On the treatment of primary extinction in diffraction theories based on intensity coupling

Abstract

461contrast but is crystal-structure dependent when the eye is used to determine changes in image contrast. Thus, quantification of image intensities should be used for accurate composition determination by ARM. Lastly, although this study only considers systems containing two elements, the results indicate that similar principles can be used to interpret the contrast in systems containing combinations of three or more elements. (1983). Inst. Phys. Conf. Ser. No. 68, pp. 185-190. GOODMAN, P. & MOODIE, m. F. (1974). Acta Cryst. A30, 280-290.HIRSCH, P., HOWIE, A., NICHOLSON, R. B., PASHLEY, D. W. & WHELAN, J. (1977). Electron Microscopy of Thin Crystals,. Malabar: R. E. Krieger. HOWE, J. M., DAHMEN, U. & GRONSKY, R. (1987). Philos. Mac. A56, 31-61. HOWIE, A. & BASINSKI, Z. S. (1969). Philos. Mac. 149, 1039-1063. IIJIMA, S. (1977. Optik (Stuttgart), 48,(193)(194)(195)(196)(197)(198)(199)(200)(201)(202)(203)(204)(205)(206)(207)(208). ISAACSON, M. S., LANGMORE, J., PARKER, N. W., KOPF, D. & UTLAUT, M. (1976). Ultramicroscopy, 1,359-376. LYNCH, D. F. & O'KEEFE, M. A. (1972). Acta Cryst. A28, 536-548. MOTT, N. F. (1930). Proc. R. Soc. London Ser. A, 127, 658-672. O'KEEFE, M. A. (1973). Acta Cryst. A29, 389-401. O'KEEFE, M. A. & BUSECK, P. R. (1979). Trans. Am. Crystallogr. Assoc. 15,[27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46] OURMAZD, A. (1987 unrealistic Lorentzian mosaic distribution models the effect of primary extinction in an extinction theory based on the energy-transfer model. The sharp central part of the Lorentzian distribution produces a reduction of the effective sample thickness due to primary extinction, whereas the wings of the distribution dominate the correction for secondary extinction in the remaining part of the sample. A more flexible mosaic distribution function is proposed, which should be useful in cases of severe extinction. IntroductionToday in most accurate structure refinements, the effect of extinction is corrected on the basis of an energy-transfer model presented by Zachariasen (1967) and Becker & Coppens (1974). The imperfections in the crystal are described within Darwin's mosaic model using parameters for the average size of the perfect blocks, and the standard deviation of a Gaussian or a Lorentzian mosaic distribution which describes their angular misorientation. This approach has some basic limitations as discussed by Kato (1976Kato ( , 1979Kato ( , 1980a, who more recently developed a statistical dynamical diffraction theory (Kato, 1980b) which, in principle, covers the full range from dynamical to kinematical diffraction behaviour as a function of two correlation parameters r and E, the first describing short-range and the second long-range correlation. The relative merits of the two approaches to the extinction problem have been discussed by Becker & Dunstetter (1984). People have been puzzled by the fact that the assumption of a Lorentzian mosaic distribution within the conventional energy-transfer coupling model often leads to a be...

Accuracy of single-crystal time-of-flight neutron diffraction: a comparative study of MnF2

“…The overall agreement between the observed and fitted mosaic spread width is excellent. Our results are also in accord with those of Schneider, Gon~alves & Graf (1988) who have shown that the Lorentzian width should be one half of the corresponding Gaussian width (model Z). From this we deduce that the extinction parameters represent a real physical situation and are not only adjustment parameters.…”

X-ray Multiple Diffraction Phenomenon in the Evaluation of Semiconductor Crystalline Perfection

“…In two-beam cases, the extinction distance necessary for occurrence of primary extinction inside one block (perfect crystal) is proportional to the square root of the diffracted beam direction cosine and to the inverse of the real part of the structure factor (Schneider, Gonqalves & Graf, 1988). The use of the strong GaAs 111 reflection under extreme asymmetric conditions (direction cosine of the beam 2 is zero) should diminish the extinction distance of the beam 2 and enhance the primary extinction effect.…”

Experimental tests of the statistical dynamical theory

“…Complementary information on the defect scattering has been obtained from neutron back-scattering experiments performed on the same samples Liss, Magerl, Schneider & Zulehner, 1991). Because of the expected statistical nature of the defects, Cz silicon crystals, heat treated at temperatures above 1273 K, have been used to test extinction models based on Darwin's mosaic model (Schneider, Gon~alves & Graf, 1988).…”

“…Complementary information on the defect scattering has been obtained from neutron back-scattering experiments performed on the same samples Liss, Magerl, Schneider & Zulehner, 1991). Because of the expected statistical nature of the defects, Cz silicon crystals, heat treated at temperatures above 1273 K, have been used to test extinction models based on Darwin's mosaic model (Schneider, Gon~alves & Graf, 1988).In the present paper, [001] grown silicon crystals containing approximately 7.7 and 18 × 1017 O atoms cm -3 that have been annealed at 1043 and 1023 K, respectively, are studied. They should contain different amounts of SiO2 precipitates of different shape and size but no dislocations.…”