ALBERT

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: A method for quantitative phase analysis of powder mixtures by X-ray diffraction is described, using the phase to be determined as an internal standard.

Notes: Eleven alloys from the binary and ternary range (VMn)2Ga5 have been investigated using neutron powder diffraction methods supported by measurements of magnetic susceptibility and superconducting transition temperatures. A magnetic structure is present in alloys in the composition range around (Mn0.2V0.8)2Ga5 to Mn2Ga5. The magnetic moment found in the alloy Mn2Ga5 increases on the addition of vanadium to a maximum around the composition (Mn0.2V0.2)2Ga5. It then decreases and disappears around the composition (Mn0.2V0.8)2Ga5. Possible changes in the magnetic structure are suggested in order to account for this. There is some evidence of weak superconductivity in the alloy V2Ga5. This disappears on the addition of manganese.

Notes: X-ray powder diffraction data have been obtained for U3O5P2O7. This compound has not yet been mentioned in the literature, although similar diffraction data have been reported for a compound described as (UO)3(PO4)2.

Notes: A computer program utilizing the Cooley–Tukey algorithm for rapid Fourier transformation is described. It has the following main features: (1) Fortran language compatible with most present day computers (the program was tested on Univac 1106/8, IBM 360, CDC 6600) is used; (2) limited core-storage is required (30,000–40,000 words); (3) except for the electron-density output, no auxiliary storage is required; (4) all space groups can be treated without any modification in the program; in every case only the independent reflections must be supplied; (5) repetitive syntheses, such as are required in working with direct multi-solution methods, can be carried out; (6) automatic search for the electron-density peaks, calculation of the distances between them and direct drawing of the structure on the computer printout are provided.

Notes: A new technique is presented for the automatic determination of peak positions, intensities and widths from complex numerically recorded X-ray powder diagrams. The method uses standard powders for the determination of the actual repartition of incoming radiations and the determination of the apparatus function (aberrations, calibration etc.). The first trials give results the accuracy of which is much better than one could except from manual determinations.

Notes: Neutron diffraction studies of perfect, non-absorbing crystals have been used to explore aspects of dynamical diffraction theory. The Pendellösung fringe patterns obtained from Laue transmitting crystals with full-spectrum incident radiation have been used to determine crystal structure factors with high precision. It has been established that spherical wave theory is called for, and small crystal curvature must be allowed for, in the interpretation of the fringe patterns. Novel information about the characteristics of the neutron wave packet becomes available from the experimental studies.

Notes: A series of long-period superstructures have been found in the quasi-binary Co3V–Ni3V system. These structures are specified by the stacking sequence of close-packed planes and the atomic order within the planes, and appear successively in the order 3\bar 3T (Co3V), (2\bar 1)3T, 1\bar 1T, 1\bar 1TR, 1\bar 1TR2, 1\barR, (3\bar 1)3R, 3\bar 3R and 1\bar 0R (Ni3V) with the increase of nickel concentration. The stabilization of the long-period structures is discussed briefly in terms of oscillatory interatomic potentials.

Notes: Single-crystal diffraction intensities can be derived from maximum-peak-height measurements at any Bragg angle, provided the mosaic is small and isotropic and the shape of the crystal is not far from spherical.

Notes: A specimen cell has been designed for orientation of liquid-crystalline specimens by shear between transparent single-crystal windows for examination by X-ray diffraction, or by the polarizing microscope.

Notes: An outline is given of the Birkbeck programme of work describing the statistics of regular (crystal) structures and the regularities of statistical (liquid and glass) structures in reaction to the tendency to regard all structures as crystalline but with imperfections. Central to this is the development of the description of arrangements of atoms in terms which do not depend on arbitrary axes. Attempts are made to show crystal structure in the wider context of large-scale biological and other structures.

Notes: The frequency distribution of the relative lengths of cubic stacking sequences in vapour-phase-grown ZnS polytypes is presented. It is shown that this distribution conflicts with the correlation between atomic structures and stacking-fault energy expected on the assumption of a layer-transposition mechanism for polytype formation.

Notes: The graphic display version of ORTEP (program INGRID), has been modified and speeded up by use of the IBM Graphic Programming Services.

