Articles

Spectroscopy, June 2019

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The Raman spectrum of water measured on a fixed grating near-infrared (NIR) spectrograph with a dual wavelength laser enables recording the signal in both the fingerprint and the OH stretching region. This article will show spectra recorded between 5 °C and 80 °C, and treated with both band-fitting and the 2D-COS algorithm. The results will show the complementarity of the two data treatments in providing different insights to the spectral behavior.  

	The Raman spectrum of deionized water was recorded at temperatures between 4 °C and 80 °C in a near-infrared (NIR) Raman spectrograph (MacroRam), which is designed around a fixed grating spectrograph and a 785 nm laser. When the Raman spectrum is dominated with broad overlapping bands, it often becomes difficult to use the spectrum for structural analysis. In this case, we will examine the behavior of the spectrum of water as a function of temperature between 4 °C and 80 °C. In principle, there should be an HOH deformation, and symmetric and antisymmetric combinations of the motions of the two OH functional groups. In the liquid phase, while the deformation near 1640 cm

 appears to be a single band, the spectrum in the OH stretching region (3000 to 3700 cm

) is clearly composed of more than two bands. The assumption is that there are complicated effects of H-bonding in the OH-stretching region that can account for this behavior. Our goal here was to determine what structural insight could be gained by comparing band-fitting with 2D-COS analysis. Because the OH stretching vibration is beyond the range of the detector with this excitation wavelength, we used the dual wavelength laser from IPS (1). The OH region of the spectrum (3000 to 3800 cm

) was excited at 680 nm, which places the spectrum at the same wavelength range as the fingerprint part of the spectrum excited at 785 nm. Thus, by using the 680 nm laser line, one gets good sensitivity, even in the OH region of the spectrum. Figure 1 shows the full spectrum of water recorded with this laser at 4 °C and 70 °C. The laser was delivered with a fiber optic, and the Raman light was collected with a fiber bundle. Because there was no effort to make polarization measurements, the spectra reflect the isotropic component.


	Figure 1: The full Raman spectrum of di-ionized water recorded on an NIR Raman spectrograph with a dual wavelength (785/680 nm) laser.

	The Raman spectrum of water has been studied by several groups as a means to understand the structure of water as a function of temperature, in the context of the H-bonding (2,3). In our measurements, the entire spectrum below 1300 cm

 is dominated by the bands of the silica cuvette. In the midrange of the spectrum, one can see the O

 dissolved in the water at 1556 and 2331 cm

. While there are water bands of interest in the region dominated by the silica (3), we are going to focus on the OH stretching bands above 2900 cm

Temperature Dependence of the Water Spectrum

	In the past, I have done temperature-dependent studies of proteins dissolved in water buffer, and observed the important changes with temperature, which can be seen in Figure 2. At first glance, one assumes that the OH envelope can be fit by two bands, but closer inspection indicates that there is more going on. Attempts to fit the spectra to two bands never yielded good fits, as shown in Figure 2; the figure also shows five-band fits, which produced absolutely flat residuals in the spectra. Note that others have also fit the OH spectra to five bands (2).


	Figure 2: Spectral fits of the OH spectra of water at 80 °C and 5 °C. On the left are shown two-band fits with significant residuals displayed in purple. On the right are five-band fits with vanishing residuals.

	Figure 3 shows the spectra taken as a function of decreasing temperature. On the right side is the integrated intensity between the cursors shown in the spectral multifile. However, after band-fitting the entire hyperspectral cube shown in Figure 3, we can plot the peak position, the integrated intensity, and the peak width as a function of time (which means temperature because the sample was cooling), and that behavior is shown in Figure 4.


	Figure 3: Spectra of water in the OH stretching region (on the left) taken as a function of time while cooling from 80 °C to 4 °C. The vertical red and green lines indicate the brackets used to calculate the integrated intensities. On the right is shown the integrated intensities as a function of time and temperature.

Temperature-Dependence of the Fitted Bands

	Figure 4 shows the results of the band-fitting of the entire file. A total of five peaks were used for the fitting. In addition to the strong peaks near 3200 and 3400 cm

, peaks were added on the low side, on the high side, and one between the two strong bands. The peak positions were fixed during the fitting procedure. The integrated intensities of the strongest peaks near 3200 and 3400 cm

 are changing in opposite directions, which is consistent with what is seen in Figure 3. The widths of the middle band (~3340 cm

, considerably sharper than the other bands, although their behavior with temperature are somewhat different. The width of the lowest frequency band (blue) has almost the same width as the strong bands, but it increased as the sample was cooled.


	Figure 4: The peak position, integrated intensity in each peak, and the peak width as a function of time and temperature.

	Another method of analysis that is possible is to subject the hyperspectral cube with temperature dependence to multiplicative curve resolution (MCR), something that was done in the cited publication (2). Figure 5 shows the results of this calculation, but doesn't seem to offer any insight. The two factors identified are very close to the cold spectrum (red) and the warm spectrum (green), and the addition of a third factor did not produce an additional independent spectrum. Because the spectra were acquired while cooling, the cold spectrum increases as the warm spectrum decreases.


	Figure 5: Factors and Scores from the MCR calculation.

	Because spectral fitting is an "art", and in particular that the fits are often not unique, when these spectra are fit more than once, there is some variation in the results (in fact, that is why the fitting shown in Figure 4 was done by fixing the peak positions). For this reason I felt that implementing 2D-COS might be a more rigorous technique, so I was optimistic that applying 2D-COS to this set of measurements might provide a more "accurate" reflection of the behavior of the various overlapping features in the spectra.

	What will the 2D-COS show us in comparison? Figure 6 shows the results of the 2D-COS application to this set of measurements. The synchronous and asynchronous plots are shown with four sets of intensity scales. The reason for this is that I only observe two peaks in the 2D-COS plots; one peak is center at 3114 cm

, neither of which overlays with the peaks in the band-fitted spectra. I was surprised that I did not see a correspondence with fitted spectra, so I used multiple plots to determine what was "hidden" in the results. In fact, changing the scale for plotting did not reveal any new structure. But I was able to accurately determine the centers of the 2D-COS structures, and determine if they corresponded to peaks in the original spectra.


