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Quantification of minerals from ATR-FTIR spectra with spectral interferences using the MRC method
Accepted Manuscript Quantification of minerals from ATR-FTIR spectra with spectral interferences using the MRC method
Francisco Bosch-Reig, José Vicente Gimeno-Adelantado, Francisco Bosch-Mossi, Antonio Doménech-Carbó PII: DOI: Reference:
S1386-1425(17)30100-2 doi: 10.1016/j.saa.2017.02.012 SAA 14934
To appear in:
Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy
Received date: Revised date: Accepted date:
16 September 2016 2 February 2017 5 February 2017
Please cite this article as: Francisco Bosch-Reig, José Vicente Gimeno-Adelantado, Francisco Bosch-Mossi, Antonio Doménech-Carbó , Quantification of minerals from ATR-FTIR spectra with spectral interferences using the MRC method. The address for the corresponding author was captured as affiliation for all authors. Please check if appropriate. Saa(2017), doi: 10.1016/j.saa.2017.02.012
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ACCEPTED MANUSCRIPT Quantification of minerals from ATR-FTIR spectra with spectral interferences using the MRC method
Francisco Bosch-Reig*, José Vicente Gimeno-Adelantado, Francisco Bosch-Mossi,
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Antonio Doménech-Carbó*
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Departament de Química Analítica, Universitat de València, Dr. Moliner 50, 46100
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Burjassot, Valencia, Spain.
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* Corresponding authors: e-mail: [email protected], [email protected].
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ACCEPTED MANUSCRIPT Abstract
A method for quantifying the individual components of mineral samples based on attenuated total reflectance – Fourier transform infrared spectroscopy (ATR-FTIR) is described, extending the constant ratio (CR) method to analytes absorbing in a common
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range of wavenumbers. Absorbance values in the spectral region where the analytes
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absorb relative to the absorbance of an internal standard absorbing at a wavenumber
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where the analytes do not absorb, permits the quantification of N analytes using measurements at N fixed wavenumbers. The method was tested for mixtures of albite,
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orthoclase, kaolin and quartz.
Keywords: ATR-FTIR; Quantification; Sodium feldspar; Potassium feldspar; Quartz;
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Kaolin.
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ACCEPTED MANUSCRIPT 1. Introduction
The identification and quantification of individual components in mixtures is an obvious analytical demand in mineral analysis. Infrared spectroscopy is a well-established technique for the identification of organic and inorganic species [1,2] of extended
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application in mineral analysis [3-7]. Fourier- Transform infrared spectroscopy (FTIR)
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is of particular interest in the case of complex systems containing organic and inorganic
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components [8,9] where there is an increasingly growth use of measurements in the attenuated total reflectance (ATR) mode [10,11]. The use of infrared spectroscopy for
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quantification purposes is, however, relatively scarce in the context of mineral analysis,
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with few studies specifically devoted to quantification [12-15].
In the simplest case of a binary mixture of two components displaying overlapping
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bands, quantification can be in principle obtained using the Vierordt’s method from
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absorbance measurements at two selected wavenumbers. The same scheme is of application to a N-component system using absorbance measurements at N The
application
of
this
method
in
conventional
Vis-UV
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wavenumbers.
spectrophotometry is straightforward because the optical path is constant in this
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technique. In ATR-FITR, however, the situation is different because the absorbance/transmittance response depends, among other factors, on anomalous dispersion and the shape and size distribution of the sample [16,17] so that the optical path depends in general of the thickness, granulometry and composition of the entire sample, including any possible IR-transparent matrix (a frequent situation in mineral samples). In these circumstances, the Vierordt’s method cannot strictly be applied.
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ACCEPTED MANUSCRIPT In order to provide ‘absolute’ concentrations for a system containing N absorbing substances, we described in a previous report [18] a quantification method based on the addition of an internal absorbing standard in known and constant concentration. In this method, the use of the ratio between the absorbances of the problem and the internal standard permits to avoid the problem of the variable optical path. The so-called
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constant ratio method (CR), was applied to Fourier-transform infrared spectroscopy
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(FTIR) for quantifying individual components in mineral mixtures, being applied to
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calcite/quartz binary mixtures.
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The previously reported method [18] assumed that all the compounds of interest (the A, B, C, … analytes and the added standard) displayed non-overlapping bands. In the
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current report, we describe a generalized CR method for mineral quantification, based on ATR-FTIR measurements, to be applied for mixtures of components whose
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absorption bands overlap. This modified constant ratio method, MCR, ideally permits
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the quantification of N analytes in a mixture providing that their separate spectra are known, using an internal standard which provides an absorption band separated from
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the spectra of the analytes from the absorbance measurement at N wavenumbers where all analytes absorb. As a result, in contrast with the Vierordt’s method, the absolute
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concentrations of the A, B, C, … analytes can be determined in the presence of a nonabsorbing matrix with no influence of the matrix-dependent optical path.
The application of this methodology is illustrated here by the quantification of individual minerals in mixtures of albite and orthoclase using ATR-FTIR measurements. The method can be also applied to other FTIR measurement modes. Albite, NaAlSi3O8, and orthoclase, KAlSi3O8, are the extreme members of the
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ACCEPTED MANUSCRIPT plagioclase minerals forming, respectively, sodium and potassium feldspars. The composition of sodium and potassium feldspars is an important parameter in regard to the densification behavior on thermal treatment of pastes for porcelain bodies [19], but is of importance in environmental [20], mineralogical [21,22] and archaeological [2325] studies. In this work, potassium hexacyanoferrate(II) was chosen as the internal
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standard. This compound displays an absorption band at 2115 cm1, due to the vibration
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of the triple carbon-nitrogen bond, which does not interfere with the absorptions of quartz and silicates, which are concentrated in the wavenumber region between 450 and
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1200 cm1 [26]. In the current report, the MCR method was applied to the quantification
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of albite, orthoclase, quartz and/or kaolin in synthetic mixtures of these minerals.
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2. Experimental
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Potassium hexacyanoferrate(II) (Carlo Erba) was used as a standard for ATR-FTIR
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measurements. Mixtures of analyte/standard were prepared in different proportions, weighing each component on an analytical balance to obtain different binary, ternary,
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etc. mixtures. The standards were: sodium feldspar (LGC Standards, BCS-CRM Nº 375/1), potassium feldspar (NCS DC 61102, China National Analysis Center for Iron and
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Steel), quartz (high purity silica, BCS-CRM 313/2) and kaolin (NCS DC 60123a, China National Analysis Center for Iron and Steel). The certified composition of such standards is summarized in Table 1. KBr (Merck) was used as a non-absorbing diluting species for relative uncertainty determination after preparing binary mixtures with the reference minerals.
For obtaining ATR-FTIR spectra of reference minerals, an amount of 0.200 g of the
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ACCEPTED MANUSCRIPT mineral was finely powdered with an agatha mortar and pestle and mixed with 0.25 mL of nujol oil until forming a homogeneous paste; then a fraction was transferred onto the diamond window of the ATR device. Synthetic mixtures were prepared as before by mixing weighted amounts (0.0001 g) of the different minerals to a total mass of 0.200 g. Infrared spectra were obtained between 4000 and 400 cm1, using an average of 32
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scans and 4 cm1 resolution. The spectra were recorded with respect to a background
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taken on the air or on a drop of nujol oil previously to each spectrum and under the
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same measurement conditions. In the registers obtained for each sample, the absorbances of the peaks chosen for the analyte or analytes and the standard were
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measured at the selected wavenumbers taking a horizontal base line defined in the region between 1400 and 1200 cm1. In order to determine the uncertainty in
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absorbance measurements, five independent measurements were taken on different
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standard + KBr mixtures having mass fractions of KBr between 0 and 1.
