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Determination of the Al2O3 Content in NaF−AlF3−CaF2−Al2O3 Melts at 950 °C by Raman Spectroscopy Cedric Malherbe, Gauthier Eppe, and Bernard Gilbert* Laboratory of Inorganic Analytical Chemistry, Department of Chemistry, University of Liege, 3 Allée de la Chimie, B4000 Liege, Belgium ABSTRACT: The in situ control of the chemical composition of industrial aluminum smelter is a challenge mainly for physicochemical reasons: high temperature, high surrounding electromagnetic field, and the highly corrosive molten salt electrolyte to deal with. In previous works, we proposed that Raman spectroscopy is a method of choice that could be adapted to real smelters. The laboratory study presented here relies on reproducible Raman spectra recorded on molten mixtures whose compositions are identical to those used during the production of aluminum. A normalization procedure for the Raman spectra is proposed based on the equilibria taking place in the bath. In addition, we discuss two quantitative models to determine the alumina content from the Raman spectra of the molten NaF−AlF3−CaF2−Al2O3 electrolytes. Univariate and multivariate approaches are applied to determine both the COx (alumina content) and the CR (NaF/AlF3 molar ratio) by Raman spectroscopy without referring to an additional internal reference of intensity. The procedure was successfully tested and validated on industrial samples.

F

dioxide and they may end up into an insulating layer on the carbon anodes so that the voltage will subsequently rise sharply. On the other hand, for alumina content higher than 5 wt %, the solubility limit may be reached (depending on the electrolyte composition and temperature) and solid particles will sink below the aluminum cathode, decreasing the cell conductivity and the voltage to be applied on the cell grows accordingly.7 This phenomenon is known as the sludge formation. Although the control of the alumina content is a very important parameter to keep the efficiency of the electrolysis at its optimum, there is, up until now, no direct method to determine the bath composition of the melt during the process. It is indeed very difficult to develop such a method due to the high operating temperature and high corrosivity of the electrolyte itself. Actually, most process control systems rely only on direct measurement of the cell pseudoresistance and temperature,4,8 the first being partly related to the alumina content and the second to the AlF3 content which evaporates slowly during the process.9 Unfortunately, variations of those quantities (bath resistance and temperature) depend not only on composition changes but also on various physical factors such as electrodes spacing, cell temperature, amount of undissolved material, or even the age of the cell.2,8 The control must therefore be reinforced by time to time verifications of the composition which are made off-line on frozen bath samples in analytical laboratories.4 The alumina content is generally

or more than 100 years, alumina (Al2O3) is the primary source of metallic aluminum produced at large scale by electrodeposition in the Hall-Heroult process. The aluminum oxide is solubilized in a liquid electrolyte mainly made up of molten cryolite (Na3AlF6) and aluminum fluoride.1 Typically, an industrial melt contains some cryolite plus 6−13 wt % of AlF3, 4−6 wt % of CaF2, and 2−4 wt % of Al2O3.2−4 Although the current efficiency is up to 95%, the energy loss in the form of heat is rather high. Part of this loss is used to maintain the electrolyte in the liquid state at around 950 °C by warming up the smelters. However, a large part, about half the global energy requirement of the process, is dispersed to the environment. To an economic point of view, it is essential to reduce the high energy consumption of the process.5 It is then very important to control the composition of the melt which strongly influences the energy consumption. For example, and to our concern in this paper, the required overvoltage for the electrolysis turns out to depend particularly on the alumina content, COx (expressed in weight percent), which decreases during the electrolysis. Alumina must then be added recurrently, and its concentration is kept between 2 and 4 wt % in order that the process runs under the minimal energy input conditions.3,6 Indeed, the variation of the overvoltage as a function of the alumina content in the melt follows a u-shape curve with a minimum around 3 wt %. An alumina content lower than 2 wt % will lead to the so-called “anode effect”. At this composition, the oxide content is too low and the actual oxidation of the carbon anodes into CO2 is disfavored compared to their oxidation into fluorinated gases such as CF4 and C2F6. Those will form larger bubbles than the carbon © 2014 American Chemical Society

