ALBERT

Notes: The dielectric constants (εr) of several cadmium iodide polytypes have been measured and found to be higher than that of the parent 4H structure. The dielectric constants for several long-period polytypes have been found to lie between 60 and 190 whereas the 4H parent structure has a value in the range of about 15 to 30. In particular, both increasing polytype periodicity and increasing disorder increase the dielectric constant, e.g. from 16 for an ordered 4H structure to 114 for a 32H structure and 67 for a highly disordered 4H structure. In the absence of disorder a particular polytype has its own characteristic dielectric constant value, e.g. the two 14H polytypes which have a common εr value of 63.

Notes: The separation or overlapping of adjacent subgrain images in Berg–Barrett X-ray (reflection) micrographs is described for a reasonably general misorientation between the crystal subgrains. The five crystallographic parameters which describe the diffraction experiment also specify, effectively, the direction of the rotation axis for the misorientation, the amount of the angular misorientation, and the relative orientation of the subgrain boundary interface.

Notes: An effective method for greatly reducing the electron exposure of radiation-sensitive organic or biological specimens while recording their diffraction patterns in a high-voltage (MeV range) electron microscope is described. It involves recording on double-coated screen-type medical X-ray film and backing it with a luminescent radiographic screen which intercepts the transmitted electrons and emits visible light that exposes the bottom emulsion of the film. Values of sensitivity, resolution, and enhancement ratio are tabulated: the latter values range up to 41. Typical patterns taken with l-valine are shown.

Notes: A new procedure for solving the integral equation which connects the crystallite-diameter distribution function pν(D) to the pure diffraction profile is presented here. The representation of pν(D) is based on a polynomial expansion modulated by a generalized Cauchy function. The influence of the truncation of the diffraction profile and of the number of coefficients of the polynomial expansion is studied. This procedure has been applied with success to some catalysts, the granulometry of which is known by other experimental approaches.

Notes: Methylammonium manganese(II) trichloride dihydrate crystallizes with a monoclinic unit cell, a = 7.795 (2), b = 9.154 (2), c = 11.462 (4) Å, β = 91.28 (3)°, space group P21/c. Its structure is related to that of α-RbMnCl3.2H2O.

Notes: Pb3(VO4)2 is monoclinic at low temperatures with space group P21. The lattice constants are a = 15.042, b = 6.106, c = 18.586 Å, β = 111.88°. The indexed powder diagram is given.

Notes: An analysis of thickness variances from an electron-microscope cross-section of myelin sheath shows that the standard deviation varies proportionally to the square root of the number of intervening lamellae. This result implies that the lamellar irregularities are additive and that a paracrystalline stacking model is an appropriate representation for the myelin structure. The X-ray diffraction data from myelin exhibit the characteristics of a paracrystalline material. Both electron microscope and X-ray diffraction evidence suggest that myelin is paracrystalline rather than crystalline.

Notes: The paper refers to a previously described two-dimensional model of crystal-growth disorder in which the type of molecule or atom at a given lattice site is dependent on the previous neighbour in the two crystal directions. It is shown that a special case of the model for which some mathematical and simulation results have been published corresponds to the situation when the statistical properties of the lattice are symmetric to reflection in a plane. This symmetry may be achieved by applying a constraint to the growth probability parameters and, moreover, enables a solution to be found for the statistical properties of the lattices.

Notes: It is shown that the neutron small-angle scattering of pure polycrystalline metals is strongly connected with surface imperfections in the samples (surface irregularities and oxide layers) rather then with the grain boundaries. It is also shown that the asymptotic form of the scattering cross section of the surface imperfections is q−4 like the Porod law.

Notes: Precision strain-gauge measurements of the basal-plane lattice asymmetry (a−b)/[(a + b)/2] in gallium metal have been made in the temperature range 190 K 〈 T〈 300 K. When analyzed in conjunction with previously published data these results indicate that the asymmetry is positive from the melting point, TM = 303 K, down to at least 2 K. The asymmetry reaches a limiting value of 5750 × 10−6 at low temperatures and is decreasing rapidly toward zero near TM. The extrapolated `tetragonality' temperature is T* ̃354 K.

Notes: Data have been collected from a standard silicon sample with Cu Kβ radiation selected by means of a pyrolytic graphite monochromator mounted in the scattered beam. The peak shapes can be described reasonably well by Lorentz-type functions, but not by a Gaussian function. These results have been applied to the profile refinement of data for rhombohedral La0.75Sr0.25CrO3, a perovskite-type compound which is slightly distorted from the ideal cubic structure. The analysis, which employs a slightly modified version of a neutron profile program [Rietveld (1969), J. Appl. Cryst. 2, 65–71] indicates that the best compromise for the peak shape is a modified Lorentz function of the form A[1 + C(Δ2&thgr;)2]−1.5 fitted over a range of two halfwidths on each side of the Bragg peak position. The results are compared with a similar refinement of neutron data collected from the same sample.

