ALBERT

Notes: The background correction method proposed by the author [Meng (1992). J. Appl. Cryst. 25, 646–647] has been applied to small-angle scattering data from aged Cu73Sn6Ni8P15 metallic glass. The scattering intensities observed from an as-quenched sample were used for the background correction of the intensities observed from an aged sample, after correction for the volume fraction of the crystalline phase that occurred in the aged glass. The corrected intensities satisfied Porod's law.

Notes: An apparatus function is derived in order to separate the influences of the diffractometer from those of the investigated sample crystal. Then, rocking curves can be calculated by the convolution of the apparatus function with the reflection profile of the sample. The resolution of the diffractometer is achieved by examining the dependence of the apparatus function on the Bragg angle of the sample. The characteristics of the primary beam leaving the monochromator are described by the transmittance. This transmittance forms the basis for the graphical understanding of the resolution of the diffractometer. The mathematical treatment is sufficiently flexible to be adapted to other multiple-crystal arrangements and includes the two polarizations. Furthermore, the correlation between the resolutions of the diffractometer and the coherence of the primary beam is discussed. The formalism, utilizing the apparatus function, is applied to measured rocking curves of a silicon crystal and shows an almost perfect accordance between theory and experiment. All necessary reflection profiles are calculated according to the dynamical scattering theory of X-rays.

Notes: The structure of Zr(OH)2SO4.3H2O has been determined ab initio by conventional powder diffractometry using monochromatic X-rays. The pattern was indexed using the successive-dichotomy method yielding cell dimensions a = 8.3645 (4), b = 15.1694 (9), c = 5.4427 (3) Å, and β = 103.145 (5)°. The space group is P21/c with Z = 2. 519 integrated intensities were extracted by whole-pattern fitting and these were used to calculate the heavy-atom positions by the Patterson method. Successive Fourier syntheses located the nine O atoms. Rietveld refinement was carried out over an angular range of 15 to 135°(2θ) and this converged with RF = 0.030, RB = 0.066, Rp = 0.085 and Rwp = 0.109. The structure consists of zigzag chains in the direction of [001] formed by edge-sharing eightfold-coordinated zirconium polyhedra in the shape of a bicapped trigonal prism. Sulfate tetrahedra bridge within chains whilst a network of hydrogen bonding stabilizes interchain interactions to form `corrugated sheets' parallel to the (100) plane; between these sheets lie `free' water molecules that do not take part in the polyhedra but do play a major role in the hydrogen-bonding network. The ICDD Powder Diffraction File No. is 44–1493.

Notes: A method is proposed for the determination of the optimum value of the regularization parameter (Lagrange multiplier) when applying indirect transform techniques in small-angle scattering data analysis. The method is based on perceptual criteria of what is the best solution. A set of simple criteria is used to construct a total estimate describing the quality of the solution. Maximization of the total estimate is straightforward. Model computations show the effectiveness of the technique. The method is implemented in the program GNOM [Svergun, Semenyuk & Feigin (1988). Acta Cryst. A44, 244–250].

Notes: A preceding paper handled, by way of application, the usefulness of Porod's law extended to the second nonoscillating term. The h−6 term allows the structure of the phases to be better characterized. This paper is mainly concerned with the setting up of the main equations used in this preceding paper. The h−6 term is analysed from the correlation function γ(r) and related to the `stick probability function'. It can be positive or negative. The positive case appears in smooth phases and has been previously analysed by Kirste & Porod. The negative case occurs in the presence of linear edges resulting from the meeting of surfaces that are planar in the vicinity of their intersection. More precisely, it is shown that the h−6 negative term results from the finite length of the edge. Its magnitude depends on the dihedral angles at the vertex defined by the limited sharp edges. The smaller the dihedral angles, the greater the h−6 term amplitude. The new concept of angulosity, θ, a pure number characterizing the geometry of the phase, is introduced. In this way, it is possible to develop similar equations for a specific surface, angularity and angulosity. Some simple-geometry examples are developed. The region where the extended Kirste–Porod law is useful in analysing small-angle scattering curves is discussed.

Notes: Small-angle neutron scattering instruments use large source and sample areas with long flight paths to obtain the necessary resolution. Increased count rates may be obtained using collimators that converge to a point on the detector. Further increases may be obtained by converging guides in the form of a focusing lens. A low-resolution small-angle scattering instrument that uses converging capillary fibers as a focusing lens is proposed. Such a device requires the use of a detector that has a fine spatial resolution, perhaps less than 0.1 mm. Expressions are derived for the resolution and the intensity optimized for such an instrument. The relationship is determined between the guide dimensions, the focal length and the critical angle of the internal coating of the individual fiber channels. The critical angle of the focusing lens dominates the resolution, and such an instrument is useful only for low-resolution measurements. However, the greatly reduced length is only valuable if there is a high-resolution detector to match the dimensions of the guide. Despite its low resolution, such an instrument might eventually be useful for survey or characterization measurements.

Notes: A general method has been developed for determining the number of molecules per asymmetric unit, Za, of a protein crystal. The method, volume-specific amino acid analysis, relies on the direct measurement of the number of protein molecules in a crystal as normalized by the crystal volume. The method is accurate, straightforward to implement and sensitive enough for application to small (0.002 m3) crystals. Although the procedures described here are specific to proteins, extension to nucleic acid crystals should be possible.

Notes: High-temperature single-crystal measurements of metamict zircon were performed up to 2000 K and the recrystallization was monitored using the width and intensity of selected peaks. Full data sets were collected at room temperature, 1573 and 1823 K. The changes in the probability density function (p.d.f.) of the O atoms revealed important features of the recrystallization. The measurements were done in air using a mirror furnace and performed on the D19 four-circle diffractometer at the ILL equipped with a vertically curved two-dimensional position-sensitive detector.

Notes: Micro-bridges, small devices in the shape of a bridge, have been designed to carry out sitting-drop crystallizations on a microscale. Micro-bridges have an indentation in the top of the bridge to contain the protein drop during a crystallization experiment and to prevent the droplet from spreading over a large area. The special feature of micro-bridges is that they fit into the wells of standard tissue-culture multiwell plates.

Notes: The crystal structure of Mg(OD)2 has been refined from time-of-flight (TOF) neutron diffraction data. Mr = 60.304, trigonal, P{\bar 3}m1, a = 3.1455 (1), c = 4.7646 (3) Å, V = 40.831 (4) Å3, Z = 4, Dx = 2.453 g cm−3, neutron time of flight, Rietveld refinement, Rwp = 3.84%, Rp = 2.83%, reduced χ2 = 2.98 for 70 variables, data collected at 305 K. The O–D bond length is 0.937 (1) Å (0.956 Å corrected for `riding' motion). The use of a pseudo-Voigt profile function to allow for strain and particle-size broadening in TOF neutron diffraction of fine anisotropic powders is described.

Notes: The optical rotatory power of SrS2O6.4H2O was measured at room temperature along and perpendicular to the optic axis for a wavelength λ = 633 nm. The values ρ|| = 2.65 and ρ⊥ = −0.6° mm−1 were obtained, where || and ⊥ mean along and perpendicular to the optic axis, respectively. For the measurements of the optical activity along a birefringent crystal section, the so-called HAUP device (High-Accuracy Universal Polarimeter) has been used. The values of the different optical parameters have been successfully explained using the classical point-dipole–dipole polarizability theory and a recently determined ordered superstructure assigned to the space group P31. In this way, a connection between the absolute structure of the crystal and the sign of the optical rotation has been established. The conclusion is reached that the main contributors to the optical activity are the water oxygen atoms; in particular, the gyration along the optic axis is satisfactorily described by the exclusive effect of these atoms.

Notes: Aluminium hydroxide particles, created by hydrolysis of aluminium nitrate solutions with sodium carbonate, aggregate rapidly to form mass fractal structures for which the fractal dimension varies from 1.7 to 2.1 depending on the OH/Al-ion ratio of the solution. This system has been studied by small-angle X-ray scattering (SAXS). The OH/Al ratios for the solutions were 1.5, 2.0 and 2.15. The maximum radius of gyration of the aggregates of about 50 Å is found in the solutions having the highest OH/Al ratio. SAXS measurements made at various stages of the aging process show that, in addition to fractal aggregation, there is a second process active in the solutions that leads to the break up of the fractal structure and formation of nonfractal particles, which are probably Al13 ions, [AlO4Al12(OH)24(OH2)12]7+. This process, which is strongly temperature dependent, is governed by an activation energy of approximately 162 kJ mol−1.

Notes: Two Fortran programs are described for conducting various statistical tests for centrosymmetry. The first program, STATCW, is for crystals that satisfy the requirements of basic Wilson distributions while the second, STATCN, is for any crystal for which the probability density functions of the normalized structure-factor-magnitude variable y for hypothesis testing are available only in the form of a numerical table. As well as seven quantitative statistical tests, the moments of truncated distributions are also included in these programs as test criteria and a unique decision is arrived at using suitable decision rules. The two programs were tested in a number of cases and typical results obtained are reported.