	Figure 6: 2D-COS of the OH stretching part of the water spectrum, displayed with varying intensity scales. Synchronous plots on top, and asynchronous on the bottom.

	Figure 7 shows the 2D-COS results plotted along with the 5 °C and 80 °C fitted spectra, in order to determine more detail in the results. What we find is that the center of the 2D-COS higher frequency structure is at 3460 cm

 which is shifted from the higher frequency strong band in the spectra at 3406 cm

. The lower frequency structure is peaked near 3114 cm

, which is shifted from the lower frequency strong band at 3189 cm


	Figure 7: 2D-COS results enlarged and superimposed on the 4 °C and 80 °C band-fitted spectra.

	How do we make sense of the 2D-COS results compared to the band-fitted results? The important fact to keep in mind is that the 2D-COS is sensitive to anything in the spectrum that is changing, while the band-fitting reports bands whether they are changing or not. In fact, because there are asynchronous peaks, there must be more than two components (this follows from the fact that when there are only two components, one is simultaneously replaced by the other, and there is no asynchronous component). Notice as well that the asynchronous peak spans the space for both positive and negative synchronous peaks. If the peaks in the 2D-COS plots do not correspond to the peaks in the band-fitted spectra, that means that changes in all the peaks are contributing to the changes encoded in the 2D-COS.

	What is interesting is that the intensities of the three small spectral features are fairly constant over this temperature range, yet their widths are all varying, but with different behaviors, which can be seen in Figure 4. Actually, the band-fitted spectra show us that only the two strong bands are changing in intensity to any significant amount; one is increasing in intensity, and one is decreasing, and they are broad enough that they overlap. This accounts for the inflection point in the 2D-COS plots at 3260 cm

. All of this, of course, is a result of hydrogen bonding and the formation and evolution of various clusters in the water, which is discussed with much more detail in the references (2,3).

	Interestingly, temperature-dependent NIR (near IR) measurements have also been measured and subjected to 2D-COS analysis (4). It is gratifying to see that similar conclusions have been drawn here. There is a broad asymmetric combination band of the symmetric and anti-symmetric OH stretches that appears as two components in the 2D-COS. PCA was applied and it was shown that 99% of the spectral variations occurred at 7089 and 6718 cm

 combination in two different species of water whose relative concentrations were changing with temperature. While the full story of the structure of water (2,3) is much more complicated than what I have described here, it is always encouraging to see that different techniques produce similar information.

	Something that did not occur to me while I was doing this work is whether changing the peak positions of the band-fitted spectra would provide a different comparison to the 2D-COS. After submitting the manuscript, I did vary the fitting parameters, and confirmed that these fits are not unique. A future study where the fitting would be varied systematically might provide better insight, but I leave this to a future column.

	I was motivated to do these measurements for several reasons. I wanted to see the results of using this analytical approach to analyze water, whose OH band would not be detectable with a 785 nm laser. But I have also been fascinated by the potential of 2D-COS to reveal differences that are difficult to see spectrally because of band overlap. Unfortunately (for me) the story is much more complicated than I expected, a fact that was revealed to me by Professor Isao Noda. Again I am grateful to him for helping through this painful learning process, and I hope that my candor in describing what I am doing will be helpful to my readers.

	(1) Innovative Photonic Systems, Monmouth Junction, NJ 08852.

	(3) T. Morawietz, O. Marsalek, S.R. Pattenaude, L.M. Streacker, D. Ben-Amotz. and T.E. Markland, 

Two-Dimensional Correlation Spectroscopy: Applications in Vibrational and Optical Spectroscopy 

(John Wiley & Sons, Chichester, England, 2004).

 is the Principal Raman Applications Scientist for Horiba Scientific in Edison, New Jersey. Direct correspondence to: 

Molecular Spectroscopy Workbench

The spectral behavior of water is studied using Raman with an NIR spectrograph and dual wavelength lasers for measurements of both the fingerprint and the OH stretching regions. Raman spectra are recorded between 5 ⁰C and 80 ⁰C, and treated with both band-fitting and the 2D-COS algorithm revealing improved insights into the spectral behavior of water.

Measurement of the Temperature Dependence of Water Using a Near-Infrared Raman Spectrograph

This column is the first of a set that expands our previous discussions of the classical least squares (CLS) algorithm. Having found a new effect that can introduce a large error in calibration results, we extend our investigation of the effects of this phenomenon to calibrations using principal component regression (PCR) and partial least squares (PLS) that we were previously unable to do. 

	A while back, we published a series of columns, and a formal paper, about classical least squares (CLS) analysis of liquid mixtures (1–15) to deal with and explain the use and behavior of CLS analysis for calibration. We review and summarize here what we found from the results of those columns, preparatory to analyzing a similar but more extensive experiment.

	That all started out from a very modest goal: to explain CLS analysis of spectra, and the relationship of the CLS mathematics to the mathematics used for multiple linear regression (MLR) applied to determination of the composition of mixtures. We also wanted to further demonstrate the application of the CLS approach to determining the composition of some simple liquid mixtures. Along the way, we discovered some unexpected relationships between the spectral measurements and the chemical composition, which we explored in those columns.

	However, along with the discovery of the unexpected effects, we also gained insight into many previously known, but unexplained, phenomena that have been afflicting spectroscopic analysis since time immemorial. Since the beginnings of modern near-infrared (NIR) analysis, there have been many symptoms of problems that are known to affect our ability to find the relationship between the spectral data and the sample composition, but nobody had been able to definitively pin down the causes of those symptoms. Hence, in our own minds we have considered these as "mysteries" of spectroscopic analysis. Table I presents a list of these mysteries. Much of this column is based on a presentation at the Eastern Analytical Symposium in 2013 (20).

	These mysteries, and confusion over them, have existed since the beginnings of modern NIR analysis. Indeed, when one of this article's authors (HM) first joined Technicon Instruments in 1976 (one of the first commercial companies to manufacture NIR spectrometers to address the requirements of this new analytical method based on Karl Norris's pioneering work), he found the same questions were already being asked by the engineers and scientists at that company, questions that have persisted until recently. Other newcomers to the company would also say things like, "I studied and thought I knew spectroscopy and how it's used, but here we have no baselines, no standards, no pure-component spectra, no a priori theory, and no spectral interpretation. But it works!" Indeed, not having explanations at that time for the effects seen made NIR analysis appear to be divorced from the mainstream of spectroscopy, and existing in a universe of its own separated from the universe of the rest of science.

