Spatial Emission Profiles for Flagging Matrix ... - ACS Publications

Dec 3, 2012 - Andrew J. Schwartz , Steven J. Ray , George C.-Y. Chan , Gary M. Hieftje ... E. Hywel Evans , Jorge Pisonero , Clare M. M. Smith , Rex N...
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Spatial Emission Profiles for Flagging Matrix Interferences in AxialViewing Inductively Coupled Plasma-Atomic Emission Spectrometry: 2. Statistical Protocol George C.-Y. Chan* and Gary M. Hieftje Department of Chemistry, Indiana University, 800 E. Kirkwood Avenue, Bloomington, IN 47405, United States S Supporting Information *

ABSTRACT: A statistical protocol was developed and verified for automated signaling of matrix interferences in inductively coupled plasma-atomic emission spectrometry (ICP-AES). Spatial emission profiles in ICP-AES are versatile indicators for flagging matrix interference. A family of calibration curves is first generated by measurements of standard solutions at different spatial locations in the plasma. The determined-concentration profile of the analyte along a spatial measurement axis of the plasma is then obtained by analyzing the sample at each spatial location by reference to the respective calibration curve. The absence or presence of a matrix interference is gauged from the shape of the determinedconcentration profile of the analyte. A flat determined-concentration profile indicates absence of matrix interference, whereas a dissimilar (i.e., curved) concentration profile offers a clear warning signal that the analytical results are compromised by interferences. The developed protocol automatically classifies a spatial profile as flat or curved; it involves the computation of three statistical parameters: relative range0.05−0.95, σsample, and σsuccessive. The term relative range0.05−0.95 refers to the ratio of the range to the mean of the relative-intensity (or determined concentration) values between the 5th and 95th percentiles in a spatial profile, whereas σsample and σsuccessive refer to the sample standard deviation and the standard deviation of successive values, respectively, of all values in a spatial profile. It was found that whenever the relative range0.05−0.95 of a spatial profile is below 1.5%, the profile can be considered to be flat and no further statistical testing is needed. If relative range0.05−0.95 > 1.5%, the σsuccessive/ σsample ratio provides useful information on the flatness of the profile. If the profile is flat, σsuccessive will be statistically equivalent to σsample (i.e., σsuccessive/σsample = 1). In contrast, if curvature is present in the profile, σsuccessive will be statistically smaller than σsample (i.e., σsuccessive/σsample < 1). A statistical test, based on the transformation of the experimental σsuccessive/σsample ratio to the z value of a standard normal distribution, was used to judge if the difference between σsuccessive and σsample is statistically significant. This statistical protocol for characterization of flatness in a spatial profile was verified in experiments carried out under the influence of various matrix interferences and different plasma operating conditions.

T

interference, the use of simple calibration leads to analysis errors that can be 30% or more.6−10 Clearly, reducing interferences would be a desirable advancement. Unfortunately, this goal of interference-free analysis is not yet achievable; it is therefore crucial to have indicators that can successfully flag the presence of a matrix effect so immediate remedial work can be undertaken. Previously,11,12 we developed a simple all-in-one indicator to flag interferences caused by any of the three major matrix-effect categories (spectral interferences, sample-introduction-related, and plasma-related), in an online fashion during an analysis. The applicability of this indicator was originally demonstrated in conventional lateral-viewing ICPAES11 and extended to axial viewing, in the companion paper.12 The new methods are based on the fact that spatial emission patterns in ICP-AES (regardless of viewing mode) are strong functions of a sample matrix. In turn, this dependence arises

oday, most elemental determinations are carried out by the inductively coupled plasma (ICP), operated in either the atomic emission spectrometry (AES) or the mass spectrometry (MS) mode. Obviously, a chemical analysis will serve its purpose only if the results are accurate. The accuracy budget could be particularly tight for some samples because a small change in trace-element composition might drastically change the behavior and performance of a sample. Examples are the effects of impurities on the electrical properties of some electromaterials and on the efficiency of a nuclear material as a fuel. Other recent published examples, in which ICP-AES is utilized for the determination of major to trace elements in advanced materials, include crystalline ZnGeP2 optical material,1 Bi2Te3 and Sb2Te3 thermoelectric film,2 Am and Th determination,3 U isotopic analysis4 (through high-resolution AES) in nuclear fuel, and lead zirconate-titanate piezoelectric ceramics.5 Although ICP-AES is considered by some to be a trustworthy analytical method, matrix effects abound in this and all other plasma-based analytical methods. In the presence of an © 2012 American Chemical Society

Received: July 24, 2012 Accepted: December 3, 2012 Published: December 3, 2012 58

