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An exact analytic solution of Darwin's difference equations

1984; Wiley; Volume: 40; Issue: 6 Linguagem: Inglês

10.1107/s0108767384001276

1600-5724

Raymond T. Perkins, Larry V. Knight,

Advanced Thermodynamics and Statistical Mechanics

Darwin derived a system of difference equations which relate the incident and reflected amplitudes of X-rays in a crystal in Bragg diffraction. These equations are recast in matrix form. Using a well known result from optical multilayer theory, an exact analytic solution of these difference equations is obtained for a crystal of an arbitrary number of atomic planes. In the limiting case of a semi-infinite crystal, and with the appropriate approximations, Darwin's expression for the reflectivity of a crystal in Bragg diffraction is obtained.