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 | JOURNAL OF APPLIED CRYSTALLOGRAPHY |
A new method for quantitative phase analysis using X-ray powder diffraction: direct derivation of weight fractions from observed integrated intensities and chemical compositions of individual phases. Corrigendum
aRigaku Corporation, 3-9-12 Matsubara, Akishima, Tokyo, 196-8666, Japan
*Correspondence e-mail: toraya@rigaku.co.jp
Erroneous equations in the paper by Toraya [J. Appl. Cryst. (2016), 49, 1508–1516] are corrected.
Keywords: X-ray powder diffraction; quantitative phase analysis; direct derivation; intensity–composition formula.
In the paper by Toraya (2016![[Toraya, H. (2016). J. Appl. Cryst. 49, 1508-1516.]](../../../../../../logos/arrows/j_arr.gif "Toraya, H. (2016). J. Appl. Cryst. 49, 1508-1516.")
), equations (9) and (10) on page 1511 were erroneously given. The correct equations are as follows:
![[\eqalign{ &{\rm For} \,\,{k}{{'}} =k \cr & \quad{{{\partial w}_{k}}\over{\partial {I}_{jk}}}={w}_{k}(1-{w}_{k} ){G}_{jk}{\left(\textstyle\sum\limits _{j=1}^{{N}_{k}}{I}_{jk}{G}_{jk} \right)}^{-1}. \cr & {\rm For}\,\, {k}{{'}} \ne k \cr & \quad {{{\partial w}_{k}}\over{\partial {I}_{j{k}{{'}}}}}{=-w}_{k}{{w}_{{k}{{'}}} G}_{j{k}{{'}}}{\left(\textstyle\sum\limits _{j=1}^{{N}_{{k}{{'}}}} {I}_{j{k}{{'}}}{G}_{j{k}{{'}}}\right)}^{-1}. \quad\quad\quad\quad\quad\quad\,\,\,\,\,} \eqno(9)]](teximages/to9157fd1.gif)
![[\eqalignno{ {\rm s.u.}( {{w_k}} ) =&\, {w_k}\Bigg[ \left( {1 - 2{w_k}} \right) \left( \textstyle \sum \limits_{j = 1}^{{N_k}} {I_{jk}}{G_{jk}} \right)^{ - 2} \textstyle \sum \limits_{j = 1}^{{N_k}} G_{jk}^2{\sigma ^2}( {{I_{jk}}} ) \cr & + \textstyle \sum \limits_{k' = 1}^K w_{k'}^2 \left( \textstyle \sum \limits_{j = 1}^{{N_{k'}}} {I_{jk'}}{G_{jk'}} \right)^{ - 2} \textstyle \sum \limits_{j = 1}^{{N_{k'}}} G_{jk'}^2{\sigma ^2}( {{I_{jk'}}} ) \Bigg]^{1/2} .&(10)}]](teximages/to9157fd2.gif)
The amounts of underestimation by the erroneous equations were in the range of 18–37% for individual test samples and 24% in grand average.
References
Toraya, H. (2016). J. Appl. Cryst. 49, 1508–1516. Web of Science CrossRef CAS IUCr Journals Google Scholar
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| JOURNAL OF APPLIED CRYSTALLOGRAPHY |
