or a focal median filter. Applying different filters to the original X-ray maps can reduce or eliminate background noise, refining the principal components. A low pass filter smoothes the data by taking the mean for each 3 × 3 pixel area. A focal median neighborhood filter takes the shape of a neighborhood (i.e., circle or rectangle) and processes the map cells accordingly. Similar results were obtained using the low pass filter and the rectangular focal median filter. For comparison, we examined the element maps using a low pass filter and a circle focal median filter with a radius of 2 cells.
The greatest asset to using XRMA is that it eliminates decision-making by the user and highlights textural features that are not obvious in optical microscopy or BSE images of thin sections .
2.5. Principal Components Analysis
PCA defines a multidimensional coordinate system, where each axis is known as a principal component (PC). PCs can be considered as new super variables that replace sets of variables that are correlated, or in our case, sets of elements that are spatially correlated. In our application, we can consider a PC as likely representing a mineral present in the sample. In general, the largest portion of the information in a data set is found within the first three to five PCs. In our thin sections the first 3 PCs corresponded to the three major minerals found at Round Top. The following PCs described minor and accessory minerals. This paper emphasizes the first 6 PCs due to their importance and relevance to this economic deposit.
Figure 1. Intensity maps obtained by EPMA of sample RT 10 thin section for elements potassium (left) and iron (right). Brighter areas indicate higher concentrations of the element. Field of View (FOV) 2 × 2 mm.
The ArcGIS™ raster calculator tool was used to take multiple individual element X-ray maps such as K, Al, and Si and integrate them to create separate mineral maps, e.g., K-spar, by displaying the pixels in which only those three elements occur together. These individual mineral maps were further refined using the reclassify tool to lower background noise, which narrows the data by labeling pixels with the highest intensity of the mineral with (1) and where it is not, with (0). Refined maps thus are generated delineating only where the mineral is present, and leaving the map blank where the mineral is not present. This allows the analyst to connect the different layers of individual maps and see potential overlapping of minerals or pore space.
2.7. Integrating EPMA, XRMA-PCA, and ArcGIS™
Our overall initial data processing comprised this flow: 1) generate X-ray maps from the EPMA; 2) input the X-ray map into XRMA to determine PCs using no filter, low pass filter, and circle focal median filter; 3) “ground truth” our results by comparing them to mineral compositions obtained in prior published research.
3. Results and Discussion
3.1. Principal Component Analyses
The PCA images generated using the low pass filter yielded the most consistent results and map images overall. Results with no filter appeared noisy and those with the circle focal median filter removed too much of the data. The computer-generated mineral compositions based on the low pass filtered PCA data fall within the range of mineral percentages found in prior research indicating our approach works well. The advantage of the computer-generated approach is that we were able to image smaller minerals and generate a more detailed map of the element locations than previous studies could provide. This is important in analyzing methods for mineral extraction at Round Top Mountain because the principle mineral, yttrofluorite, is typically less than 20 μm in length.
3.2. Principal Components: Major Minerals
In all 7 thin sections the highest weighted variables comprising the first 3 PCs were K, Al, Si, and Na. These four elements are known from bulk elemental analyses   to make up approximately 90% or more of Round Top rhyolite. The three minerals corresponding to the first 3 principal components are the major minerals of the Round Top rhyolite: orthoclase feldspar (K-spar, KAlSi3O8, monoclinic), plagioclase feldspar (albite, NaAlSi3O8, triclinic) and quartz (SiO2, trigonal). Figures 2-4 present X-ray maps for K, Al, Si, and Na, along with larger red-green-blue (RGB) maps of the first 3 principal components, for samples RT 4, RT 7 and RT 9. The X-ray maps, represented on a gray scale, display the highest concentration of the specified element as white.
Note the similarity of the gray areas on the Al and Si maps. These correspond to the similar Al and Si stoichiometries of K-spar and albite. The K map depicts K-spar as rims around black (no K) albite cores. The width of the K-spar rims depends on the size of the albite cores; the smaller the albite core, the wider the K-spar rim, as was observed originally in .
