Monte Carlo Simulation in Electron Probe Microanalysis. Comparison of Different Simulation Algorithms

Practical aspects of Monte Carlo simulation of EPMA experiments are considered. Simulations are performed using the general-purpose Monte Carlo code system Penelope, which is briefly described. This code includes geometry tools and variance reduction methods that allow the practical simulation of x-ray spectra from samples with complex geometries in moderate computing times. The reliability of simple interaction models and approximations, which have been frequently used in EPMA studies, is analyzed by studying their effects on the simulated x-ray spectra.     

EPMA of Porous Media: A Monte Carlo Approach

 We examine the influence of the sample porosity on the X-ray emission from mesoporous alumina bombarded with kilovolt electrons. Experimental results show that there is a loss of X-rays (Al Kα and O Kα) from those samples when compared to a fully dense mono-crystalline alumina (sapphire), which depends on the X-ray line, the measurement time and the embedding medium. Both geometrical and charging effects may be responsibl e for this signal loss. Monte Carlo simulations of the X-ray intensity emitted from porous alumina, using different models to describe sample porosity, show that the geometrical effect of porosity itself cannot account for the X-ray loss. Charge trapping effect and/or its combination with porosity is therefore expected to be the major cause of the signal loss.     

Quantitative Analysis of Thin Aluminium-Oxynitride Films by EPMA

 Thin films of aluminium oxynitride with diverse composition were prepared by dc-magnetron sputtering of aluminium, utilising sputtering power as well as argon, oxygen and nitrogen gas flows to vary the composition. Since film properties depend mainly on the content of incorporated oxygen and nitrogen, a method for quantitative analysis of the main constituents based on electron probe micro analysis with energy dispersive detection was developed. The excellent precision of the quantitative results for aluminium as well as oxygen and nitrogen are shown. Furthermore, a film layer analysis program was applied for the quantification of several films deposited under the same deposition parameters on silicon wafers, from 520 nm down to 40 nm thickness, showing that electron probe micro analysis with energy dispersive detection is a reliable method for quantitative compositional analysis of thin aluminium oxynitride films down to approximately 20 nm thickness. Since this method of analysis provides only bulk information, expected inhomogeneities of the depth distribution of the film components were checked by secondary ion mass spectrometry depth profiles of two thin films and correlated to the EPMA results. The thickness of the films was determined by ellipsometry. Received September 1, 1998     

Determination of thickness distribution and composition of thin coatings by EPMA: Application in the field of steel sheet production

A new method for the investigation of surface coatings by EPMA is presented. It is based on a physical model which takes into account the X-ray intensity depth distribution, the absorption and the electron backscattering effects at the interface between film and substrate. When combined with the concentration mapping (CM) technique, a two-dimensional film thickness distribution and the film composition can be determined simultaneously. Only bulk standards are required for this method.With some examples in the field of steel sheet production and electrogalvanizing the versatility of the method as well as its high sensitivity are pointed out. Particularly important for practical work is the applicability to almost any combinations of film and substrate materials as well as the wide thickness range from almost the total X-ray emergence depth down to the monolayer range.Dedicated to Professor Günther Tölg on the occasion of his 60th birthday     

Quantitative Trace Analysis by Wavelength-Dispersive EPMA

 “Trace” elements may be defined as elements whose concentrations are of a similar order to the detection limit. In WD analysis the detection limit is a function of the ‘figure of merit’ P²/B, where P is the pure-element peak intensity and B the background intensity. With normal analysis conditions detection limits of ∼100 ppm are typical, but substantial improvements can be achieved by using higher values of accelerating voltage and beam current. Long counting times are also advantageous, but should preferably be divided into relatively short alternating peak and background measurements to minimise the effect of instrumental drift. Using separate routines for trace and major element analysis is desirable owing to their different requirements. As the statistically defined detection limit is reduced, errors due to background nonlinearity and interferences (overlaps) from other elemental peaks become more probable. Spectrum simulation is useful for optimising background offsets and choice of crystal to minimise interferences, and estimating interference corrections when these are necessary. ‘Blank’ standards containing none of the trace elements of interest are also useful for quantifying background nonlinearity.     

