Determination of strain concentration by microfluorescent densitometry of X-ray topography: A bridge between microfracture and continuum mechanics

Abstract

The strain distribution in the vicinity of the notches of a double-notched, elastically bent silicon crystal was determined by measuring the diffracted X-ray intensities. The measurements were carried out on traverse-oscillation topographs of a crystal section extending through both notches. Strain distributions were determined by measuring the local densities of silver deposits (measurements of 'opacities') with a scanning electron microscope. It was shown that both the density range and spatial resolution of X-ray densitometry were larger by an order of magnitude than those of optical densitometry. The strain concentration factors associated with the notches were measured experimentally and calculated by continuum mechanics. The results were in satisfactory agreement. Also, the experimentally found rise of strains, to a maximum in the critical area adjacent to the notch root, followed the trend predicted by continuum mechanics.

On the X-ray reflectivity of elastically bent perfect crystals

“…Absorption, or rather normal absorption, was accounted for by multiplying (7) by an absorption factor A which is very nearly equal to ta, (6). This procedure describes quite well the slope of the reflectivity-versuscurvature curve (except for weak bending) and can be (5) used with reasonable accuracy to determine relative curvatures from reflected intensities (Kalman & Weissmann, 1979;Kalman et al, 1980;Chaudhuri et al, 1982), particularly if positive curvatures are measured throughout. For higher accuracy, however, anomalous absorption must be taken into account.…”

“…Hence, the reflectivity in this curvature region can, in principle, be utilized to detect and measure with good accuracy curvature and curvature variations. This has indeed been done, in conjunction with topographic methods, to determine local curvature variations due to strain concentration, and thus to measure quantitatively the strain concentration factors near inhomogeneities of various geometries (Kalman & Weissmann, 1979;Kalman, Chaudhuri, Weng & Weissmann, 1980;Chaudhuri, Kalman, Weng & Weissmann, 1982). The accuracy of these and similar measurements depends on the degree of accuracy of the reflectivity-versus-curvature calibration curve.…”

Quantitative analysis of intensitities in X-ray topographs by enhanced microfluorescence

“…Ilford L4 nuclear plates were exposed to monochromatic Mo K:~ l radiation of rectangular cross section 1 x 10 mm, different parts of the plate being exposed for different times. Simultaneously with each exposure, the intensity transmitted through the nuclear plate was monitored by a proportional counter in a manner analogous to that described previously (Kalman et al, 1980). Four identical nuclear plates were prepared.…”

“…3 shows the dependence of the MFA measurements on the incident X-ray intensity for different metal-film deposits. For the sake of comparison the previously given data of optical densitometry and MFA for carbon deposit (Kalman et al, 1980) have been inserted in the plot. The data pertaining to the optical densitometry show the rapid saturation of opacity if the measurements are carried out by light densitometry.…”

“…The measurements are based on the principle that for a constant time exposure the silver contained in the emulsion of the developed X-ray topograph is proportional to the incident radiative photon flux. The opacity of the topograph, enhanced in the vicinity of the stress raiser, is measured by a point-to-point microfluorescent analysis (MFA) using a scanning electron microscope (SEM) and its associated energy dispersive system (Blech & Tai, 1977;Tai & Ohring, 1977;Kalman et al, 1980;Chaudhuri et al, 1982). Because the accuracy of the strain measurements depends on the accuracy of the intensity measurements, large improvements can be obtained by enhancing the microfluorescent yield.…”