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RESULTS AND DISCUSSION Description of the Problem with Examples from Plasma-Related Matrix Interferences. Figure 1 shows the

because plasma behavior and excitation conditions are heterogeneous along the ICP observation axes (i.e., vertical axis for side-on measurements11 and cross-sectional axis for end-on measurements12). Therefore, the relative magnitude and sometimes even the direction of the change in emission intensity caused by a matrix are not constant but are functions of plasma location. As a result, the determined concentration of an analyte, under the influence of a matrix interference, will show a spatial dependence and thereby allow the interference to be detected. The absence or presence of matrix interference is gauged from the determined-concentration profile of the analyte along the measurement axes of the plasma, which is obtained by analyzing the sample at each spatial location by reference to the respective calibration curve. A flat determinedconcentration profile indicates absence of matrix interference, whereas a dissimilar concentration profile offers a clear warning that the analytical results are compromised by interferences. The main objective of the present study is to develop a robust statistical protocol that can classify spatial profiles as flat or curved, as a step toward automated matrix-effect detection and potentially as a building block for future expert systems for ICP-AES.

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Figure 1. Cross-sectional relative-intensity profiles of Fe II 259.94 nm emission in the presence of 0.05 M Na, Ca, Ba, or La matrices at 1400 W plasma forward power and 0.80 L/min total central channel gas flow. Injector diameter was 3 mm.

EXPERIMENTAL SECTION

With a few exceptions, the experimental procedures were identical to those described in the companion paper.12 In one experiment, which will be noted in the discussion, a plasma forward power of 1400 W was used; all other experiments were carried out at 1100 W of plasma power. Four matrices (Na, Ca, Ba, and La) at an equimolar concentration of 0.05 M were selected for experiments involving plasma-related matrix interferences; all matrix and analyte solutions were prepared and diluted with 2% v/v HNO3. In additional to the three previously12 discussed analyte−matrix (As−Cd, Er−Co, and Er−Ce) pairs, two analyte−matrix couples (Ce−Fe, and Ru− Fe) were added for the investigation of spectral interferences. Table 1 lists the ionization13 and excitation potentials14,15 of these emission-line pairs.

relative intensities of a representative emission line, the Fe II 259.94 nm line, in the presence of 0.05 M Na, Ca, Ba, or La matrices at 1400 W plasma forward power and 0.80 L/min total central channel gas flow. Relative intensity will be used throughout the whole paper and is defined as the signal from the test element in the presence of the matrix divided by that under the reference conditions (i.e., Imatrix/Ireference). It should be noted that relative intensity is equivalent to the determined analyte concentration; the reference acts as the calibration standard in a one-point calibration. Even under these operating conditions that favor a highly robust plasma, the matrix effects persist and can be recognized by their effect on the absolute intensity (in the absence of interference, the relative intensity = 1.0). Fortunately, the relative-intensity (and also its equivalent, the determined-concentration) profiles show distinct curvature along the cross-sectional profile of the plasma, allowing the interferences to be flagged. Figure 1 confirms that the cross-sectional profile can be employed to flag interference in axial-viewing ICP, even at the high RF power and low carrier-gas flow that are common for robust plasma operation. In contrast, the vertical emission profile in lateral viewing ICP-AES is not sensitive enough to flag plasma-related matrix effects in a highly robust plasma; under those conditions, the crossover points are usually located within the load-coil region and the observable relative-intensity profiles are spatially flat.11,16 Interestingly, the severity of plasma-related matrix effects in axial viewing ICP-AES follows a slightly different order than in conventional lateral viewing. In particular, under robust plasma conditions, matrix effects follow the order Na < Ca < Ba < La in the normal analytical zone of the plasma in lateral viewing,10,17,18 whereas in axial viewing the order becomes Na ∼ Ba < Ca < La (cf. Figure 1). The reason for this difference is not known; however, it can be concluded that experience in and knowledge of matrix effects in conventional side-on ICP-AES might not be directly transfer-

Table 1. Emission-Line Pairs and Their Ionization13 and Excitation Potentials,14,15 for Spectral Interference Study spectral line As I 228.81 nm Cd I 228.80 nm Er II 239.73 nm Co II 239.74 nm Ce II 381.59 nm Fe I 381.58 nm Er II 302.27 nm Ce II 302.28 nm Ru II 238.20 nm Fe II 238.20 nm

ionization potential (eV)

excitation potential (eV)

As−Cd line pair   Er−Co line pair 6.108 7.881 Ce−Fe line pair 5.539  Er−Ce line pair 6.108 5.539 Ru−Fe line pair 7.361 7.902

total energy (eV)

