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  • International Union of Crystallography (IUCr)  (1,316)
  • 2005-2009
  • 1990-1994
  • 1980-1984  (1,316)
  • 1955-1959
  • 1980  (1,316)
  • 1929
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  • 2005-2009
  • 1990-1994
  • 1980-1984  (1,316)
  • 1955-1959
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  • 101
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    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 3212-3212 
    ISSN: 1600-5740
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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  • 102
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    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 13 (1980), S. 7-11 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: Small-angle scattering data from polydisperse systems can be evaluated under the assumption that all particles have the same shape and that the size distribution depends only on one linear size parameter R. The shape of the particles is assumed to be known a priori. The corresponding size distribution function for the number of particles Dn(R) or for the volume Dv(R) can be computed from the smeared, unsmoothed scattering data by the indirect transformation method restricting the range of definition of the D(R) functions to a finite range Rmin ≤ Rmax. Rmin may be equal to zero, Rmax is limited by the sampling theorem of the Fourier transformation. The resolution in real space is given by the distance of the knots of the B spline functions approximating the size distribution function. The propagated statistical error band in real space can be computed using the inverted matrix of the normal equations. The method gives satisfactory results even in those cases where the shape of the particles is not known exactly, and is superior to analytical methods if the termination effect is critical.
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  • 103
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    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 13 (1980), S. 17-23 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: Ordering of carbon atoms in (V1 − xNbx)2C, (Nb1 − xTax)2C and (V1−xTax)2C has been studied by electron diffraction. In addition to three basic structures of V2C (ζ-Fe2N type), Nb2C and Ta2C [anti-Cd(OH)2 type], two superstructures are found at intermediate compositions of (V1 − xTax)2C. One of them appears also in (V1 − xNbx)2C at x = 0.2–0.5 and the other in (Nb1 − xTax)2C at x = 0.1–0.5. In these five structures, carbon atoms are aligned along the c axis occupying alternate octahedral interstices in the h.c.p. metal cell. The existence conditions of these structures are interpreted by a pairwise interaction model regarding the carbon atom-vacant interstice rows parallel to the c axis. The interaction energies for these rows up to the third-neighboring pairs are estimated from diffuse-scattering profiles observed on the specimens quenched from high temperatures. The results are discussed in comparison with the theoretical proposals for the ground-state structures based on a triangular-lattice gas model.
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  • 104
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    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 13 (1980), S. 24-30 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: The phases, their lattice parameters and the linear coefficient of the lattice thermal expansion were determined by high-temperature X-ray diffraction between room temperature and the melting point for the system (GaxIn1 − x)2Se3 (1 ≥ x ≥ 0). A wide homogeneity range of zinc blende structure was found in the Ga-rich region when a certain critical temperature was reached. In the In-rich region the alloys were isostructural with γ-In2Se3 at all temperatures, and the linear thermal-expansion coefficient was composition dependent.
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  • 105
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    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 13 (1980), S. 31-33 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: Crystal-lattice strain induced by impurity doping may be compensated for by diffusion of another kind of impurity. This was tried with successive diffusion of germanium and boron into (111) silicon wafers and was confirmed in a nondestructive way from the intensity profiles of the 333 Bragg reflection of Cu Kα X-rays. The intensity profile is related to the strain distribution along the depth through numerical computations, the programme for which has been developed and utilized previously [Fukuhara & Takano (1977). Acta Cryst. A33, 137–142] in quantitative discussions on strain and impurity concentration in silicon.
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  • 106
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    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 13 (1980), S. 34-45 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: Thermal density fluctuations within phases and finite interphase widths lead to systematic deviations from Porod's law. The validity of present methods used to analyze these deviations and determine diffuse-boundary widths is determined. In view of the inadequacies found in these methods, a simple yet accurate method is proposed to determine the diffuse-boundary width from direct graphical analysis of slit-smeared intensity data. The diffuse interface is modelled by a sigmoidal-gradient model which is justified on thermodynamic grounds, with the interphase thickness as a function of the Flory–Huggins interaction parameter.
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  • 107
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    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 13 (1980), S. 46-49 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: A miniature piston-cylinder high-pressure cell has been constructed for experiments with energy-dispersive X-ray diffraction. The maximum pressure achieved was 37 × 108 Pa. Examples are given for KCl and MgO, both measured with NaCl as an internal standard. The phase transition in KCl has been observed and the CsCl structure type verified.
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  • 108
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    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 13 (1980), S. 359-363 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: The construction principles for a flexible X-ray spectrometer which can be equipped either with a single curved crystal or with two curved crystals are described. A few of the theoretical 4 + 32 possible working modes are selected for a closer investigation and examples of recorded spectra are given. It is shown in the general single-crystal case that for a wavelength close to a cut-off energy the narrow diffraction cone has an elliptic section, as predicted by the theory. The spectrometer is discussed in terms of intensity, resolution and dispersive power. A comparison with other types of spectrometer is made.
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  • 109
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    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 13 (1980), S. 370-374 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: The aim of this paper is to develop a calculation method which allows the theoretical profiles of X-ray powder reflections to be obtained in the case of very small needle-like crystallites. This method takes into account not only the shape transform of the crystallite but also the variation of the structure factor. The study is limited to the case where the cross section of the needles contains two of the principal crystallographic axes and the third axis is along the crystallite direction of elongation. An example of the application of this method is given for a microcrystallized fibrous silicate known as sepiolite.
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  • 110
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    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 13 (1980), S. 452-453 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: (±)Rh(en)3(SCN)3 and (+)Rh(en)3(SCN)3, Rh(C2H8N2)3.(SCN)3, C6H24N6Rh.C3N3S3, crystallize in orthorhombic cells. The lattice constants are respectively a = 14.652 (5), b = 14.268 (6), c = 17.480 (6) Å and a = 14.711 (4), b = 13.481 (3), c = 9.166 (2) Å. They are isomorphic with their homologues (±)Co(en)3(SCN)3 and (−)Cr(en)3(SCN)3. The active racemate [(+)Rh(en)3(+)Cr(en)3](SCN)6 is isomorphic with the monoclinic form of [(+)Co(en)3(−)Cr(en)3](SCN)6. Its lattice constants are a = 15.707 (5), b = 17.739 (4), c = 9.426 (3) Å and γ = 131.04 (2)°.