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3. Description of the method
Let us consider the case of a sample containing a binary mixture of two components, R,
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S, which display a series of overlapping absorption bands. In principle, the ‘absolute’ concentrations of R and S in the mixture can be determined from absorbance measurements at two selected wavenumbers. Here, we consider the more realistic case in which the components R and S are accompanied by a non-absorbing matrix T of unknown composition. In this system, one can assume that there will be a linear dependence of the absorbance associated to each one of the absorbing components on its concentration, cJ. Then, the absorbance contribution of the J-component at a given
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ACCEPTED MANUSCRIPT wavenumber, AJ(k) will be:
AJ (k ) J (k )bcJ ; J R, S
(1)
where J(k) represents the molar or mass absorptivity of the J-component at the
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wavenumber k, and b the unknown optical path.
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In principle, the concentrations of two analytes R and S, cR, cS, can be calculated, using
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the Vierordt’s method, by solving the following two-equation system from absorbance
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measurements at two wavenumbers 1, 2, in the problem R + S + T mixture:
(2)
A(2 ) R (2 )bcR S (2 )bcS
(3)
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A(1 ) R (1 )bcR S (1 )bcS
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To determine the concentrations cR, cS, the absorptivities R(1), R(2), S(1), S(2),
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have to be independently determined from absorbance measurements in R + T and S +
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T mixtures of known composition.
The application of the above scheme, however, is only possible if the optical path b is
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the same for all the above experiments. In ATR-FTIR spectroscopy, however, several effects, in particular anomalous dispersion and those associated to the shape and size distribution of solid particles [15,16], make variable the optical path which will be in general dependent on the granulometry and composition of the analytes and the matrix; i.e., the value of b will be in principle different for each measurement, being function of the thickness of the sample and the granulometry all the components of the sample. Accordingly, the absorptivity coefficients calculated in calibration experiments at R + T
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ACCEPTED MANUSCRIPT and S + T mixtures do not equal those operating in the R + S + T problem mixture (the “optical path problem”) so that, strictly, the Vierordt’s method cannot be applied to ATR-FTIR. In these circumstances, one can write b = b(cJ , cT ) , cJ representing the concentration of all J-absorbing components and cT the (unknown) concentration of the
rewritten as:
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AJ (k ) J (k )b(cJ , cT )cJ ; J R, S
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matrix. Accordingly, the Vierordt’s method cannot be applied and Eq. (1) should be
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(4)
The problem of the variable optical path can be avoided by means of the use of an
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internal standard, as previously described for the case of mixtures of components
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displaying non-overlapping bands [18]. For this purpose, a known amount of the R + S + T sample will be mixed with a known amount of a new substance, the internal
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reference material, P, which absorbs at a wavenumber P with no spectral interference
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with R and S. For several applications, the above system will be accompanied by a dispersing substance, typically nujol oil, with no absorption at the wavenumbers 1, 2,
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P; this system will be labeled as the ‘modified problem’. The ratio between the absorbance of this system at a given wavenumber k and the absorbance of the internal
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standard at its characteristic wavenumber P will be:
A(k ) R (k )b(cR , cS , cT )cR S (k )b(cR , cS , cT )cS AP ( P ) P (P )b(c A , cB , cT )cP
(5)
This ratio is independent on b(cJ , cT ) so that, taking absorbance measurements at two wavenumbers,1, 2:
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ACCEPTED MANUSCRIPT A(1 ) ( )c ( )c c c R 1 R S 1 S K RP (1P ) R KSP (1P ) S AP ( P ) P (P )cP cP cP
(6)
A(2 ) R (2 )cR S (2 ) S c c K RP (2P ) R KSP (2P ) S AP ( P ) P (P )cP cP cP
(7)
In these equations, KRP(1P) (= R(1)/P(P)) and KSP(1P) (= S(1)/P(P)) are the
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‘specific absorbance parameters’ which replace the absorptivity coefficients. Accordingly, the ‘absolute’ concentrations cR, cS can be calculated by solving the above
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system of two equations providing that the K-coefficients are determined from
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calibration experiments in R + P and S + P mixtures optionally incorporating a given
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matrix T. In these experiments:
(8)
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A(k ) ( )b(cR , cS , cT )cJ c J k K JP (k P ) J ; J R, S AP ( P ) P (P )b(cR , cS , cT )cP cP
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The relevant point to emphasize is that, as the optical path terms cancel for all series of
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measurements, such K-parameters are independent of the optical path so that they are independent on sample thickness, granulometry, etc. an essential property for analyzing
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solid materials by ATR-FTIR. Notice that A(k) and AP(P) are directly measured in the spectrum of the P-enriched sample and KRP(1P), KSP(1P) can be determined from
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calibration experiments in R + P and S + P binary mixtures, respectively.
The MCR method can be extended to an N-component system based on the above assumptions. Thus, the absorbance of the sample at a given wavenumber, k, relative to the absorbance of the internal standard at its characteristic wavenumber, P, will be:
A(k ) A ( ) ··· AN (k ) c c 1 k K1P (1P ) 1 ··· KSP ( NP ) N AP ( P ) AP (P ) cP cP
(9)
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If we dispose of absorbance measurements at N fixed wavenumbers, we obtain a system of N equations (one for each k wavenumber) with N unknowns (the c1, c2, … , cN concentrations of the analytes) which can be solved if the K-coefficients are determined from the spectra of each one of the individual J-components enriched with the internal
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standard from absorbance measurements at J + P mixtures of known composition. In
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these experiments:
(10)
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A(k ) ( )b(cJ , cT )cJ c J k K JP (k P ) J AP ( P ) P (P )b(c A , cB , cT )cP cP
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4. Results and discussion
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Figure 1 shows the ATR-FTIR spectra of Nafeld and Kfeld reference materials in the region between 600 and 1400 cm1 where all absorption bands are located. The infrared
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spectra of quartz, feldspars and kaolin is dominated by a series of overlapping bands
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between 800 and 1200 cm1, accompanied by less intense bands between 600 and 800 cm1. The bands in the range between 1200 and 900 cm1 can be assigned to the
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asymmetric stretching vibration of the Si–O groups (maximum at 1080 cm1), the symmetric stretch at 800 and 780 cm1, and the symmetric and asymmetric Si–O
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bending mode at 695, 520, and 450 cm1, respectively [26]. Table 2 summarizes the wavenumbers at which the absorption maxima appear in the spectra of the studied reference minerals. The spectrum of K4Fe(CN)6 consisted, as previously noted [10], on a unique band at 2115 cm1. Then, no spectral interference with the clays under study is associated to this compound so that it can be used as an internal standard for absorbance measurements. This can be seen in Figure 3 where the spectra of samples Nafeld and Kfeld enriched with 17% wt. K4Fe(CN)6 are shown.
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The repeatability of the measurements is a critical aspect to be considered. Under our experimental conditions, the ATR-FTIR spectra of both reference materials and their mixtures exhibited an excellent repeatability, as can be seen in Figure 2, where four independently recorded spectra of quartz and kaolin reference materials are
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superimposed.