	The general NIR community, which at that time was very small, shared the confusion over the behavior of NIR data. Attempts to explain this anomalous behavior went on for many years. Several of the common explanations that were proposed are listed in Table II. Some of those common explanations have within them subcategories. For example, use of the "wrong" calibration algorithm has, along with it, the use of an incorrect number of factors (for the principal component regression [PCR] or partial least squares [PLS] algorithm), or the wrong number of wavelengths (for the MLR algorithm). The use of MLR also carries with it the possibility of using the "wrong" wavelengths (even if the number of wavelengths is correct). Note that the equivalent is also true; for example, for PCR or PLS. However, that possibility usually goes unrecognized and unnoted, because most of the software packages available do not allow the user to select arbitrary subsets of the factors computed during the execution of the PCR or PLS algorithm. For example, a user who decides to create a model that uses four principal components (PCs) is generally not free to select which four components to use; with all the software packages for spectroscopic analysis we're familiar with, only the first four PCs may be used. This limitation is both a curse, and a blessing. The curse is that the limitation prevents users from selecting just the minimum number of factors needed to optimally analyze the samples of interest. If, for example, the sixth factor is important, the user cannot select four factors that include the sixth, but are forced to include extra, unnecessary factors, such as the third and fifth, perhaps, that contribute to overfitting. The blessing is that most users are already confused by complicated algorithms they are not comfortable dealing with, and are happy to not have another whole set of choices to make.

	Over the years, many scientists have tried to address one or more of the suspected problems. The approach usually consisted of hypothesizing a cause of the problem, and then taking an empirical approach by applying an ad hoc solution, usually as part of the routine chemometric algorithm in use. Surprisingly, often this approach "worked," insofar as the scientist was able to obtain satisfactory calibration and prediction performance for the analyte of interest in his samples, and assumed that his "fix" was actually correcting the situation. On the other hand, even when that was the case, this approach usually gave little insight into the underlying causes of the difficulties encountered. Even worse, the results obtained could rarely be generalized or extended to other applications of NIR, or for other types of analysis.

	As described above, around 2009–2010, with the assistance of colleagues, we performed some experiments that we expected would shed some light on the subject (15). The goal was to physically remove as many of the suspected error sources as could be managed. Therefore, samples were made up as binary and ternary mixtures of clear liquids (dichloromethane, toluene, n-heptane). These materials were all mutually soluble in all proportions, and had well-defined and distinct spectra. The use of clear liquids removed any possible difficulties due to optical scatter in the samples. Making up the samples gravimetrically removed the "reference lab errors" usually encountered when performing routine NIR calibrations, since no "reference lab analysis" was performed, and the sample compositions were known as accurately as the weighing technology used. An experimental mixture design specifying 15 ternary samples, each sample containing the three completely miscible organic liquids, was generated and analyzed. The design contained mixtures at evenly spaced concentration (by weight) levels, going from 0 to 100% of each of the three components. The experimental design is described in reference 5.

	Spectra of all 15 samples were measured in transmission, and Beer's law holds. This experiment used is, therefore, the simplest one we could think of that covers the full range of all components and binary and ternary mixtures. Similarly, the data analysis applied to the spectral data was the simplest data analysis we could think of: We used the CLS algorithm, and applied it to the spectral data without any mathematical pretreatments. This was also described in the previous columns (2,16). The use of the CLS algorithm does impose some requirements on the data:

		Spectra of the pure raw materials must be known.

		There must be no interactions that affect the spectra, between the mixture components.

		There must be no partial molal volume effects.

	As long as the conditions are met, this experiment constituted the simplest spectroscopic system for applying chemometric algorithms. The results showed that there was nonlinearity in the relationship between the spectroscopic measurements and the reference values for concentration when the reference values were expressed as weight percent (or weight fractions), as is common practice for many NIR analytical methods of interest.

	However, the relationship between the spectroscopic measurements and the reference values for concentration was found to be linear when the reference values were expressed as volume fractions. The underlying root cause turned out to be grounded not in the spectroscopy, but in the very straightforward and elementary physical chemistry involved: When liquids of different densities are mixed, the weight fraction and volume fraction of any given component of the mixture are not the same. These relationships are shown in Figure 1, for the three-component mixtures used for the experiments we described above. Another effect, well known to physicists, but apparently not so well known to chemists and spectroscopists, is that light interacts with matter in proportion to the volume the matter occupies (full disclosure here: We did, in fact, recently come across a rare exception noted in a recent article that used volume fractions when specifying interactions of light with matter, but that was not in the context of performing analysis [19]). Thus from the physical theory of absorption as well as the experimental results, we find that it is the volume fraction of the mixture components that determines the Beer's law absorbance.


	Figure 1: Underlying cause of nonlinearity: weight fraction (y-axis) versus volume fraction (x-axis) ternary mixtures containing toluene, n-heptane and dichloromethane exhibit non-linearity between weight fraction and volume fraction as measures of concentration of the components. The heading of each graph indicates which constituent is having its weight-versus-volume fraction plotted. Each graph contains a family of curves, due to the changing relative amounts of the other two constituents.

	Because the volume fraction is the "concentration" measure that is linearly related to the spectral measurements, it is clear that any other measure of concentration that is nonlinearly related to the volume fraction must also be nonlinearly related to the spectroscopic values.

	These results were also published in an 

 article (15). Figure 1 shows how the continuum of values exhibits the curvature. Plotting residuals is a time-honored way to gain the ability to examine calibration results more closely than the straight forward 

 plot allows. By preventing the range of the data from filling up the 

 scale in favor of the residuals which then expand the errors to fill the scale, this way of plotting data allows the analyst to look at the data through what amounts to a digital "magnifying glass," thereby seeing aspects of the data that are hidden in the standard 

 plot. Figure 2 displays the result of plotting residuals of the data, instead of the raw data, on the ordinate. It is obvious how the plot becomes expanded.