6.771 5.418

6.771 5.418

6.017 6.387

12.125 14.268

4.057 4.733

9.595 4.733

6.256 6.152

12.363 11.691

6.549 5.204

13.910 13.106

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rable to axial viewing, due to the different probed volumes in the two observation modes. Curvature in the cross-sectional relative-intensity profiles shown in Figure 1 is unambiguous. In this particular example, the lowest signal-to-noise ratio (i.e., at the edges of the presented spatial profiles) of the Fe II 259.94 nm line was about 40. However, when the concentration of the analyte is low or much weaker emission lines are measured, signal-to-noise ratios degrade, and hence, relative measurement uncertainties become greater. As a result, noise will eventually become dominant, which might make detection of the curvature difficult, even when the fractional change in signal induced by the matrix is significant. Figure 2a shows cross-sectional relative-intensity profiles of three weak emission lines: Mn II 261.81 nm, Mn II 263.82 nm, and Mg II 279.08 nm, under the influence of a 0.05 M Ba matrix at a plasma forward power of 1100 W. The extreme edges of the profiles appear particularly noisy because

emission is the weakest there; the averaged signal-to-noise ratio was 2.5, 2.9, and 3.7 for the Mn II 261.81 nm, Mn II 263.82 nm, and Mg II 279.08 nm lines, respectively, at the edges. All three lines clearly suffer interference from the Ba matrix because the relative intensities deviate from unity; however, the curvature (in particular that for the Mn II 263.82 nm line) might not be evident. A statistical test would clearly improve this situation. Statistical Tests for Curvature. Limitation of Relative Range0.05−0.95. In our previous study,11 a method to evaluate profile flatness was developed. The range between the 5th and 95th percentiles of the relative intensity (or its equivalent, the determined concentration) profile was first calculated. A term denoted “relative range0.05−0.95”, defined as the ratio of the range to the mean of the relative-intensity values between the 5th and 95th percentiles, was then computed. For strong (compared to the ICP-background fluctuations, with a signal to backgroundnoise ratio >100) emission lines, the flatness of the relativeintensity profile, expressed as a relative range0.05−0.95, was found to be typically about 1% in conventional lateral-viewing ICPAES.11 This 1% baseline flatness was assigned as the reference. A predefined factor was then selected (e.g., 1.5× to 2×), and a threshold value was obtained by multiplying this predefined factor and the 1% reference value. Curvature in the relativeintensity profile was judged to be significant whenever the relative range0.05−0.95 was larger than the preset threshold. Although this approach was proven effective, this 1.5% or 2% threshold is valid only for relative-intensity spatial profiles that are not governed by noise; it is not applicable to situations in which the measurement noise is dominant. The relative-intensity profiles of the same set of emission lines as in Figure 2a, but in a drift test (no Ba was present), are presented in Figure 2b. The drift test is performed by measurement of the calibration standard after the matrix-effect experiment and represents the repeatability of the crosssectional profile. Although the relative intensities are all scattered around unity, indicating the absence of interference or drift, comparatively large fluctuations are observed because of the weak emission, particularly on the edges of the profiles. The span (i.e., difference between maximum and minimum) for the Mn II 263.82 nm line is around 0.43, which is comparable to that in the presence of a Ba matrix (span = 0.50 in Figure 2a). The computed relative ranges0.05−0.95 are 0.395 and 0.473 in the absence and presence of a matrix, respectively, and are very similar for the two samples. Moreover, in this situation in which the emission line is weak compared to that of the background, the relative range0.05−0.95 should be a strong function of the analyte concentration. As a result, the reference value of 0.395 for the Mn II 263.82 nm line is applicable only at this particular Mn concentration and under these exact plasma operating conditions. Of course, this reference relative range0.05−0.95 value can be determined here at the same Mn concentration in the standards and in the Ba-containing sample, only because all solutions are synthetic; in a real analysis, the analyte concentration is unknown, which will make the realization of a reference value difficult. If the analyte concentration is close to one of the calibration standards, the critical value of the relative range0.05−0.95 could be estimated from replicates of that calibration standard. However, the reference value obtained from such an approach would be only approximate. The ratios of the relative range0.05−0.95 in the presence and absence of the Ba matrix are 1.52, 1.20, and 2.04 for the

Figure 2. Cross-sectional relative-intensity profiles of three weak emission lines: Mn II 261.81 nm, Mn II 263.82 nm, and Mg II 279.08 nm (a) in the presence of 0.05 M Ba matrix and (b) during a drift test when no Ba was present. Total central gas flow rate was 0.90 L/min, plasma power was 1100 W, and injector diameter was 3 mm. 60

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Table 2. Statistics for the Cross-Sectional Relative-Intensity Profiles Presented in Figure 2 (panels a and b)a spectral line

mean

Mn II 261.81 nm Mn II 263.82 nm Mg II 279.08 nm

1.0784 0.8373 1.2491

Mn II 261.81 nm Mn II 263.82 nm Mg II 279.08 nm

0.9919 0.9990 0.9530

relative range0.05−0.95

σsuccessive

σsample

σsuccessive/σsample

z

p value

0.609 0.665 0.694

−4.50 −3.98 −3.70

3.4 × 10−6 3.4 × 10−5 0.00011

0.921 1.066 1.080

−1.09 0.975 1.19

0.138 0.165 0.117

In the Presence of Ba Matrix (cf. Figure 2a) 0.4699 0.1643 0.2698 0.4734 0.0838 0.1260 0.8023 0.2651 0.3820 In the Absence of Matrix (cf. Figure 2b) 0.3097 0.1160 0.1260 0.3947 0.1049 0.0984 0.3930 0.2102 0.1946