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As expected, the spectra of mixtures of the above components displayed a series of overlapped bands corresponding to the superposition of the above signals. This can be
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seen in Figure 4, where the spectrum a of mixture of sodium feldspar (50.58 %wt), potassium feldspar (36.28 %wt) and K4Fe(CN)6 (13.14 %wt) is depicted. It is pertinent
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to note, however, that unless quartz, the reference materials were no ‘pure’ minerals (see Table 1) so that the K(kP) values are standard-sensitive. It is also pertinent to note
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that the absorbance ratios varied slightly with the granulometry of the materials, a
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phenomenon also observed in infrared spectra on KBr pellets [18]. To minimize this effect, the spectra were recorded on samples of finely powdered minerals and prepared by pasting
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the solid material with nujol oil. The optimum dosage, balancing repeatability and amount of sample (logically the use of a minimal amount of sample as possible is desirable) was
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obtained for a total mass of solid materials of 0.200000.00010 g pasted with 0.25 mL of nujol oil, as described in the Experimental section. Under these conditions, the ATR-FTIR measurements on K4Fe(CN)6–enriched mineral specimens presented a high repeatability, as can be seen in Figure 4, where three independent measurements of the aforementioned mixture of Nafeld plus Kfeld and K4Fe(CN)6 are depicted.
Calibration plots were performed on binary mixtures of sodium and potassium feldspars
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ACCEPTED MANUSCRIPT with K4Fe(CN)6 using absorbance measurements at the absorption maxima previously indicated in the feldspar spectra and the absorbance at 2115 cm1, corresponding to the absorption of K4Fe(CN)6. Figure 5 depicts the results for Nafeld reference material using two wavenumbers, 1090 (squares) and 745 (triangles) cm1. The plots of the ratio between the absorbance of the feldspar at the selected wavenumber, ANafel(), and the absorbance of
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the internal standard, AFe(Fe) vs. the ratio of the respective concentrations, cNafel/cFe,
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exhibited an excellent linearity in terms of linear correlation coefficients, but the slopes
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differed slightly but significantly, as expected, from the reference sodium feldspar to the
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sample.
Table 3 summarizes the K(kP) values determined from ATR-FTIR spectra of the
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reference minerals at a set of selected wavenumbers. The uncertainty in the K(kP) values was estimated from the standard deviation in the absorbance values from three
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independent measurements in experiments such as in Figure 2. Using such data, the
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composition of different binary mixtures prepared from weighted amounts of the standards was calculated. It is pertinent to note that the differences in such coefficients
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using replicate spectra were lower than the 5% in the average K(kP) value. The results obtained for different binary and ternary mixtures of the studied reference materials are
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summarized in Table 4 where standard deviations in concentrations were calculated from those in absorbance measurements combined with those estimated for K(kP) coefficients in Table 3. A satisfactory agreement was obtained in the studied systems between the composition from weight of the standards and that calculated from ATR-FTIR spectra.
Apart from contamination, general error sources in FTIR spectroscopy are associated to atmospheric intrusion, interference fringes, stray light, anomalous dispersion, and
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ACCEPTED MANUSCRIPT detector non-linearity [1,2,16,17], among others, which should be separately considered for transmission, diffuse reflectance, and ATR. In this last mode, irregular reflection features [1,2,26,27], instability in the wavenumber scale [28] and particle size and particle size heterogeneity [16] are of importance. As a result, the uncertainty in absorbance measurements varies in general with the wavenumber defining an
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instrument/mode-characteristic error curve. In the context of mineral/inorganic analysis,
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analysis of errors has been focused on linear regression [13-15] and multivariate [8-11] methods. To evaluate errors associated to the proposed MRC method, it will be assumed
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here that the uncertainty (in the following represented by ) in the concentration of a
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given analyte, c, relative to the internal standard in concentration cP depends on the uncertainties of the respective absorbances A() and AP(P) at the indicated
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wavenumbers and those of the absorptivity coefficients, () , (P) (or, equivalently,
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the K-coefficients). Then:
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(c / cP ) [ A( ) / AP ( P )] [ ( ) / P ( P )] c / cP A( ) / AP ( P ) ( ) / P ( P )
(11)
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Experimental data for absorbance measurements carried out in mixtures of the studied mineral standards and K4Fe(CN)6 with a non-absorbing compound, KBr, revealed that
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the relative uncertainty, A()/A(), was maintained within the 0.01 to 0.04 range, increasing slowly upon increasing the proportion of KBr. Figure 6 shows the variation of this quantity, determined from five independent measurements for each KBr + mineral mixture, with the mass fraction of KBr (fKBr) in mixtures of KBr plus Nafeld (squares, 994 cm1), Kfeld (solid squares, 992 cm1) and Kao (triangles, 998 cm1). Since the values of the relative uncertainty remain confined into a narrow range, it is in principle plausible to assume, for simplicity, that the uncertainty in the individual measurements of the
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ACCEPTED MANUSCRIPT absorbances AP(P) and A() is the same (A) so that:
[ A( ) / AP ( P )] 1 1 A A( ) / AP ( P ) A( ) AP ( P )
(12)
Additionally, one can assume that the sum of the absorbances of the problem compound
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and the standard become approximately equal to an averaged value Ao. Then,
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designating by the A()/AP(P) ratio, the individual absorbances would be A() =
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Ao/(1+) and AP(P) = Ao/(1+). Accordingly, one can obtain:
(13)
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[ A( ) / AP ( P )] A (1 ) 2 A( ) / AP ( P ) Ao
The main result is that, assuming that the A/Ao ratio, representing the averaged relative uncertainty in absorbance measurements, is constant, the uncertainty in the absorbance
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ratio A()/AP(P) tends to a minimum value for = 1. This reasoning can in principle be extended to the absorptivity ratio so that:
(14)
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[ P ( P ) / ( )] (1 ) 2 ( ) / ( ) P P o
where (= P(P)/()) represents the absorptivity ratio and /o an averaged relative uncertainty of the absorptivity values. Again, the lower uncertainty value would be reached for () = P(p). This means that, ideally, the lower uncertainty in the c/cP ratio would be obtained when the above condition applies simultaneously to A() = AP(p). Both conditions lead to a minimum uncertainty for c/cP = 1, but this condition, by practical reasons, is not operative.
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(c / cP ) A (1 ) 2 (1 ) 2 o c / cP Ao
(15)
Figure 7 compares the variation of the relative uncertainty in the concentration ratio, (c/cP)/(c/cP), on the concentration ratio, c/cP, assuming A/Ao = 1% and /o = 1%,
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for different values of the P(P)/() ratio. One can see that the uncertainty in the
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concentration increases rapidly on decreasing c/cP ratio below 0.2 whereas increases
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more slowly for c/cP ratio larger than 1.
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5. Conclusions
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ATR-FTIR spectroscopy can be used for quantifying the individual components of mineral mixtures based on absorbance measurements at fixed wavenumbers where all components
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absorb avoiding the problem of the variable optical path. The application of the method
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requires the measurement of the absorbance of an internal standard, added in known proportion to the sample, at a wavenumber where the analytes do not absorb significantly.
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The method can ideally be applied to determine the content of N analytes in a multicomponent mineral sample from absorbance measurements at N wavenumbers.
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Application to mixtures of sodium feldspar, potassium feldspar, kaolin and/or quartz provide satisfactory results under the described experimental conditions thus denoting the suitability of ATR-FTIR as a technique usable for quantification in mineral anlysis.
Acknowledgements: Financial support from the MINECO Project CTQ2014-53736-C32-P, which is supported with ERDF funds is gratefully acknowledged.
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[23] R. Ravisankar, G. Raja Annamalai, A. Naseerutheen, A Chandrasekaran, M.V.R.
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Prasad, K.K. Satpathy, C. Maheswaran, Analytical characterization of recently excavated megalithic sarcophagi potsherds in Veeranam village, Tiruvannamalai dist.,
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Tamilnadu, India. Spectrochim. Acta A 115 (2013) 845853.
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[24] G. Raja Annamalai, R. Ravisankar, A. Rrajalakshmi, A Chandrasekaran, K. Rajan,
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Spectroscopic characterization of recently excavated archaeological potsherds from
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112118.
