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 | JOURNAL OF APPLIED CRYSTALLOGRAPHY |
Elastic strain and stress determination by generalized treatment for textured polycrystals for all Second corrigendum
aNational Institute for Materials Physics, PO Box MG 7, Bucharest, Romania, and bDepartment of Physics and Astronomy, University of Denver, 2112 East Wesley Avenue, Denver, CO 80208, USA
*Correspondence e-mail: balzar@du.edu
Keywords: stress; strain; texture; polycrystals; Laue classes; Rietveld refinement.
This corrigendum (C2) replaces the first corrigendum (C1; Popa & Balzar, 2012![[Popa, N. C. & Balzar, D. (2012). J. Appl. Cryst. 45, 838-839.]](../../../../../../logos/arrows/j_arr.gif "Popa, N. C. & Balzar, D. (2012). J. Appl. Cryst. 45, 838-839.")
), which was published to correct errors in the article by Popa & Balzar (2001). The basic equation considered in C1 is the integral of spherical harmonics over the crystallites contributing to the Bragg reflection. In C1, this integral is represented by equation (1), which is the expression (14.160) originally calculated by Bunge (1982). In C1, we added the factor ( - 1)n to that expression. This factor resulted from a coding error that, unfortunately, we discovered only recently in the computer routine used to calculate such integrals. With the correct coding, the factor ( - 1)n disappears, and the Bunge (1982) equation (14.120) is correct.
The necessary corrections in the paper by Popa & Balzar (2001) are the following:
(1) Table 1: multiply the right side of each equation by 2.
(2) Table 15: delete the factor 2 in the right side of the equations for R0 and R1.
(3) Several errors in Table 16. The correct table is shown as Table 1 of the present article.
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![[\eqalign{k = 0: & \quad {\bar w_{ij0}} = 1/3\,\,{\rm{for}}\,\,i,j = 1,3 \cr k = 1:&\quad {{\bar w}_{ij1}} = 1/30\,\,{\rm{ for }}\,\,i,j = 1,2\semi {{\bar w}_{ij1}} = 2/15\,\,{\rm{ for }}\,\,(3,3) \semi{{\bar w}_{ij1}} = - 1/15\,\,{\rm{ for }}\,\,(1,3),(2,3),(3,1),(3,2) \cr k = 2:&\quad {{\bar w}_{ij2}} = - 1/30{(3/2)^{1/2}}\,\,{\rm{ for }}\,\,(5,1),(5,2)\semi{{\bar w}_{ij2}} = 1/15{(3/2)^{1/2}}\,\,{\rm{ for }}\,\,(5,3) \cr k = 3:&\quad{{\bar w}_{ij3}} = - 1/30{(3/2)^{1/2}}\,\,{\rm{ for }}\,\,(4,1),(4,2)\semi{{\bar w}_{ij2}} = 1/15{(3/2)^{1/2}}\,\,{\rm{ for }}\,\,(4,3) \cr k = 4:&\quad{{\bar w}_{ij4}} = - 1/30{(3/2)^{1/2}}\,\,{\rm{ for }}\,\,(1,1),(1,2)\semi{{\bar w}_{ij4}} = 1/15{(3/2)^{1/2}}\,\,{\rm{ for }}\,\,(1,3) \semi {{\bar w}_{ij4}} = 1/30{(3/2)^{1/2}}\,\,{\rm{ for }}\,\,(2,1),(2,2)\semi{{\bar w}_{ij4}} = - 1/15{(3/2)^{1/2}}\,\,{\rm{ for }}\,\,(2,3) \cr k = 5:&\quad{{\bar w}_{ij5}} = - 1/30{(3/2)^{1/2}}\,\,{\rm{ for }}\,\,(6,1),(6,2)\semi{{\bar w}_{ij5}} = 1/15{(3/2)^{1/2}}\,\,{\rm{ for }}\,\,(6,3) \cr k = 6:& \quad{{\bar