Figure 2. Top, left to right: X-ray maps of K and Al. Bottom, left to right: X-ray maps of Si and Na in the same area of the petrographic thin section of sample (RT 4) of Round Top Mountain. Far right: RGB map of first 3 principal components (R = K-spar, G = Quartz, B = Albite). FOV 2 × 2 mm.
Figure 3. Top, left to right: X-ray maps of K and Al. Bottom, left to right: X-ray maps of Si and Na in the same area of the petrographic thin section of sample (RT 7) of Round Top Mountain. Far Right: RGB map of first 3 principal components (R = K-spar, G = Quartz, B = Albite). FOV 2 × 2 mm.
Figure 4. Top, left to right: X-ray maps of K and Al. Bottom, left to right: X-ray maps of Si and Na in the same area of the petrographic thin section of sample (RT 9) of Round Top Mountain. Far right: RGB map of first 3 principal components (R = K-spar, G = Quartz, B = Albite). FOV 2 × 2 mm.
3.2.1. Potassium Feldspar
PC 1 shows the highest values for potassium, aluminum, and silicon, which corresponds to potassium feldspar (K-spar), KAlSi3O8. The K map has a close association with rubidium (Rb) for all 7 RT samples. Monovalent rubidium, an alkali metal, commonly substitutes for its alkali neighbor potassium in the K-spar structure. With respect to the RGB map (Figure 2) the pink outlines the location of K-spar, which in the average of our 7 samples comprises 51 volume percent (vol%) of the rhyolite (Table 1), nearly identical to the 52 vol% and 48 - 52 vol% of the earlier studies  .
PC 2 shows a peak high value of silicon, which corresponds to the mineral quartz, SiO2, for 6 out of 7 RT samples. Figures 2-4 depict the quartz grains in green. Quartz makes up approximately 23 vol% of the composition of the rhyolite (Table 1), a value somewhat lower than the 30 vol% and 28 - 30 vol% in the prior estimates  .
PC 3 also displays high values for silicon, followed by aluminum and sodium (albite-NaAlSi3O8). Albite phenocrysts are located in blue within the RGB map. Albite comprises 13 vol% (Table 1), consistent with the earlier 11 vol% and 8% - 14%  .
3.3. Principal Components: Minor and Accessory Minerals
The minor minerals annite mica, magnetite, and zircon comprise 7% - 10% of the rhyolite. The accessory minerals yttrofluorite, columbite, thorite, and cassiterite are seen in all 7 samples in trace amounts.
3.3.1. Annite Mica
Annite mica corresponds to high loadings for Fe, Si, and Al with minor loadings of Dy (an EPMA artifact due to an overlap of X-ray emissions with Fe), F, U and Yb. The Fe map has gray shades that align well with Al and Si, consistent with
Table 1. Comparison of round top mineral compositions.
the composition of an Fe-rich biotite, annite (KFe32+AlSi3O10(OH,F)2, monoclinic). The mica found within the thin sections averages 4.3 vol% (Table 1), close to the 4.5 vol% and 4 - 5 vol% of the earlier studies  .
The brightest areas on the EPMA Fe X-ray maps are assumed to be magnetite (Fe3O4, isometric), and possibly some hematite. Magnetite percentages fall within the range from 1% to 4.8% in the rhyolite samples. Table 1 shows magnetite at 2.1 vol%, consistent with the 1 vol% and 2 - 3 vol% in the prior studies  .
The rare earth elements (REEs) yttrium, ytterbium, and dysprosium are among the high value economic target elements in the Round Top Mountain deposit. Dy, Y, and Yb grains correspond with one another and are incorporated in yttrofluorite. The target mineral yttrofluorite (YF), the most valuable mineral in the deposit, is present in very small amounts. Yttrofluorite (Ca, Y, HREE)F2, isometric) is a variety of fluorite (CaF2, isometric) where up to approximately 30% of the Ca2+ is substituted for by Y and other mostly HREEs. Yttrofluorite averaged 0.25 vol% (Table 1).
One of the minor minerals that shows up as a principal component describes where zirconium (Zr) and silicon (Si) have the highest loadings. These elements combined, as minerals, define the mineral zircon (Zr(SiO4), tetragonal) This mineral was present at the 0.32 vol% level (Table 1).