Received: March 12, 2014 Accepted: July 21, 2014 Published: July 21, 2014 8073

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evaluated from Leco measurements where all oxides are transformed into CO2 in the presence of carbon powder at very high temperature, under anaerobic atmosphere. The CO2 gas emanating from the sample is quantitatively measured by infrared absorption, leading to the determination of the oxide content.10 On the other hand, the cryolitic ratio, CR, defined as the molar ratio of NaF and AlF3, is determined by X-ray fluorescence or X-ray diffraction.11 An analytical procedure allowing the direct chemical control of the bath composition should be much more valuable than an off-line measurement. However, the highly corrosive molten electrolyte and the high electromagnetic field surrounding the industrial smelter (preventing any electronic device to approach the smelter) make such an in situ composition determination really difficult. However, back in 2000, we have proposed to apply Raman spectroscopy for the direct determination of the melt composition, using a remote optical probe connected to a laser and a spectrometer by optical fibers.12 Unfortunately instrumental limitations did not permit the exportation of the procedure to the industrial smelters for two reasons. First, the laser line collected by the remote probe must be cut off by holographic optical filters before entering the optical fiber carrying the Raman signal to the spectrometer, in order to avoid generating the Raman spectrum of the fiber itself and to decrease the Rayleigh contribution. It turns out that the most likely Raman band for the oxide determination is located at around 180−200 cm−1 (see here after) and to perform a proper evaluation of the baseline in this area, measurements must be made well below 100 cm−1. To our knowledge, up to 2008, no holographic filter allowed measurements below 80 cm−1. Second, on a real electrolysis cell, the melt is covered by a crust of solidified electrolyte that prevents the laser to reach the liquid. The Raman analysis must be performed after breaking the crust and before it will reform. In the factory, this period of time was evaluated to be 20 s. For a long time, the efficiency of the Raman spectrometers and detectors was still not sufficient to record high-quality spectra within such a short period of time using an acceptable input laser power not damaging the optical fibers. Recently, considering instrumental developments on charge coupled device (CCD) based spectrometers, we presented a quantitative procedure based on the Raman spectrum of a melt recorded at high temperature and without adding any internal standard of intensity. This procedure allows calculating the cryolitic ratio (CR) with a relative error of 3.5%.13 It was also discussed that this procedure could possibly be exported to the direct measurement of the CR on a real industrial bath. The procedure relies on the variation of the intensity ratio of the major Raman bands at 560 and 622 cm−1. Indeed, the spectrum of a NaF−AlF3−CaF2 melt, described previously,14,15 is mainly composed of the signals scattered by the three fluoroaluminate complexes that constitute the melt: AlF63−, AlF52−, and AlF4− (listed in Table 1). The contributions of each complex vary with the composition allowing the determination of the CR. It was also demonstrated that the higher the CR (the less acidic the melt), the more the equilibria in eqs 1 and 2 are displaced toward AlF63−. AlF6 3 − ⇌ AlF52 − + F−

(1)

AlF52 − ⇌ AlF4 − + F−

(2)

Table 1. Summary of the Bands Present in the Raman Spectrum of a Liquid NaF−AlF3−CaF2−Al2O3 Mixture14,16 a scatterer AlF4− AlF52− AlF63− Al2OF62− Al2O2F42−

location 215 345 320 180 180

(w,d); 320 (w,d); 622 (s,p); and 760 (w,d) (w,d) and 560 (s,p) (w,d) and 515 (s,p) (m,d); 450 (w,p); and 530 (w,p) (m,d); 300 (w,d); 430 (w,p); and 520 (m,p)

a

A band can be weak (w), medium (m), or strong (s) in intensity and depolarized (d) or polarized (p).

Al2O3 is added to a NaF−AlF3−CaF2 melt (that will be referred to as the solvent throughout this paper), no strong acid-basic effect was noticed. Al2O3 appears to be neutral in cryolite and faintly basic in more acidic melts. It contributes to the spectrum with four new bands located around 180, 300, 400−450, and 520 cm−1. No major band was found above 900 cm−1 which demonstrates that the oxygen atoms are most probably bridging two aluminum atoms.16 The bands at 180 and 520 cm−1 are directly correlated and rise when the alumina content increases. Measurements on the 520 cm−1 band are however difficult since it overlaps heavily with the other aluminum fluorides bands. Also, the band located at 430−440 cm−1 shifts to 410 cm−1 when the amount of Al2O3 grows. The shift was proved not to be an artifact resulting from a small band on the shoulder of a larger band. It was suggested that this behavior supports that alumina forms two aluminum oxyfluoride compounds: Al2OF62− forms at low alumina content (below 1 wt %) whereas Al2O2F42− forms at higher alumina content (eqs 3 and 4).10 This is also sustained by electrochemical, thermodynamic and NMR measurements.10,18,19 The location of the dissolved alumina Raman bands are collected in Table 1. Al 2O3 + 4AlF52 − ⇌ 3Al 2OF6 2 − + 2F−

(3)

Al 2O3 + Al 2OF6 2 − + 2F− ⇌ 2Al 2O2 F4 2 −

(4) 13

As a continuation of our previous publication, the present paper demonstrates a laboratory scale analytical procedure which leads to the determination of the alumina content from the Raman spectrum of a melt, without referring to an additional internal reference of intensity. For that purpose, we propose an original spectrum normalization procedure based on all the equilibria between fluoroaluminates within the molten solvent. We also report here a combined procedure for the determination of both the alumina content and the cryolitic ratio from the same Raman spectrum. Indeed, because of the interference of the oxides, in order to use the previously published calibration curve, a correction for the intensity ratios at 560 and 622 cm−1 is necessary. Multivariate partial leastsquares regression, PLS, was also tentatively used to extract the values of both the CR and the COx from the Raman spectra. Although it is described as a specific application, we believe that the proposed method is indeed a general method. For experimental reasons, the internal reference here is the solvent. However, the spectrum of the solvent is strongly affected by the solute in a complex way which makes the concept of using the solvent spectrum as an internal reference difficult to apply. The method we have developed could certainly be applied to systems showing similar complex behavior, provided the interactions between the solvent and the solute and their influence on the solvent spectrum are quantitatively known. This is the case here.

