Simultaneous reflections and the mosaic spread in a crystal plate

Caticha‐Ellis, S.

doi:10.1107/s0567739469001525

Cited by 39 publications

(30 citation statements)

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“…This is clearly demonstrated in Fig. 1, which shows (a) a complete 0 scan for the weak 200 reflection and (b) the corresponding simulation of (a) using the computer programs UM WEG of Prager (1971) (for peak positions) and MDDSCRM of Stevenson (1983) [which provides an approximate intensity calculation and uses the polarization corrections of Caticha-Ellis (1969)]. In an attempt to avoid multiple-diffraction effects, every reflection was measured at six different azimuthal positions (0 and 0+ 180 ° for 0=0 and +_1 °) and the outlying pair of measurements discarded.…”

Section: Methodsmentioning

confidence: 99%

Thermal vibrations and bonding in GaAs: an extended-face crystal study

Stevenson¹

1994

Acta Cryst Sect A

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Accurate X-ray integrated-intensity data collected from an extended-face crystal of GaAs are analysed to provide detailed information on the thermal vibrations of atomic species, including cubic anharmonicity, at room temperature. The values obtained for the thermal parameters are BGa = 0.622 (3) A 2, B s = 0.483(5)A 2 and ~GaAs'-" --0.6(1) X 10-18jX -3 (defined in the text). The inclusion of cubic anharmonic thermal vibrations is shown to be highly significant. In order to interpret the data collected for certain low-angle Bragg reflections for which m h + k + l = 4n + 2 (in particular, 200, 222 and 222), it is necessary to consider bonding effects. It is shown that there is a net transfer of electron charge from gallium to arsenic [Q --0.12 (3) e] and that the inclusion of bonding effects in the least-squares analysis is highly significant. The analysis includes allowance for the extremely severe extinction effects present for such a perfect sample (minimum extinction factor 0.286). The refined value of the mean radius of © 1994 International Union of Crystallography Printed in Great Britain -all rights reserved perfect-crystal domains is 4.6 (2)I~m. The final fit, for 153 independent Bragg reflections, is excellent, as indicated by the weighted R factor of 0.683% and the goodness-of-fit parameter of 1.083. The results of the least-squares analysis are compared for the cases of relativistic Hartree-Fock, Thomas-Fermi-Dirac and relativistic Dirac-Slater atomic scattering factors, the former being favoured.

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Section: Methodsmentioning

confidence: 99%

Thermal vibrations and bonding in GaAs: an extended-face crystal study

Stevenson¹

1994

Acta Cryst Sect A

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“…The MD events assuming either ideally imperfect or highly perfect crystals have been studied by several authors, namely Chang (1984), Caticha-Ellis (1969), Moon & Shull (1964), Colella (1974) and Pinsker (1977). In the ideally imperfect crystal, small perfect regions (mosaic blocks) diffract according to the kinematical theory and the diffracted beams are the sum of incoherent intensities scattered by several mosaic blocks.…”

Section: Mosaic Crystalsmentioning

confidence: 99%

“…At the same time, other blocks are under Bragg condition for the 21 reflection and thus enhance the beam 1 intensity. According to Caticha-Ellis (1969), the peak profile in a three-beam case is better defined when the 01 reflection is forbidden by the crystal space group or is very weak in comparison with 02 and 21 reflections. Then, assuming an isotropic Gausian distribution of block misorientation, the peak profile for a mosaic crystal will be given by the following expression:…”

Section: Mosaic Crystalsmentioning

confidence: 99%

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

Morelhão¹,

Cardoso²

1996

J Appl Cryst

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In this work, a method that takes advantage of the threedimensional nature of the X-ray multiple-diffraction (MD) phenomenon for evaluating the crystalline perfection of semiconductors is proposed. The energy-transfer process among the MD beams can occur in a kinematical (secondary extinction) or a dynamical (primary extinction) regime. The effects that each regime can have on MD Bragg condition are theoretically investigated. The method provides information on size and misorientation of perfect-crystal regions as well as on the probability of interaction between them. The perfection of GaAs and Ge (001) surfaces after mechanical and/or chemical polishing has been investigated with this method and, as an extension of its applicability, porous silicon and GaAs (001) with Se ions implanted were also investigated.

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“…The profile of these peaks is the convolution of the diffraction condition for the secondary and coupling reflections. According to Caticha-Ellis (1969), the profile of a BSD peak in a three-beam case is better defined when the 01 reflection is forbidden by the crystal space group or is very weak in comparison with the 02 and 21 reflections. When a BSD with a forbidden or very weak Bragg reflection is chosen, the diffraction regime (dynamical, kinematical or mixed) depends on the perfect region dimension (block) parallel to the crystal surface (Morelhã o & Cardoso, 1996).…”

Section: X-ray Multiple Diffractionmentioning

confidence: 99%

Lattice strain distribution resolved by X-ray Bragg-surface diffraction in an Si matrix distorted by embedded FeSi₂nanoparticles

Lang

Menezes²,

Santos³

et al. 2013

J Appl Cryst

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Out-of-plane and primarily in-plane lattice strain distributions, along the two perpendicular crystallographic directions on the subsurface of a silicon layer with embedded FeSi 2 nanoparticles, were analyzed and resolved as a function of the synchrotron X-ray beam energy by using !:' mappings of the (111) and (111) Bragg-surface diffraction peaks. The nanoparticles, synthesized by ionbeam-induced epitaxial crystallization of Fe + -implanted Si(001), were observed to have different orientations and morphologies (sphere-and plate-like nanoparticles) within the implanted/recrystallized region. The results show that the shape of the synthesized material singularly affects the surrounding Si lattice. The lattice strain distribution elucidated by the nonconventional X-ray Bragg-surface diffraction technique clearly exhibits an anisotropic effect, predominantly caused by plate-shaped nanoparticles. This type of refined detection reflects a key application of the method, which could be used to allow discrimination of strains in distorted semiconductor substrate layers.

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Simultaneous reflections and the mosaic spread in a crystal plate

Cited by 39 publications

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Thermal vibrations and bonding in GaAs: an extended-face crystal study

Thermal vibrations and bonding in GaAs: an extended-face crystal study

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

Lattice strain distribution resolved by X-ray Bragg-surface diffraction in an Si matrix distorted by embedded FeSi₂nanoparticles

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Simultaneous reflections and the mosaic spread in a crystal plate

Cited by 39 publications

References 0 publications

Thermal vibrations and bonding in GaAs: an extended-face crystal study

Thermal vibrations and bonding in GaAs: an extended-face crystal study

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

Lattice strain distribution resolved by X-ray Bragg-surface diffraction in an Si matrix distorted by embedded FeSi2nanoparticles

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Lattice strain distribution resolved by X-ray Bragg-surface diffraction in an Si matrix distorted by embedded FeSi₂nanoparticles