ALBERT

Notes: A technique is described for the determination of crystallographic polarity which is generally applicable to large polar crystals containing an element heavier than K. It is an extension and simplification of Cole & Stemple's method in which the intensities diffracted by (00 l) and (00\overline l) planes are compared at wavelengths close to an absorption edge of a constituent element. A definitive polarity determination may now be made without previously measuring or assuming values of Δf′ and Δf′′ at the edge.

Notes: A method is suggested, using diffraction line displacements, to facilitate simultaneous determination of one-dimensional strain in a particular direction in the surface of a polycrystalline material and of the lattice parameter corresponding to the unstressed state. A single exposure at perpendicular incidence of the primary X-ray beam enables both values to be obtained. Full advantage is taken of the ratios of diffraction ring diameters.

Notes: A computer program has been written for the evaluation of the size of coherently diffracting domains, microstrains, and stacking fault probabilities for f.c.c. and h.c.p. single crystals. After correcting for instrumental effects, the Warren–Averbach analysis is applied to reflections which are not affected by stacking faults. The fault-broadened peaks are then analyzed and the results plotted.

Notes: The methods of Lake [Acta Cryst. (1967) 23, 191] and Schmidt [Acta Cryst. (1965) 19, 938] for calculating slit-length collimation corrections in small angle X-ray scattering have been compared in a number of tests. The tests showed that under most conditions neither method introduces errors larger than the expected uncertainty in present-day scattering data and that slit-length corrections are relatively insensitive to small changes or errors in the weighting function. Neither method is extremely sensitive to random errors in the measured intensity but the effect of these errors is somewhat smaller with Schmidt's method than with Lake's. Three cases were found in which one of the correction methods should be avoided or used with caution: with Schmidt's method errors are produced in the outer part of the scattering curve if the angular increment is too large – a criterion has been developed for determining acceptable increments; if Lake's method is used in an angular region in which a scattering curve has subsidiary maxima or minima, more iterations may be necessary than are required for monotonically decreasing scattering curves; the usual form of Lake's method, which was developed to converge rapidly with curves which have a zero-angle maximum, was sometimes found to give appreciable errors for curves with a pronounced minimum at zero scattering angle. When the latter type of curve is corrected by this method, precautions should be taken to ensure that the collimation correction is not introducing errors.

Notes: A modification of the refinement procedure proposed by Shoemaker & Bassi [Acta Cryst. (1970). A26, 97] is described in which the correction to the unitary orientation matrix, valid to second order in the small rotational adjustment, is applied after constraints due to crystal symmetry (which is presumably lost owing to measurement errors) have been applied to the lattice constants, and in such a way as to preserve (to second order) the unitary character of that matrix.

Notes: Two computer programs, for use with an Elliot 803 machine, are described. These programs enable atomic projections from any crystal system, other than the triclinic, to be constructed in a relatively short time.

Notes: Three methods are described of eliminating the influence of the satellite group in the variance method of X-ray line profile analysis. The first is to interpolate the line profile under the satellite group: however, the satellite group must be reasonably well distinguished from the α1 tail and from the background. The second method is to correct the experimental variance-range curve by a graphical construction: this assumes that the satellite lines and the broadening function are Cauchy in form. The third method is to compute the necessary corrections to the slope and intercept of the linear variance-range function by using model spectral distributions with and without the satellite group. The first two methods are applied to profiles from powders of iron and iron alloys studied with iron radiation, the third method uses an analytical model of the spectral distribution of the iron Kα multiplet. The corrections given by these methods to be made to the slope and the intercept of the variance-range function are nearly constant for all but the smallest amounts of particle-size broadening. It is also shown that particle sizes determined either from slope or intercept of the variance will be underestimated if correction is not made for the satellite group.

Notes: Samples of the ferrimagnetic material Ba3Co2Fe24O41, pre-aligned in a magnetic field and sintered at various temperatures, have been examined for preferred orientation. Schulz's reflection technique and the standardizing method of Holland were used to determine quantitative pole figures of several lattice planes. The texture bears a close resemblance to a `fan texture' in which the crystallites have their basal planes parallel to a preferred direction. The sharpness of the texture increases with increasing sintering temperature. At 1320°C an exaggerated grain growth takes place. Inhomogeneity of the magnetic field throughout the sample results in local differences in orientation.

Notes: A procedure involving the use of Fourier coefficients is suggested for the separation of the el component from an experimental diffraction profile. In contrast to the well known Rachinger method, the procedure described here does not require experimental data at any predetermined intervals. Furthermore, the separation error, if any, is evenly distributed. As in the Rachinger method, prior knowledge of the α1−α2 angular separation and the ratio R = Iα2(max)/Iα1(max) is assumed. If, however, R is unknown, then the mathematical analysis can be extended to determine the value of R.

Notes: The local atomic arrangements in an Au-40 at.% Pd alloy were investigated by measuring the X-ray diffuse scattering from a single crystal. A computer simulation of the short-range structure was used in the interpretation of the diffuse scattering results. The interpretation indicated a tendency toward the formation of a tetragonal AB long period superlattice which has not previously been observed to occur. The static displacements of the atoms from their average positions were shown to be very small in this alloy.

