Chemometric and Multivariate Statistical Analysis of Time-of-Flight

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Chemometric and Multivariate Statistical Analysis of Time-of-Flight Secondary Ion Mass Spectrometry Spectra from Complex Cu−Fe Sulfides Yogesh Kalegowda and Sarah L Harmer* †

Ian Wark Research Institute, ARC Special Research Centre for Particle and Material Interfaces, University of South Australia, Mawson Lakes, South Australia 5095 S Supporting Information *

ABSTRACT: Time-of-flight secondary ion mass spectrometry (TOFSIMS) spectra of mineral samples are complex, comprised of large mass ranges and many peaks. Consequently, characterization and classification analysis of these systems is challenging. In this study, different chemometric and statistical data evaluation methods, based on monolayer sensitive TOF-SIMS data, have been tested for the characterization and classification of copper−iron sulfide minerals (chalcopyrite, chalcocite, bornite, and pyrite) at different flotation pulp conditions (feed, conditioned feed, and Eh modified). The complex mass spectral data sets were analyzed using the following chemometric and statistical techniques: principal component analysis (PCA); principal component-discriminant functional analysis (PC-DFA); soft independent modeling of class analogy (SIMCA); and k-Nearest Neighbor (k-NN) classification. PCA was found to be an important first step in multivariate analysis, providing insight into both the relative grouping of samples and the elemental/molecular basis for those groupings. For samples exposed to oxidative conditions (at Eh ∼430 mV), each technique (PCA, PC-DFA, SIMCA, and k-NN) was found to produce excellent classification. For samples at reductive conditions (at Eh ∼ −200 mV SHE), k-NN and SIMCA produced the most accurate classification. Phase identification of particles that contain the same elements but a different crystal structure in a mixed multimetal mineral system has been achieved.

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a mineral surface.9,10 The combination of mass spectrometry and imaging makes the TOF-SIMS technique sensitive and capable of precisely identifying local surface chemistry and its distribution across the surface. Determination of hydrophobic/ hydrophilic balance, on a particle by particle basis, requires the selection of a particular mineral phase and statistical analysis of the particles with an estimation of the variability of the value. The mineral particles are generally identified by imaging for a major element of their composition, e.g., Cu, Fe, S, and Zn.11,12 The identification of a particular mineral phase which consists of the same elements in mixed mineral system (e.g., chalcopyrite, CuFeS2; bornite, Cu5FeS4) presents a unique challenge for TOF-SIMS.10 Additionally, precipitated, adsorbed, reacted, and contaminant species in the outermost molecular layers produce complex mass spectra that are difficult, if not impossible, to interpret using conventional methods. For effective analysis of such mineral systems, sufficient sensitivity to detect significant components and sufficient selectivity is required to discriminate between the closely related mineral phases and their similar surface chemistry.13 Furthermore, the determination of surface chemistry, on a particle by particle basis, requires the selection

aluable sulfide minerals are commonly concentrated from their gangue counterparts using froth flotation. Froth flotation can be selective and used to achieve specific separation of a variety of ores (i.e., copper sulfide, iron sulfide, zinc sulfide, and lead sulfide ores). Improvement in the selective separation of ore components is achieved by controlling the flotation conditions such as pulp potential (Eh), pH (aeration, reducing or oxidizing conditions), and addition of different types of collectors and modifiers at different concentrations.1−3 Galvanic interaction between grains of two different minerals has tremendous consequences for the surface chemistry that governs separation.4,5 Therefore, understanding the surface chemistry (the hydrophobic/hydrophilic species balance) by particle and its statistical average by mineral phase is the principle determinant to predict, control, and modify the macroscopic surface properties that govern the efficiency of separation technologies.6−8 The range of information available for the effective use of surface sensitive spectroscopic/ spectrometric techniques has greatly assisted this understanding. The most successful techniques have included X-ray photoelectron spectroscopy (XPS), scanning Auger microscopy (SAM), and time-of-flight secondary ion mass spectrometry (TOF-SIMS) and a combination thereof. TOF-SIMS is a monolayer-sensitive surface analytical technique and has been extensively used in mineral processing to identify the chemical (elemental/molecular) composition of © 2012 American Chemical Society

