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  • International Union of Crystallography (IUCr)  (1,258)
  • 1975-1979  (1,258)
  • 1976  (1,258)
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  • 1975-1979  (1,258)
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  • 1
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 32 (1976), S. 53-56 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In space groups of symmetry higher than P1 misplacement of a single atom implies the misplacement of all those in the same Wyckoff position, and hence the effect on the residual is larger than in P1. 'Exact' values of the residual R2 are obtained, with explicit allowance for dispersion.
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  • 2
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 32 (1976), S. 168-168 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: It is agreed that the miscut must be kept small in the method of Christiansen, Gerward & Alstrup [Acta Cryst. (1975). A31, 142-145], as pointed out by Mclntyre & Barnea [Acta Cryst. (1976). A32, 168]. The comment on dispersion was covered in the original paper.
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  • 3
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 32 (1976), S. 174-174 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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  • 4
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 32 (1976), S. 311-315 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The formal refinement methods of least-squares adjustment or difference-map analysis give atomic positions in protein structures with standard deviations which are large compared with the standard deviations of accepted molecular dimensions. This paper describes a method of adjusting the Cartesian coordinates to obtain a properly weighted fit to both the positions from the refinement and the molecular parameters. The equations which have to be solved have many unknowns but few coefficients, and an effective iterative method can be used. The results of applications of the method to insulin are summarized.
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  • 5
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 32 (1976), S. 11-16 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The thermal expansion of non-cubic crystal structures may be simulated by a geometric least-squares refinement of the known structure after predicting the thermal expansions of various coordination polyhedra. This method has been applied to forsterite, Mg2SiO4, anhydrite, CaSO4, and scheelite, CaWO4. The expansions of different M-O bonds (M = Mg or Ca) are predicted by using an empirical relationship between the expansion cofficient, α, and bond-strength, s. The expansions of the polyhedral edges are approximated from the changes in the average M-O bond lengths. The rigid tetrahedral groups (SiO4, SO4 or WO4) were assumed to retain their size and shape during the process of thermal expansion. The structural changes are simulated at 300°C for forsterite and at 200°C for anhydrite and scheelite. Calculated changes in the position parameters for forsterite are generally in the same direction as those observed experimentally. The lattice parameters compare well and calculated values of the expansion coefficients along the three crystallographic axes show the same trend as the observed values namely αa 〈 αc 〈 αb. Thermal expansion behavior of anhydrite has been determined experimentally in the temperature range 20-275°C and the structure has been simulated at 200°C. The observed and calculated values of the expansion coefficients agree well; both show that αa 〉 αc 〉〉 αb. The calculations on scheelite successfully reveal the characteristic anisotropic thermal expansion behavior of scheelite-type structures, which is αa 〈 αc.
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  • 6
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 32 (1976), S. 558-565 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The contrast of electron microscope lattice images of a vanadium monosulphide with superstructures was dynamically calculated on the basis of the multislice method. Interactions of 80 waves were analysed. It was shown that the vacancy-rich vanadium sites were imaged as white spots not only at the very thin part but also at the thicker part inside the first equal-thickness contour, which appeared at the thickness of 60 Å. A non-stoichiometric vanadium monosulphide, VS1.155, quenched imperfectly from the preparation temperature at 1217 °C, was examined on the basis of the lattice image observation by a 100 kV high-resolution electron microscope. Orderings in the inter- as well as intralayers could be recognized directly from the arrangement of the white spots. Interpretable lattice images appeared exclusively inside the first equal-thickness contour. A mixture of some different types of images was observed in a crystal fragment; in some band-like regions the 4C-type superstructure was found with almost the same structure as Fe7S8. Each band extended parallel to the (001) plane with thickness of at most 50 Å and the orientation was in a twin relation to that of the adjoining one. The other regions showed less well-defined lattice images, although they gave the broad diffraction peaks ranging from the 4C- to 3C-type reflexions. In order to determine the phase relations at high temperatures the specimen was heated by focusing an electron beam on the portion slightly apart from the area under examination. The technique enabled us to observe only the heating effect. Upon heating, the 4C type first increased in volume, seen by the thickening of some bands. On further heating the 3C type increased in intensity on the diffraction pattern. The structure of the 3C type was estimated to be almost the same as Fe7Se8 except that the vacancy concentration fuctuated among the partially occupied vanadium layers.
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  • 7
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 32 (1976), S. 587-591 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The magnetic structure of Mn(Nb0.5Ta0.5)2O6 with columbite structure was determined by means of neutron diffraction using single-crystal data. The intensities were gained by means of a small cold Eulerian cradle. The evaluation leads to a canted magnetic structure GxAz (G: S1 = - S2 = S3 = - S4; A: S1 = - S2 = - S3 = S4). The magnetic moments form an angle of 35.4° with the a axis. The magnetic space group is Pb'cn. The canting angle depends on the Nb content.
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  • 8
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 32 (1976), S. 88-91 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Continuous streaks and the displacement of diffraction maxima from the perfect-crystal positions, observed in electron diffraction patterns of magnesium fluorogermanate suggest the existence of planar faults at which the c-axis dimension of the unit cell is contracted by 25%. High-resolution electron microscope images of thin crystals confirm this deduction. It is shown that even in the presence of strong dynamical-diffraction effects, electron diffraction patterns from thin crystals can be interpreted, within well defined limitations, by use of a kinematical theory such as is given in part I [Cowley (1976). Acta Cryst. A32, 83-87]. Using this kinematical theory calculations of diffraction intensity are made for reasonable assumptions of the form of the faults. The effect of the modification of the structure at the fault planes on the peak intensities is shown to be small so that structure analyses based on peak intensities only should give the structure of the unfaulted crystal.
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  • 9
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 32 (1976), S. 166-167 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: It is shown by neutron diffraction that a relatively weak magnetic field (1.75 kG), is able to induce an order in a large terephthal-bis-(4n-butylaniline) (TBBA) sample in the smectic A phase. A monodomain is obtained with the planes perpendicular to the magnetic field. Rocking curves are performed whose full widths at half maximum give a value of a few degrees for the misorientations of the planes.
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  • 10
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 32 (1976), S. 170-170 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The results for ζ and α/β of Koumelis & Rozis [Acta Cryst. (1975). A31, 84-88] should read: ζ = 0.77 ± 0.04, α/β = 1.20 ± 0.04.