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  • 111
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    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 13 (1980), S. 454-458 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: A series of samples in the system Al2Se3–In2Se3 in the In-rich region have been synthesized and studied by X-ray diffraction. In the interval of the Al/In (molar) ratio r from r≳ 1/50 to r≲ 1/20 the system has a two-phase region, α + γ1, where α is isostructural with the room-temperature modification of In2Se3, and γ1 is isostructural with the second high-temperature modification, γ, of In2Se3. For r ≳ 1/20, ternary γ1 alloys (AlxIn1−x)2Se3 are present alone and their unit-cell parameters decrease continuously as the Al content increases. These results are analogous with those obtained for the system Ga2Se3–In2Se3 in the In-rich region. The samples have also been studied by differential thermal analysis and electron-probe microanalysis.
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  • 112
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    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 13 (1980), S. 462-463 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
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  • 113
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    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 13 (1980), S. 96-97 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: Crystal data are given for both α and β forms of barium dichromate, BaCr2O7. The α form is monoclinic (C2/c) with a = 16.29 (5), b = 16.63 (5), c = 9.456 (1) Å; β = 92.52 (5)° and Z = 16. The β form, isotypic with SrCr2O7 and PbCr2O7, is tetragonal (P42/nmc) with a = 11.72 (5), c = 9.440 (3) Å and Z = 8.
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  • 114
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    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 13 (1980), S. 98-99 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: Crystals of LiGaO2.8H2O are trigonal, space group P3c1, with four molecules in a unit cell of dimensions a = b = 6,804, c = 25,63 Å. X-ray powder diffraction data are given.
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  • 115
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    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 13 (1980), S. 99-100 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: The structure of the high-temperature phase Mn2Ge is isotypic with Ni2In. The hexagonal unit-cell parameters are: a = 4.171±0.001, b = 5.278±0.002 Å. X-ray powder diffraction data are reported.
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  • 116
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    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 13 (1980), S. 100-101 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: A computer program is described which is suitable for calculating the angular positions of Bragg reflections compatible with a given type of unit cell, taking into account any systematic absences.
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  • 117
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    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 13 (1980), S. 105-105 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
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  • 118
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    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 13 (1980), S. 521-523 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: X-ray diffraction data for various materials reveal that naturally occurring microparacrystals cannot exceed a certain limiting size. The empirically obtained linear relationship between the square root of the limiting number of lattice planes within a paracrystal and the reciprocal value of the relative distance fluctuation between planes (degree of distortion) is discussed in the light of the paracrystal approach.
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  • 119
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    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 13 (1980), S. 516-520 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: The absolute sense of a large single-crystal of Ba(NO2)2.H2O (point group 6), and of one of Cs2S2O6 (point group 6mm), was determined by use of X-ray anomalous scattering methods. The piezoelectric d33 and pyroelectric p3 coefficients were measured on the same crystals, thereby leading to the assignment of the absolute sense of both coefficients. The magnitudes and senses found for Ba(NO2)2.H2O at 298 K are p3 = −14 (1) × 10−5 C m−2 K−1 and d33 = +3.1 (2) × 10−12 C N−1. The absolute coefficients for Cs2S2O6 at 298 K are p3 = +0.9 (2) × 10−6 C m−2 K−1 and d33 = + 14.7 (1.0) x 10−12 C N−1. The atomic displacements in Ba(NO2)2.H2O corresponding to p3 are 5.7 × 10−4 Å K−1 by the Ba2+ ion or dipolar rotations of 7.7 arc min K−1 by NO2 or H2O: for d33, the displacements are about 0.1 × 10−4 Å (106 N m−2)−1 by Ba2+ or dipolar rotations of 0.2 arc min(106 N m−2)−1. In the case of Cs2S2O6, the Cs+ ion displacements are 0.1 × 10−4 Å K−1 on heating and 0.2 × 10−3 Å (106 N m−2)−1 under stress. Dipolar rotations do not contribute either to p3 or to d33 in Cs2S2O6.
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  • 120
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    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 13 (1980), S. 611-612 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: 5′-azido-5′-deoxy-3′-O-acetylthymidine (C12H15N5O5) is orthorhombic. The crystal data for the primitive space lattice are a = 5.584 (1), b = 14.347 (4), c = 18.021 (4) Å, Dm= 1.41 (1), Dx = 1.422 Mg m−3 and Z = 4. The quantitative figure of merit (FN) is F30 = 96 (0.006, 52). Indexed X-ray powder data are reported.
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  • 121
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    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 13 (1980), S. 613-613 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: Powder X-ray diffraction data for two new rare-earth thallates, MIIITlIIIO3 (M = La, Nd), have been reported. These thallates have been prepared using two chemical routes by heating homogeneous 1:1 molar reaction mixtures of (a) rare-earth carbonates, MIII2 (CO3)3.nH2O, and thallous carbonate, Tl2CO3, and (b) rare-earth oxides, MIII2O3, and thallous carbonate, in air at 823±10 K for 7 h.
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  • 122
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    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 13 (1980), S. 614-615 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: Unit-cell parameters and space groups have been determined for three ammonium potassium pyrophosphates. The compound (NH4, K)2H2P2O7 is triclinic with space group P1 or \overline P1, and a = 7.950 (3), b = 7.270 (3), c = 7.184 (3) Å, α = 90.89 (4), β = 117.61 (3), γ = 81.56 (4)°, Z = 2. The hydrated salt (NH4, K)2H2P2O7.0.5H2O is orthorhombic with space group Pnma or Pna21, and a = 19.22 (2), b = 7.64 (1), c = 10.39 (1) Å, Z = 8. The tribasic salt (NH4, K)3HP2O7.H2O is monoclinic with space group Cc or C2/c. The X-ray data show that a = 19.41 (2), b = 6.158 (6), c = 16.90 (2) Å, β = 107.5 (1)°, Z = 8. The indexed powder diffraction patterns are given for the three salts.
