Analysis of temperature‐dependent Raman spectra of minerals: Statistical approaches

Abstract

The application of statistical methods to Raman spectroscopy is due to the need to analyse arrays of poorly resolved mineral spectra having low symmetry, large unit cells, and so forth. For the diagnosis of spectral changes under the influence of an external factor, as well as for the determination of critical values, statistical methods for the treatment of the spectrum profile provide more accuracy than a peak‐fitting procedure. The following algorithms for calculating statistical ξ parameters are used to parameterise I(ν,T) arrays of temperature‐dependent Raman spectra: Pearson correlation coefficient characterising the similarity/difference of signals; autocorrelation function, proposed earlier for estimating the weighted average width of spectral lines; and skewness and kurtosis, the parameters of the distribution of signal intensity. The ξ(T) relations were analysed for the synthetic and experimental spectra of natural zircon, titanite, and synthetic quartz in the range of T = 80–870 K. For zircon, the differences in the anharmonic behaviour of modes having various properties and symmetry are shown through the use of ξ(T). For quartz, at the temperatures preceding the displacive α–β phase transition, statistical analysis reveals the spectral region of soft modes, allowing their T‐behaviour to be analysed. For titanite, the critical temperature range corresponding to the displacive α–βγ phase transition is determined by differentiating ξ(T). The results show the potential of using a statistical approach for the rapid detection of spectral and temperature regions responding differently to an external effect, as well as for evaluating the critical values of an external parameter.

Statistical approaches in the analysis of in situ thermo‐Raman spectroscopic data for gypsum as a basis for studying dehydration and phase transformations in crystalline hydrates

“…Pearson r coefficient of correlation carries information about the degree of “similarity” of a certain spectral fragment, obtained at a temperature in the range of 80–870 K, with a similar fragment of a “reference” spectrum, obtained at the temperature of the lower boundary range, at 80 K. Earlier, [ 40 ] it was established on the basis of the analysis of model spectra that r values change significantly with the shift and relative change in the intensity of the lines but change insignificantly with their broadening. On the temperature dependences of the r coefficient obtained for all four (I–IV) spectral fragments (Figure 4a,d,g,j), the differences between the spectra and the reference spectrum are effectively detected by an intermittent change in r(T) in the region of gypsum dehydration and in the region of CaSO 4 γ → β transition.…”

“…Statistical analysis was aimed to obtain ξ(T) functional dependences of a certain ξ signal parameter on T external factor. The temperature dependences of a number of well‐known statistical parameters [ 40 ] were selected as ξ(T) functions: the Pearson's r coefficient, the Δcorr based on the calculation of the autocorrelation function, and the skewness.…”

“… where α(ω) is the primary spectrum, α(ω + ω’) is a replica of the spectrum shifted by ω′. A detailed description of the Δcorr calculation is given in Chang et al, [ 29 ] and the modified algorithm of its calculation in Pankrushina et al [ 40 ]…”

“…In such cases, it is promising to use statistical methods for analyzing datasets without spectral deconvolution into components. In Pankrushina et al, [ 40 ] a review and test results of a number of statistical methods for processing temperature‐dependent in situ Raman spectroscopic datasets are presented for the diagnostics of thermally induced processes in minerals by the full spectral profile or its individual fragment. The present work continues our research in this area.…”

GeoRaman

“…Waeselmann et al [12] provide new data useful for the association of positions, widths and intensities of the Raman-active modes to the crystal-chemical formulae of amphiboles: They add to the information extracted from the OH stretching range, further features deriving from the framework Raman spectrum. The potential of using a statistical approach as a more accurate alternative to peak fitting has been explored by Pankrushina et al [13] exploiting synthetic and experimental spectra of natural zircon, titanite and synthetic quartz in the 80-870 K temperature range. Díez-Pastor et al [14] employ machine learning algorithms to identify spectral differences pertaining to mineral structure and/or composition of a variety of variscites, an aluminium phosphate mineral, from Gavà with respect to delineating their mine of origin and extraction depth.…”