INTRODUCTION

An ongoing challenge in Short Wave Infrared Reflectance Spectroscopy is the determination of percentages of individual mineral components present in mixed samples, or more simply, the quantitative analysis of mineral-bearing samples. There are many reasons why this is difficult to achieve.

One of the main problems is that the relationship between mineral mixtures in rocks and spectral absorption wavelength shifts is non-linear. The absorption coefficients for the molecular bonds detectable in the SWIR range of the Electromagnetic Spectrum are not adequately known, and these coefficients are required to define the non-linear relationships present in mineral mixtures.

From the spectral data, therefore, minerals do not appear in linear mixed configurations, but rather as a function of these unknown absorption coefficients. The intensities of the absorption features, therefore, cannot be used as a one-to-one correlation that relate directly to the amount of mineral present. For instance, an iron chlorite will absorb more energy at its diagnostic wavelengths and reflect less back to the detector than an aluminum-bearing mineral, such as an illite, which more efficiently reflects back-absorbed energies.

These same problems are inherent in X-ray diffraction analysis, and also explain why this technique often fails to yield quantifiable results.

Additionally, a matrix effect occurs when non-infrared active minerals are present, and absorb, but do not reflect, the excitation energy.

APPROACH

Until absorption coefficients are known, all approaches taken must assume a linear relationship between mineral phases in a sample. Since this introduces immediate error, the most valid test of the method would lie with minerals within the same structural group and with similar or known chemical composition.

Working from this premise, Spectral International has been developing (with William Peppin of Advanced Software Applications) a mineral percentage program based on linear unmixing. The approach taken is somewhat simplistic. However, it appears to be accurate in determining two of the components present in a mixture, when they have similar absorption coefficients and when together they dominate the sample.

A sample suite containing carbonate samples with calcite and dolomite was acquired with semi-quantitative X-ray diffraction analysis data, and percentage information was available so comparisons could be directly made to PIMA spectral data.

Those samples were analyzed with PIMA and the wavelengths noted. To test the algorithm, reference end-member spectra for calcite and dolomite were chosen from SPECMIN™. These were used to create computer models of the spectra of mixtures with varying percentages of both minerals.

The next step was to choose end-members from the sample suite and build calibration models from them, which established the wavelengths for this data set. The unknowns were then run through the program and percentages obtained. These were compared against the X-ray diffraction results.

The following section will present an overview of the project.

Additional information is available through Spectral International.

METHOD

Figure 1 is a compilation plot of various carbonate minerals in the series containing iron, calcium and magnesium carbonates. It illustrates why carbonates are a good choice for a quantification study. Compositional mixtures of different species will shift wavelength positions of the main absorption feature in a predictable way.

Figure 1. - Different carbonate minerals are plotted in the series from [A] siderite (Fe) to [B] ankerite (Fe, Mg, Ca) to [C] aragonite (Ca) to [D] calcite (Ca) to [F] dolomite (Ca, Mg) to [E] Fe-dolomite (Fe, Mg, Ca) to[G] magnesite (Mg).

Note how the wavelength position of the major feature shifts with the substitution of different cations from 2344nm for siderite to 2298nm for magnesite. This wavelength shift can be used to determine chemical compositions and to semi-quantify carbonate minerals occurring in a sample suite.

With the carbonates in this case study, the absorption coefficient problem is somewhat reduced as the absorption coefficients of the two species (calcite and dolomite) are similar and, therefore, they can be treated essentially as a linear mixture.

The simplest approach is to first try to produce percentages in a two-component system. In this case the two obvious components are calcite and dolomite.

Calibration File from Ideal End Members

Therefore, to test the algorithm, end member spectra for calcite (hydrothermal from Alligator Ridge Mine, Nevada) and dolomite (USGS Clay Laboratory Collection, location unknown) were chosen from the SPECMIN™ Spectral Library. The two references chosen were highly ordered and display sharp, well, defined profiles. The results are shown in Figure 2.

Figure 2 - Spectral plots of computer-generated percentage mixtures (in 10% increments) from SPECMIN™ reference spectra for calcite (CalcNv1) and dolomite (DoloNg1). The series is from calcite at the top to dolomite at the bottom. Note the shift in the 2300nm feature. William Peppin, Advanced Software Applications, Inc.

The objective in choosing these was not necessarily to emulate the sedimentary minerals from the Case Study Project, but to provide the computer algorithm with the best possible spectral end-member examples for the mixing routine, while still using spectra from the same mineral species found in the case study.

These two end-members were mixed artificially in 10 percent increments from zero to 100% of each end-member. The graphic results for this mixing experiment are shown in Figure 2, which plots the entire spectral range from 1300 nm to 2500 nm, and in Figure 3, which is an expanded view of the region from 2100 to 2500 nm. Note in the latter the wavelength shift from the calcite at approximately 2334 nm to the dolomite at approximately 2318 nm. This shift demonstrates the potential for differentiating the two end-member minerals and mixtures of them from wavelength positions. This is shown in Figure 2 and an expanded view in Figure 3.