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  • 123
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    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 13 (1980), S. 176-179 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: The sense of the spontaneous polarization Ps for ferroelectric LiH3(SeO3)2 has been related to the absolute atomic arrangement with the use of anomalous scattering of neutrons from 6Li. The polar axis is almost parallel to the crystallographic c* axis. The absolute sense of Ps is antiparallel to c* with an experimentally determined magnitude of 15 × 10−2 C m−2. The calculated value, assuming point charges for Li+, H+, Se4+ and O2− is −9.8 x 10−2 C m−2. LiH3(SeO3)2 belongs to the three-dimensional class of ferroelectrics with essentially random displacement directions of the atoms at polarity reversal. The large value of Ps is the result of the oxygen displacements all having the same sense along the polar axis.
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  • 124
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    Applied crystallography online 13 (1980), S. 190-190 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: The title compound crystallizes in the orthorhombic system (possible space groups: C2cm, Cmcm and Cmc21). The unit-cell data are a = 6.313 (5), b = 16.60 (2), c =7.555 (3) Å. The indexed powder data is given.
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  • 125
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    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 13 (1980), S. 199-199 
    ISSN: 1600-5767
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  • 126
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    Applied crystallography online 13 (1980), S. 199-200 
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  • 127
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    Applied crystallography online 13 (1980), S. 200-200 
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  • 128
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    Applied crystallography online 13 (1980), S. 200-200 
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  • 129
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    Applied crystallography online 13 (1980), S. 200-200 
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  • 130
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    Applied crystallography online 13 (1980), S. 207-210 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: A dual-beam three-crystal spectrometer for high-sensitivity lattice-parameter comparison measurements of high-perfection crystals is described. It has a sensitivity, Δd/d, of up to ±3 x 10−8 when CuKα1 radiation is used. This spectrometer is also employed as a high-sensitivity double-crystal topographic camera. Examples of applications to doped float-zone and epitaxic layers of silicon crystals are reported, together with low- and high-temperature measurements done with a cryostat designed for high thermal stability.
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  • 131
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    Applied crystallography online 13 (1980), S. 211-216 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
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    Notes: PbZrxTi1−xO3 ceramics around the morphotropic phase boundary (MPB) have been prepared under different firing conditions using the usual ceramic techniques. The phases of the compounds have been investigated with X-ray diffraction photographs. It has been found that the MPB is not a narrow and vertically straight boundary but a region whose width depends on the firing time and temperature. The microstructures of the ceramics have been studied with a scanning electron microscope and can be correlated with the firing conditions. Measurements of lattice parameters, dielectric constants and transition temperatures are reported.
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  • 132
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    Applied crystallography online 13 (1980), S. 201-206 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: A new goniometer for X-ray powder diffractometry and its setting are described. The diffraction angles are easily and quickly measured with high accuracy (10−3°&thgr;), even if experiments require the use of some large or heavy device such as a cryostat or furnace. An original mechanical design allows a direct measurement of the angular position, 20, of the receiving slit, by means of an incremental (10−3°) photoelectric encoder. Three independent stepping motors, for the &thgr; and 2&thgr; scans and the sample translation, allow one to define with a very good reproducibility the `zero' goniometer position. Diagrams of Pb3O4 and Pb(NO3)2 have been recorded in continuous scanning (0.05° &thgr;/min): differences between &thgr; of the two diffraction lines recorded on each side of the goniometer do not exceed ±2 × 10−3°, and reproducibility of measurements is better than +1 × 10−3°. Sensitivity of angular measurements is very good; it is proved by studying, in the range 9–40° (&thgr;), the thermal expansion of Pb(NO3)2 between 273 and 291 K. Moreover, use of a large radius (500 mm) and of a set of undivergent slits improves angular resolution, principally for &thgr;〈20°, which is very important for molecular-compound studies: an example is given showing diffraction line splitting due to a monoclinic triclinic phase transition.
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  • 133
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    Applied crystallography online 13 (1980), S. 217-223 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: A brief review of methods of measuring birefringence is given. Apparatus for the accurate measurement of optical birefringence at high temperatures using a modulation (rotating-analyser) method is described in detail, together with suggestions for further applications of the equipment. The technique is applied to the particular case of the ferroelastic monoclinic–tetragonal phase transition in BiVO4. The birefringence was found to show mean-field behaviour over a wide temperature range with a mean-field transition temperature of 519.9 (3) K.
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  • 134
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    Applied crystallography online 13 (1980), S. 230-232 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: The paper deals with an optical method for measuring both growth and dissolution rates of birefringent crystals in solution. This method, based on a suitable adaptation of Fresnel's formula, is particularly useful when the normal rates of the crystal faces are very low.
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  • 135
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    Applied crystallography online 13 (1980), S. 224-229 
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    Topics: Geosciences , Physics
    Notes: The accurate measurement of optical birefringence at simultaneous high pressures and temperatures using a diamond-anvil pressure cell is described. Data are presented for BiVO4 which show that the optical birefringence may be described by mean-field behaviour. An applied hydrostatic pressure of only 8 × 108 Pa reduces the mean-field temperature of the ferroelastic monoclinic tetragonal phase transition from 519.7 to 393 K. A birefringence–pressure–temperature phase diagram is presented.
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  • 136
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    Applied crystallography online 13 (1980), S. 233-243 
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    Topics: Geosciences , Physics
    Notes: The method for correcting slit-height smeared small-angle X-ray data, presented in the two previous articles in this series [Deutsch & Luban (1978). J. Appl. Cryst. 11, 87–97, 98–101], calls for the use of a correction function g(t). In this article g(t) is derived for a number of single and compound slit configurations.
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  • 137
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    Applied crystallography online 13 (1980), S. 533-538 
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    Notes: The ferroelastic domain structure of CsPbCl3, in its monoclinic phase, is analyzed by two theories: group symmetry and tensor method, or twinning by pseudo-symmetry. The loss of symmetry between the prototypic and the monoclinic phases is important and allows the existence of twelve kinds of domains. Theories provide a coherent description of domain pairs and a determination of the position of W and S walls.
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  • 138
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    Applied crystallography online 13 (1980), S. 544-554 
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    Topics: Geosciences , Physics
    Notes: Polycrystalline samples of non-centrosymmetrical enantiomorphic materials may be considered as two-phase materials consisting of a right-handed and a left-handed phase, each of which has its own texture. Centrosymmetrical crystals may be considered as right- or left-handed at the same time. If the right- and left-handed nature of the crystals is fully to be taken into account then the statistical sample symmetry is correctly to be described by black–white point groups rather than by the ordinary ones. If the sample symmetry does not belong to one of the `grey' groups then the series expansion of the texture functions contains terms of odd order which are blotted out in polycrystal diffraction experiments by virtue of the inversion centre in the crystal symmetry or by Friedel's law. In certain cases it seems possible, however, to obtain an approximation to the odd part by making use of the non-negativity condition in the zero ranges of the texture function. Many important physical properties are centrosymmetric (even if the crystals themselves are not). In these cases the odd part of the texture function does not enter into the expression relating the polycrystal property to the corresponding one of the single crystals.
