The Use of Tracer Experiments and Monte Carlo Calculations in the φ(ρz) Determination for Electron Probe Microanalysis

Abstract

Electron Probe Microanalysis (EPMA) is a well-established technique for the quantitative elemental analysis of solid materials on a microscopic scale. For a reliable quantification of the characteristic x-ray measurements an appropriate set of standards would be necessary, to cover all possible elements and compounds. In practice only a limited set of pure elements or compounds is available. Therefore for a general use of the technique the relation between the emitted x-ray intensity and the weight fraction c _i of the emitting element in the sample should be known for all elements and their possible combinations in compounds. Following the work of Castaing [1] one can write the general form for the emitted primary intensity of element i-radiation:

EquationSource% MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysamaaDa % aaleaacaWGPbaabaGaamyzaaaakiabg2da9iaadogacaWGVbGaamOB % aiaadohacaWG0bGaaiOlaiabgwSixlaadogadaWgaaWcbaGaamyAaa % qabaGccqGHflY1cqaHjpWDdaWgaaWcbaGaamyAaaqabaGccqGHflY1 % caWGrbWaaSbaaSqaaiaadMgaaeqaaOWaaeWaaeaacaWGfbWaaSbaaS % qaaiaaicdaaeqaaaGccaGLOaGaayzkaaWaa8qmaeaacqaHvpGzdaWg % aaWcbaGaamyAaaqabaGcdaqadaqaaiabeg8aYjaadQhaaiaawIcaca % GLPaaaciGGLbGaaiiEaiaacchadaqadaqaaiabgkHiTiabeE8aJnaa % BaaaleaacaWGPbaabeaakiabeg8aYjaadQhaaiaawIcacaGLPaaaca % WGKbGaeqyWdiNaamOEaaWcbaGaaGimaaqaaiabg6HiLcqdcqGHRiI8 % aaaa!6A7C!]]</EquationSource><EquationSource Format="TEX"><![CDATA[$$I_i^e = const. \cdot {c_i} \cdot {\omega _i} \cdot {Q_i}\left( {{E_0}} \right)\int_0^\infty {{\phi _i}\left( {\rho z} \right)\exp \left( { - {\chi _i}\rho z} \right)d\rho z} $$

(1)

Q _i is the ionization cross section for the ith level, c _i the weight fraction of element i, ω _i , the fluorescent yield of the ith level, ρz the mass depth and χ _i = (μ/ρ) cos θ with the absorption coefficient μ/ρ and the take-off angle θ. φ _i is the absolute distribution of the characteristic x radiation excited by the electrons in a depth ρz of the target.