Received: November 22, 2011 Accepted: February 10, 2012 Published: February 10, 2012 2754

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Each mineral sample was mixed with graphite particles of a similar size to assist in separation of particles. Fragments of mixed samples were mounted into 25 mm resin blocks consisting of a separate section for each mineral sample. The face of the sample block was ground, polished, and ultrasonicated in Milli Q water before conditioning. The sample blocks were conditioned along with an ore slurry (∼600 g of homogenized plant preleach concentrate) in Agitair flotation cell and subsampled at “feed” (untreated samples), “conditioned feed” (conditioned with collector at oxidative potential), and “Eh modified” (at reductive potential, Eh ∼ −200 mV SHE) for TOF-SIMS analysis. A reducing reagent (dithionite, Na2S2O4) was used to decrease the Eh of the slurry to −200 mV SHE. The aim was to test how galvanic interactions between different mineral grains can influence the surface chemistry of each mineral particle and its implications on classification analysis (e.g., Cu activation of pyrite). The samples were stored in liquid nitrogen until TOFSIMS analysis could be performed.6 TOF-SIMS Measurements. TOF-SIMS spectra were obtained using a PHI TRIFT5 nanoTOF equipped with a gold (Au) liquid metal ion gun (LMIG) operated in pulsed mode. An excitation voltage of 30 kV with “unbunched” beam setting was used to maximize the spatial resolution. A pulsed low-energy electron flood gun was used for charge neutralization. The analysis time was 2 min/frame for each group of particles. Both positive and negative ion spectra were acquired using a raster size of either 200 × 200 μm or 100 × 100 μm depending on number of particles analyzed per frame. Each particle was defined as a region of interest (ROI). ROI boundaries were set within the contrast edges of the regions. Positive ion mass spectra were calibrated to CH3+, C2H5+, and C3H7+ and negative ion mass spectra were calibrated to CH−, C2H−, and Cl− peaks. The mass resolution (m/Δm) at the Cu+ (m/z = 63) and Fe+ (m/z = 56) peaks were typically above 1150 and 1000, respectively. The base pressure in the analysis chamber was 2 × 10−7 Pascal. Statistical and Chemometric Analysis. Chemometric and statistical multivariate analysis was carried out using two standard software packages. The Statistica software package, version 9.0 (StatSoft, Inc. USA), was used for PCA and PCDFA. MatLAB software v.R2010a (MathWorks Inc., MA, USA) along with PLS Toolbox v.6.0 (eigenvector Research, WA) was used for SIMCA and k-NN. However, PCA was performed using both software packages, and in all cases, identical results were obtained. The intensities of positive and negative secondary ions (SIs) were normalized to the total positive and negative ion yields, respectively, and mean centered prior to multivariate analysis.10,25,26 Quantitative Performance Evaluation of Classification Techniques. Cohen’s kappa statistics27,28 and overall classification accuracy (the ratio of number of samples classified correctly to the total number of samples in data set)29 evaluation methods were used to quantitatively measure the performance of the different classification techniques. Interpretation of the kappa values is based on Landis categories. Higher kappa values mean stronger agreement.