Notes: A method is presented for correction of integrated X-ray intensities for preferred orientation in cubic powders. It is based upon examination of the polar axis density distribution, which describes the orientation of crystallites in the specimen, and upon the use of a cubic harmonic expansion in its representation. The method was tested on four specimens of aluminium, which showed different degrees of preferred orientation. The (111), (200) and (220) lattice plane normal distributions of the specimens were determined by measurement of the integrated intensities for various polar angles. Cylindrical symmetry was effected with a specimen spinner. The corrections to the Bragg reflections were derived from the orientation distribution obtained; they ranged from 0.5 to 12%. The final values were in agreement, to the extent of 1% or less, with those of a specimen in which the orientation distribution was random within the limits of experimental error.

Notes: A simple and rapid procedure for orientating electron diffraction patterns required for the simultaneous determination of the Burgers vectors of dislocations in twin related or coincidence site related crystals is described. The determination of the Burgers vectors of dislocations in twin related zinc crystals is used as an example of the procedure. The procedure is applicable to all crystal structures and is based on the detailed analysis of the rotations about the optical axis and goniometer tilt stage axis of an electron microscope required to produce desired diffraction patterns from the two crystals of interest. The analysis also illustrates the way in which the tensor notation may be used in elementary vector algebra applied to lattice geometry.

Notes: The diffuse X-ray scattering from single crystals of 36:64 and 50:50 KCl–KBr solid solutions has been studied. The analysis of the results, which follows the method described by Borie, is based on the approximation of a solid solution Cl−–Br−. The observed values of the distortion constant for the chloride ion are 2–3 times greater than those calculated on the basis of the conventional values of ionic radii.

Notes: The isomorphisms and the transition points of K2MoO4, K2WO4, RbMoO4 and Rb2WO4 were studied and the cell constants of the occurring phases computed.

Notes: A method is described for obtaining X-ray diffraction photographs, equivalent to those obtained under single-crystal rotation conditions, from materials available only in the form of fine microcrystalline powders of acicular or platy habit. The technique involves dispersing the crystalline powder in an appropriate thermoplastic polymer followed by streaming orientation of the particles in an extrusion process. The particles are held in their new positions by solidification of the polymer melt. With acicular powders, and using a polyethylene matrix, the orientation is improved by cold drawing. The oriented composite is immediately ready for X-ray studies.

Notes: A correlation is presented between the root-mean-square strain as measured for cold-worked f.c.c. metals and that calculated from anisotropic dislocation theory.

Notes: Single crystals of hexagonal LiIO3 and its new tetragonal modification were grown in an aqueous solution using the evaporation method under almost identical growing conditions. The hexagonal crystal changed irreversibly to the tetragonal one at about 255°C. The latter belonged to the point group 4/m. The lattice constants were a = 9.73 and c = 6.15 Å.

Notes: Cation ordering in magnesium and nickel ferrites was studied by X-ray diffraction measurements carried out at the temperature of equilibration and also on quenched specimens. The order parameters on quenched specimens agreed with results previously reported by others but not with values measured at temperature. Previous results on quenched specimens had been described by a simple mass action relation with constant ordering energy. The new results on equilibrated specimens require a modified Bragg–Williams-type relation in which the ordering energy varies with the degree of order. Both ferrites are inverted when in equilibrium at low temperature. Magnesium ferrite approaches a random distribution at high temperature with a Curie point at about 1070°C. Oxygen positional parameters were 0.243±0.001 for both ferrites at room temperature. The lattice parameter of nickel ferrite quenched from temperatures up to 1255°C was 8.3295±0.0001 Å. For magnesium ferrite the lattice parameter varied from 8.3775±0.0001 Å, when quenched from 784°C. to 8.3848, when quenched from 1271°C.

Notes: The speed of the conventional process of X-ray diffraction photography can be greatly improved by the use of a new industrial X-ray film and a fluorescent screen. This process produces a transparent film with about a tenfold decrease in exposure time and at a cost less than that of standard nonscreen film.

Notes: The lattice type of the co phase in Ti–30%V alloy was determined with the X-ray precession method. Plane-net patterns of reciprocal lattice levels, normal to [110], [100], and [111] directions of the β phase, indicate that the ω phase has a b.c.c. structure with a lattice parameter three times that of the β phase.

Notes: The increasing use of the electron microprobe analyser in research laboratories in recent years renewed the interest in the Kossel line method. Since it is possible to obtain diffraction patterns from selected areas – smaller than 5 microns diameter – this technique has been applied to measure the grain orientation in polycrystalline materials. Comparing the different published methods of interpreting the Kossel patterns, it has been found more convenient to use a digital computer with a peripheral graph plotter to obtain charts.

Notes: For accurate absorption-correction calculations, a precise knowledge of the crystal shape is essential. A least-squares determination of the coordinates of the crystal apices according to the analytical expressions derived is obtained by taking a series of silhouette photographs of the crystal directly on an X-ray diffractometer with a pinhole in the incident beam and using soft continuous X-radiation.