Raman spectroscopy has also been valuable to study the structure of dissolved alumina in cryolitic melts.10,16,17 When 8074

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to a cryolitic melt reduces its vapor pressure10 and, consequently, the Raman spectra are more stable and easier to record. Experiments similar as those presented in our previous publication13 were then made on the new samples and the conclusions are very close. No changes in the spectra are observed during a period of time as large as 15 min for a given melt. No change in the composition is neither noticed after temperature stabilization indicating a fast equilibrium establishment overall of the melt. The signal/noise ratio has consequently been improved during the method development by averaging successive spectra recorded on the same melt (maximum of 8 spectra). In any case, to avoid a possible unexpected change in composition by vaporization of the NaAlF4, all measurements on a sample are performed in less than 10 min. Moreover, the relative intensities of the bands were found identical for different samples of the same batch powder mixture. The fluctuations on the intensities are of the order of 1.0% relatively to the highest signal in the spectrum. This indicates that reproducible spectra are obtained for a same reference mixture. When Al2O3 is added, beside the appearance of the new bands relative to the oxyfluoride species (mainly at 180 and 520 cm−1) as shown in Figure 1, it was reported10,17 that the

EXPERIMENTAL SECTION Chemicals. Na3AlF6 (hand-picked cryolite from Greenland) was dried under vacuum (8 × 10−2 mbar) at 600 °C overnight. CaF2 (Sigma-Aldrich, optical grade) and Al2O3 (Janssen Chemica, 99%) were dried under vacuum (8 × 10−2 mbar) at 600 °C overnight. AlF3 (BDH Fluortran grade) was sublimed twice20 at 930 °C under vacuum in a graphite container. All chemicals were stored within a nitrogen-filled glovebox where the water content never exceeded 3 ppm. Preparation of Reference Samples. In the glovebox, solvent powder mixtures of reference were prepared by weighing, mixing, and crushing the accurate masses of chemicals (Na3AlF6, AlF3, and CaF2) in an agate mortar to ensure mechanical homogeneity. These reference solvents do not contain any Al2O3. They are characterized by cryolitic ratios varying between 2.0 and 3.0. Other batch mixtures containing around 6 wt % of Al2O3 are prepared similarly from accurate masses of solvent mixture and alumina. These will be referred to as the concentrated mixtures. They have the same cryolitic ratio as the solvent they are prepared from. Ultimately, reference samples with different amount of Al2O3 between 0 and 6 wt % are prepared by weighing, mixing, and crushing again the required amount of the solvent and the corresponding concentrated mixture together in an agate mortar. The amount of CaF2 is kept constant (5.01 ± 0.61 wt %) in all the melts investigated in this paper in order to simulate, as much as possible, the composition of a real industrial bath. Raman Spectroscopy and Furnace Apparatus. A homemade cell-furnace assembly15 has been used for the development of the analytical method. The sample is held in a small glassy carbon crucible and the excitation laser light hits the melt from the top. More details are available in ref 13. In the present study, for the recording of the Raman spectra, the melts were kept under inert argon atmosphere at 946 ± 5 °C. The Horiba Jobin-Yvon Labram 300 confocal spectrometer was provided with new edge optical filters which cut off the signal below 40 cm−1 (Iridian Spectral Technologies). The 488 nm line of a Spectra Physics model 164 argon ion laser was used with a power of 100 mW in the sample. Every spectrum was accumulated twice for 20 s in the 77−1800 cm−1 range. The spectral resolution is about 3 cm−1, and the spectrum is retrieved in our software as 1 data point every 1 cm−1. The background originating from the blackbody emission of the hot vitreous carbon crucible was recorded in the exact same conditions as the Raman spectrum (integration time and temperature) for each sample but with the laser turned off. This background was then quantitatively subtracted from the sample spectrum. In order to maintain the quality of the data, no smoothing was ever applied on the spectra. Statistics. Linear multivariate calibrations and predictions were performed using “The Unscrambler” 10.1 (Camo Software) and Statistica 10 (StatSoft). The software return a p-value associated with the multivariate model indicating whether the model is reliable or not. Since the associated pvalues were all lower than 0.05, the models are considered as reliable at the confidence level of 95%.

