Determination of chlorite, muscovite, albite and quartz in claystones and clay shales by infrared spectroscopy and partial least-squares regression

Acta Geodyn. Geomater., Vol. 9, No. 4 (168), 511–520, 2012 DETERMINATION OF CHLORITE, MUSCOVITE, ALBITE AND QUARTZ IN CLAYSTONES AND CLAY SHALES BY INFRARED SPECTROSCOPY AND PARTIAL LEAST-SQUARES REGRESSION Michal RITZ 1) *, Lenka VACULÍKOVÁ 2), Eva PLEVOVÁ 2), Dalibor MATÝSEK1) and Jiří MALIŠ 1) 1) VŠB-Technical University Ostrava, 17. listopadu 15, 708 33 Ostrava-Poruba, Czech Republic 2) Institute of Geonics of the AS CR, Studentská 1768, 708 00 Ostrava-Poruba, Czech Republic *Corresponding author‘s e-mail: [email protected] (Received April 2012, accepted September 2012) ABSTRACT The objective of this work is the chemometric quantification of minerals in rocks. A chemometric method was developed fo r the determination of chlorite, muscovite, albite and quartz in claystones and clay shales using infrared spectroscopy. Bromide pellets and diffuse reflectance were used to measure the infrared spectra; principal component analysis and partial leastsquares regression were used as chemometric methods. Spectral regions (4000-3000 cm-1 and 1300-400 cm-1) containing important spectral information were chosen by principal component analysis. The calibration models were created by a partial least-squares regression. The mean relative error and relative standard deviation were calculated for the assessment o f accuracy and reproducibility. The value of the mean relative error was about 10 % for most of the calibration models. The value of the relative standard deviation ranged from 1.1 to 3.0 % for most calibration models based on diffuse reflectance spectra and from 4.0 to 9.2 % for most calibration models based on spectra obtained with bromide pellets. KEYWORDS: claystone and clay shale, infrared spectroscopy, chemometrics, chlorite, muscovite, albite, quartz methods can also be used for the purpose o f quantitative analysis. The theory of chemometric methods has been described in many papers and books, such as Fredericks et al., 1985; Geladi and Kowalski, 1986; Lorber and Kowalski, 1988; Martens and Naes, 1989. Numerical methods, such as multiple linear regression (MLR), principal componen t regression (PCR) or partial least-squares (PLS) regression, are increasingly being used to circumvent the problems posed by the presence of interferences, spectral overlap or major matrix effects (Luis et al., 2004). There are many applications of the chemometric method to IR spectroscopic analysis (Fuller et at., 1988; Haaland and Thomas, 1988; Iñón et al., 2003; Armenta et al., 2007; Breen et al., 2008). In recent years, chemometric methods have also been applied to other analytical methods, such as voltammetry or chromatography (Moneeb, 2006; AlDegs et al., 2008; Wagieh et al., 2010; Zapata-Urzua et al., 2010). The spectroscopic applications of chemometric methods tend to use the full spectrum. This approach p rovides a more accurate description of the model than a single measurement at a specific wavelength o r wavenumber, respectively. However, the fullspectrum applications pose some problems: 1) part o f the information that is gathered can be redundant; and 2) the measured signal for some wavelengths may be noisy or nonlinear (Luis et al., 2004). The most useful INTRODUCTION The type and content of minerals present in rocks have a significant influence on the behavior and p roperties of the rocks as well as on the whole roc k massif. A detailed qualitative and quantitative mineral analysis is therefore a necessary step for the characterization of the properties of the rocks in geological, geochemical and geomechanical studies. The experimental results can be applied subsequently in geomechanics and mining activities. Several existing conventional analytical methods can be used to examine the mineral composition o f rocks: optical microscopy, electron microscopy, X-ray diffraction (XRD), infrared (IR) spectroscopy, Raman spectroscopy, thermal gravimetric/differential thermal analysis (TG/DTA) and bulk