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Tamilnadu, India with multi-analytical approach. Spectrochim. Acta A 123 (2014)
[25] R. Ravisankar, A. Naseerutheen, G. Raja Annamalai, A Chandrasekaran, A. Rrajalakshmi, K.V. Kanagasapathy, M.V.R. Prasad, K.K. Satpathy, The analytical investigations of ancient pottery from Kaveripakkam, Vellore dist, Tamilnadu by spectroscopic techniques. Spectrochim. Acta A 121 (2014) 457463.
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ACCEPTED MANUSCRIPT [26] B.J. Saikia, G. Parthasarathy, N.C. Sarmah, Fourier transform infrared spectroscopic estimation of crystallinity in SiO2 based rocks. Bull. Mater. Sci. 31 (2008) 775–779.
[27] J.R. Birch, F.J.J. Clarke, Interreflection errors in Fourier transform infrared
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spectroscopy: a preliminary appraisal. Anal. Chim. Acta, 380 (1999) 369–378.
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[28] D.D. Weis, G.E. Ewing, Absorption Anomalies in Ratio and Subtraction FT-IR
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Spectroscopy. Anal. Chem. 70 (1998) 3175–3183.
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ACCEPTED MANUSCRIPT Figures Figure 1. Absorbance ATR-FTIR spectra of: a) sodium feldspar (Nafeld) and b) potassium feldspar (Kfeld) reference materials.
Figure 2. Absorbance ATR-FTIR spectrum of a) quartz and b) kaolin reference materials.
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Two replicate spectra are superimposed.
Figure 3. Absorbance ATR-FTIR spectra of samples a) Nafeld and b) Kfeld spiked with
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carbon-nitrogen bond of the K4Fe(CN)6 internal standard.
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17 % wt K4Fe(CN)6. The arrows mark the band associated to the vibration of the triple
Figure 4. Absorbance ATR-FTIR spectrum of a synthetic mixture of sodium (50.58 %wt)
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and potassium feldspar (36.28 %wt) plus K4Fe(CN)6 (13.14 % wt). Three replicate spectra are superimposed. The arrow marks the band associated to the vibration of the triple
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carbon-nitrogen bond of the K4Fe(CN)6 internal standard. Figure 5. Absorbance ratio vs. concentration ratio plots for Nafeld reference material
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spiked with K4Fe(CN)6 forming nujol oil-embedded pellets using absorbance
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measurements at = 1090 (squares) and 745 (triangles) cm1 and Fe = 2115 cm1.
Figure 6. Variation with the mass fraction of KBr of the relative uncertainty in absorbance
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measurements at the indicated wavenumbers in mixtures of KBr plus Nafeld (squares, 994 cm1), Kfeld (solid squares, 992 cm1) and Kao (triangles, 998 cm1). Values of
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Figure 7. Theoretical variation of the relative uncertainty in the concentration ratio, (c/cP)/(c/cP), on the concentration ratio, c/cP, from Eq. (15) assuming A/Aoº = 1% and /o = 1%, for different values of the P(P)/() ratio.
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ACCEPTED MANUSCRIPT Table 1. Certified composition of the standards used in this study. Nafeld: sodium feldspar (LGC Standards, BCS-CRM Nº 375/1); Kfeld: potassium feldspar (NCS DC 61102, China National Analysis Center for Iron and Steel); Kao: kaolin (NCS DC 60123a, China National Analysis Center for Iron and Steel); Qua: quartz (BCS-CRM 313/2). nd non detected.
nd 8.89 1.47 0.78 0.180 nd nd nd nd nd 0.226 nd 0.72
nd 3.69 9.60 0.76 0.054 nd nd nd nd nd nd nd 0.86
nd 0.0057 0.0108 0.0160 0.0038 0.00032 0.00067 0.00024 nd nd nd nd nd
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Qua 99.73 0.0243 0.068 0.0229
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Fe2O3T Na2O K2O CaO MgO MnO BaO SrO SO3 H2O P2O5 CO2 LOI
Kao 45.30 0.060 37.70 Fe2O3T 0.35 FeO (0.026) 0.35 0.045 0.042 0.064 0.021 0.0018 nd nd 0.76 15.26 0.16 (0.026) 14.81
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Kfeld 66.26 0.048 18.63 0.19
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Nafeld 69.26 0.313 17.89 0.291
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%wt SiO2 TiO2 Al2O3 Fe2O3
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ACCEPTED MANUSCRIPT Table 2. Absorption bands in the ATR-FTIR spectra of the mineral standards used in this study. st strong band; sh shoulder. Wavenumber at the absorption maximum / cm1 1145sh, 1095sh, 1040st, 994st, 786, 761, 743, 724, 692, 648 1140, 1090sh, 1045sh, 992st, 767, 725, 647 1114, 1024st, 998st, 935, 910, 788, 750, 678, 645 1160sh, 1090sh, 796, 777, 690 2115st
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Mineral Nafeld Kfeld Kao Qua K4Fe(CN)6
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ACCEPTED MANUSCRIPT Table 3. Peaks and K(kP)-parameters for quantification at selected wavenumbers, using potassium hexacyanoferrate(II) standard. Number between parenthesis represent the standard deviation in the last significant figure.
(cm1) (cm1) (cm1) (cm1) (cm1) (cm1) (cm1) 1135 0.523(5) 0.308(3) 0.160(2) 0.417(4)
1095 0.534(5) 0.317(3) 0.167(2) 0.667(7)
1035 0.861(8) 0.566(6) 0.693(7) 0.874(9)
990 0.941(9) 0.857(9) 0.707(8) 0.842(8)
935 0.540(5) 0.360(4) 0.413(4) 0.595(6)
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1150 0.494(5) 0.257(3) 0.067(1) 0.342(3)
905 0.366(4) 0.223(2) 0.693(7) 0.401(4)
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Component K(kP) Nafeld Kfeld Kao Qua
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ACCEPTED MANUSCRIPT Table 4. Statistical data for the analysis of different binary and ternary mixtures of the studied reference minerals from ATR-FTIR data using K4Fe(CN)6 as a internal standard. a Composition for wighted amounts of the standards (all 0.001 g); bcomposition from ATR-FTIR data using the K(kP) values in Table 3. (2nd)b
(3rd)b
57.01.2 72.81.5 21.00.4 49.21.0 42.00.8 57.71.2 38.90.7 28.30.5 35.60.7 29.40.6
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(3rd)a (1st)b (0.02) 44.00.8 27.20.5 79.01.6 50.81.1 58.01.2 42.30.8 28.40 32.80.6 30.69 35.00.7
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Components (%wt) (1st)a (0.02) Nafel + Kfel 42.57 Nafel + Kfel 26.33 Nafel + Kfel 77.81 Nafel+Kao 51.22 Kafel+Kao 55.37 Nafel+Qua 46.77 Nafel + Kao + Qua 33.16 Kfel + Kao + Qua 34,08
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Graphical Abstract
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ACCEPTED MANUSCRIPT Highlights:
1) ATR-FTIR is applied to quantify individual components of mineral samples.
2) Theoretical expressions for modified constant ratio (MCR) method are developed.
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3) Absorbance measurements at N fixed wavenumbers ideally permits to quantify N
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analytes.
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4) Application to mixtures of albite, orthoclase, kaolin and quartz is described.