■

Figure 1. Raman spectra of the series CR = 2.00. The oxide content (expressed in weight percent) for the different melts are (a) 0.00%, (b) 2.16%, (c) 3.87%, (d) 5.61%. The spectra are recorded at 946 °C.

addition of alumina modifies the signals of the solvent itself at 350 cm−1 and more importantly between 500 and 600 cm−1. Indeed, the alumina is a weak fluorobase meaning that, while lowering the vapor pressure, it displaces the equilibria 1 and 2 toward the AlF63−, thus changing the proportion of all aluminum fluoride species. Consequently, none of the main Raman bands of the solvent can be used as an internal reference of intensity for quantitative purpose since all depend on the alumina content. A more complex normalization procedure as that proposed in our previous publication13 is then necessary. Measurement of the 180 cm−1 Alumina Band. We suggest here to determine the amount of Al2O3 in a cryolitic melt from the intensity of the 180 cm−1 band. As shown in Figure 1, the 180 cm−1 band is indeed the major feature which appears in the spectra upon addition of alumina. Its measurement is however complicated and is really challenging: (1) its intensity is weak, (2) it overlaps somewhat a band

RESULTS AND DISCUSSION

Spectrum Reproducibility. The stability and the homogeneity of the reference melts throughout Raman analyses have been first investigated. In this connection, it is interesting to recall that, according to its basic behavior, addition of alumina 8075

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belonging to AlF4− (located at 215 cm−1), and (3) it is located on top of the intense Rayleigh decay. The band intensity is indeed weak but considering the quality of our spectra, it is good enough to lead to statistically meaningful results. The contribution of the AlF4− band is small and simply results in a nonzero value of the extrapolation to the origin of the oxide content calibration curves (see below). Finally, the problem of taking into account the Rayleigh decay needed more concern. In order to isolate accurately the Raman band at 180 cm−1, the Rayleigh decay contribution must be evaluated, using data points outside any Raman band. The iterative evaluation procedure is explained in details elsewhere (ref 13, Supporting Information) where we have shown that the Rayleigh decay can be modeled by the side of a simplified Gauss−Lorentz profile, applied to data points between 60 and 110 cm−1 and above 1200 cm−1. Initially the Rayleigh decay was estimated by our homemade software on every spectrum. However, we found that, when the Rayleigh decays are simply scaled up at the same intensity at 100 cm−1, their shape was quite identical for all spectra according to a Grubbs’ test (p < 0.05). Consequently only one single Rayleigh decay profile, calculated as the average of all the decay profiles evaluated on the solvent spectra, was subtracted for all the spectra. The only adjustment is multiplication by a scale factor which was calculated to match the intensity of the average profile to the intensity of the analyzed spectrum at 100 and 1400 cm−1, where no Raman signal is detected. By subtracting the correspondingly scaled Rayleigh decay from the original spectrum, it was then possible to properly obtain the 180 cm−1 band with a flat baseline. Despite our efforts, the absolute Raman intensities were not found always perfectly reproducible because of phenomena occasionally reducing the intensity of the incident laser beam entering the sample: (1) the presence of carbon dusts, originating from the vitreous carbon crucible, which float on the upper side of the melt where the laser beam is coming and (2) the condensation of melt vapors which sometimes forms a thin film deposit onto the quartz window at the top of the oven, especially when more volatile samples are analyzed (small CR values). Hence only relative intensity measurements can here be considered. However, besides these experimental problems, the cryolitic melts are so highly reactive that no suitable molecular compound is inert enough to serve as internal spectral reference. Classical intensity normalization by addition of an internal standard is therefore impossible. Finally, the procedure used in our previous publication (based on intensity ratios of the main bands) is not applicable either. As we just mentioned above, here, the entire spectrum varies as a function of the melt composition (CR and COx), consequently none of the bands can be considered as an internal reference to normalize the intensities measured at 180 cm−1. Normalization Procedure. Considering the arguments presented above, the present paper proposes a normalization procedure based on the chemical behavior of all the fluoroaluminates species within the cryolitic melts. Here, as a first approximation, we shall neglect the consumption of AlF52− resulting from the dissolution of alumina, considering that the amount of alumina is always small with respect to the total AlF3 content. Knowing that the total amount of AlF3 is a constant for a given solvent with a given value of CR, we propose that, taking into account our approximation and for 1 mole of mixture, the AlF3 mole fraction is given by eq 5. This equation also expresses that the AlF3 will be distributed in the three fluoroaluminate complexes according to eqs 1 and 2, the

