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Effects on Accuracy and Detection Limits

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Effects on Accuracy and Detection Limits WHITE Sensitivity, Background, Noise, and Calibration in Atomic PAPER Spectroscopy: Effects on Accuracy and Detection Limits Introduction Proper calibration in atomic spectroscopy and an understanding The three most common atomic spectroscopy techniques of uncertainty is fundamental to achieving accurate results. This are atomic absorption (AA) spectroscopy, ICP optical emission paper provides a practical discussion of the effects of noise, error spectroscopy (ICP-OES) and ICP mass spectrometry (ICP-MS). and concentration range of calibration curves on the ability to Of these, ICP-OES and ICP-MS are very linear; that is, a plot determine the concentration of a given element with reasonable of concentration vs. intensity forms a straight line over a accuracy. The determination of lower limits of quantitation and wide range of concentrations (Figure 1). AA is linear over a lower limits of detection will also be discussed. much smaller range and begins to curve downward at higher Results accuracy is highly dependent on blank contamination, concentrations (Figure 2). Linear ranges are well understood, linearity of calibration standards, curve-fitting choices and the and, for AA, a rule of thumb can be applied to estimate the range of concentrations chosen for calibration. Additional factors maximum working range using a non-linear algorithm. include the use of internal standards (and proper selection of This paper will discuss the contributions of sensitivity, internal standards) and instrumental settings. background, noise, calibration range, calibration mathematics This paper is not intended to be a rigorous treatment of statistics and contamination on the ability to achieve best accuracy and in calibration; many references are available for this, such as lowest detection limits. “Statistics in Analytical Chemistry1". The techniques of atomic spectroscopy have been extensively developed and widely accepted in laboratories engaged in a broad range of elemental analyses, from ultra-trace quantitation at the sub-ppt level, to trace metal determination in the ppb to ppm range, to major component analysis at percent level composition. A fundamental part of analysis is establishing a calibration curve for quantitative analysis. A series of known solutions is analyzed, including a “blank” prepared to contain no measurable amounts of the elements of interest. This solution is designated as “zero“ concentration and, together with one or more known standards, comprises the calibration curve. Samples are then analyzed and compared to the mathematic calculation of signal vs. concentration established by the calibration standards. Unfortunately, preparation of contamination-free blanks and diluents (especially when analyzing for many elements), perfectly accurate standards, and perfect laboratory measurements are all impossible. Figure 1. Example of a linear calibration curve in ICP-MS. graphite furnace AA, based on a more thorough and widely- ranging definition2. However, these procedures are specific to water, wastewater and other environmental samples. There are few widely accepted approaches for other matrices such as food, alloys, geological and plant materials, etc. It is left to the lab doing the analysis to establish an approach to answer the question “How low a concentration of a given element can we detect in a particular sample matrix?” Because there exists a long history in most labs and many different techniques are employed (e.g., GC, LC, UV/Vis, FT-IR, AA, ICP, and many others) there are many opinions and approaches to this subject. How, Then, Do We Establish “How Low We Can Go”? The simplest definition of a detection limit is the lowest concentration that can be differentiated from a blank. The blank should be free of analyte, at least to the limit of the technique used to measure it. Assuming the blank is “clean”, what is the Figure 3 lowest concentration that can be detected above the average blank signal? Figure 2. Example of a non-linear calibration curve in AA. One way to determine this is to first calibrate the instrument Detection Limits – “How Low Can We Go?” with a blank and some standards, calculate a calibration curve, Under ideal conditions, the detection limits of the various and then attempt to measure known solutions as samples at techniques range from sub part per trillion (ppt) to sub part per lower and lower concentrations until we reach the point that million (ppm), as shown in Figure 3. As seen in this figure, the the reported concentration is indistinguishable from the blank. best technique for an analysis will be largely dependent on the Unfortunately, no measurement at any concentration is perfect levels that need to measured, among other considerations. – that is, there is always an uncertainty associated with every measurement in a lab. This is often called “noise”, and this uncertainty has several components. (A detailed discussion of sources of uncertainty is also a lengthy discussion3 