Analysis of geometric factors for an X-ray fluorescence analyzer designed via the Monte Carlo method

Abstract

Abstract. This paper presents a theoretical study on the design of an X-ray fluorescence (XRF) analyzer. The relative geometric positions of the analyzer's source, detector and specimen are emphasized, which impacts the analyte's characteristic X-ray fluorescence counts. The theoretical formula for the X-ray fluorescence intensity was derived. The geometric factors (angle and distance) were simulated using Monte Carlo Neutron-Particle Transport Code MCNP5. The Cu's X-ray characteristic peak counts were calculated. These Monte Carlo model calculations analyzed two types of geometry changes. The best geometric positions for the XRF analyzer had the incident angle for the excitation source (Į) equivalent to the exit angle for the specimen's characteristic X-ray (ȕ). The maximal characteristic X-ray peak counts were obtained when Į and ȕ were orthogonal, and the minimum counts were obtained when parallel. To increase the fluorescence counts, the source and detector should be set as close to the specimen as possible. This method and these conclusions can provide technical guidance for designing XRF analyzers. Key words: Geometric factors; X-ray fluorescence analyzer; Monte Carlo method; MCNP code 1 Instruction X-ray fluorescence (XRF) analyzers are one of the most important analytical instrument types for element analyses [1][2][3][4][5][6]. The analyte's characteristic X-ray fluorescence counts relate not only to its physical and chemical properties but also the geometric positions of the source, specimen and detector [7][8][9]. The XRF analyzer's geometric setup can change the detector's excitation area, detection area and X-ray absorption by the surrounding medium. The best geometric conditions yield the maximal counts, highest analytical accuracy, and minimal measuring time. Many methods are used to find the optimal geometric conditions when designing XRF analyzers. The Monte Carlo Neutron-Particle Transport Code MCNP5, produced by Los Alamos National Laboratory, is important software for nuclear analysis including simulating and calculating XRF spectroscopy [10]. With relative errors below 5%, the spectral intensity accuracy predicted by the MCNP5 code is approximately 95%, and the prediction accuracy ranges from 90% to 97% for unknown specimen compositions [11]. Several models were established in this paper using the MCNP5 code for XRF analyzers. The best geometric conditions were obtained by varying the geometric parameters for the XRF analyzer design via the Monte Carlo method. Theoretical calculationsThe basic hypotheses follow: the specimen surface is smooth; the elements in the analyte are evenly distributed; the excitation source is monoenergetic; the incident X-ray beam is parallel to the analyte's characteristic X-ray beam. According to the Beer-Lambert Law, the original incident X-ray fluorescence intensity of the specimen is:In Eq. (1), 0 I is the incident X-ray fluorescence intensity in primary-sectional units. ( , ) S P Ois the combined mass absorption coefficient. S is the analyte. 0O is the incide...