chemistry analysis (Kodama et al., 1989; Chipera and Bish, 2001; Srodon, 2002; Vogt et al., 2002). Unfortunately, the exact determination of minerals (especially clay minerals) in the rocks by these methods is rather complicated and often inaccurate. The main analytical difficulties are related to the variable chemical composition and common structural anomalies of clay minerals. The individual clay minerals occur in the form of mixtures with various ratios of the particula r clay minerals. Current IR spectroscopy represents a fast, reliable and efficient tool for phase analysis. This method especially combined with chemometric M. Ritz et al. 512 Graphically, equations (3) and (4) can b e shown as in Figure 1 (Geladi and Kowalski, 1986). In Figure 1, n is number of samples, m is number of independent variables (e.g. absorbance values), a is number o f factors and pis number of dependent variables (concentration values). PLS comprises relatively complicated calculation procedures. Their detailed description is beyond the intention of this p aper. A more detailed description of a mathematical algorithm of PLS modeling can be found in many books or paper (e.g.: Geladi and Kowalski, 1986; Wold et al., 2001; Hasegawa, 2002). The PLS regression can be categorized into two p rocedures. PLS1 (sometimes called standard PLS) and PLS2 (sometimes called global PLS). PLS1 employs information from only one chemical constituent to make the calibration; PLS1method works with the one-column Ymatrix. PLS2 uses two and more chemical constituent simultaneously. The aim of this study is the determination o f majority minerals (chlorite, muscovite, albite and quartz) in claystones and clay shales by I R spectroscopy combined with partial least-squares regression. EXPERIMENTAL S AMPLES Eighty-six samples (B1-B78 and CS1-CS8) o f claystones and clay shales were used for this research. The seventy-eight samples (B1-B78) were used as a calibration set and eight samples (CS1-CS8) were used as control samples. In calibration set were thirtytwo samples of claystones (B1-B32) and forty-six samples of clay shales (B33-B78). Four control samples (CS1-CS4) were claystones; four control samples (CS5-CS8) were clay shales. The selection of control samples was performed with regard to cover the entire concentration range of the analyzed minerals. All the samples were obtained from the collection of VŠB-Technical University, Ostrava. techniques for chemometric approach in infrared spectroscopy are principal component regression (PCR) and partial least-squares (PLS) regression. An important feature of PCR is fact that only spectral information (e.g. absorbance, Kubelka-Munk unit, etc…) is used for the generation of basis factors. This was not a problem when the concentration information is absolutely accurate. However, in practice the concentration matrix contains error or noise. Another problem of PCR is that collinearity o f absorbance data will make the calibration unstable (Hasegawa, 2002). Some potential problems can be solved by using a more stable chemometric method which takes both (absorbance and concentration) matrices into account simultaneously. For this purpose PLS regression can be used as suitable method. In PLS regression absorbance and concentration matrices are used complementarily in a stable calibration. PLS regression works with two matrices, Xand Y. The X matrix contains independent variables – the spectral data (e.g. in absorbance unit). The Y matrix consists of the dependent variables – quantitative (concentration) data. The NIPALS (Nonlinear Iterative Partial Least Squares) algorithm is most often used for creation of PLS models. The PLS models can be considered as consisting of outer relations (X matrix and Y matrix individually) and an inner relation (linking both matrices) (Geladi and Kowalski, 1986). The outer relations for the X and Y matrices can be written as follows: ETPEptX xh h h  (3) FUQEquY Yh hh  (4) where th and uh are score vectors, ph and qh are loading vectors; T and U are score matrices, P and Qare loading matrices, E and F are