contribution of the oxyfluoro complexes being neglected. Furthermore, the intensities of the Raman bands at 515, 560, and 622 cm−1 are related to the respective molar fractions of AlF63−, AlF52−, and AlF4− in the bath through the scattering coefficients Di where i takes the values 6, 5, or 4 when it belongs to AlF63−, AlF52−, or AlF4−, respectively (eq 6). The relative Raman scattering coefficients were previously determined in the laboratory from dilute solutions of fluoroaluminates in molten NaCl.21 We indeed found that such media did not attack quartz, and only using quartz cells, very reproducible absolute intensities measurements (within 1%) could be made from one melt to another allowing to evaluate the scattering coefficients. They were expressed relative to the scattering coefficient of AlF4−, which was set arbitrarily to 1 and were found as follows: D6* = 2, D5* = 1.5, and D4* = 1.0. It was also reported that adding some NaCl did not affect the nature of the fluoroaluminate complexes (no chloro-fluoro species was found in that specific case, the fluoride complexes being by far more stable than the chloride complexes). In addition, because they are expressed relatively, we assumed that the Di could be also used in pure molten fluoroaluminates, within experimental errors. Since the actual Raman scattering coefficients are proportional to the relative ones, the sum of the intensities of the fluoroaluminate species, weighted by the relative Raman scattering coefficients, should remain constant within a series of samples since they are characterized by the same CR. This is expressed in (eq 7) which includes an arbitrary intensity proportionality coefficient (Kprop). 0 X AIF ≈ X AIF36− + X AIF52− + X AIF−4 ≈ 1 3

(5)

Ii = DiXi

(6)

0 X AIF ≈ 3

I I ⎞ 1 ⎛ I6 ⎜ + 5 + 4 ⎟ K prop ⎝ D6* D5* D4* ⎠

(7)

During the normalization procedure here proposed, we calculate a normalization factor, f Norma, such as the sum of the weighted intensities of the 515, 560, and 622 cm−1 bands, thus taking into account the different scattering coefficients, is a constant value which was arbitrarily chosen as 2000. Finally, the normalized spectrum is obtained by multiplying the experimental flattened spectrum by the normalization factor (eq 8). INormalized Spectrum = fNorma × IFlat Spectrum

(8)

Despite the strong overlap, the intensities I6, I5, and I4 are here simply the heights measured from the baseline at the respective locations. No decomposition of the spectrum envelop (into each band related to each species in the melt) was done. The number of parameters to include for the iterative numerical decomposition process is indeed high. For each component, our software must iterate on the band position, its intensity (height), width at midheight, and the fraction of the Gaussian toward the Lorentz function as we use a Voigt function to model a Raman band. For one given spectrum, the mathematical calculus is robust, but the obtained productmoment correlation coefficient of the calibration regressions (obtained with the entire set of spectra) were always lower, compared to the one obtained by considering the intensities without decomposition. We assumed that this lower efficiency (in the frame of the quantitative application) arises from the fluctuations of the numerous parameters needed for the decomposition process. 8076

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addition on the solvent spectrum. Two main conclusions can be deduced from an examination of Figures 2 and 3. (1) As it was previously mentioned (Table 1), when alumina is added to the pure solvent, new bands appear at 180, 430, and 520 cm−1. In particular, the intensity of the 180 cm−1 band increases steadily as a function of the aluminum oxide content in the melt. This behavior is the base of the quantification of the Al2O3 discussed here below. Of course, another band located around 515 cm−1 follows the same trend but since it belongs to alumina and AlF63− it cannot be used for the quantification. (2) When the normalized spectra are superimposed with the same scale, welldefined isosbestic points22 are found at various Raman shifts (Figure 2). This observation indicates that equilibria consistent with eqs 1−4 indeed occur between the scattering species constituting the melt. When alumina is added, fluorides ions are released, thus producing AlF63−. Accordingly, the intensity at 515 cm−1 increases. On the other hand, the AlF52− and AlF4− content decreases. This is also clearly indicated by the increasingly negative intensities at 350, 560, and 622 cm−1 (Figure 3). This means that the equilibria between the fluoroaluminates in the solvent are displaced toward the formation of AlF63−, which is consistent with the fluorobasic behavior of the Al2O3. It should be emphasized however that Figure 3 has been scaled up by a factor of 5 with respect to Figure 2. The observed variations on the solvent spectrum upon alumina addition are thus actually globally weak, explaining probably why our normalization procedure, which involves as first approximation only fluoroaluminate complexes and not the oxides, still leads to isosbestic points. Modelizations. At first, the variation of the intensity at 180 cm−1 was modeled as a function of the alumina content for each series. This is a univariate approach since only the intensity at one Raman shift is studied as a function of the COx. In the next sections, we shall present a model based on the spectral variation of all data points, following then a multivariate approach. Indeed, as emphasized in the Normalization Procedure section of this paper, the Raman bands are almost always interfering with each other and every single one varies with the composition of the melt. Multivariate statistics applied on all spectroscopic data (chemometrics) are therefore indicated to interpret the signal variations. Univariate Quantitative Model. The calibration curves were obtained from the normalized spectra by plotting the intensity measured at 180 cm−1 (averaged on 5 points) versus the COx. No statistically significant influence of the cryolitic ratio CR was found. Consequently, all the intensities are set on one curve only and the experimental points organize themselves along a quadratic curve (R2 = 0.986), independent of the CR (varying from 2.0 to 3.0) as shown in Figure 4. This observation also means that it is not necessary to know the CR of the melt prior to determine the COx in the range between 0 and 6 wt %. The slight curvature could arise from the transition of Al2OF62− to Al2O2F42− as a function of the alumina content. This calibration curve (eq 10) can then be further used to determine the COx of an unknown sample, starting from the intensity at 180 cm−1 measured on the normalized spectrum.