and beyond the scope of this document.) So, to minimize uncertainty, it is common to perform replicate measurements and average them. The challenge, then, is to find the lowest concentration that can be distinguished from the uncertainty of the blank. This can be estimated by using a simple statistical approach. For example, U.S. EPA methods for water use such an approach. After calibration, a blank is run as a sample 10 times, the 10 reported concentrations are averaged and the standard deviation is calculated. A test for statistical significance is applied (the Student’s t-test) to calculate what the concentration would be that could be successfully differentiated from the blank with a high degree of confidence. In the U.S. EPA protocol, a 99% confidence is required. This equates Detection Limit Ranges (μg/L) to three times the standard deviation of 10 replicate readings. This is also known as a 3σ (sigma) detection limit and is designated as Figure 3. Detection limit ranges of the various atomic spectroscopy techniques. the Instrument Detection Limit (IDL) for U.S. EPA methods. It is important to realize that detection limits are not the same as It is important to note that the statistically calculated detection reporting limits: just because a concentration can be detected does limit is the lowest concentration that could even be detected in not mean it can be reported with confidence. There are many a simple, clean matrix such as 1% HNO3 – it is not repeatable or factors associated with both detection limits and reporting limits reliable as a reported value in a real sample. which distinguish each, as will be seen in the following discussion. To be more repeatable, the signal (with its associated uncertainty) A discussion of detection limits can be lengthy and is subject must be significantly higher than the uncertainty of the blank, to many interpretations and assumptions – there are even perhaps 5-10 times the standard deviation of the blank. This is a several definitions of “detection limits”. In atomic spectroscopy, judgment by the lab as to how confident the reported value should there are some commonly accepted approaches. Under some be. This concentration level might be called the lowest quantitation analytical protocols, the determination of detection limits is limit, sometimes known as PQL (practical quantitation limit), LOQ explicitly defined in a procedure, as in U.S. EPA methods 200.7 (limit of quantitation) or RL (reporting limit). There are no universally and 6010 for ICP, 200.8 and 6020 for ICP-MS, and 200.9 for accepted rules for determining this limit. 2 Again, the EPA has guidelines in some methods for water samples limits. For example, if contamination is present, a 10-fold increase that establish a lower reporting limit as a concentration that can in signal will also increase the background 10-fold. In an ideal be measured with no worse than +/- 30% accuracy in a prepared situation (i.e. the absence of high background or excessive noise) standard. This rule is only applicable to the specific EPA method detection limits theoretically improve by the square root of the and in water samples. increase in signal intensity (i.e. a 9x increase in intensity will improve Many labs apply the EPA detection limit methodologies simply detection limits 3x). However, as we will see, background level and because there are few commonly accepted and carefully defined noise have as much of a contribution to detection limits as intensity. approaches for other sample types. Some industries follow In ICP-OES and ICP-MS, a common way to express intensity ASTM, AOAC or other industry guidelines, and some of these is “counts per second”, or cps. We will use this unit in the procedures include lower-limit discussions. following discussion. When analyzing a solid sample, the sample must first be brought Background Signal Plays an Important Role in into solution, which necessarily involves dilution. The estimation Detection Limits of detection or quantitation limits now needs to account for the Consider an example with a signal that gives an easily measurable dilution factor and matrix effects. For example, if 1 g of sample is intensity of 1000 cps. However, if the background is 10,000 cps dissolved and brought to a final volume of 100 mL, the detection the signal is small relative to the background. It is common to limit in the solution must be multiplied by the dilution factor express the relationship between signal and background as the (100x in this example) to know what level of analyte in the “signal-to-background ratio” or S/B. (This is often referred to as original solid sample could have been measured if it could “signal-to-noise” or S/N, but background and noise are two distinct have been analyzed directly. characteristics). The above example would have an S/B of 0.1. However, if the background were only 1 cps, the same 1000 cps To use the statistical estimate technique (3σ detection limit), a “clean” matrix sample must be available, but this is not always signal would have a S/B of 1000, or 10,000 times better than the possible.
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