The p value (one-sided) represents the probability of obtaining the σsuccessive/σsample ratio as extreme as the experimentally observed ones, if the null hypothesis that two standard deviations are equal is true. Total number of data points (n) in the profile was 49. a

fluctuations. In contrast, σsuccessive indicates chiefly local fluctuations; the global pattern of the profile contributes very little to σsuccessive because it is computed through the difference between adjacent points, which excludes any slowly varying pattern in the data.20 Therefore, if the profile is flat (i.e., there is no drift or curvature), σsuccessive will be statistically equivalent to σsample. In contrast, if drift or curvature is present in the profile, σsuccessive will be statistically smaller than σsample.19 A comparison of σsuccessive and σsample offers a convenient means for unambiguous detection of any curvature in the cross-sectional profile. Methodologies to test statistical significance of the differences between these two standard deviations (or variances) are well-developed and can be easily applied.21,22 The ratio (η) between the squares of σsuccessive and σsample (i.e., their variances) is a well-characterized statistical method to test for randomness in a data sequence.21

Mn II 261.81 nm, Mn II 263.82 nm, and Mg II 279.08 nm lines, respectively. Although the values of the relative range0.05−0.95 are all larger for the Ba-containing samples, the difference is marginal (in particular for the Mn II 263.82 line), which can lead to ambiguity in the identification of curvature. Therefore, in this situation in which noise is dominant in the profile, the relative range0.05−0.95 approach11 might not be effective to assess profile flatness. As will be discussed below, if the relative range0.05−0.95 of a cross-sectional profile is greater than 1.5%, a further statistical evaluation using the σsuccessive/σsample ratio is needed. Conversely, whenever the relative range0.05−0.95 is below 1.5%, it is safe to assume that the profile is flat and no further statistical test is needed. Standard Deviation of Sample (σsample) and Successive Values (σsuccessive). Clearly, it would be better if a reference value at an analyte concentration identical to that in the unknown sample is not required and if curvature in a relativeintensity (or its equivalent, the determined concentration) profile could be gauged through examination of the profile alone. Assessment of flatness in a spatial profile is, in principle, identical to evaluation of drift in a temporal profile. Carré at al.19 employed a statistical method to diagnose drift in ICPAES. The theory behind the statistics is discussed in detail elsewhere20,21 and need not be repeated here. Briefly, profile flatness can be estimated by comparison of the sample standard deviation (σsample) and the standard deviation of successive values (σsuccessive). The σsample follows the classical definition and is

⎛σ ⎞2 successive ⎟⎟ η = ⎜⎜ ⎝ σsample ⎠

This ratio (η) is sometimes referred to as the von Neumann’s23,24 ratio; its statistical behavior has been wellcharacterized,23,24 and statistical tables25 are available in the literature. In addition, several approximation methods22,26,27 have been developed. It has been shown22 that for a large number of data points (n > 20), η converges to a normal distribution if all data are independent (i.e., no trend in the data), with a mean of 1 and a variance of (n − 2)/(n2 − 1). In other words, the ratio can be further transformed to a standard normal distribution through22

n

σsample =

∑i = 1 (xi − x ̅ )2 n−1

z = (η − 1)

The σsuccessive is defined as

Once the ratio is transformed into z, it becomes straightforward to compute the significance probability of an observed η and decide if a trend is present in the data. Let us go through this statistical method with an example. For the Mn II 263.82 nm cross-sectional profile in the presence of a Ba matrix (cf. Figure 2a), σsuccessive and σsample are 0.084 and 0.126, respectively. The ratio of these two SDs is 0.665. Transformation of this experimental σsuccessive/σsample ratio to the standard normal distribution results in a z value of −3.98. The probability of obtaining such a z value, if assuming that σsuccessive and σsample are identical and any difference is just due to random statistical nature, is only 3.4 × 10−5. Such a vanishing small probability clearly suggests that σsuccessive is statistically smaller than σsample for the Mn II 263.82 nm profile in the presence of a Ba matrix; hence, a curvature can be

n−1

σsuccessive =

n2 − 1 n−2

∑i = 1 (xi + 1 − xi)2 2(n − 1)

where n is the total number of data points in the profile and xi and x̅ represent the ith data point and the sample mean of the data in the profile, respectively. There are two types of fluctuations in a profile: (1) a local fluctuation defined as the reproducibility of the measurements as if the profile contains no specific pattern (i.e., when the profile is flat) and (2) pattern fluctuation as a result of slowly changing drift or curvature in the profile. When the temporal or spatial distance between the data points is much closer than the rate at which the drift or curvature occurs, σsample represents the overall point-to-point reproducibility, including both the local and pattern (if any) 61

