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  • 1
    Electronic Resource
    Electronic Resource
    Tensor properties and rotational symmetry of crystals. III. Use of symmetrized components in group 3(3z) (1983)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 39 (1983), S. 245-251 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: 'Symmetrized' components are introduced in place of the standard ones to improve the method presented in paper I [Fumi & Ripamonti (1980). Acta Cryst. A36, 535-551]. These components, which are simply related to the standard ones, allow a further reduction of the computational task and also a further simplification of the results and of their use. This is illustrated by application to general two-dimensional tensors of ranks 6 and 8 and by particularization of the results to the cases of the third- and fourth-order elastic tensors.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767383000525
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  • 2
    Electronic Resource
    Electronic Resource
    Electron density in KCl and LiF crystals in the self-consistent local-density-functional approximation (LDA) (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 175-177 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The γ-ray single-crystal structure factors of Schmidt, Colella & Yoder-Short [Acta Cryst. (1985), A41, 171-175] for the 'isoelectronic' salt KCl are shown to be in excellent agreement with the values computed by us using the method of augmented spherical waves in the LDA approximation. Small differences exist for the 600 and 400 reflections whose structure factors indicate some 'asphericity' in the valence charge density - an effect not included in the theoretical calculation. The corresponding data by the same authors for the ('non-isoelectronic') salt LiF are also in good agreement with the LDA theoretical values available in the literature. A discrepancy remains, instead, between the γ-ray structure factors for 'isoelectronic' NaF by Yoder & Colella [Phys. Rev. B. (1982), 25, 2545-2549] and the LDA theoretical values.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767385000356
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  • 3
    Electronic Resource
    Electronic Resource
    Tables for the third-order elastic tensor in crystals (1987)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 43 (1987), S. 587-588 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: It is pointed out that the tables for the third-order elastic tensor in crystals first given by Fumi [Phys. Rev. (1951). 83, 1274-1275; Phys. Rev. (1952). 86, 561] have been inconsistently reported for trigonal and hexagonal groups by Huntington [Solid State Physics (1958). Vol. 7, pp. 213-351. New York: Academic Press] and by Mason [Crystal Physics of Interaction Processes (1966). New York: Academic Press], and this has caused confusion in the literature. The tables reported by Brugger [J. Appl. Phys. (1965). 36, 759-768] for all crystallographic groups, which are often quoted in the more recent literature, actually coincide with those given by Fumi (1951, 1952) even in the choice of independent components.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767387098969
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  • 4
    Electronic Resource
    Electronic Resource
    Electron density in the alkali halide crystals (1989)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 45 (1989), S. 112-115 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Structure factors at room temperature are computed for LiF, NaF, NaCl and KCl by means of theoretical ionic form factors and theoretical Debye-Waller factors. The values obtained are compared with the best available experimental data. For LiF, KCl and NaF - for which good experimental data are available - there is generally very good agreement, with only a few sizeable discrepancies for NaF that can be attributed to deficiencies of the experimental data. It is concluded that there is no apparent need to question the validity of the Debye-Waller theory as recently proposed in the literature.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767388009523
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  • 5
    Electronic Resource
    Electronic Resource
    Electron density in RbBr and CsI crystals in the self-consistent local-density-functional approximation (LDA) (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 618-619 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The electron density in RbBr and CsI crystals - composed of 'isoelectronic' alkali and halogen ions - has been computed self-consistently by the method of augmented spherical waves in the LDA approximation. The heat of formation of the salts from the alkali metal and the halogen molecule - calculated from the pertinent total energies - is in very good agreement with experiment. The LDA structure factors for the low-order 'sum' and 'difference' reflections are compared with the structure factors obtained from Hartree-Fock free-ion wave functions. The agreement is excellent for the 'sum' reflections, but for the 'difference' reflections the LDA structure factors are smaller. This result parallels our earlier results for NaF and KCI crystals and again indicates a 'contraction' of the anion and an 'expansion' of the cation in passing from free ion to ion in crystal.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767385001349
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  • 6
    Electronic Resource
    Electronic Resource
