Difference between revisions of "Dynamical theory"
From Online Dictionary of Crystallography
AndreAuthier (talk | contribs) |
AndreAuthier (talk | contribs) |
||
| Line 2: | Line 2: | ||
== Overview == | == Overview == | ||
| − | In the geometrical, or [[ | + | In the geometrical, or [[kinematical theory]], the amplitudes diffracted by a three-dimensional periodic assembly of atoms (Laue) or by a stack of planes (Darwin) is derived by adding the amplitudes of the waves diffracted by each atom or by each plane, simply taking into account the optical path differences between them, but neglecting the interaction of the propagating waves and matter. This approximation is not compatible with the law of conservation of energy and is only valid for very small or highly imperect crystals. The purpose of the dynamical theory is to take these interaction into account. There are three forms of the dynamical theory: |
== Darwin's theory == | == Darwin's theory == | ||
| Line 15: | Line 15: | ||
== History == | == History == | ||
| − | + | * Laue's geometrical theory: Friedrich W., Knipping P. & Laue M. von (1912), ''Sitzungsberichte der Kgl. Bayer. Akad. der Wiss.'', 303-322, reprinted in ''Ann. Phys.'' (1913), '''41''', 971. Interferenz-Erscheinungen bei Röntgenstrahlen.<br> | |
| − | + | * Darwin's geometrical theory: Darwin C.G., (1914), ''Phil. Mag.'', '''27''', 315-333. ''The Theory of X-ray Reflection''.<br> | |
| − | + | * Darwin's geometrical theory: Darwin C.G., (1914), ''Phil. Mag.'', '''27''', 675-690. ''The Theory of X-ray Reflection. Part II''.<br> | |
| − | + | * Ewald's dynamical theory: Ewald P.P. (1917), Ann. Physik, '''54''', 519-597, ''Zur Begründung der Kristalloptik. III. Die Kristalloptik der Röntgenstrahlen.''<br> | |
| − | + | * Laue's dynamical theory: Laue M. von, (1931), ''Ergeb. Exakt. Naturwiss.'', '''10''', 133-158, ''Die dynamische Theorie der Röntgenstrahlinterferenzen in neuer Form.'' & (1931), ''Röntgenstrahl-Interferenzen.'', Akademische Verlagsgesellschaft, Frankfurt am Main.<br> | |
For a detailed eaccount of the historical developments, see P. P. Ewald, 1962, IUCr, [http://www.iucr.org/iucr-top/publ/50YearsOfXrayDiffraction/ 50 Years of X-ray Diffraction], Section 15. | For a detailed eaccount of the historical developments, see P. P. Ewald, 1962, IUCr, [http://www.iucr.org/iucr-top/publ/50YearsOfXrayDiffraction/ 50 Years of X-ray Diffraction], Section 15. | ||
Revision as of 07:21, 26 February 2006
Théorie dynamique (Fr). Dynamische Theorie (Ge). Teoria dynámica (Sp).
Overview
In the geometrical, or kinematical theory, the amplitudes diffracted by a three-dimensional periodic assembly of atoms (Laue) or by a stack of planes (Darwin) is derived by adding the amplitudes of the waves diffracted by each atom or by each plane, simply taking into account the optical path differences between them, but neglecting the interaction of the propagating waves and matter. This approximation is not compatible with the law of conservation of energy and is only valid for very small or highly imperect crystals. The purpose of the dynamical theory is to take these interaction into account. There are three forms of the dynamical theory:
Darwin's theory
Charles Darwin (the grandson of the author of the theory of evolution) takes into account the interaction between the waves partially transmitted and partially reflected at each atomic plane by recurrence equations.
Ewald's theory
Laue's theory
History
- Laue's geometrical theory: Friedrich W., Knipping P. & Laue M. von (1912), Sitzungsberichte der Kgl. Bayer. Akad. der Wiss., 303-322, reprinted in Ann. Phys. (1913), 41, 971. Interferenz-Erscheinungen bei Röntgenstrahlen.
- Darwin's geometrical theory: Darwin C.G., (1914), Phil. Mag., 27, 315-333. The Theory of X-ray Reflection.
- Darwin's geometrical theory: Darwin C.G., (1914), Phil. Mag., 27, 675-690. The Theory of X-ray Reflection. Part II.
- Ewald's dynamical theory: Ewald P.P. (1917), Ann. Physik, 54, 519-597, Zur Begründung der Kristalloptik. III. Die Kristalloptik der Röntgenstrahlen.
- Laue's dynamical theory: Laue M. von, (1931), Ergeb. Exakt. Naturwiss., 10, 133-158, Die dynamische Theorie der Röntgenstrahlinterferenzen in neuer Form. & (1931), Röntgenstrahl-Interferenzen., Akademische Verlagsgesellschaft, Frankfurt am Main.
For a detailed eaccount of the historical developments, see P. P. Ewald, 1962, IUCr, 50 Years of X-ray Diffraction, Section 15.
See also
Section 5.1 of International Tables of Crystallography, Volume B for X-rays
Section 5.2 of International Tables of Crystallography, Volume B for electrons
Section 5.3 of International Tables of Crystallography, Volume B for neutrons