	Figure 2: Residuals: differences between the volume percent values (x-axis) predicted by the model, minus the actual weight percent values (y-axis). This type of plot expands the differences for closer scrutiny, by plotting these residuals instead of the raw ordinate data (as in Figure 1). By removing the range of the data from the y-axis, plotting residuals allows us to put a "magnifying glass" on the behavior of the data. This expands the differences for more careful study. Note that these plots are schematic, to show the effect of non-linearity between weight-based and volume-based units. The effect on representative data will be illustrated in Figure 4.

	The continuous curves are useful for displaying the underlying nonlinearities that the data are subjected to. Ordinarily, however, actual samples do not display a continuum of values. In the most common scenario representing analytical procedures, samples are selected at random, and therefore contain, and represent, some random selection of concentrations of incidental ingredients as well as of the analyte. This random selection of samples, in our hypothetical case, therefore contains a quasi random sample of the three-component mixtures represented by Figure 1. This random selection is shown in Figure 3, where the round dots, representing the actually selected samples, are displayed simultaneously with the continuum. However, the points all lie so close to the continuum, and to each other, that it's difficult at best to see anything else that might be in this data plot.


	Figure 3: Underlying cause: weight fraction (y-axis) versus volume fraction (x-axis), showing the effect of random sample selection, overlaid with an actual straight line. The black circles on each plot represent the random samples that might have been taken from the underlying continuum of mixtures. When samples are selected at random, you don't see the underlying curvature. The error values seem randomly scattered around the average curve, just as though the error was random instead of systematic, as a result of the random sample selection. A calibration, however, will show curvature in the residuals.

	When samples are selected at random, therefore, you don't see the continuum or the underlying curvature, because the random selection of samples only allow randomly distributed data points to be displayed on the plot. The error values appear randomly scattered around the average curve, just as if the error, despite being completely systematic, were itself random, due to the random sample selection. This is demonstrated in Figure 3. Although Figures 3 and 4 are schematic, the plotted points in Figure 3 illustrate how the points tend to cluster around the calibration line, but the range of values of the data makes it difficult to see the departures from linearity. Figure 4, showing the residuals from the data of Figure 3, again shows how plotting the residuals applies a digital "magnifying glass" to the results of Figure 3. A calibration containing nonlinearity will, therefore, show curvature in the residuals, which might not show up in a plot like Figure 3. This is demonstrated in Figure 4, where the residuals are again plotted on the ordinate instead of the raw ordinate values. This method of inspecting the results not only shows up nonlinearity, but also enables observing any clustering of data, as well as other potential fault conditions to be displayed for the user's inspection. When we look at actual data, we will see how this new tool can be helpful in finding out what is going on "under the hood" of the data analysis.


	Figure 4: Plot of the residuals from Figure 3, as the differences between the volume percent values (x-axis) minus the actual weight percent values (y-axis). This type of plot magnifies the differences and allows more sensitive detection of the non-linearity. Note that these plots are schematic, to compare the effects of using volume-based units to weight-based units. The continuum of values from which individual samples' values are taken is shown for comparison, as per Figure 2.

	To be sure, this new finding that the volume fraction is the correct analytical quantity to use for calibration does not automatically solve all problems with NIR calibrations. A chain is only as strong as its weakest link. Finding a new "weak link" does not eliminate the possibility of one or more of the classic potential problems plaguing our efforts to create calibrations, listed in Table II, from entering and creating difficulties in the calibration process. But it is one more item to consider when problems arise, and a good scientist wants to understand an analytical system instead of blindly applying "brute force" chemometrics to cover the problem up.


	Figure 5: NIR spectra of the five pure constituents in the expanded set of mixtures. X-axis is wavelength (in nm) and y-axis is absorbance.

	The foregoing makes a compelling case that, for spectroscopic analysis, EM radiation "sees" the absorbance according to the volume fractions of their components (given some assumptions to ensure ideality, or near ideality). Physical theory tells us that this is what we should expect, and we find that the CLS algorithm is responding according to the theory. This does not automatically ensure that conventional calibration algorithms will respond the same way, and a strictly scientific approach requires that we verify that the performance of the calibration algorithms are evaluated by actually applying them to the set of data. The fifteen samples' worth of data we had available, and used for this study, is not sufficiently large to reliably test the conventional calibration algorithms. A search for another, larger, suitable sample led us to a pair of reports, by Willem Windig and colleagues, based on data suitable for our purposes (17,18). With the assistance of Tony Davies and Tormod Naes, Prof. Windig was contacted and graciously offered to supply the data used for his studies. The dataset contained spectra of mixtures of five ingredients: acetone, 2-butanol, 1,2 dichloropropane, methanol, and methylene dichloride. In addition to the mixtures, the spectra of the pure components had also been measured, and are part of the set. This dataset is not perfect; the presence of two different alcohols may lead to potential interactions. There may also be interactions caused by the two chlorine (Cl)-containing polar materials in the set, but the design is completely symmetric and balanced, and is otherwise a nearly ideal set of mixture spectra. All samples specified by the design were made up and scanned twice. Examination of the scans revealed that plots of the two repeat scans from any sample were indistinguishable by eye on the computer's monitor.


	Figure 6: Overall characteristics of the orthogonal, balanced, symmetric statistical experimental design used to define the samples. The five different ingredients allow for ten pair wise comparisons; each of the ten possibilities provides a plot that looks like the one presented below. Any and all pairs of ingredients, when their percentage composition is plotted on an x-y plot, generate this pattern.

	The characteristics of the dataset are described in Table III. For reference, the spectra of the pure ingredients are shown in Figure 5. There were two spectra measured for each pure ingredient; when plotted together, as in Figure 5, we see that the two spectra completely overlap, indicating that spectral noise or other source of variation is negligible.

	Because there are five ingredients, there are 10 combinations of ingredients that can be plotted pairwise. The experimental design is such that any and all pairs of ingredients, when plotted on a 

 plot, generates a pattern like the one shown in Figure 6. The method of generating the design is described by Windig (17,18).