All spectrometric data treatments starting from the background and Rayleigh wing subtraction to the normalization were performed with our software written with subprograms specific to this study. As example of data treatment, we chose to present the normalized spectra for one given series (CR = 2, increasing amounts of alumina) since it is one of the most difficult to record owing to its vapor pressure. The corresponding spectra are depicted in Figure 2. Knowing the

Figure 2. Raman spectra of the series CR = 2.00 after subtraction of the Rayleigh decay and normalization. The oxide content are (in weight percent): (a) 0.00%, (b) 1.07%, (c) 2.16%, (d) 2.87%, (e) 3.87%, (f) 4.93%, and (g) 5.61%. The spectra were recorded at 946 °C.

normalized spectra, it is now possible to quantitatively subtract the spectrum of the solvent from all those of the mixtures containing alumina. For example, the results of the subtraction for the CR = 2.00 series are shown in Figure 3 where the ordinate scale has been expanded by a factor of 5 with respect to that of Figure 2, to improve the presentation. It turns out that following our normalization procedure, it is possible to show in more detail the influence of the alumina

I180 = (35 ± 3) + (47 ± 2) × COx − (1.5 ± 0.3) × COx 2 (10)

Figure 3. Subtraction of the solvent Raman spectrum from the Raman spectra of the series CR = 2.00, after subtraction of the Rayleigh decay and normalization. The oxide content are (in weight percent): (a) 0.00%, (b) 1.07%, (c) 2.16%, (d) 2.87%, (e) 3.87%, (f) 4.93%, and (g) 5.61%. The spectra were recorded at 946 °C.

In our previous publication,13 we presented that for melts not containing any added oxides, the CR can be estimated from the intensities ratio measured at 560 and 622 cm−1 on the flattened spectra of the solvents. Although the calibration curve for the 8077

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to quantitative spectral analyses,23 was applied on our Raman data. Other methods such as multiple linear regression (MLR), principal component analysis (PCA), and principal component regression (PCR) were also tested (data not shown), but we thought that the PLS method was the most appropriate to solve our system. We also found that applying statistical methods on raw initial spectral data did not lead to a clear solution, and the above-described normalization procedure had to be kept for the data processing. Since the signal intensity is likely to vary with the experimental parameters, the statistical treatment was then applied on the normalized spectra. The linear PLS analysis was carried on 93 reference samples with their two associated composition variables, CR and COx, and their 811 spectral variables, the intensities for each Raman data point in the range from 90 to 900 cm−1. In the PLS analyses, the normalized spectral variables are used to create a new set of variables (called the factors) in which the first factors explains most of the variance of the system. The factors are estimated to maximize the variance of the predictive 811 spectral variables as in PCA analysis, but taking into account here the variations of COx and CR (composition variables). In this study, the two first factors explain 90.3% of the variance for the two composition variables and 93.6% of the variance for the 811 spectral variables. The projection of the 93 reference samples on the factorial plane is represented in Figure 5. The samples are

Figure 4. Calibration curve of the normalized Raman intensity at 180 cm−1 (I180) versus the aluminum oxide content (COx, expressed in weight percent).

CR determination has been established on flattened spectra before the normalization procedure, it remains applicable on normalized spectra since the intensities ratio is not affected by the normalization step. However, when Al2O3 is added to a given CR melt, the intensities ratio at 560 and 622 cm−1, IR, changes as it was emphasized in Figures 2 and 3. Actually, we found it increases linearly with COx, following eq 11, where IRCorr (for IR corrected) is the IR extrapolated at COx = 0 and SIR the slope of the linear regression. In addition, we found that the slope SIR also varies as a function of the CR as a linear relationship expressed by eq 12. The IRCorr, intensity ratio for the solvent of the melt containing no alumina, can thus be calculated by a simple combination of eqs 11 and 12 as shown in eq 13. Therefore, in cases where alumina is present, this IRCorr must be used instead of the IR in order to apply the calibration curve we have established on the solvent spectra.13 IR = IR Corr + SIR × COx

(11)

SIR = 0.0691 − 0.0180 × CR

(12)

IR Corr = IR − (0.0691 − 0.0180 × CR) × COx

(13)

