Abstract
The basic idea how three-beam diffraction can be used for physical determination of phase relations originates from (1949). He proposed to exploit the diffracted intensity when two Bragg reflections are simultaneously excited. This situation is called three-beam diffraction since besides of the forwardly transmitted two additional diffracted rays, in total three strong rays, are simultaneously be propagated (cf. Figure 1). More generally, N-beam diffraction occurs when besides of the origin N-1 nodes of the reciprocal lattice lie very close to or on the Ewald sphere.
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References
Bethe, H. A., 1928, Theorie der Beugung von Elektronen an Kristallen, Ann. Phys.(Leipzig) 87:55.
Bijvoet, J. M., Peerdeman, A. F., and Bommel van, A. F., 1951, Determination of the absolute configuration of optically active compounds by means of X-ray, Nature (London) 168:271.
Boer de, J. L., 1993, private communication.
Burzlaff, H. and Hümmer, K., 1988, On the ambiguities in merohedral crystal structures, Acta Cryst A44:506.
Cahn, J. W., Shechtman, D., and Gratias, D., 1986, Indexing of icosahedral quasiperiodic crystals, J.Mater.Res. 1:13.
Chang, S. L., 1982, Direct determination of X-ray reflection phases, Phys.Rev.Lett. 48:163.
Chang, S. L., 1984, Multiple Diffraction of X-rays in Crystals, Springer Verlag, Berlin, Heidelberg, New York.
Colella, R., 1974, Multiple diffraction of x-rays and the phase problem. computational procedures and comparison with experiment, Acta Cryst. A30:413.
Ewald, P., 1917, Zur Begründung der Kristalloptik. III. Röntgenstrahlen, Ann. Phys. (Leipzig) 54:519.
Ewald, P. P., 1965, Crystal optics for visible light and X-rays, Acta Cryst. 37:46.
Ewald, P. P. and Heno, Y., 1968, X-ray diffraction in the case of three strong rays. I. Crystal composed of non-absorbing point atoms, Acta Cryst. A24:5.
Hoier, R. and Marthinsen, K., 1983, Effective structure factors in many-beam X-ray diffraction — use of the second Bethe approximation, Acta Cryst. A39:854.
Hümmer, K. and Billy, H., 1986, Experimental determination of triplet phase and enantiomorphs of non-centrosymmetric structures. I. Theoretical considerations, Acta Cryst A42:127.
Hümmer, K., Schwegle, W., and Weckert, E., 1991, A feasibility study of experimental triplet-phase determination in small proteins, Acta Cryst. A47:60.
Hümmer, K. and Weckert, E., 1995, Enantiomorphism and three-beam X-ray diffraction: determination of the absolute structure, Acta Cryst. A51:431.
Hümmer, K., Weckert, E., and Bondza, H., 1990, Direct measurements of triplet phase relationships of organic non-centrosymmetric structures using synchrotron radiation, Acta Cryst. A46:393.
Jones, P.-G., 1986, The determination of absolute structure. III. An ambiguity table for the non-centrosymmetric crystal classes, Acta Cryst. A42:57.
Juretschke, H. J., 1982a, Invariant-phase information of X-ray structure factors in the two-beam Bragg intensity near a three-beam point, Phys.Rev.Lett. 48:1487.
Juretschke, H. J., 1982b, Non-centrosymmetric effects in the integrated two-beam Bragg intensity near a three-beam point, Phys.Lett. A92:183.
Juretschke, H. J., 1984, Modified two-beam description of X-ray fields and intensities near a three-beam diffraction point. general formulation and first-order solution, Acta Cryst. A40:379.
Kurinov, I. V. and Harrison, R. W., 1995, The influence of temperature on lysozyme crystals, structure and dynamics of protein and water, Acta Cryst. D51:98.
Laue von, M., 1960, Röntgenstrahl-Interferenzen, Akademische Verlagsgesellschaft m. b. H., Frankfurt/Main.
Lipscomb, W. N., 1949, Relative phases of diffraction maxima by multiple reflection, Acta Cryst. 2:193.
Mo, F., Hauback, B. C., and Thorkildsen, G., 1988, Physical estimation of X-ray triplet phases in a centrosymmetric, mosaic crysal with unit cell volume ~ 3000 Å3, Acta Chem. Scand. A42:130.
Moon, R. M. and Shull, C. G., 1964, The effects of simultaneous reflection on single-crystal neutron diffraction intensities, Acta Cryst. A17:805.
Renninger, M., 1937, Röntgenometrische Beiträge zur Kenntnis der Ladungsverteilung im Diamantgitter, Z Kristallogr. 97:107.
Rogers, D., 1980, Definition of origin and enantiomorph and calculation of |E| values, in:Theory and Practice of Direct Methods in Crystallography, M. F. C. Ladd and R. A. Palmer, ed., Plenum Press, New York.
Schutte, W. J. and Boer de, J. L., 1988, Valence fluctuations in the incommensurately modulated structure of calaverite AuTe2, Acta Cryst. B44:486.
Shen, Q. and Colella, R., 1988, Phase observation in an organic crystal (benzil: C 14 H 10 O 2) using long-wavelength X-rays, Acta Cryst. A44:17.
Tang, M. T. and Chang, S. L., 1988, Quantitative determination of phases of X-ray reflections from three-beam diffractions. II. Experiments for perfect crystals, Acta Cryst. A44:1073.
Thorkildsen G 1987, Three-beam diffraction in a finite perfect crystal, Acta Cryst. A43:361.
Weckert, E. and Hümmer, K., 1990, On the quantitative determination of triplet phases by X-ray three beam diffraction, Acta Cryst. A46:387.
Weckert, E., Schwegle, W., and Hümmer, K., 1993, Direct phasing of macromolecular structures by three-beam diffraction, Proc. R. Soc. Lond. A 442:33.
Wolf de, P. M., Janssen, T., and Janner, A., 1981, The superspace groups for incommensurate crystal structures with a one-dimensional modulation, Acta Cryst. A37:625.
Zachariasen, W. H., 1967, A general theory of X-ray diffraction in crystals, Acta Cryst. 23:558.
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Hümmer, K., Weckert, E. (1996). Determination of Reflection Phases by Three-Beam Diffraction. In: Authier, A., Lagomarsino, S., Tanner, B.K. (eds) X-Ray and Neutron Dynamical Diffraction. NATO ASI Series, vol 357. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5879-8_24
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