Notes: Large-radius Weissenberg cameras equipped with image plates have become popular for the collection of X-ray diffraction from protein crystals. However, it is not always easy to ensure in either design or practice that the image plates assume cylindrical geometry with respect to the crystal rotation axis. This article describes an algorithm that is capable of correcting for general distortions in image-plate or camera geometry on these instruments.

Notes: An X-ray powder diffractometer has been modified by the addition of a narrow-bandpass germanium pre-monochromator and a linear position-sensitive detector (LPSD) with its centre set at the normal θ–2θ focusing condition. Diffraction data are recorded using a step-scan procedure in which the patterns recorded at each step are summed to form the final pattern over a wide angular range. In this way, diffraction patterns covering 120 2θ can be recorded 100 times more rapidly than with conventional receiving-slit diffractometers for the same level of counting statistics. In this paper, an analysis has been carried out of the contribution of the instrumental parameters to the shapes of the X-ray diffraction lines obtained with either a stationary or a step-scanned LPSD. This is done by calculating theoretical profiles for defocusing, parallax error, thermal-noise broadening and LPSD pixel size and convoluting them with the Cu Kα emission spectrum and aberration profiles associated with a standard focusing powder diffractometer. Theoretical profiles for fitting to experimental step-scan data are synthesized by summing convoluted profiles across the detector window. The validity of this procedure is tested by fitting to experimental step-scan data from well characterized reference specimens of MgO and Y3Al5O12 (YAG). The extra broadening associated with the inclusion of a LPSD is refined in terms of the depth of the detector, the angular window of the LPSD and the angle of divergence of the incident beam. Good fits have been obtained to the reference profiles and the physical parameters of the diffractometer determined in this way agree well with directly measured values.

Notes: Instrumentation for measuring the X-ray diffraction pattern of optically excited crystals is described. The experiment uses a high-power (1̃ W) laser and a single-crystal diffractometer equipped with a helium cryostat (T 〈 70 K). The laser beam is modulated by a mechanical chopper and the diffraction signal gated in synchronization with the chopper phase. The modulation method is capable of observing small changes (down to about 0.01%) in the structure factors upon excitation of a fraction of the molecules in the crystal, given adequate counting statistics. The technique can be used for relatively long lived electronic excited states (τ ∼ 0.1–10 ms). The optical system is also suitable for time-resolved measurements using the time structure of synchrotron radiation.

Notes: A texture model suitable for use in Rietveld-refinement programs is proposed. It is based on the series expansion of the pole distribution function in symmetrized harmonics. The model was tested on a textured plate sample of Al2O3.

Notes: The crystal structure of lithium diborate hydrate, LiB2O3(OH).H2O, has been solved ab initio and refined by the Rietveld method from powder diffraction data collected with a curved position-sensitive detector (INEL CPS120) using Debye–Scherrer diffraction geometry with monochromatic X-rays. In the first stage the indexing of the powder pattern was performed by the successive dichotomy method from data collected with a diffractometer using Bragg–Brentano geometry. The lattice parameters are a = 9.7984 (10), b = 8.2759 (7) and c = 9.6138 (8) Å and the space group is Pnna. The structural model was obtained from direct methods and two difference Fourier maps. The Rietveld refinement converged to final crystal structure and profile indicators RF = 0.05, RB = 0.05, Rp = 0.03 and Rwp = 0.04. The structure consists of BO4 tetrahedra (T) and BO2(OH) triangles (&Dgr;) sharing corners in order to form infinite chains along [010], with the shorthand notation 3:∞1(&Dgr; + 2T). The particular linkage of the B3O3 rings leads to a new diborate anion {[B2O3(OH)]n−n}, in which two tetrahedral B atoms have an occupation factor of 0.5. Li atoms, tetrahedrally surrounded by four O atoms, three belonging to separate chains and one to a water molecule maintain the cohesion of the structure.

Notes: An experimental verification of the method of investigating texture inhomogeneity in the near-surface layers of a flat sample using the X-ray technique is presented. The investigations were performed on deformed aluminium. The results show that this method can be applied when finding the texture of the layers in the material is essential. Some limitations in the application of this method are due to its sensitivity to measurement errors.

Notes: An exact scaling function for the finite-sized fractal aggregates sharply bounded by a sphere of radius R has been established by using the convolution square of the shape function of aggregates and the inhomogeneity function, which is introduced to take into account the presence of inhomogeneity in fractal aggregates. The scaling function for an inhomogeneous aggregate is mainly determined by the geometric shape of the aggregate but is also dependent upon the degree of inhomogeneity present in the aggregate. The differences between the scaling function reported in this paper and the commonly used ones, exp (−r/ξ) and exp [−(r/ξ)2], are discussed. The simulating calculations have shown that the use of different scaling functions will not only influence the cross-over behavior between the Guinier regime and the fractal regime, but also make the low-q scattering intensity converge to different values.

Notes: A method for the simulation of Laue-grams has been developed according to geometrical considerations and the equations for easy solution of the problem are given. At the same time, with the model proposed by Riquet & Bonet [J. Appl. Cryst. (1979), 12, 39–41] taken into account, an algorithm has been developed for indexing all the experimental spots obtained by Laue back reflection of an unknown orientation of any single-crystal material. In this work, the simulation and indexing have been successfully applied to LiNbO3 crystals.

Notes: The Commission on Powder Diffraction of the IUCr has undertaken a round robin of Rietveld refinement with the aims of: (i) evaluating a cross section of currently used software; (ii) examining the range and effect of various strategies of refinement; (iii) assessing the precision and accuracy (spread) of the derived parameters; (iv) comparing and contrasting various instruments and methods of data collection. These aims were addressed by circulating to 51 participants upon request: (i) two constant-wavelength X-ray and neutron powder diffraction patterns collected on PbSO4 for refinement; (ii) a sample of phase-pure monoclinic ZrO2 for both data collection and refinement. In the latter case, the raw data were requested to be returned for reanalysis with a `standard' version of Rietveld software and an `optimal' refinement protocol. A total of 23 respondents provided 18 X-ray and 20 neutron refinements of the PbSO4 crystal structure from the 'standard' data sets using 12 different Rietveld analysis programs. These results constitute Part I of the round robin and have been described previously [Hill (1992). J. Appl. Cryst. 25, 589–610]. The 28 contributors to the m-ZrO2 section of the survey were based in 12 countries and collected 27 X-ray and 14 neutron data sets, using 20 different X-ray and 11 different neutron powder diffraction instruments. The conventional X-ray instruments included 13 reflection (flat-plate) and eight transmission (capillary or thin-film) machines and used three different radiations (Co, Cu and Mo). Two additional flat-plate data sets were collected with synchrotron X-rays. The neutron data were collected on 12 constant-wavelength and two time-of-flight instruments, the former utilizing wavelengths between 1.0 and 1.9 Å. The data sets yielded 27 X-ray and 15 neutron refinements of the m-ZrO2 crystal structure. The conditions used for data collection varied widely for both types of radiation: wavelengths ranged from 0.7 to 1.9 Å, step widths from 0.01 to 0.12°2θ, step counting times from 0.1 to 46 s for X-rays and up to 30 min for neutrons, data-collection time from 4 min to 3 d, maximum step intensities from 350 to 99000 counts, minimum d spacings from 0.53 to 1.17 Å and numbers of unique reflections from 71 to 912 (not including the time-of-flight neutron data). Variations in resolution between instruments were especially marked in the case of the neutron data but were less pronounced for the X-ray machines; the two instruments situated at synchrotron X-ray sources displayed the narrowest peak widths. The peak-to-background ratios varied markedly; in descending order of peak-to-background ratio were single-wavelength X-rays (conventional and synchrotron sources, using incident-beam monochromators), two-wavelength X-rays in parafocusing (reflection) mode, two-wavelength X-rays in transmission mode and constant-wavelength neutrons. Refinement conditions were also markedly inconsistent, with the total number of refined parameters varying from 20 to 46. The major factors associated with lower accuracy of the derived crystal structure parameters were: (i) the use of insufficiently flexible peak-shape and/or background functions; (ii) omission of the high-angle data from the refinement, especially the data with d spacings below about 1 Å; (iii) use of an insufficiently wide range of diffraction angles on either side of the peak (i.e. peak truncation), especially for the reflection profiles with substantial Lorentzian (or Cauchy) character; (iv) poor instrumental resolution and/or a peak-to-background ratio less than about 50; (v) low pattern intensity (i.e. maximum step intensity less than about 2000 counts), especially at small d spacings; (vi) an observations-to-parameters ratio of less than about five. The X-ray- and neutron-data Zr-atom coordinates are distributed over a relatively narrow and similar range of values about the weighted mean values, viz 0.014 to 0.028 Å and 0.009 to 0.014 Å, respectively. On the other hand, while the values of the O-atom coordinates derived from the neutron data are determined with about the same accuracy as those of the Zr-atom ones, viz 0.006 to 0.017 Å about the mean, the corresponding values derived from the X-ray data are distributed over a very much wider range, viz 0.091 to 0.193 Å, no doubt due to the lower scattering power of the O atom. The atomic displacement (`thermal') parameters are reasonably determined with X-rays when flat-plate reflection-geometry instruments are used but transmission geometry produces very poor parameters ranging from large negative to large positive values; the poor quality of the latter results is due to the strong correlation between displacement and absorption effects and the generally smaller number of reflections included in the data. All but the lowest-resolution neutron data support a sensible anisotropic displacement ellipsoid for the atoms. The precision and accuracy of the population of crystal structural parameters produced from the participants' refinements were almost always substantially improved by reanalysis of the data using a `standard' program and an `optimal' refinement protocol. The mean probable errors, taken as the mean deviations of the individual estimates of the parameters from the weighted mean value, show that about two-thirds of the variation in the m-ZrO2 parameters is due to differences in the instrumental and data-collection conditions. The remaining one-third of the variation is due to differences in the software and/or the refinement strategy used. On average, the mean probable errors of the Rietveld parameters are larger than their derived estimated standard deviations by a factor of around two for coordinates, about five for the displacement parameters and around 16 for unit-cell dimensions. Of the X-ray instruments, flat-plate reflection-geometry ones provided the best crystal structure parameters for the sample of m-ZrO2 distributed in this study, but the quality was degraded when the data were cut off at d spacings larger than about 1 Å. The X-ray transmission geometries produced the poorest atomic parameters because of the generally poorer peak-to-background ratio and the limited range of data available (with resultant lower observations-to-parameters ratio). The results obtained with neutron data were of roughly equivalent quality to those obtained from X-rays in the case of the Zr atom, but neutrons were markedly superior for the determination of the O-atom coordinates and displacement parameters, as expected. The time-of-flight neutron and synchrotron X-ray results were not significantly different from those obtained in the conventional neutron and better-quality conventional X-ray analyses.