of a particular mineral phase and statistical analysis of particles with an estimation of the variability of the value. Multivariate analysis (MVA) techniques for high-dimensional analytical chemical data (i.e., chemometrics) have become essential for chemical data analysis.14,15 The application of multivariate pattern recognition, classification, and calibration or correlation techniques within chemistry,16,17 biology,18 pharmaceutical,19 and recently in mineral processing,10,20,21 has proved its importance for surface analysis. Pattern recognition techniques aid analysts in the exploration of the entire mass spectrum at once, instead of only selected features and in the detection of major patterns in a given data set. These techniques can be grouped into two categories: “unsupervised” pattern recognition, where prior knowledge about the data is not used during the analysis, and “supervised” pattern recognition, where the data is separated into user defined groups before analysis. Few studies have focused on the use of multivariate analysis technique like principal component analysis (PCA) for the analysis of TOF-SIMS data of mineral samples. Hart et al. used PCA for phase recognition of a mixture of sulfides (chalcopyrite, pyrite, and sphalerite)10 that contain different metal ions. Brito e Abreu et al.20 used PCA to identify accurately which surface chemical signals are major contributors to the variation in particle hydrophobicity. In general, PCA has been mainly used for data reduction and pattern identification in multivariate system. 22 However, since PCA is an unsupervised pattern recognition technique which explains the overall variation in the data set, the discrimination between groups is not necessarily maximized. Soft independent modeling of class analogy (SIMCA),23 k-Nearest Neighbor (k-NN),21and principal component-discriminant functional analysis (PC-DFA)24 are “supervised” MVA techniques which capitalize on the differences between known groups of samples. The classification model is developed on a training set of samples with known categories. This study specifically focuses on utilizing four common chemometric and statistical techniques to the classification of TOF-SIMS spectral data of similar sulfide minerals (chalcopyrite, CuFeS2; chalcocite, Cu2S; bornite, Cu5FeS4; and pyrite, FeS2) at different flotation conditions and quantitatively measures the performance of different algorithms using Cohen’s kappa statistics.

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EXPERIMENTAL SECTION Materials and Reagents. Chalcopyrite (Moonta Mines, Australia), bornite (USA), chalcocite (Mount Oxide Copper Mine, Australia), and pyrite (Peru) natural mineral samples were obtained from GEO discoveries (The Willyama Group), NSW. Each sample was characterized using Quantitative Evaluation of Minerals by scanning electron microscopy (QEMSCAN) to determine their composition and purity. The QEMSCAN analyses show that both chalcocite (95.7% pure) and pyrite (88% pure) are of high purity, while the bornite and chalcopyrite contain significant portions of chalcocite (13%) and bornite (17%), respectively (refer Figure S-1 in the Supporting Information). Analytical grade collector, sodium ethyl xanthate (NaEX), and commercially available frother (IF 567) were used for the flotation test. Collector solution was prepared using demineralized water. Sample Preparation. Single mineral samples chalcopyrite, chalcocite, bornite, and pyrite were dry ground separately with a mortar and pestle and dry sieved to obtain d80 of −20 μm.

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EXPERIMENTAL RESULTS AND DISCUSSION Mass Spectra of Copper Sulfide Minerals. The representative TOF-SIMS mass spectra from complex Cu−Fe sulfide minerals are shown in Figure 1. These mass spectra show the high degree of fragmentation produced by the TOF2755

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Table 1. Principal Component Loadings of Feed Samples

Figure 1. Representative positive ion mass spectra of complex copper sulfide minerals at reductive potential (∼−200 mV SHE); (a) bornite; (b) chalcocite; (c) chalcopyrite; and (d) pyrite (inadvertently Cu activated). a

SIMS ionization, as it is evident from the large range of molecular mass peaks. Due to the high complexity and similarity between the mass spectra of these copper sulfide minerals, identification of the molecular fragments which vary most significantly between samples by conventional methods appears impossible. Chemometric multivariate statistical data analysis is able to consider peak intensities at many masses and thereby provides a greater potential for clustering and classifying samples.21 Data Patterns and Data Reduction. The first step in chemometric multivariate analysis, PCA, was performed on the whole body (including all SIs) of TOF-SIMS data, collected from feed, conditioned feed, and Eh modified samples, separately. The aims were to: (1) extract the surface chemical pattern, i.e., overall variation in the surface chemistry of mineral samples at different flotation conditions and (2) identify the significant SIs that contribute most to the surface chemical variation observed and reduce the dimensionality of TOF-SIMS data. Table 1 shows the principal components (PCs) derived from the PCA applied to the feed sample data set. In a similar manner, PCs for conditioned feed and Eh modified samples were also derived. In all cases, only PCs with eigen values greater than 1 were retained and all PCs with eigen values below 1 were omitted. In this case, samples were prepared as flat polished blocks, thereby rendering values for PC1 >1 reflective of the material analyzed rather topography. The SIs with score above 0.70 in absolute value are thought to be very important and included in the analysis.20 By careful application of this rule to the PCs derived for all samples, a small group of SIs including Fe+, Cu+, FeOH+, O−, S−, OC2H5−, S2−, and S3− were retained. The signal OH was omitted because of double counting (signals derived from same chemical species, O/OH). The signals S4, S5, and S6 were omitted because of overlapping with S2 in Factor plot of PC1 X PC2 (shown in Figure 2a). A scatter plot of the scores on two multivariate axes can be used to visualize multivariate data in two-dimensional space (Figure 3). The surface chemical pattern across particles is