Notes: An X-ray powder diffraction method is described which can determine the phases present in hydrogen–zirconium alloys containing ≥ 100 p.p.m. hydrogen. The method is applied to show that γ- and δ-hydrides are formed when hydrogen–zirconium alloys are cooled from the α-phase field. It is shown that quenching favours the formation of the γ phase.

Notes: Three crystalline forms (cubic, orthorhombic I and orthorhombic II) exist in the Na2O–Ca3Al2O6 solid-solution series at room temperature. A tetragonal form may be obtained by quenching. All the phases have lattices extremely close to the cubic form. The cubic and tetragonal varieties show no polymorphic transformations. The orthorhombic OI and OII phases become tetragonal at high temperature. There is complete agreement between the transition points revealed by X-ray diffraction and microscopy. However, only the order–disorder OII→T transition is observed by μDTA.

Notes: Two proposed expressions, I1(&phgr;) = cosm &phgr; and I2(&phgr;) = (1 + b2 sin2 )−1, for the orientation function, I(&phgr;), of pyrolytic graphites have been shown analytically to give quite different values for the Bacon anisotropy factor (BAF) for oriented materials. BAF values derived from the angle of half-maximum intensity using I1(&phgr;) are within 20% of numerically calculated values for the BAF range 10–90, whereas values obtained using I2(&phgr;) are smaller by as much as a factor of twenty. The effect of sample preparation on such measurements has been found to be negligible. Diamagnetic susceptibility measurements on the graphites investigated validated the calculated BAF values in that the derived single-crystal susceptibilities were in reasonable agreement with known values. BAF values calculated via I2(&phgr;) produced unacceptable paramagnetic values parallel to the basal plane. It is suggested that I1(&phgr;) be used for rapid BAF determinations; although numerical calculation is preferred, the difficulty of measuring I(&phgr;) at large &phgr;, for highly oriented materials, may make the full numerical procedure impracticable and this approximate procedure the more desirable.

Notes: A method is proposed which can be used for an analysis of small-angle X-ray scattering curves exhibited by solid polymers with lamellar structure. The scattering curve is considered to be determined by the positions and the structure of the `amorphous' boundary layers around the lamellar interfaces. The analysis is performed directly, i.e. without the use of model calculations. Application of the method results in giving values for the mean L and the range of fluctuation, δL, of the lamellar thickness, the electron-density defect κ per square unit of the lamellar interface, and the second moment σ2 of the electron-density profile of the boundary layer.

Notes: The program presented here performs an automatic indexing of powder patterns by means of a trial-and-error method. It has been optimized and presents a good flexibility. It can account for various additional information, known a priori. In addition, extensive error computations are included in it, leading to a good reliability, even with some incidental errors. Moreover its input and printout have been implemented so that the program can be easily used even by non-specialists.

Notes: A narrow two-phase region (of composition width about 1 at. %) separates alloys of types AuCu and AuCu3 in the neighbourhood of the composition Au36Cu64. A tetragonal deformation of the unit cell is observed as much in the ordered AuCu3 I structure as in the periodic antiphase structure, AuCu II, the deformation being due to preferential occupation of certain sites by gold atoms. Two one-dimensional periodic antiphase structures of the type AuCu3 II are observed, with one antiphase direction parallel to a, AuCu3 II′-a, the other parallel to c, AuCu3 II′-c. The symmetry of the elementary cell of AuCu3 II′-a would appear to be not tetragonal but orthorhombic.

Notes: The formation of GP zones cannot be suppressed by a liqiusol-quenching method, where the quenching rate is very high. The mean value for the zone radius in the quenched specimens was relatively small (about 8 Å). The formation of the ε′(h.c.p.) phase begins at temperatures above 100°C after a short incubation period.

Notes: Crystals of TlGaSe2 were grown by solidification from melts. The space group a = 7.60, c = 31.36 Å, β = 90°20′, is P21/m.