matrices of residuals. Fig. 1 Graphical representation of PLS (Geladi and Kowalski, 1986). DETERMINATION OF CHLORITE, MUSCOVITE, ALBITE AND QUARTZ IN … 513 Approximately 5-10 mg of sample was ground with approximately 400 mg of dried KBr. This mixture was used to collect IR spectra by the DRIFT technique. The IR spectra were collected using the FTIR spectrometer Nexus 470 (ThermoScientific, USA) with a deuterated TriGlycine sulfate (DTGS) detector. The measurement parameters were the following: spectral region 4000-400 cm-1; spectral resolution 8 cm-1; 128 scans; and Happ-Genzel apodization. Freshly dried KBr was used for the b ackground measurement. Every sample was prepare d and measured 3-5 times. The mean IR spectrum o f every sample was calculated. The mean IR spectra were subsequently used for the creation o f chemometric models. Exactly 0.5 mg of sample was ground with 200 mg of dried KBr. This mixture was used to prepare the bromide pellet. In this study, 13 m m diameter pellets were used. The pellets were presse d b y 10 tons for 30 seconds under vacuum. The I R spectra were collected using the FTIR spectrometer Avatar 320 (ThermoScientific, USA) with DTGS detector. The measurement parameters were the following: spectral region 4000-400 cm-1; spectral resolution 8 cm-1; 64 scans; and Happ-Genzel apodization. An empty sample compartment was use d for background measurement. Every sample was p repared and measured only once. The IR spectr a were subsequently used for the creation o f chemometric models. CHEMOMETRIC ANALYSIS The chemometric analysis was performed using The Unscrambler 9.7 software package (CAMO Software AS, Norway). PCA and PLS regressions were used as representative of chemometric methods. PCA was used for preliminary data analysis: detecting outlier spectra and the specification of importan t spectral regions. The PLS1 technique was employed to create chemometric models for the determination o f minerals (chlorite, muscovite, albite and quartz) in claystones and clay shales. Multiplicative scatte r correction (full MSC) was performed for transformation of DRIFT spectra. The number of optimal PLS parameters were determined by statistical comparison of PRESS values as a function of numbers of factor. The model validation was performed by the cross-validation (CV). The segmented crossvalidation was performed as the validation method fo r calibration models. The size of the cross-validation segment was two samples. The data matrices of spectral and concentration information of all samples in calibration set were p repared. One data matrix was prepared from I R spectra of bromide pellets; the next data matrix was p repared from DRIFT spectra. Principal componen t analysis (PCA) was performed for detecting the outlier spectra in the calibration set and for selection of the important spectral regions. The following plots were prepared: the score plot of the first two principal components, the influence plot of the first three Claystone is a compact very fine-grained sedimentary rock consisting primarily of clay-size mineral particles that are commonly represented by clay minerals. Claystones are only partially decomposed in water and their porosity generally varies from 25 to 5 %. Clay shales are similar in composition but do not decompose in the water, and their total porosity is less than 5 %. Moreover, shale is laminated (the rock is made up of many thin layers). Shales that are subject to heat and pressure o f metamorphism alter into a hard, fissile (the roc k readily splits into thin pieces along the laminations), metamorphic rock known as slate. The samples o f claystones were taken from several lower-to-middle Cretaceous strata belonging to the Silesian unit of the Moravian-Silesian Beskydy Mountains. The samples of clay shales are taken from the Kyjovice layers that are stratigraphically adherent to the Lowe r Carboniferous period of the Moravian-Silesian area. Every sample was pulverized in an agate mill. Pulverized samples were homogenized by careful shuffling and by repeatedly being spilled. A list of