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Francisco Bosch-Reig, José Vicente Gimeno-Adelantado, Francisco Bosch-Mossi, Antonio Doménech-Carbó PII: DOI: Reference:
S1386-1425(17)30100-2 doi: 10.1016/j.saa.2017.02.012 SAA 14934
To appear in:
Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy
Received date: Revised date: Accepted date:
16 September 2016 2 February 2017 5 February 2017
Please cite this article as: Francisco Bosch-Reig, José Vicente Gimeno-Adelantado, Francisco Bosch-Mossi, Antonio Doménech-Carbó , Quantification of minerals from ATR-FTIR spectra with spectral interferences using the MRC method. The address for the corresponding author was captured as affiliation for all authors. Please check if appropriate. Saa(2017), doi: 10.1016/j.saa.2017.02.012
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT Quantification of minerals from ATR-FTIR spectra with spectral interferences using the MRC method
Francisco Bosch-Reig*, José Vicente Gimeno-Adelantado, Francisco Bosch-Mossi,
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Antonio Doménech-Carbó*
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Departament de Química Analítica, Universitat de València, Dr. Moliner 50, 46100
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Burjassot, Valencia, Spain.
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* Corresponding authors: e-mail: [email protected], [email protected].
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ACCEPTED MANUSCRIPT Abstract
A method for quantifying the individual components of mineral samples based on attenuated total reflectance – Fourier transform infrared spectroscopy (ATR-FTIR) is described, extending the constant ratio (CR) method to analytes absorbing in a common
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range of wavenumbers. Absorbance values in the spectral region where the analytes
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absorb relative to the absorbance of an internal standard absorbing at a wavenumber
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where the analytes do not absorb, permits the quantification of N analytes using measurements at N fixed wavenumbers. The method was tested for mixtures of albite,
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orthoclase, kaolin and quartz.
Keywords: ATR-FTIR; Quantification; Sodium feldspar; Potassium feldspar; Quartz;
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Kaolin.
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ACCEPTED MANUSCRIPT 1. Introduction
The identification and quantification of individual components in mixtures is an obvious analytical demand in mineral analysis. Infrared spectroscopy is a well-established technique for the identification of organic and inorganic species [1,2] of extended
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application in mineral analysis [3-7]. Fourier- Transform infrared spectroscopy (FTIR)
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is of particular interest in the case of complex systems containing organic and inorganic
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components [8,9] where there is an increasingly growth use of measurements in the attenuated total reflectance (ATR) mode [10,11]. The use of infrared spectroscopy for
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quantification purposes is, however, relatively scarce in the context of mineral analysis,
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with few studies specifically devoted to quantification [12-15].
In the simplest case of a binary mixture of two components displaying overlapping
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bands, quantification can be in principle obtained using the Vierordt’s method from
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absorbance measurements at two selected wavenumbers. The same scheme is of application to a N-component system using absorbance measurements at N The
application
of
this
method
in
conventional
Vis-UV
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wavenumbers.
spectrophotometry is straightforward because the optical path is constant in this
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technique. In ATR-FITR, however, the situation is different because the absorbance/transmittance response depends, among other factors, on anomalous dispersion and the shape and size distribution of the sample [16,17] so that the optical path depends in general of the thickness, granulometry and composition of the entire sample, including any possible IR-transparent matrix (a frequent situation in mineral samples). In these circumstances, the Vierordt’s method cannot strictly be applied.
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ACCEPTED MANUSCRIPT In order to provide ‘absolute’ concentrations for a system containing N absorbing substances, we described in a previous report [18] a quantification method based on the addition of an internal absorbing standard in known and constant concentration. In this method, the use of the ratio between the absorbances of the problem and the internal standard permits to avoid the problem of the variable optical path. The so-called
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constant ratio method (CR), was applied to Fourier-transform infrared spectroscopy
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(FTIR) for quantifying individual components in mineral mixtures, being applied to
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calcite/quartz binary mixtures.
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The previously reported method [18] assumed that all the compounds of interest (the A, B, C, … analytes and the added standard) displayed non-overlapping bands. In the
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current report, we describe a generalized CR method for mineral quantification, based on ATR-FTIR measurements, to be applied for mixtures of components whose
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absorption bands overlap. This modified constant ratio method, MCR, ideally permits
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the quantification of N analytes in a mixture providing that their separate spectra are known, using an internal standard which provides an absorption band separated from
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the spectra of the analytes from the absorbance measurement at N wavenumbers where all analytes absorb. As a result, in contrast with the Vierordt’s method, the absolute
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concentrations of the A, B, C, … analytes can be determined in the presence of a nonabsorbing matrix with no influence of the matrix-dependent optical path.
The application of this methodology is illustrated here by the quantification of individual minerals in mixtures of albite and orthoclase using ATR-FTIR measurements. The method can be also applied to other FTIR measurement modes. Albite, NaAlSi3O8, and orthoclase, KAlSi3O8, are the extreme members of the
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ACCEPTED MANUSCRIPT plagioclase minerals forming, respectively, sodium and potassium feldspars. The composition of sodium and potassium feldspars is an important parameter in regard to the densification behavior on thermal treatment of pastes for porcelain bodies [19], but is of importance in environmental [20], mineralogical [21,22] and archaeological [2325] studies. In this work, potassium hexacyanoferrate(II) was chosen as the internal
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standard. This compound displays an absorption band at 2115 cm1, due to the vibration
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of the triple carbon-nitrogen bond, which does not interfere with the absorptions of quartz and silicates, which are concentrated in the wavenumber region between 450 and
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1200 cm1 [26]. In the current report, the MCR method was applied to the quantification
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of albite, orthoclase, quartz and/or kaolin in synthetic mixtures of these minerals.
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2. Experimental
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Potassium hexacyanoferrate(II) (Carlo Erba) was used as a standard for ATR-FTIR
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measurements. Mixtures of analyte/standard were prepared in different proportions, weighing each component on an analytical balance to obtain different binary, ternary,
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etc. mixtures. The standards were: sodium feldspar (LGC Standards, BCS-CRM Nº 375/1), potassium feldspar (NCS DC 61102, China National Analysis Center for Iron and
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Steel), quartz (high purity silica, BCS-CRM 313/2) and kaolin (NCS DC 60123a, China National Analysis Center for Iron and Steel). The certified composition of such standards is summarized in Table 1. KBr (Merck) was used as a non-absorbing diluting species for relative uncertainty determination after preparing binary mixtures with the reference minerals.
For obtaining ATR-FTIR spectra of reference minerals, an amount of 0.200 g of the
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ACCEPTED MANUSCRIPT mineral was finely powdered with an agatha mortar and pestle and mixed with 0.25 mL of nujol oil until forming a homogeneous paste; then a fraction was transferred onto the diamond window of the ATR device. Synthetic mixtures were prepared as before by mixing weighted amounts (0.0001 g) of the different minerals to a total mass of 0.200 g. Infrared spectra were obtained between 4000 and 400 cm1, using an average of 32
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scans and 4 cm1 resolution. The spectra were recorded with respect to a background
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taken on the air or on a drop of nujol oil previously to each spectrum and under the
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same measurement conditions. In the registers obtained for each sample, the absorbances of the peaks chosen for the analyte or analytes and the standard were
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measured at the selected wavenumbers taking a horizontal base line defined in the region between 1400 and 1200 cm1. In order to determine the uncertainty in
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standard + KBr mixtures having mass fractions of KBr between 0 and 1.
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3. Description of the method
Let us consider the case of a sample containing a binary mixture of two components, R,
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S, which display a series of overlapping absorption bands. In principle, the ‘absolute’ concentrations of R and S in the mixture can be determined from absorbance measurements at two selected wavenumbers. Here, we consider the more realistic case in which the components R and S are accompanied by a non-absorbing matrix T of unknown composition. In this system, one can assume that there will be a linear dependence of the absorbance associated to each one of the absorbing components on its concentration, cJ. Then, the absorbance contribution of the J-component at a given
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AJ (k ) J (k )bcJ ; J R, S
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In principle, the concentrations of two analytes R and S, cR, cS, can be calculated, using
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have to be independently determined from absorbance measurements in R + T and S +
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T mixtures of known composition.