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  • 11
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 32 (1976), S. 169-170 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Results of Sayre and Woolfson can be used to derive a structure-factor equation of type: F(h) = ΣA(h, m)F(m)F(h-m), where the coefficients A(h, m) can be calculated from the form factors of the atoms present in the structure. The equation will be discussed and an empirical test will be given.
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  • 12
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 32 (1976), S. 170-170 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Corrections are given to Press [Acta Cryst. (1973). A29, 257-263]. Two misprints in Table 2 should be corrected to cT61 = \sqrt{26}, {{4}\over{9}} and cT71 = - \sqrt{455/9}. In the 3rd line of equation (2.1) js(QQ) should be changed to j6(QQ).
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  • 13
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 32 (1976), S. 172-173 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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  • 14
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 32 (1976), S. 171-171 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The previously published result for the anisotropic fourth-order anharmonic thermal vibrations in KCI, determined from neutron diffraction measurements, contained an error in sign. The parameter δC1, which characterizes the appropriate term in the effective one-particle potential, should be negative, indicating the predominance of Coulombic attractive forces between the ions in determining this contribution.
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  • 15
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 32 (1976), S. 175-175 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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  • 16
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 32 (1976), S. 185-192 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The electron density in LiOH has been determined by X-ray diffraction. The intensities were measured on single-crystal plates and corrected for extinction, double reflexion and thermal diffuse scattering. The values found by integration over the electron density were 2.0 e in lithium (Li+), 8.7 e in oxygen (0-°.7) and 0.3 e in the hydrogen (H+°'7). One electron is distributed over a wide range between the LiOH layers in the lattice.
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  • 17
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 32 (1976), S. 749-749 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
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  • 18
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 32 (1976), S. 749-750 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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  • 19
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 32 (1976), S. 768-771 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The probability distributions of the normalized Bijvoet differences x and Δ are derived for non-centrosymmetric crystals with type-I and type-II degree of centrosymmetry assuming that there is a single anomalous scatterer in the unit cell besides a sufficiently large number of similar normal scatterers. The theoretical results are used to study the influence of degree of centrosymmetry on the measurability of Bijvoet differences. It is found that, for given values of k and σ22, the measurability is in general poorer in the type-I case than in the type-II case.
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  • 20
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 32 (1976), S. 774-777 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The necessary alebra is derived for the least-squares refinement of heavy-atom parameters in a series of isomorphous derivatives where the heavy atoms are related by non-crystallographic symmetry. In addition the simultaneous refinement of the particle (or molecular) orientation and position is considered, permitting the precise adjustment of the system of non-crystallographic rotation axes.
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  • 21
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    Acta crystallographica 32 (1976), S. 771-773 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Precise measurement of the thermal expansion of natural olivines at elevated temperatures by X-ray diffraction yields the following equations for the cell volume (V) with temperature (t): Fo92.5: Vt = 291.13 + 83.6 × 10-4t + 6.5 × 10-7t2, 25 〈 t 〈 973°C; Fo90.4: Vt = 291.45 + 80.4 × 10-4t + 11.3 × 10-7t2, 25 〈 t 〈 963°C;Fo53.8: Vt = 298.58 + 76.4 × 10-4t + 17.2 × 10-7t2, 25 〈 t 〈 432°C, where the units are Å3 and °C. Similar expressions are reported for the individual lattice parameters. Expressions for thermal expansions are derived. Volume thermal expansion varies linearly with temperature. A decrease in the Mg/Fe ratio in olivine decreases the thermal expansion in the observed temperature range.
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  • 22
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    Acta crystallographica 32 (1976), S. 104-109 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The intensity variations of X-rays diffracted from a nearly perfect GaAs plate have been measured in symmetrical Laue and Bragg cases in the energy region near the As K absorption edge with small energy intervals, by the use of an energy-dispersive diffractometer and continuous X-rays from a sealed-off tube. The corresponding intensity variations have been calculated with the dynamical theory. These measurements and calculations have shown a good agreement. Moreover, the curve measured for the Bragg case on the same crystal, but after polishing, has shown good agreement with the corresponding curve calculated by the kinematical theory. However, there is a minor discrepancy in the energy region very near the absorption edge. This is probably due to the fact that the values of anomalous-scattering factors used for calculation are not precise enough to explain fine structures at the edge.
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  • 23
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    Acta crystallographica 32 (1976), S. 110-115 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Integrated intensities for the Bragg reflexion of 1.070 Å neutrons by a single crystal of NH4Cl have been measured at 295 K. The experimental data were corrected for extinction. An analysis based on direct calculation of properties of nuclear smearing functions is applied to the data. The results show that the motions of chlorine and the ammonium ion as a whole can be described within experimental accuracy by the harmonic model with the values B_ = 1.90 ± 0.08 Å2 and B+ = 2.00 ± 0.08 Å2 of Debye-Waller factors for chlorine and the ammonium ion respectively. Values of parameters describing libration of the ammonium ion and the value r0 = 1.050 ± 0.005 Å for the N-H bond length were determined from the radial scattering amplitudes of the ammonium ion. The radial nuclear density shows evidence for radial vibrations of the hydrogen atoms with mean-square amplitude Δ2 = 0.006 ± 0.001 Å2.
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  • 24
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    Acta crystallographica 32 (1976), S. 297-298 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: An algorithm is proposed which enables one, starting from an arbitrary primitive cell of a three-dimensional Bravais lattice, to reach the Niggli form requisite for the lattice type determination.
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  • 25
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    Acta crystallographica 32 (1976), S. 308-310 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The dispersion equation for the four-wave case of X-ray diffraction is obtained in a compact form. The intermediate region between two-wave and arbitrary many-wave cases of diffraction is examined.
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  • 26
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    Acta crystallographica 32 (1976), S. 302-305 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Values for the mathematical expectation of the normalized Bijvoet difference x are derived for noncentrosymmetric crystals belonging to triclinic, monoclinic and orthorhombic space groups containing a small number (i.e. p = 1 or 2) of anomalous scatterers in the asymmetric unit besides a large number of similar normal scatterers. These results are used to study the influence of space-group symmetry on the measurability of Bijvoet differences.
