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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.

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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.


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Moiré images of transmitted wave (O wave), computed under the same conditions as for Figs. 6 ▸ and 8(a) ▸ regarding the values of , , the crystal and gap thicknesses and the crystal curvature; . (a) Moiré image when zero absorption was assumed. (b) Moiré image when the real value of absorption was used.
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fig14: Moiré images of transmitted wave (O wave), computed under the same conditions as for Figs. 6 ▸ and 8(a) ▸ regarding the values of , , the crystal and gap thicknesses and the crystal curvature; . (a) Moiré image when zero absorption was assumed. (b) Moiré image when the real value of absorption was used.

Mentions: Figs. 13 ▸(a), 13 ▸(b) show moiré images computed for a parallel moiré of and , with the assumption of no curvature () and the curvature of s = 0.045′′ per mm in crystal B, respectively. The deviation parameters u, and were calculated by equations (43) and (44a), (44b) in the same way as for Fig. 8 ▸(a). Though not so large as to be easily noticed without close comparison, the fringe spacing in Fig. 13 ▸(b) is modified relative to that in Fig. 13 ▸(a). The image intensity in Fig. 13 ▸(b) is also considerably modified compared with that in Fig. 13 ▸(a). (The intensity modulation was large and rapid at , and therefore the images at of a weaker modulation are presented.) Thus, the combined effect of the crystal curvature and the PL phase can also be seen in such differences between the two images of parallel moiré. Finally, an example of moiré images of the O wave is shown in Figs. 14 ▸(a), 14 ▸(b), although the associated intensity equation was omitted. The computation was conducted using the same values of , , s, , and , as for Fig. 8 ▸(a). Fig. 14 ▸(a) shows the image when zero absorption was assumed and is to be compared with Fig. 6 ▸. Fig. 14 ▸(b) was computed with the real value of absorption, and is compared with Fig. 8 ▸(a). Calculated curves of fringe contrast and of phase-related variables , and associated with the image in Fig. 14 ▸(b) are shown in Fig. 15 ▸(a). [, and correspond to , and for the G image, respectively.] The fringe pattern in Fig. 14 ▸(a) is almost the same as that in Fig. 6 ▸, but the fringe position is displaced by half a period, as shown in the top figure in Fig. 15 ▸(b). As the intensity profiles of these two fringe patterns show, the complementarity of diffracted intensities between the O and G images holds in this case. When absorption has the real value, vertical bands of abrupt fringe jumps in the O and G images are displaced from each other by nearly half the interval, as can be seen in Fig. 8 ▸(a) and Fig. 14 ▸(b). On the other hand, their fringe positions come nearer to each other, as shown in the bottom figure in Fig. 15 ▸(b). A comparison of experimental O and G images of moiré fringes in such a relation has been presented in Yoshimura (1997a ▸).


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

Yoshimura J - Acta Crystallogr A Found Adv (2015)

Moiré images of transmitted wave (O wave), computed under the same conditions as for Figs. 6 ▸ and 8(a) ▸ regarding the values of , , the crystal and gap thicknesses and the crystal curvature; . (a) Moiré image when zero absorption was assumed. (b) Moiré image when the real value of absorption was used.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig14: Moiré images of transmitted wave (O wave), computed under the same conditions as for Figs. 6 ▸ and 8(a) ▸ regarding the values of , , the crystal and gap thicknesses and the crystal curvature; . (a) Moiré image when zero absorption was assumed. (b) Moiré image when the real value of absorption was used.
Mentions: Figs. 13 ▸(a), 13 ▸(b) show moiré images computed for a parallel moiré of and , with the assumption of no curvature () and the curvature of s = 0.045′′ per mm in crystal B, respectively. The deviation parameters u, and were calculated by equations (43) and (44a), (44b) in the same way as for Fig. 8 ▸(a). Though not so large as to be easily noticed without close comparison, the fringe spacing in Fig. 13 ▸(b) is modified relative to that in Fig. 13 ▸(a). The image intensity in Fig. 13 ▸(b) is also considerably modified compared with that in Fig. 13 ▸(a). (The intensity modulation was large and rapid at , and therefore the images at of a weaker modulation are presented.) Thus, the combined effect of the crystal curvature and the PL phase can also be seen in such differences between the two images of parallel moiré. Finally, an example of moiré images of the O wave is shown in Figs. 14 ▸(a), 14 ▸(b), although the associated intensity equation was omitted. The computation was conducted using the same values of , , s, , and , as for Fig. 8 ▸(a). Fig. 14 ▸(a) shows the image when zero absorption was assumed and is to be compared with Fig. 6 ▸. Fig. 14 ▸(b) was computed with the real value of absorption, and is compared with Fig. 8 ▸(a). Calculated curves of fringe contrast and of phase-related variables , and associated with the image in Fig. 14 ▸(b) are shown in Fig. 15 ▸(a). [, and correspond to , and for the G image, respectively.] The fringe pattern in Fig. 14 ▸(a) is almost the same as that in Fig. 6 ▸, but the fringe position is displaced by half a period, as shown in the top figure in Fig. 15 ▸(b). As the intensity profiles of these two fringe patterns show, the complementarity of diffracted intensities between the O and G images holds in this case. When absorption has the real value, vertical bands of abrupt fringe jumps in the O and G images are displaced from each other by nearly half the interval, as can be seen in Fig. 8 ▸(a) and Fig. 14 ▸(b). On the other hand, their fringe positions come nearer to each other, as shown in the bottom figure in Fig. 15 ▸(b). A comparison of experimental O and G images of moiré fringes in such a relation has been presented in Yoshimura (1997a ▸).

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