By Richard S Varga
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Extra info for Topics in polynomial and rational interpolation and approximation
200 (2Q) and 6. 08 X. planes, may well be confused with a regular diffraction line. This effect may be distinguished from other spurious peaks as they should only occur for compounds having a high concentration of elements like Cs, Ba, La and Ce with absorption edges not too far above that of Xe. 45 QUESTION 17 Counting statistics - variation of standard deviation with counting time A A certain analysis line gave 800 c/s under certain instrumental conditions. Given that the standard deviation ( ct) of a given number of f counts (N) is equal to N, calculate the standard deviation expected in a counting time of 20 seconds.
_ l -- r-- r. Standard deviol ioro Fig. lO f'/o) 47 QUESTION 18 Estimation of error introduced by ignoring the background Whenever X-ray intensity measurements are made on a selected peak, occuring at a certain setting of the goniometer, some fraction of the measured counting rate is always due to background. The significance of this background is dependent on its relative magnitude, and it is often difficult to judge whether or not it can be ignored in the calculation of the counting error. The true counting error e % is related to the peak RP and background R• counting rates in the following way: 100 1 e%= yT· yRp-YR.
The effect was observed both in specimens containing only low atomic number elements and specimens containing high atomic number elements. The patterns were always taken using Cu radiation, proportional counter (Xe -filled) and pulse height selection. The pulse height selector was set at the 45% acceptance level since the resolution of the counter (peak width at half height) was 18% for Cu Ka radiation. Explain the occurence of this peak for a pure quartz specimen, using the following experimental findings.
Topics in polynomial and rational interpolation and approximation by Richard S Varga