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  • 27
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    Acta crystallographica 32 (1976), S. 816-821 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Direct methods are applied to the difference structure factors for a structure containing one or more heavy atoms in known positions. The present procedure is initiated by subtracting the known heavy-atom contribution from the observed structure factor (assuming that the observed and calculated structure factors have the same phase) to obtain the magnitude and phase of the light-atom contribution. The Σ2 phase relationship (tangent formula) is used to recalculate the phases of the light-atom contributions, and - consequently - to recalculate the magnitude of the light-atom contribution. An iterative procedure is used to optimize the phases and amplitudes before a difference Fourier map is calculated. The method is applicable also for the solution of partially known structures.
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  • 28
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    Acta crystallographica 32 (1976), S. 783-785 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The possibility that two arbitrary lattices, 1 and 2, have a coincidence-site lattice (CSL) in common is examined. Let T be the 3 × 3 matrix that maps a basis of lattice 1 onto a basis of lattice 2 and let ||T|| be the absolute value of its determinant. It may be assumed that ||T|| ≥ 1. There is a CSL if, and only if, T is rational. The main result is that the density ratio, Σ2, of coincidence points to points of lattice 2 is equal to the least positive integer n such that nT and n||T||T-1 are integral matrices. A basis for the CSL can be determined quickly if lattices 1 and 2 are related by a rotation.
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  • 29
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    Acta crystallographica 32 (1976), S. 347-348 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: X-ray scattering factors for bonded hydrogen atoms are derived for the case where the aspherical electron density distribution due to the chemical bonding, is approximated by additional scattering centres. It is assumed that in the vicinity of the proton the electron density does not change much when the bond is formed.
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  • 30
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    Acta crystallographica 32 (1976), S. 351-351 
    ISSN: 1600-5724
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  • 31
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    Acta crystallographica 32 (1976), S. 351-351 
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  • 32
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    Acta crystallographica 32 (1976), S. 353-355 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Theoretical deformation densities for Ni(CH3)2, MnO4- and CoO610- have been calculated by ab initio Hartree-Fock and configuration interaction methods. Peaks similar to those found in diffraction experiments at short distances from the transition metal atoms are observed. They can be interpreted in terms of the specific electronic occupations of the d orbitals.
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  • 33
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    Acta crystallographica 32 (1976), S. 359-362 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: On the basis that quartet invariants are the difference between triplet invariants, we have determined a theoretical distribution of the quartet invariant phases. New formulae to estimate triplet invariant cosines are described and the results they give for a known test structure are compared.
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  • 34
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    Acta crystallographica 32 (1976), S. 373-375 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A new polytype 18R[1212]3 with space group R{\bar 3}m1 has been discovered. When the layer sequence of each rhombohedral polytype, nR, reported so far is divided into three equal parts, they are found to have the same layer sequence as that of a frequently occurring polytype, 4H, 6H, 8H, 10H or 14H. A layer-slip process is considered, in which a rhombohedral polytype can be generated from a hexagonal polytype.
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  • 35
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    Acta crystallographica 32 (1976), S. 409-411 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The possibility is discussed of applying the theoretical intensity distribution formulae to the structural analysis of solid solution crystals of ZnS-CdS and ZnS-ZnSe with stacking faults. It is pointed out that the irregular shape of the photometric curves, the appearance of intensity maxima connected with areas of disordered type structure, and splitting of the diffuse reflexions, renders impossible the application of theoretical intensity formulae. Theoretical intensity curves, obtained for the model of a structure with stacking faults, are proposed for structural analysis.
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  • 36
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 32 (1976), S. 387-395 
    ISSN: 1600-5724
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Integrated intensities were measured from VOx single crystals with x = 0.80, 0.94, 1.01, 1.11 and 1.25. A least-squares refinement was carried out for the scale factor and the isotropic temperature factors of vanadium and oxygen ions for each composition, for a range of interstitial vanadium contents. The R values after the refinement were 0.04-0.05. There are vanadium ions at tetrahedral interstitial sites, the concentration of which changes from 0-0.5% to 3% with composition x; this confirms quantitatively previous studies which employed dynamical electron diffraction effects. The temperature factors of vanadium (BV) and oxygen (BO) increase with x; BV = 1.02-1.38 Å2 and BO = 0.58-1.24 Å2. The composition dependence of the overall temperature factor is similar to that of the lattice parameter. The 002 structure factor for electrons U002 and the critical voltage Ec at which the second-order Kikuchi line disappears were calculated for VO0.82 and VO1.20, using the individual temperature factors determined by this study. The 002 structure factors measured by the critical-voltage and the intersecting-Kikuchi-line method [Watanabe, Andersson, Gjønnes & Terasaki (1974). Acta Cryst. A30, 772-776] were in agreement within less than 2%. The results support the idea that the ionic state of the cation lies between neutral and singly ionized.
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    Acta crystallographica 32 (1976), S. 1010-1011 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: For the refinement of a systematic two-, three-, ... beam system, the higher-order reflexions to be considered should be carefully chosen. In particular for calculations on the second-order critical voltage effect (C.V.E.), the system 0, g, 2g, should be extended to a (2N + 1)-beam system containing the reflexions -(N-1)g to (N + 1)g. Another choice (e.g. the system - Ng to Ng) may lead here to serious errors unless N is very large.
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  • 38
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    Acta crystallographica 32 (1976), S. 1011-1013 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Variances of X-ray reflexions calculated with the procedure as proposed by McCandlish, Stout & Andrews [Acta Cryst. (1975), A31, 245-249] have been tested against variances determined in an independent way. A satisfying agreement is obtained.
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  • 39
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    Acta crystallographica 32 (1976), S. 895-897 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: To refine the orientation and location of a rigid group of atoms in a crystal it is not necessary to store the atom coordinates relative to a localized axial system. All atoms in the asymmetric unit are defined relative to a single orthonormal axial system. A local axial system is created by taking an atom in the rigid group as origin and defining the local axes as parallel to these orthonormal axes. The evaluation of the required derivatives is then very easy. The replacement of approximate atom positions by idealized atom positions is described.
