Tables for
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2006). Vol. B, ch. 1.2, pp. 10-24   | 1 | 2 |

Chapter 1.2. The structure factor

P. Coppensa*

aDepartment of Chemistry, Natural Sciences & Mathematics Complex, State University of New York at Buffalo, Buffalo, New York 14260-3000, USA
Correspondence e-mail:


Arfken, G. (1970). Mathematical models for physicists, 2nd ed. New York, London: Academic Press.Google Scholar
Avery, J. & Ørmen, P.-J. (1979). Generalized scattering factors and generalized Fourier transforms. Acta Cryst. A35, 849–851.Google Scholar
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.Google Scholar
Bentley, J. & Stewart, R. F. (1973). Two-centre calculations for X-ray scattering. J. Comput. Phys. 11, 127–145.Google Scholar
Born, M. (1926). Quantenmechanik der Stoszvorgänge. Z. Phys. 38, 803.Google Scholar
Clementi, E. & Raimondi, D. L. (1963). Atomic screening constants from SCF functions. J. Chem. Phys. 38, 2686–2689.Google Scholar
Clementi, E. & Roetti, C. (1974). Roothaan–Hartree–Fock atomic wavefunctions. At. Data Nucl. Data Tables, 14, 177–478.Google Scholar
Cohen-Tannoudji, C., Diu, B. & Laloe, F. (1977). Quantum mechanics. New York: John Wiley and Paris: Hermann.Google Scholar
Condon, E. V. & Shortley, G. H. (1957). The theory of atomic spectra. London, New York: Cambridge University Press.Google Scholar
Coppens, P. (1980). Thermal smearing and chemical bonding. In Electron and magnetization densities in molecules and solids, edited by P. J. Becker, pp. 521–544. New York: Plenum.Google Scholar
Coppens, P., Guru Row, T. N., Leung, P., Stevens, E. D., Becker, P. J. & Yang, Y. W. (1979). Net atomic charges and molecular dipole moments from spherical-atom X-ray refinements, and the relation between atomic charges and shape. Acta Cryst. A35, 63–72.Google Scholar
Coulson, C. A. (1961). Valence. Oxford University Press.Google Scholar
Cruickshank, D. W. J. (1956). The analysis of the anisotropic thermal motion of molecules in crystals. Acta Cryst. 9, 754–756.Google Scholar
Dawson, B. (1967). A general structure factor formalism for interpreting accurate X-ray and neutron diffraction data. Proc. R. Soc. London Ser. A, 248, 235–288.Google Scholar
Dawson, B. (1975). Studies of atomic charge density by X-ray and neutron diffraction – a perspective. In Advances in structure research by diffraction methods. Vol. 6, edited by W. Hoppe & R. Mason. Oxford: Pergamon Press.Google Scholar
Dawson, B., Hurley, A. C. & Maslen, V. W. (1967). Anharmonic vibration in fluorite-structures. Proc. R. Soc. London Ser. A, 298, 289–306.Google Scholar
Dunitz, J. D. (1979). X-ray analysis and the structure of organic molecules. Ithaca and London: Cornell University Press.Google Scholar
Feil, D. (1977). Diffraction physics. Isr. J. Chem. 16, 103–110.Google Scholar
Hansen, N. K. & Coppens, P. (1978). Testing aspherical atom refinements on small-molecule data sets. Acta Cryst. A34, 909–921.Google Scholar
Hehre, W. J., Ditchfield, R., Stewart, R. F. & Pople, J. A. (1970). Self-consistent molecular orbital methods. IV. Use of Gaussian expansions of Slater-type orbitals. Extension to second-row molecules. J. Chem. Phys. 52, 2769–2773.Google Scholar
Hehre, W. J., Stewart, R. F. & Pople, J. A. (1969). Self-consistent molecular orbital methods. I. Use of Gaussian expansions of Slater-type atomic orbitals. J. Chem. Phys. 51, 2657–2664.Google Scholar
Hirshfeld, F. L. (1977). A deformation density refinement program. Isr. J. Chem. 16, 226–229.Google Scholar
International Tables for Crystallography (2004). Vol. C. Mathematical, physical and chemical tables, edited by E. Prince. Dordrecht: Kluwer Academic Publishers.Google Scholar
International Tables for X-ray Crystallography (1974). Vol. IV. Birmingham: Kynoch Press. (Present distributor Kluwer Academic Publishers, Dordrecht.)Google Scholar
James, R. W. (1982). The optical principles of the diffraction of X-rays. Woodbridge, Connecticut: Oxbow Press.Google Scholar
Johnson, C. K. (1969). Addition of higher cumulants to the crystallographic structure-factor equation: a generalized treatment for thermal-motion effects. Acta Cryst. A25, 187–194.Google Scholar
Johnson, C. K. (1970a). Series expansion models for thermal motion. ACA Program and Abstracts, 1970 Winter Meeting, Tulane University, p. 60.Google Scholar