Notes: The gel transformations and subsequent crystallization that occur in the precursor reaction mixture of silicalite were investigated using simultaneous small- and wide-angle X-ray scattering (SAXS–WAXS). The SAXS–WAXS measurements, together with the use of a high flux of synchrotron radiation and a newly developed high-pressure reaction cell, provide the possibility of in situ hydrothermal and time-resolved monitoring of amorphous gel transformations and crystallization.

Notes: Ammonium succinate has been found to be a useful substitute for ammonium sulfate in protein crystallography.

Notes: X-ray reflectivity, widths, centroid shifts and profiles for curved perfect crystals are calculated from a model. The crystal is approximated by a stack of perfect-crystal lamellae or blocks with a gradually changing (mean) orientation. A computer program has been developed to calculate the above quantities in the Johann geometry for the composite crystal from the dynamic theory of diffraction. Focusing and defocusing aberrations and the use of photographic detection methods are included. Correction of omissions from earlier theory and modelling is noted, together with observed effects. Incoherent scattering can give dramatic changes in diffracted intensities and significant shifts of final parameters. Effects of depth penetration on shifts, cosine ratios and other parameters are included. Assumptions of the model and implementation are detailed. It is shown that interference effects between waves of roughly equal amplitudes require use of lamellar thicknesses greater than those corresponding to the Darwin range. Internal tests demonstrate agreement with the literature at extremes. The theory is applied to first- and fourth-order spectra in differential Lyman α wavelength measurements. Results for pentaerythritol 002 crystals are presented. Paper II of this series extends this model to non-ideally imperfect crystals and other crystals of interest and discusses experimental agreement.

Notes: An earlier model for finite curved perfect crystals is extended to the non-ideally imperfect regime, allowing for mosaic structure from dislocations, vacancies or phase boundaries. Effects of Johann crystal mounting and depth penetration in the Bragg geometry are included. The model estimates diffraction shifts for mosaic crystals with regular local structure. Integrated reflectivities, diffraction widths, shifts and profiles against several parameters demonstrate agreement with the earlier model as an extreme and hence agreement with the literature. The theory is applied to first- and fourth-order spectra in differential quantum electrodynamic (QED) measurements and to pentaerythritol 002 crystals. A study of widths, reflectivities and shifts shows that comparison of profiles from wavelengths differing by large factors can yield the mean mosaic block thickness, angular misorientation half-width, incident polarization and beam divergence and can provide sensitive experimental tests of theory and modelling. Results for ammonium dihydrogen phosphate 101 and silicon 111 crystals agree with experiment for parameters investigated. Qualitative contributions to shifts and other parameters are identified. Results for precision QED measurements of iron and germanium Lyman αand Balmer β radiation are presented. Uncertainties in shifts due to input parameters are provided for each crystal. Crystal thickness can be a major variable in the determination of diffraction shifts, and differences between perfect and mosaic crystals are reduced for curved crystals.

Notes: A procedure for modelling the Bragg-case dynamical diffraction profiles from crystals with defects has been developed. This simulation of profiles has been applied to partially relaxed semiconductor layer structures whose lattice parameter and layer thickness were sufficient to induce interfacial defects. The procedure has a minimum of input parameters and is therefore applicable to routine use and has been shown to give good agreement with experimental data and also can predict the extent of the strain fields generated at the interfaces. The evaluation of the relaxation parameters in these strained layer structures is presented for some examples making use of high-resolution diffraction-space mapping and topography.

Notes: In phase transformation one initial orientation gives rise to several final orientations called crystallographic variants. In this paper it is shown that the number of physically distinct variants depends not only on the lattice symmetry of the initial phase but also on the mutual orientation relations between the lattices. This number is lower than the order of the rotational symmetry group when commutation relations exist between some rotations of the rotational symmetry group and rotations which describe the mutual orientations between lattices. Different examples are given for illustration.

Notes: A new layer-coupling model is developed for the derivation of the neutron reflectivity and transmissivity for deformed mosaic crystals with absorption in asymmetrical Bragg and Laue geometries. In this model, the mosaic distribution, domain size and crystalline orientation of each layer within the crystal can be different. Correction for primary extinction can also be included. Rocking curves for bent mosaic crystals predicted here based on known parameters are presented together with experimental results to shown the validity of this model.

Notes: The problem of calculating polycrystalline elasticity from texture has been treated in the most general way in the framework of the Voigt–Reuss–Hill (VRH) approximation. The analytical solution involves only the even texture coefficients up to fourth order, which can be derived with a limited number of experimental pole figures (e.g. one pole figure for hexagonal polycrystals). The present analysis has been applied to the prediction of the fourth-rank elastic tensors and Young's modulus for a rolled zinc sheet.

Notes: The crystal symmetry of the mineral chalcopyrite has been investigated using Kikuchi-line intersections. It has been found that Kikuchi lines which intersect within systematic rows of reflections are very sensitive to small differences in interplanar spacings and can be used for symmetry determination. A small displacement of the point of intersection of the Kikuchi lines 3,3,{\bar 1} {\bar 4} and {\bar 3}7{\bar 6} within the 02{\bar 4} and 0{\bar 2}4 systematic row of Kikuchi reflections was seen, indicating that the 02{\bar 4} and 0{\bar 2}4 Kikuchi lines do not lie on a mirror plane. Similar observations were also made for the intersection points of the {\bar 3}, {\bar 1}, 10, 3{\bar 5}2 and {\bar 5}, {\bar 1}, 14, 5{\bar 7}2 Kikuchi lines within the 02{\bar 4} and 0{\bar 2}4 systematic row of reflections. The Kikuchi lines intersecting within the 0h0 systematic rows of reflections showed no displacements, which is consistent with the point group, {\bar 4}2m, of chalcopyrite. The antiferromagnetic superstructure of chalcopyrite has also been investigated. Dark-field transmission electron microscope (TEM) images obtained with the 110 superstructure reflection showed antiferromagnetic domains, which altered their configurations on heating by the electron beam. The alterations were reversible and were interpreted as originating from magneto-elastic deformation.

Notes: The prediction of elastic properties from different models requires numerical calculations, notably integrations of the products of functions respectively representing the elastic property and describing the texture information. After a brief description of the different models used, this paper gives some advice on the calculation of elastic properties with averaging type models and discusses the conditions of good convergency in the case of a self-consistent approach.

