Comments on 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 by Toraya (2016)

Response to comments on 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

“…Regarding the comments by He & Li (2022), the simulated data sets of Li 2 CO 3 + Ag 2 Te(III) and Li 2 CO 3 + -Ga 2 O 3 used by them would highlight the deviation from the approximation C ' C i . In other words, the Patterson peaks at the origins would have appreciably different profiles for both Li 2 CO 3 and Ag 2 Te(III).…”

“…He & Li adopted zero atomic displacement parameters in calculating F(hkl) in their simulated intensity data sets, and the derived weight fractions, for example, of Li 2 CO 3 in Li 2 CO 3 + Ag 2 Te(III) (50:50 wt%) are reported to be in the range of 29.9-38.1 wt% for the simulated data sets with 70 2 UL 130 (2 UL : the upper limit of the 2 range for summing the diffracted intensities). Recalculations in the present work using the atomic coordinates and 'non-zero' atomic displacement parameters [taken from the literature cited by He & Li (2022)] derived corresponding weight fractions in the range of 36.5-41.4 wt%. It may be commented that adopting zero atomic displacement parameters will enforce the termination effect in calculating the total intensities in a limited observable 2 range.…”

“…This formulation was first derived on the basis of the proportionality between the height and integrated value of the peak at the origin of the Patterson function, defined as the convolution of the electron density distribution functions (Toraya, 2016). Comments by He & Li (2022) on the validity of the intensity-composition formula can be summarized as follows: (1) the assumption of this proportionality is based entirely on intuition and experience and has no theoretical basis, and (2) the assumption that the proportionality constant is common and independent of individual phases does not hold. In regard to the first comment, this proportionality was considered to be widely known by crystallographers, as was described in a review article in a corporate journal (Toraya, 2018a).…”