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  • 139
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    Applied crystallography online 13 (1980), S. 577-584 
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    Topics: Geosciences , Physics
    Notes: The cross-section scattering function and the cross-section distance distribution function are of special interest when lamellar or cylindrical particles are investigated by small-angle scattering techniques with high resolution. These functions can be computed from the unsmoothed, smeared scattering data by the indirect transformation method. This method requires an estimate for the maximum cross-section dimension, which can be found from the distance distribution function of the particle. The influence of finite size, the termination effect and the limits of resolution are discussed using results from simulated experiments.
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  • 140
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    Applied crystallography online 13 (1980), S. 601-604 
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    Notes: A tensile hot stage capable of temperatures up to 1470 K was constructed for the purpose of taking video X-ray topographs during the plastic deformation of silicon single crystals. The temperature is monitored by Pt–PtRh thermocouples and a pyrometer. The apparatus is designed for operation in vacuum or inert-gas atmosphere.
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  • 141
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    Applied crystallography online 13 (1980), S. 539-543 
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    Topics: Geosciences , Physics
    Notes: The experimental observations of the ferroelastic domain structure of CsPbCl3, in its monoclinic phase, are compared to the results obtained by a theoretical analysis using twinning by pseudo-symmetry, or a tensor method. The various kinds of observed domain walls are identified with the permissible W and S walls.
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  • 142
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    Applied crystallography online 13 (1980), S. 563-571 
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    Notes: A data processing method is presented which allows reliable intensities to be obtained from the weak neutron diffraction produced by protein crystals. Three components are used to reduce the errors in the intensities: (1) a pattern-recognition technique to find the peak centers; (2) a position-sensitive linear detector, whose spatial resolution characteristics increase the accuracy with which the boundary between the peak and background may be defined; and (3) an averaging technique to obtain accurate backgrounds. Test results with a 2.2 Å data set collected from a small crystal of the proteolytic enzyme trypsin indicate that data processed by this method are superior in both reproducibility and statistical reliability to the same data processed by more conventional methods. Refinement results with the trypsin structure indicate that the data are accurate as well.
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  • 143
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    Applied crystallography online 13 (1980), S. 585-590 
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    Notes: Procedures for correcting experimental diffraction intensities in the small-angle region for the determination of one-dimensional structures are presented. The diffraction patterns in question consist of meridional streaks which are transversely broadened due to: (1) finite fibril radius, (2) imperfect fibrillar orientation, (3) lamellar curvature or (4) instrumental broadening. Three methods are developed and compared for obtaining corrected intensities in the presence of these effects. One method uses direct integration over all reciprocal space. Two complementary techniques involve correction of integrated layer line or meridional peak intensities; the correction factors are shown to be the transverse integral widths of the layer lines, suitably modified for instrumental broadening.
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  • 144
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    Applied crystallography online 13 (1980), S. 597-600 
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    Notes: The boundaries of the regions within which a specific set of slip systems maximizes the Taylor factor M (g, q) are plotted in a stereographic triangle for several values of the contraction ratio q and an axially symmetric flow. For q = 0.5 these boundaries are shown to be mostly circles on the unit sphere.
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  • 145
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    Applied crystallography online 13 (1980), S. 608-610 
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    Notes: Microscopic, single crystals of sodium dodecylsulphate, Na+.C12H25O4S−, have been investigated by electron diffraction under conditions of carefully controlled temperature. The studies showed that the specimens are two-dimensional in the crystallographic sense and that a first-order solid-solid transition takes place at 283 K. The existence of the transition is shown by the discontinuous change of lattice parameters and the abrupt disappearance of all hk0 reflections with h + k odd at this temperature. Linear, thermal-expansion coefficients along the a and b directions are reported for the low-temperature form. The phenomenon is compared with similar transitions occurring in paraffins, and interpreted as the onset of rotational motions by the hydrocarbon chains of sodium dodecylsulphate about their longitudinal axes.
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  • 146
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    Applied crystallography online 13 (1980), S. 616-617 
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    Notes: (−)-[Rh(en)3Br3.H2O is isomorphic with cobalt salts (+)-[Co(en)3Br3.H2O and (+)-[Co(en)3]Cl3.H2O. It crystallizes in the quadratic space group P4321. Lattice constants are a = 10.070 (2) and c= 16.688 (5) Å with four formula units in the unit cell.
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  • 147
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    Applied crystallography online 13 (1980), S. 621-621 
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    Notes: Crystal data of barium iodate monohydrate single crystals obtained with oscillation and Weissenberg photographs are reported. Crystals are grown by gel technique. Ba(IO3)2.H2O is orthorhombic with space group Fdd2. The lattice parameters with four formula units per cell are a = 7.96 (2), b = 9.01 (3) and c = 9.78 (5) Å.
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  • 148
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    Applied crystallography online 13 (1980), S. 630-633 
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    Notes: A powder profile refinement program written specifically for the easy application of structural constraints is made generally available. It is based on ORFLS and written in Fortran IV. Details of the philosophy of the program are outlined, with emphasis on the areas where more research is necessary. Examples of usage in the literature are cited.
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    Applied crystallography online 13 (1980), S. 625-629 
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    Notes: A program system is described whereby high-quality drawings of crystal and molecular structures may be prepared with relatively modest hardware, such as a desktop plotter driven by a similar computer or minicomputer. It is written in Basic and consists of a suite of six overlay programs, each performing a specific task in the process of setting up and executing a drawing. The mode of operation is fully interactive, through features such as console prompting, provision of preview plotting and immediately accessible correction or editing facilities. The system is easy to use, even for inexperienced users, and demands the minimum of time and effort on the part of the user.
