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Calculation of absorption and secondary scattering of X-rays by spherical amorphous materials in an asymmetric transmission geometry. Corrigendum
aDepartment of Physics, Washington University, St Louis, Missouri 63130-4899, USA
*Correspondence e-mail: jbendert@physics.wustl.edu
A revised version of Table 2 of Bendert et al. [Acta Cryst. (2013). A69, 131–139] is provided.
The expressions for Ai for i = 3 and 4 reported in Table 2 of Bendert et al. (2013)![[Bendert, J. C., Blodgett, M. E. & Kelton, K. F. (2013). Acta Cryst. A69, 131-139.]](../../../../../../logos/arrows/a_arr.gif "Bendert, J. C., Blodgett, M. E. & Kelton, K. F. (2013). Acta Cryst. A69, 131-139.")
should be negative. The correct values are given in the table shown below.
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![[+\cos (\phi )\mu {{r}_{\rm s}} {{x}_{\rm s}}]](teximages/ib9014fi1.gif)
![[\eqalign{{{+\mu {r_{\rm s}}}\over {6( {x_{\rm s}}^2 - 1)}}&\,[2\mu {r_{\rm s}}\cos (\phi)^2 {x_{\rm s}}^4 - {x_{\rm s}}^2 (1 - {x_{\rm s}}^2)^{1/2 }\cr &- 2\mu {r_{\rm s}}\cos (\phi)^2 {x_{\rm s}}^2 + (1 - {x_{\rm s}}^2)^{1/2 }\cr &- 2{x_{\rm s}}^2\cos (\phi )^2 (1 - {x_{\rm s}}^2)^{1/2 }]\cr}\qquad\qquad\qquad\qquad\qquad\qquad]](teximages/ib9014fd1.gif)
![[{{{-x_{\rm s}}\cos (\phi )\mu {r_{\rm s}}}\over {6({x_{\rm s}}^2 - 1)}}[2\mu {r_{\rm s}}\cos (\phi )^2 {x_{\rm s}}^2 (1 - {x_{\rm s}}^2)^{1/2} + {x_{\rm s}}^2 - 1]\qquad\qquad\qquad\qquad\qquad\qquad]](teximages/ib9014fd2.gif)
![[\eqalign {{{-\mu {r_{\rm s}}}\over {360( {x_{\rm s}}^2 - 1)}}&\,[8(\mu {r_{\rm s}} )^3 {x_{\rm s}}^6\cos(\phi )^4 + 40\mu {r_{\rm s}}{x_{\rm s}}^4\cos (\phi )^4\cr &- 14\mu {r_{\rm s}}{x_{\rm s}}^4 + 32( \mu {r_{\rm s}} )^2 {x_{\rm s}}^4\cos(\phi )^4 (1 - {x_{\rm s}}^2)^{1/2} \cr &- 8( \mu {r_{\rm s}} )^3{x_{\rm s}}^4\cos (\phi )^4\cr &- 32( \mu {r_{\rm s}} )^2{x_{\rm s}}^4\cos (\phi )^2 (1 - {x_{\rm s}}^2)^{1/2}\cr & + 44\mu {r_{\rm s}}{x_{\rm s}}^4\cos (\phi )^2 - 11(1 - {x_{\rm s}}^2)^{1/2} {x_{\rm s}}^2\cr &- 4{x^2}\cos (\phi )^2 (1 - {x_{\rm s}}^2)^{1/2} - 44\mu {r_{\rm s}}{x_{\rm s}}^2\cos (\phi )^2\cr &+ 32( \mu {r_{\rm s}})^2 {x_{\rm s}}^2\cos (\phi )^2 (1 - {x_{\rm s}}^2)^{1/2} \cr &+ 11(1 - {x_{\rm s}}^2)^{1/2} - 14\mu {r_{\rm s}} + 28\mu {r_{\rm s}}{x_{\rm s}}^2]\cr} \qquad\qquad\qquad\qquad\qquad\qquad]](teximages/ib9014fd3.gif)
![[\eqalign{{{+\mu {r_{\rm s}} x_{\rm s} \cos(\phi)}\over {360( {x_{\rm s}}^2 - 1)}}&\,[8( \mu {r_s} )^3 {x_s}^4\cos (\phi )^4 (1 - {x_s}^2)^{1/2}\cr &+ 16( \mu {r_s} )^2 {x_s}^4- 40( \mu {r_s} )^2 {x_s}^4\cos (\phi )^4\cr &+ 8( \mu {r_s} )^3 {x_s}^4\cos (\phi )^2 (1 - {x_s}^2)^{1/2} \cr &+ 24( \mu {r_s} )^2 {x_s}^4\cos (\phi )^2 + 3{x_s}^2 \cr &- 6\mu {r_s}{x_s}^2 (1 - {x_s}^2)^{1/2}- 3 + 16( \mu {r_s} )^2\cr & - 8( \mu {r_s} )^3{x_s}^2\cos(\phi )^2 (1 - {x_s}^2)^{1/2}\cr &+ 6\mu {r_s}(1 - {x_s}^2)^{1/2}- 32( \mu {r_s} )^2{x_s}^2 \cr &+ 36\mu {r_s}{x_s}^2\cos (\phi )^2 (1 - {x_s}^2)^{1/2}\cr &- 24( \mu {r_s} )^2 {x_s}^2\cos (\phi )^2]\cr}\qquad\qquad\qquad\qquad\qquad\qquad\quad]](teximages/ib9014fd4.gif)
References
Bendert, J. C., Blodgett, M. E. & Kelton, K. F. (2013). Acta Cryst. A69, 131–139. Web of Science CrossRef CAS IUCr Journals Google Scholar
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