calibration set including the content o f the minerals is shown in Table 1. P OWDER XRD ANALYSI S The content of minerals in samples of claystones and clay shales was determined by the quantitative reference method - powder XRD analysis. The Rietveld technique, used as the quantification technique for diffraction data (Rietveld, 1969), is the quantitative technique for the crystal structure analysis from powder diffraction data. The theoretical diffractogram is calculated on the basis of structural data (e.g., crystal symmetry, unit cell parameters, atomic coordinates and occupancy) of the minerals that are present. The theoretical diffractogram is subsequently compared with the measured diffraction p attern using multidimensional regression. The Rietveld technique is considered one of the best techniques for the quantification of powder diffraction data, and it has been used in many studies (Chipera and Bish, 2001; Bringley, 1980; Bish and Howard, 1988; Hillier, 2000). The pulverized and homogenized samples were measured in the cuvettes. Powder diffraction measurements were carried out on a fully-automated diffractometer ID3003 (Rich Seifert-FPM, Germany) under the following conditions: CoKradiation/Fe filter, 2 goniometer geometry, step mode with 0.05o 2steps, 3s measurement time per step and with the digital processing of resultant data. Fo r measurement and semi-qualitative evaluation, the software packages RayfleX and RayfleX Autoquan (GE Sensing & Inspection Technologies, USA) were used. I R MEASUREMENT S Two techniques of IR spectrosco p y were used in this study; b romide pellets and diffuse reflectance I R Fourier Transform (DRIFT) spectroscopy. M. Ritz et al. 514 Table 1 List of calibration set of minerals. Sample Chlorite (w/w %) Muscovite (w/w %) Albite (w/w %) Quartz (w/w %) B1 8.2 40.3 3.0 44.9 B2 8.2 42.1 3.3 39.5 B3 8.9 39.0 2.6 46.2 B4 3.5 38.2 3.1 39.1 B5 5.4 8.0 3.5 56.4 B6 9.7 23.5 2.5 64.3 B7 10.5 35.1 1.8 52.6 B8 7.9 48.8 9.2 34.1 B9 6.2 65.5 8.4 20.0 B10 7.8 53.3 4.7 29.4 B11 8.8 56.0 5.6 36.1 B12 5.1 52.1 4.0 33.2 B13 < 1.0 2.2 < 1.0 48.7 B14 3.8 9.7 < 1.0 57.0 B15 < 1.0 16.5 < 1.0 30.6 B16 3.4 17.7 1.5 19.1 B17 < 1.0 1.6 < 1.0 31.4 B18 5.0 12.4 < 1.0 15.7 B19 2.8 17.5 < 1.0 37.2 B20 3.8 10.5 < 1.0 13.5 B21 5.5 14.4 < 1.0 27.3 B22 5.8 14.9 2.3 41.6 B23 < 1.0 10.9 < 1.0 23.1 B24 < 1.0 9.1 < 1.0 23.5 B25 6.0 10.1 1.8 22.1 B26 < 1.0 19.0 2.6 26.6 B27 < 1.0 10.7 1.1 25.2 B28 < 1.0 28.4 < 1.0 28.4 B29 < 1.0 13.4 < 1.0 34.5 B30 1.6 22.6 < 1.0 61.4 B31 < 1.0 9.3 1.7 34.0 B32 5.4 15.4 < 1.0 23.9 B33 22.2 39.5 18.9 19.5 B34 17.6 32.4 19.8 30.1 B35 15.6 27.8 16.8 39.8 B36 9.1 21.6 15.6 53.8 B37 < 1.0 < 1.0 1.8 69.6 B38 < 1.0 34.1 < 1.0 29.2 B39 < 1.0 24.1 < 1.0 6.5 B40 10.4 23.2 18.0 48.4 B41 28.1 41.6 9.1 18.9 B42 17.2 31.1 17.9 26.3 B43 17.2 53.8 3.7 25.2 B44 22.7 25.1 21.4 30.3 B45 17.6 37.2 8.9 22.0 B46 < 1.0 71.9 2.9 5.0 B47 17.0 29.2 14.6 25.8 B48 11.6 47.6 3.8 36.9 B49 29.6 43.3 7.0 20.2 B50 19.2 33.7 19.0 28.1 B51 54.6 12.5 2.5 27.4 B52 3.3 38.1 11.2 43.0 B53 9.6 18.6 41.5 30.4 B54 12.3 25.0 2.3 49.5 B55 20.2 33.3 13.4 32.5 B56 18.0 25.4 14.7 36.9 B57 22.8 43.9 10.6 21.1 B58 25.5 42.5 2.7 27.5 B59 19.8 50.4 1.4 29.4 B60 19.6 30.4 13.2 33.1 B61 20.9 31.1 12.9 35.2 B62 23.4 36.5 12.3 27.8 B63 22.8 34.0 10.9 32.4 B64 13.9 33.8 16.4 35.9 B65 10.8 9.9 27.0 52.3 B66 9.9 42.0 13.5 34.3 B67 17.3 27.3 17.3 32.7 B68 17.6 34.7 13.2 34.5 B69 21.0 44.9 3.0 27.7 B70 22.5 45.9 3.0 25.9 B71 18.9 32.5 15.3 33.4 B72 16.9 23.6 13.0 40.6 B73 21.6 31.9 12.6 34.0 B74 19.5 35.0 16.2 25.0 B75 14.7 31.8 18.3 31.0 B76 16.6 31.3 16.7 33.7 B77 20.5 30.2 17.0 31.3 B78 19.0 29.7 15.8 35.5 DETERMINATION OF CHLORITE, MUSCOVITE, ALBITE AND QUARTZ IN … 515 Fig. 2 Score plot (a) and influence plot (b) of DRIFT spectra. Fig. 3 Line loading plot of bromide pellets spectra. loading plots were used for the selection of the important spectral regions. This type of loading plo t looks like spectrum. Thus the important spectral regions have character of spectral bands. The important spectral regions determined by loading plots of both data matrices were 