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    Acta crystallographica 32 (1976), S. 901-903 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A summary is given of some work which has been performed to identify those special points, lines, and planes of symmetry that have been omitted from published tables of irreducible representations of space groups. In order to have a complete set of all the irreducible representations of every space group, it is necessary to determine the irreducible representations for these additional wave vectors in order to supplement the existing published sets of tables. The generation of these supplementary tables is reported.
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    Acta crystallographica 32 (1976), S. 904-909 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Anharmonic contributions to the Debye-Waller factor of Zn for vibrations parallel to the c axis were obtained from the temperature dependence of integrated intensities for Bragg scattering at high temperatures. The Mössbauer technique was used to measure the purely elastic scattering. Both Gaussian and non-Gaussian contributions were found to be important. Their magnitude and sign were derived from the experimental data.
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    Acta crystallographica 32 (1976), S. 1036-1037 
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    Acta crystallographica 32 (1976), S. 1037-1038 
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    Acta crystallographica 32 (1976), S. 1038-1038 
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    Acta crystallographica 32 (1976), S. 1038-1038 
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    Acta crystallographica 32 (1976), S. 473-476 
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    Notes: Both of the conventional 'double-difference' or 'residual' syntheses used in protein crystallography to detect errors in refined heavy-atom parameters are approximations to the desired vector difference synthesis between the observed and calculated heavy-atom structure factors. By using the measured anomalous differences between Friedel-related pairs of reflexions from the parent-plus-heavy-atom crystal, it is possible to calculate the coefficients for the vector difference synthesis. Tests indicate that this synthesis can provide a better signal-to-noise ratio than the conventional syntheses. In the Appendix it is shown that {\bar F}PH parent-plus-heavy-atom structure amplitude in the absence of anomalous scattering, is properly calculated as the mean of the structure amplitudes of the Friedel-related reflexions, not the root mean square.
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    Acta crystallographica 32 (1976), S. 467-472 
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    Notes: A new method is reported for evaluating the temperature dependence of Debye-Waller factors, or equivalently the mean-square atomic displacements (MSD), from X-ray spectroscopic data. By irradiating a properly oriented single crystal with polychromatic radiation, several orders of a given Bragg reflection can be simultaneously excited at a fixed scattering angle. These multi-order peaks can then be recorded in a single measurement with an energy dispersive detector. For experiments requiring only relative intensity data, this method offers a number of improvements over conventional techniques, e.g., (i) a substantial reduction in data acquisition time, (ii) a possible reduction in angular flexibility requirements and (iii) access to regions of reciprocal space which might otherwise be inaccessible. This procedure has been employed to determine the temperature dependence of the mean-square displacements of NbC0.98 over the temperature range from 296 to 600 K. These results are compared with published values computed from a double-shell lattice-dynamical force model; the agreement is found to be satisfactory. The data have also been used to evaluate the thermal expansivity of NbC0.98 over the temperature range of measurement; excellent agreement is found upon comparison with published thermal expansion data.
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  • 48
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    Acta crystallographica 32 (1976), S. 575-586 
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    Notes: The theoretical equations required for the experimental determination of the complete set of piezoelectric constants from X-ray measurements are presented. For this purpose the expression for the quantity (∂θ/∂E), where θ denotes the Bragg angle and E the magnitude of an applied electric field is calculated as a function of the field direction and the reflecting lattice plane normal. For all 20 crystal classes exhibiting the piezoelectric effect explicit expressions are given for the longitudinal and transverse piezoelectric effect, corresponding to parallel-field and perpendicular-field reflection, respectively. For the 19 piezoelectric classes of the monoclinic, orthorhombic, tetragonal, trigonal, hexagonal and cubic systems explicit expressions for (∂θ/∂E) in terms of the Miller indices of the reflecting planes are given for the simplest crystal cuts with respect to the symmetry elements present. The use of the equations is illustrated by a numerical example dealing with a crystal of symmetry mm2.
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    Acta crystallographica 32 (1976), S. 565-574 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The one-electron density function for a group of atoms within the asymmetric region of a unit cell is represented by a finite multipole expansion of the charge density about each atomic center. Each atomic expansion is called a pseudoatom. If the pseudoatom charge density is effectively rigid with nuclear motion, then the model may be used for a static charge density analysis of X-ray diffraction data. A valence density multipole model for pseudoatoms is restricted to single exponential radial functions. The representation is rotationally invariant. The model may be used for determination of static charge physical properties as well as aspects of chemical bonding. These results can be a critical test of the X-ray diffraction experiment for the determination of electron density distributions. The pseudoatoms discussed are primarily intended for crystals comprised of first and second-row atoms. The valence scattering model demands extensive data sets (probably at low temperatures) or an independent determination of atomic positions and mean square amplitudes of vibration.
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    Acta crystallographica 32 (1976), S. 675-675 
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    Notes: The following errors should be corrected in Harker's article [Acta Cryst. (1976). A32, 133-139]. In the author's address the number 14253 should be changed to 14263. In the Table, in section IV, under the heading F, the first entry should be C1 not C2; in section IX, under the heading d, the eighth entry should be 11! not 60, the fourteenth entry should be 120 not 20, and the fifteenth entry should be 60 not 160.
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    Acta crystallographica 32 (1976), S. 691-745 
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    Acta crystallographica 32 (1976), S. 745-747 
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    Acta crystallographica 32 (1976), S. 747-747 
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    Acta crystallographica 32 (1976), S. 748-749 
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    Acta crystallographica 32 (1976), S. 749-749 
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    Acta crystallographica 32 (1976), S. 67-74 
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    Notes: The neutron small-angle scattering of hen egg-white lysozyme chloride in solution has been determined. The scattering density of the solvent and accordingly its contrast with the dissolved particles has been varied by changing the H2O/D2O ratio of the solvent. The zero-angle scattering was derived and it was shown that the square root of the zero-angle intensity is proportional to the contrast. The experimental value of the radius of gyration is R = 13.8 Å, in good agreement with the same quantity calculated on the basis of the crystal structure model of tetragonal lysozyme. The three basic scattering functions were derived from the experimental data and compared with the corresponding scattering pattern calculated from the coordinates of the X-ray structure. The results do not suggest a deviation of the conformation and structure of lysozyme in solution from the crystal structure. The spherical average of the overall dimensions has been separated from the internal structure. The influence of higher multipoles of the shape of the lysozyme molecule on the scattering curve is discussed.
