International
Tables for
Crystallography
Volume H
Powder diffraction
Edited by C. J. Gilmore, J. A. Kaduk and H. Schenk

International Tables for Crystallography (2018). Vol. H, ch. 3.10, p. 381

Section 3.10.7. Increasing inorganic crystalline phase content series

L. León-Reina,a A. Cuesta,b M. García-Maté,c,d G. Álvarez-Pinazo,c,d I. Santacruz,c O. Vallcorba,b A. G. De la Torrec and M. A. G. Arandab,c*

aServicios Centrales de Apoyo a la Investigación, Universidad de Málaga, 29071 Málaga, Spain,bALBA Synchrotron, Carrer de la Llum 2–26, Cerdanyola, 08290 Barcelona, Spain,cDepartamento de Química Inorgánica, Cristalografía y Mineralogía, Universidad de Málaga, 29071 Málaga, Spain, and dX-Ray Data Services S.L., Edificio de institutos universitarios, c/ Severo Ochoa 4, Parque tecnológico de Andalucía, 29590 Málaga, Spain
Correspondence e-mail:  g_aranda@uma.es

3.10.7. Increasing inorganic crystalline phase content series

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Table 3.10.2[link] reports the RQPA results for six inorganic mixtures with increasing amounts of i-A measured with Mo Kα1 (transmission) and Cu Kα1 (reflection). The Rietveld plots of the mixture with 4 wt% i-A are shown in Fig. 3.10.6[link]. For most of the samples, the AKLD values (see Table 3.10.2[link]) for Mo Kα1 radiation are slightly smaller than the corresponding values obtained for Cu Kα1 radiation. For this reason, we can conclude that the Mo Kα1 analyses are slightly better than those derived using Cu Kα1 radiation.

Table 3.10.2| top | pdf |
Rietveld quantitative phase analyses for the crystalline inorganic mixtures measured with Cu Kα1 and Mo Kα1 radiations

Weighed amounts (wt%) are also shown for comparison. Absolute values of the Kullback–Liebler distance (AKLD) for each mixture and the KLD value for i-anhydrite are also included. Trm, transmission; rfl, reflection.

 CGpQ_0.0ACGpQ_0.25ACGpQ_0.50A
Phaseswt%Mo trmCu rflwt%Mo trmCu rflwt%Mo trmCu rfl
C 32.9 32.6 (1) 30.4 (2) 32.8 32.0 (1) 33.6 (1) 32.7 33.2 (1) 32.8 (1)
Gp 31.7 31.7 (1) 34.5 (1) 31.7 32.5 (1) 31.6 (1) 31.6 30.1 (1) 30.7 (1)
Q 34.2 34.6 (1) 33.7 (1) 34.1 33.9 (1) 33.0 (1) 34.0 34.6 (1) 34.2 (1)
s-A 0.8 0.66 (3) 0.76 (5) 0.8 0.77 (4) 0.78 (5) 0.8 0.97 (3) 1.15 (5)
SrSO4 0.4 0.44 (4) 0.70 (6) 0.4 0.44 (4) 0.67 (5) 0.4 0.39 (4) 0.56 (5)
i-A 0.28 0.42 (3) 0.42 (4) 0.52 0.71 (3) 0.71 (4)
                   
AKLD sum   0.0089 0.0605   0.0198 0.0235   0.0295 0.0180
(i-A) KLD         −0.001 −0.001   −0.002 −0.002

 CGpQ_1.0ACGpQ_2.0ACGpQ_4.0A
Phaseswt%Mo trmCu rflwt%Mo trmCu rflwt%Mo trmCu rfl
C 32.5 32.8 (1) 32.6 (2) 32.2 31.3 (1) 31.4 (1) 31.6 31.2 (1) 31.8 (1)
Gp 31.5 30.4 (1) 30.7 (1) 31.1 32.1 (1) 32.3 (1) 30.5 30.7 (1) 30.5 (1)
Q 33.8 34.1 (1) 33.8 (1) 33.5 33.5 (1) 32.6 (1) 32.8 32.8 (1) 32.0 (1)
s-A 0.8 1.03 (4) 1.11 (5) 0.7 0.54 (3) 0.58 (5) 0.7 0.67 (3) 0.77 (4)
SrSO4 0.4 0.43 (4) 0.68 (5) 0.4 0.48 (4) 0.68 (6) 0.4 0.45 (4) 0.63 (5)
i-A 1.02 1.23 (3) 1.17 (5) 2.02 2.05 (4) 2.38 (9) 4.02 4.30 (8) 4.33 (9)
                   
AKLD sum   0.0214 0.0152   0.0218 0.0358   0.0095 0.0156
(i-A) KLD   −0.002 −0.001   0.000 −0.003   −0.004 −0.003
[Figure 3.10.6]

Figure 3.10.6 | top | pdf |

Selected range of the Rietveld plots for CGpQ_4.0A: (a) Mo Kα1 and (b) Cu Kα1 patterns. The inset highlights the effect of preferred orientation for gypsum and calcite.

On the other hand, calcite and gypsum presented preferred orientations, with the axes being [104] and [010], respectively. This effect was modelled using the March–Dollase algorithm. Preferred orientation makes the 0l0 reflections for gypsum have higher intensities in the Cu Kα1 patterns, and smaller intensities in the Mo Kα1 patterns, than those calculated from the crystal structure (see insets in Fig. 3.10.6[link]). As a consequence, the refined values for flat samples in reflection and transmission geometries were smaller and larger than 1.0, respectively (Cuesta et al., 2015[link]). Although preferred orientation is present in all patterns, the Cu Kα1 patterns were recorded in reflection geometry (flat samples), while the Mo Kα1 measurements were collected in transmission (also flat samples). This results in opposite diffraction intensity changes and points towards another (possible) fruitful use: joint refinement of these two types of patterns to counterbalance the effects of preferred orientation in RQPA.

Fig. 3.10.7[link](a) shows the quantified i-A contents (wt%), as determined by the Rietveld methodology, as a function of the weighed i-A amount. The two R2 values for the fits are very close to 1.00, and the intercept values are very close to zero, showing the appropriateness of the Rietveld methodology for quantifying crystalline materials. Furthermore, the slopes of the calibration curves are also 1.00 in both cases. Consequently, this study allows it to be concluded that RQPA for crystalline inorganic phases using powder-diffraction patterns collected using Mo Kα1 radiation yields results that are as accurate as those obtained from the well established method using Cu Kα1.

[Figure 3.10.7]

Figure 3.10.7 | top | pdf |

Rietveld quantification results for (a) the insoluble anhydrite series (within an inorganic crystalline matrix), (b) the xylose series (within an organic crystalline matrix) and (c) the ground-glass series (within an inorganic crystalline matrix) as a function of the weighed amount of each phase. Open symbols represent the derived amorphous contents in the mixtures without any added glass. The results of the least-squares fits are also shown.

References

Cuesta, A., Álvarez-Pinazo, G., García-Maté, M., Santacruz, I., Aranda, M. A. G., De la Torre, Á. G. & León-Reina, L. (2015). Rietveld quantitative phase analysis with molybdenum radiation. Powder Diffr. 30, 25–35.Google Scholar








































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