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  • 1
    Electronic Resource
    Electronic Resource
    Anisotropic corrections of measured integrated Bragg intensities for thermal diffuse scattering – general formula (1974)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 30 (1974), S. 77-82 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The correction of measured integrated intensities for the first-order thermal diffuse scattering (TDS) is considered on the basis of the existing theory of X-ray thermal diffuse scattering for an elastic wave of long wave length. Generalized formula for the TDS correction α is found to be represented by a quadratic form in the Miller indices h, k, l and a tensor Δβ, as α = Δβ11h2 + Δβ22k2 + Δβ33l2 + 2Δβ12hk + 2Δβ23kl + 2Δβ31lh. Δβ is a tensor introduced in this paper which characterizes the anisotropy of the TDS correction. The form of the tensor Δβ is shown to depend only on the crystallographic system. The relation between Δβ and the temperature-parameter tensor is presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S056773947400012X
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  • 2
    Electronic Resource
    Electronic Resource
    Neutron diffraction study of asymmetric anharmonic vibration of the copper atom in cuprous chloride (1974)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 30 (1974), S. 655-661 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Neutron diffraction measurements of CuCl with the zincblende structure were carried out at room temperature and the results examined on the basis of three possible structure models: (1) harmonic thermal vibration of atoms, (2) asymmetric anharmonic vibrations and (3) statistical disorder arrangement of the copper atom. It was found that the anharmonic model was the most plausible for the structure of CuCl. The final R value in the least-squares analysis was 0.037. The parameters in the effective one-atomic-potential fields for the zincblende structure Vj(r) = V0j + ½αj(u21 + u22 + u23) + βju1u2u3 + . . . were obtained as αCu = 0.74 ± 0.01, αC1 = 1.35 ± 0.02 × 10-12erg Å-2, and βCu = 1.15 ± 0.66, βC1 = 0.0 ± 1.6 × 10-12erg Å-3. It is also shown that the temperature dependence of the Bragg reflexion observed from room temperature to 523°K can be explained very well with the use of the above parameters.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739474001574
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  • 3
    Electronic Resource
    Electronic Resource
    A neutron diffraction study of the wavelength dependence of extinction in UO2 (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 336-341 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Neutron diffraction measurements have been carried out on a single crystal of UO2 examined at four different wavelengths; 0.85, 1.12, 1.54 and 1.84 Å. The Bragg intensities were analysed for the wavelength dependence of extinction using both the Cooper-Rouse and the Becker-Coppens formulations. Both treatments showed that the crystal is of type I (i.e. r 〉〉 λg, where r is the domain radius, λ the wavelength and g the mosaic-spread parameter). The value of g is the same, within one standard deviation, for each wavelength; its magnitude is appreciably less than for other crystals (SrF2,ZnS,ZnTe,KCl) which have been examined by neutron diffraction at a number of wavelengths. Keeping the isotropic temperature factor for uranium fixed at 0.28 Å2, the value of 0.55 ± 0.02 Å2 is derived for the temperature factor of oxygen. There are no significant differences between the values of the extinction parameters and temperature factors obtained using the Cooper-Rouse treatment and the Becker-Coppens treatment based on either a Gaussian or a Lorentzian mosaic-spread distribution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739478000601
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  • 4
    Electronic Resource
    Electronic Resource
    Anisotropic corrections of measured integrated Bragg intensities for thermal diffuse scattering. II (1976)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 32 (1976), S. 426-433 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739476000971
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  • 5
    Electronic Resource
    Electronic Resource
    Extinction in single crystals of UO2 (1979)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 35 (1979), S. 250-251 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: he measurements of nuclear neutron diffraction intensities for a single crystal of UO2 by Faber & Lander [Phys. Rev. B. (1976), 14, 1151-1164] have been reanalysed using both the Cooper-Rouse and Becker-Coppens extinction formalisms. The results indicate that this crystal is type I in nature, not type II as was suggested by Faber & Lander, and this conclusion is essentially the same as that obtained for a different single crystal of UO2 used in our earlier study of the wavelength dependence of extinction in this material [Sakata, Cooper, Rouse & Willis (1978). Acta Cryst. A34, 336-3411. The analysis of the Faber & Lander data gave a value for the scattering-length ratio bU/bO = 1.448 (2).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739479000462
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  • 6
    Electronic Resource
    Electronic Resource
    The interpretation of neutron powder diffraction measurements on α-AgI (1979)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 35 (1979), S. 989-991 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Recent neutron powder diffraction measurements on α-AgI by Wright & Fender [J. Phys. C (1977), 10, 2261- 2267] have been reanalysed using conventional least-squares analysis of the integrated Bragg intensities and have been shown to be consistent with other recent neutron diffraction measurements and with recent extended X-ray absorption fine structure (EXAFS) measurements. It is concluded that, although the distribution of silver ions within the unit cell can be modelled by locating isotropically vibrating ions in a number of crystallographic sites with partial occupancy, the most appropriate model is one in which the silver ions are located entirely in a single site but have significant anisotropic harmonic and higher-order components in their thermal vibration.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739479002187
