Multivariate statistical analysis (MSA) is a powerful tool for the analysis of series of spectra. This paper explores an application of MSA to a series of energy dispersive X-ray (EDX) spectra acquired in the scanning electron microscope (SEM) from a series of particles. The raw data were series of spectra previously acquired to test analytical procedures for trace element detection. This paper explores the possibility of performing the trace element detection with MSA components that have been extracted from the raw data without any a priori assumptions about the information content of the particle spectra. Particles were prepared from two analytical glasses, dispersed onto carbon substrates and coated with carbon. The compositions of the two glasses are substantially similar, except that one glass (K-3106) contains 0.7 wt.% Fe, whereas the other glass (K-3069) does not contain Fe at a detectable level.

The introduction of Multivariate Statistical Analysis techniques such as Principal Component Analysis (PCA) to the study of EDS and EELS spectra has opened up new possibilities for processing spectral data. In conventional EDS analysis each spectrum provides information about the elemental composition of the sample at a specific probe position. Where the signal arises from a single phase this elemental composition corresponds to the chemical composition of the phase. However, where the probe is incident on a multiphase region of the sample it is impossible to make a direct identification of the different chemical phases contributing to the overall spectrum.

With PCA it is no longer necessary to consider the spectra as isolated pieces of information. It is now possible to analyze a series of spectra as a single entity, looking for correlations between the variations in the elemental signals present in the individual spectra.

This paper present new results about x-ray emission from porous materials obtained from Monte Carlo simulations. This is an update from the results which have been presented for the first time last year. In particular, the absorption correction is now simulated in the same way as the electron scattering. In the results presented last year, x-ray absorption was calculated with the integration of the φ(ρz) curves via the usual equation :

where I is the intensity emitted from the porous specimen, I0 is the intensity emitted from a thin foil with no porosity, x is the mass absorption coefficient times the cosine of the take off angle, z is the depth in the specimen and ρ is the density of the porous materials. Since the density term does not include the effect of the size of the pores, integration of this equation will give wrong results when the size of the pores are big relative to the electron range.

The overall precision of electron microprobe measurements has not been studied extensively. It is often only described in terms of the precision of individual x-ray measurements or worse yet by relying on some rule of thumb based on historical experience. This is unfortunate because the analyst is expected to determine whether his or her measurements can distinguish between two samples or if a particular component can be detected above background or in the presence of other elements. Thus precision is at the heart of establishing composition/structure/property relationships and clearly deserves more attention.

There are many sources of variability encountered in determining composition whether using energy dispersive (EDS) or wavelength dispersive (WDS) spectrometery. These include Instrumental Variables, i.e., beam voltage and current, specimen position and orientation, detector position, and measurement electronics; Specimen Preparation, i.e., how representative the sample is of the problem to be solved, specimen preparation and contamination, and quality of standards; Data Processing, i.e.,

There are no “absolutes” in terms of performance and wherever possible, performance measures need to reflect conditions similar to those in the intended application. Unfortunately, measurements are frequently constrained by practical and economic considerations. For example, the most convenient radiation source for testing EDX systems is the Fe55 radioactive source which produces Mn Kα radiation at 5.9keV and can be used with an air path between source and detector. However, the fwhm resolution at 5.9keV is a rather poor measure of what the resolution will be for x-ray energies below 0.5 keV. Furthermore, “P/B”, the ratio of Mn Kα peak height to background level at IkeV, is only a crude indication of incomplete charge collection ICC, and does not reveal problems that may give rise to shift and broadening of the C Kα peak for example.

In high-resolution biological energy-dispersive x-ray (EDX) microanalysis it is often necessary to measure very low elemental concentrations. As an example, calcium, a physiologically important element, typically occurs in subcellular compartments at concentrations of 10-100 atomic parts per million (corresponding to 1-10 millimole/kg dry weight of sample) and it is ultimately desirable to measure the concentration of this element with a standard error of ±1 atomic ppm (or ± 0.1 millimole/kg). Detection of calcium in biological specimens is further complicated by the presence of relatively high levels of potassium (around 0.5 atomic % or 500 millimole/kg), which gives rise to overlap of the K Kβ and Ca Kα peaks in the EDX spectrum. Counting statistics are frequently the limiting factor for detectability, but this is not necessarily the case because in the analytical electron microscope it is possible to collect spectra for long periods using a high probe current.

Monitoring the performance and capabilities of energy dispersive X-ray spectrometers (EDS) and related x-ray analysis electronics and software is important for maintaining and improving the reliability, sensitivity, and accuracy of the x-ray analysis system. There is growing demand for quality systems through laboratory accreditation, ISO 9000, ISO Guide 25 and related programs that require set quality control procedures for analytical instrumentation. In such cases it is frequently more useful to have one national/international standard. This approach is not only more efficient than having each analyst devise their own system, but the use of the same standard procedures among labs would allow direct intercomparison of results. This intercomparison can help labs and manufacturers determine what are normal versus abnormal results and lead to higher quality instruments and analyses.

We are designing a standard procedure to maximize the efficiency of each quality control (QC) measurement so that we spend as little time monitoring the analysis system as is possible.