Determination of Nb, Ta, Zr and Hf in Micro-Phases at Low Concentrations by EPMA

 Depletion of high field strength elements (HFSE: Nb, Ta, Zr, Hf ) relative to other lithophile trace elements in arc magmas and variations of Nb/Ta and Zr/Hf ratios in mantle-derived rocks can be addressed through studies of minerals, which concentrate and fractionate these elements. The presence of rutile, a common accessory Ti-oxide phase in various mantle rocks, has often been invoked to explain the Nb and Ta depletion in arc lavas because it has the highest HFSE abundances among the known mantle minerals. In this study, we measure the concentrations of Nb, Ta, Zr and Hf (at > 200 ppm) in rutile of two metasomatized mantle lherzolites using a Cameca SX-100 electron microprobe and obtain Nb/Ta ratios with an accuracy of about ± 5%. Mass balance calculations indicate that ≤ 1−5% of Nb and Ta in the rocks reside in major minerals and that the balance is hosted by accessory Ti-oxides. The Nb/Ta ratios vary significantly in nearby rutile grains in both peridotites (17–33, average 23; 12–37, average 21). Therefore, individual rutile grains may not be representative of the total grain population. However, Nb/Ta ratios measured in the bulk rock lherzolites by solution ICP-MS (21 ± 0.3) are within the analytical error of the average Nb/Ta values calculated for 5–7 rutile grains in both samples. These results emphasise that a representative grain selection must be analysed in order to determine trace elements contents of bulk rocks from data on accessory phases.     

Accurate Determination of Trace Amounts of Oxygen in CrAlN Hard Coatings by a Combination of WDS–EPMA and SIMS

Low amounts of oxygen in AlCrN hard coatings have been quantitatively analysed by means of WDS–EPMA. By combination with SIMS depth profiling, applying a calibration sample produced by ion implantation, the accuracy of the EPMA results was proven. Values as low as 0.07 at% were measured and the calculated detection limit is in the range of 0.01 at%.     

EPMA Investigation of Roman Coin Silvering Techniques

Ancient Roman silver coins, especially forgeries, contain various amounts of silver on the surfaces. The state of preservation of the outer layer can vary strongly among different areas of the same coin, thus an investigation of the entire surface is indispensable. The measurement of the silver distribution is a first step towards uncovering the manufacturing techniques. Element mapping by electron probe micro-analysis (EPMA) with increasing step size allows a survey of the complete coin surface. The suitability of this approach is shown and applied to coins having a dark optical appearance and unknown minting technique.     

Morphologies of Diblock Copolymer/Homopolymer Blend Films

Summary: Using bond length fluctuation and cavity diffusion algorithm, the morphologies of diblock copolymer/homopolymer blend films, AB/C and AB/A, confined between two hard walls are studied via Monte Carlo (MC) simulation on a cubic lattice. For the AB/C film, the C homopolymer is supposed to be more compatible with the A block than with the B block, while A and B are mutually incompatible. Effects of the composition of the diblock copolymer/homopolymer mixture, the symmetry of the diblock copolymer chain, the film thickness and the selective wall field on morphologies are studied in detail. Furthermore, the simulated results are compared with that of corresponding ABA and ABC triblock copolymer thin films. Comparisons with experiments and SCF theory also show good agreement. The results indicate that both the AB/C and AB/A can be used to prepare porous AB diblock copolymer membranes, the size of the pore channel can be controlled by the volume fraction of homopolymer C or homopolymer A.

Morphology of A₆B₁₄/C₁₀ polymer blend film.     

Quantitative analysis of silicon-oxynitride films by EPMA

Thin films of silicon oxynitride with diverse compositions were prepared by de-magnetron sputtering of silicon, utilising oxygen and nitrogen gas flows and the sputtering power to vary the composition. In order to investigate the composition of these films, a method of analysis by electron probe micro analysis with energy dispersive detection was developed and the figures of merit were compared to the wavelength dispersive method used by other authors. The precision and repeatability of the results are evaluated and the accuracy is checked by comparison with Rutherford backscattering and nuclear reaction analysis. Energy dispersive X-ray spectrometry was proven to be applicable to analyse silicon oxynitride films of any composition yielding quantitative results for nitrogen and oxygen as well as silicon. Besides the good analytical performance, electron probe micro analysis with energy dispersive X-ray spectrometry has turned out to be a non-destructive, quick, easy to use and cost effective tool for the routine analysis of light elements in thin films.     

Microanalysis of Hydrogen, Boron and Fluorine in Vesuvianite by Means of SIMS, EPMA and FTIR

Vesuvianite, a complex sorosilicate, often contains variable (from trace-to-minor-element) amounts of H, B and F. We describe a microanalytical study of H, B and F in vesuvianite by means of Electron Probe Microanalysis (EPMA), Secondary Ion Mass Spectrometry (SIMS), and single-crystal Fourier-Transform InfraRed (FTIR) spectroscopy. Most crystals investigated are B- (up to 3.67 wt% B₂O₃) and F-rich (up to 2.38 wt%); H₂O ranges from 0.243 to 0.665 wt%. The H data obtained by SIMS allowed us to calibrate the quantitative analysis of H₂O by FTIR spectroscopy. The resulting molar absorption coefficient (ɛ _i = 100 000 ± 2000 L · mol⁻¹ · cm⁻²) is in excellent agreement with working curves available from the literature. Moreover, the SIMS data allowed us to obtain the calibration curve to estimate the B₂O₃ content on the basis on the FTIR absorbance: a _i = 34000 ± 1400 · B₂O₃ (wt%).     