PC

PC1

PC2

PC3

PC4

Eigen value total variance (%) Na Al Si K Fe Cu FeOH CuOH O OH F S Cl OC2H5 S2/SO2 SO3 OCS2 S3 S4 S5 S6

10.66 50.77 0.30 0.37 0.04 0.51 0.91a −0.86a 0.90a −0.66 0.90a 0.76a 0.86a −0.92a −0.14 0.91a −0.80a −0.44 0.39 −0.89a −0.82a −0.67 −0.81a

3.97 18.89 −0.68 −0.37 0.07 −0.61 −0.30 0.49 −0.23 0.51 −0.21 −0.43 0.34 −0.17 0.81a 0.11 −0.53 0.00 0.56 −0.28 −0.49 −0.44 −0.45

2.62 12.46 0.40 0.55 0.56 0.43 −0.19 −0.05 −0.09 0.34 −0.16 0.38 −0.27 −0.27 0.46 −0.16 −0.17 0.84a 0.33 0.07 −0.15 0.21 −0.13

1.19 5.65 0.46 −0.50 −0.68 0.24 −0.05 −0.05 −0.21 0.00 −0.03 −0.03 0.00 −0.04 0.03 0.04 −0.02 0.23 0.29 0.01 −0.06 0.05 −0.11

Values above the threshold score.

Figure 2. Factor plot of feed samples on PC1 X PC2 planes (a) including all SIs (21 SIs) and (b) new set of SIs (Fe+, Cu+, FeOH+, O−, S−, OC2H5−, S2−, and S3−). 2756

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chalcocite and chalcopyrite. It is very important to note that, at the early stage of flotation (at Eh ∼430 mV SHE), mineral samples have relatively pristine surface that have not reacted with reagents and oxidized at different rates with the order: Cc > Bo > Cp.31,32 Under these conditions, the mineral surface will be metal deficient (i.e., rich in sulfur) lesser concentrations of metal oxides (FeO and Cu2O). PCA was able to pick the relative difference among major SIs, Fe2+, Cu2+, S−, O−, and OH− collected from different mineral groups. On the basis of the results of PCA (unsupervised multivariate) analysis, it is not surprising that the supervised classification techniques, SIMCA, k-NN, and PC-DFA are easily able to classify sulfide minerals of feed sample with 100% accuracy. Conditioned Feed Sample Classification. Separation of the TOF-SIMS spectra of mineral samples treated with collector (conditioned feed) into groups was first attempted using PCA. Figure 4b shows score plot of particles on the PC1

Figure 3. Score plot of feed samples on PC1 X PC2 planes: (a) including all SIs (21 SIs) and (b) new set of SIs (Fe+, Cu+, FeOH+, O−, S−, OC2H5−, S2−, and S3−).