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concluded, which in turn signifies the existence of interference. In contrast, the same cross-sectional profile in the absence of a matrix (cf. Figure 2b) yields statistically identical SD values; the σsuccessive and σsample are 0.105 and 0.098, respectively. Curvature is therefore not indicated, and one can draw the conclusion that no interference is detected. Table 2 details the relative range0.05−0.95, σsuccessive, σsample, and their ratios for the detection of curvature in the cross-sectional relative-intensity profiles in Figure 2 (panels a and b). The σsuccessive/σsample ratios are transformed to a z value of the standard normal distribution and then evaluated under a onesided test with the null hypothesis that the two standard deviations are statistically identical. The p value listed in Table 2 represents the probability of obtaining a standard deviation ratio as extreme as the experimentally observed ones if the null hypothesis is true. The σsuccessive/σsample ratios provide a clearer indication that curvature is present in all the cross-sectional relative-intensity profiles for the Ba-containing samples. In the presence of the Ba matrix, the p values for all three emission lines are less than 0.001 (i.e., ∼3 SD). Therefore, the hypothesis that σsuccessive < σsample is statistically valid, which in turn indicates that the profiles are not flat. In contrast, in the absence of a matrix, only the Mn II 261.81 nm line showed a slightly smaller σsuccessive than σsample; however, the z value is only −1.09 and the associated p-value is comparatively large (0.138), which suggests that the difference is not statistically significant. As a result, all three emission lines shown in Figure 2b do not exhibit statistically significant curvature. The Statistical Protocol with relative range0.05−0.95, σsample, and σsuccessive. Despite these findings, the relative range0.05−0.95 method should not be completely discarded and replaced by the σsuccessive/σsample ratio approach. As will be shown in the following example, the two procedures have different domains of validity and are complementary to each other; therefore, these two tests should be concurrently carried out for the evaluation of profile curvature. Typical fluctuations within a cross-sectional emission profile in axial viewing ICP-AES for a strong analyte emission line (e.g., with lowest signal to background-noise ratio > 100) are about 1 to 2%, slightly greater than but comparable to that for the vertical-emission profile in conventional lateral viewing ICP-AES (typically about 1%11). Therefore, whenever the relative range0.05−0.95 of a cross-sectional profile is below 1.5%, it is safe to assume that the profile is flat and no further statistical test is required. In fact, as will be shown in the example below, the σsuccessive/σsample ratio is not a reliable test in this situation. In contrast, when the relative range0.05−0.95 of a spatial profile is greater than 1.5%, the σsuccessive/σsample ratio provides useful information on the flatness of the profile. A simple criterion to classify a spatial profile as curved is that both conditions must be met: (a) relative range0.05−0.95 > 1.5% and (b) σsuccessive/ σsample ratio is statistically smaller than 1. Figure 3 shows the cross-sectional relative-intensity profiles of some representative emission lines during a drift test (i.e., no matrix is present). The lines are systematically offset by 0.05 relative-intensity units from each other. These six lines were chosen based on their different combinations of relative range0.05−0.95 and σsuccessive/σsample ratios (cf. Table S-1 of the Supporting Information). When the values of relative range0.05−0.95 are low (e.g., 0.56% for Zn I 213.87 nm and 0.67% for Fe II 259.94 nm), it implies that variations along the spatial profile are not significant, so the profiles should be

Figure 3. Cross-sectional relative-intensity profiles of six representative emission lines during a drift test. These six lines were chosen based on their different combinations of relative range0.05−0.95 and σsample/ σsuccessive ratios. With the exception of the Fe II 239.92 line, plots for other lines are systematically offset by 0.05 relative-intensity units. Total central gas flow rate was 0.80 L/min, plasma power was 1100 W, and injector diameter was 3 mm.

considered to be practically flat. However, because of the high degree of consistency in the measurements, any small bump along the profile will be interpreted as curvature by the σsuccessive/σsample statistical test. For example, the σsuccessive/σsample ratio for the Zn I 213.57 nm line is statistically smaller than unity (cf. Table S-1 of the Supporting Information); however, it is clear from Figure 3 that this “curvature” is normal due to noise in the highly reproducible profile. In other words, the small relative range0.05−0.95 by itself is sufficient to rule out curvature in this case. For a profile with a relative range0.05−0.95 value close to the 1.5% threshold (e.g., Mn II 260.57 nm and Fe II 239.92 nm), the σsuccessive/σsample ratio is helpful for judging profile flatness. Relatively large p values of 0.096 for the Mn II 260.57 nm and 0.0051 for the Fe II 239.92 nm lines were found for the σsuccessive/σsample ratios, indicating that the difference between σsample and σsuccessive is not statistically significant. As a result, curvature is statistically not likely in these two profiles, again in agreement with visual inspection (cf. Figure 3). When the relative range0.05−0.95 is significantly larger than the threshold (e.g., the Mg I 285.21 nm and the Fe I 371.99 nm lines), the existence of curvature is then determined solely by the σsuccessive/σsample ratio. Again, statistical tests indicate that σsuccessive is not significantly smaller than σsample for both lines (cf. Table S-1 of the Supporting Information); so both profiles can confidently be concluded to be flat. The statistical protocol described above for characterization of flatness in a relative-intensity spatial profile was verified with many experiments carried out under different experimental conditions (gas flow rate, power, and injector diameter). The criterion to detect curvature in a spatial profile, based on a combination of relative range0.05−0.95 and σsuccessive/σsample ratio, has proven to be sensitive and reliable (i.e., no false positives). It was found that the σsuccessive/σsample ratios are much lower than unity [with corresponding p values ≪0.001 (i.e., ∼3 SD) in most cases] if matrix interferences are significant (defined as >5% analytical bias). Therefore, a higher significance level can be employed without much increase in the risk of a false 62