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    Applied crystallography online 13 (1980), S. 635-635 
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    Applied crystallography online 13 (1980), S. 636-636 
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    Applied crystallography online 13 (1980), S. 637-638 
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  • 153
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    Applied crystallography online 13 (1980), S. 252-255 
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    Notes: The theory, design principles and performance data of asymmetrically cut grooved perfect-crystal diffractometers for small-angle X-ray scattering measurements are presented. A way of optimizing the diffractometer with respect to resolution, intensity and S/N ratio for a given experiment is indicated. The measured data is found to support closely the theoretical conclusions.
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    Applied crystallography online 13 (1980), S. 280-283 
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    Notes: The largest dimension, L, of a scattering particle is an essential structure parameter of the sample and is necessary both for designing and carrying out experiments and also for analysis of the scattering data. It is shown that L, which is identical to the upper-limit frequency of the scattering curve, can always be evaluated from a Fourier cosine transformation of scattering data which are not corrected for collimation effects, regardless of the shape of the primary beam.
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  • 155
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    Applied crystallography online 13 (1980), S. 290-296 
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    Notes: The strain distribution in the vicinity of the notches of a double-notched, elastically bent silicon crystal was determined by measuring the diffracted X-ray intensities. The measurements were carried out on traverse-oscillation topographs of a crystal section extending through both notches. Strain distributions were determined by measuring the local densities of silver deposits (measurements of `opacities') with a scanning electron microscope. It was shown that both the density range and spatial resolution of X-ray densitometry were larger by an order of magnitude than those of optical densitometry. The strain concentration factors associated with the notches were measured experimentally and calculated by continuum mechanics. The results were in satisfactory agreement. Also, the experimentally found rise of strains, to a maximum in the critical area adjacent to the notch root, followed the trend predicted by continuum mechanics.
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    Applied crystallography online 13 (1980), S. 304-305 
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    Notes: A strategy is described for the collection of isomorphous derivative data using the oscillation method. An example of this procedure is given using the uranyl derivative of southern bean mosaic virus. The method is based on rapid collection and processing of an initial low-resolution (large oscillation angle) data set which is used to characterize the derivative before proceeding to high-resolution (small oscillation angle) photography.
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    Applied crystallography online 13 (1980), S. 339-340 
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    Notes: When the accurate determination of inter-planar spacings from a standard Debye–Scherrer powder-camera film is required for unit-cell dimension and indexing purposes, then several corrections have to be applied to the measured arc dimensions before the required precision can be achieved.
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    Applied crystallography online 13 (1980), S. 346-353 
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    Notes: Matrix-transformation techniques are developed to describe the numerous higher-order orientation relationships possible between hematite and magnetite when multiple twinning of both phases is allowed. Structural models for the various interfaces are described. The matrices are used to predict the peak positions expected for the 400M pole figure of magnetite on hematite. Comparison with the experimental pole figure [Becker, Heizmann & Baro (1977). J. Appl. Cryst. 10, 77–78] showed that it was also necessary to allow for oriented recrystallization of hematite. This involves a new distinct type of orientation relationship which is labelled transformation twinning.
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    Applied crystallography online 13 (1980), S. 380-384 
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    Notes: A method is presented for improving the accuracy of the determination of peak positions from step-scanned X-ray powder diffraction data. This method is intended to be used in situations where the nature of the sample produces broad asymmetric peaks with a low peak-to-background ratio. A Fourier series is fitted to the experimental step-scan observations and the peak position is calculated from this functional representation. The method has been tried on the mineral apatite from biological sources, mainly bone, where ionic substitutions affect the cell parameters.
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    Applied crystallography online 13 (1980), S. 74-77 
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    Notes: In deconvolution procedures of X-ray diffraction line profiles, a non-ideal standard specimen often has to be used to measure the broadening due to the instrumental aberrations and the X-ray spectrum used. This leads to a non-ideal standard line profile at an incorrect sin 0 range with an incorrect broadening. Large errors in the structural parameters to be determined may result. These errors can be minimized by choosing a proper origin for the evaluation of the Fourier series of the line profiles measured. Rules are presented for the necessary shifts of the origin of a non-ideal standard line profile compared to the origin of the line profile to be analyzed. If these shifts of origin are carried out, errors are still present from the difference in broadening between ideal and non-ideal standard specimens. Simple correction factors are presented to eliminate also these errors. The treatment is given for non-ideal standard specimens with (i) an incorrect spacing, (ii) an incorrect specimen transparency and (iii) remaining structural defects.
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    Applied crystallography online 13 (1980), S. 402-402 
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    Applied crystallography online 13 (1980), S. 417-424 
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    Notes: Based on the principles of conservation of momentum and energy for X-ray diffraction, a vector description is obtained for the displacement of adjacent subgrain images in reflection topographs. The analysis includes, in addition to those crystal parameters defining the misorientation at a subgrain boundary, the combined effects of (horizontal and vertical) divergence in the incident X-ray beam and of the position where the X-ray images are recorded. The vector description is matched with a stereographic projection method of analysis for describing the subgrain misorientations. These total considerations are applied to the characterization of subgrain boundaries grown into a nickel single-crystal solidified along [010], including specification of the dislocation structure within the boundaries.
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    Applied crystallography online 13 (1980), S. 463-463 
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    Applied crystallography online 13 (1980), S. 472-478 
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    Notes: Position–angle–wavelength space is introduced to describe X-ray optical properties of various optical elements and their combined systems. This three-dimensional space is a combination of the position-angle space used in the phase-space method and the angle-wavelength space used in the DuMond diagram. Representations in the position–angle–wavelength space are shown for a synchrotron radiation source, a flat perfect crystal, a curved crystal and a double-crystal arrangement. A method of estimating the spatial width, angular divergence, wavelength spread and intensity of the X-ray beam emitted by a given optical system is described by making use of descriptions in the position–angle–wavelength space.
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    Applied crystallography online 13 (1980), S. 500-504 
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    Notes: The loss of the orthogonality relationships in the incomplete pole-figure method leads to the necessity of solving a large set of equations to obtain the C coefficients of the orientation distribution function (ODF). The knowledge of the normalization factor Ni of each pole figure allows the large set of equations to be divided into subsets of reduced size. This paper presents a way to determine the Ni factor from the nullity of the F02 coefficient of the series expansion of the pole figure for cubic lattice symmetry. Calculations have been carried out for a sample with a triclinic symmetry.