	Because we want to observe the effects of using both weight fractions and volume fractions as the component concentrations, we used the values for density of the various compounds displayed in Table IV to convert one set of units to the alternate set of units. The list of sample compositions is presented in Table V. Because the samples were made up by weight, the values in Table V reflect the weight fractions of the ingredients. Volume fractions were calculated from these weight fractions and the known densities of the ingredients, as listed in Table IV.

	Figure 1 also illustrates another phenomenon not previously recognized. Plotting the theoretical results of weight fractions versus volume fractions, we can create a continuum of data points along the curves corresponding to constant ratios of two of the constituents, the ones NOT being plotted on that graph. For the three-component mixtures being considered in Figure 1, we can see that, for the dichloromethane plots, the curvature of all lines are concave in the same direction, and similarly for the 

-heptane plots. For the toluene plots, that is not the case; some of the individual curves are concave up and some concave down. Overall, the "average" curve is very close to a straight line. This is all very clear when we can look at these theoretical constructions and see all the continuous lines representing the set of mixtures.


	Table V (continued): List of percent concentrations of the various constituents in the samples specified by the experimental design. Note that the values in this table reflect the actual values of the constituents in the samples, as opposed to the theoretical target values specified by the experimental design. Also note that the samples are not in any particular prescribed order, despite that the values were sorted before printing this table.

	On the other hand, when we are dealing with data from real mixtures, and only have some finite number of randomly selected representative mixtures, what is going on "under the hood" is not always clear. This is illustrated in the graphs presented in Figure 3, where the theoretical continua are overlaid with individual points representing samples randomly selected from the continuous values. From the way they were constructed, we know that each of the data points in Figure 3 lies on one of the lines, and therefore shares in the nonlinear nature of that line. For the 

-heptane and dichloromethane, it can be seen that there is curvature in the plot of the data points, if not by themselves, then certainly by comparison, with straight lines superimposed on each of those graphs.

	For the toluene, however, this is not the case. Since the sense of the curvature of some of the lines is opposite to the sense of the curvature of others of the lines, the "averaging" effect mentioned above makes the overall appearance of the graph look like there is a linear relationship between the weight fraction and volume fraction expressions of the concentrations. This is an artifact, however, one that gives the appearance of linearity when all the underlying relationships are inherently nonlinear. Thus, we've termed this relationship as being faux-linear (as in the title to this subsection). In this situation the nonlinearity cannot be detected, and the results appear to indicate only a much-exaggerated random error.

	Further analysis of this data set will be considered in a subsequent column.

	(15) H. Mark, R. Rubinovitz, D. Heaps, P. Gemperline, D. Dahm, and K. Dahm, 

	(20) H. Mark, Eastern Analytical Symposium, Somerset, NJ, Paper #279, Nov. 18-20 (2013).

 serves on the Editorial Advisory Board of 

. He is also a Certified Core Adjunct Professor at National University in San Diego, CA and a Principal at Biotechnology Business Associates. He was formerly the Executive Vice President of Research and Engineering for Unity Scientific and Process Sensors Corporation.

 and runs a consulting service, Mark Electronics, in Suffern, New York. Direct correspondence to: 

Chemometrics in Spectroscopy

A newly discovered effect can introduce large errors in many multivariate
spectroscopic calibration results. The CLS algorithm can be used to explain this effect. Having found this new effect that can introduce large errors in calibration results, an investigation of the effects of this phenomenon to calibrations using principal component regression (PCR) and partial least squares (PLS) is examined.

More About CLS, Part 1: Expanding the Concept

The use of handheld X-ray fluorescence (XRF) can be extremely beneficial to analyze platinum group metals in catalytic converters. Ultimately, handheld XRF can provide accurate, precise, fast, and nondestructive analysis of finely ground car catalyst material.

	Platinum (Pt), palladium (Pd), and rhodium (Rh) fall into the platinum group metals (PGMs), where several elements that share similar physical properties are grouped together. These three PGMs are used in catalytic converters to increase fuel efficiency and reduce harmful emissions (1).

	Catalysts function to decrease the amount of energy required to activate a chemical reaction by accelerating the rate of a reaction, without direct involvement of the catalyst itself (2)

	In catalytic converters, catalysts are mounted on a monolith for use in catalytic converters. In the 1960s, the material this monolith was made of had large temperature ranges that caused it to expand, crack, and break. This problem was later resolved with the creation of the cordierite monolith (2MgO*2Al

), which did not share the same material properties as its predecessors, and would not thermally expand to the point of breaking.

) of a chemical reaction, (a) without a catalyst, and (b) with a catalyst. This shows that the activation energy of a chemical reaction decreases and increases reaction speed, thus increasing product yield (2).

	In 1975, the two-way catalytic converter enabled the oxidation of carbon monoxide and hydrocarbons. These catalysts served to increase the rate of oxidation (for example, to increase oxygen in an environment and convert carbon monoxide to carbon dioxide or hydrocarbons to water). By 1981, the catalytic converter was optimized once more with the introduction of the three-way catalytic converter, which reduced nitrogen oxides (3–5) These three-way devices, which used PGMs, reduced the amount of oxygen, and converted nitrous oxide to nitrogen and oxygen (2,5).


	Figure 2: Three reactions take place in a three-way catalytic converter. One is the reduction of nitrous oxide into nitrogen and oxygen, the second is the oxidation of carbon monoxide to carbon dioxide, and the third is the oxidation of hydrocarbons and oxygen into carbon dioxide in water (2).

	These monoliths have a honeycomb structure, as shown in Figure 3 (6). The cross section in this structure optimizes the reactions by increasing the surface area and the contact between the catalysts and the emissions. This, in turn, allows more reactions to take place (7). The combined concentration of Pt, Pd, and Rh expected within a catalytic converter is below 1% (4).


	Figure 3: Cross section of a honeycomb catalytic converter (6).

	These monoliths are covered in a coating of aluminum oxide, called a 

, which is comprised of ~90% aluminum oxide. Including the three PGMs of interest, there are other additives in the coating that enhance the performance of the PGMs within the catalytic converter (8) For example, cerium and zirconium are used to create an oxygen-rich environment to help oxidize carbon monoxide into carbon dioxide (9). Another example is barium, which is used mostly in diesel engines as a lean trap to reduce nitrous oxide to nitrogen (10). These aforementioned additives can be found in concentrations up to 10%, and are considered large contributors to the constitution of catalytic material (4).