4000-3000 cm-1 and 1300400 cm-1. The spectral bands present at the spectral region 4000-3000 cm-1 belonged to the stretching vibration of structural hydroxyl groups (3630 cm-1) principal components and the loading plot for the first p rincipal component. The score plots and the influence plots were used to detect the outlier spectra. In the score plot, the outlier spectra are located outside of main cluster. In the influence plot, the outlie r spectra do not show decreasing tendency. No outlier spectra were found in either of the data matrices. Examples of both plots for spectra measured by DRIFT technique are shown in Figure 2. The line M. Ritz et al. 516 Table 2 Parameters of PLS models. Mineral Method RMSEC (% w/w) RMSECV (% w/w) No. of factors Explained variance (%) Chlorite DRIFT 2.67 3.34 8 98.3 KBr pellet 3.71 4.51 9 96.3 Muscovite DRIFT 5.58 6.85 8 97.8 KBr pellet 11.39 11.74 9 95.9 Albite DRIFT 2.38 2.71 8 98.5 KBr pellet 2.22 3.44 9 96.5 Quartz DRIFT 4.91 6.50 11 90.1 KBr pellet 4.79 6.64 11 87.7 validation. The validation error of the model was expressed by RMSECV, analogous to RMSEC: n cc RMSECV n ireferipredvali    1 2 ,,, )( (2) where ci,val,pred is the value of the mineral content o f the ith validation sample predicted by the PLS model, and ci,refer is the value of the mineral content of the ith validation sample obtained by the reference method and nis the number of samples in the calibration set. The number of factors is the optimal number of “latent variables” necessary to effectively describe the PLS model. The number of factors was obtained by so called PRESS plot (i.e., the plot of PRESS vs. the number of factors). PRESS mean predicted residual error sum of squares and this parameter was calculated as:    n ireferipredi ccPRESS 1 2 ,, )( (3) where ci,pred is the value of the mineral content of the ith sample predicted from the PLS model, and ci,refer is the value of the mineral content of the ith sample obtained by the reference method and n is the number of samples in the calibration set. The explained variance is the percentage of the variance of the system described by the expressed number of factors. RESULTS AND DISCUSSION A NALYSIS OF CONTROL SAMPLES (ACCURACY A ND PRECISION) The predictive ability of the PLS models was tested by analysis of the eight control samples (CS1CS8). The KBr pellets were prepared for each control sample and the IR spectra of these control samples were subsequently measured. The IR spectra of the control samples were also obtained by the DRIFT technique (each spectrum was prepared like the mean spectrum from three independent DRIFT measureand to the stretching vibration of water (3350 cm-1). The most significant spectral bands in the region 1300-400 cm-1 could be assigned to following vibrations: Si-O stretching vibration (1030 cm-1), the deformation vibration of Al-Al-OH (930 cm-1), the Si-O stretching vibrations of quartz (800 cm-1 and 780 cm-1) and the deformation vibrations of Al-O-Si and Si-O-Si (530 cm-1 and 480 cm-1, respectively). The assignment of spectral bands was performed according to (Ritz et al., 2010). Example of line loading plot for spectra of bromide pellets (including significant wavenumbers) are shown in Figure 3. The “negative” feature in Figure 3 belonged to the vibration of carbonates; this band was not used fo r creation of calibration models. The data matrices mentioned previously were used for the creation of the PLS models. The PLS1 technique was used: a separate calibration model was created for determination of each mineral. The important parameters of the PLS models that were created are shown in Table 2. The example o f regression between predicted and measured values for PLS model of muscovite (DRIFT spectra) is shown in Figure 4. The following parameters are shown in Table 2: RMSEC (root mean squared error of calibration), RMSECV (root mean squared error of crossvalidation), number of PLS factors and percentage o f explained variance. The calibration error of the PLS model was expressed by RMSEC: n cc RMSEC n ireferipredcali    1 2 ,,, )( (1) where