addenda and errata\(\def\hfill{\hskip 5em}\def\hfil{\hskip 3em}\def\eqno#1{\hfil {#1}}\)

Journal logoJOURNAL OF
APPLIED
CRYSTALLOGRAPHY
ISSN: 1600-5767

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

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aRigaku Corporation, 3-9-12 Matsubara, Akishima, Tokyo, 196-8666, Japan
*Correspondence e-mail: toraya@rigaku.co.jp

(Received 20 February 2017; accepted 20 February 2017; online 14 March 2017)

Erroneous equations in the paper by Toraya [J. Appl. Cryst. (2016), 49, 1508–1516] are corrected.

In the paper by Toraya (2016[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)]

[\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)}]

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

First citationToraya, H. (2016). J. Appl. Cryst. 49, 1508–1516.  Web of Science CrossRef CAS IUCr Journals Google Scholar

© International Union of Crystallography. Prior permission is not required to reproduce short quotations, tables and figures from this article, provided the original authors and source are cited. For more information, click here.

Journal logoJOURNAL OF
APPLIED
CRYSTALLOGRAPHY
ISSN: 1600-5767
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