Notes: Ferroelectric domains in lithium niobate are equivalent to inversion twins and can be displayed in X-ray diffraction topographs using the phenomenon of anomalous dispersion of X-rays.

Notes: A new method for the phase control in an optical diffractometer is described. A photographic negative of the weighted reciprocal net is used as the mask of the diffractometer. The phase of each reciprocal point is represented by the shift of the position in the reciprocal plane. Although this method cannot reproduce the periodic image of a crystal, it is particularly suitable for reconstructing the image of a molecule in a crystal.

Notes: Unit-cell parameters and space groups have been determined on four ammonium polyphosphate salts. (NH4)5P3O10.2H2O is monoclinic with space group P21/n, a = 16.643, b = 6.719, c = 13.843, β = 98.61. (NH4)5P3O10.H2O is monoclinic, space group P2/n or Pn, a = 10.949, b = 10.377, c = 6.426, β = 91.06. (NH4)6P4O13.2H2O is triclinic, a =13.426, b = 11.874, c = 6.524, α = 93.80, β = 84.78, γ = 106.97. (NH4)4 H2P4O13 is orthorhombic, space group P22121, a = 13.359, b = 13.244, c = 8.214.

Notes: Crystal data for Zn(H2PO4)2. 2H2O and ZnH2P2O7 are given. The two compounds crystallize in the monoclinic system. The monophosphate is isotypic with Cd(H2PO4)2.2H2O.

Notes: Unusual SiC polytypic features have been studied by X-ray diffraction and chemical etching to increase understanding of their growth mechanism. The feasibility of periodic slip as a possible mode of growth of SiC polytypes has been examined. It is proposed that island formation on the helicoidal growth surface is responsible for most of the unusual SiC polytypes not explicable purely in terms of a screw-dislocation mechanism.

Notes: All the information relating to the quantitative composition of a mixture is coded and stored in its X-ray diffraction pattern. It has been the goal of X-ray diffraction analysts since the discovery of X-rays to retrieve and decode this information directly from the X-ray diffraction pattern rather than resort to calibration curves or internal standards. This goal appears to be attained by the application of the `matrix-flushing theory' and the now-proposed `adiabatic principle' in applied X-ray diffraction analysis. The matrix-flushing theory offers a simple intensity-concentration equation free from matrix effects which degenerates to `auto-flushing' for binary systems. The adiabatic principle establishes that the intensity–concentration relationship between each and every pair of components in a multi component system is not perturbed by the presence or absence of other components. A key equation is derived which conducts the decoding process. Both the matrix-flushing theory and the adiabatic principle are experimentally verified.

Notes: X-ray diffraction topography using transmission geometry has revealed an interesting array of extremely straight and narrow long-line images in sizeable copper single crystals grown under particular growth conditions by the Czochralski technique. These images are analyzed and elucidated by a model of Lomer–Cottrell dislocations. The formation of these sessile dislocations usually aids the growth of large copper crystals of high perfection. The high degree of perfection over the entire volume of the crystals accounts for macroscopic arrangements of Lomer–Cottrell dislocations which have not previously been observed by electron microscopic techniques.

Notes: Investigations of many imperfect single crystals of different materials by means of a γ-diffractometer show that the mosaic structure of large single crystals is often very inhomogeneous: the mosaic distribution function has neither a Gaussian nor a Lorentzian shape and the shapes differ remarkably for different volume elements in the sample. Current extinction theories must be considered with reservation because Darwin's intensity transport equations are solved assuming the scattering length for a given angle of incidence to be constant all over the irradiated crystal volume. This is not true for samples with inhomogeneous mosaic structure.

Notes: Superlattice formation in thin films of copper–gold alloys has been studied by the use of optical-diffraction analogues. Fraunhofer diffraction patterns of arrangements of holes in opaque screens have been compared with electron-diffraction patterns of the alloy films. It has been found possible to draw some general conclusions about the ways in which the antiphase domains fit together to produce certain characteristics of the electron-diffraction patterns. Some ideas are put forward about the growth of superlattices.

Notes: A drum-scanning microdensitometer has been automated with a minicomputer equipped with a magnetic disk memory. Part of the disk is used for temporary data storage, in a manner allowing rapid retrieval. X-ray diffraction photographs from macromolecular crystals can be measured at rates up to about 25 reflections per second, with the flexibility of an `on-line' system. The method can also be used when the computer is time-shared, but with lowered film-processing rates dependent on the number of `simultaneous' (time-sharing) users.

