Quantification of phases with partial or no known crystal structures

Abstract

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.

Quantitative Rietveld analysis of the crystalline and amorphous phases in coal fly ashes

“…were left as free parameters. Given that the Z a M a V a product has no physical meaning [19], the area under the curve of the SPV function was directly used as effective scale factor for the amorphous phase. The XRD reflections for the crystalline phases were adjusted with conventional pseudo-voigt functions, whereas a first-order polynomial function was found to yield a good fit of the background signal.…”

“…Alternatively, it is possible to carry out quantitative Rietveld analyses of phases that have 4 an unknown (or amorphous) crystal structure by using a simple calibration procedure [19]. This type of approach, based in the extraction of the intensity of the XRD peaks of the unknown phase, simply requires the calibration of the product Z a M a V a for the unknown phase, where Z a , M a and V a are, respectively, the number of formula units, molecular mass of the formula unit and volume of the unit cell of the unknown phase, labeled as a.…”

“…This type of approach, based in the extraction of the intensity of the XRD peaks of the unknown phase, simply requires the calibration of the product Z a M a V a for the unknown phase, where Z a , M a and V a are, respectively, the number of formula units, molecular mass of the formula unit and volume of the unit cell of the unknown phase, labeled as a. The product Z a M a V a enters in the expression for the calculation of the relative weight fraction of the unknown phase W a within the mixture [17,19] …”

“…(1) goes through all crystalline and amorphous phases in the mixture. For the calibration procedure, which allows one to relate the scale factor of the unknown phase (S a ) to its actual weight percent in the samples, the diffraction pattern from a well-characterized sample containing the unknown phase is required [19].…”

The HighScore suite

“…Empirical structure factors are extracted via a Pawley or a LeBail fit and are used for HKL file fit (together with a pseudo-formula mass derived from the known concentration in the binary mixture) for further quantifications following the Rietveld formalism. This method was first described by Scarlett and Madsen (2006) and is now implemented in HighScore with the Plus option (HighScore Plus). This is particularly important for complex materials of industrial relevance such as blended cement containing slag, pozzolana, and fly ash (Fuellmann et al, 2013).…”