[B._Beckhoff,_et_al.]_Handbook_of_Practical_X-Ray_(b-ok.org).pdf

Griffiths and webster discussed the derivation of

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Griffiths and Webster discussed the derivation of matrix correction equa- tions in detail. They adopted the modified Lachance–Traill equation [83]. The calibration constants of the X-ray intensity terms were determined by regres- sion analysis and the correction factors were calculated with the ALPHAS program which was theoretically derived by de Jongh [84]. The two kinds of RMS-differences of authenticated sample analysis are shown in Table 1.3. The
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1 Introduction 25 values in the upper line are the calculated results based on normal matrix cor- rection in the ALPHAS program, and the second values in the lower line are derived with the use of correction coefficients calculated under the condition of a fixed 60:20:20 constituent sample. Itoh, Sato, Ide, and Okochi studied the analysis of high alloys using the theoretically calculated correction coefficients of the ALPHAS program. They also compared the ALPHAS program and the JIS correction method and clar- ified that there were no differences between them. The results of analytical accuracy were two or more times higher than those of X-ray analytical preci- sion [85]. Rigaku Industrial Corporation analyzed high nickel alloys of NBS and specially prepared samples. For the matrix correction, they adopted their own fundamental parameter method and prepared calibration curves, which were used for the determination of the constituent elements. The RMS-differences in these studies were fairly small. 1.4.3 Segregation Influencing Analytical Accuracy The influence of inhomogeneity phenomena on analytical accuracy is one of the most important factors. The internal soundness of an ingot which was studied by Marburg [86] conferred that the inhomogeneity induced in the cooling process from molten metals intimated strong effects to analytical problems to be solved. Stoops and McKee studied the reduction of analytical accuracy for ti- tanium concentrations owing to segregation of nickel base alloys of M252 (19 wt% chromium, 10 wt% cobalt, 10 wt% molybdenum, 2.5 wt% titanium, 3 wt% iron, 1 wt% aluminum, 0.15 wt % carbon, and 0.35 wt% silicon). As a major portion of the titanium could be found in the grain boundaries of carbide or carbon-nitride particles, the differences between regular chemical and X-ray analysis values indicated a wider distribution, which was 5–10% of the amount of titanium present. When chemical analysis was carried out using samples scooped up from the X-ray analytical surface, X-ray values were nearly equal to that of chemical analysis, i.e., 0.5–1% of the amount of titanium present [87]. It is well known that in rapidly cooled steel, a low concentration of man- ganese and impurity sulfur are dispersed and that a high analytical accuracy in manganese and sulfur determination can be found. In sufficiently annealed steel, small particles of manganese sulfide are precipitated in the grain bound- aries of steel grains and large deviations of Mn-K α and S-K α X-rays are found [88].
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