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Theoretical study of the properties of X-ray diffraction moiré fringes. I.

Yoshimura J - Acta Crystallogr A Found Adv (2015)

Bottom Line: Acta Cryst.Then, the properties of moiré fringes derived from the above theory are explained for the case of a plane-wave diffraction image, where the significant effect of Pendellösung intensity oscillation on the moiré pattern when the crystal is strained is described in detail with theoretically simulated moiré images.Although such plane-wave moiré images are not widely observed in a nearly pure form, knowledge of their properties is essential for the understanding of diffraction moiré fringes in general.

View Article: PubMed Central - HTML - PubMed

Affiliation: Photon Factory, Institute of Materials Structure Science, High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan.

ABSTRACT
A detailed and comprehensive theoretical description of X-ray diffraction moiré fringes for a bicrystal specimen is given on the basis of a calculation by plane-wave dynamical diffraction theory. Firstly, prior to discussing the main subject of the paper, a previous article [Yoshimura (1997). Acta Cryst. A53, 810-812] on the two-dimensionality of diffraction moiré patterns is restated on a thorough calculation of the moiré interference phase. Then, the properties of moiré fringes derived from the above theory are explained for the case of a plane-wave diffraction image, where the significant effect of Pendellösung intensity oscillation on the moiré pattern when the crystal is strained is described in detail with theoretically simulated moiré images. Although such plane-wave moiré images are not widely observed in a nearly pure form, knowledge of their properties is essential for the understanding of diffraction moiré fringes in general.

No MeSH data available.


Dispersion-surface construction for the double diffraction in a bicrystal, with . , . See text for details.
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fig2: Dispersion-surface construction for the double diffraction in a bicrystal, with . , . See text for details.

Mentions: As a model for developing the theory, we consider a bicrystal as shown in Fig. 2 ▸, which is composed of parallel-sided crystals A and B having a difference in their reciprocal-lattice vectors, and a narrow interspace gap between them. For simplicity, the surfaces of crystals A and B are all assumed to be parallel to one another, but the angle between the crystal surfaces and the diffracting lattice plane is taken to be arbitrary, so that the theory can deal with the asymmetric Laue case. If the dielectric susceptibility in crystal A having reciprocal-lattice vector is given by then that in crystal B having the reciprocal-lattice vector is written as [because ]. Here, is the g-th Fourier component of and ; is the displacement in the real lattice of crystal B relative to that in crystal A, corresponding to the occurrence of ; is the position vector denoting the point of on surface b of crystal B. This origin is not a very special point, but is explicitly written here for a later discussion.


Theoretical study of the properties of X-ray diffraction moiré fringes. I.

Yoshimura J - Acta Crystallogr A Found Adv (2015)

Dispersion-surface construction for the double diffraction in a bicrystal, with . , . See text for details.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4487425&req=5

fig2: Dispersion-surface construction for the double diffraction in a bicrystal, with . , . See text for details.
Mentions: As a model for developing the theory, we consider a bicrystal as shown in Fig. 2 ▸, which is composed of parallel-sided crystals A and B having a difference in their reciprocal-lattice vectors, and a narrow interspace gap between them. For simplicity, the surfaces of crystals A and B are all assumed to be parallel to one another, but the angle between the crystal surfaces and the diffracting lattice plane is taken to be arbitrary, so that the theory can deal with the asymmetric Laue case. If the dielectric susceptibility in crystal A having reciprocal-lattice vector is given by then that in crystal B having the reciprocal-lattice vector is written as [because ]. Here, is the g-th Fourier component of and ; is the displacement in the real lattice of crystal B relative to that in crystal A, corresponding to the occurrence of ; is the position vector denoting the point of on surface b of crystal B. This origin is not a very special point, but is explicitly written here for a later discussion.

Bottom Line: Acta Cryst.Then, the properties of moiré fringes derived from the above theory are explained for the case of a plane-wave diffraction image, where the significant effect of Pendellösung intensity oscillation on the moiré pattern when the crystal is strained is described in detail with theoretically simulated moiré images.Although such plane-wave moiré images are not widely observed in a nearly pure form, knowledge of their properties is essential for the understanding of diffraction moiré fringes in general.

View Article: PubMed Central - HTML - PubMed

Affiliation: Photon Factory, Institute of Materials Structure Science, High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan.

ABSTRACT
A detailed and comprehensive theoretical description of X-ray diffraction moiré fringes for a bicrystal specimen is given on the basis of a calculation by plane-wave dynamical diffraction theory. Firstly, prior to discussing the main subject of the paper, a previous article [Yoshimura (1997). Acta Cryst. A53, 810-812] on the two-dimensionality of diffraction moiré patterns is restated on a thorough calculation of the moiré interference phase. Then, the properties of moiré fringes derived from the above theory are explained for the case of a plane-wave diffraction image, where the significant effect of Pendellösung intensity oscillation on the moiré pattern when the crystal is strained is described in detail with theoretically simulated moiré images. Although such plane-wave moiré images are not widely observed in a nearly pure form, knowledge of their properties is essential for the understanding of diffraction moiré fringes in general.

No MeSH data available.