Notes: This paper describes the use of energy-dispersive diffraction using synchrotron radiation to obtain preliminary measurements of pole figures for a 6000 Å erbium film deposited by UHV evaporation on molybdenum substrates. A low glancing angle is used and the pole-figure polar distance is scanned by rotating the sample about the direction of the incident beam. Correction formulae are derived for pole-figure intensity and position in this geometry. Results confirm strong 002 orientation of films deposited at a 673 K substrate temperature (near the middle of zone II for erbium), show that at an ambient substrate temperature (zone I) there is a mixture of 002 and 101 orientations, and demonstrate strong dependence of the 002 orientation direction (for zone II temperatures) on the angle of vapour incidence during deposition.

Notes: The crystal structures of a large number of proteins and nucleic acids are known and the corresponding sets of coordinates are stored in the Brookhaven Protein Data Bank. For structure investigations of biological macromolecules in solution, scattering and hydrodynamical methods are powerful biophysical tools when starting the data interpretation on the basis of the crystal structure of the molecules. The database BIOSCAT covers the main structural parameters estimable by X-ray scattering, translation and rotation diffusion methods and the X-ray scattering intensities and low- and high-resolution real-space electron distance distribution functions of 70 biological macromolecules and of oligonucleotides in standard conformation. The parameters and the scattered intensities are calculated from the atomic coordinates using the improved cube method and the real-space functions are estimated via a termination-error-reduced Fourier sine transformation. The database access is organized by the program PASSDB, which can generally be used for `readable' databases. A simple query language allows enquiries into the database without knowledge of a programming language. The program CONVSQL converts the database into normalized relations that can be handled by structured query languages (SQLs).

Notes: The program WEIS is used for the processing of macromolecular diffraction data recorded on a Weissenberg camera. Modifications have been made to WEIS in order to improve the number and quality of data obtained from integration over the diffraction peaks. Additional refinable parameters have been incorporated into the program in order to take account of small misalignments of the camera. Inclusion of these parameters in the refinement of the setting parameters results in a significantly better fit between the simulated and actual patterns. The modified program was used to process a set of diffraction data that had been collected using synchrotron radiation as the X-ray source and imaging plates as detectors. Improvement in the quality of the data was indicated by a significant increase in the number of accepted reflections per plate.

Notes: The construction of a new high-pressure cell is presented. It is a piston-cylinder type of apparatus. The entrance and exit of X-rays or light are possible through two parallel diamond-plate windows placed on V-shaped slits covering almost the whole range of reflection angles. This makes the cell particularly suitable for X-ray diffraction examinations of monocrystals. The potential accuracy of absolute-bulk-modulus determination by lattice-constant measurements using the Bond method [Bond (1960). Acta Cryst. 13, 814–816] at pressures of 108–109 Pa can be estimated at 1–2%. The cell enables the simultaneous examination of two samples, which makes possible the comparison of their compressibilities with an accuracy of 0.01–0.1%. As examples, the results of compressibility measurements on GaAs and GaN are given.

Notes: A modification is described of the singular value decomposition (SVD) method suitable for underdetermined linear least squares (LLS). When a set of data to be fitted is incomplete and does not allow an independent determination of all model parameters, the modified method automatically merges a previously available approximate solution into the LLS results. The solution so produced is more appropriate to the particular problem than the usual SVD solution, while still being a LLS estimate of the whole set of parameters. The method is discussed with reference to the LLS determination of unit-cell dimensions during the step-by-step assignment of h, k, l indices of a diffraction pattern.

Notes: The use of position-sensitive area detectors with high-flux radiation sources demands high-rate data-acquisition systems. Ideally, such devices should be commercially available and machine independent. In this paper, the basic features of such a system are described. The steps are highlighted that determine the counting rates of present-day addressing-logic and computer-bus speeds. The improvements expected with a new industrial standard bus system are briefly described.

Notes: The PIPEX system, an inexpensive pipetting station for the preparation of protein crystallization buffers, is described. The system, built around a computer-controlled motorized pipette, contains a spreadsheet application for the planning of experiments in, for example, standard Linbro plates, a program for the control of the pipette and a customized electronic interface. The PIPEX system performs most of the software tasks offered by current automatic crystallization systems.

Notes: With the assumption that both size- and strain-broadened profiles of the pure-specimen function are described with a Voigt function, it is shown that the analysis of Fourier coefficients leads to the Warren–Averbach method of separation of size and strain contributions. The analysis of size coefficients shows that the `hook' effect occurs when the Cauchy content of the size-broadened profile is underestimated. The ratio of volume-weighted and surface-weighted domain sizes can change from 1̃.31, for the minimum allowed Cauchy content, to 2, when the size-broadened profile is given solely by a Cauchy function. If the distortion Subscripts coefficient is approximated by a harmonic term, mean-square strains decrease linearly with increasing the averaging distance. The local strain is finite only in the case of purely Gaussian strain broadening, because strains are then independent of averaging distance.

Notes: The one-dimensional contrast modulation along the b axis of [001] high-resolution reverse images of the compounds Bi2Sr2(Ca1 − xNdx)Cu2O8 + δ (x = 0.05 + 0.1n; n = 1, 2, 6 and 7) is examined closely using the density distribution recorded from a wide area of the negative film by microphotometric densitometry. Three typical short units of the density distribution, of lengths 4.5b0, 5b0 and 4b0, characterized by twin peaks or a single maximum peak with subpeaks in the middle of the unit, are discerned. The density distributions of the three units and the contrast modulations of their images are reproduced well by computer simulations, using three structure models modulated with longitudinal displacement waves along the b axis of the metal atoms. The one-dimensional contrast modulation is attributed to sinusoidal changes in the effective scattering amplitudes for the [001] electron beam of the metal-atom chains along the c axis. The results of the simulation are applied to investigation of the (2, 1)5 and (3, 1)4 modulation modes in the modulated structure.

Notes: Theoretical calculation shows that suitable approximations of the line-shape asymmetry in powder diffraction profiles should be represented by functions having limited codomains.

Notes: (0{\bar 1}11) twin boundaries of Y-cut synthetically grown quartz crystals are studied by means of X-ray section topographs. The images show an anomalous contrast and no extinction condition can be found. Simulated images demonstrate that the twin boundaries are not simple planar defects. They may be described as lamellae of a non-diffracting material. Their thickness is of the order of 15 μm and, within these boundaries, the Fourier components of the dielectric susceptibility are drastically reduced by one order of magnitude.

Notes: A set of cylindrical vacuum chambers made of a carbonaceous composite material coated with a thin layer of aluminium is described. Its performance with a Displex cryostat and Mo Kα radiation has been tested.

Notes: PEDX is a newly developed interactive computer program for the radial-distribution-function analysis of measured energy-dispersive X-ray diffraction (EDXD) data from disordered systems. The program is furnished with efficient computing procedures and all the standard data for 96 neutral atoms necessary for the calculations. With the help of PEDX, the rather involved EDXD data processing is reduced to a routine operation.

Notes: Diffusion in Ni–Ti multilayers with periods of 120 Å is studied in the temperature range 293–743 K by grazing-angle unpolarized neutron reflectometry. The effective diffusion coefficient, Deff, of nickel into titanium and its corresponding activation energy, Qa, are determined by measurement of the decay of the reflectivity of the first Bragg peak, which arises from the nuclear scattering-length density modulation, as a function of annealing temperature at constant time. The direction of diffusion is determined by simulation of the Kiessig fringes located between the total-reflection plateau and the first Bragg peak. Two diffusion regimes with a transition temperature Tc ∼ 543 K are observed in this Ni–Ti multilayer; the corresponding activation energy values are 0.21 and 0.43 eV, respectively.

Notes: A sample environment apparatus, such as a diamond-anvil cell (DAC), cryostat or furnace, presents a unique problem for the crystallographer because some of the diffraction data are shadowed by its components. The first algorithm for sorting diffraction data from a sample consisting of several crystals enclosed in a sample environment apparatus is described. This algorithm requires no previous knowledge of the crystal structure of the sample, so it can be used to solve the structures of substances when the growth of one unstrained crystal is unsuccessful. An example is given to illustrate the development and the implementation of this algorithm: the identification of the unit cell of a high-pressure phase of oxygen known as epsilon-oxygen (ε-O2). The ε-O2 sample contains at least seven individual crystals and is enclosed in a DAC. The ε-O2 unit cell is monoclinic, it contains eight molecules per unit cell and the lattice constants at 19.7 GPa and room temperature are a = 3.642, b = 5.491, c = 7.705 Å and β = 116.2°. In the example, monochromatic X-ray diffraction data from this high-pressure sample are sorted, but the algorithm is a general-purpose technique; it can also be used to sort single-crystal time-of-flight neutron diffraction data. Additionally, this method may be used to sort reflections from several crystal samples containing a mixture of materials. The algorithm is given in symbolic logic so that it can be translated and inserted into available crystallographic software packages.