Electron Probe Microanalysis of HfO2 Thin Films on Conductive and Insulating Substrates

Quantitative electron probe microanalysis of highly insulating materials is a complicated problem, partially solved by coating samples with grounded thin conductive layers or using novel scanning electron microscopy (SEM) techniques, such as low-voltage and/or variable pressure SEM. In this work, some problems of quantitative X-ray microanalysis of thin HfO₂ films, in particular the possibility to determine mass thickness correlated to the density of the layer material, are discussed. For comparison, Al₂O₃, Ta₂O₅ and TiO₂ films grown onto both semiconductive Si and insulating quartz substrates were also analysed. All the films studied were synthesized by atomic layer deposition method.     

Chemical nonhomogeneity of the electro-slag remelting steel measured by EPMA

The chemical and structural homogeneity of the electro-slag remelting (ESR) alloyed structural Cr-Ni-Mo steel (18H2N4MA) is investigated with electron probe microanalysis. The level of nonhomogeneity is expressed in terms of microsegregation coefficients (C_max/C_min of an investigated element) [1]. Microsegregation coefficients are higher for molybdenum than for chromium and vary from 1.5 to 2.05 for Mo and from 1.13 to 1.3 for Cr. Both at low (< 350 kg/h) and high (> 400 kg/h) melting rates, the increase of microsegregation is more pronounced for both elements investigated.     

Comparative Analysis of a Solar Control Coating on Glass by AES, EPMA, SNMS and SIMS

 A solar control coating was analysed by different methods of surface analysis with respect to the layer sequence and the composition and thickness of each sublayer. The methods used for depth profiling were Auger electron spectroscopy, electron probe microanalysis, secondary neutral mass spectroscopy and secondary ion mass spectroscopy based on MCs⁺. The structure of the coating was unknown at first. All methods found a system of two metallic Ag layers, embedded between dielectric SnO_X layers. Additionally, thin Ni-Cr layers of 1–2 nm were detected on top of the Ag layers. Thus the detected layer sequence is SnO_X/Ni-Cr/Ag/SnO_X/Ni-Cr/Ag/SnO_X/glass. The Ni:Cr ratio in the nm-thin layers could be quantified by every method, the Cr fraction corresponding to less than one monolayer. We compare the capabilities and limitations of each method in routinely investigating this solar control coating. Importance was attached to an effective investigation. Nevertheless, by combining all methods, measuring artefacts could be uncovered and a comprehensive characterisation of the system was obtained.     

Light Element Analysis of Individual Microparticles Using Thin-Window EPMA

 The determination of the concentration of light elements, such as carbon, nitrogen and oxygen, in e.g. atmospheric aerosol particles is important to study the chemical behaviour of atmospheric pollution. The knowledge of low-Z element concentrations gives us information on the speciation of nutrients (species having nutritional value for plants) and toxic heavy metals in the particles. The capability of the conventional energy-dispersive EPMA is strongly limited for the analysis of low-Z elements, mainly because the Be window in the EDX detector hinders the detection of characteristic X-rays of light elements such as C, N, O and Na. WDS is suitable for analysis of light elements, but the measurement of beam sensitive microparticles requires the minimisation of the beam current and the measurement time. A semi-quantitative analytical method based on EPMA using an ultra-thin window EDX detector was developed. It was found that the matrix and geometric effects that are important for low-energy X-rays can be reliably evaluated by Monte Carlo calculations. Therefore, the quantification part of the method contains reverse Monte Carlo calculation done by iterative simulations. The method was standardised and tested by measurements on single particles with known chemical compositions. Beam-sensitive particles such as ammonium-sulphate and ammonium-nitrate were analysed using a liquid nitrogen cooled sample stage. The shape and size of the particles, which are important for the simulations, were determined using a high-magnification secondary electron image. Individual marine aerosol particles collected over the North Sea by a nine-stage Berner cascade impactor were analysed using this new method. Preliminary results on five samples and 4500 particles show that the method can be used to study the modification of sea-salt particles in the troposphere.     

