Diffraction Contrast Profiles of Voids

Abstract

Diffraction contrast profiles have been calculated using the two beam approximation for a thin crystal foil which contains a spherical void. The influence of the foil thickness, foil orientation, void radius, and void depth on the total contrast, a combination of both the strain contrast due to distortion of the foil by the void and the thickness contrast due to the absence of scattering material within the void, was examined, the lengths being expressed in units of ξg* =ξg(1+w2)−1/2 where w=Sgξg with Sg the deviation from the exact Bragg condition and ξg the extinction distance. Maximum strain contrast occurs for the profiles of both beams at depths d*= (N/2)ξg* (N an integer); the black and white sides of these profiles alternate as the depth changes by 1/2ξg*. The amplitude of the strain contrast is maximum at thicknesses t*=Nξg* and (N+1/2)ξg* for the scattered beam and the transmitted beam respectively. In either case, the inbetween thicknesses give a smaller strain contrast for which the white sides of the profiles are suppressed for voids within an extended region of the foil. This region of small amplitude is centered on the midplane of the foil for w=0, but shifts for only the scattered beam toward the entrance (exit) surface as w increases positively (negatively); a much larger amplitude can then occur near the opposite surface. Although the strain contrast for either beam is largest for void radius R0*=1/4ξg*, the thickness contrast at w=0 dominates the image of the void at this and larger radii. For R0*≲1/16ξg*, the strain contrast, when maximum, becomes the dominant image forming mechanism. As the foil is rotated away from the exact Bragg condition, w≠0, the thickness contrast can firstly become quite small compared to the strain contrast even at R0*=1/4ξg*, but upon further rotation it predominates once again as in the case w=0 while showing an image of opposite character to the former case.