The application of the above scheme, however, is only possible if the optical path b is
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the same for all the above experiments. In ATR-FTIR spectroscopy, however, several effects, in particular anomalous dispersion and those associated to the shape and size distribution of solid particles [15,16], make variable the optical path which will be in general dependent on the granulometry and composition of the analytes and the matrix; i.e., the value of b will be in principle different for each measurement, being function of the thickness of the sample and the granulometry all the components of the sample. Accordingly, the absorptivity coefficients calculated in calibration experiments at R + T
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rewritten as:
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AJ (k ) J (k )b(cJ , cT )cJ ; J R, S
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matrix. Accordingly, the Vierordt’s method cannot be applied and Eq. (1) should be
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(4)
The problem of the variable optical path can be avoided by means of the use of an
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internal standard, as previously described for the case of mixtures of components
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displaying non-overlapping bands [18]. For this purpose, a known amount of the R + S + T sample will be mixed with a known amount of a new substance, the internal
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reference material, P, which absorbs at a wavenumber P with no spectral interference
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with R and S. For several applications, the above system will be accompanied by a dispersing substance, typically nujol oil, with no absorption at the wavenumbers 1, 2,
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P; this system will be labeled as the ‘modified problem’. The ratio between the absorbance of this system at a given wavenumber k and the absorbance of the internal
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standard at its characteristic wavenumber P will be:
A(k ) R (k )b(cR , cS , cT )cR S (k )b(cR , cS , cT )cS AP ( P ) P (P )b(c A , cB , cT )cP
(5)
This ratio is independent on b(cJ , cT ) so that, taking absorbance measurements at two wavenumbers,1, 2:
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(6)
A(2 ) R (2 )cR S (2 ) S c c K RP (2P ) R KSP (2P ) S AP ( P ) P (P )cP cP cP
(7)
In these equations, KRP(1P) (= R(1)/P(P)) and KSP(1P) (= S(1)/P(P)) are the
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‘specific absorbance parameters’ which replace the absorptivity coefficients. Accordingly, the ‘absolute’ concentrations cR, cS can be calculated by solving the above
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measurements, such K-parameters are independent of the optical path so that they are independent on sample thickness, granulometry, etc. an essential property for analyzing
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solid materials by ATR-FTIR. Notice that A(k) and AP(P) are directly measured in the spectrum of the P-enriched sample and KRP(1P), KSP(1P) can be determined from
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calibration experiments in R + P and S + P binary mixtures, respectively.
The MCR method can be extended to an N-component system based on the above assumptions. Thus, the absorbance of the sample at a given wavenumber, k, relative to the absorbance of the internal standard at its characteristic wavenumber, P, will be:
A(k ) A ( ) ··· AN (k ) c c 1 k K1P (1P ) 1 ··· KSP ( NP ) N AP ( P ) AP (P ) cP cP
(9)
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If we dispose of absorbance measurements at N fixed wavenumbers, we obtain a system of N equations (one for each k wavenumber) with N unknowns (the c1, c2, … , cN concentrations of the analytes) which can be solved if the K-coefficients are determined from the spectra of each one of the individual J-components enriched with the internal
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standard from absorbance measurements at J + P mixtures of known composition. In
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these experiments:
(10)
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A(k ) ( )b(cJ , cT )cJ c J k K JP (k P ) J AP ( P ) P (P )b(c A , cB , cT )cP cP
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4. Results and discussion
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Figure 1 shows the ATR-FTIR spectra of Nafeld and Kfeld reference materials in the region between 600 and 1400 cm1 where all absorption bands are located. The infrared
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spectra of quartz, feldspars and kaolin is dominated by a series of overlapping bands
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between 800 and 1200 cm1, accompanied by less intense bands between 600 and 800 cm1. The bands in the range between 1200 and 900 cm1 can be assigned to the
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asymmetric stretching vibration of the Si–O groups (maximum at 1080 cm1), the symmetric stretch at 800 and 780 cm1, and the symmetric and asymmetric Si–O
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bending mode at 695, 520, and 450 cm1, respectively [26]. Table 2 summarizes the wavenumbers at which the absorption maxima appear in the spectra of the studied reference minerals. The spectrum of K4Fe(CN)6 consisted, as previously noted [10], on a unique band at 2115 cm1. Then, no spectral interference with the clays under study is associated to this compound so that it can be used as an internal standard for absorbance measurements. This can be seen in Figure 3 where the spectra of samples Nafeld and Kfeld enriched with 17% wt. K4Fe(CN)6 are shown.
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The repeatability of the measurements is a critical aspect to be considered. Under our experimental conditions, the ATR-FTIR spectra of both reference materials and their mixtures exhibited an excellent repeatability, as can be seen in Figure 2, where four independently recorded spectra of quartz and kaolin reference materials are
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superimposed.
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As expected, the spectra of mixtures of the above components displayed a series of overlapped bands corresponding to the superposition of the above signals. This can be
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seen in Figure 4, where the spectrum a of mixture of sodium feldspar (50.58 %wt), potassium feldspar (36.28 %wt) and K4Fe(CN)6 (13.14 %wt) is depicted. It is pertinent
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to note, however, that unless quartz, the reference materials were no ‘pure’ minerals (see Table 1) so that the K(kP) values are standard-sensitive. It is also pertinent to note
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that the absorbance ratios varied slightly with the granulometry of the materials, a
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phenomenon also observed in infrared spectra on KBr pellets [18]. To minimize this effect, the spectra were recorded on samples of finely powdered minerals and prepared by pasting
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the solid material with nujol oil. The optimum dosage, balancing repeatability and amount of sample (logically the use of a minimal amount of sample as possible is desirable) was
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obtained for a total mass of solid materials of 0.200000.00010 g pasted with 0.25 mL of nujol oil, as described in the Experimental section. Under these conditions, the ATR-FTIR measurements on K4Fe(CN)6–enriched mineral specimens presented a high repeatability, as can be seen in Figure 4, where three independent measurements of the aforementioned mixture of Nafeld plus Kfeld and K4Fe(CN)6 are depicted.
Calibration plots were performed on binary mixtures of sodium and potassium feldspars
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ACCEPTED MANUSCRIPT with K4Fe(CN)6 using absorbance measurements at the absorption maxima previously indicated in the feldspar spectra and the absorbance at 2115 cm1, corresponding to the absorption of K4Fe(CN)6. Figure 5 depicts the results for Nafeld reference material using two wavenumbers, 1090 (squares) and 745 (triangles) cm1. The plots of the ratio between the absorbance of the feldspar at the selected wavenumber, ANafel(), and the absorbance of
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the internal standard, AFe(Fe) vs. the ratio of the respective concentrations, cNafel/cFe,
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exhibited an excellent linearity in terms of linear correlation coefficients, but the slopes
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differed slightly but significantly, as expected, from the reference sodium feldspar to the
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sample.
Table 3 summarizes the K(kP) values determined from ATR-FTIR spectra of the
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reference minerals at a set of selected wavenumbers. The uncertainty in the K(kP) values was estimated from the standard deviation in the absorbance values from three
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independent measurements in experiments such as in Figure 2. Using such data, the
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composition of different binary mixtures prepared from weighted amounts of the standards was calculated. It is pertinent to note that the differences in such coefficients
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using replicate spectra were lower than the 5% in the average K(kP) value. The results obtained for different binary and ternary mixtures of the studied reference materials are
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summarized in Table 4 where standard deviations in concentrations were calculated from those in absorbance measurements combined with those estimated for K(kP) coefficients in Table 3. A satisfactory agreement was obtained in the studied systems between the composition from weight of the standards and that calculated from ATR-FTIR spectra.