Few quantitative analysis techniques attempt as large an extrapolation between the compositions of standards and samples than is attempted in electron microbeam x-ray emission analysis. In-situ x-ray microanalysis can be performed for essentially all elements in the periodic table in complex matricies that may contain, in extreme cases, thirty or more detectable elements. Analyses are attempted for the same elements, using the same standards, in various matrices whose average atomic numbers might range from 4 to 94. Unlike most analytical techniques, where suites of standards are synthesized having similar bulk compositions as the samples and bracketing the concentrations of the elements of interest, the standards employed in microbeam analysis are most commonly pure elements, simple oxides, or other binary element compounds. This is true even though matrix effects on electron retardation and scattering, x-ray absorption, and secondary x-ray fluorescence can cause major variations in the differences between relative intensity and relative concentration.

Interest in electron beam x-ray microanalysis with low incident beam energies, defined arbitrarily as 5 keV and below, has been greatly stimulated in recent years by the development of the high performance field emission gun scanning electron microscope (FEG-SEM), which can produce a nanometer-scale probe with sufficient current to operate with both energy dispersive (EDS) and wavelength dispersive (WDS) spectrometers. Microanalysis in this regime requires the analyst to confront new spectrometry problems that are not typically encountered, or that can be safely ignored, when operating with conventional beam energies, 10 keV or greater. With low energy operation, the choice of atomic shells that can be accessed is restricted, forcing the analyst to make use of shells that have low fluorescence yields for intermediate and high atomic number elements, and possibly strong chemical effects, which are evident with high resolution x-ray spectrometry.

Wavelength-dispersive analysis of the ultra-light elements boron, carbon, nitrogen, and oxygen requires much more complicated experimental procedures than the analysis of medium-to-high Z (Z >11) elements. For a large part this is the result of a number of fundamental physical problems which cannot be circumvented. The most difficult problems of this nature are those related to the differences in the x-ray emission profiles from one ultra-light element compound to another. These differences are caused by the fact that in exciting ultra-light element x-rays electronic transitions of the bonding electrons are involved. As a consequence one has to deal with large peak shifts and large peak shape alterations in WDS analysis of ultra-light elements. While peak shifts can easily be accounted for by simply retuning the spectrometer when moving from standard to specimen the effects of peak shape alterations are much more difficult to deal with and in general it is imperative to perform the intensity measurements in an integral fashion.

A number of problematic analytical situations are known to exist in electron probe microanalysis (EPMA) where characteristic x-ray spectral overlaps are not only severe, but are also of the “self-interfering” or “cascade” variety. The “self-interfering” variety is exemplified by the innocuous Ba Lα ↔ Ti Kα; to the fearsome Pb Lα↔As Kα binaries, while “cascade” interferences are often seen among the transition metal series as in Ti Kβ → V Kα - V Kα Cr Kα or as seen with a secondary fluorescence interference effect as in Ni K ⇒ Fe Kα - Fe Kβ → Co Kα. Unlike simple interferences of the type Mn Kβ → Fe Kα, both of these types of spectral interferences are often quite troublesome for the analyst to correct for, especially for Si(Li) and Ge energy dispersive spectrometers (EDS) where the analytical peaks are often so overlapped as to prevent graphical deconvolution, and even for the higher resolution wavelength dispersive spectrometers (WDS) along with the yet to come bolometric energy dispersive detectors (based on projected resolution), the task can still be formidable.

Quantitative analysis of Mg and Fe in olivines, pyroxenes, and garnets is important for geochemical studies. Natural olivines have compositions close to the forsterite (Mg2SiO4) and fayalite (Fe2SiO4) binary system, with relatively minor substitution of other components. Pyroxenes and garnets are problematic in that they exhibit more diverse solid solution, and may contain both Fe2+ and Fe3+, the relative concentrations of which cannot be directly measured with the microprobe. The forsterite-fayalite olivine binary is a convenient system for studying the accuracy of Mg and Fe analysis without other complicating factors.

Bence and Albee utilized the a-factor approach for quantitative analysis of silicates, based on the empirical observation:

where CA,AB is the weight fraction of the oxide A in a binary oxide system AB, and KA,AB is the measured x-ray intensity of A relative to that of the pure oxide A.

Among the more important semiconductor materials, with commercially important applications in microelectronics, photonics, and nanodevice development are alloys in the system GaP-GaAs-AlAs- InAs (e.g., 1). These components have extensive regions of solid solution. With the wide variety of phases that can be grown in this system, it is possible to “tailor” heterojunctions that have desired band offsets or quantum wells that have a given shape of confinement potential, which is the basis of “bandgap engineering” (e.g., 2-4). In order to characterize the properties of these phases and maintain quality control in the manufacturing of devices utilizing these phases, it is critical to be able to perform accurate determinations of their compositions. This can be especially difficult, since many of the applications utilizing these phases involve micro- or nano-devices or thin multilayer coatings. In terms of the spatial analysis requirements, electron microbeam x-ray microanalysis is ideally suited for characterization of such specimens.