ci,cal,pred is the value of the mineral content o f the ith calibration sample predicted from the PLS model, and ci,refer is the value of the mineral content o f the ith calibration sample obtained by the reference method (XRD analysis) and nis the number o f samples in the calibration set. The validation of PLS models was performed by the segmented cross- DETERMINATION OF CHLORITE, MUSCOVITE, ALBITE AND QUARTZ IN … 517 Fig. 4 Predicted vs. measured plot (Muscovite PLS model; DRIFT spectra). Table 3 List of control samples and results of their analysis. Chlorite (% w/w) Muscovite (% w/w) Albite (% w/w) Quartz (% w/w) PLS PLS PLS PLS Sample XRD DRIFT Pellets XRD DRIFT Pellets XRD DRIFT Pellets XRD DRIFT Pellets CS-1 10.7 8.1 7.5 12.1 16.2 10.9 4.5 5.6 3.9 31.6 23.9 26.2 CS-2 3.0 5.0 2.6 37.4 39.8 42.3 6.7 4.8 6.2 52.9 47.2 47.9 CS-3 5.0 5.2 5.0 40.8 43.2 37.7 8.2 4.6 7.0 48.9 46.1 44.9 CS-4 14.8 12.4 13.0 87.5 59.2 33.8 5.9 7.3 5.8 14.9 15.8 19.5 CS-5 19.1 19.9 18.7 36.5 37.0 36.3 14.3 13.6 15.1 30.0 30.4 32.9 CS-6 24.3 20.8 23.8 30.9 29.8 33.5 14.5 15.2 14.2 29.4 28.3 29.4 CS-7 11.7 15.5 10.2 30.0 27.1 29.0 41.5 31.8 47.0 30.4 32.5 26.8 CS-8 21.0 20.3 16.5 27.2 30.2 25.1 12.0 12.3 10.4 39.8 33.3 34.4 The predictive ability of chemometric models can be described using several validation diagnostics. The following parameters were used in this study: b ias, standard error of prediction (SEP) and mean relative error (RE). Bias and SEP parameters were used according (Esbensen, 2006); RE parameters was created for the purpose of this study:   n cc bias n ireferipredi    1,, (4)  n cc SEP n ireferipredi    1 2 ,, (5) ments). All of these spectra were used for prediction of the content of minerals by the PLS models that were created. The results of the analysis of control samples from PLS models are shown in Table 3 together with the content of minerals in the control samples obtained from the reference method (XRD analysis). First, the results of prediction of the content o f minerals in control samples were tested for statistical compliance with the reference values (results of XRD analysis) of the control samples. The testing techniques were the following: F-test, t-test (Student’s test) and paired comparison (Meloun and Militký, 2004). All of these techniques showed statistical compliance between the predicted and reference values for the control samples. M. Ritz et al. 518 Table 4 Parameters of predicted ability of PLS models. Chlorite Muscovite Albite Quartz Parameter DRIFT Pelets DRIFT Pelets DRIFT Pelets DRIFT Pelets bias (w/w %) -0.3 -1.5 -2.5 -6.7 -0.1 0.1 -1.9 -1.2 SEP (w/w %) 2.4 2.1 10.3 19.1 1.7 1.6 4.9 4.2 RE (%) 20.7 11.5 12.9 13.9 19.4 9.1 10.5 12.6 Table 5 Reproducibility - list of results. Chlorite (w/w %) Muscovite (w/w %) Albite (w/w %) Quartz (w/w %) CS5 B25 CS5 B25 CS5 B25 CS5 B25 DRIFT Pellets DRIFT Pellets DRIFT Pellets DRIFT Pellets DRIFT P ellets DRIFT Pellets DRIFT Pellets DRIFT Pellets 18.8 17.3 2.5 6.2 38.0 28.4 12.7 11.5 11.9 11.4 1.4 2.6 32.7 32.2 27.6 23.9 19.0 21.5 2.2 6.1 37.6 30.9 12.0 12.8 12.3 14.2 1.7 1.0 31.9 30.6 27.6 23.1 19.3 17.1 2.3 5.2 38.1 27.1 11.7 10.8 12.1 14.3 1.9 1.5 31.6 33.5 27.3 25.3 18.5 19.4 2.1 6.3 36.2 32.3 11.9 11.8 11.8 12.4 1.5 1.3 31.7 33.3 27.7 25.7 18.8 18.7 2.2 4.5 37.3 27.4 11.8 11.0 11.9 14.0 1.6 1.6 31.9 33.2 27.2 22.1 18.8 20.7 2.3 6.9 37.0 28.6 12.0 11.5 11.8 12.7 1.3 3.2 31.2 34.0 27.6 24.5 18.5 18.7 2.1 6.7 37.1 25.3 10.9 10.1 11.4 11.7 1.6 2.5 32.4 30.8 28.2 25.7 18.7 17.2 2.7 5.6 38.0 27.9 9.7 9.4 11.2 13.6 1.7 3.2 32.7 34.4 28.1 25.5 18.5 18.0 3.0 5.5 37.2 26.8 10.3 12.2 11.4 14.1 1.4 1.1 32.7 32.0 27.6 22.3 18.9 17.5 2.1 5.6 37.9 28.5 11.9 10.7 11.6 13.2 1.5 2.2 32.8 32.6 27.8 23.3 RSD (%) 1.4 8.3 12.8 12.1 1.6 7.1 7.9 8.8 3.0 9.2 10.9 40.5 1.7 4.0 1.1 5.8 expressed by the RE showed values similar to the RE of the rest of models. The reason is obvious from the different mathematical formulas for bias and RE (see equations 4 and 6). The bias equation (4) does not operate with the absolute values of the difference predicted and the reference content of the mineral. N egative