w}_{ij6}} = - 1/15{(3/2)^{1/2}}\,\,{\rm{ for }}\,\,(1,5),(2,5)\semi{{\bar w}_{ij6}} = 2/15{(3/2)^{1/2}}\,\,{\rm{ for }}\,\,(3,5) \cr k = 7:&\quad{{\bar w}_{ij7}} = 1/10\,\,{\rm{ for }}\,\,(5,5) \cr k = 8:&\quad{{\bar w}_{ij8}} = 1/10\,\,{\rm{ for }}\,\,(4,5) \cr k = 9:&\quad{{\bar w}_{ij9}} = 1/10\,\,{\rm{ for }}\,\,(1,5)\semi {{\bar w}_{ij9}} = - 1/10\,\,{\rm{ for }}\,\,(2,5) \cr k = 10:&\quad{{\bar w}_{ij,10}} = 1/10\,\,{\rm{ for }}\,\,(6,5) \cr k = 11: & \quad{{\bar w}_{ij,11}} = - 1/15{(3/2)^{1/2}}\,\,{\rm{ for }}\,\,(1,4),(2,4)\semi{{\bar w}_{ij,11}} = 2/15{(3/2)^{1/2}}\,\,{\rm{ for }}\,\,(2,4) \cr k = 12:&\quad{{\bar w}_{ij,12}} = 1/10\,\,{\rm{ for }}\,\,(5,4) \cr k = 13: &\quad{{\bar w}_{ij,13}} = 1/10\,\,{\rm{ for }}\,\,(4,4) \cr k = 14: & \quad {{\bar w}_{ij,14}} = 1/10\,\,{\rm{ for }}\,\,(1,4)\semi{{\bar w}_{ij,14}} = - 1/10\,\,{\rm{ for }}\,\,(2,4) \cr k = 15: &\quad {{\bar w}_{ij,15}} = 1/10\,\,{\rm{ for }}\,\,(6,4) \cr k = 16:&\quad{{\bar w}_{ij,16}} = - 1/30{(3/2)^{1/2}}\,\,{\rm{ for }}\,\,(1,1),(2,1)\semi{{\bar w}_{ij,16}} = 1/30{(3/2)^{1/2}}\,\,{\rm{ for }}\,\,(1,2),(2,2) \semi {{\bar w}_{ij,16}} = 1/15{(3/2)^{1/2}}\,\,{\rm{ for }}\,\,(3,1)\semi{{\bar w}_{ij,16}} = - 1/15{(3/2)^{1/2}}\,\,{\rm{ for }}\,\,(3,2) \cr k = 17:&\quad{{\bar w}_{ij,17}} = 1/20\,\,{\rm{ for }}\,\,(5,1)\semi{{\bar w}_{ij,17}} = - 1/20\,\,{\rm{ for }}\,\,(5,2) \cr k = 18:&\quad{{\bar w}_{ij,18}} = 1/20\,\,{\rm{ for }}\,\,(4,1)\semi{{\bar w}_{ij,18}} = - 1/20\,\,{\rm{ for }}\,\,(4,2) \cr k = 19: &\quad{{\bar w}_{ij,19}} = 1/20\,\,{\rm{ for }}\,\,(1,1),(2,2)\semi{{\bar w}_{ij,19}} = - 1/20\,\,{\rm{ for }}\,\,(1,2),(2,1) \cr k = 20:&\quad{{\bar w}_{ij,20}} = 1/20\,\,{\rm{ for }}\,\,(6,1)\semi{{\bar w}_{ij,20}} = - 1/20\,\,{\rm{ for }}\,\,(6,2) \cr k = 21:&\quad{{\bar w}_{ij,21}} = - 1/15{(3/2)^{1/2}}\,\,{\rm{ for }}\,\,(1,6),(2,6)\semi {{\bar w}_{ij,21}} = 2/15{(3/2)^{1/2}}\,\,{\rm{ for }}\,\,(3,6) \cr k = 22: &\quad {{\bar w}_{ij,22}} = 1/10\,\,{\rm{ for }}\,\,(5,6) \cr k = 23:& \quad {{\bar w}_{ij,23}} = 1/10\,\,{\rm{ for }}\,\,(4,6) \cr k = 24: & \quad{{\bar w}_{ij,24}} = 1/10\,\,{\rm{ for }}\,\,(1,6)\semi {{\bar w}_{ij,24}} = - 1/10\,\,{\rm{ for }}\,\,(2,6) \cr k = 25: & \quad{{\bar w}_{ij,25}} = 1/10\,\,{\rm{ for }}\,\,(6,6) \cr } ]](teximages/ks5454fd1.gif)
(4) The first unnumbered equation after equation (24) becomes ![[{g'_{jk}} = \textstyle\sum_{l = 1}^6 {{C_{jl}}\,{\rho _l}\,{g_{lk}}}]](teximages/ks5454fi5.gif)
.
References
Bunge, H. I. (1982). Texture Analysis in Materials Science. London: Butterworth. Google Scholar
Popa, N. C. & Balzar, D. (2001). J. Appl. Cryst. 34, 187–195. Web of Science CrossRef CAS IUCr Journals Google Scholar
Popa, N. C. & Balzar, D. (2012). J. Appl. Cryst. 45, 838–839. Web of Science CrossRef CAS IUCr Journals Google Scholar
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