative test examples is shown.

Notes: An interactive program for creating and displaying molecular models on an inexpensive hardware system of medium performance is described. IMAGE is capable of (i) facilitating examination and interpretation of electron density maps and (ii) the depiction and manipulation of the covalent representation of molecules. IMAGE is written in Fortran 77 and is running on a PDP 11/44 under RSX 11 M version 4.1. The graphics screen is a DEC VT 125 and the plotter is a Tektronix 4662.

Notes: The space-group symmetry implied in the atomic coordinates of a structure can be reconstructed by deriving the metric symmetry elements of the lattice from the cell data, and finding the location and the glide for corresponding space-group symmetry elements with the same orientation using the list of atomic coordinates. The MISSYM computer program designed along these principles treated correctly the known examples of overlooked symmetry or quasi-symmetry that were submitted to it. As no computer program operating on refined atomic coordinates can prove the presence of extra symmetry in the crystal, the user should scrutinize the experimental evidence and report either a different space group or the existence of pseudo-symmetry whenever extra structural symmetry elements are disclosed by the program. The MISSYM program is part of the NRCVAX system of programs.

Notes: A simple method of calculating the resolution of small-angle neutron data from diffractometers which use time-of-flight techniques has been derived in terms of the variances of the time and spatial channels of the measurement. The method is used to calculate the resolution in scattering-vector space of scattering intensity from a simulated isotropic scatterer on the small-angle neutron diffractometer at the Intense Pulsed Neutron Source at Argonne National Laboratory. The effects of the various instrumental geometries, time-of-flight measurement strategies and data reduction methods that can be chosen by the experimenter are considered. It is found that the best resolution is obtained with weighted constant Δt/t time-of-flight data acquisition schemes, with the detector placed in the beam in such a way that the highest possible angular range is accessed.

Notes: A method is described of synthesizing a real-space distribution of scattering points which will give rise to virtually any required diffraction pattern. The distribution may be used in the form of an optical diffraction screen to give an immediate visual check on both the real-space and reciprocal-space distributions. The method is applied to two examples which exhibit electron diffraction patterns with diffuse intensity distributed in the form of complex loci in reciprocal space: certain transition-metal niobium sulfide intercalates in which ordering of metal ions and vacancies occurs; and the high-temperature phase of 1T tantalum disulfide in which phenomena due to charge-density waves (CDW) and accompanying periodic lattice distortions (PLD) are observed. It is shown how useful statistical information concerning the local ordering may be obtained from the resulting lattice realizations.

Notes: A statistical model of step-scanning of Bragg reflections on an X-ray diffractometer has been suggested [Dietrich (1976). J. Appl. Cryst. 9, 205–208]. A method and software for stability checking of X-ray automatic diffractometers at the user's laboratory have been developed on the basis of this model. The method is an extension of the technique proposed by Dietrich (1976) and reveals the operational instability of the instrument by processing the data of repeated measurements of a reflection intensity profile of a test crystal. The developed software package gives information about the error in initial positioning, the speed instability of the goniometer and the instability of the X-ray source and detector. The method was applied to a number of automatic four-circle X-ray CAD-4 (Enraf–Nonius, Holland) and Syntex (USA) diffractometers. The results obtained indicate that the method has high sensitivity and can be useful for practical crystallographers to reveal defects of their instruments.

Notes: The contribution of a particular atom in a molecule to the total X-ray scattering can be altered by varying the wavelength in the region of the absorption edge of the atom. It is shown that only the changes in the real part of the anomalous scattering of the atom provide significant changes in a pattern from a fibre containing molecules with helical symmetry. Changes due to the imaginary component are small and Friedel differences cannot be observed, owing to the fibre disorder. The information which can be obtained is equivalent to that given by a truly isomorphous heavy-atom derivative. For the general case this is not sufficient to provide unambiguous phase information. If a twofold axis is present at right angles to the fibre axis then the amplitudes are real and the phase problem can, in favourable cases, be solved.

Notes: Samples of the catalyst Pt/γ-Al2O3 have been examined by high-resolution transmission electron microscopy (HRTEM), scanning transmission electron microscopy (STEM) and microdiffraction techniques. An epitaxic relationship of metallic Pt crystals on the γ-Al2O3 has been established. In both calcined and reduced samples, the crystalline oxide α-PtO2 was found along with metallic Pt. The oxide has a hexagonal lattice with unit-cell dimensions about 6% smaller than those previously reported. Microdiffraction from areas less than 20 Å in diameter, combined with HRTEM, STEM and secondary electron microscopy (SEM), has proved to be a very powerful technique for the study of the structures of particles less than 50 Å in size.

Notes: Lattice constants have been determined for solid solutions of the form LaxCe1−xPO4. A plot of the cube root of the unit-cell volume as a function of x shows that this system follows Végard's law.

Notes: Routines for crystal orientation and the prediction of expected reflections which are part of the data collection software package MADNES for area-detector diffractometer systems in macromolecular crystallography are described. This package is designed to be area-detector-system independent. In addition to refining crystal cell lengths and angles, crystal orientation, crystal-to-detector distance, position of the primary beam on the detector, and rotation of the detector around the primary beam, the orientation routine also refines the effective mosaic spread of the crystal, the beam inclination angle μand the detector tilt angle τ. A prealignment procedure is described for rapid rough orientation of the crystal. The routines are written in Fortran 77 in a modular way, so that they may be used independently of MADNES and each other.

