International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

International Tables for Crystallography (2006). Vol. C, ch. 6.1, pp. 554-595
https://doi.org/10.1107/97809553602060000600

Chapter 6.1. Intensity of diffracted intensities

P. J. Brown,a A. G. Fox,b E. N. Maslen,e M. A. O'Keefec and B. T. M. Willisd

aInstitut Laue–Langevin, Avenue des Martyrs, BP 156X, F-38042 Grenoble CEDEX, France,bCenter for Materials Science and Engineering, Naval Postgraduate School, Monterey, CA 93943-5000, USA,cNational Center for Electron Microscopy, Lawrence Berkeley National Laboratory MS-72, University of California, Berkeley, CA 94720, USA,dChemical Crystallography Laboratory, University of Oxford, 9 Parks Road, Oxford OX1 3PD, England, and eCrystallography Centre, The University of Western Australia, Nedlands, Western Australia 6009, Australia

References

Abramowitz, M. & Stegun, I. A. (1964). Handbook of mathematical functions. National Bureau of Standards Publication AMS 55.
Ahlrichs, R. & Taylor, P. R. (1981). The choice of Gaussian basis sets for molecular electronic structure calculations. J. Chim. Phys. 78, 316–323.
Altmann, S. L. & Cracknell, A. P. (1965). Lattice harmonics. I. Cubic groups. Rev. Mod. Phys. 37, 19–32.
Atoji, M., Watanabe, T. & Lipscomb, W. N. (1953). The X-ray scattering from a hindered rotator. Acta Cryst. 6, 62–66.
Avery, J. & Watson, K. J. (1977). Generalized X-ray scattering factors. Simple closed-form expressions for the one-centre case with Slater-type orbitals. Acta Cryst. A33, 679–680.
Bacon, G. E. (1975). Neutron diffraction, 3rd ed. Oxford: Clarendon Press.
Bellman, R. (1961). A brief introduction to theta functions. New York: Holt, Reinhart and Winston.
Blume, M. (1963). Polarization effects in the magnetic elastic scattering of slow neutrons. Phys. Rev. 130, 1670–1676.
Chidambaram, R. & Brown, G. M. (1973). A model for a torsional oscillator in crystallographic least-squares refinement. Acta Cryst. B29, 2388–2392.
Clementi, E. & Roetti, C. (1974). Roothaan–Hartree–Fock atomic wavefunctions. Basis functions and their coefficients for ground and certain excited states of neutral and ionized atoms. At. Data Nucl. Data Tables, 14, 177–478.
Coulthard, M. A. (1967). A relativistic Hartree–Fock atomic field calculation. Proc. Phys. Soc. 91, 44–49.
Cromer, D. T. & Mann, J. B. (1968). X-ray scattering factors computed from numerical Hartree–Fock wave functions. Los Alamos Scientific Laboratory Report LA-3816.
Cromer, D. T. & Waber, J. T. (1968). Unpublished work reported in International tables for X-ray crystallography (1974), Vol. IV, p. 71. Birmingham: Kynoch Press.
Dawson, B. (1970). Neutron studies of nuclear charge distributions in barium fluoride and hexamethylenetetramine. Thermal neutron diffraction, edited by B. T. M. Willis, pp. 101–123. Oxford University Press.
Desclaux, J. P. & Freeman, A. J. (1978). Dirac–Fock studies of some electronic properties of actinide ions. J. Magn. Magn. Mater. 8, 119–129.
Doyle, P. A. & Turner, P. S. (1968). Relativistic Hartree–Fock and electron scattering factors. Acta Cryst. A24, 390–397.
Duijneveldt, F. B. van (1971). IBM Technical Report RJ-945.
Dunning, T. H. Jr & Jeffrey-Hay, P. (1977). Gaussian basis sets for molecular calculations. Modern theoretical chemistry 3. Methods of electronic structure theory, edited by H. F. Schaefer III, pp. 1–27. New York: Plenum.