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drift test was performed after the whole set of experiment, and the last sample in this series was the 20% v/v H2SO4 matrix. Interference from nitric acid at volumetric concentrations from 1 to 5% is very mild, and the resultant analytical biases are all within 5% in the center of the central channel (cf. Figure 4). The cross-sectional profiles for 1%, 2%, and 3% nitric acid are relatively flat with all determined relative range0.05−0.95 values within 1.5%; as a result, the interference cannot be flagged. However, this should not be a major concern because the magnitude of the interference is very low (only about 3%). For 5% nitric acid, the relative range0.05−0.95 value exceeded the preset 1.5% threshold and σsuccessive was found to be statistically smaller than σsample (with a z value of −6.05 and a corresponding p value 7 × 10−10, cf. Table S-2 of the Supporting Information). As a result, curvature, and hence, the presence of an interference, are indicated. Although the interference is modest in the presence of 5% HNO3 (the accuracy is still within 5%), the interference can already be unambiguously flagged. This finding suggests that the cross-sectional profile is highly sensitive to the matrix interference and that the proposed statistical protocol for the evaluation of profile flatness is effective. When the nitric acid concentration was increased to 10% or 20% v/v, the inaccuracy is more than 5% and clear curvature in the cross-sectional profiles can be observed either through visual inspection (cf. Figure 4) or through the statistical approach (cf. Table S-2 of the Supporting Information). The analytical biases caused by 3% v/v HNO3 are less than 5% in the center of the central channel for most emission lines. This weak interference effect makes the 3% v/v HNO3 a good candidate for further evaluation of the proposed statistical protocol. The relative-intensity profiles of several selected emission lines (same group as in Figure 3) in the presence of 3% v/v additional nitric acid are shown in Figure 5, and the statistics are summarized in Table S-1 of the Supporting Information. The profiles have been systematically shifted upward by 0.05 relative-intensity units for clarity. For the Fe II

negative but will ensure the rate of false positive to be kept to a negligible level. A significance level of 0.001 is therefore recommended. An alternative and possibly simpler approach is to use the z value directly and judge from everyday experience. For example, if one assumes that any data in a normal distribution that deviates from the mean by 3 standard deviations can be regarded as rare, one can then simply use the criterion of whether the magnitude of the z value is larger or smaller than 3 to classify a profile as curved or flat, respectively. Also, unlike the relative range0.05−0.95 in which the standard value will change with the signal-to-noise ratio of analyte emission, the same threshold (i.e., the p- or z values) applies to the statistical test for the σsuccessive/σsample ratio, regardless of the strength of the emission line. Let us now examine how these tests of curvature apply to the various classes of matrix interference. Application of the Statistical Protocol with Examples from Sample-Introduction-Related Matrix Interferences. Figure 4 shows the cross-sectional relative-intensity profiles of

Figure 4. Cross-sectional relative-intensity profiles of the Mn II 259.37 nm line in additional concentrations of nitric acid. The reference sample was prepared in 1% v/v nitric acid. Plasma-operating parameters were identical to those listed in the caption to Figure 3.

the Mn II 259.37 nm line in samples containing nitric acid at different volumetric concentrations. Table S-2 of the Supporting Information summarizes the statistics for the cross-sectional profiles in sulfuric and nitric acids. Crosssectional relative-intensity profiles for samples containing sulfuric acid are presented in the companion paper.12 The statistical test (cf. Table S-2 of the Supporting Information) confirms that the profiles for all sulfuric acid-containing samples are all curved, which agrees with visual inspection of the profiles.12 The result of the drift test for sulfuric acid is also included in Table S-2 of the Supporting Information. Its 1.67% relative range0.05−0.95 value is slightly higher than the 1.5% threshold; the p value for the observed σsample/σsuccessive ratio is 0.0012, which is only marginally higher than the preset 0.001 threshold. In this particular case, the drift-test profile can be concluded to be flat but it is very close to the boundary to be classified as curved. The comparatively poor reproducibility of the drift test might be related to the transient acid effects;28 the