Notes: A profile-fitting algorithm has been applied to the determination of X-ray diffraction intensities from precession photographs. It is assumed that each reflection on the film has the same profile or scaled intensity distribution, over a two-dimensional array of points about its center. The integrated intensity of a reflection is that scale factor which gives the best fit between a scaled model profile and the optical density measurements of the reflection. The systematic error in the calculated intensity was evaluated from the discrepancy between the model and observed profiles and was about 2% for strong reflections (about 1.5 OD units). Profile fitting reduced the likely random error in the intensity, produced by errors in optical density measurements, to half the value given by conventional integration. This gain is especially significant for weak reflections which form the bulk of protein data sets. A comparison between film data processed by this method and diffractometer data for the protein lactate dehydrogenase, (34000 Dalton in asymmetric unit), showed that film data agreed with diffractometer data as well as diffractometer data sets agreed among themselves. Film data for glyceraldehyde-3-phosphate dehydrogenase (144000 Dalton in asymmetric unit) had a reliability index of 6% and significant Bijvoet differences were measured for mercury derivatives of the protein. Methods for the correction for non-linear effects in film data are evaluated for model data. It is shown that these corrections give significant improvement only when the data satisfy two conditions: they extend over a wide range of optical densities (at least 20D units) and they are reliable (better than 4% reliability index). Under these conditions an extended version of the Hamilton, Rollett and Sparks scaling algorithm performs better than the other methods considered.

Notes: The construction and successful operation of a Laue-case skew-symmetric two-crystal X-ray interferometer is described. The alignment is accomplished with an auxiliary X-ray beam, which is multiply reflected by both interferometer parts. As expected, the skew-symmetric two-crystal interferometer is found to be considerably less affected by vibrations than is the symmetric two-crystal interferometer. [Bonse & te Kaat (1968), Z. Phys. 214, 16–21]. The dependence of the crystal lattice moiré pattern on rotations about the Δρ and Δ&thgr; axes are investigated.

Notes: Precession X-ray films were scanned with a rotating-drum microdensitometer. It is necessary to correct for non-linearity between the scanner input and output. Reliability factors for estimating the precision of scanner measurements are compared. The values of the symmetry-averaged reliability factor, Rsym, vary between 3.9 and 12% and depend strongly on the quality of films, while the values of the scanning reproducibility factor, Rrept (3.5–4%), and the film-scaling reliability factor, Rscale (4.5–5.5%), depend more on the quality of scanner software and electronics than on films.

Notes: This article is the text of a general lecture given at the Ninth International Congress of Crystallography, September 1972, at Kyoto, Japan. The lecture begins with the famous experiment of Kikuchi and continues with results of work carried out under the leadership of Miyake and the author. The main topics in the former part are: anomalous enhancement and splitting of Bragg peaks, appearance of non-Bragg maxima, dynamical multiple refraction, etc. Dynamical theories including inelastic scattering are introduced, and the formation mechanism of Kikuchi bands and absorption effects are explained. Electron diffraction and electron microscopy, which were originally developed as different fields, have been unified after 1950. The development of high-voltage electron microscopy is emphasized. The reason for the enhancement of dynamical effects at very high voltages is explained in terms of relativistic diffraction theory. As an example of some most remarkable dynamical effects, the vanishing of the second-order reflexion is described. Finally, the findings and developments in moiré patterns and lattice images are reviewed briefly. The lecture is devoted to diffraction phenomena themselves and applications to structural studies are excluded.

Notes: X-ray divergent-beam anomalous-transmission patterns of [111] Gd3Ga5O12 crystal wafers cut from Czochralski-grown boules were obtained with Co radiation. The patterns contained {800} Kα transmission conics which just miss having a triple intersection. The intersection region was analyzed to determine the lattice parameter. The values of lattice parameter for wafers cut from several different boules ranged from 12.3807 to 12.383 Å with an estimated precision of ±0.0004 Å. The method is simple and non-destructive and offers sufficient precision to investigate compositional variations and to evaluate the crystals in terms of lattice parameter matching requirements for epitaxic film deposition.

Notes: Measurements made by small-angle X-ray scattering on Al–Ag alloys aged at various temperatures have shown that the asymptotic Porod's law was obeyed except for a constant term. This additional term represents a Laue monotonic intensity, due mainly to atomic concentration fluctuations inside G.P. zones. The integrated intensity Q0 of the G.P. zones themselves can then be calculated, and the boundaries of the metastable miscibility gap estimated with more precision than previously. Furthermore, the integrated intensities in the first reciprocal-space shell make it possible to discuss the crystallographic structure of the G.P. zones. After quenching from 550 to −80°C, the measured intensities agree with the theoretical values, which implies that small G.P. zones ε′ are disordered. However, for aging above room temperature, there is no agreement between measured and theoretical values. When the aging temperature is increased from 140 to 190°C, an evolution towards a complex structure of G.P. zones is shown.

Notes: Optical-transform methods remain useful aids in determining the structures of polymers, and other disordered materials, from X-ray scattering data. Hitherto a major difficulty has been the preparation of diffracting screens which contain sufficient information to specify adequately the material being studied. The Optronics P-1500 Photowrite system overcomes this difficulty. The equipment is described briefly and two examples of its use in optical transform methods are given.

Notes: Absolute reflectivities, width of rocking curves and effective absorption coefficients for many pyrolytic graphite crystals at different wavelengths were measured. The results can be described within a few percent by the formulae for the ideal mosaic crystal with absorption. Effective absorption is caused by unavoidable parasitic reflections. The measured effective absorption coefficient is the same for different specimens; it does not depend on the mosaic width. By means of this effective absorption, the peak reflectivity decreases with increasing mosaic width.