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    Acta crystallographica 32 (1976), S. 182-185 
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    Notes: An anisotropic harmonic oscillator has mean-square amplitudes of vibration U1, U2 and U3. The geometric mean, Ugm, is (U1 U2 U3)1/3 and the arithmetic mean Uam, is (U1 + U2 + U3)/3. It is shown that estimates of Uiso which minimize the least-square error of structure factors is bounded by the inequalities Ugm ≤ UN ≤ Ux ≤ Uam where UN is the equivalent isotropic U for the neutron diffraction experiment and Ux is the corresponding estimate of Uiso for the X-ray diffraction experiment. The results have been applied to H atoms in sucrose where the U1, U2 and U3 are taken from the neutron diffraction analysis of Brown & Levy [Acta Cryst. (1973). B29, 790-797]. It is found that Ux ∼ 0.75Uam + 0.25Ugm. When Ux is compared to Uiso (X-ray) from Hanson, Sieker & Jensen [Acta Cryst. (1973). B29, 797-808], Ux's for the fourteen H atoms bonded to C atoms exceed Uiso (X-ray) by ̃0.022 Å2 (or equivalently ̃1.7 Å2 in B units, where B = 8π2U). A systematic trend for the eight hydroxyl hydrogens is not found; the average difference Ux - Uiso (X-ray) is - 0.006 Å2. The discrepancy for H bonded to C is consistent with quantum-chemical calculations of small molecules; the apparent agreement of Ux and Uiso (X-ray) for H bonded to O may reflect the influence of hydrogen bonding in crystalline sucrose.
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    Acta crystallographica 32 (1976), S. 207-215 
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    Notes: Single-crystal hk0 electron diffraction patterns from thin ( ≤ 240 Å) rhomboid n-hexatriacontane (n-C36H74) crystals contain intensity data which are well fit by the commonly observed O⊥ methylene subcell phasing model but not by a true unit cell model which contains two mutually displaced monolayers. The apparent diffraction from a monolayer in these lamellar crystals is thought to be due to bend distortions of the crystal plate. Intensity data conform to a kinematical interpretation as a first approximation, thus allowing a priori structural elucidation, but eventually will require an n-beam dynamical correction.
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    Acta crystallographica 32 (1976), S. 233-238 
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    Notes: Based on a topological definition the possible space groups for a perovskite-like structure are derived for small unit cells. The irreducible representations are calculated from them for interpretation of the phonon spectra. To compare the character of the bonds in some oxides, Raman spectra have been taken and interpreted on the basis of a simple lattice-dynamical model. It was found that covalent interaction occurs in NaxWO3 and XIO3 (X = NH4, K, Rb, Cs) whereas titanates and niobates are mainly ionic. A model for classification of perovskite-like compounds is discussed.
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    Acta crystallographica 32 (1976), S. 250-255 
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    Notes: A semiquantitative analysis of the X-ray diffuse scattering from β-alumina between 20 K and room temperature shows the change with temperature of the organization of the conducting ions. The earlier reported low-temperature superstructure never achieves long-range order. Both the size of the 2D domains and the order within the domains, as reflected by the occupation factors, saturate around 77 K. Above this temperature, the size decreases from its saturation value of 45 Å to about 10 Å at 400 K, with a parallel decrease of the order inside the domains. The occupation factors could be determined up to 220 K, and they extrapolate at room temperature to values close to the average occupation determined by conventional structure analysis.
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    Acta crystallographica 32 (1976), S. 274-280 
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    Notes: A comparison between least-squares phase refinement as formulated in direct and reciprocal spaces is given. After analysing some common features of different iterative phase determination procedures, these procedures are seen with respect to the least-squares phase refinement techniques. Some results with a myoglobin model structure using an iterative technique are presented.
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    Acta crystallographica 32 (1976), S. 299-301 
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    Notes: Hamilton's equations for secondary extinction are considered in the light of Riemann's integration of the hyperbolic differential equation. It is shown that Green's function for diffraction from a crystal in the Bragg geometry is determined by an integral equation. The equation is valid for an arbitrarily shaped crystal boundary curve as long as the boundary does not become tangent to the incident or diffracted beam directions.
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    Acta crystallographica 32 (1976), S. 356-359 
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    Notes: Theorems on directed graphs are used to obtain results on the enumeration of orthogonal space groups in arbitrary dimensions. In dimension 3 the graphs themselves provide a convenient notation for the orthorhombic space groups.
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    Acta crystallographica 32 (1976), S. 375-379 
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    Notes: The forward nuclear scattering amplitudes of Ge, Cu and O for thermal neutrons have been determined from the refractive bending by pure single-crystal right prisms of germanium, copper, and quartz. The results are bGe = 8.1929 (17) fm and bCu = 7.689 (6) fm which are in good agreement with previous less accurate determinations by other methods and bO = 5.830 (2) fm which disagrees with an independent accurate determination by four standard deviations.
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    Acta crystallographica 32 (1976), S. 380-387 
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    Notes: Once the symmetry operations and the general positions of the C and I groups of class mmm are given in the form of ordered standard blocks, their principal subgroups can be presented in such a way that their general point positions are easily recognized. New full standard symbols are proposed.
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    Acta crystallographica 32 (1976), S. 415-426 
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    Notes: A new example of long-period stacking order is described in the Au-Mn system for the composition Au11Mn4 (26.7 at. % Mn). The structure was determined by X-ray and electron diffraction and confirmed by neutron diffraction. The stacking order is the so-called 3R type in Sato's nomenclature [Sato, Toth & Honjo, J. Phys. Chem. Solids, (1967). 28, 137-160]. The structure includes 27 layers, building up a giant monoclinic cell containing 810 atoms. This phase undergoes a magnetic transition at about 140 K. As opposed to examples given by Sato et al. (1967), the Au11Mn4 structure is not based on a long- period superlattice with antiphase boundaries.
