Effect of the Silicon Drift Detector
Figure 2: Spectrum from a Ni/Hf sample acquired with an SDD. Accelerating voltage=20 kV; counting time=30 seconds; count rate 13 kcps. Calculated background and spectrum reconstruction are shown.
both P and B and dividing the equations. Tus, (P/B)i ()ai
PB cq S S
/ =ω ,, ai ii
ai ch
ai br
, ,
() ()
RA F RA
ai ch
,
ai br
, Compared to the eZAF formula, some parameters dropped
out of Equation 5 so that the number of unknown variables is equal to the number of equations. Te solution does not require normalization of the composition values so that they sum to 100%. Tere is no physical effect to generate bremsstrahlung radiation by other X-rays (all bremsstrahlung is generated by charged particles), thus there is no F-factor for the bremsstrahlung model. Tis P/B model has been developed and improved from the 1980s until today [3,13,2,14]. All ZAF factors within Equation 5, except the F-correction, are ratios between characteristic radiation and bremsstrahlung. Comparison of the two
methods. Both approaches have advantages and disadvantages. Te original design idea was that the P/B would always be the method of choice if the sample surface is not flat (particles, rough surfaces) because many effects in excitation and absorption cancel out. But during early work with this method, it was found that the P/B produced good accuracy [15] in general, even for flat specimens. Te challenge with PeBaZAF method is to extract the proper P/B values from a measured spectrum. An accurate background deter- mination is required at the same
repre-
sents the number of net characteristic (ch) peak counts divided by the measured bremsstrahlung (br) at the same energy:
(5)
energy as the peak, and the EDAX soſtware pro- vides this with an iterative bremsstrahlung calcu- lation [4]. But the small number of counts in the measured background intensity (B) significantly influences the value of P/B, causing the PeBaZAF to exhibit a worse value of precision compared to eZAF. Tis means that PeBaZAF has poorer repeatability, which is detrimental for compari- son tasks. On the other hand, the ZAF correction in the PeBaZAF is smaller (correction factors are closer to 1), leading to fewer systematic errors and good mean accuracy. Te eZAF method exhibits larger correction factors, which reduces accuracy, but it has better precision. So one could say these two methods are “complementary” [16]. To evaluate the expected uncertainty with
these quantitative measurements, an error parameter was calculated for each result. Te parameter Err% is based on company soſtware
that combines the level of systematic error in the quantitative method with the level of precision in the measurement. Tus, if the number of counts is large enough, the precision part will be small, leaving Err% to report primarily the systematic error, which includes uncertainties with the inputs for, and the formulation of, the ZAF matrix correction method.
Results Figure 4 shows how the accuracy and precision of these meth-
ods play out in an analysis of GaP. Te top two tables show results with a low total number of counts typical of a Si(Li) spectrometer. Te eZAF method has relatively large correction factors, which results in relatively large systematic errors, but the precision in
Figure 3: Two ways of representing standardless ZAF results. (top) Net-count-based eZAF analysis of a Ni/Hf sample with “classical” k-ratio notation; all corrections are in relation to estimated “pure” element standards (Equa- tion 3). (bottom) Generic standardless notation where all corrections are in relation to primary electron excited X-rays (Equation 4). The standardless unnormalized results were obtained using a single reference measurement made on pure Cu to determine the absolute relation. Note that the measurement input and the final analytical results are identical. The difference is only the notation of presented factors. The calculated error is based on dif- ferent assumptions for each correction. Only the second view is a correct depiction of the corrections employed in standardless case.
2020 March •
www.microscopy-today.com 37
Page 1 |
Page 2 |
Page 3 |
Page 4 |
Page 5 |
Page 6 |
Page 7 |
Page 8 |
Page 9 |
Page 10 |
Page 11 |
Page 12 |
Page 13 |
Page 14 |
Page 15 |
Page 16 |
Page 17 |
Page 18 |
Page 19 |
Page 20 |
Page 21 |
Page 22 |
Page 23 |
Page 24 |
Page 25 |
Page 26 |
Page 27 |
Page 28 |
Page 29 |
Page 30 |
Page 31 |
Page 32 |
Page 33 |
Page 34 |
Page 35 |
Page 36 |
Page 37 |
Page 38 |
Page 39 |
Page 40 |
Page 41 |
Page 42 |
Page 43 |
Page 44 |
Page 45 |
Page 46 |
Page 47 |
Page 48 |
Page 49 |
Page 50 |
Page 51 |
Page 52 |
Page 53 |
Page 54 |
Page 55 |
Page 56 |
Page 57 |
Page 58 |
Page 59 |
Page 60 |
Page 61 |
Page 62 |
Page 63 |
Page 64 |
Page 65 |
Page 66 |
Page 67 |
Page 68 |
Page 69 |
Page 70 |
Page 71 |
Page 72 |
Page 73 |
Page 74 |
Page 75 |
Page 76
