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, pp. 379-381

Section 3.10.6. Limits of detection and quantification

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

3.10.6. Limits of detection and quantification

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LoD and LoQ are two important quantities in the validation of any analytical method. LoD/LoQ are terms that are used to describe the smallest concentration of an analyte that can be reliably detected/assessed by an analytical procedure, as discussed in Section [link]3.10.1. In techniques such as Rietveld analysis, the approach of having a powder pattern with its strongest (not overlapped) diffraction peak with an S/N ratio of larger than 3.0 is not straightforward because the full powder pattern is evaluated.

Fig. 3.10.3[link] shows Mo Kα1 and Cu Kα1 raw patterns for the inorganic series with increasing amounts of insoluble anhydrite (labelled with solid squares) and Fig. 3.10.4[link] shows the strongest diffraction peak for i-A in the mixtures containing 0.123 wt% anhydrite (CGpQ_0.12A) and 0.25 wt% anhydrite (CGpQ_0.25A) to evaluate the limits of detection in the conditions reported in Section [link]3.10.5. For CGpQ_0.12A, both laboratory powder patterns yielded peaks with S/N ratios lower than 3.0 (top panels in Fig. 3.10.4[link]). For CGpQ_0.25A, the Cu Kα1 pattern yielded a clear peak with S/N = 4.1; therefore, it can be concluded that the LoD for insoluble anhydrite with this radiation in this mixture is slightly lower than 0.2 wt%. For Mo Kα1 radiation, the CGpQ_0.25A and CGpQ_0.50A samples yielded patterns with peaks with S/N ratios of 2.4 and 5.1, respectively. Hence, it can be concluded that the LoD for i-A with this radiation in this mixture is quite close to 0.3 wt%.

[Figure 3.10.3]

Figure 3.10.3 | top | pdf |

(a) Raw Mo Kα1 powder patterns for the inorganic series composed of a constant matrix of calcite, gypsum and quartz, and increasing amounts of insoluble anhydrite (peaks highlighted with a solid square). (b) Raw Cu Kα1 powder patterns for the same inorganic series. (c) Raw SXRPD patterns for CGpQ_0.12A collected at three different positions of the capillary (red, black and blue traces). The intensity values in (c) have been artificially offset to show the three different patterns.

[Figure 3.10.4]

Figure 3.10.4 | top | pdf |

Selected region of the powder patterns showing the main diffraction peak of insoluble anhydrite for the low-content samples to investigate the limit of detection. Top left: Cu Kα1 pattern for CGpQ_0.12A. Middle left, Cu Kα1 pattern for CGpQ_0.25A. Bottom left, SXRPD pattern for CGpQ_0.12A. Top right, Mo Kα1 pattern for CGpQ_0.12A. Middle right, Mo Kα1 pattern for CGpQ_0.25A. Bottom right, Mo Kα1 pattern for CGpQ_0.50A. The main peak of anhydrite, (θ)/λ = 0.143 Å−1, is located at 25.4, 11.6 and 12.7° 2θ for Cu Kα1, Mo Kα1 and synchrotron radiations, respectively. The peak at sin(θ)/λ = 0.1445 Å−1 is due to the soluble anhydrite from gypsum (constant content in all the samples). The very tiny peak at sin(θ)/λ = 0.1457 Å−1, which is slightly visible only in the SXRPD pattern, arises from SrSO4 (0.39 wt%) from gypsum.

The LoQ for i-A in this matrix was also studied. Three Mo Kα1 and Cu Kα1 patterns were collected for CGpQ_0.12A. For the three Mo Kα1 patterns, the average analysis result for i-A was 0.28 (2) wt%, but the accuracy of the obtained value is poor, as the expected value was 0.12 wt%. Similarly, the average value for the analyses of three Cu Kα1 patterns was 0.24 (2) wt%. The RQPA results are given as supporting information in León-Reina et al. (2016[link]). It was concluded that i-A can be quantified in this mixture at the level of 0.12 wt%, but with a relative error close to 100%. If the `acceptable reliability' criterion in the analysis is taken into consideration, the LoQ value would be close to 1.0 wt% in order to have a relative associated error lower than 20%.