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    Applied crystallography online 13 (1980), S. 494-499 
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    Notes: Quantitative analysis of textures of materials requires calculation of the crystallite orientation distribution function (CODF) by expanding pole figures as series of spherical harmonics; the accuracy of the function depends on the truncation order l of the developments. A criterion TRC has been used to obtain comparable truncation error estimations for different pole figures of a sample with a given order of development; in this way this criterion gives the value of the truncation order corresponding to a given accuracy. In the case of materials having cubic crystal symmetry, the expansion coefficients of the CODF have to satisfy relations of linear dependence: these relations have been determined for l up to 34, so that sharp textures may be considered. The calculation of the CODF at l = 34 is applied to textures having orthotropic symmetry in aluminium sheets. It is shown that an insufficient order of the series expansions may lead to important errors in the CODF values and in the nature of the preponderant preferred orientations.
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    Applied crystallography online 13 (1980), S. 622-624 
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    Notes: Powder patterns are reported for all the phases stable between 130 K and the melting points. Potassium propanoate, K+.C3H5O2, is monoclinic between 258 and 353 K [a = 3.971 (3), b = 5.799 (4), c = 11.476 (7) Å, β = 91.42 (1)° at 322.0 K] and orthorhombic at higher temperatures [a = 4.051 (5), b = 5.772 (7), c = 11.706 (15) Å at 414.0 K]. Rubidium propanoate, Rb+.C3H5O2, shows two orthorhombic phases above 317 K: a = 4.235 (2), b = 5.951 (3), c = 11.557 (6) Å at 371.5 K and a = 4.335 (2), b = 5.920 (3), c = 11.767 (5) Å at 573.2 K.
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    Applied crystallography online 13 (1980), S. 633-634 
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    Applied crystallography online 13 (1980), S. 634-635 
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    Applied crystallography online 13 (1980), S. 636-636 
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    Applied crystallography online 13 (1980), S. 637-637 
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    Applied crystallography online 13 (1980), S. 188-189 
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    Notes: Coordination polyhedra in crystals are identified by matching interbond angle matrices for observed and ideal polyhedra. An algorithm for permuting the N vertices of the observed polyhedron is described in which not all of the N! combinations are examined. The method has been used to identify a number of higher-coordination polyhedra.
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    Applied crystallography online 13 (1980), S. 197-198 
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    Topics: Geosciences , Physics
    Notes: A simple method, based on real space, is described to calculate on a PW 1100 diffractometer D and RD vectors for anisotropic extinction corrections. and for every 0 (0 = rotation around the reciprocal vector). This problem has already been solved for other diffractometers in reciprocal space (Coppens, Leiserowitz & Rabinovich, 1965; Coppens, 1970) and has been re-examined for the PW 1100, using a simple procedure in real space.
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    Applied crystallography online 13 (1980), S. 244-251 
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    Notes: An Optronics P-1700 film-writing device is used to produce simulations of disordered organic molecular crystals. The simulations may be used directly to obtain optical diffraction patterns for comparison with X-ray diffuse scattering photographs of real crystals. Examples of some substituted anthracenes are given to demonstrate the diversity of disorder effects which may be included and the level of precision achieved.
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  • 175
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    Applied crystallography online 13 (1980), S. 256-258 
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    Topics: Geosciences , Physics
    Notes: The asymmetrically cut, optimized BH diffractometer for small-angle X-ray scattering experiments is compared with the Kratky camera. It is shown that a crossover point exists in the resolution so that at a lower resolution the Kratky camera is superior and at a higher resolution the BH system is preferable. The crossover point depends on the number of reflections used. Methods of reducing the spurious signal and increasing the S/N ratio of the BH system are also discussed.
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  • 176
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    Applied crystallography online 13 (1980), S. 399-399 
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    Topics: Geosciences , Physics
    Notes: Crystal data are reported for two compounds obtained by catalytic hydrogenation of triptycene (C20H14), ACC(C20H26) and TTC(C20H32).
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  • 177
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    Applied crystallography online 13 (1980), S. 513-515 
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    Topics: Geosciences , Physics
    Notes: The chemical composition of Ga1−xInxP (0 ≤ x ≤ 0.10) alloys epitaxically grown on GaP substrates has been determined by electron microprobe analysis and by lattice-parameter measurement (a). The a(x) calibration curve follows Vegard's law which confirms the regular character of the solid solution and the existence of strain relaxation in the epitaxic layers.
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    Applied crystallography online 13 (1980), S. 618-621 
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    Topics: Geosciences , Physics
    Notes: Ca10(PO4)6CO3 is an `apatite' with pseudo-hexagonal symmetry with monoclinic space group Pb and lattice constants a = 9.557 (3) Å, b ∼ 2a, c = 6.872 (2) Å and γ = 120.36±0.04°.
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  • 179
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    Applied crystallography online 13 (1980), S. 633-633 
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  • 180
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    Acta crystallographica 36 (1980), S. 43-50 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A restrained least-squares (RLS) computer program and two interactive graphics (IG) systems have been used in combination to refine the structure of deer type III hemoglobin. By alternating applications of RLS with examinations and corrections of the atomic model superposed on electron density maps (IG), the residual has been reduced from 0̃.42 to 0̃.25 and the sites of dubious fit between model and map reduced to 6̃% of the residues or 3̃% of the atoms. It was possible to fit routinely 4̃600 atoms to X-ray intensity data sets ranging from less than 6000 (9.0-4.0 Å resolution) to 2̃1 500 points (6.0-1.98 Å resolution) employing RLS, which uses interatomic distances to retain structural integrity. Convergence was rapid and many shifts greater than 1 Å were recorded. An in-house graphics display allowed the placement of atoms not in the original atomic model and GRIP, a fast-response interactive graphics system, was used to correct any gross conformational misfit of the atomic model to the electron density maps. The man hours needed to run both GRIP and RLS is less than previously reported real-space methods. The strategy of how RLS and IG can be best applied and how the molecular structure changed during refinement are discussed.
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  • 181
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    Acta crystallographica 36 (1980), S. 68-74 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The present paper deals with the finding and the estimation of negative quartets. The use of symmetry is also discussed and the results obtained for four structures of increasing size are reported. Conditional probability distributions using magnitudes contained in the second representation of the quartets provides improved estimates of their phases.