Notes: A small, colorless, single-crystal with appreciable vapor pressure at room temperature was presumed to be a new oxyfluoride compound of osmium. An X-ray study on a precession camera at a variety of temperatures from 20 to −100°C with many recrystallizations of the material revealed that it was dimorphic. One structure is monoclinic in space group C2/c with a unit cell nearly identical to that reported for OsO4. The second structure is cubic, a = 8.595 Å, Z = 8, space group P\bar 43n, with an extraordinary assortment of systematic absences which yield the most remarkable diffraction patterns the writer has ever encountered. The observations are accounted for by a structure comprising 8 tetrahedral molecules with the anions in cubic close packing at an anion–anion distance of 3.04 Å and with an Os–anion distance of 1.86 Å. The most likely possibilities for the chemical composition appear to be OsO2F2 or OsO3F.

Notes: An improved iterative deconvolution procedure is described which involves convolution of an assumed function, which represents the imperfectly known result, with the instrument function and operation on the differences between the convoluted function and the observed data function. Its advantage over the simple Fourier–Stokes treatment lies in improved resolution, its capability to handle functions with discontinuities in the function or in its derivative, and the possibility of using a variable instrument function.

Notes: The ordered structures of Cu–Pt alloys containing 65–78 at. % Pt have been investigated by a combined technique of selected-area electron diffraction and dark-field electron microscopy using thin foils prepared from bulk specimens, and three different types of ordered structure have been observed. Below the order–disorder transformation temperatures, alloys containing less than about 70 at. % Pt have the rhombohedral superlattice of the Cu3Pt5 type and those with more than 70 at. % Pt, the CuPt3-type superlattice with cubic symmetry. At lower temperatures, however, the orthorhombic superlattice is stable in the composition range from about 68 to 75 at. % Pt. On the basis of the present observations, a partial phase diagram around the composition CuPt3 has been determined.

Notes: Neutron diffraction topography with thermal neutrons has been used to observe the three-dimensional strain fields in a hot-pressed germanium crystal 8 mm thick. In the stereo-paired and section topographs the strain fields were found to be columnar along the press direction. This result was confirmed by X-ray diffraction topography performed on slices cut from the same crystal.

Notes: Gold films of several hundred Ångströms in thickness were evaporated on heated glass substrates. Fourier analysis of the 111 reflexion obtained with Cu Kα radiation showed that the thickness of the film must be fairly constant. After correction for instrumental broadening the 111 line profile was very similar to the theoretical profile of a reflexion from a plate of constant thickness. The thickness was measured in three different ways. It was shown that the first secondary maxima may be unreliable in the measurement of the thickness.

Notes: The structure of the interstitially ordered lattice formed in zirconium–oxygen alloys has been studied with use of single-crystal data obtained by X-ray and neutron diffraction methods. The structure belongs to space group P312 and the lattice parameters a and c are related to a0 and c0 of the host hexagonal metal lattice by a = √3a0 and c = c0. The ordered arrangement of interstitial oxygen atoms is described as a regular stacking of layers parallel to the (00.1) plane with the sequence (AC)B(AC)B... which is of the same type as that of nitrogen atoms in ε-Fe2N. The occupancy probability of oxygen atoms is high for interstitial sites of the A and B types while it is low for sites of the C type. The host metal lattice is distorted in such a way that spacings of successive (00.2) planes are not the same and a hexagonal network of atoms in these planes is periodically deformed.

Notes: Algebraic criteria are presented by means of which it can be decided whether a given zonal net can belong to a cubic, tetragonal, hexagonal or rhombohedral lattice or not. Methods of calculating the axes of the possible lattices from the nets are discussed.

Notes: An extensive computer program has been developed to check the internal consistency of published, numeric, crystallographic data prior to storage in the data files of the Cambridge Crystallographic Data Centre. The coding is in Fortran IV for an IBM 3701165 with 1 megabyte store. The atomic coordinates, constitution and connectivity of the unique bonded residue(s) are determined from the published asymmetric unit coordinates. Bond lengths are calculated and compared with published values, and any discrepancies are flagged. Checks are made to ensure that the valency requirements of certain elemental types are not violated. The connectivity of the system is expressed in a compact notation. Axial projection plots may optionally be produced on the line printer. The program is likely to be generally useful to individual crystallographers at various stages of an analysis as well as for checking of published data.

Notes: Experimental measurements were performed on a 48.4 at. % Ni/51.6 at. % Pt alloy. The order parameter S in equilibrium was measured as a function of temperature T by means of X-ray diffraction. Up to 592±3°C the sample is a single-phase ordered alloy with an order parameter above 0.98. Between 592 and 625±3°C there exists a two-phase region in which the ordered and disordered phases are in equilibrium. Above 625±3°C a disordered f.c.c. structure exists. Diffuse X-ray intensity measurements were performed at T = 1.1 Tc and both the short-range parameters αi and the size-effect parameters βi were calculated. From the αi parameters so derived three ordering energies νi were determined. It was found that these energies were consistent with the symmetry of the ordered phase below the critical temperature.