The 7th and 8th principal component consistently displays high loadings for sodium (Na), fluorine (F), and aluminum (Al). These elements combined, as a mineral, describe the mineral cryolite (Na3AlF6, monoclinic). The mineral percent composition for cryolite was 1.2 vol%, somewhat lower than the 2.5 vol% in .
One of the accessory minerals shows up as a principal component in high loadings for niobium (Nb), ytterbium (Yb), and iron (Fe). These elements together, as an oxide, describe the mineral columbite (Fe2+Nb2O6 to Mn2+Nb2O6, orthorhombic). Columbite vol% averaged 0.3%.
The 14th principal component consistently displays high loadings for thorium (Th), uranium (U), and silicon (Si). These elements combined describe the mineral thorite (Th(SiO4), tetragonal). Thorite was present at 0.1 vol%.
The 15th principal component consistently displays high loadings for uranium (U). This element combined with oxygen, as a mineral, describes the mineral uraninite (UO2), isometric. This mineral was present at the 0.1 vol% level.
Another accessory mineral displays high loadings for tin (Sn). This element, as an oxide, describes the mineral cassiterite (SnO2, tetragonal). The mineral cassiterite comprised 0.02 vol% of the rhyolite.
3.4. Evaluation of Comparison of Results with Those of Earlier Studies
To test the validity of the combined PCA and Arc GISTM methods the previous section and Table 1 compared our computer-generated composition (averages of 7 samples) to published mineralogical results from earlier studies  . The first study  converted their bulk chemical (elements) analysis of a Round Top sample to a mineral composition via the CIPW norm, a long-established method in petrology. The CIPW calculation originated with the need to estimate the mineral composition of an aphanitic igneous rock (one so fine-grained that the minerals could not be point counted with a petrographic microscope) from its bulk elemental composition, based on chemical analysis . The earlier study provided a table with normative volume percents of the main minerals. These can be compared directly to our results, which are based on measurements of the area occupied by the different minerals in the thin sections, area and volume percents being equivalent. Our results were systematically adjusted upwards by 3% to reflect the estimated effect of pore space on the mineral composition, which was not measured in the bulk elemental analysis of .
The compositional ranges from the second comparative study  were based on microscopic examination of thin sections from nearly 50 samples. These data were presented as volume percents, based on occupied areas in the thin sections.
As anticipated, there was general agreement between the studies, suggesting that our approach is valid (Table 1). But note that this test is an imperfect one. The earlier studies collected surface samples from the deposit. These might have been altered by proximity to country rock during emplacement of the laccolith or been subjected to weathering in their surficial environment. Our samples were from drill cuttings and likely are more representative of the actual bulk of the deposit. Further, we must emphasize that the actual overall composition of the laccolith is both unknown and unknowable, and all attempts to characterize that composition are limited by sampling and analytical considerations.
The similarities among the studies emphasize the earlier finding that the mineralization at Round Top is remarkably homogeneous . That earlier geochemical study involved some 1400 samples from more than 100 drill holes spread across the mountain. That represents homogeneity at a scale of tens to hundreds of meters. Here we compared our seven 2 × 2 mm sampling areas, examined by electron probe microanalysis to a depths of a few micrometers, to a mineralogy analysis based on bulk elemental chemistry  and analysis of numerous full thin sections . This suggests that the Round Top Mountain rhyolite composition is homogeneous for many elements down to the mm scale. Viewed another way, the electron probe analysis for most of the elements extended less than 10 µm into the sample. Thus, the total analyzed mass in our study was minuscule, likely some 700 micrograms!
3.5. Mineralogical Textural Analysis: Major and Minor Elements
Figure 5 presents mineral maps of samples RT 2 and RT 12. The K-spar (pink) phenocrysts found in these two samples range in size between 50 and 250 μm in length. The K-spar surrounds the albite cores (light gray) as rims; the albite ranges from 20 to 100 μm in length. The location of the quartz is indicated in yellow and is seen dispersed randomly throughout the thin sections. The quartz grains range from 20 to 150 μm and are anhedral to subhedral in appearance. Magnetite (black) and annite biotite (brown) are both found dispersed throughout, with phenocrysts ranging between 10 and 100 μm in length. Also present are such minor or accessory minerals as zircon, cryolite, yttrofluorite, cassiterite, columbite, uraninite and thorite, although these minerals are present in trace amounts and thus they are not depicted here.