and positive increments could therefore cancel each other. The RE equation (6) used absolute values of the difference. RE is therefore the more robust parameter for accuracy, whereas bias can describe the systematic error of the PLS model. The accuracy parameter (RE) showed similar values in most of the models (approximately 10 %). Only DRIFT models for the prediction of chlorite and albite had values of RE of approximately 20 %. The values of the accuracy for the PLS models that were created are very similar to the values of accuracy for the results of the XRD analysis cited in the literature (e.g. Moore and Reynolds, 1997). Requirement of practice for RE parameter of quantitative phase analysis results of rock are about 20-25 %. The values of RE p arameters of control samples achieved by reference quantitative method (XRD analysis) in this study were between 10 % and 20 %. Thus both methods (XRD analysis and chemometric analysis of I R spectra) provided results acceptable by potential customers. The best values for the parameter of precision (SEP) had PLS models for the prediction of albite an d chlorite (values of SEP about 2 w/w %). The models for prediction of quartz showed slightly worse precision. The model for the prediction of muscovite had dramatically worse precision than other PLS models, probably caused by the worse parameters o f the muscovite PLS models (see Table 2). With the 100 1, ,,             n c cc RE n ireferi referipredi (6) where ci,pred is the value of the mineral content of the ith control sample predicted from the PLS model, ci,refer is the value of the mineral content of the ith control sample obtained by the reference method (XRD) and n is number of control samples. Bias represents the average difference between the predicted values and the reference values for control samples and is a commonly-used measure o f the accuracy of a chemometric model. Bias is also used to check any systematic differences observed b etween the average values of the control samples and the validation samples (Esbensen, 2006). Another way to express the accuracy of a chemometric model is the mean relative error. The standard error of prediction (SEP) expresses the precision of the predicted results. The values of the parameters of the validation diagnostics are shown in Table 4. The bias of almost all of the PLS models was negative; only the bias of the PLS model of albite for KBr pellets had a positive value. The absolute values for bias were usually very low, ranging from 0.1 to 1.9. Only the bias of the models of muscovite showed higher values; the model for DRIFT had a bias of -2.5 and the model for the KBr pellets had a bias value o f -6.7. These high values of bias were very probably caused by the worse values of the parameters of the muscovite PLS models (see Table 2). The accuracy as expressed by the bias showed worse values for the muscovite PLS models, whereas the accuracy of the muscovite PLS models as DETERMINATION OF CHLORITE, MUSCOVITE, ALBITE AND QUARTZ IN … 519 However, the use of a heavier sample could induce total absorbance of some spectral bands and cause poorer utilization of spectral information. CONCLUSIONS Principal component analysis (PCA) and especially PLS regression were used as chemometric methods in this paper. PCAs were used for detecting outliers and for selection of important spectral regions. No outliers were detected. Regions 40003000 cm-1 and 1300-400 cm-1 were selected for the creation of calibration models by the PLS regression technique. The series of PLS models proposed in this work showed RMSEC and RMSECV values up to 56 w/w % (with the exception of the PLS model for p rediction of muscovite based on the KBr pellet technique). For a set of control samples, values o f mean relative error (RE) of about 10 % were achieved in most of the PLS models that were created. The slightly better values of RE were achieved for PLS models based on the KBr pellet technique. The reproducibility of the PLS models was evaluated for two samples and the reproducibility was expressed by the relative standard