Apart from contamination, general error sources in FTIR spectroscopy are associated to atmospheric intrusion, interference fringes, stray light, anomalous dispersion, and
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ACCEPTED MANUSCRIPT detector non-linearity [1,2,16,17], among others, which should be separately considered for transmission, diffuse reflectance, and ATR. In this last mode, irregular reflection features [1,2,26,27], instability in the wavenumber scale [28] and particle size and particle size heterogeneity [16] are of importance. As a result, the uncertainty in absorbance measurements varies in general with the wavenumber defining an
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instrument/mode-characteristic error curve. In the context of mineral/inorganic analysis,
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analysis of errors has been focused on linear regression [13-15] and multivariate [8-11] methods. To evaluate errors associated to the proposed MRC method, it will be assumed
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here that the uncertainty (in the following represented by ) in the concentration of a
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given analyte, c, relative to the internal standard in concentration cP depends on the uncertainties of the respective absorbances A() and AP(P) at the indicated
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wavenumbers and those of the absorptivity coefficients, () , (P) (or, equivalently,
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the K-coefficients). Then:
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(c / cP ) [ A( ) / AP ( P )] [ ( ) / P ( P )] c / cP A( ) / AP ( P ) ( ) / P ( P )
(11)
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Experimental data for absorbance measurements carried out in mixtures of the studied mineral standards and K4Fe(CN)6 with a non-absorbing compound, KBr, revealed that
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the relative uncertainty, A()/A(), was maintained within the 0.01 to 0.04 range, increasing slowly upon increasing the proportion of KBr. Figure 6 shows the variation of this quantity, determined from five independent measurements for each KBr + mineral mixture, with the mass fraction of KBr (fKBr) in mixtures of KBr plus Nafeld (squares, 994 cm1), Kfeld (solid squares, 992 cm1) and Kao (triangles, 998 cm1). Since the values of the relative uncertainty remain confined into a narrow range, it is in principle plausible to assume, for simplicity, that the uncertainty in the individual measurements of the
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ACCEPTED MANUSCRIPT absorbances AP(P) and A() is the same (A) so that:
[ A( ) / AP ( P )] 1 1 A A( ) / AP ( P ) A( ) AP ( P )
(12)
Additionally, one can assume that the sum of the absorbances of the problem compound
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and the standard become approximately equal to an averaged value Ao. Then,
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designating by the A()/AP(P) ratio, the individual absorbances would be A() =
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Ao/(1+) and AP(P) = Ao/(1+). Accordingly, one can obtain:
(13)
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[ A( ) / AP ( P )] A (1 ) 2 A( ) / AP ( P ) Ao
The main result is that, assuming that the A/Ao ratio, representing the averaged relative uncertainty in absorbance measurements, is constant, the uncertainty in the absorbance
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ratio A()/AP(P) tends to a minimum value for = 1. This reasoning can in principle be extended to the absorptivity ratio so that:
(14)
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[ P ( P ) / ( )] (1 ) 2 ( ) / ( ) P P o
where (= P(P)/()) represents the absorptivity ratio and /o an averaged relative uncertainty of the absorptivity values. Again, the lower uncertainty value would be reached for () = P(p). This means that, ideally, the lower uncertainty in the c/cP ratio would be obtained when the above condition applies simultaneously to A() = AP(p). Both conditions lead to a minimum uncertainty for c/cP = 1, but this condition, by practical reasons, is not operative.
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(c / cP ) A (1 ) 2 (1 ) 2 o c / cP Ao
(15)
Figure 7 compares the variation of the relative uncertainty in the concentration ratio, (c/cP)/(c/cP), on the concentration ratio, c/cP, assuming A/Ao = 1% and /o = 1%,
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for different values of the P(P)/() ratio. One can see that the uncertainty in the
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concentration increases rapidly on decreasing c/cP ratio below 0.2 whereas increases
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more slowly for c/cP ratio larger than 1.
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5. Conclusions
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ATR-FTIR spectroscopy can be used for quantifying the individual components of mineral mixtures based on absorbance measurements at fixed wavenumbers where all components
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absorb avoiding the problem of the variable optical path. The application of the method
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requires the measurement of the absorbance of an internal standard, added in known proportion to the sample, at a wavenumber where the analytes do not absorb significantly.
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The method can ideally be applied to determine the content of N analytes in a multicomponent mineral sample from absorbance measurements at N wavenumbers.
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Application to mixtures of sodium feldspar, potassium feldspar, kaolin and/or quartz provide satisfactory results under the described experimental conditions thus denoting the suitability of ATR-FTIR as a technique usable for quantification in mineral anlysis.
Acknowledgements: Financial support from the MINECO Project CTQ2014-53736-C32-P, which is supported with ERDF funds is gratefully acknowledged.
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ACCEPTED MANUSCRIPT References [1] U.P. Fringeli, ATR and reflectance IR spectroscopy, applications. In: Lindon, J., Tranter, G.E., Koppenaal, D. (Eds.), Encyclopedia of Spectroscopy and Spectrometry.
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[3] M.E. Böttcher, P.-L. Gehlken, The vibrational spectra of BaMg(CO3)2 (norsethite).
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[8] K.E. Washburn, J.E. Birdwell, Multivariate analysis of ATR-FTIR spectra for assessment of oil shale organic geochemical properties. Org. geochem. 63 (2013) 17.
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[11] C.M. Müller, B. Pejcic, L. Esteban, C. Delle Piane, M. Raven, B. Mizaikoff, Infrared Attenuated Total Reflectance Spectroscopy: An Innovative Strategy for
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Analyzing Mineral Components in Energy Relevant Systems. Sci. Rep. 4 (2014) 6764.
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FTIR Spectral Analysis. J. Sediment. Petrol. 63 (1993) 1144–1148.
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[13] J. Bertaux, F. Frohlich, P. Ildefonse, Multicomponent analysis of FTIR spectra: quantification of amorphous and crystallized mineral phases in synthetic and natural sediments. J. Sediment. Res. 68 (1998) 440447.
[14] S. Kaufhold, M. Hein, R. Dohrmann, K. Ufer, Quantification of the mineralogical composition of clays using FTIR spectroscopy. Vib. Spectrosc. 59 (2012) 29–39.
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ACCEPTED MANUSCRIPT [15] S.S. Palayangoda, Q.P. Nguyen, An ATR-FTIR Procedure for Quantitative Analysis of Mineral Constituents and Kerogen in Oil Shale. Oil Shale 29 (2012) 344356.
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Techniques, J.M. Chalmers Edit. John Wiley & Sons (2002) pp. 2327–2347.
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[19] S.Kr. Das, K. Dana, Differences in densification behaviour of K- and Na-feldspar-
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ACCEPTED MANUSCRIPT [21] V. Ramasamy, K. Paramasivam, G. Suresh, M.T. Jose, Function of minerals in the natural radioactivity level of Vaigai River sediments, Tamilnadu, India – Spectroscopical approach. Spectrochim. Acta A 117 (2014) 340350.
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nepheline syenite (mariupolite) of the Oktiabrski massif, SE Ukraine, and its growth
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history. Spectrochim. Acta A 157 (2016) 211219.
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Prasad, K.K. Satpathy, C. Maheswaran, Analytical characterization of recently excavated megalithic sarcophagi potsherds in Veeranam village, Tiruvannamalai dist.,
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Tamilnadu, India. Spectrochim. Acta A 115 (2013) 845853.