Notes: Two crystals of monoclinic hen egg-white lysozyme were irradiated in a monochromatic synchrotron X-ray beam (λ = 1.488 Å), the first as a rapidly frozen crystal mounted at the end of a glass fiber at low temperature (120 K) and the second mounted in a capillary tube at ambient temperature (298 K). Comparison of oscillation photographs, extending in resolution to 1.85 Å, and taken from both crystals at zero time and again after a period of exposure in the synchrotron beam (60 min exposure at 120 K; 8 min at 298 K), reveals that radiation-induced decay is not observed at 120 K but is observed, particularly at high resolution, at 298 K. In a separate set of experiments, data sets to 1.9 Å resolution at 100 and 298 K were collected from two monoclinic and two tetragonal hen egg-white lysozyme crystals using a rotating-anode source (λ = 1.5418 Å). Before inclusion of solvent molecules, the monoclinic and tetragonal structures at low temperature, where data were collected from rapidly frozen crystals, refined to R = 27.5 and 25.2%, respectively. The structures at ambient temperature, however, where crystals were mounted in capillary tubes, refined to significantly lower values of R = 20.9 and 20.6%. After inclusion of solvent, the R values at convergence were 20.3 and 17.6% for the monoclinic and tetragonal low-temperature structures and 17.9 and 16.2% for the room-temperature structures. Approximately twice the number of water molecules were included in the low-temperature structures at convergence (406 and 237) than could be assigned in the room-temperature structures (191 and 100). These results suggest that data sets from rapidly frozen crystals might generally be expected to yield higher initial R factors, compared to similar room-temperature structures, but that this difference should diminish appreciably as ordered solvent is included in the model. Apart from the general reduction in atomic temperature factors, the enhancement in resolution observed in diffraction patterns obtained from rapidly frozen crystals is probably due, to some significant degree, to the increase in the ordered-solvent content of the low-temperature structures.

Notes: A new method has been developed for the improved intensity assignment of severely or exactly overlapping Bragg reflections in a powder diffraction pattern. This fast iterative Patterson squaring (FIPS) method addresses, in particular, the systematic lack of small and large normalized intensities (|E| values) in severely overlapping powder data, which causes (a) the intensity statistics to be strongly acentric (even when the structure itself is centrosymmetric) and (b) the under-estimation of strong structure-invariant relationships. Direct methods for structure determination are more likely to succeed with FIPS-improved data than with conventionally used equipartitioned data (ratio of |E| values for overlapping reflections set to 1.0). In the case of the molecular sieve AFR (in which 65% of the reflections severely overlap), the ab initio structure solution was only possible after a redistribution of the intensities by the FIPS method.

Notes: Thin films of β-FeSi2, grown on Si(111) by the technique of solid-phase epitaxy (SPE) in ultra-high vacuum (UHV) conditions, were analysed by transmission electron microscopy (TEM). The expected epitaxies, β-FeSi2(101)/Si(111) and β-FeSi2(110)/ Si(111), were detected for film thicknesses smaller than 2̃50 Å. The present analysis reveals an unusual microstructure: the films are composed of very thin lamellae (5–30 Å) of both orientations induced by planar defects. Such lamellar films are strained, with a parameter shift estimated to be about 0.4%. For these films, grain sizes in the μm range were obtained and the interface roughness increased with increasing film thickness. An unexpected film orientation, β-FeSi2(100)/Si(111), was also found.

Notes: Reflection curves of bent crystals were calculated using the Takagi–Taupin theory of dependence on bending radius, wavelength, crystal thickness and Bragg angle. The reflection properties of bent crystals were measured for bending radii down to 90 mm. Usually, for the measurement of rocking curves of crystals with large bending radii, the double-crystal diffractometer was used in parallel position (n, −n). A special achromatic diffractometer consisting of a plane and a bent crystal is proposed. It is used to measure rocking curves of bent crystals with small bending radii (R 〈 1 m). Experimental values show close agreement with the theory. The reflection properties are important for X-ray microscopy with two-dimensionally bent crystals and for X-ray spectroscopy with bent crystals.

Notes: MEED (maximum-entropy electron density) is a program package to calculate the electron-density distribution from a set of structure-factor data by the maximum-entropy method. MEED is an upgraded version of the original maximum-entropy program, MEMTARO, which was used in the first study to use the maximum-entropy method (MEM) on silicon [Sakata & Sato (1990). Acta Cryst. A46, 263–270]. MEED is applicable to any space group and can cope with both single-crystal and powder X-ray diffraction data, whereas MEMTARO can only after modification. Another upgraded feature is the speed of calculation. By employing a new algorithm, MEED is much faster than MEMTARO for the same calculation. Computing time depends on various factors, such as the number of reflection data, accuracy of data and the number of symmetry operations. It is estimated that MEED is typically 100 times faster than MEMTARO. In an extreme case like the beryllium powder-data case, MEED is 600 times faster than MEMTARO. MEED is coded in Fortran77 for both a scaler computer, FACOM M780, and a vector computer, FACOM VP2600, which are mainframe computers at the Computation Center of Nagoya University. MEED enables the electron-density distribution to be calculated for any crystalline material, with a fine pixel size, e.g. with 128 × 128 × 128 pixels to a unit cell, provided that accurate diffraction data are available. MEED can overcome, to some extent, one of the biggest drawbacks of MEM analysis, the vast computing time required.

Notes: An inexpensive system has been designed that eliminates most of the collisions that might occur between the goniostat and the stationary items and complements the Rigaku RU 200 X-ray generator, Huber goniostat, Blake Industries' 2θ mechanism and San Diego multiwire area detector used in the CABM/Waksman X-ray crystallography laboratory.

Notes: Owing to the breakdown of Friedel's law when anomalous scatterers are present, unique values of the three-phase structure invariants in the whole range from 0 to 2π are determined by measured values of diffraction intensities alone. Two methods are described for going from presumed known values of these invariants to the values of the individual phases. The first, dependent on a scheme for resolving the 2π ambiguity in the estimate ωHK of the triplet φH + φK + φ−H−K, solves by least squares the resulting redundant system of linear equations φH + φK + φ−H−K = ωHK. The second attempts to minimize the weighted sum of squares of differences between the true values of the cosine and sine invariants and their estimates. The latter method is closely related to one based on the `minimal principle' which determines the values of a large set of phases as the constrained global minimum of a function of all the phases in the set. Both methods work in the sense that they yield values of the individual phases substantially better than the values of the initial estimates of the triplets. However, the second method proves to be superior to the first but requires, in addition to estimates of the triplets, initial estimates of the values of the individual phases.

Notes: Conventional small-molecule methods of solving the phase problem from native data alone, without the use of heavy-atom derivatives, known fragment geometries or anomalous dispersion, have been tested on 0.9 Å resolution data for two small proteins: rubredoxin, from Desulfovibrio vulgaris, and crambin. The presence of three disulfide bridges in crambin and an FeS4 unit in rubredoxin enabled automated Patterson interpretation as well as direct methods to be tried. Although both structures were already well established, the known structures were not used in the phasing attempts, except for identifying successful solutions. Direct methods were not successful for crambin, although the correct phases were stable to phase refinement and gave figures of merit clearly superior to any obtained in the ca 500 000 random starting phase sets that were refined. It appears that the presence of an iron atom in rubredoxin reduces the scale of the search problem by many orders of magnitude, but at the cost of producing `over-consistent' phase sets that overemphasize the iron atom and involve partial loss of enantiomorph information. However, about 1% of direct-methods trials were successful for rubredoxin, giving mean phase errors of about 56° (for all E 〉 1.2) that could be reduced to about 20° by standard E-Fourier recycling methods. Limiting the resolution of the data degraded the quality of the solutions and suggested that the limiting resolution for routine direct-methods solution of rubredoxin is about 1.2 Å. With the 0.9 Å data, automated Patterson interpretation convincingly finds the three disulfide bridges in crambin and the FeS4 unit in rubredoxin, and in both cases E-Fourier recycling starting from these `heavier' atoms yields almost the complete structure. Whereas crambin could only be solved in this way at very high resolution, rubredoxin could be solved by Patterson interpretation down to 1.6 Å. These results emphasize the benefits of collecting protein data to the highest possible resolution, and indicate that when a few `heavier' atoms are present, it may prove possible in favorable cases to solve the phase problem from a single native data set collected to `atomic resolution'.

Notes: An automated refinement procedure (ARP) for protein models is proposed, and its convergence properties discussed. It is comparable to the iterative least-squares minimization/difference Fourier synthesis approach for small molecules. ARP has been successfully applied to three proteins, and for two of them resulted in models very similar to those obtained by conventional least-squares refinement and rebuilding with FRODO. In real time ARP is about ten times faster than conventional refinement. In its present form ARP requires high (2.0 Å or better) resolution data, which should be of high quality and a starting protein model having about 75% of the atoms in roughly the correct position. For the third protein at 2.4 Å resolution, ARP was significantly less powerful but nevertheless gave definite improvement, in the density map at least.

