P. Trebbia

EELS elemental mapping with unconventional methods I. Theoretical basis: Image analysis with multivariate statistics and entropy concepts

Electron energy loss filtered images recorded within a transmission analytical electron microscope are now widely used for the mapping of the elemental distribution of a given atomic species in a specimen prepared as a thin film. Such an image processing may produce both valuable results and artifacts if a careful inspection of all the hypotheses needed by the calculation is not carried out. This paper presents some general statistical methods for a contrast information analysis of a noisy image data set. After a brief introduction of different concepts such as contrast, variance, information and entropy, two unconventional approaches for image analysis are explained: the relative entropy computed with respect to a pure random and signal-free image and the factorial analysis of correspondence (a branch of multivariate statistics). In the companion article (part II), these concepts are applied to real experiments and the results compared with those obtained with a conventional method. Although electron energy loss spectroscopy is the only technique considered here, these methods for image analysis can be applied to a wide variety of noisy data sets (spectra, images, ...) recorded from various sources (electrons, photons, ...).

About the use of electron energy-loss spectroscopy for chemical mapping of thin foils with high spatial resolution

Core-loss energy-filtered images have been suggested as a substantial contribution to the development of an analytical electron microscope with high spatial resolution. However, for many problems in complex materials, the characteristic signals can only be detected as slope variations of the continuously decreasing background. Therefore further data processing techniques are needed to extract satisfactorily the true chemical information. A discussion of the present limits and of the existing solutions clearly shows that the method can only be developed at the expense of more elaborate systems such as simultaneous detection channels (quite well suited to the STEM instruments). Typical numbers for realistic situations illustrate the field of application of the technique.

Theoretical and experimental study of plasmon excitations in small metallic spheres

Abstract The excitation of bulk and surface plasmons in small metallic spheres is studied by means of electron loss spectroscopy in a scanning transmission electron microscope. The results are compared with theoretical calculations. The possibilities and limitations of the technique are discussed

EELS elemental mapping with unconventional methods II. Applications to biological specimens

This article presents two applications of image analysis and processing using the unconventional methods described in the companion paper (part I). Both the information analysis via relative entropy measurement and mapping and the factorial analysis of correspondence are demonstrated to be valuable tools for building an elemental map from a set of noisy energy-filtered images recorded in an analytical transmission electron microscope. Although the only technique considered here is electron energy loss spectroscopy, there is no doubt that such methods can be applied to a wide variety of similar problems: only a reduced number of underlying hypotheses are needed.

Unbiased method for signal estimation in electron energy loss spectroscopy, concentration measurements and detection limits in quantitative microanalysis: Methods and programs

Abstract We present an unbiased method for the estimation of the background in EELS spectra. It looks for the maximum likelihood of a power law model whose two dependent parameters A and R are estimated together with their variances and covariance. Applying the usual rules of error propagation, core-loss characteristic signals and thier variances are estimated. Confidence intervals for the relevant atomic concentrations are then established. Special attention is paid to the first- and second-kind risks when detection limits are attained: they respectively correspond to the risk of stating that a concentration is positive when actually it is zero, and to the risk of stating that a concentration is zero when actually it is positive. A special algorithm, based on a chi-square test, is developed giving the weighted mean of successive estimations of the same unknown. This test can select significant data from a set of experimental results. We also present an algorithm which estimates the effective angle of collection β∗ in the case of convergent beam EELS experiments. These methods and algorithms are used in a set of five programs, written in DEC-FORTRAN 77. These programs can be obtained, upon request, from the author.

Performance and applications of electron energy loss spectroscopy in stem

Abstract When coupled in the image mode to a VG-HB501 microscope, the spectrometer designed by O. Krivanek and manufactured by Gatan Inc. is well suited for resolving analytical problems with a high spatial resolution. It actually records energy loss spectra from areas as small as 0.5 nm with a typical energy resolution of 1 eV over the energy loss range and with a good efficiency in collecting inelastic electrons. During the last few months, this high performance combination of microscope and spectrometer has been used to investigate (a) detection limits in EELS which are presently estimated of the order of ten atoms in a test situation such as metallic clusters deposited on a very thin carbon layer; (b) quantitative chemical analysis of representative nanovolumes of complex oxide specimens, emphasizing several aspects of elemental segregation in the neighborhood of grain boundaries and within vitreous areas; (c) changes of fine structures close to the K-oxygen threshold, due to different bonding states; and (d) efficient Z-contrast imaging modes on sections of embedded biological material without metallic staining.

CLEDX: A stand-alone program for quantitative X-ray analysis using the cliff-lorimer procedure

Abstract CLEDX is a FORTRAN program giving, from experimental conditions (beam energy, specimen and energy-dispersive detector geometry, detector specifications, net peak and background intensities), the weight and atomic concentrations of up to 20 detected elements in a thin film specimen. The Cliff-Lorimer method is applied with up-to-date formulate for cross sections, fluorescence yields and X-ray absorption coefficients. Kα and Kβ lines are analyzed for elements Na to Lu ( Z = 11 to 71); Lα and Lβ lines for elements Ni to U ( Z = 28 to 92). The program gives an estimation of the maximum thickness beyond which an absorption correction may be required, and provides a statistical analysis of the calculated concentrations (standard deviations, covariances, confidence intervals for different first-kind risks) based on the number of detected X-rays (net peak and background). CLEDX is available, free of charge and upon request, from the author either in a DEC version (for VAX, MICROVAX, LSI or PDP computers) or in a PC version for IBM (or compatible) Personal Computers.