similar for both the cases. This indicates the information retained by a new set of SIs sufficient to differentiate different surface chemical distribution present in the samples. PCA allowed the reduction of variables while retaining the major variation in the surface chemistry of the mineral samples. Classification Analysis. Four complex sulfide minerals chalcopyrite (Cp), chalcocite (Cc), bornite (Bo), and pyrite (Py) are examined as four classes. Each class has 19 samples, and together, there are 76 samples at each flotation condition. Among which, 56 samples (particles) were used to train the model. Twenty randomly selected samples, 5 from each class, which are not used in the training set, were used to test the model. This is a challenging multiclass classification task to demonstrate discrimination of the highly complex multimetal mineral samples. A sufficient number of PCs, which represents 85−95% explained variance, is considered while building SIMCA and PC-DFA models. Leave-one-out cross validation (LOO−CV) is adopted in this study to test the generalizability of multivariate techniques to classify unknown samples.30 Feed Sample Classification. From Figure 3, it is very clear that the PCA of feed sample shows excellent classification among the TOF-SIMS spectra of sulfide mineral samples. The elements Fe and O, strongly positively correlated to the PC1 (Figure 2b), are responsible for the discrimination of bornite and pyrite particles. This indicates that the surface of untreated bornite and pyrite have a high amount of Fe present. The elements Cu and S which are negatively correlated to the PC1 are most responsible for the differentiation between the

Figure 4. (a) Factor plot and (b) score plot of conditioned feed samples on PC1 X PC2 plane including derived set of SIs Fe+, Cu+, FeOH+, O−, S−, OC2H5−, S2− and S3−.

X PC2 factor plane for conditioned feed sample. Fragments Fe+, FeOH+, and S3− which are negatively correlated to the PC1 (Figure 4a) are responsible for the classification of pyrite and chalcopyrite. Elements Cu and O strongly positively correlated to the PC1 are contributed to the grouping of bornite and chalcocite. The first three PCs captured 82% of the variance in the data set, and PCA was able to differentiate pyrite and chalcopyrite mineral particles from the remaining set. At the conditioned feed stage, mineral samples were treated with collector at pH 8 for 5 min. Collector interaction with the mineral particles makes the mineral surface more chemically 2757

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(serpentine, enstatite, olivine, and talc) exceeds 90% for k-NN classification. In a similar study using TOF-SIMS, Xue Tian et al.29 attributed the poor classification of UTI (urinary tract infection) bacterial samples using PC-DFA mainly due to its inability to capture the intraclass variability. However, it is important to note that surface chemistry of mineral particle will be very complex under these conditions. Eh Modified Sample. The scores plot of Eh modified samples (at Eh ∼ −200 mV SHE and pH 9.5) are illustrated in Figure 5b. The element Cu, which is strongly positively

complex. The chemical nature of the adsorbed xanthate species (metal xanthate or dixanthogen), the spatial distribution of oxidation products, and dissolved and precipitated species complicate the conditions. Furthermore, direct contact of different mineral particles with different rest potentials results in a galvanic effect, which may trigger the copper adsorption on cathodic pyrite surfaces.5 However, under these conditions, little copper adsorption was observed on pyrite surface, where Cc and Bo had a copper rich surface (refer to Figure S-3 in the Supporting Information). The Cp surface had apparently an equal amount of Fe and Cu. The PCA of conditioned feed samples could be able to pick three major differences in the data set, resulting in three groups of minerals. However, the PCA analysis alone is clearly insufficient for a complete classification of the mineral groups at conditioned feed stage. The classification results for conditioned feed sample by supervised classification techniques are tabulated in Table 2. Table 2. Classification Results for Conditioned Feed Sample sample ID

SIMCA

K-NN

PC-DFA

true lable

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 correct accuracy % kappa

Bo Bo Bo Bo Bo Bo Cc Bo Bo Bo Cp Cp Cp Bo Cp Py Py Bo Py Py 14 70 0.60

Bo Bo Bo Bo Bo Cc Cp Cc Cc Bo Bo Cp Cp Cp Cp Py Py Py Py Py 17 85 0.80

Bo Bo Bo Bo Cp Bo Bo Bo Bo Bo Cp Cp Bo Bo Cp Py Py Cp Py Py 11 55 0.40

Bo Bo Bo Bo Bo Cc Cc Cc Cc Cc Cp Cp Cp Cp Cp Py Py Py Py Py

Figure 5. (a) Factor plot and (b) score plot of Eh modified samples (at Eh ∼ −200 mV SHE) on PC1 X PC2 plane including derived set of SIs Fe+, Cu+, FeOH+, O−, S−, OC2H5−, S2−, and S3−.

