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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.


Related in: MedlinePlus

Schematic illustration to explain the generation of moiré fringes based on equation (37c) with Δρ = 0.
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fig4: Schematic illustration to explain the generation of moiré fringes based on equation (37c) with Δρ = 0.

Mentions: As seen from the above discussion, in equation (37a) is a vector on surface b. Therefore, the moiré phase in equations (37a)–(37c) is practically determined on surface b. The observed moiré fringes are related to such a moiré phase. An experimental fact evidencing this point is that regarding moiré dislocations. As illustrated in Fig. 4 ▸, the moiré phase increases by 2π to add one moiré fringe, every site where the positions of two sets of lattice planes having a difference of exactly coincide with each other. In this property, moiré fringes may be referred to as a counter of excess or deficient lattice planes. From this viewpoint, it can be well understood that, when a dislocation outcrops on one of the facing surfaces a′ or b, the moiré pattern sensitively responds to it to form a moiré dislocation. As Lang (1968 ▸) demonstrated, only such dislocations as outcropping on the inner facing surfaces give rise to moiré dislocations, and other dislocations do not affect the moiré pattern. Diffraction moiré fringes, though being interference fringes of light waves, produce a moiré pattern of superposed lattice planes by the same mechanism as geometrical moiré patterns. It is difficult to consider that a discontinuity in the lattice-plane arrangement such as that in Fig. 4 ▸ can occur on boundaries or surfaces other than those where the lattice cut actually occurs, as in a bicrystal and a cracked crystal. We now arrive at an inference that the absence of the lattice cut as above would be the reason why moiré fringes have not been found in diffraction images of growth-sector boundaries, despite the occurrence of . Discussion and analysis on moiré fringes agreeing with the above discussion of equation (37a) have also been given by Ohler et al. (1999 ▸). Although the discussion in this section has in substance been written in Yoshimura (1997a ▸), it was rewritten here to revive the previous remark on the two-dimensionality of the moiré pattern and to complete the moiré theory here.


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

Yoshimura J - Acta Crystallogr A Found Adv (2015)

Schematic illustration to explain the generation of moiré fringes based on equation (37c) with Δρ = 0.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig4: Schematic illustration to explain the generation of moiré fringes based on equation (37c) with Δρ = 0.
Mentions: As seen from the above discussion, in equation (37a) is a vector on surface b. Therefore, the moiré phase in equations (37a)–(37c) is practically determined on surface b. The observed moiré fringes are related to such a moiré phase. An experimental fact evidencing this point is that regarding moiré dislocations. As illustrated in Fig. 4 ▸, the moiré phase increases by 2π to add one moiré fringe, every site where the positions of two sets of lattice planes having a difference of exactly coincide with each other. In this property, moiré fringes may be referred to as a counter of excess or deficient lattice planes. From this viewpoint, it can be well understood that, when a dislocation outcrops on one of the facing surfaces a′ or b, the moiré pattern sensitively responds to it to form a moiré dislocation. As Lang (1968 ▸) demonstrated, only such dislocations as outcropping on the inner facing surfaces give rise to moiré dislocations, and other dislocations do not affect the moiré pattern. Diffraction moiré fringes, though being interference fringes of light waves, produce a moiré pattern of superposed lattice planes by the same mechanism as geometrical moiré patterns. It is difficult to consider that a discontinuity in the lattice-plane arrangement such as that in Fig. 4 ▸ can occur on boundaries or surfaces other than those where the lattice cut actually occurs, as in a bicrystal and a cracked crystal. We now arrive at an inference that the absence of the lattice cut as above would be the reason why moiré fringes have not been found in diffraction images of growth-sector boundaries, despite the occurrence of . Discussion and analysis on moiré fringes agreeing with the above discussion of equation (37a) have also been given by Ohler et al. (1999 ▸). Although the discussion in this section has in substance been written in Yoshimura (1997a ▸), it was rewritten here to revive the previous remark on the two-dimensionality of the moiré pattern and to complete the moiré theory here.

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.


Related in: MedlinePlus