ALBERT

Notes: The variance of the X-ray spectral distribution in the Cu Kα multiplet has been redetermined with improved accuracy and over a wider range than previously. This investigation is parallel to that of Edwards & Toman on iron radiation, with which comparison is made on the following points: (i) the effect of using a β-filter and (ii) the effect of interpolating the line profile under the Kα satellite group. Both definitions of the variance are considered and three linear regions can generally be distinguished in the variance–range function. The choice of definition and the usefulness of the different linear regions in any practical application are also discussed.

Notes: At the stoichiometric 1 : 1 ratio of atoms, the cubic NaCl-type monoxides TiO, VO and NbO have a large number of vacant sites on both the metal and oxygen sublattices. X-ray determinations of the thermal expansions of these materials show quite distinct differences. At 298 °K, the coefficients of linear expansion defined as α = (1/a)(da/dT) are as follows: (TiO)0.856(\square)0.144, α = 6.6 (7) x 10−6; (VO)0.848(\square)0.152, α = 9.3 (6) x 10−6; (NbO)0.750(\square)0.250, α = 4.8 (0) x 10−6. Progressive filling of the vacancies in titanium monoxide merely shifts the expansion curves parallel to each other in the direction of higher lattice parameters.

Notes: The theory of the X-ray double-crystal spectrometer is outlined. For a vertical rotation axis, crystal planes should be vertical and the X-ray beam horizontal. Geometrical errors are introduced by crystal tilts (departure from vertical) and misalignment (departure of central ray from horizontal). Even with perfect alignment a vertical divergence correction is required. A typographical error in Schwarzschild's analysis of these geometrical effects led to erroneous results by Schnopper, later corrected in an erratum. The physical significance of this revision is considered here. The resulting expression for relative wavelength error indicates that, for zero tilt, misalignment produces no significant errors in relative wavelengths. Geometrical errors are shown to be negligible in recent measurements of Bearden and very small in earlier work of Bearden & Shaw. The Williams vertical divergence correction, used by Bearden, is proven valid; the Parratt form, preferred by Schnopper, is incorrect. An alignment procedure which can reduce geometrical errors below 1 part per million is described. It employs a precision engineer's level (with autocollimating telescope) and a simple technique for grinding crystal faces parallel to atomic planes.

Notes: Several applications of X-ray topography with Ru-filtered Ag Kα2 radiation are described. Two of these are variations of the Lang method combined with a Ru filter. The first one is to improve the Lang traverse pattern from a specimen crystal including locally highly distorted regions such as inclusions, as demonstrated for a pure iron crystal. The second is to obtain a traverse pattern from the whole area on the same topograph for a specimen including appreciably misoriented parts, by making the first slit wider than usual. This example has been shown for a Ge crystal. Another application is concerned with taking a topograph of an area as wide as of the order of the length of a line focus, in a shorter exposure time, with high resolution. Examples have been shown for Ge and Si crystals.

Notes: Primary normal alkylammonium halides crystallize in a preferred crystallographic orientation, forming single or twinned layers. The basal spacings are related to the number of carbon atoms within the homologous series, and are doubled in the twin layers. The orientation of the hydrocarbon chains between the ionic heads is discussed.

Notes: Charts are given which provide a rapid and unambiguous way of attributing ideal orientations to regions of crystallite orientation distribution function plots for hexagonal materials.

Notes: The design of a vacuum jacketed multiple-exposure back-reflection camera and the adaptation of this camera to a closed circuit pressurized helium cryostat has made it possible to determine lattice parameters by X-ray diffraction to temperatures as low as 25 °K without liquid gases. The advantages of this new design are: short exposure periods (5 to 30 minutes), multiple (usually 6) exposures on a single film at any temperature between 25 and 180 °K, elimination of film shrinkage and hence, high precision lattice constants and thermal expansion coefficient determinations; easy detection of phase transformations. The lowest temperatures can be reached in 30 minutes.

Notes: A method is proposed for precise parameter measurements based on the accurate recording of angular separation between Kα and Kβ diffraction lines. The accuracy and sensitivity of the method are discussed.

Notes: A modification of the Lang traversing technique is described, which allows X-ray topographs of crystal arrangements, which are sensitive to mechanical vibration, to be taken. The application of the method to X-ray interferometry and moiré topography is discussed.

Notes: A metastable phase TiCu3(m) has been prepared by rapid quenching from the melt (splat cooling). TiCu3(m) is orthorhombic, D0a type, with a0 = 5.450, b0 = 4.426, and c0 = 4.307 Å. Although TiCu3(m) is isotypic with a nonexistent equilibrium phase `TiCu3' reported in the literature, its structure is distinctly different from that of `TiCu3'; instead, TiCu3(m) is closely related to ZrAu3. A large metastable solid solubility of Ti in Cu was found.