    Numerical vector representation of physical properties of crystals (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 293-296 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The idea of a numerical vector representation (NVR) of a physical property of a crystal, introduced in a previous paper [Fumi & Ripamonti (1980). Acta Cryst. A36, 535-551], is a convenient way to account for its rotational invariance properties. The main advantages of the NVR are the possibility of dealing with single invariance relations independently from the others and the direct display of the simplest features of the invariance relations (vanishing of components, equalities or proportionalities among components, independence of components and 'form invariance' with respect to interchange of components). The NVR also provides a direct-expansion method of the set of tensor components of a crystal property in terms of a minimal subset. A simple rule is reported for obtaining a NVR of any given tensorial set (i.e. a set of given rank and rotational and permutational symmetry) in the axial rotational groups. The use of the NVR in establishing general results such as isomorphisms between tensorial sets is also illustrated. Finally, a few examples are reported of NVR's for high-rank tensorial sets in axial rotational groups (specifically the second-order piezoelectric tensor, the second-order Pockels elastooptic tensor and the fourth-order elastic tensor).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767386099233
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  • 7
    Electronic Resource
    Electronic Resource
    Non-tensorial arrays for physical properties and the direct-inspection method (1987)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 43 (1987), S. 431-432 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: It is shown that the invariance relations between the elements of a non-tensorial array for a physical property are identical to the invariance relations between the corresponding tensorial components when one is only dealing with symmetry elements of order 1, 2 or 4 and with the trigonal axis 3[111] of the cubic groups.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767387099185
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  • 8
    Electronic Resource
    Electronic Resource
    Crystal physics – Macroscopic physics of anisotropic solids by H. J. Juretschke (1976)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 32 (1976), S. 924-925 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739476001927
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  • 9
    Electronic Resource
    Electronic Resource
    Tensor properties and rotational symmetry of crystals. II. Groups with 1-, 2- and 4-fold principal symmetry and trigonal and hexagonal groups different from group 3 (1980)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 551-558 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The first part of the paper emphasizes that the problem of the effect of the rotational symmetry of crystals on their tensor properties is completely solved for the groups of 1-, 2- and 4-fold principal symmetry since simple general formulas can be given which provide the schemes of a (polar or axial) general tensor of any rank in these groups, thus yielding a closed-form solution. These formulas are derived both by the new method of vector representatives [introduced in paper I: Fumi & Ripamonti (1980). Acta Cryst. A36, 535-551] and by the direct-inspection method. In the second part, it is emphasized that simple general rules can be given to obtain the schemes of a (general or particular, polar or axial) tensor of any rank in the trigonal and hexagonal groups other than group 3 from the corresponding scheme in group 3(3z). These rules are given directly by the formulas obtained in the first part for the groups (or generators) of order 2. These compact formulas and rules are applied to two specific tensor properties discussed in recent literature, pointing out errors in some of the reported schemes. Brief discussions are finally given of various techniques to obtain the tensor schemes in the cylindrical and spherical groups, in particular of the new methods introduced in paper I.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739480001209
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  • 10
    Electronic Resource
    Electronic Resource
    Tensor properties and rotational symmetry of crystals. I. A new method for group 3(3z) and its application to general tensors up to rank 8 (1980)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 535-551 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A new method is presented to overcome the cumbersomeness of the existing methods in the derivation and tabulation of the results for general tensors when the elements of the group do not all simply permute coordinates apart from sign; here the method is described for the generator 3z. The method uses a conjectured, optimal choice of independent components (verified up to rank 8) and a new procedure to obtain the expressions of the dependent components. The independent components adopted consist of sets of components related by appropriate permutations of component indices: this choice is suggested by the similarity of transformation properties of these components. The procedure for the determination of the expressions of dependent components is based on the representation of all components by suitable numerical vectors. The procedure allows the exploitation of the restrictions on the general form of the expressions which follow from the optimal choice of independent components. The method is applied to the derivation of the schemes of general tensors up to rank 8 in group 3(3z). The simolification provided by the method is considerable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739480001192
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