Clearly, k-NN outperforms the other two supervised algorithms by classifying 17 of 20 samples. The other two algorithms SIMCA and DFA classified bornite and pyrite samples with nearly 85% accuracy. However, these algorithms misclassified chalcocite and chalcopyrite particles as prominently bornite. Dimension reduction property of SIMCA and DFA only helped to resolve the difference between pyrite and chalcopyrite. They failed to capture the intraclass variability among bornite and chalcocite. SIMCA and PC-DFA algorithms hold “moderate agreement” and “Fair agreement” with kappa rating 0.6 and 0.4, respectively. On the other hand, even though k-NN algorithm does not consider intraclass variability, it predicts the new object to the class which has the largest number of objects among the k neighbors. Note that k is always an odd number to ensure that a majority vote is obtained locally.33 Hence k-NN was able to classify all mineral groups with “substantial agreement” kappa rating (0.80). Engrand et al.21 reported the predictive ability for classification of terrestrial mineral samples

correlated to both PC1 and PC2 and the fragments S− and OC2H5−, which are positively correlated to PC2 (Figure 5a), are responsible for clustering of bornite and chalcocite. This suggests that the surface of bornite and chalcocite have a high amount of copper and sulfur present at reductive pulp potential. Fragments Fe+, FeOH+, and S3− most strongly negatively correlated to the PC1 are responsible for the discrimination of pyrite and chalcopyrite. PCA projected three major variations in the Eh modified data set. Well separated pyrite and chalcopyrite mineral particles into two groups and Cc and Bo into a third group. At reductive potentials due to galvanic interaction between copper sulfide minerals, there was a decrease in copper concentration on chalcocite and bornite was observed. Simultaneously, copper concentration on pyrite was significantly increased (refer Figure S-4 in the Supporting Information). However, Fe remained to be the strong signal 2758

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visualization and interpretation of the data. Using a mixture of complex copper−iron sulfide minerals, positive and negative ion TOF-SIMS mass spectra of feed, conditioned feed, and Eh modified samples, we have shown that PCA is an excellent first step in the evaluation of TOF-SIMS spectral data of complex multimetal mineral samples. PCA provides insight into the overall variation among the data set and into the mass spectral peaks which are significant in determining and classifying the samples. PCA was able to classify all four minerals correctly at feed conditions. For conditioned feed samples, k-NN produced excellent classification with kappa rating “substantial agreement” (85% accuracy). For Eh modified samples, all three supervised classification techniques (k-NN, SIMCA, and DFA) produced excellent classification with kappa rating “almost perfect agreement” (nearly 90% accuracy). Phase identification of individual mineral particles using TOF-SIMS is of critical importance to the analysis of complex mixed mineral ores. The classification of copper sulfide minerals with the same elemental composition but different crystal structure in a mixed mineral system has been achieved using both k-NN and SIMCA. These results prove TOF-SIMS can be used to track the surface chemistry of an individual particle throughout complex processing procedures.

from pyrite. A slight increase in copper concentration on chalcopyrite was observed due to copper adsorption. The variation in the concentration of major SIs (Cu, Fe, O, and S) between chalcocite and bornite was reduced, and the surface became chemically similar and complex. PCA fails to resolve the variation between chalcocite and bornite at reductive potentials. At low pulp potentials (reductive potentials) in the presence of pyrite, chalcocite undergoes anodic oxidation with production of soluble Cu2+ ions into solution.34 Finch and Lascelles reported that chalcocite produced about 50 times Cu ion than chalcopyrite at near and above neutral pH.35 They also observed that chalcopyrite-bearing ores (chalcocite, bornite and chalcopyrite together) gave higher copper ion production than for mineral alone, ascribed to galvanic interactions. Weisener and Gerson36 found that Cu2+ adsorbed on pyrite at pH 9 and then converted into Cu+. They also observed that, after completion of initial Cu+ adsorption for 5 min, the adsorption of copper continued in the form of precipitated Cu(OH)2. Cohen’s kappa and overall accuracy of SIMCA, k-NN, and PC-DFA for Eh modified samples are given in Table 3. SIMCA, Table 3. Classification Results for Eh Modified Sample sample ID