Notes: A knowledge-based approach to crystal structure determination is presented. The approach integrates direct-methods and artificial-intelligence strategies to rephrase the structure determination process as an exercise in scene analysis. A general joint probability distribution framework, which allows the incorporation of isomorphous replacement, anomalous scattering and a priori structural information, forms the basis of the direct-methods strategies. The accumulated knowledge on crystal and molecular structures is exploited through the use of artificial-intelligence strategies, which include techniques of knowledge representation, search and machine learning.

Notes: A complementary relationship between the entropy (S) and the variance (σ2) of an electron-density map is derived by approximating the logarithmic term in the entropy expression by a series expansion around the average map density. The resulting expression is S ∼ ln N − {1 \over 2}σ2, where N is the number of grid points and σ is the r.m.s. deviation from the mean in a map normalized to unit mean. The algebraic expression is of interest because it is consistent with and allows numerical evaluation of the surprising argument that noise decreases the entropy of a map. The argument is that a noise contribution by itself generates a certain variance that is independent of the atomic structure and that adds to the variance due to the structure. Increased variance corresponds to decreased entropy. This property of noise provides an intuitively reasonable justification for maximizing the entropy of an electron-density map in the quest for more readily interpretable maps of macromolecules. The entropy–variance relationship also extends the range of applicability of the entropy concept to maps with a limited amount of negative density. The approximation which leads to the entropy–variance relationship is most applicable where it is most likely to be useful – in experimental maps of relatively low structure definition.

Notes: A practical generally applicable procedure for exponential modeling to maximum likelihood of macromolecular data sets constrained by a moderately large basis set of reliable phases and a molecular envelope is described, based on the computer program MICE [Bricogne & Gilmore (1990). Acta Cryst. A46, 284–297]. Procedures were first tested with simulated data sets. Exact and randomly perturbed amplitudes and phases were generated, together with a known envelope for solvent-free protein and for protein in an electron-dense crystal mother liquor typical of many real protein crystals. These experiments established useful guidelines and values for various parameters. Tests with basis sets chosen from the largest amplitudes indicate that exponential models with considerable correct extrapolated phase and amplitude information can be constructed from as few as 16% of the total number of reflections, with mean phase errors of about 30°, at resolution limits of either 5 or 3 Å. When the shape of the solvent channels in macromolecular crystals is known, it offers an important additional source of information. MICE was, therefore, adapted to average the density outside the molecular boundary defined by an input envelope. This flattening process imposes a uniform density distribution in solvent-filled channels as an additional constraint on the exponential model and is analogous to the treatment of solvent in conventional solvent flattening. Experimental data for cytidine deaminase, a structure recently solved by making extensive use of conventional solvent flattening, provides an example of the performance of maximum-entropy methods in a real situation and a compelling comparison of this method to standard procedures. Exponential models of the electron density constrained by the most reliable phases obtained by multiple isomorphous replacement with anomalous scattering (MIRAS) (figure of merit 〉 0.7, representing 34% of the total number of reflections) and by the envelope give rise to centroid electron-density maps which are quantitatively superior by numerous statistical criteria to conventionally solvent-flattened density. Similarity of these maps to the 2Fobs − Fcalc map calculated with phases obtained after crystallographic refinement of the model implies that maximum-entropy extrapolation provides better phases for the remaining 66% of the reflections than the original centroid MIRAS distributions. Importantly, the solvent-flattened electron density, although it did permit interpretation of the map which was not readily accomplished with the MIRAS map, contains substantial errors. It is proposed that errors of this sort may account for previously noted deficiencies of the solvent-flattening method [Fenderson, Herriott & Adman (1990). J. Appl. Cryst. 23, 115–131] and for the occasional tendency of incorrect interpretations to be `locked in' by crystallographic refinement [Brändén & Jones (1990). Nature (London), 343, 687–689, and references cited therein]. Solvent flattening with combined maximization of entropy and likelihood represents a phase-refinement path independent of atomic models, using the experimental amplitudes and the most reliable phases. It should, therefore, become a valuable and generally useful procedure in macromolecular crystal structure determination.

Notes: The crystal structure of a complex of ribonuclease from Streptomyces aureofaciens (RNase Sa) with guanosine-2′-monophosphate (2′-GMP) has been refined against synchrotron data recorded from a single crystal using radiation from beamline X31 at EMBL, Hamburg, and an imaging plate scanner. The crystals are in space group P212121 with cell dimensions a = 64.7, b = 78.8 and c = 39.1 Å. The structure has two enzyme molecules in the asymmetric unit, complexed with 2′-GMP inhibitor with occupancies of 1 and {2 \over 3} (different to the 3′-GMP complex crystal structure where only one of the two independent RNase Sa molecules binds nucleotide), 492 associated water molecules and one sulfate ion, and was refined using all data between 10.0 and 1.7 Å to a final crystallographic R factor of 13.25%. Binding of the base to the enzyme confirms the basis for the guanine specificity but the structural results still do not provide direct evidence of the identity and role of the particular residues involved in the catalytic process. New native RNase Sa data to 1.8 Å were recorded to provide a reference set measured under comparable experimental conditions. The crystals are in the same space group and have the same lattice as those of the 2′-GMP complex. The native structure with 423 water molecules was refined in a similar manner to the complex to a final R factor of 13.87%. 1.77 Å resolution data were independently measured on a 2′-GMP complex crystal at UCLA using an R-AXIS II image plate scanner mounted on a conventional source. The cell dimensions were essentially the same as above. 2′-GMP was bound more fully to molecule A than to molecule B of the RNase Sa. The structure was refined to an R factor of 14.64% with 388 water molecules. This work follows on from the structure determination of native RNase Sa and its complex with 3′-GMP [Sevcik, Dodson & Dodson (1991). Acta Cryst. B47, 240–253].

Notes: . Sulfur atoms, an integral part of many proteins, are possible candidates for anomalous scattering in phase determination by multiple-wavelength methods. The main difficulty encountered is that a wavelength of about 5 Å is required to obtain a large anomalous signal from these atoms, leading to very large absorption effects. Initial experiments have been carried out using a synchrotron X-ray source, evacuated beam tubes, a diffractometer inside a vacuum chamber, a special sample holder and a suitable scattering geometry. The results are encouraging, showing that Bragg reflections can be measured, and that changes in their intensities around the absorption edge are observable.

Notes: The previous paper described a phase-refinement strategy for protein crystallography which exploited the information that proteins consist of connected linear chains of atoms. Here the method is applied to a molecular-replacement problem, the structure of the protease inhibitor ecotin bound to trypsin, and a single isomorphous replacement problem, the structure of the N-terminal domain of apolipoprotein E. The starting phases for the ecotin-trypsin complex were based on a partial model (trypsin) containing 61% of the atoms in the complex. Iterative skeletonization gave better results than either solvent flattening or twofold non-crystallographic symmetry averaging as measured by the reduction in the free R factor [Brünger (1992). Nature (London), 355, 472–474]. Protection of the trypsin density during the course of the refinement greatly improved the performance of both skeletonizing and solvent flattening. In the case of apolipoprotein E, previous attempts using solvent flattening had failed to improve the SIR phases to the point of obtaining an interpretable map. The combination of iterative skeletonization and solvent flattening decreased the phase error with respect to the final refined structure, significantly more than solvent flattening alone. The final maps generated by the skeletonization procedure for both the ecotin–trypsin complex and apolipoprotein E were readily interpretable.

Notes: In an earlier study [Heinemann & Hahn (1992). J. Biol. Chem. 267, 7332–7341], the crystal structure of the double-stranded B-DNA decamer d(CCAGGCm5CTGG) was refined with NUCLSQ to R = 17.4% against 3799 2σ structure amplitudes in the resolution range 8–1.7 Å. This structure has now been re-refined against the same diffraction data using either TNT or X-PLOR in order to determine to what extent the resulting DNA conformations would differ and to examine the suitability of these programs for the refinement of oligonucleotide structures. The R value from the NUCLSQ refinement could not be reached with either TNT or X-PLOR, although both programs yield reasonably refined DNA models showing root-mean-square deviations against the NUCLSQ model of the decamer duplex of 0.25 and 0.32 Å, respectively. Some derived local structure parameters differ depending on the refinement procedure used. This holds true for several exocyclic torsion angles of the sugar-phosphate backbone, whereas sugar puckers as well as helical and base-pair stacking parameters are only weakly influenced. A subset of 15 solvent sites with low temperature factors is conserved in all three models.

Notes: A survey of 129 protein crystal structures with more than one molecule per asymmetric unit shows that local (non-crystallographic) symmetry axes are not randomly oriented. When compared to the crystal cell edges, face diagonals, body diagonal and reciprocal cell edges, 65% of the local symmetry axes are found to be parallel to one of the reference directions to within 15°; another 18% are orthogonal to within 3°; only 17% are in general orientations. In monoclinic, trigonal and hexagonal crystals, a majority of the local symmetry axes are orthogonal to the unique axis, while preferred orientations are parallel to the cell edges in orthorhombic crystals.