CGpQ_0.12A was also studied by SXRPD. Fig. 3.10.3[link](c) shows the SXRPD patterns collected at three different positions of the capillary, which were almost identical, and Fig. 3.10.4[link] (bottom left) shows the main diffraction peak of anhydrite. The S/N ratio for the strongest diffraction peak of anhydrite was 12.8 and hence the limit of detection for i-A with synchrotron radiation in this matrix is below 0.10 wt%.

To quantify the accuracy of the analyses, the KLD methodology was used. The AKLD values for each analysis as well as the KLD values for i-A are reported in León-Reina et al. (2016[link]). The synchrotron analyses clearly had better accuracy than those using laboratory radiation. Moreover, the Mo Kα1 radiation analyses were slightly better than those obtained using Cu Kα1 radiation.

Fig. 3.10.5[link] shows Mo Kα1 and Cu Kα1 raw patterns of the organic mixtures with increasing amounts of xylose. The strongest powder-diffraction peak for xylose in the GFL_0.12X patterns (with both Mo and Cu radiations) was not observed. The corresponding peak was observed in the GFL_0.25X patterns. Therefore, the LoD can be established as close to 0.25 wt%. The analysis results for xylose in GFL_0.25X were reported in León-Reina et al. (2016[link]). These values showed that the results from Mo Kα1 powder diffraction were slightly more accurate.

[Figure 3.10.5]

Figure 3.10.5 | top | pdf |

(a) Raw Mo Kα1 powder patterns for the organic series composed of a constant matrix of glucose, fructose and lactose, and increasing amounts of xylose (peaks highlighted with an asterisk). (b) Raw Cu Kα1 powder patterns for the same organic series. (c) Raw SXRPD patterns for GFL_0.12X collected at three different positions of the capillary (as collected).

The LoQ for xylose was also studied. Once again, three Mo Kα1 and Cu Kα1 patterns were collected for GFL_0.12X. The average value for the analysis of the three Mo patterns was 0.18 (8) wt%. Similarly, the average result for the analyses of three Cu patterns was 0.34 (6) wt%. Full RQPA results are reported in the supporting information of León-Reina et al. (2016[link]). The LoQ for xylose in this mixture for the two radiations can be established as close to 0.12 wt%. Indeed, if one applies an `acceptable reliability' criterion, the LoQ would be much higher at above 1 wt%. The output of this study was that Cu Kα1 radiation yielded a slightly less accurate result than that obtained from the Mo Kα1 data.

GFL_0.12X was also studied by SXRPD in a rotating glass capillary in transmission mode. Fig. 3.10.5[link](c) shows SXRPD patterns for GFL_0.12X collected at three different positions of the same capillary. The powder patterns showed quite different peak ratios. It is important to bear in mind that filling a glass capillary with organic compounds is sometimes not easy due to electrostatic charge effects. For this reason, the phase ratio within the part of capillary bathed by the X-rays might not be the same as that of the sample under study. The behaviour observed in Fig. 3.10.5[link](c) could be explained by inhomogeneous capillary filling. Hence, in this case, the RQPA results are unreliable. Even in `well behaved' samples, inhomogeneous filling of small capillaries could result in problems. Readers should be aware of this, and the authors strongly recommend that at least three patterns should be collected along the capillary and superimposed. If there is inhomogeneous filling the patterns will differ, and extreme care has to be exercised when filling capillaries in order to minimize this problem.

References

León-Reina, L., García-Maté, M., Álvarez-Pinazo, G., Santacruz, I., Vallcorba, O., De la Torre, A. G. & Aranda, M. A. G. (2016). Accuracy in Rietveld quantitative phase analysis: a comparative study of strictly monochromatic Mo and Cu radiations. J. Appl. Cryst. 49, 722–735.Google Scholar








































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