SIMCA

k-NN

PC-DFA

true lable

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 correct accuracy % kappa

Bo Bo Bo Bo Bo Bo Cc Cc Cp Bo Cp Cp Cp Cp Cp Py Py Py Py Py 18 90 0.87

Cp Bo Bo Cc Bo Cc Cc Cc Cc Cc Cp Cp Cp Cp Cp Py Py Py Py Py 18 90 0.87

Bo Bo Bo Bo Bo Cc Bo Bo Cc Cc Bo Cp Cp Cp Cp Py Py Py Py Py 17 85 0.80

Bo Bo Bo Bo Bo Cc Cc Cc Cc Cc Cp Cp Cp Cp Cp Py Py Py Py Py

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ASSOCIATED CONTENT

* Supporting Information S

Additional information as noted in text. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +618 8302 6864. Fax: +618 83023683. E-mail: Sarah. [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors would like to acknowledge financial support from the Australian Research Council Linkage Scheme (LP0989689). The authors would also like to thank Dr. Igor Ametov and Mr. Czeslaw Poprawski for their advice and training in froth flotation. We are grateful to Dr. John Denman and Ms. Zofia Swierczek for their efforts in training students and maintaining the TOF-SIMS and QEMSCAN instruments.

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REFERENCES

(1) Natarajan, K. A.; Iwasaki, I. Trans AIME 1972, 252, 437−439. (2) Woods, R. In Principles of mineral flotation; Jones, M. H.; Woodcock, J. T., Eds., The Wark Symposium; Aus. Inst. Min. Metall: Parkville, Australia, 1984; pp 91−116. (3) Heyes, G. W.; Trahar, W. J. Int. J. Miner. Process. 1977, 4 (4), 317−344. (4) Huang, G.; Grano, S. Miner. Eng. 2005, 18 (12), 1152−1163. (5) Acres, R. G.; Harmer, S. L.; Beattie, D. A. Int. J. Miner. Process. 2010, 94, 43−51. (6) Smart, R. St. C. Miner. Eng. 1991, 4, 891−909. (7) Ralston, J. In Colloid Chemistry in Mineral Processing; Laskowski, J. S.; Ralston, J., Eds.; Elsevier: Amsterdam, 1992; pp 203−224. (8) Richardson, P. E. In Mineral Surfaces; Vaughan, D. J.; Pattrick, R. A. D., Eds.; Chapman and Hall: London, 1995; pp 261−302. (9) Piantadosi, C; Smart, R. St. C. Int. J. Miner. Process. 2002, 64 (1), 43−54. (10) Hart, B.; Biesinger, M.; Smart, R. St. C. Miner. Eng. 2006, 19 (6−8), 790−798.

k-NN, and PC-DFA performed well at reductive potentials. For all three techniques, the agreement between true label and sample classified label was “almost perfect agreement” kappa rating (>0.8). SIMCA and k-NN successfully classified 18 of 20 samples. PC-DFA was also able to classify 17 out of 20 samples. Roggo et al.30 used SIMCA with near-infrared spectroscopy (NIRS) to classify sugar beet with 82% prediction rate. They reported SIMCA outperformed k-NN and discriminant analysis (LDA) for classification of sugar beet.

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CONCLUSIONS In this study, we have demonstrated that thorough analysis of complex TOF-SIMS data sets requires the use of the chemometric multivariate pattern recognition techniques for 2759

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Analytical Chemistry

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dx.doi.org/10.1021/ac202971y | Anal. Chem. 2012, 84, 2754−2760