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.

Owing to the depletion of world lump iron ore stocks, pre-treated agglomerates of ®ne ores are making up a growing proportion of blast-furnace feedstock ($80%). These agglomerations, or`sinters', are generally composed of iron oxides, ferrites (most of which are silicoferrites of calcium and aluminium, SFCAs), glasses and dicalcium silicates (C2S). SFCA is the most important bonding phase in iron ore sinter, and its composition, structural type and texture greatly affect its physical properties. Despite its prevalence and importance, the mechanism of SFCA formation is not fully understood. In situ powder X-ray diffraction investigations have been conducted into the formation of SFCA, allowing the study of the mechanism of its formation and the observation of intermediate phases with respect to time and temperature. Studies have been carried out to investigate the effects of changing the substitution levels of aluminium for iron. The use of the Rietveld method for phase quanti®cation gives an indication of the order and comparative rates of phase formation throughout the experiments.

Infinite frameworks composed of tetrahedral centers linked together by 2-connecting units often adopt a topology related to that of diamond. In SiO, where silicon is tetrahedral and oxygen is 2-connecting, the diamond-related topology, fi-cristobalite, is thermodynamically less stable than the alternative 4-connected topology of quartz. It is therefore perhaps a little surprising how few classes of substances are known with the quartz topology. Examples generally involve a single atom bridge between two tetrahedral centers as in GaPO,,['] Aqueous solutions containing zinc nitrate and potassium dicyanoaurate deposit crystals of composition ZnAu,(CN), , whose structure we have determined by single-crystal X-ray diffraction. The hexagonal unit cell is shown in Figure 1 178 and 173"; a: C-Au-C, 174.6"). The 3D net generated thereby has a topology identical to that of quartz, in which each tetrahedral Si atom is replaced by a Zn atom and each Si-0-Si connection by Zn-CN-Au-CN-Zn (Zn ... Zn, 10.041 A). A consequence of this lengthening of the connections is that there is room for the interpenetration of six identical but independent nets. Fragments of these six independent nets can be seen in the unit cell in Figure 1.A single extended net is represented in Figure 2. The quartzlike connectivity is immediately evident. The six independent nets consist of three pairs, the members of any particular pair Figure 3 shows how the three pairs interpenetrate (paired colors as in Figure 1).Like the quartz prototype, ZnAu,(CN), is enantiomorphic. All six nets have the same handedness; in the particular crystal studied, the absolute configuration of the threefold helices within each net is that of a righthanded screw.The closest approach between nets is a Au . . . Au contact of 3.1 1 A, examples of which can be seen in Figure 1 between yellow and dark blue frameworks and between green and light blue frameworks; these and other analogous Au . . . Au contacts can also be seen in Figure 3. The bowing in the Zn-NC-Au-CNZn links apparent in Figures 1 b and 3 is suggestive of an attractive Au-Au interaction. Schmidbaur has previously presented convincing evidence for the reality of such Au'-Au' bonding interactions, which he notes are comparable in strength with hydrogen bonds and, like hydrogen bonds, may be "conformation determining";['"] homoatomic dl0-d" interactions. in general. have been reviewed bv , . ,

A tomographic study of electrochemical cells to observe scales formed on inert anodes has been conducted using energy‐dispersive synchrotron X‐ray diffraction. This study is preparatory to an investigation that will observe this formation in situ during the cells' operation. The purpose of the current work was to determine whether this technique would be appropriate for such a study in terms of its sensitivity and whether the results could be quantified satisfactorily. A method has been developed for the quantitative phase analysis of energy‐dispersive data using crystal‐structure‐based Rietveld refinement. This has been tested with standard materials and found to be comparable in accuracy to results obtained from traditional angular‐dispersive diffraction. The lower limits of detection of the method have not been established quantitatively but qualitative differences can be seen between cells that have been cycled at different times. These differences indicate a linear relationship between scale formation and electrolysis time.