3.6. Mineralogical Textural Analysis: Yttrofluorite Distribution
To discern which minerals neighbor the valuable target yttrofluorite we overlaid the YF map on top of maps of the major and minor minerals (Figure 6). Zooming into individual YF grains, approximately 1 - 20 μm in length, those neighbors could be determined. Six out of the seven mineral maps showed that the majority of the YF grains were associated with K-spar and quartz grains. Occasionally, the YF grains abut albite grains and, less commonly, the iron-rich phases, magnetite or annite mica. RT 10 exhibited a different behavior in which the YF grains are solely found on the Fe-rich mica (annite).
We had expected that perhaps the YF would be clustered adjacent to, or in discrete micro-pods with, other minerals containing incompatible elements that were precipitated contemporaneously with the YF in the late-stage fluorine mineralization event. This does not appear always to have been the case, with most of the yttrofluorite isolated from, and some associated with the minor and accessory minerals. Concentration of the valuable YF with such other potential targets as columbite-tantalite, cassiterite, zircon, and uraninite would have suggested that fine grinding and mechanical separation of such clusters could be an economically viable approach to exploiting this multi-mineral deposit.
3.7. Mineralogical Textural Analysis: Porosity
Figure 7 shows sample RT 4, a pink rhyolite, with a pulled out section of the upper right-hand corner enlarged in order to highlight this porosity. The black areas are the pore spaces found between minerals. Each pixel is approximately 4 μm in size.
Previous studies have shown that Round Top Mountain rhyolites have 1% to 2% porosity in the gray varieties and 3% - 8% porosity in the pink varieties . This porosity is evident in the mineral maps. Using ArcGIS™, the percentage of pore spaces was calculated to range from 1.4% to 4.0% in the 7 samples, consistent with earlier measurements of porosity by water saturation .
Figure 5. Mineral maps of thin sections of samples RT 2 and RT 12. K-spar (pink), albite (light gray), quartz (yellow), magnetite (black), annite mica (brown). FOV 2 × 2 mm.
Figure 6. All 7 RT mineral maps with major, minor, and accessory minerals, K-spar (pink), albite (10% gray), quartz (yellow), magnetite (black), annite mica (brown), zircon (blue), cryolite (orange), uraninite (40% gray), thorite (purple), cassiterite (light blue), columbite (green), and yttrofluorite (red and circled). FOV 2 × 2 mm.
Figure 7. Mineral map of sample RT 4 showing pore space (black areas). FOV 2 × 2 mm.
Multivariate analysis was performed on seven thin sections of Round Top Mountain rhyolite. Through the use of the XRMA tool package in ArcGIS™, principal components were derived and percentages of major and minor minerals were determined. By overlaying the X-ray element maps in ArcGIS™, element-mineral correlations were observed for each principal component at each pixel. This enabled conversion of the elemental maps into mineral maps. Resulting overall mineralogy proved consistent with results from prior investigations. This new approach presents the opportunity to use computer-generated information to provide an unbiased basis for creation of mineralogical maps from elemental maps. The study further demonstrated the overall homogeneity of the Round Top Mountain deposit at the microscopic scale.
The authors thank Texas Mineral Resources Corporation for providing access to proprietary technical data and samples. This project was supported by joint research contracts 26-8211-12 and 26-8211-16 between TMRC and the University of Texas at El Paso. Funds to cover the costs to publish in open access were obtained from this source. Also, we thank Prof. Gaetano Ortolano and Ph.D. candidate Roberto Visalli from the University of Catania, Italy for access to their X-ray Map Analyzer application.
M.P., M.A., and L.N. declare no potential conflicts and received no compensation for project participation. D.G. is the CEO of TMRC and serves on its Board of Directors. N.P. serves on the Board of Directors of TMRC. He is not and has never been an employee of TMRC, nor has he received any compensation from the research contracts that supported this research. The funding sponsor, TMRC, had no role in the decision to publish the results.
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