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[24] G. Raja Annamalai, R. Ravisankar, A. Rrajalakshmi, A Chandrasekaran, K. Rajan,
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Spectroscopic characterization of recently excavated archaeological potsherds from
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Tamilnadu, India with multi-analytical approach. Spectrochim. Acta A 123 (2014)
[25] R. Ravisankar, A. Naseerutheen, G. Raja Annamalai, A Chandrasekaran, A. Rrajalakshmi, K.V. Kanagasapathy, M.V.R. Prasad, K.K. Satpathy, The analytical investigations of ancient pottery from Kaveripakkam, Vellore dist, Tamilnadu by spectroscopic techniques. Spectrochim. Acta A 121 (2014) 457463.
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ACCEPTED MANUSCRIPT [26] B.J. Saikia, G. Parthasarathy, N.C. Sarmah, Fourier transform infrared spectroscopic estimation of crystallinity in SiO2 based rocks. Bull. Mater. Sci. 31 (2008) 775–779.
[27] J.R. Birch, F.J.J. Clarke, Interreflection errors in Fourier transform infrared
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[28] D.D. Weis, G.E. Ewing, Absorption Anomalies in Ratio and Subtraction FT-IR
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ACCEPTED MANUSCRIPT Figures Figure 1. Absorbance ATR-FTIR spectra of: a) sodium feldspar (Nafeld) and b) potassium feldspar (Kfeld) reference materials.
Figure 2. Absorbance ATR-FTIR spectrum of a) quartz and b) kaolin reference materials.
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Two replicate spectra are superimposed.
Figure 3. Absorbance ATR-FTIR spectra of samples a) Nafeld and b) Kfeld spiked with
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carbon-nitrogen bond of the K4Fe(CN)6 internal standard.
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17 % wt K4Fe(CN)6. The arrows mark the band associated to the vibration of the triple
Figure 4. Absorbance ATR-FTIR spectrum of a synthetic mixture of sodium (50.58 %wt)
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and potassium feldspar (36.28 %wt) plus K4Fe(CN)6 (13.14 % wt). Three replicate spectra are superimposed. The arrow marks the band associated to the vibration of the triple
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carbon-nitrogen bond of the K4Fe(CN)6 internal standard. Figure 5. Absorbance ratio vs. concentration ratio plots for Nafeld reference material
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spiked with K4Fe(CN)6 forming nujol oil-embedded pellets using absorbance
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measurements at = 1090 (squares) and 745 (triangles) cm1 and Fe = 2115 cm1.
Figure 6. Variation with the mass fraction of KBr of the relative uncertainty in absorbance
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measurements at the indicated wavenumbers in mixtures of KBr plus Nafeld (squares, 994 cm1), Kfeld (solid squares, 992 cm1) and Kao (triangles, 998 cm1). Values of
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A()/A() from five independent spectra for each KBr plus mineral mixture. Bars correspond to deviations of 0.01. Dotted line corresponds to an averaged uncertainty value.
Figure 7. Theoretical variation of the relative uncertainty in the concentration ratio, (c/cP)/(c/cP), on the concentration ratio, c/cP, from Eq. (15) assuming A/Aoº = 1% and /o = 1%, for different values of the P(P)/() ratio.
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ACCEPTED MANUSCRIPT Figure 1.
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ACCEPTED MANUSCRIPT Table 1. Certified composition of the standards used in this study. Nafeld: sodium feldspar (LGC Standards, BCS-CRM Nº 375/1); Kfeld: potassium feldspar (NCS DC 61102, China National Analysis Center for Iron and Steel); Kao: kaolin (NCS DC 60123a, China National Analysis Center for Iron and Steel); Qua: quartz (BCS-CRM 313/2). nd non detected.
nd 8.89 1.47 0.78 0.180 nd nd nd nd nd 0.226 nd 0.72
nd 3.69 9.60 0.76 0.054 nd nd nd nd nd nd nd 0.86
nd 0.0057 0.0108 0.0160 0.0038 0.00032 0.00067 0.00024 nd nd nd nd nd
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Qua 99.73 0.0243 0.068 0.0229
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Fe2O3T Na2O K2O CaO MgO MnO BaO SrO SO3 H2O P2O5 CO2 LOI
Kao 45.30 0.060 37.70 Fe2O3T 0.35 FeO (0.026) 0.35 0.045 0.042 0.064 0.021 0.0018 nd nd 0.76 15.26 0.16 (0.026) 14.81
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Kfeld 66.26 0.048 18.63 0.19
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Nafeld 69.26 0.313 17.89 0.291
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%wt SiO2 TiO2 Al2O3 Fe2O3
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ACCEPTED MANUSCRIPT Table 2. Absorption bands in the ATR-FTIR spectra of the mineral standards used in this study. st strong band; sh shoulder. Wavenumber at the absorption maximum / cm1 1145sh, 1095sh, 1040st, 994st, 786, 761, 743, 724, 692, 648 1140, 1090sh, 1045sh, 992st, 767, 725, 647 1114, 1024st, 998st, 935, 910, 788, 750, 678, 645 1160sh, 1090sh, 796, 777, 690 2115st
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Mineral Nafeld Kfeld Kao Qua K4Fe(CN)6
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ACCEPTED MANUSCRIPT Table 3. Peaks and K(kP)-parameters for quantification at selected wavenumbers, using potassium hexacyanoferrate(II) standard. Number between parenthesis represent the standard deviation in the last significant figure.
(cm1) (cm1) (cm1) (cm1) (cm1) (cm1) (cm1) 1135 0.523(5) 0.308(3) 0.160(2) 0.417(4)
1095 0.534(5) 0.317(3) 0.167(2) 0.667(7)
1035 0.861(8) 0.566(6) 0.693(7) 0.874(9)
990 0.941(9) 0.857(9) 0.707(8) 0.842(8)
935 0.540(5) 0.360(4) 0.413(4) 0.595(6)
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1150 0.494(5) 0.257(3) 0.067(1) 0.342(3)
905 0.366(4) 0.223(2) 0.693(7) 0.401(4)
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Component K(kP) Nafeld Kfeld Kao Qua
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ACCEPTED MANUSCRIPT Table 4. Statistical data for the analysis of different binary and ternary mixtures of the studied reference minerals from ATR-FTIR data using K4Fe(CN)6 as a internal standard. a Composition for wighted amounts of the standards (all 0.001 g); bcomposition from ATR-FTIR data using the K(kP) values in Table 3. (2nd)b
(3rd)b
57.01.2 72.81.5 21.00.4 49.21.0 42.00.8 57.71.2 38.90.7 28.30.5 35.60.7 29.40.6
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(3rd)a (1st)b (0.02) 44.00.8 27.20.5 79.01.6 50.81.1 58.01.2 42.30.8 28.40 32.80.6 30.69 35.00.7
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(2nd)a (0.02) 57.43 73.67 22.19 48.78 44.63 53.23 38.44 35.23
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Components (%wt) (1st)a (0.02) Nafel + Kfel 42.57 Nafel + Kfel 26.33 Nafel + Kfel 77.81 Nafel+Kao 51.22 Kafel+Kao 55.37 Nafel+Qua 46.77 Nafel + Kao + Qua 33.16 Kfel + Kao + Qua 34,08
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ACCEPTED MANUSCRIPT
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Graphical Abstract
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ACCEPTED MANUSCRIPT Highlights:
1) ATR-FTIR is applied to quantify individual components of mineral samples.
2) Theoretical expressions for modified constant ratio (MCR) method are developed.
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3) Absorbance measurements at N fixed wavenumbers ideally permits to quantify N
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analytes.
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4) Application to mixtures of albite, orthoclase, kaolin and quartz is described.
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