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  • 7
    Electronic Resource
    Electronic Resource
    A neutron diffraction study of anharmonic thermal vibrations in cubic CsPbX3 (1980)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 7-15 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A neutron diffraction study of cubic CsPbX3 (X = Cl or Br) has been carried out over the temperature ranges 325-623 K for CsPbCl3 and 408-673 K for CsPbBr3. The temperature factors for the perovskite structure were derived following the method of Matsubara [Prog. Theor. Phys. (1975), 53, 1210-1211] which includes the use of cumulant coefficients to characterize anharmonic components for an Einstein model. The potential parameters were then obtained using a numerical integration method to analyse the temperature dependence of the temperature factors. It was found that the anharmonic components in the potential were very large for the Cs and X atoms which undergo displacements on passing through the phase transitions at lower temperatures (321 K for CsPbCl3 and 403 K for CsPbBr3). On the other hand, a harmonic potential is quite adequate to describe the thermal vibration of the Pb atoms, which are not displaced at the phase transitions. Thus, the existence of the anharmonicity in the cubic phase seems to be anticipating the atomic displacement through the successive phase transitions for these substances. In addition to this anharmonicity, the temperature factors of the X atoms parallel to the (100) plane show an anomalous behaviour near the cubic to tetragonal phase-transition temperature, which should be connected with the softening of phonon mode at this phase transition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739480000022
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  • 8
    Electronic Resource
    Electronic Resource
    Triple-crystal diffraction studies on ion-implanted and other silicon crystals using a synchrotron source (1988)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 44 (1988), S. 828-833 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Triple-crystal diffraction studies are capable of cleanly separating the various experimental components of the scattering in the vicinity of a Brags peak. The two-dimensional intensity distributions obtained in such an experiment consist of various components which extend in distinct directions in (Δωs, Δ2θS) space, where Δωs and Δ2θS are the offset angles of the sample and analyzer/detector from the Bragg condition. One-dimensional 'slice' scans can be used in studying specific details, given a known disposition of the components, be they dynamical, kinematical or aspects of the instrumental arrangement. In this paper triple-crystal diffraction results obtained for given ion-implanted and other Si crystals using both a conventional X-ray tube and a synchrotron source are presented and compared.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767388004702
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  • 9
    Electronic Resource
    Electronic Resource
    Accurate structure analysis by the maximum-entropy method (1990)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 46 (1990), S. 263-270 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The electron-density map of an Si crystal is drawn by the maximum-entropy method (MEM) with 30 structure factors which were determined very accurately on an absolute scale by the Pendellösung method [Saka & Kato (1986). Acta Cryst. A42, 469-478]. It is shown that the following three beneficial points arise from the use of the MEM for accurate structure analysis. Firstly, a precise electron-density map can be obtained; the existence of bonding electrons is clearly visible in the maximum-entropy map, even though no forbidden reflections are included in the analysis. The structure factors calculated from the maximum-entropy map for the 222 and the 442 forbidden reflections show good agreement with those measured by different experiments. The final R factor was 0.05% as a consequence of the high accuracy of the measured structure factors. Secondly, there is no need to seek a better structural model which could be a complicated and time-consuming process in accurate structure analysis. Thirdly, the resolution of the maximum-entropy map is much higher than that of the map drawn by conventional Fourier transformation. It is also found in the case of silicon that phase information is not absolutely necessary because exactly the same density-distribution map can be obtained without any phase information as the map drawn with all the phase information.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767389012377
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  • 10
    Electronic Resource
    Electronic Resource
    On the phase factor due to antisymmetric components of density distributions (1979)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 35 (1979), S. 821-824 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In the Fourier and the difference Fourier syntheses, the contribution of antisymmetric components of the density distribution to the phases of structure factors are usually ignored. From an analysis of the asymmetric thermal vibration of the Cu atom in a CuCl crystal by neutron diffraction, the effects of phase error are shown to appear in the following two forms on the difference Fourier map: (i) the peak heights due to antisymmetric density distribution are reduced considerably, and (ii) parasitic peaks appear on the map and modulate the difference density distribution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739479001856
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