Figure 3 - Spectral plots of computer-generated percentage mixtures (in 10% increments) from SPECMIN™ reference spectra for calcite (CalcNv1) and dolomite (DoloNg1). The series is from calcite at the top to dolomite at the bottom. This is an expanded view showing the wavelength shifts between the two end-members. William Peppin, Advanced Software Applications, Inc.

Calibration File from Case Study Project Samples

The next step is to transfer the method to the Case Study Project samples, which are "real world". Using the X-ray diffraction data and spectral profiles, two end-members were chosen. These are CS19 (98% calcite by XRD) and CS18 (97% dolomite by XRD).

As with the SPECMIN™ references, these two end-members were mixed artificially in 10 percent increments from zero to 100%. The graphic results for this mixing experiment are shown in Figure 4, which plots the entire spectral range from 1300 nm to 2500 nm, and in Figure 5, which is an expanded view of the region from 2100 to 2500 nm.

Figure 4 - Spectral plots of computer-generated percentage mixtures (in 10% increments) from Case Study Project spectra for calcite (CS19) and dolomite(CS18). The series is from calcite at the top to dolomite at the bottom. William Peppin, Advanced Software Applications, Inc.

Note, as in the previous SPECMIN™ data, the wavelength shift between calcite and dolomite is also apparent.

Figure 5 - Spectral plots of computer-generated percentage mixtures (in 10% increments) from Case Study Project spectra for calcite (CS19) and dolomite(CS18). The series is from calcite at the top to dolomite at the bottom. This is an expanded view showing the wavelength shifts between the two end-members. William Peppin, Advanced Software Applications, Inc.

These Case Study Project end-members were run through the artificial mixing algorithm with the results seen in Table I.

Table I ­ Artificial Mixtures of Case Study Project end members

Note how the wavelength values shift from 2340nm for 100% calcite to 2318nm for 100% dolomite. This shift in wavelength can be used to verify the percentage computations. These therefore, are the reference answers for the artificial mixtures from the two Case Study end-members.

The results are reasonable, as these end-members are not completely pure samples. CS19 is 98% calcite and Sample CS18 is 97% dolomite. The error for these computations all falls within one standard deviation.

Algorithm Applied to the Case Study Data Set

The percentage algorithm was then applied to the entire Case Study Project data set, and the mineral percentages derived compared to X-ray Diffraction data. The results are shown in Table II.

The linear unmixing algorithm has the potential of being more accurate than the X-ray diffraction method. In the table, where the greatest difference between percentages derived from PIMA data and those from XRD occur (highlighted), the absorption feature wavelength values will, for the most part, corroborate the values computed from PIMA spectra.

Therefore, the wavelength acts as a check against the percentage algorithm.

The XRD values for CS14 appear to be transposed, an error in the original data set.

Table II ­ Mineral Percentages of Case Study Project Data Set vs XRD

The key to accurate results lies in building calibration files from the sample suite under investigation. Monomineralic end-members, that are site-specific, must be chosen for the models to succeed.

Accuracy, with matrix effects, appears to be, on average, 3-5%.

Figures 6A and 6B show correlations between X-ray diffraction percentage values and those derived form PIMA data. Figures 7A and 7B shows correlations.

Figure 6 ­ These figures show the correlation between mineral percentages derived from PIMA infrared data and XRD analyses for Calcite [A] and Dolomite [B]

Figure 7 ­Wavelength of diagnostic absorption features for Calcite [A] and dolomite [B] against mineral percent as determined by XRD (black) and PIMA (red).

Figure 6A compares PIMA against XRD for calcite, and Figure 6B for dolomite, with high correlation coefficients. The same type of correlation is done with wavelength values against the XRD-derived values, and the scatter plots are shown in Figure 7 A for Calcite and Figure 7B for dolomite.

It is important to emphasize here that the best correlations are derived from calibration files built from site-specific end-members. The values derived from the two SPECMIN™ references do not give as good a match, although they were a good test for the algorithm.

Accuracy, with matrix effects, appears to be, on average, 3-5%. This can be improved slightly, but requires an order of magnitude more processing time to do so.

The other point to remember is the limits of the instrumentation. PIMA-II has about a 5nm resolution and samples are collected in 2nm steps. This oversampling is done to improve the reproducibility of the method, however, it does not necessarily improve the accuracy. Therefore, the limit of the method for resolving the wavelength positions is from 2 to 4 nm. This is also influenced by the calibration of the PIMA-II instruments, some of which can be as far as 4 nm off calibration. PIMA#16, which was used to collect this data, is rated as + 2nm, which is as good as can be expected in a scanning instrument.

This method shows sufficiently high correlation that it should be investigated further and refined.