Figure 5. Cross-sectional relative-intensity profiles of six representative emission lines in the presence of additional nitric acid at 3% v/v concentration. With the exception of the Fe II 239.92 nm line, data for other lines have been systematically offset by 0.05 relative-intensity units. Plasma-operating parameters were identical to those listed in the caption to Figure 3. 63

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sectional emission profiles become similar. The total excitation energies of the Ce−Er line pair differ by less than 0.7 eV, and all cross-sectional profiles for the Er II 302.27 nm line appeared flat in samples containing Ce at concentrations from 3 to 100 mg/L.12 Statistics performed on the σsuccessive/σsample ratios agree that the profiles exhibit no curvature (cf. Table S-3 of the Supporting Information), so the interference cannot be flagged. To further assess whether the cross-sectional emission profile can flag spectral interferences with line pairs that are close in total excitation energies, the Fe−Ru line pair was studied. The difference in the total excitation energies of Fe II 238.20 nm and Ru II 238.20 nm is about 0.8 eV (cf. Table 1). Figure 6

259.94 nm line, the relative range0.05−0.95 value is lower than the 1.5% threshold, so the profile is judged to be flat. For the Fe II 239.92 nm, Fe I 371.99 nm, and Mg I 285.21 nm lines, the σsuccessive/σsample ratio was found not to be statistically smaller than unity, so those profiles are also considered to be flat. For the Mn II 260.57 nm line, a p value of 1 × 10−5 was obtained for the σsuccessive/σsample ratio. Visual inspection of the profile reveals that it exhibits some marginal curvature (cf. Figure 5). For the Zn I 213.57 nm line, the profile in Figure 5 displays an unambiguous curvature (yet the analytical inaccuracy is within 5%, the Zn I 213.87 nm profile is offset by a total of 0.25 relative-intensity units); the σsuccessive/σsample ratio shows a p value of 1 × 10−15 (with a corresponding −7.9 z value), indicating that the pattern is very unlikely due to randomness. Application of the Statistical Protocol with Examples from Spectral Interferences. Five analyte−matrix (cf. Table 1) pairs were chosen for the investigation of spectral interferences. Some of the cross-sectional relative-intensity profiles were presented and discussed in the companion paper.12 Here, we will focus on the statistical treatment of the data. Table S-3 of the Supporting Information summarizes the statistical results for the cross-sectional relative-intensity profiles of the five studied spectrally interfering line pairs. For the As I 228.81 nm line, spectral interference from Cd at a concentration of 0.01 mg/L is negligible (mean relative intensity = 0.9985). Statistical treatment (cf. Table S-3 of the Supporting Information) of the cross-sectional profile classifies the profile as flat (p value = 0.231). At a Cd concentration of 0.03 mg/L, the spectral interference causes an averaged error of about 2.6%; statistical treatment of the data confirm that the observation σsuccessive < σsample is statistically valid (cf. Table S-3 of the Supporting Information). Even though the analytical error is comparatively minor, the interference can be confidently flagged. The cross-sectional relative-intensity profiles of the Er II 239.73 nm line in samples with varying concentrations of Co were also presented previously.12 The analytical bias caused by Co at a concentration of 0.3 mg/L was only about 1% and can be considered negligible. Statistical treatment of the profile data (cf. Table S-3 of the Supporting Information) supports this conclusion. The average error became about 5% when the Co concentration was increased to 1 mg/L. The previously12 presented cross-sectional profile exhibited marginal curvature on the two extremes. The p value, under the null hypothesis that σsuccessive is not smaller than σsample, is 0.00014 (a z value of −3.6) for the experimentally observed σsuccessive/σsample ratio. As a result, the profile will be classified as curved, and the interference will be flagged. The statistical test also clearly indicates the nonflat characteristics of the profile for the sample containing 3 and 10 mg/L Co (cf. Table S-3 of the Supporting Information), in which the spectral interference causes an average error of about 18% and 50%, respectively. The Ce−Fe line pair (Ce II 381.59 nm and Fe I 381.58 nm) produces spectrally interfering emission lines from different ionization states. The statistics of the cross-sectional profile data are included in Table S-3 of the Supporting Information. As expected from their different ionization states, distinct curvature in the relative-intensity plots for Ce was found for samples containing Fe. In the companion paper,12 we demonstrated with the Er−Ce line pair that spectral interference might not be readily recognized when the excitation and ionization energies of the spectral-line pairs are too close because their normalized cross-

Figure 6. Cross-sectional relative-intensity profiles for the Ru II 238.20 nm line under the influence of coexisting Fe from 0.03 to 1 mg/L. The concentration of Ru was 100 mg/L. Plasma operating parameters were identical to those listed in the caption of Figure 3.