The most common cause of composition modification to a specimen during electron probe microanalysis is the field induced migration of light elements. This is an indirect effect which occurs in response to the long range electric fields that form when dielectric specimens suffer charge imbalance. The result is that the ions are redistributed within the sample according to their respective mobilities and the affect is enhanced rather than eliminated when the sample is coated. The ions typically move radially outward in thin samples because of the excess production of secondary electrons from the specimen surfaces, Cazaux(1986)and downwards in conventional SEM samples when the field is due primarily to the deposition of electrons within the bulk of the specimen

Field induced migration is responsible for most of the elemental signal variations observed during the microanalysis of silicate glasses containing sodium or potassium ions.

Although elements of low atomic number (Z<11) are detectable in TEM specimens using a modem energy-dispersive (EDX) detector, quantification remains a challenge. Problems include the large absorption corrections needed for specimens of typical thickness and the need for calibration specimens which provide k-factors appropriate to a particular detector/window arrangement. We have addressed this second problem by fabricating thin films containing several light elements in combination with silicon, which typically acts as the reference element when specifying k-factors.

Because the EDX peaks of adjacent light elements overlap considerably, it is preferable to have two specimens: one containing C, O and Si, the other B, N, F and Si. We have used both e-beam evaporation and sputtering techniques to deposit thin films on a substrate which can later be removed to leave a freestanding film mounted on a TEM grid.

In conventional quantitative electron microprobe analysis, methods like ZAF and φ(ρz), are used to convert x-ray intensity data to chemical composition utilizing equations that describe electron solid interactions, the x-ray generation process, absorption of the generated x-rays and secondary fluorescence effects. These equations capture the overall response of a sample or standard rather than consider the fate of individual electrons over time. For example, f(χ) is simply the ratio of x-rays emitted to the number generated. While for the most part these methods are built on solid physical models, the models were never exact enough to completely match measured data. Consequently, they have been modified by various adjustable parameters to ensure a high level of accuracy for a wide variety of systems and experimental conditions. However, since most of the adjustments were based on data taken at normal incidence, there has always been a question of how to obtain accurate results from tilted samples.

Wavelength dispersive spectrometry of long wavelength lines by EPMA can give information on the site symmetry and bonding of the x-ray-emitting atom. For fully focussing spectrometers, the energy resolution can be as high as 2eV or better at a spatial resolution of 1 μm, but electron beam currents often must be set to damaging levels. Fluorescent spectroscopy of the same lines in the commercial laboratory XRF spectrometer is far less damaging but spatial resolution is non-existent or, with collimators, relatively poor. With a combination of electron induced and x-ray induced fluorescent spectroscopy, and the insight provided by molecular orbital calculations, speciation or state analysis can be achieved even on damage prone specimens.

Electron and x-ray induced fluorescence has been employed to investigate surface coatings on magnesium metal. Oxygen Kα spectra for crystalline MgO, MgCO3 and powdered 4MgCO3.Mg(OH)2.5H2O were recorded using a TAP(2d=2.5757 nm) analysing crystal on a JEOL 8900R EPMA and a Philips PW 1404 XRF.

The efficiency and reliability of WD analysis can be enhanced substantially by means of computer simulation carried out before embarking on the actual analysis, thereby eliminating the need for a time-wasting ‘trial and error’ process and preventing errors in quantitative analysis due to line overlaps etc. which otherwise might be undetected. By displaying on-screen the combined spectra of elements known or expected to be present in a given sample, overlaps can be studied in detail, which may indicate the preferability of using an alternative analytical peak (e.g. L(Lβ1 instead of Lα1). The selection of optimum background positions with minimal overlap from neighbouring elements is also facilitated. These choices can be made much more rapidly and reliably than by depending on wavelength tables, while also saving the considerable instrument time required to carry out wavelength scans for each new type of sample.

Each field of electron microprobe analysis has its own specific analytical difficulties. Problems relating to the analysis of geologic materials can be primarily attributed to the fact that the samples are nonconductive, some are unstable under the beam, and they have a complex matrix. There are various techniques to solve these analytical problems, but the selection of appropriate standards is one of most important factors.

In study of geologic materials a convention prevails that the summation approximates 100%. For most analyses summation is an indication of the quality of analysis, although some elements could be over or under corrected. Significant progress has been made in developing correction procedures, yet some fundamental parameters still are not well known, and the results will vary depending on which procedures or fundamental parameters are used. One of the most practical solutions to eliminate significant matrix effects is to select reference materials with a close composition to the unknown.

Well-characterized calibration standards for microanalytical applications are difficult to obtain, often poorly characterized, and often not homogeneous from piece to piece. In addition, many microanalytical standards are available only in very small quantities making inter-laboratory comparisons difficult. To further complicate the situation, destructive microbeam techniques such as secondary ion mass spectrometry (SIMS) and laser source mass spectrometries (LSMS) require larger quantities of material than nondestructive techniques.

The U.S. Geological Survey, Geologic Division is in the process of evaluating ways to produce relatively large quantities of well-characterized standards. We are interested in producing standards of geological materials appropriate for multiple microbeam techniques including electron probe microanalysis (EPMA), SIMS and LSMS. The microbeam standards are produced by melting powders of standards of naturally occurring materials that the USGS has previously provided as bulk analytical standards.