Favro, L. D. (1960). Theory of the rotational motion of a free rigid body. Phys. Rev. 119, 53–62.
Feller, W. (1966). An introduction to probability theory and its applications, Vol. II, Chap. 19. New York: John Wiley.
Fisher, R. (1953). Dispersion on a sphere. Proc. R. Soc. London Ser. A, 217, 295–305.
Fox, A. G., O'Keefe, M. A. & Tabbernor, M. A. (1989). Relativistic Hartree–Fock X-ray and electron atomic scattering factors at high angles. Acta Cryst. A45, 786–793.
Freeman, A. J. & Desclaux, J. P. (1972). Neutron magnetic form factor of gadolinium. Int. J. Magn. 3, 311–317.
Furry, W. H. (1957). Isotropic rotational Brownian motion. Phys. Rev. 107, 7–13.
Gumbel, E. J., Greenwood, J. A. & Durand, D. (1953). The circular normal distribution: theory and tables. J. Am. Stat. Assoc. 48, 131–152.
Huzinaga, S. (1971). Approximate atomic functions I, II, III. Technical Report, University of Alberta, Edmonton, Alberta, Canada.
International Tables for Crystallography (2005). Vol. A, edited by Th. Hahn. Heidelberg: Springer.
International Tables for Crystallography (2001). Vol. B, edited by U. Shmueli, 2nd ed. Dordrecht: Kluwer Academic Publishers.
Johnson, C. K. & Levy, H. A. (1974). Thermal motion of independent atoms. International tables for X-ray crystallography. Vol. IV, pp. 317–319. Birmingham: Kynoch Press.
Kay, M. I. & Behrendt, D. R. (1963). The structure factor for a harmonic quasi-torsional oscillator. Acta Cryst. 16, 157–162.
Kendall, M. G. & Stuart, A. (1963). The advanced theory of statistics, Vol. 1, Chaps 2, 3 and 6. London: Griffin.
King, M. V. & Lipscomb, W. N. (1950). The X-ray scattering from a hindered rotator. Acta Cryst. 3, 155–158.
Kuhs, W. F. (1983). Statistical description of multimodal atomic probability densities. Acta Cryst. A39, 149–158.
Kurki-Suonio, K. (1977). Electron density mapping in molecules and crystals. IV. Symmetry and its implications. Isr. J. Chem. 16, 115–123.
Kurki-Suonio, K., Merisalo, M. & Peltonen, H. (1979). Site symmetrized Fourier invariant treatment of anharmonic temperature factors. Phys. Scr. 19, 57–63.
Kuznetsov, P. I., Stratonovich, R. L. & Tikhonov, V. I. (1960). Quasi-moment functions in the theory of random processes. Theory Probab. Appl. (USSR), 5, 80–97.
Lévy, P. (1938). C. R. Soc. Math. Fr. p. 32. Also Processus stochastiques et mouvement Brownian, p. 182. Paris: Gauthier-Villars.
Lovesey, S. W. (1984). Theory of neutron scattering from condensed matter. Vol. 2. Polarization effects and magnetic scattering. The International Series of Monographs on Physics No. 72. Oxford University Press.
Mackenzie, J. K. & Mair, S. L. (1985). Anharmonic temperature factors: the limitations of perturbation-theory expressions. Acta Cryst. A41, 81–85.
McLean, A. D. & Chandler, G. S. (1979). IBM Research Report RJ-2665 (34180).
McLean, A. D. & Chandler, G. S. (1980). Contracted basis sets for molecular calculations. I. Second row atoms, Z = 11–18 . J. Chem. Phys. 72, 5639–5648.
Mair, S. L. (1980a). Temperature dependence of the anharmonic Debye–Waller factor. J. Phys. C, 13, 2857–2868.
Mair, S. L. (1980b). The anharmonic Debye–Waller factor in the classical limit. J. Phys. C, 13, 1419–1425.
Mair, S. L. & Wilkins, S. W. (1976). Anharmonic Debye–Waller factor using quantum statistics. J. Phys. C, 9, 1145–1158.
Mann, J. B. (1968a). Unpublished work reported in International tables for X-ray crystallography (1974), Vol. IV, p. 71. Birmingham: Kynoch Press.