Notes: The structure of the ADP complex of the enzyme 3-phosphoglycerate kinase (PGK, E.C. 2.7.2.3) from Bacillus stearothermophilus NCA-1503 has been determined by the method of molecular replacement. The structure has been refined to an R factor of 0.16 for all data between 10.0 and 1.65 Å resolution, using data collected on the Hendrix–Lentfer imaging plate at the EMBL outstation in Hamburg. The r.m.s. deviations from stereochemical ideality are 0.010 and 0.011 Å for bonds and planes, respectively. Although crystallized in the presence of the nucleotide product MgATP, the high-resolution structure reveals the bound nucleotide to be MgADP reflecting the low intrinsic ATPase activity of PGK. Although the two domains of this enzyme are found to be some 4.5° closer together than is found in the yeast and horse-muscle apo-enzyme structures, this structure represents the `open' rather than the `closed', catalytically competent form, of the enzyme.

Notes: Xylose isomerase from Bacillus coagulans has been crystallized in two different crystal forms. One crystal form is in space group P21212, cell dimensions a = 462, b = 165, c = 82 Å. The other is in space group I422, cell dimensions a = b = 113, c = 153 Å.

Notes: The speed of electron-density fitting during X-ray structure solution and refinement, and the quality of the protein model resulting, can both be enhanced by the use of databases of main- and side-chain conformations. Three structures are compared in this report, one refined at high resolution (1.7 Å), and two at lower resolutions using either the database method (2.4 Å resolution) or more traditional empirical electron-density fitting (1.9 Å resolution). An analysis of peptide orientation was used as an aid in finding unusual portions of main-chain structure. The fit of side chains to known rotamer conformations was used to help determine the accuracy of these atomic positions. In addition, the use of an objective measure of the fit of structures to electron-density maps was evaluated, both alone and in combination with side-chain conformational information.

Notes: Crystals of cadmium-substituted azurin have been prepared by diffusing CdII into crystals of apo-azurin grown previously and their structure has been determined at high resolution by X-ray crystallography. Data to 1.8 Å resolution were collected by Weissenberg photography (with image plates) using synchrotron radiation. These data were combined with a 2.2 Å diffractometer data set to give 90% coverage to 1.8 Å. An initial model was derived from the isomorphous CuII-azurin structure, and the cadmium and ligand positions added from `omit' maps. Refinement was by restrained least squares (program PROLSQ), to a final R value of 0.168 for all data in the range 10.0–1.8 Å (23 349 reflections). The final model of 1954 protein atoms, two CdII ions (occupancy 0.75), four SO{_4^{2-}} ions and 239 water molecules has r.m.s. deviations of 0.015, 0.045 and 0.013 Å from standard bond lengths, angle distances and planar groups. The protein structure is essentially the same as that of CuII-azurin, with an r.m.s. deviation of 0.18 Å for 97% of main-chain atoms after superposition of the two structures. The Cd atom is within 0.2 Å of the equivalent copper position, displaced slightly away from the axial Met ligand towards the carbonyl O atom of Gly45. The latter has also moved slightly towards the metal, by a rotation of the peptide unit, to give a Cd—O bond of 2.76 Å. The Cd—S(Cys) bond is lengthened to 2.39 Å. The coordination geometry is slightly more tetrahedral than for CuII, and the cadmium–oxygen interaction is consistent with the presence of an oxygen ligand in the coordination sphere of stellacyanin.

Notes: The automated microbatch technique developed at Imperial College has been used to establish a phase diagram for crystallization. The concentrations of the protein (carboxypeptidase G2) and precipitant (PEG 4000) were varied, while pH and temperature were kept constant. The diagram consists of an undersaturation and a supersaturation zone, the latter being subdivided into the metastable, nucleation and precipitation zones. In the metastable zone, crystals may grow but nucleation of crystals does not occur. It is the best zone for growth of X-ray diffraction quality crystals because of the slower growth rate and the avoidance of uncontrolled nucleation, which uses up protein in the formation of tiny crystals. Nevertheless, in practice, it is rarely well defined or used because nuclei must be introduced artificially into the system. The new method used here consists of setting crystallization droplets at nucleation conditions and later diluting them to conditions where nucleation has not been observed. Single diffracting crystals of typical dimensions 0.3 × 0.3 × 0.2 mm were routinely obtained in the metastable zone, equivalent to the best (very rarely) obtained crystals in the nucleation zone.

Notes: Chloromuconate cycloisomerase (E.C. 5.5.1.7) is an enzyme involved in the 2,4-dichlorophenoxyacetate degradation pathway of Alcaligenes eutrophus JMP134 (pJP4). The crystal structure of this protein was determined at 3 Å resolution by molecular-replacement techniques using atomic coordinates from the reported crystal structure of the homologous muconate cycloisomerase (E.C. 5.5.1.1) from Pseudomonas putida as the search model (42% identical positions in the sequences). Structure refinement by simulated-annealing and restrained least-squares techniques converged at R = 0.195. In the crystals studied, space group I4, the protein is present as two octamers per unit cell with two subunits per asymmetric unit. Each subunit consists of two globular domains, one of which forms an α/β-barrel. Comparison of this structure with that of muconate cycloisomerase reveals the reasons for the altered substrate specificity of chloromuconate cycloisomerase. Marked differences are observed in polarity, accessibility and hydrogen-bonding potential in the channel leading into the active site as well as in the active center itself.

Notes: Studies of binding of substrates and inhibitors of the enzyme D-xylose isomerase show, from X-ray diffraction data at 1.6–1.9 Å resolution, that there are a variety of binding modes. These vary in the manner in which the substrate or its analogue extend, on binding, across the carboxy end of the (βα)8-barrel structure. These binding sites are His54 and the metal ion (magnesium or manganese) that is held in place by Glul81, Asp245, Glu217 and Asp287. Possible catalytic groups have been identified in proposed mechanisms and their role in the binding of ligands is illustrated.

Notes: Glucose isomerase from Streptomyces murinus has been crystallized in space group P41212, cell dimensions a = b = 137.65 and c = 132.20 Å. One dimer of the tetrametric molecule is found per asymmetric unit. An initial structure solution was obtained by the molecular replacement method. The crystallographic refinement was performed using molecular dynamics techniques with X-ray restraints. The final crystallographic R value is 21.4% at 2.6 Å resolution including 3023 non-H atoms, two metal ions and two water molecules per monomer.

Notes: Diffraction data to 2.7 Å resolution were measured on crystals of the homotetramers of components II and III of the cytoplasmic hemoglobin of the symbiont-harboring clam Lucina pectinata. Even though the crystallization conditions are different and the sequence homology of the two hemoglobins is only 63%, the crystals are isomorphous to each other and to the heterotetramer Hb II/III, implying that the residues primarily involved in the intermolecular interactions and responsible for crystal cohesion may be invariant.

Notes: We have crystallized a variety of RNA oligonucleotides in a form suitable for X-ray diffraction studies using polyethylene glycol with a low-molecular-weight distribution (PEG 400) as the precipitant. Crystallization experiments on a set of 26 RNA oligomers ranging from eight to 12 nucleotides in length resulted in eight diffraction-quality crystals. Of these eight RNA crystals, six utilized PEG 400 as the precipitating agent. We have also been able to obtain large single crystals of a DNA–RNA hybrid, transfer RNA (two different conditions) and a catalytic RNA from PEG 400 solutions. These results suggest that PEG 400 may be a generally useful alternative to 2-methyl-2,4-pentanediol (MPD) which has, thus far, been the most successful precipitant for DNA oligomers.

Notes: The molecular structures of cobalt- and nickel-substituted concanavalin A have been refined at 1.6 and 2.0 Å resolution, respectively. Both metal derivatives crystallize in space group I222 with approximate cell dimensions a = 89, b = 87 and c = 63 Å and one monomer in the asymmetric unit. The final R factor for Co-substituted concanavalin A is 17.8% for 29 211 reflections with F 〉 1.0σ(F) between 8.0 and 1.6 Å. For Ni-substituted concanavalin A the final R factor is 15.9% for 16 128 reflections with F 〉 1.0σ(F) between 8.0 and 2.0 Å resolution. Both structures contain a transition-metal binding site and a calcium-binding site but, unlike Cd-substituted concanavalin A, do not have a third metal-binding site. The Co-substituted concanavalin A structure diffracts to the highest resolution of any concanavalin A structure reported to date. A comparison of the structures of Ni-, Co-, Cd-substituted and native concanavalin A gives an indication of coordinate errors, which is a useful baseline for comparisons with saccharide complexes of concanavalin A described in other work. We also give a detailed account of multiple conformations which were found for five side-chain residues.

