Large-Area Quantitative Phase Mapping
Table 1 : Phases found with COMPASS in one 33 µm scan width and the average atomic number of each. Seven mineral phases were found.
Phase carbon
Titanate - (CaO TiO2 SiO2) Pyroxene (CaO FeO SiO2)
Pyroxene (FeMg)O2 SiO2 K-feldspar (KAlSi3O8)
Chalcopyrite (CuFeS2) Sphalerite ((ZnFe)S)
Pyrite (FeS2)
Average atomic number
6.0
12.0 13.1
10.8 10.6
21.8 22.0
19.3
Detection by image contrast
unique
mixed mixed
mixed mixed
mixed mixed
unique
as compared to element mapping, the data acquisition process is shortened signifi cantly.
For the technique described here, these principal component maps must be translated into phase maps. In a PCA map, every pixel has a fi nite statistical probability of belonging to any given component. In a phase map, each pixel belongs to just one—and only one—phase. T is enables both quantitative analysis of the EDS X-ray spectrum within each phase and the quantitative measurement of the size and distribution of each phase. Translating the component maps into phase maps is accomplished using the same types of intensity thresholding algorithms used for traditional element-based phase mapping. The spectrum for each phase is the sum total of the spectra from each pixel in the phase. T e identity of each phase is then determined either by quantitative analysis of the spectrum or by matching against an X-ray spectral library. At the end of this process, the identity of each phase was closely identifi ed, given that uncertainties can arise from strong fl uorescence eff ects, spatial sampling frequency, and the possible presence of polymorphs, for example, rutile versus anatase for TiO2.
Results
Analysis of crushed mining sample Number of distinct phases. Figure 1 shows a low- magnification backscattered electron (BSE) image of some grains in a crushed rock sample from a mining operation. Figure 2a shows the grayscale SEM image, exhibiting atomic- number contrast from backscatter electrons, of a single grain similar to that selected in the red box of Figure 1 . If the operator had no other clues to the locations of the various phases, the EDS system could be used to probe the light and dark regions to provide qualitative and quantitative analyses of what appear to be diff erent phases. However, this procedure has limitations. One limitation is that the BSE image does not conclusively determine the number of phases present. Figure 2b shows an image histogram (number of pixels of each gray level) with
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thresholds set at what appear to be four intensity levels above the lowest few gray levels (which correlate with the carbon- based mounting material). Each threshold is marked by a color, and these colors are mapped to colorize the BSE image ( Figure 2c ). T e enlarged-area color map ( Figure 2d ) shows four regions for EDS analysis. Performing an EDS analysis inside each of the identifi ed regions could provide a qualitative and quantitative elemental analysis for each expected phase. Element mapping. It is still not clear that all of the phases have been found. Figure 3 shows X-ray maps for each element detected in this grain. Regions of major diff erences in material composition are identifi able by visual inspection. Neglecting the carbon from the mounting material, these element maps indicate the presence of at least six phases. Moreover, when three element maps are converted to red, green, and blue primary colors and combined, element associations can be easily discerned—but only three elements at a time. T ese qualitative X-ray maps tell us what elements are present and some element associations, but any composition more complex than just the major elements is diffi cult to determine. Quantitative analysis of a phase may be used to indicate its composition, but a phase is usually defi ned by its crystal structure. Moreover, solid solution effects can change the composition within certain crystal structures. Normally we would use a diff raction method, powder X-ray diff raction, or electron diff raction in the transmission electron microscope to determine the crystal structure by matching d-values to standard phases stored in a database (for example, the powder diff raction fi le databases of the International Centre for Diff raction Data). Principal component analysis. T ere is a quicker way to determine the identity of the phases present. By invoking multivariate statistical analysis and performing a principal component analysis, as described above, distinctive groupings of elements can be identifi ed. Figure 4 shows COMPASS phase maps of the same grain examined in Figures 2 and 3 . T e Compass phase map for this sample was constructed with only 76 X-rays per pixel and required an acquisition time of 30 seconds. In this case seven distinct phases (beyond carbon-based mounting compound) have been identifi ed as shown in Table 1 . Why is the BSE image inadequate? The additional phase regions not identifi ed in Figures 2 and 3 all had similar electron- image contrasts to nearby phases. Because backscattered image contrast is directly related to the average atomic number of any given region, these missed identifi cations are not surprising when the average atomic number of each phase is calculated ( Table 1 ). T e following instances of similar average atomic number are worth noting because these pairs are diffi cult to discriminate in BSE images: • Sphalerite (ZnFe)S and chalcopyrite CuFeS 2 with average atomic numbers of 21.8 and 22.0.
• Titanate (CaO TiO 2 SiO 2 ) and pyroxene (CaO FeO 2 SiO 2 ), where only the Ti and Fe component are interchanged, have average atomic numbers of 12.0 and 13.1, respectively.
• Pyroxene ((FeMg)O 2 SiO 2 ) and K-feldspar (KAlSi 3 O 8 ), where the average atomic numbers are 10.8 vs. 10.6. Phase identification by spectrum analysis. After selecting the distinct regions for analysis, sufficient X-ray
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