	Other additives are added in smaller concentrations for different purposes. For example, lanthanum and other rare earth elements are used more frequently in Asian markets to increase the catalytic converter's lifespan (4). Nickel is also useful because it is used to catch sulfur in fuel (4). Sulfur is considered a poison to a catalyst (9,10). Often, the gas passing through the catalyst causes some sulfur particulates to accumulate on the surface. A poison such as sulfur can be partially absorbed on this surface, and decrease the available surface area for the catalyst's reactions to take place. In turn, this decreases the catalyst's effectiveness and lifespan. Lead is another example of poison; it coats the catalyst materials and prevents the exhaust fumes from undergoing redox reactions.

	The effect of some of these poisons can be reversed by running the engine at hot temperatures, which increases the heat of the exhaust flowing through the converter. However, the effect of a poison is not reversible if the poison is lead, because it has a high boiling point (2). Lead was used as a fuel additive from the 1920s up to the 1970s, when it was phased out (5).

	The removal of lead from fuel additives helped push environmental laws for the regulation of emissions. In 1967, Ford and General Motors (GM) ran studies to measure the relative rates of catalyst degradation, and whether the degradation was due to thermal effects or a poison. The study concluded that when using unleaded gasoline, the catalysts were durable, dependable, and resistant to engine malfunctions. It was also determined that unleaded gasoline had a negligible effect to engine performance and fuel intake. The results were made public two years later, and, following their release, the data were presented to the Society of Automotive Engineers (SAE) to make advanced emissions control feasible by removing lead from gasoline. It was proposed that catalytic converters should be installed on all cars by 1975 (11). Following this, the US Congress enacted the Clean Air Amendment to reduce emissions by 90% for hydrocarbons, carbon monoxide, and nitrous oxides by the mid-1970s. Similar laws were passed in Japan and Canada in 1976 (12).

	Many countries then followed and demanded regulations for emissions, although this depended on their ability to research, develop, and enforce legislation. For example, the European Union is an amalgamation of countries, and although some countries adopted regulations, others did not, whether due to funds or other pending disagreements. Regulations for emissions came in later years, and since 1993, car catalysts have been mandatory in all new cars (11).

	Air regulation laws were implemented in automobiles on a country-by-country basis, each with their own rules and regulations. Today, most regulations require that every new automobile is fitted with a catalytic converter (11,12). Regulations also varied country to country. For example, the United Nations (UN) Economic Commission for Europe (ECE) emission regulations apply only when a car was produced. However, in the United States, emissions regulations apply for a car's lifespan. Thus, if an older car entered service, manufacturers in the United States are accountable to retrofit it. This was not the case in Europe; however, Europe eventually caught up on regulations, and, in the 2000s, enacted legislations such as the End-of-Life Vehicle Directive and the Waste Electrical and Electronic Equipment Directive to recycle PGMs from catalytic converters due to their high rate of recovery (13).

	Due to initiatives for environmental legislation and the low availability of these three PGMs in nature, platinum, palladium, and rhodium are heavily recycled, and can be recovered with approximately 95% efficiency (13). These three PGMs are mostly recycled from catalytic converters, as shown in the process presented in Figure 4.


	Figure 4: The above shows a concept diagram for recycling catalytic converters (7).

	Once the powder within a catalytic converter is ground and homogenous, it is sent to be analyzed for elemental composition. Those values are then used to optimize the process to obtain the highest recovery rate of PGMs from the input feed.


	Figure 5: Overlap of XRF for the oxides of platinum (Pt) and selenium (Se).

	A handheld XRF instrument can be divided into three main parts: an X-ray source, a detector, and a processor. First, a tube source emits X-rays toward a target sample. The sample then emits a characteristic wavelength of X-rays as photons that enter the analyzer, which are read by the detector. X-ray energies are specific to an element, so the processor uses this information and interprets the data into chemistry that can be read by a user (14).

	Handheld XRF has methods that cater to different applications and different elements of interest. X-ray analysis depth is dependent on the physical properties of the sample and the information reaching the detector (Table I).

	To obtain maximum accuracy with handheld XRF, the powder being analyzed needs to be dry, homogenized, and finely ground. If the sample is not ground finely enough, the difference in particle sizes may cause a sifting effect, resulting in an unmixed sample. This would result in a granular effect, where elements of a larger size gravitate toward the top, and those of a smaller size fall towards the bottom of a sample cup. For catalytic converters, the monoliths must be ground prior to handheld XRF testing. Some users desire in situ testing without sample preparation. For this to work effectively, user-defined software factors need to be applied to account for the differences in the physical state of the sample.

	Five samples were tested with an Olympus Vanta handheld XRF analyzer to assess accuracy. The results (shown in Figure 6) are ordered from the highest to lowest concentrations. For testing conditions, each sample was kept in place for all five repeats. The test times for the 40 kV beam varied from 10, 20, and 30 s, and the test time for the 10 kV beam was 30 s for all tests.


	Figure 6: The charts show accuracy with the assay (ppm) on the x-axis and the XRF analysis results (ppm) on the y-axis. The illustration shows (a) Pt accuracy, (b) Pd accuracy, and (c) Rh accuracy.

	We tested precision using the same parameters described above for the accuracy tests, and the results are shown in Figure 7 for Pt, Pd, and Rh. For each sample, the 1-sigma error was shown to decrease as test (measurement) time increases. In other words, as test times increase, precision also increases. At a certain point, longer test times diminish returns, so it is not useful to increase test times beyond this point.


	Figure 7: All charts show the precision for 5 samples (each repeat of 5 shown) for different 40 kV beam 1 times (in seconds). The illustration shows (a) the Pt precision, (b) the Pd precision, and (c) the Rh precision.

	Lastly, the relative standard deviation is shown in Figure 8 for each of the five samples, arranged from highest to lowest concentrations. The same test parameters were used as described above.


	Figure 8: The charts show the relative standard deviation (RSD) for 5 samples (each repeat of 5 shown) for different 40 kV beam 1 time (in seconds). The figure shows (a) the Pt RSD, (b) the Pd RSD, and (c) the Rh RSD.