Notes: During the fabrication of a Schottky barrier diode for use at microwave frequencies a thin layer of nickel is evaporated on to a gallium arsenide crystal followed by an evaporated layer of gold. During the bonding of contacts to the base of the crystal, a temperature approaching 400 °C is reached. It has been demonstrated that a reaction takes place between the gallium arsenide and the evaporated layers resulting in the formation of a monocrystalline layer of nickel arsenide in a topotactic relationship to the substrate and an ordered alloy of gold and gallium. A number of X-ray diffraction techniques have been employed to analyse the reaction products and identify the topotactic relationships for substrates of both 〈001〉 and 〈111〉 orientation.

Notes: A system for growing single crystals and making X-ray diffraction measurements by both photographic and counter means at low temperatures over extended periods of time is described.

Notes: The lattice-parameter error due to a relative misorientation between the specimen and the flat film in the transmission divergent X-ray beam and Kossel techniques developed for α-iron has been studied in detail. It has been shown that the most frequently encountered case of film misorientation can be theoretically divided into two pure components. The Type I component has been shown to have no influence whatsoever on the lattice parameter measured by this or any other method involving the ratio technique. The lattice-parameter error is thus due exclusively to the Type II component. In addition, it has been shown that these errors, which can become relatively important, are present in all linearly non-symmetric methods. In contrast, errors due to Type II components in linearly symmetrical methods should be very small if not experimentally undetectable. The geometry involved is such that the lattice parameter error cannot be experimentally determined. However, such film misorientations and their resulting lattice-parameter errors can be reduced to a very low value by means of the reticule method previously proposed and described.

Notes: A comparison of the Raman spectra of single crystals with those made using their powder reveals the following differences: (1) The intensity of the Raman lines decreases with grain size. (2) The breadth of the lines increases with grain size. (3) The spectra of powder specimens show additional lines. The decrease in the intensity is mainly due to surface scattering, whereas the broadening of the lines can be caused by two different factors: (a) In the case of polar crystals different spectra overlap because of different orientations of the grains. (b) Additional interactions with `surface modes' of the individual crystals, which may also show a dispersion depending on the shape of the grains. Na2WO4 with its higher symmetry and the weakly polar SiO2 show the decrease in intensity, while the examples showing the interactions with `surface modes', are quartz and platy crystals of SiC. Anomalous broadening can be demonstrated using strongly polar KIO3. The results of this study have been applied to determining the effect of such lamellar structures, as in labradorites, on Raman lines.

Notes: An X-ray camera has been constructed for rapid three-dimensional data collection from macromolecular crystals by means of a series of contiguous small-angle oscillation photographs without layer-line screens. The use of the camera, the microdensitometry of the film and the correction and processing of data are discussed.

Notes: A Cu-1,35 at. % Sn alloy is deformed by compression up to a degree of deformation reaching 45%. The X-ray diffraction study of the bulk specimens thus deformed makes it possible to follow the evolution of elements such as the lattice parameter, the residual stresses and r.m.s. strains, the particle size, dislocation density and the stacking-fault probability in terms of the deformation. The different results observed are compared with those obtained when studying pure Cu as well as the above-mentioned alloy deformed by filing at room temperature. When bulk specimens were studied by transmission electron microscopy, the dislocation density was measured. An approximate method of determination of the stacking-fault energy in this alloy, which presents no extended nodes, is also described.

Notes: The results of an X-ray investigation of thin-structure parameters of textured hexagonal GaTe films by the fourth-moment method are given. A correlation between the thin structure and some of the physical properties of the films is shown.

Notes: The effect of an arbitrary sample curvature on the centroid-shift and the broadening (variance) of a diffraction-line profile is discussed for the Seemann–Bohlin geometry of a diffractometer. The errors in stress measurement arising from the curvature of the sample surface are estimated. The shift of the centroid and, hence, the error in stress increase with increasing equatorial divergence and curvature of the sample. For example, for a cylinder of radius 10 mm, Δσ/K increases from 0.075° at 1° divergence to 0.32° at 2° divergence for &psgr; = 0°, 60° and Bragg angle 70°. The analysis helps one to choose the experimental parameters to keep the errors small; in case this is not possible, the expressions derived in this paper can be used to compute the correction factors. The position on the detector arm of the receiving slit corresponding to the minimum variance is different from that given by the Seemann–Bohlin para-focusing condition. However, the line-widths for the two positions do not differ appreciably.

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%.