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  • 182
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    Acta crystallographica 36 (1980), S. 74-82 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A phase relationship involving triplet and quartet contributions is given. It is able to take account of the correlation between triplet and quartet relations. The information exploited by the formula is discussed and compared with that exploited by phase relationships arising from the properties of the Fourier transform of periodic positive functions. In particular, the information contained in a Karle-Hauptman determinant of low order is briefly considered.
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  • 183
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    Acta crystallographica 36 (1980), S. 89-96 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: At room temperature the background of X-ray single-crystal photographs exhibits diffuse streaks along the line Δ from Γ to X and less sharp diffuse domains in the directions Σ. The streaks are explained by a soft rotary phonon A2(Δ) corresponding to an in-phase rotation of the octahedra in a plane. The displacements of the Cl ions due to their librations are identified in a difference-Fourier chart. The second diffuse system is explained by a transversal accoustical mode B1(Σ). The in-phase rotation of the octahedra in a plane minimizes the electrostatic energy, independently of the phase of the rotation in adjacent planes. In the model the repulsive parameter between the Cl and K ions decides whether the space group P4/mnc, as a result of an A2g(X) condensation, or the orthorhombic Pnnn, as a result of a second rotary mode condensation, is energetically favorable.
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  • 184
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    Acta crystallographica 36 (1980), S. 104-116 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A focusing monochromatic X-ray single-crystal technique (Noromosic technique) is applied to investigate shape and interference phenomena of multiply scattered X-ray reflections. It is shown that this technique allows for rapid elimination of spurious 'peaks' caused by coherent or incoherent multiple-scattering processes (Umweganregung). No rotation of the crystal around the reciprocal vector in question is necessary. Furthermore, it is shown that phase determination can be done in principle if two secondary reflected beams are brought to interference within the crystal. This may generally be realized in the n-beam case of diffraction (n ≥ 4) by changing the wavelength or the lattice geometry. The method is applied to a-phenazine, C12H8N2, where four- and six-beam cases occur accidentally without a variation of the wavelength. It is shown that phase determination is possible even in such cases where a certain mosaic spread of the crystal is unavoidable.
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  • 185
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    Acta crystallographica 36 (1980), S. 122-126 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The controversial space-group problem of spinel, MgAl2O4, whether it is Fd3m or F{\bar 4}3m, was studied by electron diffraction. It was confirmed that the appearance of 'forbidden reflections' such as {200} was caused by the double reflection process of reflections with high indices on the non-zero-order Laue zone. Consequently, the space group of spinel is Fd3m, and the assignment of the space group to F{\bar 4}3m is ruled out. The change of space group from F{\bar 4}3m to Fd3m associated with a phase transition, proposed by Mishra & Thomas [Acta Cryst. (1977), A33, 678], can also be explained by double diffraction: the magnitudes of primary reflections with high indices rapidly decrease due to the increase of the Debye-Waller factors at elevated temperatures.
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  • 186
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    Acta crystallographica 36 (1980), S. 139-142 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In polarized-neutron diffractometry, one often observes a variation of the polarization ratio over the rocking curve. This paper outlines a simple method which uses this interesting feature to estimate quantitatively the secondary-extinction parameter in the specimen crystal.
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  • 187
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    Acta crystallographica 36 (1980), S. 143-146 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: It is pointed out that there is some uncertainty as to the correct behaviour of the integrated reflectivity as a function of the degree of asymmetry for the scattering of X-rays from imperfect crystals in the extremely asymmetric Bragg case. Numerical calculations based on the Takagi-Taupin equations are exemplified and indicate that the integrated reflectivity for such crystals tends asymptotically to the perfect-crystal result in the asymmetric limits, the perfect-crystal result, in turn, tends to the kinematical value at these limits, as has been shown previously. In addition, comments are offered on the relevance of the present work to the study of highly imperfect crystals by section topography, and in particular to the study of the near-surface grain-boundary structure of crystals.
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  • 188
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    Acta crystallographica 36 (1980), S. 147-148 
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    Notes: The mean Debye-Waller parameter {\bar {\it B}}of TlCl has been determined by double- as well as triple-axis neutron diffraction for a powder sample. Thermal diffuse scattering (TDS) corrections have also been made to the intensity of the diffraction peaks obtained by these techniques. TDS was found negligible in the triple-axis diffraction pattern as expected. The {\bar {\it B}} values thus found are 3.08 ± 0.43 and 3.07 ± 0.22 Å2, respectively, for double- and triple-axis methods. These values are in good agreement with those found by recent X- ray diffraction measurements.
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  • 189
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    Acta crystallographica 36 (1980), S. 153-154 
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    Notes: A general expression for the diffracted intensities from an aggregate of cylindrically curved crystallites with rotational shifts of layers by different amounts has been worked out using a model and treatments similar to those of previous work [Ray, De & Bhattacherjee (1978). Acta Cryst. A34, 637-638]. Numerical computations for several cases of layer shift showed that the heights of the diffraction peaks decrease accompanying slight changes in peak positions as the unit of angular shift decreases.
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  • 190
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    Acta crystallographica 36 (1980), S. 156-156 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The Abstract by Modlin & Rodgers [Acta Cryst. (1978), A34, S4, 381] was submitted without the knowledge of the present author, who was not aware of its content. Only preliminary discussions and work on certain aspects of a research programme had taken place at the time that the Abstract was submitted. The conclusions claimed in the last sentence had not been arrived at.
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    Acta crystallographica 36 (1980), S. 157-157 
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    Notes: In Bertaut & Dulac [Acta Cryst. (1972), 28, 580-588], for clerical reasons an error has crept in so that the numerical moment values of y and z components of Cr1 are to be interchanged. One should read in the Abstract and in relation (8.9): Sz(Cr1) = -0.73 (instead of -0.45); sy(Cr1) = 0.45 (instead of + 0.73).
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  • 192
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    Acta crystallographica 36 (1980), S. 171-177 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Based on the new energy-transfer equations [Kato (1976). Acta Cryst. A32, 458-466; Kato (1979). Acta Cryst. A35, 9-16] the integrated intensities (II) are calculated. Since the energy-transfer equations have physical meanings different from the traditional ones originally given by Darwin [Philos. Mag. (1922), 43, 800-824] and extended by Hamilton [Acta Cryst. (1957), 10, 629-634], the method of calculating (II) must be modified, particularly in the case of a wide incident beam. Since the modified method does not include the angular integration, it is much simpler than the traditional method. Thus, the analytically rigorous expressions of (II) can be obtained for parallel-sided crystals including absorption, and for any diffraction conditions.