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    Acta crystallographica 32 (1976), S. 426-433 
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    Notes: The method of evaluation for the contribution of TDS to Bragg reflexions is given on the basis of the general formalism developed in the previous paper [Harada & Sakata, Acta Cryst. (1974), A30, 77-82]. TDS tensor Δβ is expressed by a matrix product as {\tilde{\sigma}}Tσ, where T is the tensor that characterizes the anisotropy of TDS in reciprocal space and σ is the transformation matrix of scattering vector from Cartesian axes to crystallographic reciprocal axes. All the components of T and σ are listed in a table for the nine groups of elastic constants for practical use. It is, however, found that there are only seven matrix forms of Δβ corresponding to the seven crystallographic systems. Two different approximations proposed previously for Nillson's formalism in the estimation of the scan area of Bragg reflexion are shown to be available also for the general formula. The numerical calculations of the TDS correction for an NaC1 single crystal are made with these approximations and they are compared with the experimental measurements by Renninger and with the results of calculations given with other approximations. No substantial difference is seen among the results of calculations and they are in good agreement with experiments.
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    Acta crystallographica 32 (1976), S. 477-482 
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    Notes: A method has been devised whereby two three-dimensional projections of a four-dimensional figure can be viewed stereoscopically to permit direct perception of the fourth dimension. The necessary concepts are introduced by a consideration of stereoscopy in two and three dimensions. It is shown that an extra degree of freedom is introduced in the stereoscopic viewing of three-dimensional stereo pairs which permits a direct experimental demonstration of the relationship between right-handed and left-handed three-dimensional figures in terms of a rotation in four-dimensional space.
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    Acta crystallographica 32 (1976), S. 493-499 
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    Notes: Phase determination of electron scattering from thin crystals via the unitarity equation including inelasticity due to plasmons is considered. It is concluded that the uniqueness properties of the solution are unlikely to be affected by plasmon production.
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    Acta crystallographica 32 (1976), S. 499-504 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Assuming that the shuffles of a solid-state single-crystal phase transformation are least-motion processes consistent with the symmetry of the phases and with the accepted interatomic distances, it follows that the structure of the higher-symmetry phase will be predictable solely from its space-group symmetry and unit-cell dimensions if the complete crystal structure of the low-symmetry phase has already been determined [Swaminathan & Srinivasan, Acta Cryst. (1975). A31, 628-634]. The possibility has been here verified successfully in the sequence V → IV → II of the phase transformations in ammonium nitrate.
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    Acta crystallographica 32 (1976), S. 504-506 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The 'power method' provides a computationally easy method for the determination of the best plane through a set of points. By repeatedly taking squares, one rapidly obtains the maximum eigenvalue and corresponding eigenvector of the inertia tensor. The result is the least-squares result when the points have independent, isotropic weights.
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    Acta crystallographica 32 (1976), S. 592-597 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The magnetic structures of the columbite NiNb2O6 and of Fe2WO6 of tri-α-PbO2 structure were solved by means of neutron diffraction. NiNb2O6 consists of a collinear magnetic structure with a doubled b axis and the direction of the magnetic moments parallel to the a axis. The magnetic space group is Pb21/c. Fe2WO6 consists of a complicated canted structure with moments forming an angle of 23.5° with the c axis. The z component orders according to + + + + - - - -, the x component orders according to + + - - - - + +. The magnetic space group is Pn'c2'.
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    Acta crystallographica 32 (1976), S. 115-119 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In the Sayre-Hughes equation the variable reciprocal-lattice vector ranges over the whole reciprocal net. It is shown that under the condition that a projection along a zone axis has no overlapping atoms the variable reciprocal-lattice vector can be restricted to range over a plane of the reciprocal net. A fortiori if a projection on an axis is free from overlap the variable vector can be restricted to range over a row of the reciprocal net. Criteria to determine the projections for which these conditions are best fulfilled are given. These criteria involve the absolute values of the structure factors only. The theory is illustrated by a test employing normalized structure factors calculated from atomic coordinates.
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    Acta crystallographica 32 (1976), S. 133-139 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: All the colored crystallographic and icosahedral point groups that obey the van der Waerden and Burckhardt definition are tabulated here, using a symbolism based on a suggestion of Shubnikov and Koptsik. Each asymmetric domain of the object has a single color - or scalar quality. The symbol of each colored point group G(H' | H) contains G, the geometrical point group of the object; its sub-group H' that is the point group of each of the object's monochromatic domains; and H, the invariant subgroup of G that is the intersection of all the conjugate subgroups H'. If H' and H are the same, the symbol G(H' | H) is changed to G(H). If H is chiral, so is the colored point group. If G is not chiral, but H is, the chirality is only chromatic. These phenomena are listed in the table. If more color permutations are possible than occur in the operations of a colored point group, different arrangements of the same colors on the same geometrical object are fundamentally different: these are called diamorphs of each other; their number is listed. 'Color', as used here, symbolizes any scalar property that can vary from one asymmetric domain to another.
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    Acta crystallographica 32 (1976), S. 163-165 
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    Notes: Twins by merohedry can be usefully divided in two classes. Class I: the twin operation is contained in the Laue symmetry of the crystal and twin-related reflexions have equal intensities; in this case the set of intensities collected from a twin is indistinguishable from that collected on a single crystal. Class II: at least one of the independent twin operations is contained in the lattice symmetry but not in the Laue symmetry of the crystal (twin-related reflexions differ in intensity); a knowledge of fractional volumes of crystals is necessary to solve the structure. The solution and refinement of a structure from measurements performed on a twin of class I are discussed.
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    Acta crystallographica 32 (1976), S. 174-174 
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    Acta crystallographica 32 (1976), S. 174-175 
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    Acta crystallographica 32 (1976), S. 24-31 
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    Notes: The asymmetry of hydrogen bonds arises from the repulsion between the O atoms forming the bonds. A bond-valence analysis of the repulsion leads to the conclusion that strong and weak hydrogen bonds are different in kind, the stronger ones (O-O less than 2.7 Å) involve strain and are linear while the weaker ones (O-O greater than 2.7 Å) have an extra degree of freedom and are generally bent. The strength of the hydrogen bond is determined by a number of factors such as the requirement that the bond valences around each atom add up to the atomic valence, a tendency for the O-O distance to be close to 2.7 Å, and by crystal-packing considerations which often lead to the formation of bent, and hence weaker, hydrogen bonds. The bond-valence analysis correctly predicts the observed correlations between H...O distance and O-H-O angle. The frequency with which various hydrogen-bond configurations are observed in crystals is used to propose a method for determining hydrogen-bond energies. This analysis of hydrogen bonding leads to an understanding of the lengthening of hydrogen bonds in high-pressure ices and to proposals for hydrated ion structures which can be used, for example, to predict the acid strengths of anions and to show that in neutral aqueous solutions the oxygen atoms of complex anions each hydrogen-bond to two or three water molecules.
