Worked Examples in X-Ray Analysis

The purpose of this book is to provide the reader with a series of work­ ed examples in X -ray spectrometry and X -ray diffractometry, in such a way that each example can be treated either as a posed question, i. e. one to which the reader must himself provide an answer, or as a guide to the method of treating a similar problem. The latter, of course, also pro­ vides a check on the answer produced by the reader. Although much basic theory can be derived by study of this work the first intention of the book is not to provide a source of basic theoretical knowledge in X -ray analy­ sis. It is hoped that the book will be utilized more as a guide line in the tackling of theoretical and practical problems and as a means of estab­ lishing whether or not the reader is able to work out for himself a certain type of problem. For example, the series of examples on counting statis­ tics has been chosen in such a way that after working through and under­ standing these, the reader should be able to handle most of the calculations that he is likely to come up against in this area. Front Matter....Pages i-xi Characteristic spectra Moseley’s law....Pages 1-3 Characteristic spectra — Prediction of possible transitions....Pages 4-5 Continuous spectra — use of Kramers’ formula....Pages 6-8 Continuous radiation — Scattered radiation....Pages 9-11 Detector resolution....Pages 12-13 Dispersion as a function of ‘d’ spacing....Pages 14-15 Choice of collimator/crystal combination....Pages 16-18 Pulse height selection — crystal fluorescence....Pages 19-21 Pulse height selection — pulse height variation....Pages 22-24 Detectors — double plateaux....Pages 25-27 Choice of detectors....Pages 28-29 Count rate differences with Geiger and proportional counters....Pages 30-31 Dispersion of the diffractometer....Pages 32-34 Removal of sample fluorescence....Pages 35-39 Spurious peaks in X-ray diffractograms....Pages 40-42 Extra lines in X-ray diffractometry....Pages 43-45 Counting statistics — variation of standard deviation with counting time....Pages 46-47 Estimation of error introduced by ignoring the background....Pages 48-50 Trace analysis — derivation of detection limit expression....Pages 51-53 Choice between fixed time and fixed count....Pages 54-55 Choice between ratio and absolute counting methods....Pages 56-57 Variation of limit of detection with analysis time....Pages 58-59 Analytical error due to counting statistics....Pages 60-61 Particle statistics in X-ray diffractometry....Pages 62-64 Determination of traces of lead in oil (absolute measurement)....Pages 65-67 Determination of CaO in cement (ratio measurement)....Pages 68-70 Determination of nickel in steel (with dead time correction)....Pages 71-73 Calculation of matrix absorption and prediction of absorption effects....Pages 74-75 Calculation of absorption coefficients and absorption effects....Pages 76-77 Absorption correction involving primary and secondary absorption....Pages 78-79 Calculation of quantity of heavy absorber needed to minimize matrix effects....Pages 80-81 Use of α correction factor (intensity correction)....Pages 82-85 Use of α correction factors (concentration correction)....Pages 86-91 Excitation probability....Pages 92-94 Quantitative diffractometry — determination of Anatase in Rutile....Pages 95-97 Quantitative X-ray diffractometry use of internal standard....Pages 98-99 Estimation of expected intensities in mixtures....Pages 100-101 Quantitative x-ray diffractometry....Pages 102-104 Determination of dead time....Pages 105-107 Estimation of gold plating thickness....Pages 108-109 Measurement of coating thickness on irregular shaped objects....Pages 110-112 Background variation....Pages 113-115 Use of primary filters for removal of characteristic tube lines....Pages 116-117 Calculation of ß filter thickness and transmission....Pages 118-119 Utilization of the ß filter and pulse height selector in diffractometry....Pages 120-122 Determination of lattice constants for a cubic lattice....Pages 123-125 Line broadening....Pages 126-129 Back Matter....Pages 130-133