Experimental tests of the statistical dynamical theory

Abstract

(nln2n3n4nsn6) can be written as h = nt + n4-n5 k = n2 + n4 + n5 (17) It = n 3 "31-n6 12 = --2n 3 --n6.Previously the diffraction spots of the o-' phase were indexed on the bases of the incommensurate composite structure (Cheng et al., 1991). After carefully analyzing the simulated and experimental EDPs of the tr' phase, the sublattice parameter of substructure II along the c direction should be doubled to c2= 7.42/~. Thus, the four indices hklll 2 based on a phason-defected 1D quasicrystal are coincident with those based on the 1D incommensurate composite structure. This confirms once again that the description proposed in the present paper is equivalent to the regular description.In principal, such a description is generally applicable for all 1D incommensurate composite crystals.As a conclusion, the incommensurate composite o-' phase is described as the intermediate state between a fictitious 1D tetragonal quasicrystal and the commensurate o-phase. In other words, the incommensurate o-' phase and commensurate o-phase can be treated as a phason-defected 1D quasicrystal although the 1D quasicrystal is fictitious and has not been found in the A1-Cu-Fe alloy thus far. This implies that the incommensurate composite structure that shows two independent periodicities along the same direction may have some inherent relation with quasiperiodicity.YFC thanks Professor Renhui Wang and Dr J G Wen for useful discussions. Lett. 63, 49-55. DUNEAU, M. & KATZ, A. (1985). Phys. Rev. Lett. 54, 2688-2691. EESER, V. (1986. Acta Cryst. A42, 36-43. FENG, Y. C., Lo, G., YE, H. Q., Kuo, K. H., WITHER, R. L. & VAN TENDELOO, G. (1990). J. Phys. Condens. Matter, 2, 9749-9755. JANNER, A. & JANSSEN, T. (1980). Acta Cryst. A36, 408-415. KALUGIN, A., KITAEV, A. & LEVITOV, L. (1985). Pis'maZh. Eksp. Teor. Fiz. 41, 119-121. KRAMER, P. & NERI, R. (1984). Acta Cryst. A40, 580-587. DE (1974). Acta Cryst. A30, 777-785. WOLFF, P. M. DE (1977). Acta Cryst. A33, 493-497. YAMAMOTO, A. & HIRAGA, K. (1988). Phys. Rev. B, 37, 6207-6214. Acta Cryst. (1992) . AbstractA homogeneous distribution of SiO2 precipitates in Czochralski-grown silicon containing different amounts of oxygen were produced by annealing the dislocation-free crystals at 1023 K. The resulting long-* Present address: Seikei University, Department of Economics, Kichijojikita-machi 3-3-1, Musashino-shi, Tokyo 180, Japan.0108-7673/92/060804-16506.00 range strain field modifies the integrated reflecting power R of the Bragg reflections measured on an absolute scale with 316 keV y-radiation. The thickness dependence of R has been modelled using the results of statistical dynamical theory. The assumption made in Kato's original theory, where the correlation length F for the wave-field amplitudes is proportional to the extinction length, has to be abandoned.© 1992 International Union of Crystallography J. R. SCHNEIDER, R. BOUCHARD, H. A. GRAF AND H. NAGASAWA 805 Recent modifications to statistical dynamical theory by Becker & A1 Haddad [Acta Cryst. (1990). A46, 123-139] lead to e...

Diffusion-driven precipitate growth and ripening of oxygen precipitates in boron doped silicon by dynamical x-ray diffraction

“…The BF and DF images taken under two beam condition for (004) show pronounced strain contrast making it difficult to unambiguously determine the shape of the precipitate. In contrast, the images taken under two beam condition for (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) clearly reveal that the precipitate has a plate-like character and lies on the (001) plane. From the smallest width of the contrast, the thickness of the precipitates can be roughly estimated.…”

“…Related to this functionality, it is crucial to have control over the density, size, and morphology of the precipitates. Diffraction techniques 2,3 and in particular dynamical X-ray diffraction expressed by Pendell€ osung fringes [4][5][6] are highly sensitive to the volume misfit between the precipitated phase and the host lattice, which is the origin of the strain fields. As an additional benefit, these techniques are capable of in-situ experiments at high temperature, which allows the monitoring of the entire precipitation kinetics.…”

Integral Structure Perfection Diagnostics of Single Crystals Using Two Wavelengths of X-Ray Spectrum

“…The value of the Debye-Waller factor (L = 0.004) in the initial state of the crystal was close to the meaning of these parameters known for Cz-Si crystals with a high oxygen concentration [4][5][6]. It testifies the reliability of the proposed procedure for determination of the L. The calculated data concerning the n and r parameters determined by utilizing the pd value are reasonable, too.…”

“…Such approximation fulfils even more exactly in the case of the gamma-radiation [6]. In the case of a thick crystal the approximation of the R; value depends on the both integral parameters of structure perfection.…”

“…a concentration n and characteristic radius r, entering the corresponding expressions for the Debye-Waller factor L [1][2][3] and the coefficient of pd, additional energy losses of X-rays due to diffuse scattering on defects, determine finally the value of the integral reflectivity Ri of a dislocation-free real crystal. There are several experimental methods basing on the Ri measurements which permit to obtain the integral characteristics of structure perfection of a crystal (L, pd) [3][4][5][6][7]. Also several combinations of these methods exist [8,9].…”