Quantification of mixtures via the Rietveld method is generally restricted to crystalline phases for which structures are well known. Phases that have not been identified or fully characterized may be easily quantified as a group, along with any amorphous material in the sample, by the addition of an internal standard to the mixture. However, quantification of individual phases that have only partial or unknown structures is carried out less routinely. This paper presents methodology for quantification of such phases. It outlines the procedure for calibration of the method and gives detailed examples from both synthetic and mineralogical systems. While the method should, in principle, be generally applicable, its implementation in the TOPAS program from Bruker AXS is demonstrated here.

The International Union of Crystallography (IUCr) Commission on Powder Diffraction (CPD) has sponsored a round robin on the determination of quantitative phase abundance from diffraction data. Specifically, the aims of the round robin were (i) to document the methods and strategies commonly employed in quantitative phase analysis (QPA), especially those involving powder diffraction, (ii) to assess levels of accuracy, precision and lower limits of detection, (iii) to identify specific problem areas and develop practical solutions, (iv) to formulate recommended procedures for QPA using diffraction data, and (v) to create a standard set of samples for future reference. Some of the analytical issues which have been addressed include (a) the type of analysis (integrated intensities or full‐profile, Rietveld or full‐profile, database of observed patterns) and (b) the type of instrument used, including geometry and radiation (X‐ray, neutron or synchrotron). While the samples used in the round robin covered a wide range of analytical complexity, this paper reports the results for only the sample 1 mixtures. Sample 1 is a simple three‐phase system prepared with eight different compositions covering a wide range of abundance for each phase. The component phases were chosen to minimize sample‐related problems, such as the degree of crystallinity, preferred orientation and microabsorption. However, these were still issues that needed to be addressed by the analysts. The results returned indicate a great deal of variation in the ability of the participating laboratories to perform QPA of this simple three‐component system. These differences result from such problems as (i) use of unsuitable reference intensity ratios, (ii) errors in whole‐pattern refinement software operation and in interpretation of results, (iii) operator errors in the use of the Rietveld method, often arising from a lack of crystallographic understanding, and (iv) application of excessive microabsorption correction. Another major area for concern is the calculation of errors in phase abundance determination, with wide variations in reported values between participants. Few details of methodology used to derive these errors were supplied and many participants provided no measure of error at all.

Complex silico-ferrites of calcium and aluminium (low-Fe form, denoted as SFCA; and high-Fe, low-Si form, denoted as SFCA-I) constitute up to 50 vol pct of the mineral composition of fluxed iron ore sinter. The reaction sequences involved in the formation of these two phases have been determined using an in-situ X-ray diffraction (XRD) technique. Experiments were carried out under partial vacuum over the temperature range of T ϭ 22°C to 1215°C (alumina-free compositions) and T ϭ 22°C to 1260°C (compositions containing 1 and 5 wt pct Al 2 O 3 ) using synthetic mixtures of hematite (Fe 2 O 3 ), calcite (CaCO 3 ), quartz (SiO 2 ), and gibbsite (Al(OH) 3 ). The formation of SFCA and SFCA-I is dominated by solid-state reactions, mainly in the system CaO-Fe 2 O 3 . Initially, hematite reacts with lime (CaO) at low temperatures (T ϳ 750°C to 780°C) to form the calcium ferrite phase 2CaOиFe 2 O 3 (C 2 F). The C 2 F phase then reacts with hematite to produce CaOиFe 2 O 3 (CF). The breakdown temperature of C 2 F to produce the higherFe 2 O 3 CF ferrite increases proportionately with the amount of alumina in the bulk sample. Quartz does not react with CaO and hematite, remaining essentially inert until SFCA and SFCA-I began to form at around T ϭ 1050°C. In contrast to previous studies of SFCA formation, the current results show that both SFCA types form initially via a low-temperature solid-state reaction mechanism. The presence of alumina increases the stability range of both SFCA phase types, lowering the temperature at which they begin to form. Crystallization proceeds more rapidly after the calcium ferrites have melted at temperatures close to T ϭ 1200°C and is also faster in the higher-alumina-containing systems.

The International Union of Crystallography (IUCr) Commission on Powder Diffraction (CPD) has sponsored a round robin on the determination of quantitative phase abundance from diffraction data. The aims of the round robin have been detailed by Madsen et al. [J. Appl. Cryst. (2001), 34, 409±426]. In summary, they were (i) to document the methods and strategies commonly employed in quantitative phases analysis (QPA), especially those involving powder diffraction, (ii) to assess levels of accuracy, precision and lower limits of detection, (iii) to identify speci®c problem areas and develop practical solutions, (iv) to formulate recommended procedures for QPA using diffraction data, and (v) to create a standard set of samples for future reference. The ®rst paper (Madsen et al., 2001) covered the results of sample 1 (a simple three-phase mixture of corundum,¯uorite and zincite). The remaining samples used in the round robin covered a wide range of analytical complexity, and presented a series of different problems to the analysts. These problems included preferred orientation (sample 2), the analysis of amorphous content (sample 3), microabsorption (sample 4), complex synthetic and natural mineral suites, along with pharmaceutical mixtures with and without an amorphous component. This paper forms the second part of the round-robin study and reports the results of samples 2 (corundum,¯uorite, zincite, brucite), 3 (corundum,¯uorite, zincite, silica¯our) and 4 (corundum, magnetite, zircon), synthetic bauxite, natural granodiorite and the synthetic pharmaceutical mixtures (mannitol, nizatidine, valine, sucrose, starch). The outcomes of this second part of the round robin support the ®ndings of the initial study. The presence of increased analytical problems within these samples has only served to exacerbate the dif®culties experienced by many operators with the sample 1 suite. The major dif®culties are caused by lack of operator expertise, which becomes more apparent with these more complex samples. Some of these samples also introduced the requirement for skill and judgement in sample preparation techniques. This second part of the round robin concluded that the greatest physical obstacle to accurate QPA for X-ray based methods is the presence of absorption contrast between phases (microabsorption), which may prove to be insurmountable in some circumstances.

The presence of amorphous materials in crystalline samples is an increasingly important issue for diffractionists. Traditional phase quantification via the Rietveld method fails to take into account the occurrence of amorphous material in the sample and without careful attention on behalf of the operator its presence would remain undetected. Awareness of this issue is increasing in importance with the advent of nanotechnology and the blurring of the boundaries between amorphous and crystalline species. The methodology of a number of different approaches to the determination of amorphous content via X-ray diffraction and an assessment of their performance, is described. Laboratory-based, X-ray diffraction data from a suite of synthetic samples, with amorphous content rangäing from 0.0 to 50 wt%, has been analysed using both direct (in which the contribution of the amorphous component to the pattern is used to obtain an estimate of concentration) and indirect (where the absolute abundances of the crystalline components are used to estimate the amorphous content by difference) methodologies. In addition, both single peak and whole pattern methodologies have been assessed. All methods produce reasonable results, however the study highlights some of the strengths, deficiencies and applicability of each of the approaches.