The secondary fluorescence correction for X‐ray microanalysis in the analytical electron microscope

Abstract

SUMMARY A general formulation for the secondary fluorescence correction is presented. It is intended to give an intuitive appreciation for the various factors that influence the magnitude of the secondary fluorescence correction, the specimen geometry in particular, and to serve as a starting point for the derivation of quantitative correction formulae. This formulation is primarily intended for the X‐ray microanalysis of electron‐transparent specimens in the analytical electron microscope (AEM). The fluoresced intensity, IYX, is expressed relative to the primary intensity of the fluorescing element, IY, rather than to that of the fluoresced element, IX, as has been customary for microanalysis. The importance of this choice of IY as a reference intensity for the electron‐transparent specimens examined in the AEM is discussed. The various factors entering the secondary fluorescence correction are grouped into three factors, representing the dependencies of the correction on specimen composition, X‐ray fluorescence probability and specimen geometry. In principle, an additional factor should be appended to account for the difference in detection efficiencies of the fluoresced and fluorescing X‐rays; however, this factor is shown to be within a few per cent of unity for practical applications of the secondary fluorescence correction. The absorption of secondary X‐rays leaving the specimen en route to the detector is also accounted for through a single parameter. In the limit that the absorption of secondary X‐rays is negligible, the geometric factor has the simple physical interpretation as the fractional solid angle subtended by the fluoresced volume from the perspective of the analysed volume. Studies of secondary fluorescence in the published literature are compared with this physical interpretation. It is shown to be qualitatively consistent with Reed's expression for secondary fluorescence in the electron probe microanalyser and with the specimen‐thickness dependence of the Nockolds expression for the parallel‐sided thin foil. This interpretation is also used to show that the ‘sec α’ dependence on specimen tilt in the latter expression is erroneous and should be omitted. The extent to which extrapolation methods can be used to correct for secondary fluorescence is also discussed. The notion that extrapolation methods, by themselves, can be used to correct for secondary fluorescence is refuted. However, extrapolation methods greatly facilitate secondary fluorescence correction for wedge‐shaped specimens when used in conjunction with correction formulae.

FIB Preparation of a NiO Wedge-Lamella and STEM X-Ray Microanalysis for the Determination of the Experimental k(O-Ni) Cliff-Lorimer Coefficient

“…It must be noted that this result would not be accurate in the presence of a significant contribution to the primary OK intensity from the secondary fluorescence due to the NiL X-rays. However, the calculation of this effect according to the formulae reported in the literature (Nockolds et al, 1980; Anderson et al, 1995) shows that this contribution is of the order of 10 −3 , thus quite negligible.…”

What Remains to Be Done to Allow Quantitative X-Ray Microanalysis Performed with EDS to Become a True Characterization Technique?

“…derived an absorption correction for thin films of uniform thickness when the line B fluoresces A~or the line A fluoresces B!. Anderson et al 1995! have developed formulas for fluorescence corrections involving more complex geometries.…”

“…where the summation for each element (A and B) is taken for the n characteristic lines present in the spectrum, having an energy greater than the characteristic line of element A or B. Nockolds et al (1980) derived an absorption correction for thin films of uniform thickness when the line B fluoresces A (or the line A fluoresces B). Anderson et al (1995) have developed formulas for fluorescence corrections involving more complex geometries. The Cliff and Lorimer method assumes that the sum of the mass fraction of all the elements equals 1.…”

Characteristic and Continuum Fluorescence in Electron Beam X-ray Microanalysis

“…Later work by Nockolds et al 15 and Twigg and Fraser 16 indicated a much larger correction for a similar sample and it was shown that the discrepancy was caused by a mathematical error in the earlier result. Most of the thin film samples used for analysis can be described as wedges rather than parallel-sided foils and a more general correction procedure to deal with the range of specimen geometries in thin film analysis has been developed by Anderson et al 17 .…”