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  • 193
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    Acta crystallographica 36 (1980), S. 164-170 
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    Notes: The analysis of the influence of the background and truncation errors on the Fourier transform of the diffraction profile is extended with respect to the work that has already been done by others and a critical evaluation of the established Fourier methods for the determination of the microstructural parameters - average dimensions of crystallites and paracrystalline microdomains, lattice-distortion parameters and cumulants of the strain distribution - is presented. It is shown that, contrary to the case of the cosine transform and of its logarithm whose functional behaviour is drastically changed by the truncation error, the first derivative of that transform is modified by this error only by an oscillatory factor which multiplies the first term of its series expansion. The suggestion follows of using this derivative function in the least-squares or curve-fitting determination of the microstructural parameters. It seemed proper to check these theoretical results by comparing them with experimental data, determining by a simple curve-fitting procedure based on this derivative function the microstructural parameters of a high-density polyethylene fibre in directions perpendicular to the fibre axis. The parameters so obtained are in good agreement with the structural data found in the literature for the same material. It is concluded that the use of this derivative function makes possible the reliable determination of important features of the microstructure of materials by a single-line Fourier technique even in the presence of a large truncation error.
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  • 194
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    Acta crystallographica 36 (1980), S. 190-193 
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    Notes: High-resolution electron microscopy can be used to differentiate between two structural models of long-period ordered alloys. These models differ in the nature of the disorder as seen in the stacking irregularities which can have planar boundaries as exemplified by Ag3Mg or wavy boundaries as in AuCu II. In the composition range 22-27 at.% Mg, Ag3Mg is built up with a regular arrangement of two kinds of structural layers, 1 or 2 L12 cells in thickness. Some stacking disorder exists, but this alloy can be locally described using a space-group notation and has the character of being an infinitely adaptative structure. High-resolution images have been used to show the perfect planarity of the boundaries in Ag3Mg, thus demonstrating the way in which disorder is accommodated in this alloy.
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    Acta crystallographica 36 (1980), S. 362-372 
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    Notes: The fundamental ideas of representation given in a preceding paper [Giacovazzo (1977). Acta Cryst. A33, 933-944] are generalized further. Some algebraic properties of structure seminvariants are stated and their importance for practical applications is discussed. The concept of a generalized first phasing shell is introduced: it allows in some cases a better estimation of the seminvariants.
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    Acta crystallographica 36 (1980), S. 378-381 
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    Notes: Termination of planar defects has been observed in the amphibole mineral nephrite [Ca2(Mg,Fe)5(Si4O11)2- (OH)2]. Isolated terminations, which disrupt the crystal structure, are rare, but the cooperative termination of two defects, in which the total number of silicate chains is conserved and structural disruption is minimized, is more common. Two different kinds of cooperative termination have been observed. Occasionally, defects are seen to terminate and shift their line of propagation through a crystal.
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  • 197
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    Acta crystallographica 36 (1980), S. 399-408 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The superspace-group approach [Janner & Janssen (1977), Phys. Rev. B, 15, 643-658] is used to solve the symmetry problem of incommensurate crystal phases in the case of displacive- and occupation-wave modulation. Generalization is given to cover magnetic modulation as well. The symmetry conditions imposed by the superspace group on the crystal structure are derived and applied to the following incommensurate crystals, whose structures have been discussed in the literature independently from the present point of view: K2SeO4, 2H-TaSe2, NaNO2 and Cr. The superspace groups describing the symmetry of these compounds are indicated and the structural implications of the corresponding symmetry elements discussed.
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  • 198
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    Acta crystallographica 36 (1980), S. 408-415 
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    Notes: In this second part [part I: Acta Cryst. (1980), A36, 399-408] the superspace-group approach is formulated for a class of crystals (called composite crystals) which involve a basic structure composed of subsystems, each one having three-dimensional space-group symmetry, but being mutually incommensurate. By taking into account the interaction among these subsystems, or other second-order effects, one is led to the actual structure, which very often is modulated, and in any case incommensurate. Neither the basic structure nor the actual one has a three-dimensional space-group symmetry but both allow a superspace-group characterization of their symmetry properties. The aim of the present paper is to show how these concepts apply in practice. Accordingly, two composite crystals, extensively studied in the literature, are considered from the present point of view: the organic compound (TTF)7I5 - x, i.e. C42H28S28.I5 - x, and the polymercury cation compound Hg3 - δAsF6. The regularities found in these two compounds are interpreted and fit naturally with the corresponding superspace-symmetry groups.
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    Acta crystallographica 36 (1980), S. 420-428 
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    Notes: The theoretical crystal morphology of the Al3Ni intermetallic compound has been deduced from energy calculations. 14 directions of atomic periodic bond chains have been defined, using the Hartman method, from which 11 facet orientations have been determined. For each of them a computer simulation has given the relative potential energy of the atoms at the different sites on the surface, the corresponding energy of fixing and hence the attachment order of the atoms. The theoretical morphology of Al3Ni is shown to be made from planes {110}, {101}, {111}, {020} and {002}. The first four plane directions have been observed on dendrites and massive crystals.
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  • 200
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    Acta crystallographica 36 (1980), S. 436-442 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Both real and imaginary components of the anomalous X-ray scattering were measured by single-crystal diffraction experiments with synchrotron radiation at wavelengths through the region of the three L absorption edges of cesium, the first such experiment for any element at the L edges. Near the L3 edge f' varies between -26.7 and -13.9 and f" between 4.0 and 16.1 electrons in a wavelength interval of 0.008 Å. Similar but smaller changes occur near the L2 edge, and still smaller ones at L1. Fine structure in the f" curve corresponds to that observed in an absorption curve and also, by a dispersion relation, to fine structure in the f' curve. These effects offer promise as a substitute for isomorphous replacement for solving the phase problem for macromolecular crystal structure. Similar experiments with cobalt near the K edge give f' values in agreement with measurements by other workers for nickel and copper by different methods at corresponding wavelengths; the lowest value observed is f' = -7.5 electrons.
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