Notes: Crystal data at −17°C are reported for the two spectroscopically important title compounds. The experimental techniques used for the growth, mounting and preservation of the crystals in a cold room are described.

Notes: Unit-cell parameters and indexed powder patterns are reported for mescaline sulfate dihydrate, hydrochloride, hydrobromide and hydroiodide. Mescaline (3,4,5-trimethoxyphenethylamine) is a hallucinogenic substance naturally occurring in the peyote cactus, Lophophora williamsii.

Notes: The title compound, prepared by evaporation, is orthorhombic, Pcab, with a= 15.570 (6), b= 16.837 (7), c = 13.715 (4) Å. It appears to be isomorphous with previously reported forms of the iron(III) and vanadium(III) compounds.

Notes: The evaluation of the small-angle scattering of two-phase systems is greatly facilitated if Porod's law can be observed in the outer angular region.

Notes: A new iterative procedure for desmearing small-angle scattering data including the three types of resolution errors and arbitrary weighting functions is presented. The statistical errors of the data are taken into account by a `weighted least-squares' approximation, i.e. the accuracy of the data controls the iterative process. The degree of smoothing is dependent on a free smoothing parameter and on the accuracy of the data. The method is not restricted to special types of scattering functions. The termination error is negligible; therefore it is possible to correct parts of scattering distributions. This is of importance for investigations in biological substances where the scattering distribution must be determined in parts with different slit widths. No artificial oscillations are generated in the solution of the integral equation. To ensure the stability of the procedure a criterion for uniform convergence of the iterative process is involved. The results of several numerical tests are shown in the figures. The Fortran program was tested for several months with very satisfactory results.

Notes: An analytic expression for the power transmitted through a Kratky small-angle X-ray scattering collimation geometry has been derived which depends on the size and position of a uniformly intense focal spot relative to the entrance slit in the width direction. Complete details on the derivation of this power expression are available from the authors. The power expression can be optimized, subject to the constraint of a predetermined and fixed minimum angle, to yield the optimum values for the collimation system parameters. This paper discusses the optimum values of the entrance and receiving slits for a given minimum angle and describes the application of these results for the entrance slit either fully or not fully illuminated. A comparison of the analytical power expression with the experimental scattered power is also given.

Notes: The relation between the form of the scattering particles and the outer part of the small-angle X-ray scattering curve has been studied. The particles are assumed to be independent, identical, and randomly oriented and to have a uniform electron density and a smooth, strictly convex boundary surface. The electron density of the solvent is also assumed to be uniform. As earlier calculations by the authors and others have shown, the effects of the particle shape on the scattered intensity can often be conveniently described by a function called the chord, or intersect, distribution G(M). A chord, or intersect, is a straight line that has both ends on the particle boundary surface, and G(M) is defined to have the property that G(M)dM is the probability that the chord length will lie between M and M+ dM. The outer part of the scattering curve is shown to depend on the form of G(M) only in the neighborhoods of M = 0 and of any M values at which G(M) or G′(M) are discontinuous. Methods are developed for finding where these discontinuities occur and for calculating the form of G(M) in the neighborhood of these M values. In the outer part of the scattering curve, the intensity I(h) is shown to have the limiting form I(h) = \pi I_{e}\rho^{2}h^{-4}\Bigg[2A+j_{-2}h^{-2}+ \sum_{i=0}^{N+1} j_{i} {{sin (hD_i + \phi _{i})}\over (hD_{i})^{\mu}_{\kern4pt i}}\Bigg] where h = 4πλ −1 sin (&thgr;/2), 2 is the X-ray wavelength, &thgr; is the scattering angle, Ie is the intensity scattered by a single electron, A is the particle surface area, the Di are the values of M at which G(M) or G′(M) is discontinuous, and j−2 and the ji, &phgr;i, and μi are quantities which can be calculated from the principal curvatures and other properties of the surface at the two points where it contacts the chord with length Di. The values of the μi are shown to lie in the interval 0 ≤ μi ≤ 1. In this equation the assumption is made that only the term or terms which vanish least rapidly as h increases are to be retained. In addition to the assumptions which conventionally are made in the analysis of the small-angle X-ray scattering from dilute suspensions, the limiting expression for the intensity for large h requires only that the particle boundary be smooth and strictly convex. This approximation is useful for determining the effect of the particle shape on the outer part of the scattering curve. In addition, the equation can be employed for numerical calculations for large h, where other methods of computation often are unwieldy or inapplicable.

Notes: The unified theory of absolute intensity measurements in small-angle X-ray scattering has been experimentally verified by determining a collimation system and wavelength-independent calibration constant for polyethylene (Lupolen). Consistent values of this constant were determined for three X-ray wavelengths (Ag Kα, Mo Kα and Cu Kα by gas scattering and multiple-foil attenuator experiments. The agreement of the results implies that all of the experimentally significant parameters involved in these absolute intensity calibrations have been identified. In addition, they show Lupolen to be a more general secondary standard than had been previously recognized.