	The results for Pt, Pd, and Rh show that, overall, the relative standard deviation decreases as measurement time increases. This is most pronounced in Pt at low concentrations (note standard numbers 3, 4, and 5 assayed to 1200, 700, and 300 ppm, respectively). Catalysts, in general, do not exceed 10,000 ppm concentration levels for any of these three elements.

	Handheld XRF can provide accurate, precise, fast, and nondestructive analysis of finely ground car catalyst material. The low levels of PGM concentrations obtained from 40, 50, and 60 s tests provided repeatable results. Precision also improved as test time increased, however at the longer test time of 30 s, the return on precision diminished, and it was not as valuable to continue increasing test times. The relative standard deviation also improved overall at longer test times.

https://chem.libretexts.org/Core/Physical_and_Theoretical_Chemistry/Kinetics/Case_Studies:_Kinetics/Catalytic_Converters

 (Taylor & Francis, Boca Raton, Florida, 2nd ed., 2005).

	(5) Manufacturers of Emissions Control Association, 

The Catalytic Converter: Technology for Clean Air 

https://www.khanacademy.org/science/chemistry/chem-kinetics/arrhenius-equation/a/types-of-catalysts

	(7) Chemical Engineering Essentials for the CPI Professional, 

http://www.chemengonline.com/new-frontiers-metals-recycling/

	(8) Manufacturers of Emission Controls Association, 

http://www.meca.org/technology/technology-details?id=5

	(9) A. York, & The Royal Society of Chemists, 

https://eic.rsc.org/feature/the-evolution-of-catalytic-converters/2020252.article

	(10) National Programme on Technology Enhanced Learning, 

Lean de-NOx Catalysts and Catalyst Poisoning

http://nptel.ac.in/courses/112104033/lecture24/24_3.html

	(11) A. Faiz, M.P. Walsh, and C. Weaver, 

Air Pollution From Motor Vehicles: Standards and Technologies for Controlling Emissions

 (The World Bank, Washington, D.C., 1996).

	(12) L. Ebdon, L. Pitts, R. Cornelis, H. Crews, O. Donard, and P. Quevauvillier, Eds. 

Trace Element Speciation for Environment, Food, and Health

 (Royal Society of Chemistry, Cambridge, United Kingdom, 2001), pp. 176–187.

	(13) International Platinum Group Metals Association, 

https://ipa-news.com/index/sustainability/case-studies.html

	(14) EPA Technology Analysis and Field Analytic Technologies, 

https://clu-in.org/characterization/technologies/xrf.cfm

 is an applications scientist at Olympus, in Waltham, Massachusetts. Direct correspondence to: 

FEATURE ARTICLES

The platinum-group metals platinum, palladium, and rhodium are essential and valuable elements in catalytic converters, and thus must be recycled. Handheld X-ray fluorescence (XRF) can be extremely beneficial for analysis of these metals in finely ground materials extracted from used catalytic converters.

Use of Handheld X-Ray Fluorescence to Analyze Platinum Group Metals in Catalytic Converters

This article theorizes about the importance and usability of Fourier transform infrared (FT-IR) spectroscopy in the identification of carbonate phases varying in magnesium content. Results of studies of Triassic limestone samples taken from the area of the Polish part of the Germanic Basin using this method are presented. The following phases were analyzed: a low-magnesium (Mg) calcite, a high-Mg calcite, a dolomite, and a huntite. These carbonate phases were identified on the basis of the peak wavenumbers that are present in the infrared absorption spectra. Low-Mg calcite dominates in the limestones, with some samples having a lower amount of high-Mg calcite. Moreover, dolomite and huntite were identified. The results of research show that substitution of Ca

 in the carbonate phase lattices leads to a continuous wavenumber increase in the band locations. Therefore, FT-IR spectroscopy was used for identification of carbonate minerals with variable contents of magnesium.

	Inorganic and biogenic rhombohedral carbonate minerals can be characterized by variable content of calcium carbonate (CaCO

) identified in Triassic limestones of the Polish part of the Germanic Basin (southwestern part of Poland, in the Opole region of Upper Silesia) (1,2). The limestones of Muschelkalk (Middle Triassic) sediments, especially formations of the Lower Muschelkalk in the Gogolin Beds (the bottom of profile), the GóraÅ¼dÅ¼e Beds, Dziewkowice Beds, and Karchowice Beds (the upper formation of profile) are built of carbonate phases differing in calcium (Ca) and magnesium (Mg) content. These deposit formation names are regional, and derive from the names of nearby towns. Variability of calcium and magnesium in carbonate rocks is associated with the presence of various magnesium-containing carbonate phases. Results of the studies show that limestones of the Polish part of the Germanic Basin are mainly built of low-magnesium calcite, high-high magnesium calcite, and dolomite. Moreover, it is possible to observe lesser amounts of huntite, ankerite, and siderite (1–8).

	The aim of this article is to show the importance and usability of Fourier transform infrared (FT-IR) spectroscopy for research of carbonate phases, which present different content of MgCO

 in middle Triassic sediments. The limestones were first investigated as part of previous research work. FT-IR was one of the analytical methods used during this previous work (3–8). However, in past studies, the accuracy of FT-IR was not evaluated for identification of carbonate phases with different amounts of magnesium, especially phases with magnesium substitution. Therefore, it was decided to evaluate this question in the present study.