deviation (RSD); the values o f the RSD ranged from 1.1 to 12.8 % (with the exception of the PLS model for prediction of albite b ased on the DRIFT technique). The relatively better values of the RSD were achieved for the PLS models based on the DRIFT technique. There are some important advantages o f chemometric analysis of IR spectra over most used quantitative phase analysis method (Rietveld technique of XRD analysis): analysis time, accessibility and simplicity. First, the analysis time o f chemometric analysis of IR spectroscopy is much shorter than analysis time of XRD analysis. Of course, creation of calibration models is rather timeconsuming. But subsequent analysis is very fast. Second, IR spectrometers are present in significantly larger numbers of laboratories than X-ray diffractometer. The main reasons are the p urchase price of IR spectrometers and operating costs, which helped to spread the use of infrared spectroscopy as a common analytical technique. And finally, chemometric result processing of IR spectra is considerably simpler than Rietveld treatment o f diffractogram data. The use of chemometric data treatment for the I R spectra is simple and reliable and can be used to determine minerals in rocks. This study showed tha t IR spectroscopy in conjunction with the PLS regression method provided an acceptable alternative to the most commonly used methods for quantitative phase analysis – the Rietveld technique of XRD analysis. ACKNOWLEDGMENTS This paper was created by the project No. CZ.1.05/2.1.00/01.0040 "Regional Materials Science exception of the models for the prediction o f muscovite, the other models had very similar values of SEP for DRIFT and KBr pellet spectra. The p recision of analysis of control samples by reference quantitative method (XRD analysis) in this study were between 10 % and 20 %. R EPRODUCIBILITY One sample from the calibration set (B25) and one control sample (CS5) were used to estimate the reproducibility of the PLS models that were created. For three weeks, ten KBr pellets were prepared from each sample, and their IR spectra were measured. In the same period, ten IR spectra were also obtained by the DRIFT technique; each spectrum was prepared like the mean spectrum from three independen t DRIFT measurements (including homogenization and grinding with KBr). All of these spectra were used fo r the prediction of the content of minerals by the PLS models that were created. The reproducibility was expressed by the relative standard deviation (RSD). RSD was calculated from the results that were obtained:  100 1 1 2       P n iiP x n xx RSD (11) where xi is the predicted value of the mineral conten t of the ith analysis of reproducibility, xPis the mean value of the predicted mineral content and nis number of analyses. The results and the calculated RSD are shown in Table 5. Worse values of reproducibility were obtained from the analysis of the IR spectra using KBr pellets. Values of the RSD in the analyses of chlorite, muscovite and albite were approximately 10 %; the values of the RSD in the analysis of quartz were approximately 5 %. The extremely high value of the RSD of sample BP5 (in the analysis of albite) was caused by the very low content of albite in this sample. Significantly better values of the RSD were obtained from the analysis of the IR spectra measured b y the DRIFT technique. Most of values of the RSD were within the range 1-3 %. The higher values of the RSD (about 10 %) were obtained from the analysis o f samples with a low content of minerals (chlorite, muscovite and albite in sample BP5). Different values of the reproducibility from the analysis of DRIFT spectra and the spectra from KBr p ellets were very probably caused by the differen t weights of samples in preparing for IR measurement. For preparation of DRIFT measurements, 5-10 mg o f the samples was used, whereas for preparing KB r pellets, only 0.5 mg of sample was used. This relatively low weight is at the limits of accurate measurement for common analytical balances and p robably caused an elevated error of weighing.