To summarize, a full evaluation of the composition of an unknown melt can be made from the following procedure: (i) The Raman spectrum is recorded at 950 °C; the Rayleigh decay is subtracted and the resulting spectrum is normalized as explained above. (ii) From the normalized spectrum, both the COx and the CR can be determined referring to the three calibration curves discussed here and in our previous paper:13 (1) the COx is calculated from the intensity measured at 180 cm−1 (eq 10); (2) a first approximate value of the cryolitic ratio CRApprox is estimated from the raw (noncorrected) IR and the equation proposed in ref 13; (3) the intensity ratio IR is then corrected for the oxide content, according to the pre-estimated CRApprox and the measured COx (eq 13), leading to IRCorr; (4) the final value of the cryolitic ratio CRFinal is calculated from the equation in ref 13 using the newly determined IRCorr. Multivariate Quantitative Model. For the reasons given above considering the complexity of the melt, linear partial least-squares regression (PLS), certainly the more common multivariate predictive statistic method involved when it comes

Figure 5. Projection of the samples on the factorial plane according to the corresponding values of the spectral variables. The samples are separated as a function of their alumina content along the first factor while they are separated according to their CR along the second factor. The COx (expressed in wt %) are as follows: between 0 and 0.5, in black; between 0.5 and 1.5, in red; between 1.5 and 2.5, in green; between 2.5 and 3.5, in blue; between 3.5 and 4.5, in pink; between 4.5 and 5.5, in cyan; between 5.5 and 6.5, in gray; and between 6.5 and 7, in violet. The CR are as follows: ● 2.0, ○ 2.1, ▲ 2.2, △ 2.3, ■ 2.4, □ 2.5, ▼ 2.6, ▽ 2.7, ⧫ 2.8, ◊ 2.9, ⬢ 3.0.

distributed as a function of (1) their COx along the first factor and (2) their CR along the second factor. This illustrates the power of the PLS analysis which is able to reduce the 811 primary spectral variables to only two statistical factors, factors which seem to discriminate the reference samples according to their composition. To complete the quantitative PLS analyses, a regression of the composition variables (COx and CR) was subsequently carried from the 2 factors constructed with the 811 primary spectral variables. 8078

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Validation of Our Quantitative Models. Without any certified reference materials, the two quantitative models (univariate and multivariate) described above were validated with two sets of samples. The first one was our 93 reference samples, prepared in the lab (see the Experimental Section). Their actual compositions were calculated from the masses weighed during their preparation in the glovebox. The values obtained by Raman spectroscopy with the quantitative models were compared to the target values (calculated from the melt composition). The second set was composed of 13 industrial samples, picked up from real smelters. Their compositions were initially determined by the factory: the cryolitic ratio and the aluminum oxide content were calculated from X-ray fluorescence and Leco measurements data, respectively. Again, by applying the two quantitative models, the values obtained by Raman spectroscopy were compared to the target values given by the industry. The conclusions of our analyses are as follows. First, Table 2 summarizes some of the results obtained from the two models: Table 2. Mean Absolute Residuals between the Values Determined by Raman Spectroscopy and the Target Values for (i) Reference Samples Prepared in the Lab and (ii) Industrial Samples Picked up on Industrial Smeltersa

expected with the reference methods used in the industry24,25 univariate (intensities normalized (i) reference according to equilibria) samples (ii) industrial samples multivariate PLS (intensities (i) reference normalized according to samples equilibria) (ii) industrial samples multivariate PLS (intensities (i) reference normalized from 0 to 100) samples (ii) industrial samples

alumina content COx (wt %)

cryolitic ratio CR

0.2−0.5

>0.1

0.29

0.08

0.31

0.15

0.28

0.08

0.47

0.13

0.35

0.09

0.63

0.17

a

For the reference samples, the target values of COx and CR were calculated from their compositions. For the industrial samples, the target values of COx and CR were given by the industry, respectively, from Leco data and X-ray fluorescence data.

Figure 6. (A) Univariate quantitative model; comparison of the values of COx evaluated from Raman data (COx,Raman) and the target values calculated from the composition of the reference samples (COx,Comp) (blue dots) or given by the Leco measurement on industrial samples (COx,Leco) (red dots). (B) Multivariate PLS quantitative model; comparison of the values of COx evaluated from Raman data (COx,Raman) and the target values calculated from the composition of the reference samples (COx,Comp) (green dots) or given by the Leco measurement on industrial samples (COx,Leco) (purple dots).

it shows the mean absolute residuals (as preferred by the industrial community) obtained on both sets of samples, for the determination of COx and CR. Considering the difficulty of the Raman analyses of such media, the accuracy is good and the mean residuals are lower than the errors expected with the methods in use in the industry. Second, a closer look at the actual regressions obtained is necessary. The comparison between the results obtained by Raman spectroscopy and the target values for the alumina content is shown in Figure 6. Applying the univariate quantitative model to our reference samples (Figure 6A, blue dots and line), a unitary slope regression is obtained. Clearly, higher residuals are observed for melts containing no alumina. This is probably the result of the contribution of the AlF4− band at 215 cm−1 which overlaps the oxide band, especially for low CR values. When the univariate quantitative model is applied on the spectra of the industrial samples (Figure 6A, red

dots and line), the slope of the regression line is again unitary, but a systematic positive bias is observed between the Leco measurements and the Raman results, indicating that the two methods may not be measuring the same thing. In our procedure, only the aluminum oxyfluoride species are selectively analyzed while the Leco procedure is sensitive to any oxide species, not only the ones containing aluminum. In other words, the Leco procedure may overestimate the alumina content when other oxides are present in the sample or have 8079