Notes: Based on amino-acid sequence homology, it is predicted that ribosomal protein L14 is a member of a recently identified family of structurally related RNA-binding proteins. To verify this, the gene for Bacillus stearothermophilus L14 has been cloned, and the protein has been purified and crystallized. The crystals are in space group C2 with cell dimensions a = 67.0, b = 32.7, c = 49.4 Å, and β = 101.8°, and there is one molecule in the asymmetric unit (Vm = 2.0 Å3 Da−1). They are of high quality, and a native data set has been collected to a resolution of 1.6 Å, with an Rmerge of 5.3%.

Notes: To assess the accuracy of refined structures, a comparison was made using independently determined structures of the same protein in the same crystal form. The models were re-refined against a common data set to minimize the effects of different data and different refinement protocols. The process did not converge to a single model. Rather the structures differed from each other by 0.84 Å which was roughly three times that predicted by a Luzzati analysis [Luzzati (1952). Acta Cryst. 5, 802–810]. The individual structures are equally valid and at least partially independent as evidenced by a reduction of the R factor by 0.013 when a simple linear combination is used. Only 29 solvent molecules were common to all four models.

Notes: Mirabilis anti-viral protein (MAP) is a ribosome-inactivating protein from Mirabilis jalapa L. Since MAP is effective over a broad spectrum of species, the protein is difficult to express in heterologous hosts such as Escherichia coli. Recently, we obtained a MAP mutant, Y72F which exhibits a lower (1/100) activity against E. coli ribosomes while retaining almost full activity against mammalian cells [Habuka, Miyano, Kataoka, Tsuge & Noma (1992). J. Biol. Chem. 267, 7758–7760]. For the crystallographic studies, the Y72F MAP expression vector with an OmpA leading sequence was constructed and expressed in E. coli. The Y72F MAP mutant was then isolated and purified from the cell culture medium. Crystals were grown using the crystallization conditions for the native MAP crystals [Miyano et al. (1992). J. Mol. Biol. 226, 281–283]: 50% ammonium sulfate containing 50 mM ammonium citrate and 2 mM adenine sulfate, pH 5.4. The crystals belong to space group P3121 (or P3221) with a = b = 104.1 and c = 134.3 Å. The crystals are isomorphous with the wild-type crystals but diffract to higher resolution. Imaging-plate photographs of the Y72F mutant showed sharp intense spots without the streaking observed in the native crystals.

Notes: Version 3.0 of the NIST/NASA/CARB Biological Macromolecule Crystallization Database (BMCD) includes crystal and crystallization data on all forms of biological macromolecules which have produced crystals suitable for X-ray diffraction studies. The data include summary information on each of the macromolecules, crystal data, crystallization conditions and comments about the crystallization procedure if it varies from the traditional methods employed for crystal growth. The database-management software maintains continuity with previous versions providing similar search procedures and displays. Version 3.0 of the BMCD includes protocols and results of crystallization experiments undertaken in space. These new data are comprised of both the NASA Protein Crystal Growth Archive, which includes information on all NASA-sponsored protein crystal growth experiments, and data describing other internationally sponsored microgravity macromolecule crystallization studies. The entries for the space growth crystallization experiments contain the crystallization protocols, apparatus descriptions, flight summary data, indication of success or failure of the experiments, references, etc. Other new features of the BMCD include the addition of crystallization procedures for small peptides and cross references to other structural biology databases.

Notes: In protein crystallography, the initial experimental problem is the identification of physical and chemical conditions that will support nucleation and crystal growth. Ideally, experiments to search for such conditions would be based on a full-factorial structure, with variation in the temperature and solution composition. However, consideration of even a moderate number of possibilities for the composition of the system will result in factorial experiments which may be prohibitively large. In this paper it is proposed that search experiments for protein crystallization might be based on orthogonal arrays. These are subsets of full-factorial experiments which possess a great deal of symmetry, such that a uniform distribution of points throughout the experimental region is preserved. Such experiments have reasonable size, explore the proposed experimental region in a systematic fashion, and form a logical basis for a sequential approach to the search for crystallization conditions. Examples of such initial search experiments are given, and their application to some recent protein crystallization problems in this laboratory is described briefly. The relationship of this approach to other protein crystallization search procedures is also discussed.

Notes: Predispensed gradient matrices allow the boundary between precipitate and clear solution to be located very rapidly for a particular protein and precipitant. In many cases crystals grow in the trials which were used to identify this boundary. The method involves dispensing a series of between 10 and 72 microbatch trials in which some parameter, such as precipitant concentration, is gradually changed. (Protein is not dispensed at this stage.) Protein is then added to selected trials using a predetermined algorithm, which takes into account the level of precipitation caused by previous additions. Thirteen crystal forms were obtained using the method with eight proteins and eight precipitants. Six forms were prisms or plates with maximum dimensions above 400 μm.

Notes: Today the determination of successful crystallization conditions for a particular macromolecule remains a highly empirical process. Sparse-matrix and grid-screening procedures are rapid and economical means to determine preliminary crystallization conditions. During optimization the variable set (pH, precipitant type and precipitant concentration) utilized in these procedures is screened in an attempt to determine appropriate conditions for the nucleation and growth of single crystals suitable for X-ray diffraction analysis. Unfortunately, in many cases this strategy will not produce single crystals suitable for X-ray diffraction analysis. We have explored, in an empirical sense, other tools for use during optimization. First, a new screening protocol is evaluated which employs less classical precipitating agents. Second, a set of 24 electrostatic crosslinking agents are evaluated for their ability to promote crystallization. Third, a panel of more than 30 detergents are evaluated for their ability to prevent sample aggregation and influence crystal growth.

Notes: The orthorhombic, or high-temperature, form of chicken egg-white lysozyme typically appears at temperatures ≥298 K. Solubility diagrams have been determined for this form of lysozyme from pH 4.0 to 5.4 in 0.2 pH increments using the micro-column technique. Data were collected in the 297–317 K temperature range which resulted in phase diagrams similar in overall shape to those obtained for the lower temperature tetragonal form. Specifically, the solubility increased with increasing temperature and decreased with increasing precipitant concentration. However, the solubility of the orthorhombic form is considerably less sensitive to temperature than the tetragonal form, resulting in a more flattened slope. On the other hand, pH effects on the high-temperature form were opposite to those on the low-temperature form. When holding the precipitant concentration constant, the solubility decreased with increasing pH for the orthorhombic form. Previous tetragonal data were incorporated with these orthorhombic data to produce intercept values. These values varied with both pH and precipitant concentration, but the general tendency of the slope was to decrease with increasing pH.

Notes: A convenient method for screening crystallization conditions using an automated fast-screen protocol has been implemented and tested on an enoyl-CoA hydratase. The crystallization solutions for the initial screening and subsequent optimizations are prepared using a crystallization robot. Enoyl-CoA hydratase (E.C. 4.2.1.17), purified from rat-liver mitochondria, is one of the enzymes from the β-oxidation pathway of fatty-acid metabolism; it catalyzes the reversible hydration of 2-trans-enoyl-CoA's to L-3-hydroxy-acyl-CoA's. Different crystal forms, diffracting to 3.0 Å, were obtained.

Notes: Recent developments of the IMPAX system for automated crystallization are presented. A five-channel microtip has been introduced into the system thereby providing an extra degree of freedom for carrying out experiments. A new mouse-driven program for screening has been introduced, which creates a much wider scope for designing and executing screens covering new conditions of crystallization. The hardware has been adapted so that the system can also be used to set up vapour-diffusion trials. A simple design of a vapour-diffusion vessel, suitable for sitting drops of 2–15 μl, using smaller reservoir volumes (up to 100 μl), facilitates large-scale systematic trials.

Notes: Poly(ethylene) glycol monomethyl ethers (Peg-mmes) are a series of methyl substituted poly(ethylene) glycols that have been used with some success in the crystallization of a number of hydrophobic proteins. Crystallization of a lipase from Humicola lanuginosa complexed with the C12 substrate analogue from Peg-mme 5000, an endoglucanase 1 and a 59 kDa fragment of human topoisomerase IIα crystallized from Peg-mme are described. The use of Peg-mme for improving the quality of crystals previously grown from normal poly(ethylene) glycol 8000 is also described. We suggest that these modified Peg-mmes should be regularly used in screening for crystallization.

Notes: Two different systems for recording crystallization results are described. Both programs are written in Microsoft Excel. Results can be entered either as text or numerical scores. In each system, one can search or query on the results, macromolecule name, experimental parameters, etc. and correlate these to specific crystallization conditions or trends in the crystallizations. Such information is valuable when optimizing crystal growth conditions and determining new crystallization parameters to test. XTAL RES is a Macintosh program that is linked to PCRYSTAL (software used to enter details of the crystallization experiments) through an Oracle database on a VAX network. A second system, the Electronic Notebook, was designed as a `stand-alone' Excel application running under Microsoft Windows.