Notes: A new numerical method is presented for simultaneous smoothing, desmearing and Fourier transformation of X-ray and neutron small-angle scattering data. The method can only be applied to scattering curves from dilute particle systems, i.e. for scattering media whose distance distributions are zero beyond a certain value. The distance distribution of the scattering medium is approximated by a linear combination of about 20 to 30 cubic B-splines. These spline functions have a restricted extension in real space. Their coefficients are adjusted by a weighted least-squares operation so that the series, after being Fourier transformed and smeared according to the geometry and wavelength distribution, represents an optimum smoothed approximation of the experimental data. Tendencies towards oscillations in the least-squares operation are suppressed by a new stabilization routine. The method offers a new possibility for the estimation of the radius of gyration, which is generally superior to the Guinier approximation.

Notes: The channel systems of (4-methylpyridine)4Ni(NCS)2 and (4-vinylpyridine)4Co(NCS)2 are described and compared. Much similarity is found and the minimum diameters of free passage are estimated in each case. It is concluded that both complexes are clathrates with notable zeolitic properties.

Notes: Gadolinium molybdate was twinned by irradiating the crystals for a few seconds with a 10.6 μm CO2 laser. Slit-shaped regions were irradiated to produce localized heating, thereby setting up suitably oriented thermal stresses of sufficient size to induce mechanical twinning. Ferroelastic twin patterns are difficult to control by this method because the required slit orientations are not parallel to domain-wall directions.

Notes: A new method for unfolding X-ray diffraction profiles is reported. The procedure is based on the minimization of an economical function defined as the sum of the squared relative differences between the experimental function and a calculated profile. The latter is numerically computed from the convolution equation by fitting the pure diffraction profile with a damped polynomial. The influence of the truncation and the width of the instrumental function is studied; some results are given concerning the evaluation of a constant background for both the experimental and instrumental functions and its influence on the precision of the results. Finally, the perturbation produced by the simulation of statistical noise is discussed.

Notes: The tetrapolyphosphate (NH4)2GeP4O13 is triclinic (P{\bar 1}), with a unit cell: a = 15.08 (1), b = 7.763 (5), c = 4.914 (5) Å, β = 98.18 (1), β = 96.53 (1), γ = 84.04 (1)° and Z = 2. This salt is isotypic with the corresponding salt of silicon: (NH4)2SiP4O13, previously described by the author.

Notes: Cell data for cubic solid electrolytes RbAg4I5 (i) and KAg4I5 (ii) are accurately given: (i) a = 11.235±0.006 Å, (ii) a = 11.143±0.006 Å. Precise crystal data are also shown for orthorhombic Rb2AgI3 (a = 19.957 + 0.006, b = 10.227±0.003, c = 4.896±0.003 Å) and K2AgI3 (a = 19.522±0.009, b = 10.011± 0.003, c = 4.775±0.003 Å). Crystallographic behaviour with respect to the value of x for (RbxK1−x)Ag4I5 and (RbxK1−x)2AgI3 solid solutions is described.

Notes: In directionally solidified Pb–Sn eutectic, prepared by the Bridgman technique, it has been found that it is possible to obtain grains of nearly perfect lamellar structure and stable at elevated temperatures. The interlamellar spacing λ is 1 μm and the mean distance \bar D between fault lines 20 λ whereas they are respectively 1.5 μm and 7 λ in neighbouring grains. The orientation relation is: growth direction || [2\bar 11]Pb and ⊥ (12\bar 1)Sn, lamellar interfaces || (47\bar 1)Pb and (523)Sn. The spacing between planes perpendicular to the growth direction is the same in both phases. By studing the orientation relation with Bollmann's theory, zero planes and interfaces are found to be parallel. The coherent interphase boundary can explain the particularities of these grains. Their origin is discussed and related to the nucleation conditions.