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correction can be applied for the determination of the solvent cryolitic ratio (molar ratio of NaF and AlF3). Two quantitative models, one univariate and one multivariate, were developed to determine both the COx and the CR in those very corrosive melts by Raman spectroscopy without referring to an internal reference of intensity. The procedure was successfully tested on industrial samples, and the CR and the COx could be estimated with a relative error of 3.1% and 11%, respectively. Both models lead to similar quantitative results except that the univariate analysis seems somewhat more precise than the multivariate one, especially on samples producing spectra of lower quality. Prospectively, the procedure and quantitative models presented here can now be adapted to the analyses of spectra recorded directly in industrial smelters with the remote probe head we have presented in our previous publication.13 This adaptation would represent the starting point of a new era in the difficult in situ control of the cryolitic melt composition in the HallHeroult process.

been introduced during the sampling process on the industrial smelter. The same discussion stands when the multivariate quantitative PLS model is applied (Figure 6B). However, here when the industrial samples were analyzed, higher residuals are obtained. This difference may arise from all spectral variables considered in the PLS model while it is not the case in the univariate model. The influence of the spectral noise is indeed higher when applying the PLS model compared to the univariate. This is especially true for the industrial melts for which the corresponding spectra quality was clearly lower. They have been picked up on real aluminum smelter (HydroAluminum, Årdal, Norway) and were not cleanly prepared in a glovebox. However, only linear PLS regressions were considered here and the results could be improved by using a nonlinear approach. Comparison of the Models. Although differences were observed from the analysis of Figure 6, both models are worth considering for determining the composition of the cryolitic melt since they both provide residuals of the same order of magnitude (Table 2). The calculations are however made, for both models, starting from flattened normalized spectra, a process which involves a somewhat complex treatment. The PLS model should, in principle, be able to extract the information we need from raw initial data. It however failed probably because there is too much variation in the global intensities from one spectrum to the other (for experimental reasons). Another normalization technique, specific to the PLS method and applied directly on the raw data, or a nonlinear evaluation of the results should be developed. In case of success, the PLS method would then be preferable to the univariate one since the latter needs a complex pretreatment of the data. As a first attempt in that direction, a simplified normalization of the data was considered. Starting from the flattened reference spectra, the intensities were expressed on a relative scale between 0 and 100, the maximum value being attributed to the highest intensity in the given spectrum. The PLS analyses were then applied on this set of reference spectra, and the residuals obtained for the COx and the CR are summarized in Table 2. As it can be seen, the residuals are now higher compared with the two previous methods. When the PLS method is applied on the spectra of the industrial samples, these residuals turned out to be even higher than the errors expected with the Leco and the XRF methods. According to our results, it seems that the simpler the pretreatment of the reference spectra, the higher are the residuals on both COx and CR. The user of the analytical models should then have to choose between a simple pretreatment of the raw data with a low predicting capability of COx and CR or a more complex pretreatment leading to a higher accuracy.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge the Norsk Hydro Company for supplying the industrial samples and for financial support.

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REFERENCES

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CONCLUSIONS It has been demonstrated that reliable and reproducible Raman spectra were obtained on mixtures whose composition is identical to the one used during aluminum production, thus containing alumina. The full composition of the melt can now be measured with an “in situ” method and no sampling. On the basis of the displacement of equilibria taking place in the cryolitic melts, a normalization procedure was proposed for the Raman spectra and a calibration curve has been established following the intensity increase of the 180 cm−1 band upon addition of alumina. It allows the determination of the aluminum oxide content within a NaF−AlF3−CaF2−Al2O3 melt. Since alumina addition perturbs the solvent equilibria, a 8080

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(20) Henry, J.; Dreisbach, S. J. Am. Chem. Soc. 1959, 81 (20), 5274− 5275. (21) Gilbert, B.; Robert, E.; Tixhon, E.; Olsen, J.; Ostvold, T. Inorg. Chem. 1996, 35, 4198−4210. (22) Walrafen, G.; Hokmabadi, M.; Yang, W. J. Chem. Phys. 1986, 85 (12), 6964−6969. (23) Frank, I.; Friedman, J. Technometrics 1993, 35 (2), 109−135. (24) Ershov, V.; Sysoev, I.; Kondrat’ev, V. Metallurgist 2013, 57 (3), 346−351. (25) Kirik, S.; Yakimov, I. Adv. X Ray Anal. 2001, 44, 85−90.

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