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    Acta crystallographica 32 (1976), S. 32-37 
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    Notes: The crystal structure of monoclinic FeCl2.2H2O (F) has been refined using single-crystal data. The metamagnetic behaviour of F and CoCl2. 2H2O (C) has been determined on the basis of single-crystal measurements. At T = 4.2 K the reflexions of the antiferromagnetic zero-field phases disappear when a magnetic field of Hc1(F) = 39 kOe [Hc1(C) = 31.8 kOe] is applied along the direction of sublattice magnetization. In both salts the intermediate-field phase is collinear with a unit cell in which the a axis is tripled. This configuration vanishes at Hc2(F) = 46 kOe [Hc2(C) = 46 kOe] when the magnetically saturated configuration is reached. The three phases meet at a triple point at TT(F) = 11.7 K and HT(F) = 42.0 kOe [TT(C) = 8.9 K and HT(C) = 37.5 kOe]. Two types of phase transitions and tricritical points have been detected between the different configurations.
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    Acta crystallographica 32 (1976), S. 50-53 
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    Notes: The crystallographer's main problem (i. e. the phasing of Fourier transform moduli) leads to the study of n-sphere periodic close packing. The geometric properties of this arrangement allow one to determine by recurrence reasoning the matrix of the general expressions for the coordinates of the points that define the cell. It is therefore easy to deduce the cell volume and the packing ratio of the unique hypersphere which is by hypothesis present in the cell. A numerical study of these expressions makes it possible to point out that 'paradoxically' this n-sphere fills only a negligible volume of the primitive cell and that this volume becomes less as the dimension n of the space increases.
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    Acta crystallographica 32 (1976), S. 65-66 
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    Notes: To extend the usefulness of the tabulation of the numbers N of positional isomers [Knop, Barker & White (1975). Acta Cryst. A31, 461-472], all the distinct cycle-index polynomials Z on which the tabulation is based have been listed in a convenient form. This condensed summary facilitates identification of Z-isomorphisms; in turn, N for univalent substitution on many polyhedra not listed previously can be evaluated simply by reference to the existing tabulation.
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    Acta crystallographica 32 (1976), S. 83-87 
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    Notes: Kinematical diffraction from a crystal having planar faults is described by a systematic writing of the Patterson function and its Fourier transform for the general case of an arbitrary number of different kinds of layer, describing the faults in terms of a fault vector plus an addition, or subtraction, of scattering matter. The general series expression is readily simplified to deal with a wide variety of special cases. Particular examples include Wadsley-type shear faults associated with non-stoichiometry of oxides and the deformation and growth faults of simple close-packed structures.
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    Acta crystallographica 32 (1976), S. 778-780 
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    Notes: A function is proposed for evaluating the liklihood of packing arrangements of macromolecules in crystals. It is based on the simple principle that the constituent molecules of a crystal should not interpenetrate. This packing function has been successfully applied in the structure solution of a hemerythrin by using the molecular shape previously determined for myohemerythrin.
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    Acta crystallographica 32 (1976), S. 255-258 
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    Notes: The method of differential difference syntheses combined with idealization for refining protein models has been tested on a dipeptide derivative. An r.m.s. error of 0.5 Å was introduced in the dipeptide model, and the data were modified by applying artificial temperature factors to simulate the case of a protein. In any one of several variations, differential difference syntheses with idealization led to convergence at R values substantially lower than for proteins, but refinement is slow, requiring many cycles.
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    Acta crystallographica 32 (1976), S. 265-271 
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    Notes: The fluoroperovskites RbCdF3 and TlCdF3 undergo, at low temperature, a phase transition associated with small rotations of CdF6 octahedra. It is shown how both experimental and theoretical study of the modes of vibration appearing at the Brillouin zone centre allows one to attribute the space group D184h to (I4/mcm) to the quadratic phase.
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    Acta crystallographica 32 (1976), S. 793-798 
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    Notes: An examination of graphite has been carried out by convergent-beam electron diffraction for the purpose of examining the symmetry of the structure, and of measuring the structure factors for the 100 and the 110 reflexions. Symmetry changes within the sample were related to the fault structure, which was imaged in the defocused convergent beam. The value determined for V100 deviates by approximately 9% from the value determined using Dirac-Slater scattering curves for a spherical atom. A difference Fourier map calculated from the experimental values and computed spherical atom values shows the trigonal regions of bonding potential, but lacks resolution, indicating a need to refine other reflexions in the zone.
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    Acta crystallographica 32 (1976), S. 813-815 
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    Notes: The possible effect of surface damage on the intensity of diffracted neutrons has been investigated by a series of measurements for a plate-shaped crystal of SrF2 with the large faces alternatively polished and roughened to various degrees. No significant effects were observed until the crystal thickness was reduced to about 1.7 mm and it is concluded that inhomogeneity of the extinction properties within the volume of the crystal is likely to be a far more important effect for normal neutron diffraction experiments.
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    Acta crystallographica 32 (1976), S. 315-319 
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    Notes: The temperature dependence of the integrated X-ray diffracted intensities in sodium metal has been determined for the 222, 400, 330, 411 and 332 reflexions in the temperature range 148 K to the melting point of 371 K. In the temperature range 148 K to about 300 K, all the data can be fitted using a quasi-harmonic approximation for the temperature factor. From room temperature to the melting point the intensities for all the reflexions were observed to decrease rapidly with temperature, and could not be fitted either with a quasi-harmonic or fourth-order anharmonic model for the temperature factor. There is no evidence for anisotropy in the intensities below room temperature, but from 293 K to the melting point, anisotropy increases rapidly. A qualitative explanation of the high-temperature phenomena in terms of a lattice relaxation around the vacancies has been advanced.
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    Acta crystallographica 32 (1976), S. 344-344 
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    Notes: The value of the residual for a randomly wrong structure when calculated from a mixture of centrosymmetrical and non-centrosymmetrical structure factors is close to the value obtained by interpolation between the centric and acentric cases of Wilson [Acta Cryst. (1950). 3, 397-398].
