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.

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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.

The origins of extensive solid−solid-state interconversions that accompany the electrochemistry of microparticles of tetracyanoquinodimethane (TCNQ) and semiconducting CuTCNQ (phases I and II) adhered to glassy carbon (GC) electrodes, in contact with CuSO4(aq) electrolyte, have been identified. Ex situ analyses with electron microscopy, infrared spectroscopy, and X-ray diffraction have been used to identify the phase changes that occur during the course of potential cycling or bulk electrolysis experiments. All redox-based transformations require extensive density, volume, and morphology changes, and consequently they are accompanied by crystal fragmentation. The net result is that extensive potential cycling ultimately leads to the thermodynamically favored TCNQ/CuTCNQ(phase II) solid−solid interconversion occurring at the nanoparticle rather than micrometer size level. The overall chemically reversible process is described by the reaction TCN + C + 2e- ⇌ CuTCNQ(S,GC)(phase I or phase II). Needle-shaped CuTCNQ(phase I) crystals having a density of 1.80 g cm-3 are predominately formed in the first stages of potential cycling experiments that commence with micrometer-sized rhombic-shaped TCNQ crystals of density 1.36 g cm-3. The rate of subsequent formation of thermodynamically stable CuTCNQ(phase II), which has an intermediate density of 1.66 g cm-3 and a crystal shape more like that of TCNQ, is dependent on the number of potential cycles, the scan rate, and the initial size of the adhered TCNQ crystals. Evidence obtained by cyclic voltametry and double potential step techniques indicate that the formation of CuTCNQ(phase I and II) involves a rate-determining nucleation and growth process, combined with the ingress and reduction of ions (from the electrolyte). The reactions involved in the process are believed to be TCN + e- + ⇌ [Cu2+][TCNQ-]S,GC and [Cu2+][TCNQ-]S,GC + e- ⇌ [Cu+][TCNQ-]S,GC in which CuTCNQ(phase I) is formed initially and then CuTCNQ(phase II) after a large number of potential cycles. The reverse oxidation process involving the transformation of solid CuTCNQ(phases I and II) to TCNQ also involves a nucleation−growth multistep process and significant crystal size and morphology changes. Finally, data led to the postulation of a mechanism for the formation of CuTCNQ compounds via chemical reaction pathways in which the existence of the electrochemically inferred transitional Cu2+ intermediate also is included.