Image Processing Systems Institute, Russian Academy of Sciences,
Samara State Aerospace University
Full text of article: Russian language.
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Abstract:
In the Introduction section, we offer a historical overview of main experimental and theoretical developments in the field of X-ray crystal analysis. The main part contains a differential approach to solving the problem of diffraction of X-rays by crystals within the scalar theory. Examples of numerical simulation for the basic types of crystal lattices are included.
Keywords:
X-ray diffraction, diffraction by crystals, differential method, the basic types of crystal lattices.
Citation:
Kharitonov SI, Volotovskiy SG, Khonina SN, Kazanskiy NL. A differential method for calculating x-ray diffraction by crystals: the scalar theory. Computer Optics 2015; 39(4): 469-79. DOI: 10.18287/0134-2452-2015-39-4-469-479.
References:
- Nature Milestones in Crystallography. Source: <http://www.nature.com/milestones/milecrystal/index.html>.
- Haüy RJ. Essai d’une Théorie sur la Structure des Crystaux. Gogué et Née de La Rochelle, 1784.
- Bravais A. Mémoire sur les systèmes formés par des points distribués regulièrement sur un plan ou dans l’espace. J l’Ecole Polytechnique 1850 ; 19 : 1.
- Fedorov ES. The elements of the study of configurations (in Russian). Trans Mineral Soc 1885; 21: 240.
- Fedorov ES. The symmetry of real systems of configura-tions (in Russian). Trans Mineral Soc Vol. 1891; 28: 1-146.
- Bragg WL. The specular reflection of X-rays. Nature 1912; 90: 410.
- Bragg WL. The structure of crystals as indicated by their diffraction of X-rays. Proc Royal Soc Lond A 1913; 89: 248-77.
- Bragg WH, Bragg WL. The structure of the diamond. Nature 1913; 91: 557.
- Bragg WH, Bragg WL. The X-ray spectrometer. Nature 1914; 94: 199-200.
- Pinsker ZG. Dynamic X-ray scattering in perfect crystals (in Russian). Moscow: "Nauka" Publisher, 1974.
- James RW. The optical principles of the diffraction of x-rays. London: G. Bell & Sons, 1948.
- Zachariasen WH. Theory of X-ray Diffraction in Crystals. Mineola, N.Y.: Dover, 2004.
- James RW. The Dynamical Theory of X-Ray Diffraction. Solid State Physics 1963; 15: 53-220.
- Borrmann G. Über Extinktionsdiagramme der Röntgenstrahlen von Quarz. Zeitschrift für Physik 1941; 42: 157-62.
- Borrmann G. Die Absorption von Röntgenstrahlen in Fall der Interferenz. Zeitschrift für Physik 1950; 127: 297-323.
- Borrmann G. Der kleinste Absorptionskoeffizient interferierender Rontgenstrahlung. Zeitschrift für Kristallographie 1954; 106: 109-21.
- Laue M. Die Absorption der Röntgenstrahlen in Kristallen im Interferenzfall. Acta Crystallographica 1949; 2: 106-13.
- Renninger M. Verstärkung schwacher und Vortäuschung verbotener Röntgenreflexe durch „Umweganregung“. Naturwissenschaften 1937; 25(3): 43. DOI: 10.1007/BF01492117.
- Borrmann G, Hartwig W. Die Absorption der Röntgenstrahlen im Dreistrahlfall der Interferenz. Zeitschrift für Kristallographie 1965; 121: 401-9.
- Ewald PP, Héno Y. X-ray diffraction in the case of three strong rays. I. Crystal composed of non-absorbing point atoms. Acta Crystallographica Section A 1968; 24(1): 5-15. DOI: 10.1107/S0567739468000033.
- Héno Y, Ewald PP. Diffraction des rayons X dans le`cas de trois rayons forts'. II. Influence de l'absorption et du facteur de diffusion atomique. Acta Crystallographica Section A 1968 ; 24(1) : 16-42. DOI: 10.1107/S0567739468000045.
- Hildebrandt G. Röntgenwellenfelder in einem Dreistrahlfall. Physica status solidi (b) 1967 ; 24(1) : 245-61.
- Afanasiev AM, Kagan Yu. The Role of Lattice Vibration in Dynamical Theory of X-Rays. Acta Crystallographica 1968; A24(2): 163-70.
- Wooster WA. Diffuse X-Ray reflections from crystals. Oxford: Clarendon Press, 1962.
- Penning P, Polder D. Anomalous transmission of X-rays in elactically deformad crystals. Philips Research Reports 1961; 16: 419-40.
- Kato N. Pendellösung fringes in distorted crystals i. fermat's principle for bloch waves. Journal of the Physical Society of Japan 1963; 18: 1785-91.
- Kato N. Pendellösung fringes in distorted crystals iii. application to homogeneously bent crystals. Journal of the Physical Society of Japan 1964; 19(67): 971-85.
- Takagi S. Dynamical theory of diffraction applicable to crystals with any kind of small distortion. Acta Crystallographica 1962; 15: 1311-2.
- Takagi S. A Dynamical theory of diffraction for a distorted crystals. Journal of the Physical Society of Japan 1969; 26: 1239-53.
- Slobodetskii ISh, Chukhovskii FN, Indenbom TL. X-ray Diffraction Under Conditions of the Spatially-inhomogeneous Dynamic Problem. JETP Letters 1968; 8(2): 55-8.
- Authier A. Application de la theorie dynamique de S. Takagi au contraste d'un defaut plan en topographie par rayons X. I. Faute d'empilement. Acta Crystallographica 1968; A24: 517-26.
- Indenbom TL, Chukhovskii FN. The problem of the im-aging in X-ray optics – Preprint (in Russian). Moscow: Institute of Crystallography, USSR Academy of Sciences, 1971.
- Landau J, Groscurth CR, Wright L, Condit CM. Visualizing Nanotechnology: The Impact of Visual Images on Lay American Audience Associations with Nanotechnology. Public Understanding of Science 2009; 18(3): 325-37.
- Milburn C. Nanovision: Engineering the Future. Durham: Duke University Press, 2008.
- Soifer VA, Kupriyanov AV. Analysis and recognition of the nanoscale images: conventional approach and novel problem statement (in Russian). Computer Optics 2011; 35(2): 136-44.
- Kupriyanov AV, Soifer VA. On the observability of the crystal lattice with the images of their projections (in Russian). Computer Optics 2012; 36(2): 249-56.
- Born M, Wolf E. Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (4th Edition). New York: Pergamon Press, 1969.
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