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    Acta crystallographica 32 (1976), S. 799-805 
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    Notes: It has been previously established that calculations of intensity distributions in high-resolution electron-microscope images of crystal structures can reproduce the experimental observations. The use of comparisons Of observed and computed images for structure analysis has been extended for the first time to the refinement of a defect structure in the case of crystals of nominal composition 'GeNb9O25. The results show that previously proposed models for the disordered atom configurations around 'tetrahedral' sites are not completely correct. A new model is proposed which shows good agreement between computed and observed images. This model suggests an interpretation for observations on other related structures in terms of a new type of defect.
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    Acta crystallographica 32 (1976), S. 806-812 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The wavelength dependence of extinction effects in X-ray and neutron diffraction predicted by recent theories is considered and compared with the results obtained for recent accurate diffraction measurements. It is shown that it is not usually possible to determine reliable values of the domain radius and mosaic spread parameters separately from data measured at only one or two conventional wavelengths. The most significant experimental test of the wavelength dependence is at present that for secondary extinction in a spherical crystal arising from neutron diffraction measurements for SrF2 at three different wavelengths. These have been analysed on both the Cooper-Rouse and the Becker-Coppens formalisms, both of which predict a simple form for the wavelength dependence. Although both these formalisms give excellent agreement with the data when those for different wavelengths are analysed separately the results indicate, in both cases, that the wavelength dependence is not accounted for adequately by the theory.
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    Acta crystallographica 32 (1976), S. 828-831 
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    Notes: Crystal energies at 0 K and 25°C of three polymorphic forms of the normal alkanes C28H58 and C36H74 have been calculated from crystal structure data with a Lennard-Jones 6-12 potential. Taking into account the side packing and end packing energies, a general expression for the heat of sublimation at 25°C has been derived, viz ΔH0sub = 8.24nC + 4.10 kJ mo-1, where nC is the number of C atoms in the molecule. The agreement with the two known experimental values (for C18H38 and C32H66) is within 1%.
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    Acta crystallographica 32 (1976), S. 832-847 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Phases can be determined for geometrically redundant amplitudes by iteration of the following procedure: compute an electron density map from the currently available phases; average the electron densities of all the crystallographically independent molecules; rebuild the crystal(s) from this averaged subunit, setting the density outside the molecular boundaries to its average value; obtain phase information from the resulting structure, and combine it with that given by isomorphous replacement to produce the phases to be used in the next iteration. This algorithm converges very rapidly, and has proved to be a powerful tool in the solution of two large unknown protein structures. This paper describes the computational techniques developed to implement it, which include a swift and general method for real-space averaging of electron density maps.
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    Acta crystallographica 32 (1976), S. 854-858 
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    Notes: The first and second homogeneous strain derivatives of the Lorentz-factor dipole-tensor lattice sum are expressed in terms of wave-vector derivatives of modulated higher multipole-tensor sums. Such derivatives can be calculated rapidly by the Ewald method, for which computationally convenient expressions are given. The first strain derivatives are highly symmetrical, but the symmetry of the second derivatives is lower and more complicated. The method is illustrated by calculations for anthracene and tetragonal hydrogen cyanide; it appears to be superior to more direct methods of calculation.
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    Acta crystallographica 32 (1976), S. 863-868 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A simple physical model is presented to predict the neutron diffraction properties of deformed crystals. The main interest of this model is its general applicability to deformed crystals and its mathematical simplicity. At first this model was applied to curved crystals and its validity was checked by comparison with the diffraction patterns obtained from the exact solution of the dynamical neutron diffraction theory. A comparison between the prediction of the model and experimental data in curved Si crystals is presented. Finally the model is used to predict neutron diffraction patterns by crystals with a gradient in the lattice spacing and by deformed crystals in the general case.
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    Acta crystallographica 32 (1976), S. 877-882 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Recent methods in the probabilistic theory of the structure invariants and seminvariants are here generalized to include the case that not all atoms in the unit cell are identical. The presence of unequal atoms, in particular a few heavy atoms, is thus clearly seen to enhance the power of the direct method. Since the method permits the presence of negative scatterers, the application to neutron diffraction is immediate. Only the conditional probability distributions associated with the first neighborhood of the three-phase structure invariant and the first two neighborhoods of the four-phase structure invariant in P1 and P{\bar 1} are treated here. However the methods are clearly sufficiently general to cope with structure invariants and seminvariants in general.
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    Acta crystallographica 32 (1976), S. 1019-1033 
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  • 98
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    Notes: This report contains general recommendations for the guidance of authors, referees, and editors on the reporting of electron diffraction data and derived structures. They are intended to facilitate reliable evaluation, ease of comparison with other data, and the retrieval of information if later reanalysis becomes desirable in the light of new theories or experiments.
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    Acta crystallographica 32 (1976), S. 447-452 
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    Notes: A computer program has been written to calculate crystal energies as sums of Coulomb, van der Waals, repulsion and covalent bonding interactions. In this paper the general theory that leads to the energy expression is explained. It is shown that the choice of parameters and the inclusion of anisotropic thermal motion leads to the successful calculation of actual minimum energies for existing structures both for ionic and non-ionic compounds. The lattice-dynamical aspects of the model are discussed and the model is shown to be applicable to the analysis of lattice vibrations as used in the refinement of X-ray structure determinations. In further papers there will be a discussion of structural chemistry of different classes of compounds in terms of crystal energy.
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    Acta crystallographica 32 (1976), S. 453-457 
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    Notes: A new formalism of the dynamical diffraction theory is proposed in order to take into account the statistical nature of lattice distortions. It is postulated that the observed intensity is given by an ensemble average of the intensity field derived from the wave equations of Takagi-Taupin type. The formalism leads to exactly the same results as those of the conventional dynamical theory for ideally perfect crystals and the results of the conventional kinematical theory for ideally imperfect crystals. The general relations are established among the integrated diffraction powers for three types of incident wave; namely, a spherical wave (narrow beam), a plane wave and the wave from an incoherent homogeneous source (wide beam). This paper is a preparation for the following one on secondary extinction [Kato, Acta Cryst. (1976) A32, 458-466].
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