Johnson, C. K. (1970b). An introduction to thermal-motion analysis. In Crystallographic computing, edited by F. R. Ahmed, S. R. Hall & C. P. Huber, pp. 207–219. Copenhagen: Munksgaard.Google Scholar
Johnson, C. K. & Levy, H. A. (1974). Thermal motion analysis using Bragg diffraction data. In International tables for X-ray crystallography (1974), Vol. IV, pp. 311–336. Birmingham: Kynoch Press. (Present distributor Kluwer Academic Publishers, Dordrecht.)Google Scholar
Kara, M. & Kurki-Suonio, K. (1981). Symmetrized multipole analysis of orientational distributions. Acta Cryst. A37, 201–210.Google Scholar
Kendall, M. G. & Stuart, A. (1958). The advanced theory of statistics. London: Griffin.Google Scholar
Kuhs, W. F. (1983). Statistical description of multimodal atomic probability structures. Acta Cryst. A39, 148–158.Google Scholar
Kurki-Suonio, K. (1977). Symmetry and its implications. Isr. J. Chem. 16, 115–123.Google Scholar
Kutznetsov, P. I., Stratonovich, R. L. & Tikhonov, V. I. (1960). Theory Probab. Its Appl. (USSR), 5, 80–97.Google Scholar
Lipson, H. & Cochran, W. (1966). The determination of crystal structures. London: Bell.Google Scholar
McIntyre, G. J., Moss, G. & Barnea, Z. (1980). Anharmonic temperature factors of zinc selenide determined by X-ray diffraction from an extended-face crystal. Acta Cryst. A36, 482–490.Google Scholar
Materlik, G., Sparks, C. J. & Fischer, K. (1994). Resonant anomalous X-ray scattering. Theory and applications. Amsterdam: North-Holland.Google Scholar
Paturle, A. & Coppens, P. (1988). Normalization factors for spherical harmonic density functions. Acta Cryst. A44, 6–7.Google Scholar
Ruedenberg, K. (1962). The nature of the chemical bond. Phys. Rev. 34, 326–376.Google Scholar
Scheringer, C. (1985a). A general expression for the anharmonic temperature factor in the isolated-atom-potential approach. Acta Cryst. A41, 73–79.Google Scholar
Scheringer, C. (1985b). A deficiency of the cumulant expansion of the anharmonic temperature factor. Acta Cryst. A41, 79–81.Google Scholar
Schomaker, V. & Trueblood, K. N. (1968). On the rigid-body motion of molecules in crystals. Acta Cryst. B24, 63–76.Google Scholar
Schwarzenbach, D. (1986). Private communication.Google Scholar
Squires, G. L. (1978). Introduction to the theory of thermal neutron scattering. Cambridge University Press.Google Scholar
Stewart, R. F. (1969a). Generalized X-ray scattering factors. J. Chem. Phys. 51, 4569–4577.Google Scholar
Stewart, R. F. (1969b). Small Gaussian expansions of atomic orbitals. J. Chem. Phys. 50, 2485–2495.Google Scholar
Stewart, R. F. (1970). Small Gaussian expansions of Slater-type orbitals. J. Chem. Phys. 52, 431–438.Google Scholar
Stewart, R. F. (1980). Electron and magnetization densities in molecules and solids, edited by P. J. Becker, pp. 439–442. New York: Plenum.Google Scholar
Stewart, R. F. & Hehre, W. J. (1970). Small Gaussian expansions of atomic orbitals: second-row atoms. J. Chem. Phys. 52, 5243–5247.Google Scholar
Su, Z. & Coppens, P. (1990). Closed-form expressions for Fourier– Bessel transforms of Slater-type functions. J. Appl. Cryst. 23, 71–73.Google Scholar
Su, Z. & Coppens, P. (1994). Normalization factors for Kubic harmonic density functions. Acta Cryst. A50, 408–409.Google Scholar
Tanaka, K. & Marumo, F. (1983). Willis formalism of anharmonic temperature factors for a general potential and its application in the least-squares method. Acta Cryst. A39, 631–641.Google Scholar
Von der Lage, F. C. & Bethe, H. A. (1947). A method for obtaining electronic functions and eigenvalues in solids with an application to sodium. Phys. Rev. 71, 612–622.Google Scholar
Waller, I. & Hartree, D. R. (1929). Intensity of total scattering X-rays. Proc. R. Soc. London Ser. A, 124, 119–142.Google Scholar
Weiss, R. J. & Freeman, A. J. (1959). X-ray and neutron scattering for electrons in a crystalline field and the determination of outer electron configurations in iron and nickel. J. Phys. Chem. Solids, 10, 147–161.Google Scholar
Willis, B. T. M. (1969). Lattice vibrations and the accurate determination of structure factors for the elastic scattering of X-rays and neutrons. Acta Cryst. A25, 277–300.Google Scholar
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.Google Scholar