ANALYTICAL PRECISION AND DETECTION LIMITS

Two measurable quantities relate to precision in EMP analysis of phosphates. The first quantity is the uncertainty of the analysis itself, i.e., standard deviation, which is the main measure of the uncertainty of either thermometry estimates or chemical age. The second quantity is the minimum detection limit, i.e., the smallest concentration of an element of interest generating characteristic X-ray counts that are statistically distinguishable from background X-rays. 

Characteristic X-rays are emitted in time, and, consequently, obey Poisson statistics, with the standard deviation a for N X-ray counts equal to (N)i and a standard deviation on the count rate (counts per s) of (N) / j e concentration of an element is generally assumed to be proportional to the total number of peak minus background counts (Scott et al. 1995), and for a count rates of Np/tp and Ne/tB (peak and background, respectively), the standard deviation (a) and standard error (e) are given by, respectively  

The standard error is identical to the relative (%) standard deviation, since ap.B relative = a/N = Sp-B. The standard deviation and standard error of the k-ratio are calculated by summing the uncertainties in both calibration of the standard (std) and analysis of the unknown (unk), i.e., 

For a relative standard deviation on X-ray counts, and by extension, composition, of 1%, 10,000 peak minus background counts of the desired element must be accumulated. Assuming that X-ray production scales linearly with analysis current, count accumulation to the desired precision can be viewed as a function of the nA sec counting product. 

Detection limits of less than 0.1 wt % (1000) ppm for FREE require a roughly 1000-2000 nA sec analysis, and the same analysis time-current product generates detection limits ranging from approximately 620 ppm for U, 1200 ppm for Th, 820 ppm for Pb, 240 ppm for Y, and 800-3500 for the HREE. A detection limit of less than 500 ppm for all elements in REE phosphate requires roughly 150000 nA sec analyses, and a detection limit of 200 ppm Pb (suitable for chemical dating of low-Th Paleozoic monazite) requires approximately 35000 nA sec analyses, or 140 s on each peak and background at an analysis current of 250 nA. 

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