Volcanic Quartz Growth Zoning Identified by Cathodoluminescence and EPMA Studies

 Quartz is a common phenocryst in acidic volcanic rocks but rarely contributes to the understanding of the magmatic or eruptive processes due to its apparent chemical homogeneity. Cathodoluminescence studies indicate that volcanic quartz is strongly zoned with respect to the trace elements. The determination of this zoning can help to elucidate the crystallisation history of the magmatic rock. Polished thin sections from rhyolitic and dacitic volcanic rocks were examined by cathodoluminescence mounted on an optical microscope and analysed by electron probe microanalysis. X-ray mapping of the trace elements incorporated in the zoned quartz was also performed. The interpretation of the data obtained from these different analytical methods provides useful information on the chemical zoning of single crystals and therefore on the chemico-physical conditions of the melt from which the quartz crystallised. Quartz from dacitic rock shows a complex cathodoluminescence oscillatory zoning, consisting of large red-brown and blue bands concentric to a resorbed core. Quartz from rhyolite shows simpler cathodoluminescence zoning, consisting of dark to bright blue luminescent bands. The EMPA analyses and the X-ray maps combined with the cathodoluminescence images suggest a clear correlation between the concentrations of some trace element (mainly Al and Ti, acting as activators of luminescence) and the cathodoluminescence colours pattern zoning. The incorporation of these trace elements during the growth of the crystals is linked to small variations in the thermo-chemical properties of the magma such as temperature and chemical composition.     

双分散高分子薄膜中短链对长链缠结和动力学的影响

采用Monte Carlo微观模拟结合原始路径分析的方法,研究了分子量双分散的高分子薄膜中短链的质量分数对长链的缠结和动力学行为的影响.模拟发现,当短链的质量分数较大时,薄膜内缠结点之间的关联性较低,缠结点易于被解开,长链动力学受到链受限程度的控制,随着膜厚的减小单调减慢;当短链的质量分数较小时,薄膜内缠结点之间的关联性较高,缠结点不易被解开,缠结点数目和关联性共同导致长链动力学随膜厚的非单调变化.模拟结果为明晰分子量分布对高分子薄膜中链缠结和动力学行为的影响规律提供了有益参考.     

Absolute Determination of Characteristic X-Ray Yields with a Wavelength-Dispersive Spectrometer

We describe a method to determine characteristic x-ray yields in absolute units with a wavelength-dispersive spectrometer. The method requires measurement and calculation of the thick-target bremsstrahlung intensity emitted from a reference sample at the photon energy of interest. Bremsstrahlung intensities are calculated by using the general-purpose Monte Carlo simulation code PENELOPE. We discuss the different sources of uncertainty and apply the developed methodology to the determination of absolute x-ray yields emitted from (i) thick samples, (ii) thin films on substrates and (iii) ultra-thin, self-supporting films. We compare measured yields with the predictions of theoretical/analytical calculations and Monte Carlo simulation, and whenever possible, with similar measurements found in the literature.     

Investigations in the ternary system Ti-Mo-N by means of EPMA and XRD

Arc-melted ternary Ti-Mo-N alloys were heat treated at 1423 K in order to evaluate the compositions of the equilibrium phases. The composition of the bcc phase-Ti _x Mo_1–x with respect to Mo and Ti was determined by electron probe microanalysis (EPMA) and lattice parameter measurements (XRD). In order to avoid the effects of plastic deformation caused by powdering the ductile-Ti _x Mo_1–x alloys, the lattice parameter measurements were carried out on small particles of the compact samples using Debye-Scherrer cameras. The EPMA and XRD results agree within the expected range of accuracy. Apparently the solubility of nitrogen in-Ti _x Mo_1–x is low and does not perceptibly affect EPMA and XRD results. The relationship between the lattice parameter and the nitrogen content of-TiN_1–x was applied to determine the composition of-TiN_1–x in equilibrium with-Ti_xMo_1-x No solid solubility of Mo in TiN_1–x could be detected. The tie lines at 1423 K between the two phases were established.     

Monte Carlo Simulations of the Morphologies and Conformations of Triblock Copolymer Thin Films

Summary: The morphologies and conformations of triblock copolymer (ABA and ABC) thin films confined between two identical walls were investigated by Monte Carlo simulation using bond length fluctuation and cavity diffusion algorithm on cubic lattice. Effects of the wall‐block interactions, copolymer chain composition and film thickness on morphologies, as well as on the fraction of chain “bridge” conformation f_bridge are presented in detail. In ABA thin film, column, parallel, perforated and perpendicular lamellas were discriminated, furthermore, the transition of morphology and the variation of f_bridge of ABA film along with the increase of thickness were revealed. In ABC thin film, lamella especially perpendicular lamella morphologies are predominant in varying the wall‐block interactions and the thickness. The results are consistent with some theoretical predictions such as DDFT and simulations reported in literature.

Isodensity profile of A₅B₅A₅ thin film.