Mann, J. B. (1968b). Los Alamos Scientific Laboratory Report LA-3961, p. 196.
Mardin, K. V. (1972). Statistics of directional data. New York: Academic Press.
Maslen, E. N. (1968). An expression for the temperature factor of a librating atom. Acta Cryst. A24, 434–437.
Mises, R. von (1918). Über die `Ganzahligheit' der Atomgewichte und verwandte Fragen. Phys. Z. 19, 490–500.
Nathans, R., Shull, C. G., Shirane, G. & Andresen, A. (1959). The use of polarised neutrons in determining the magnetic scattering by iron and nickel. J. Phys. Chem. Solids, 10, 138–146.
Normand, J.-M. (1980). A Lie group: rotations in quantum mechanics, p. 461. Amsterdam: North-Holland.
Pawley, G. S. & Willis, B. T. M. (1970). Neutron diffraction study of the atomic and molecular motion in hexamethylenetetramine. Acta Cryst. A26, 263–271.
Perrin, F. (1928). Etude mathématique du mouvement Brownien de rotation. Ann. Ecole. Norm. Suppl. 45, pp. 1–23.
Perrin, F. (1934). Mouvement Brownien d'un ellipsoïde (I). Dispersion diélectrique pour des molécules ellipsoïdales. J. Phys. Radium, 5, 497.
Press, W. & Hüller, A. (1973). Analysis of orientationally disordered structures. I. Method. Acta Cryst. A29, 252–256.
Ramaseshan, S., Ramesh, T. G. & Ranganath, G. S. (1975). A unified approach to the theory of anomalous scattering. Some novel applications of the multiple-wavelength method. Anomalous scattering, edited by S. Ramaseshan & S. C. Abrahams, pp. 139–161. Copenhagen: Munksgaard.
Roberts, P.-H. & Ursell, H. D. (1960). Random walk on a sphere. Philos. Trans. R. Soc. London Ser. A, 252, 317–356.
Roos, B. & Siegbahn, P. (1970). Gaussian basis sets for the first and second row atoms. Theor. Chim. Acta, 17, 209–215.
Scheringer, C. (1985). A general expression for the anharmonic temperature factor in the isolated-atom-potential approach. Acta Cryst. A41, 73–79.
Schoenborn, B. P. (1975). Phasing of neutron protein data by anomalous dispersion. Anomalous scattering, edited by S. Ramaseshan & S. C. Abrahams, pp. 407–421. Copenhagen: Munksgaard.
Shirane, G. (1959). A note on the magnetic intensities of powder neutron diffraction. Acta Cryst. 12, 282–285.
Shull, C. G. (1967). Neutron interactions with atoms. Trans Am. Crystallogr. Assoc. 3, 1–16.
Stephens, M. A. (1963). Random walk on a circle. Biometrika, 50, 385–390.
Stewart, R. F. (1980a). Algorithms for Fourier transforms of analytical density functions. Electron and magnetisation densities in molecules and crystals, edited by P. Becker, pp. 439–442. New York: Plenum.
Stewart, R. F. (1980b). Multipolar expansions of one-electron densities. Electron and magnetisation densities in molecules and crystals, edited by P. Becker, pp. 405–425. New York: Plenum.
Stewart, R. F., Davidson, E. R. & Simpson, W. T. (1965). Coherent X-ray scattering for the hydrogen atom in the hydrogen molecule. J. Chem. Phys. 42, 3175–3187.
Thakkar, A. J. & Smith, V. H. Jr (1992). High-accuracy ab initio form factors for the hydride anion and isoelectronic species. Acta Cryst. A48, 70–71.
Trammell, G. T. (1953). Magnetic scattering of neutrons from rare earth ions. Phys. Rev. 92, 1387–1393.
Veillard, A. (1968). Gaussian basis sets for molecular wavefunctions containing second row atoms. Theor. Chim. Acta, 12, 405–411.
Zucker, U. H. & Schulz, H. (1982). Statistical approaches for the treatment of anharmonic motion in crystals. I. A comparison of the most frequently used formalisms of anharmonic thermal vibrations. Acta Cryst. A38, 563–568.