The block-shape function for spherical and cylindrical mosaic blocks. is the radius of the mosaic block.
Intrinsic intensity distribution given by Eq. (1) is expressed by a light-grey ellipse. The instrumental resolution function is depicted by a fourfold dark-grey area. The intensity measured in a given point of the reciprocal space is given by a convolution of the instrumental and intrinsic profiles. Thus, at each point , the intensity is integrated over the dark-grey area of the instrumental resolution function.
Measured reciprocal-space maps near symmetrical reciprocal-lattice points 111 (left) and 222 (middle) and asymmetrical (224) (right). The intensity is plotted in a logarithmic scale, the contour step is .
Simulated instrumental resolution functions for the geometry and x-ray optics used for the diffractions 111 (left), 222 (middle), and 224 (right panel). The intensity is plotted in a logarithmic scale, the contour step is .
Mosaic-block-shape function and deformation correlation functions for the -thick PbTe layer. Upper left: mosaic-block-shape function . Upper right: deformation correlation function . Bottom left: deformation correlation function . Bottom right: deformation correlation function . The functions are plotted in a linear scale, the step size was 0.1.
Two-dimensional (2D) Gaussian profiles fitted to the functions . From left to the right—symmetrical diffractions 111 and 222 and asymmetrical diffraction 224. The full lines represent the experimental functions and the dashed lines are the fitted Gaussian profiles. The size of the contour steps is 0.1.
Williamson-Hall plot for the -thin PbTe layer. The open circles mark the experimental values for various diffractions and the solid line denotes the fit to Eq. (20) if we use all diffractions while for the dashed line only symmetrical diffractions were used. The diameter of the coherent diffracting volume and the deformation resulting from the fit are shown too; within the errors the same values result regardless if we use only symmetrical diffractions or not.
Comparison of the threading dislocation density vs thickness determined by different methods. Dots correspond to the measured values and lines are fits to a power-law function . See text for details. The errors of are smaller than the dot size in the log-log scale.
Comparison of the mosaic-block (MB) parameters, Williamson-Hall (WH) plot parameters, and threading dislocation densities determined by the methods mentioned. The size of the MB was determined from the plots (see Fig. 5). The threading dislocation density was estimated from the lateral size of the MB, . The diameter of the crystallites and the deformation of the blocks were obtained from the WH method using only symmetrical diffractions. The last column shows the threading dislocation density obtained from the Ayers method (Ref. 6).
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