Notes: The methods of normal probability plot analysis have been applied to two nearly complete sets of structure factors (Fmeas) and the corresponding objectively assigned standard deviations (σFmeas) obtained by diffractometer measurement with two different crystals of lutetium orthoborate. The least-squares derived positional and thermal vibration parameters are shown to be too small by a factor of 1.8, and the σFmeas to be overestimated by a factor of 1.55. The two sets of Fmeas are found to contain a small but parallel bias. The lattice constants of rhombohedral calcite-type LuBO3 are measured as aH = 4.91538±0.00002 Å and cH = 16.21200±0.00003 Å at 298°K, with six formulas in the unit cell, space group R\overline 3c. The Lu–O distance in this six-coordinated Lu compound is 2.240±0.002 Å (corrected standard deviation). The B–O distance in the BO3 triangular groups is 1.370±0.005 Å. The characteristic Θ temperature is estimated as 446±19°K.

Notes: A differential method is presented for the evaluation of small-angle X-ray scattering data. The direct determination of slight changes in the radius of gyration of colloid particles is rendered possible by the method proposed.

Notes: X-ray powder data for the compound U3Si have been obtained from an alloy prepared by arc melting uranium and silicon followed by a 7 day anneal at 800°C. The d spacing determinations have been extended into the back reflection to a 2&thgr; value of 167.4 °. The observed relative intensities are compared with calculated values.

Notes: A diffractometer-mounted device for the controlled α-irradiation of the single crystals is described.

Notes: A previously given analysis of the combined specimen and beam tilt errors in Bond's single-crystal method of determining lattice parameters is extended and used to provide a method of obtaining parameters free from such errors from three separate measurements. The method requires that either the collimator or crystal be tilted by known angles between the measurements. An analytical and a simple graphical method of applying the procedure are described.

Notes: Observations of preferred orientation in the rolled Pb substrate and in the anodically deposited tetragonal PbO of a Pb/PbO(t) voltaic cell, by X-ray diffraction, are reported. A Pb → PbO(t) transformation mechanism is described for the orientation relationship, (110)PbO(t)\mid\mid(100)Pb.

Notes: The Fourier coefficients of the X-ray diffraction line profiles from an ordered face-centred tetragonal (L10) structure such as MgIn or CuAu have been calculated assuming the presence of twin and incoherent boundaries on (101). It is found that reflection components with (h−l) = 0 are not affected by twinning on (101). The theoretical expression for the effective particle size is compared with some measured particle sizes for cold-worked MgIn.

Notes: The respective rôles of precipitation hardening and reversible martensite reactions have been analysed in relation to development of textures in 17 %Ni-8 %Co-4 %Mo steel. Cold-rolling textures after 90 % reduction are independent of the heat treatment prior to rolling, and are described as mainly {001}〈\bar 110〉α′, and {557}〈\bar 110〉α′, components, with a {111}〈\bar 1\bar 12〉α′, component of lower intensity. The corresponding recrystallization textures produced by annealing in the austenite region vary according to prior heat treatment: solution-treated material exhibits a recrystallization texture consisting mainly of {557}〈\bar 110〉α′, and {̃510}〈\bar 150〉α′, components, whereas when precipitation of Ni3Mo takes place before the recrystallization anneal, the texture is more diffuse and contains, in addition to these components, a more even distribution of orientations which fie within a 〈111〉 fibre texture normal to the rolling plane. It is considered that the {557}〈\bar 110〉α′ + {̃510}〈\bar 150〉α′, recrystallization texture could be accounted for by a double shear transformation α′ → γ → α′, combined with texture sharpening during recrystallization in the austenite. It is necessary to invoke variant selectivity during the shear transformation in order to explain the absence of certain groups of orientations in the final α′ texture. The effect of Ni3Mo is attributed to restriction of grain boundary mobility in the austenite, so preventing sharpening of the texture at this stage by recrystallization.

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°).

Notes: By the use of the electron-microscopy technique of n-beam lattice imaging with ultra-fine sections of sepiolite the quincunx arrangement of the talc-type layer, which is the characteristic of this mineral structure has been confirmed.

Notes: The appearance and identification of silicon Kα escape peaks in energy-dispersive X-ray diffraction spectra are reported.

Notes: A beryllium high-pressure cell (0–4 kbar), suitable for single-crystal studies, has been constructed so that it can be mounted either on a standard diffractometer or on other X-ray instruments and can operate over the temperature range 80–300°K. This cell has been used to determine the linear compressibilities of various materials as well as to determine shifts in atomic position with pressure of simple materials. More recently, the symmetry of phases in the pressure-temperature phase diagram for (CH3)4NMnCl3 has been determined.

Notes: The appreciable differences between the absorption coefficients of a foil for the characteristic radiation and its harmonics can be utilized to determine the wavelength composition of X-rays diffracted by a monochromator or sample. A simple experimental procedure is proposed and used to determine the intensity of the λ/2 harmonic diffracted by the 400 reflection of gallium phosphide at the 200 position of the molybdenum Kα peak. At a tube voltage of 45 kV the λ/2 contribution was found to be 9%; it decreased to 2.5% when pulse-height discrimination blocked 10% of the total counts. Our procedure provides a direct check of the effectiveness of balanced filters and electronic discrimination against harmonic radiation.