Notes: The three years since the Second International Small-Angle X-ray Scattering Conference have seen a great many important applications of small-angle X-ray scattering to the determination of biological structures.

Notes: SAXS was applied to the RNA from bacteriophage MS2.

Notes: In order to get an idea of the possible neutron small-angle scattering experiments with solutions of macromolecules at the high-flux reactor of the Institut Max von Laue–Paul Langevin at Grenoble, aqueous solutions of molecules with molecular weights from about one hundred to several millions have been studied. Changing the contrast by using different H2O/D2O mixtures the basic scattering functions could be determined. Zero-angle scattering from neutron and X-ray small-angle scattering experiments are compared. In the case of ferritin the molecular-weight distribution could be determined from the dependence of zero-angle scattering on the solvent. A considerable variation of the square of the radius of gyration R at low contrast \bar \rho was observed. R2 turned out to be a linear function of 1/\bar \rho. The slope of the straight line is a measure of the homogeneity of the internal structure. Proton–deuteron exchange reactions have been studied. A time resolution of less than two seconds had been reached with myoglobin and other globular proteins.

Notes: A model has been developed to calculate the diffraction given by a disordered set of thick coils of helical conformation. Double coils placed inside a cylinder of different density are considered. The cylinder accounts for the presence of substances which may interact with the double coil in a random manner. The thickness of each coil, pitch and radius of gyration, outer cylinder diameter and its density are the parameters that influence the diffraction maxima observed. It is demonstrated that when the parameter Z (pitch/radius) increases, the peaks tend to overlap. The relative position (α) of the two coils is also studied. When they are diametrically opposed, only even layer-line peaks are detected. At intermediate positions, other peaks appear, the intensity of which depends strongly on the precise value of α. An interesting result is that the relative position of the peaks for any single coil is constant and does not depend on the dimensions of the coil. The central scattering increases considerably if one of the two-component coils becomes a straight cylinder coaxial with the primitive coil. As a result the lower layer-line peaks do not show. On the other hand, the intensity due to the central equatorial peak diminishes when some packing order is introduced between coils. The model is suitable for interpreting the specific case of nucleohistone patterns.

Notes: A comparative study of the dimensions of a flexible polymer (atactic polystyrene) in three environments has been undertaken.

Notes: In the investigation of polymer solutions by small-angle neutron or X-ray scattering, the intermediate momentum range corresponds to the distance between the radius of gyration RG and the statistical subunit length l of the polymer chain. In this range, where the specific polymeric behaviour prevails, it can be shown, using the Debye relation, that the scattering curve presents a q−2 singularity, q being the momentum transfer.

Notes: The radius of gyration, rg, of atactic polystyrene molecules in the bulk polymer has been measured by low-angle neutron scattering from dilute solid solutions of poly-proto-styrene in poly-deutero-styrene with concentrations of 5 % and 0.5 % tagged solute molecules.

Notes: The small-angle scattering of polymers contains a component which is due to the statistical fluctuation of the density produced by imperfections in the long-range or short-range order. This fluctuation is entirely due to thermal motion and is related to the compressibility in the case of a one-component fluid system in thermodynamic equilibrium. In non-equilibrium one-component systems in the solid state, the statistical fluctuations of the density are, at least partly, due to frozen-in disordered structures.

Notes: Deux types d'échantillons permettent la mesure de l'orientation des faces limites des lamelles et du rapport R de la longueur des plis à celle des monomères.

Notes: The small-angle X-ray scattering from a dilute solution of the polystyrene/polybutadiene/polystyrene block copolymer in methyl ethyl ketone was measured.

Notes: Small-angle scattering (SAS) of neutrons is applied to the investigation of the microinhomogeneous structure of glasses. The alumina–silica titania-containing systems are taken as the subject of the investigation. The negative sign of the Ti nuclear scattering amplitude sharply extends the sensitivity to fluctuations of the atomic density. The phase-segregation kinetics was studied in the temperature region 750–950°C. A comparison of neutron SAS data with the data from X-ray phase analysis and neutron diffraction has shown that the process of segregation into two amorphous phases is accompanied by the simultaneous ordering of the titania-rich phase up to the appearance of crystallites. The `glass-in-glass' state corresponds only to the initial stages of the decomposition.

Notes: Small-angle X-ray scattering has been used to study early-stage spinodal decomposition in Al-base Zn and Al-base Ag alloys which were liquid-quenched at rates of the order of 106°C/sec.

Notes: Boron carbide is a potential neutron-absorber material for fast-reactor control systems. It is, therefore, essential that its response to prolonged fast-neutron irradiation be well characterized.

Notes: In solid-state physics small-angle scattering near the reciprocal origin is a subcase of the more general situation of studying diffuse scattering at Bragg reflexions. In this work two difficulties connected with scattering studies on metal alloys near Bragg reflexion (Huang scattering) have been overcome.

