Diffraction by a randomly distorted crystal. I. The case of short-range order

Becker, Pierre; Haddad, Moussa

doi:10.1107/s0108767389010457

Cited by 40 publications

(8 citation statements)

References 9 publications

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Section: Results Of Statistical Dynamical Theorymentioning

confidence: 99%

“…Becker & A1 Haddad (1989bHaddad ( , 1990) revised Kato's original approach to statistical dynamical theory and showed that the correlation length F for the wavefield amplitudes is variable within the sample and that it fluctuates around a value of the order of the short-range-correlation length ~-, rather than being constant and of the order of the extinction length A, as proposed with some reservation by Kato (1980a). The expression i~B&A • -=it given by Becker & A1 Haddad (1989b [~e -( T/ tze-t-1/ tz2) exp (-tzeT),…”

Section: E=exp[-(2"rr2/3)h2(u2)]mentioning

confidence: 99%

“…GOF = 0.6, R = 1.8%. Haddad (1989bHaddad ( , 1990 [ (22)] had therefore been fitted to all the data sets shown in Fig. 2.…”

Section: Determination Of Static Debye--waller Factorsmentioning

confidence: 99%

“…Because the experimental data are corrected for absorption, the integrated reflecting power is given for the case of zero absorption. Later, Becker & A1 Haddad (1989bHaddad ( , 1990 Rcoh -t-"-mixThe expressions for the coherent term Rco h are identical for the two approaches. The imperfect nature of the crystal enters the theory via the phase factor ~p(r) defined in (2).…”

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confidence: 99%

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Experimental tests of the statistical dynamical theory

Schneider¹,

Bouchard²,

Graf³

et al. 1992

Acta Cryst Sect A

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(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...

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Section: Results Of Statistical Dynamical Theorymentioning

confidence: 99%

Section: E=exp[-(2"rr2/3)h2(u2)]mentioning

confidence: 99%

“…GOF = 0.6, R = 1.8%. Haddad (1989bHaddad ( , 1990 [ (22)] had therefore been fitted to all the data sets shown in Fig. 2.…”

Section: Determination Of Static Debye--waller Factorsmentioning

confidence: 99%

mentioning

confidence: 99%

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Experimental tests of the statistical dynamical theory

Schneider¹,

Bouchard²,

Graf³

et al. 1992

Acta Cryst Sect A

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“…Kato (1991) has recently presented a new discussion of the foundations of the statistical diffraction theory using wave equations that are more general than the Takagi-Taupin equations. The present paper is strictly related to the formulation of Kato (1980a, b), including the modifications introduced by Al Haddad & Becker (1988), by Becket & A1 Haddad (1989Haddad ( , 1990 and by Guigay (1989):. In this formulation the coherent waves have the simple form given in (13), which is expected to be a good approximation in the region around the middle of the Borrmann fan.…”

Section: The General Case E #mentioning

confidence: 99%

Reformulation of the dynamical theory of coherent wave propagation by randomly distorted crystals

Guigay¹,

Chukhovskii²

1992

Acta Cryst Sect A

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The coherent terms in the spherical-wave approach of the statistical dynamical theory are reformulated using rigorous boundary conditions in contrast to the intuitive boundary conditions of the original formulation by Kato [Acta Cryst. (1980), A36, 763-769, 770-778]. These boundary conditions are explained physically by a general interference effect between the forward-diffracted wave and the incident undiffracted wave (using the optical theorem) and their consequences on the total (Bragg and forward-diffracted) incoherent intensity are also discussed.

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Bragg Diffraction of X-Rays by Single Crystals with Large Microdefects I. Generalized Dynamical Theory

Molodkin

Olikhovskii

Kislovskii

et al. 2001

phys. stat. sol. (b)

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Basic equations of the dynamical scattering theory in momentum space have been considered in the two-beam approximation for single crystals containing randomly distributed microdefects commensurable with extinction length. The amplitudes of coherent and diffusely scattered waves inside the crystal have been found by using the perturbation theory with average and fluctuating parts of crystal polarizability as small parameters. In the complex dispersion corrections to the wave vectors of coherent and diffuse waves, the imaginary parts of which describe the attenuation of these waves due to diffuse scattering, the dynamical effects in diffuse scattering and their dependences on the incidence angle have been taken into account. These corrections also take account of the influence of any multiple diffuse scattering processes. The coherent component of crystal reflectivity has been calculated in the approximation of semiinfinite crystal for an arbitrary diffraction geometry.Osnovnye uravneni¾ dinamiqeskoj teorii rasse¾ni¾ v impul#snom prostranstve rassmotreny v dvuhvolnovom pribliwenii dl¾ monokristallov, soderwa §ih sluqajno raspredelennye mikrodefekty s radiusami por¾dka +kstinkcionnoj dliny. Amplitudy kogerentnyh i diffuzno rasse¾nnyh voln vnutri kristalla najdeny s ispol#zovaniem teorii vozmu §enij so srednej i fluktuacionnoj qast¾mi pol¾rizuemosti krustalla v kaqestve malyh parametrov. V kompleksnyh dispersionnyh popravkah k volnovym vektoram kogerentnyh i diffuznyh voln, mnimye qasti kotoryh opisyvaˇt zatuhanie +tih voln iz-za diffiznogo rasse¾ni¾, uqteny dinamiqeskie +ffekty v diffuznom rasse¾nii i ih zavisimost# ot ugla padeni¾. *ti popravki uqityvaˇt takwe vli¾nie lˇbyh mnogokratnyh processov diffuznogo rasse¾ni¾. Kogerentna¾ komponenta otrawatel#noj sposobnosti kristalla vyqislena v pribliwenii polubeskoneqnogo kristalla dl¾ proizvol#noj geometrii difrakcii.

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Diffraction by a randomly distorted crystal. I. The case of short-range order

Cited by 40 publications

References 9 publications

Experimental tests of the statistical dynamical theory

Experimental tests of the statistical dynamical theory

Reformulation of the dynamical theory of coherent wave propagation by randomly distorted crystals

Bragg Diffraction of X-Rays by Single Crystals with Large Microdefects I. Generalized Dynamical Theory

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