	FT-IR spectroscopy allows one to identify carbonates characterized by variable content of calcium and magnesium: low-Mg calcite CaCO

 (space group R3-withbar c), high-Mg calcite CaMgCO

 (space group R3-withbar c), proto-dolomite Ca

 (space group R3-withbar c), ordered dolomite Ca

 (space group R3-withbar c) (9–18). Carbonate minerals are characterized by highly anisodesmic bonds, comprised of anions as CO

 in the minerals, in which atoms have covalent bonds that behave like vibrators, somewhat independent of their molecular surroundings. Their vibrations influence the absorption spectra of carbonates. The absorption bands, corresponding to the intramolecular vibrations of CO

 anions, correspond to the basic range of the infrared spectrum, and the lattice vibrations yield absorption bands in the far infrared (19–21). The free CO

 symmetry. It causes four intramolecular vibrations: v

 (bending in the plane). In the crystalline lattice of trigonal anhydrous carbonates (a group of calcite), which crystallize according to point group D

 anions located in places with local symmetry D

. Under these conditions, vibrations of the CO

 anion produce absorption bands only slightly shifted in relation to the frequency of the free ion vibrations. The band v

 is particularly useful for identification of carbonate minerals. This band clearly changes its position with the change of cation type, and takes the following peak locations for calcite: CaCO

) absorption spectrum, where the structure of the flat CO

. This band is located approximately halfway between the appropriate band of calcite and magnesite. Isomorphic substitutions cause only a slight shift of the carbonate absorption bands. The v

 absorption band, prohibited in principle for carbonates of the calcite group, is sometimes observed in the spectra of weakly crystallized samples or those specimens whose structure has been disturbed by grinding.

	Magnesium usually comes from sea waters, and less often from fresh waters. High-Mg calcite is an unstable carbonate phase with respect to low-Mg calcite. It may lose its magnesium over time, and become low-Mg calcite. If it is exposed to magnesium-rich pore waters, high-Mg calcite can gain additional magnesium and be replaced by dolomite (22). Dolomite and huntite are stable carbonate phases, because in these phases, magnesium does not substitute for calcium. Typical dolomite, stoichiometric in its chemical composition, contains 46.13% of MgCO

. It is formed during advanced stages of diagenesis, in a water environment rich in magnesium. Protodolomite is usually formed during sediment compaction and early stages of diagenesis. This is a non-stoichiometric, poorly ordered carbonate phase, often characterized by lower than stoichiometric content of MgCO

 (23–25). Huntite has increased content of magnesium, anywhere from 20–21% of Mg (from 69–71% MgCO

) (26–29). It is usually formed as an effect of hydrothermal processes, weathering of dolomite, or as a result of the transformation of high-Mg calcite under high temperature conditions. In sedimentary rocks, it occurs in the sediments of the vadose zone (27).

	FT-IR analysis was applied to investigate a total of 30 samples:

		4 samples from Gogolin Beds (G1 and G6, collected in Gogolin Quarry, LD9 and LD11, collected in GóraÅ¼dÅ¼e Quarry)

		5 samples from GóraÅ¼dÅ¼e Beds LD2, SA5, W1, W5, and W7, (LD2 collected in Ligota Dolna Quarry)

		6 samples of Dziewkowice (Terebratula) Beds SO1, SO28, S2, S8, SA10, and SA12 (SO1 and SO28 from Strzelce Opolskie Quarry; S2 and S8 from Szymiszów Quarry; SA10 and SA12 from the Saint Anne Mountain area)

		15 samples from Karchowice Beds SO7, SO14, SO20, SA2, SA13, T1, T7, T15, T22, T30, T41, T62, T65, T66, and T77 (SO7, SO14, SO20 from Strzelce Opolskie Quarry; SA2 and SA13 from the Saint Anne Mountain area; T1, T7, T15, T22, T30, T41, T62, T65, T66, and T77 from Tarnów Opolski Quarry)

	The samples were collected during previous projects connected with the study of limestone mineral composition, especially carbonate phases with different magnesium content related to diagenetic processes (4–8).

	The studies were carried out at the Institute of Geological Sciences of Jagiellonian University in Cracow (Poland), using a FTS 135 BioRad Fourier transform spectrometer. The spectra were evaluated using the software provided by the manufacturer (Bio-Rad Sadtler Division). Pellets were made from samples and analyzed. The pellets were made by mixing 0.8 mg dried sample with 300 mg spectrally pure potassium bromide (KBr). Then, the mixture was compressed into a pellet using several tons of pressure while under vacuum.

	The absorption spectra obtained provided information to identify minerals that form within the selected limestone specimens. With the increase of magnesium content, the values of peak wavenumber locations increased from those typical for "pure" calcite to the peak values characteristic for dolomite. Peak wavenumber values typical for huntite and magnesite are higher in comparison to those of dolomite (Table I) (12,16, 22,24,27).


	Figure 1: Infrared absorption spectrum of limestone sample G6 in the range from 4000 to 400 cm

	FT-IR was applied to investigate four samples in total: G1, G6, LD9, and LD11. The results of sample G6 were presented in the study (Figure 1, Table II) (5,6). The results of the study show that low-Mg calcite dominates in these samples. In three samples (G6, LD9 and LD11), high-Mg calcite was identified (Figure 1, Table II). In the G6 sample, this carbonate phase was determined on the basis of peak wavenumber v

 and in samples LD9 and LD11, on the basis of peak wavenumber v

. Absorption bands of dolomite were observed only in the infrared absorption spectrum of sample G6 (Figure 1, Table II). The dolomite phase was identified on the basis of three band wavenumbers toward the far infrared.

	Huntite (a carbonate phase with the highest Mg content) was determined in the absorption spectra of samples G6 and LD11. This carbonate phase was identified on the basis of single infrared absorption bands (Figure 1, Table II) (5). Because they are single bands, it was concluded that this carbonate phase probably occurs in these samples.


	Figure 2: Infrared absorption spectrum of limestone sample W5 in the range from 4000 to 400 cm

Mineral Phases in GóraÅ¼dÅ¼e Limestones 

In this study, FT-IR spectroscopy was used for identification of carbonate minerals in limestone with variable contents of magnesium. Associated spectral bands were identified and assigned. Results of studies of Triassic limestone samples taken from the area of the Polish part of the Germanic Basin using FT-IR are presented. The results of research show that substitution of Ca2+ by Mg2+ in the carbonate phase lattices leads to a continuous wavenumber increase in the assigned band locations.

Spectroscopy-06-01-2019

Vol 34 No 6 Spectroscopy June 2019 Regular Issue PDF

Measurement of the Temperature Dependence of Water Using a Near-Infrared Raman Spectrograph

More About CLS, Part 1: Expanding the Concept

Use of Handheld X-Ray Fluorescence to Analyze Platinum Group Metals in Catalytic Converters

The Importance of Fourier-Transform Infrared Spectroscopy in the Identification of Carbonate Phases Differentiated in Magnesium Content