Notes: Two techniques are presented for the extraction of the individual intensities of completely overlapping reflections in a powder diffraction pattern. The first is analogous to Sayre's [Acta Cryst. (1952). 5, 60–65] squaring method while the second is based upon maximizing the entropy of the Patterson function subject to the constraints imposed by the observed intensities of single and overlapping groups of reflections. Although both methods are superior to a simple equipartition of intensities amongst overlapping reflections, the maximum-entropy (ME) technique is the more robust and scientifically justifiable. The ME Patterson map extracts the maximum amount of information from the available observed intensities and is thus optimal for Patterson-technique structure determination from powder diffraction patterns. The agreement between true |F|2 values of overlapping reflections and the values obtained by maximum entropy is, in most simulated cases, excellent.

Notes: The lattice parameter of the title compound was found from X-ray Rietveld refinement to be 12.5755(1) Å; in addition to the diffractometer zero point, the specimen surface displacement was also varied. The estimated atomic positions of O and H atoms obtained from several refinements are in agreement with the values reported previously either from neutron or X-ray data. The degree of serial correlation in residuals was evaluated using the Durbin–Watson d statistic.

Notes: Structural studies of polycrystalline CuAsSe2, Cu3AsSe4 and Cu3AsSe3 are reported. These were found to be cubic with space group Pm{\bar 3}m and lattice parameters as follows: (1) CuAsSe2: a = 5.513(4) Å, V = 167.47(1) Å3, Z = 2; Dm = 5.56(6), Dx = 5.88 g cm−3. (2) Cu3AsSe4: a = 5.530(5) Å; V = 169.11(2) Å3; Z = 1; Dm = 5.51(5), Dx = 5.75 g cm−3. (3) Cu3AsSe3: a = 5.758(9) Å, V = 190.87(3) Å3, Z = 1, Dm = 5.03(9), Dx = 4.45 g cm−3. X-ray diffraction data using a Rigaku DMAX-IIIA diffractometer and Cu Kα radiation.

Notes: A small-angle X-ray scattering experimental study of tricalcium silicate (C3S) porous gel has been performed with synchrotron radiation. The experimental scattering intensity data are in accordance with the prediction for a porous fractal model. It is concluded that the porous fractal model describes the real structure better than the classical model which assumes the existence of differentiated macro-, meso- and microporosity.

Notes: The basic equations are derived for the calculation of the angle settings of a five-circle diffractometer used for surface X-ray diffraction. This is done for a specified angle of incidence. An additional constraint that may be imposed is the horizontal alignment of the diffraction rods to match the divergence of the synchrotron X-ray source or the horizontal setting of the physical surface normal. Alignment procedures and the derivation of the orientation matrix are discussed.

Notes: A new X-ray topographic method is described which images with similar contrast those parts which have the same lattice spacings in an inhomogeneous single-crystal irrespective of the lattice inclination. This method was applied to GaAs, in which a variation of Δd/d ≲ 10−5 was topographically resolved.

Notes: A technique is described to determine the orientation of a crystal from a single oscillation photograph. This procedure is particularly useful for crystals that are so radiation sensitive that stills can be taken neither before nor after the single oscillation data exposure. It also ensures optimal use of synchrotron radiation, as all available time is then used to collect data photographs, while no time is wasted in obtaining setting photographs or in correcting the crystal orientation. The method is based on correlating the unique set of calculated normals to reciprocal-lattice planes with the observed zone axes on the oscillation film. Although the method was developed to allow processing of films taken of radiation-sensitive Mengo virus crystals, it can equally well be used to analyze any film of a crystal with unknown orientation.

Notes: A modification of the approach of May, Ibel & Haas [J. Appl. Cryst. (1982). 15, 15–19] is used. Different, neutron transmissions of solution and solvent are attributed to different hydrogen concentrations and hence different levels of incoherent scattering. On this basis a correction is applied to the measured solvent scattering. Two forms of correction may be used, depending on the reliability of transmission measurements. The method has been successfully applied to highly concentrated (250 mg ml−1) protein samples.

Notes: Small-to-moderate-angle X-ray scattering studies were performed on a troponin C solution prepared from rabbit skeletal muscle. The main feature of the scattering profile is the existence of two regions in the Guinier plot, in which data points lie on a straight line. The scattering profile was analyzed by way of a structural model with 'dumbbell' shape, based on the structure given by X-ray crystallography on troponin C. The dumbbell model shows a `quasi-' straight-line region at higher scattering angles in the Guinier plot, in addition to the intrinsic straight-line region at very small scattering angles. A ln[I(S)/S] versus S2 plot of the scattering profile at higher scattering angles gives information as to the average radius of gyration of the N-terminal and C-terminal domains of troponin C. The molecular parameters determined from small-angle X-ray scattering data of troponin C (10 mg ml−1), in the absence of Ca2+ ions, are as follows: the radius of gyration of the whole troponin C molecule is 20.4 Å and the average radius of gyration of the N- and C-terminal domains is 15.6 Å. From these radii of gyration, the center-to-center distance between the two domains is estimated to be about 26 Å.

Notes: A weighted form of the Durbin–Watson d statistic [Durbin & Watson (1971). Biometrika, 58, 1–19] has been used to quantify the serial correlation between adjacent least-squares residuals in Rietveld refinements of step-scan powder diffraction data. Analyses of X-ray and neutron data from a range of materials have shown that the d statistic: provides a sensitive measure of the progress of a refinement and remains discriminating when other agreement indices fail, for example, when comparing results at different step widths; provides quantitative information about the significance of serial correlation present in the residuals; provides a convenient means of assessing the reliability of the estimates of the parameter variances; and provides a basis for the selection of values of step width and intensity corresponding to optimum and/or minimum use of experimental beam time.