shows the relative intensity plots for the Ru II line under spectral interference from Fe at concentrations from 0.03 to 1 mg/L. The averaged Ru II relative intensity in the presence of 0.03 mg/L Fe was only 1.01 and is regarded as negligible. Statistical evaluation of the profile (cf. Table S-3 of the Supporting Information) also suggests that it is flat. When Fe was present at 0.1 mg/L, the averaged Ru II relative intensity became 1.04. For other studied spectral-interference line pairs, which the total excitation potentials of the two lines are not close (i.e., the As−Cd, Er−Co, and Ce−Fe line pairs in Table S-3 of the Supporting Information), the spatial profile is sensitive enough to flag a 4% spectral interference. However, in this case, statistics of the profile classify the Ru−Fe profile as flat with a relatively large p value of 0.110. Only when the Fe concentration was further increased to 0.3 mg/L, in which the averaged Ru relative intensity became 1.14 (i.e., 14% error), the cross-sectional profile finally responded to the interference and expressed a curvature (p value for the experimental σsuccessive/ σsample ratio is 9 × 10−5). When Fe was present at 1 mg/L, the analytical bias was about 48%, and distinct curvature was also noted (cf. Table S-3 of the Supporting Information). This Fe− Ru line pair confirms the previous observation12 that the crosssectional emission profile could be insensitive to spectral interferences when the total excitation potential (ionization + excitations energies) of the interfering line is close to that of the analyte emission line. 64

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Analytical Chemistry

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(13) Miller, T. M. In CRC Handbook of Chemistry and Physics, 92th ed.; Haynes, W. M., Lide, D. R., Eds.; CRC Press: Boca Raton, FL, 2011; pp 10_196−110_198. (14) Kurucz, R. L.; Bell, B. 1995 Atomic Line Data. In Kurucz [CDROM], No. 23, Smithsonian Astrophysical Observatory: Cambridge, MA, 1995, http://www.cfa.harvard.edu/amp/ampdata/kurucz23/ sekur.html (accessed Oct 30, 2012). (15) NIST Atomic Spectra Database, version 5, No. 78. http://www. nist.gov/pml/data/asd.cfm (accessed Oct 30, 2012). (16) Chan, G. C. Y.; Hieftje, G. M. J. Anal. At. Spectrom. 2009, 24, 439−450. (17) Chan, G. C. Y.; Hieftje, G. M. Spectrochim. Acta, Part B 2006, 61, 642−659. (18) Chan, G. C. Y.; Hieftje, G. M. Spectrochim. Acta, Part B 2004, 59, 163−183. (19) Carre, M.; Poussel, E.; Mermet, J. M. J. Anal. At. Spectrom. 1992, 7, 791−797. (20) Mark, H.; Workman, J., Jr. In Statistics in Spectroscopy, 2nd. ed.; Academic Press: San Diego, CA, 2003; pp 59−69. (21) Holmes, D. S.; Mergen, A. E. Quality and Reliability Engineering International 1995, 11, 171−174. (22) Bissell, A. F.; Williamson, R. J. Journal of Applied Statistics 1988, 15, 305−323. (23) von Neumann, J. Ann. Math. Stat. 1941, 12, 367−395. (24) von Neumann, J. Ann. Math. Stat. 1942, 13, 86−88. (25) Hart, B. I.; von Neumann, J. Ann. Math. Stat. 1942, 13, 207− 214. (26) Bingham, C.; Nelson, L. S. Technometrics 1981, 23, 285−288. (27) Nelson, L. S. Journal of Quality Technology 1998, 30, 401−402. (28) Stewart, I. I.; Olesik, J. W. J. Anal. At. Spectrom. 1998, 13, 843− 854.

CONCLUSIONS As a further step toward automated matrix-effect detection, a statistical approach was developed to classify spatial profiles as flat or curved. Similar to the previous study with lateral-viewing ICP-AES, a spatial profile is classified as flat (no interference exists) if its relative range0.05−0.95 value is less than a critical threshold (chosen to be 1.5%). If the relative range0.05−0.95 of a spatial profile is greater than 1.5%, then the σsuccessive/σsample ratio provides useful information on the flatness of the profile. A profile is then classified as curved only if its σsuccessive is statistically smaller than σsample. A major advantage of this new protocol is that an analyte-concentration-dependent reference value is not required, and the classification is based on examination of only the spatial determined-concentration profile of the unknown sample. Also, established statistical tests can be applied to the experimentally observed σsuccessive/ σsample ratio, at any desired confidence level. Further, the statistical treatment is simple and can be easily programmed into a computer for automated verification of analytical results, with the potential to be implemented in future expert systems.

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ASSOCIATED CONTENT

S Supporting Information *

This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +1 812 855 7905. Fax: +1 812 855 0985. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are grateful to Horiba Jobin-Yvon (Longjumeau, France) for loaning the ACTIVA ICP spectrometer used in this work. This research was supported by the U.S. Department of Energy through Grant DE-FG02-98ER14890.

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REFERENCES

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