Notes: The small-angle neutron scattering from G. P. zones in aged Al–Mg alloys has been measured by the difference in intensity between the scattering before and after an anneal at 100°C sufficiently long for dissolving the zones. No zones have been found by this method in Al–7% Mg alloys. The scattering by zones found in Al–11.5% Mg alloys has been analysed with the help of a radial pair-correlation function written in the form of a sum of Gaussian distribution functions. Best fitting is obtained with a rather smooth function. The mean size of the zones has been determined: mean diameter of about 70 Å for an alloy aged one year at room temperature, and 110 Å, for an alloy aged the first three months at 40°C and then nine months at room temperature. The corresponding mean distance between the zones is found to be equal to about 130 and 200 Å, respectively. The concentration in Mg of the zones has been found to be of the order of magnitude of 20 to 25%.

Notes: Small-angle scattering from an Fe65Ni35 single-crystal has been measured with the magnetic field applied parallel and perpendicular to the scattering vector κ. Scattering cross sections due to longitudinal and transverse fluctuations have been calculated. The transverse cross section consists mainly of spin-wave scattering and has a long tail up to κ = 0.2 Å−1. This suggests that there are spin-wave modes heavily damped by magnetic inhomogeneities. The longitudinal cross section can be described by a Guinier approximation (dσ/dΩ)0 exp (− κ2R2g/3) for the range 0.05 〈 κ 〈 0.2 Å−1. The forward-scattering cross section (dσ/dΩ)0 and the radius of gyration Rg obtained from experiment are compared with values calculated from Kachi's model. In this model the magnetization is zero for every cluster of 60 atoms with a concentration of nickel below 29%. The comparison shows that the observed value for Rg (= 7.7 Å) is about twice as large as the calculated one. The observed forward scattering (dσ/dΩ)0 has slightly different values for different crystal orientations and is on the average 75% of the calculated value. The agreement is remarkable with regard to the crudeness of the model.

Notes: The superstructure of U4O9 above the transition was studied at 120 °C by single-crystal neutron diffraction. The space group I4132 is found not to change through the transition. The lattice constant of the superstructure is four times that of the fundamental fluorite-type UO2 mother structure. From difference Fourier synthesis for the superlattice reflections, the parameter in the special position 24(g) representing additional oxygen atoms in the fundamental structure was found to change a little at the transition.

Notes: Certain aspects of phase transformations in cadmium iodide polytypic crystals have been studied for the first time. It has been shown that the transformation of an ordered polytypic structure into another ordered structure is possible. This fact has been elucidated from the transformation 14H → 4H and 18H → 4H. Electron-microscope evidence for the occurrence of such transformations has been obtained. The phase transformations have also been viewed in the light of the structural geometrical schemes and of the stacking-fault energies of initial and transformed structures. Polytypic transformation from a rhombohedral to a hexagonal type has been observed, 42R→ 12H. Transformations involving poly types having similar stacking-fault configurations in their layer sequences have also been studied. The observed transformations of this type are 28H → 4H and 36H → 4H.

Notes: The structural characteristics of a reacted ohmic contact, platinum silicide, have been investigated using X-ray diffraction, electron diffraction and electron microscopy techniques. The contacts were formed by depositing Pt metal onto Si substrates and sintering at various temperatures in the range 225 to 725°C. Some slight initial reaction occurred at 225°C (the nominal substrate temperature) giving rise to both the thermodynamically stable PtSi and the intermediate reaction product Pt3Si. Complete reaction was accomplished when the contacts were sintered at temperatures in excess of 650°C. The compositions of the silicide contacts were independent of the method of metal deposition. The PtSi phase occurred as two distinct crystallographic components, one being moderately oriented, the other having a very high degree of the (010) type orientation. The relative proportions of these two components were solely dependent on the substrate temperature during deposition; the formation of the moderately oriented component could be suppressed by raising the substrate temperature above 500°C.

Notes: A correction method has been devised in order to eliminate spurious details from the G(M) particle-size function. The method is based on the elimination of the negative minima in G(M) by an iterative procedure. It is applied to the distribution of Pt crystallite sizes in Pt/Al2O3 reforming catalysts.

Notes: The defocusing of the diffracted beam in a texture goniometer using the reflection technique for the determination of the preferred orientation is discussed. By means of textureless (random) specimens of the ferromagnetic material Ba3Co2Fe24O41 this defocusing is measured for several diffraction planes in two cases: (1) a narrow and (2) a wide receiving slit. Calibration functions to correct for defocusing effects are calculated using an equation given by Gale & Griffiths [Brit. J. Appl. Phys. (1960). 11, 96–102]. The calculated functions plotted versus the angle of specimen tilt are compared with the relative intensities measured on random specimens.

Notes: A method is described for determination of unit-cell parameters of single crystals from zero-layer rotation patterns taken in the Straumanis position and indexed by means of corresponding Weissenberg patterns. Values obtained from reflections at the highest diffraction angles (0 〉 75°) are compared with those from a least-squares treatment of all high-angle reflections ( 〉 60°).