Notes: The intensity distribution observed in neutron diffraction experiments in Zr–20% Nb alloys is analyzed in terms of the essential anharmonicity in the free energy, believed to be important in the Group IVb transition metals. It is found that a second-order approximation in the atomic displacements for calculating the diffuse intensity readily accounts for the main features of the intensity distribution. In particular, the observed ratio of intensities between certain superlattice reflections is shown to be related in a straightforward manner to the ratio of harmonic to anharmonic free-energy coefficients. Furthermore. in order to describe the observed curvature in the diffuse streaking in some Ti and Hf alloys, the displacement field of a localized ω-like particle is obtained by adding longitudinal displacement plane waves with wave vectors distributed on one octant of a spherical surface centered at the 〈111〉 octahedral site of the reciprocal lattice, and passing through point km ∼ 0.71 [ 111 ]. Computer-generated patterns of dots simulating such displacement fields were Fourier-transformed optically, yielding diffuse intensity' in excellent agreement with the circular streaking found experimentally in electron diffraction patterns of certain Ti and Hf alloys.

Notes: An X-ray diffraction method has been used to study the influence of solute concentration on molecular associations in aqueous solutions of urea. Calculations, from experimental intensities, of unsharpened electronic radial distribution functions (RDF) are presented for the range of urea concentration from 0.83 to 16.8 mol Kg−1 (5 to 100% solutions). The changes in RDF with increasing urea concentration are complex. Unequivocal interpretation of the distribution functions is not possible, but the major effect of the relatively bulky urea molecules on the water structure appears to be caused by distortion of the water matrix. At urea concentrations of 50% and 100%, features of the RDF not visible in the RDF's at lower concentrations indicate the presence of long-range (over a distance of about 8 Å) structural relationships possibly due to urea–urea interactions: such an interpretation would make urea–urea hydrogen-bonded associations unlikely at lower urea concentrations.

Notes: A technique for including all neutrons scattered by the specimen in the refinement procedure is described. This eliminates the sensitivity of atomic parameters to the choice of background level which occurs when only the profile is used in the refinement.

Notes: The contrast of dislocations in X-ray topographs taken in the Guinier–Tennevin mode with synchrotron radiation has been studied. In reflections where high orders were insignificant, dislocation images appeared very similar to those in Lang topographs taken with characteristic radiation. At large specimen-to-plate distances orientation contrast is important in the direct image. The sense of the Burgers vector of dislocations showing double contrast can be deduced.

Notes: Aluminium single crystals have been elongated at 78 K along an axis close to 〈110)〉. During the recrystallisation process new crystals appear in the vicinity of the deformation bands (deformation heterogeneities) and have only two orientations. The mechanism of the single and double Rowland transformations of the matrix may be responsible of these orientations. It is also found that the double Rowland transformation may account for the change between the initial and final orientations of the matrix (after an 80° elongation). The correspondence between the slip deformation of the matrix and a deformation, due to the double Rowland transformation which may be localized in the deformation bands, is established.

Notes: Polystyrene latex spheres of 1.011 and 0.234 μm diameter were used to observe low-angle X-ray scattering. For particles of about 1 μm in diameter the central scattering has not been observed accurately with characteristic X-rays such as Cu Kα and Mo Kα radiations, because it is strongly affected by the primary beam and the parasitic scattering of the slits. The present results show that the central scattering of particles of this size can be measured within 22′ without such influences by the use of C Kα radiation (wavelength 44.7 Å).

Notes: The average radius of platelet-like defects in crystals may be estimated by the non-destructive technique of X-ray topography of `spike' diffuse reflections, applicable to platelet radii several orders of magnitude smaller than the resolution limit of conventional X-ray topographic techniques. With the most favourable diffraction geometry, the diffuse topograph image may be regarded simply as the convolution of the platelet number density projected along the diffracted beam direction with the Airy diffraction intensity pattern appropriate to the radius of individual platelets. Different integrals of the Airy diffraction intensity profile are involved in photometric traverses of `spike' section topographs and of `spike' projection topographs. The required integrals are evaluated and discussed.

Notes: The special features of X-ray energy-dispersive powder and single-crystal diffraction using synchrotron radiation are discussed on the basis of experiments performed at the Deutsches Elektronen-Synchrotron, DESY. The method is shown to be of particular value for fast structure identifications, experiments for which large scattering vectors are important, studies of phase transformations and chemical reactions at elevated temperatures and high-pressure studies. Studies of time-dependent phenomena using pulsed external fields are discussed.

Notes: A new method of texture analysis is presented that possesses the main advantages of both the Bunge–Roe and Williams methods. The general relations between pole densities and orientation distribution are given as well as an example of the result that can be obtained when only a single incomplete pole figure is available.

Notes: A computer-controlled diffractometer has been built which permits intensity measurements to be made in any direction in reciprocal space in the diffraction plane with step sizes down to 0.01′′ of arc. Three examples illustrate the performance and application of the instrument: (a) perfect silicon, (b) gadolinium gallium garnet with growth striations and (c) niobium with low-angle grain boundaries.

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.