J. Chem. SOC., Faraday Trans. I, 1988, 84(2), 617-629 Electron Energy-loss Spectroscopy and the Crystal Chemistry of Rhodizite Part 1 .-Instrumentation and Chemical Analysis W. Engel, H. Sauer and E. Zeitler Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 0-1000 Berlin 33, Federal Republic of Germany R. Brydson and B. G. Williams? Department of Physical Chemistry, University of Cambridge, Lensjield Road, Cambridge CB2 1EP J. M. Thomas* Davy-Faraday Laboratories, The Royal Institution, 21 Albermarle Street, London W1X 4BS An electron microscope fitted with a magnetic prism spectrometer and a parallel recording system has been used to measure the electron energy-loss spectrum of rhodizite, a naturally occurring mineral containing a number of light elements which are difficult to detect with energy-dispersive X-ray emission analysis (X.r.e.).We consider in detail the use of electron energy- loss spectroscopy (EELS) as an analytical probe and the quantitative chemical analysis for beryllium, boron and aluminium, measured with respect to oxygen, is in good agreement with the analysis obtained using wet chemical and crystallographic methods. The presence of potassium and caesium is confirmed, but for these elements the quantitative analysis is less reliable. X.r.e. measurements are also given for comparison. The potential as well as the limitations associated with the use of parallel recording arrays for chemical analysis based on EELS, is discussed. Electron energy-loss spectroscopy (EELS) carried out in a transmission or scanning transmission electron microscope (TEM or STEM) constitutes a versatile probe of the solid state.Using the facilities provided by the microscope it is possible to observe images and diffraction patterns from which structural information may be derived,' and by using a spectrometer to measure the energy-loss spectrum of the electrons which are scattered within the sample, further information concerning the elemental composition and the electronic structure may be obtained. There are several processes which give rise to distinct features in EEL spectra. The excitation of plasmons and interband transitions at energy losses from ca. 5 to 30 eV contains information concerning the valence and conduction electrons. When the energy transfer is equal to or greater than the binding energy of a particular inner-shell electron, core-edges are observed. From the energy of these edges it is possible to identify the elements which are present in the sample and, by measuring their intensities, t o quantify the analysis.The core-edges observed in experiments on free atoms are either featureless steps or broad peaks, but with solid samples detailed structure is observed close to the edge. The structure within ca. 20 eV of the edge is usually referred to as the electron energy-loss near-edge structure (ELNES), which is directly analogous to the X-ray t Present address: International Centre for Insect Physiology and Ecology (ICIPE), P.O. Box 30772, Nairobi, Kenya. 61761 8 EELS Study of Rhodizite absorption near-edge structure (XANES), and the structure extending up to a few hundred electronvolts beyond the edge is referred to as the extended electron energy-loss fine structure (EXELFS), which is analogous to the extended X-ray absorption fine structure (EXAFS).These features of the spectrum reflect the density of unoccupied states above the Fermi level and are also sensitive to the arrangement of the neighbouring atoms and therefore the nearest-neighbour distances and coordination, the oxidation and the hybridisation state of the atoms and the charge transfer between neighbouring atoms. (A number of review articles are available covering various aspects of and attention is drawn, in particular, to the book by Egert~n.~) There are a number of difficulties which must be overcome if sufficiently good data are to be obtained using EELS.The dynamic range spans eight orders of magnitude from the top of the zero-loss line to edges at an energy loss of 2 keV, and it is necessary to record the count rates at both extremes to an accuracy ca. 0.1 %. In order to reveal the details of the fine structure associated with an edge the resolution should be of the order of 0.5 eV or better at an incident energy of 60 keV or more. Furthermore, the power of EELS experiments in \he microscope stems precisely from the fact that the samples may be as small as 10-100 A in their linear dimensions, and the necessary concomitant of this is that beam damage to the sample is the ultimate limiting factor. To minimise the effects of beam damage the scattered electrons must be collected as efficiently as possible.Until recently, most EELS microscopes employed serial detection systems in which the spectrum is scanned over a slit, one channel at a time. With parallel detection, in which the entire spectrum is recorded simultaneously, the collection efficiency may be increased by up to 1000 times, and a number of such systems based either on SIT (silicon-intensified target) vidicon detectors'. ' or on photodiode arrays8-lo have been developed. The advent of effective parallel detection now promises to transform EELS from an interesting, but perhaps marginal, technique to one which will play a central role in helping to understand and to probe the chemistry of the solid state. In this paper we report on measurements of the various edges in rhodizite both to confirm the structure and properties of rhodizite and to investigate the potential, as well as the limitations, of EELS as a probe of the solid state.Rhodizite was chosen as the subject of this study for several reasons. Next to diamond it is one of the hardest solids known, and it is extremely insoluble in most solvents, making wet chemical analysis difficult. X-ray fluorescence analysis is inherently unreliable in view of the very light elements (oxygen, lithium, beryllium, boron, aluminium and sodium) which are present. It is a naturally occurring but rare mineral, containing, in addition to the light elements, varying amounts of potassium, rubidium and caesium. It has recently been the subject of a detailed X-ray diffraction and high-resolution (real-space) electron microscopic study by Pring et all1 who also used magic-angle spinning nuclear magnetic resonance, electron diffraction and wet chemistry to characterise the material. Nevertheless, further confirmation of the structure is still desirable. The present study divides naturally into two parts.In Part 1 we use EELS to determine the elemental composition of the samples andX.r.e. to provide acomparison and an independent analysis. Part 2isconcerned with the analysis of the near-edge structures which we have used to investigate the coordination of the aluminium atoms and the site occupancy of the oxygen atoms. Instrumentation and Experiment In these experiments a scanning transmission electron microscope with a spectrometer which allows parallel recording of the electron energy-loss spectra has been used.This instrument was designed and built in the electron microscopy department of the Fritz- Haber Institute. It operates with a field emission gun at 60 keV, and its probe-forming lens, which has a relatively long focaldlength of 50 mm, restricts the lower limit of the attainable probe diameter to ca. 15 A. The spectrometer unit consists of a transferW. Engel et al. 619 lens, a sector field spectrometer and two projector lenses which allow rotation-free magnification of the spectra onto a fluorescent screen. A P20 powder screen is used to convert the electrons to photons, and an optical fibre bundle is used to transfer the photons to the SIT detector of a commercial optical multi-channel analyser (OMA I1 system from EG & G).In order to improve the detector stability, its target temperature was stabilised using a device described by Rust.12 The SIT detector has 512 channels with a 25 pm spacing and a spatial resolution of ca. 3 channels f.w.h.m. (full width at half-maximum). By suitable excitation of the projector lenses the dispersion in the plane of the fluorescent screen can be varied from 1.5 eV per channel to 30 meV per channel. This feature makes it possible to trade resolution against range and to measure either small regions of the energy-loss spectrum with high resolution or larger regions of the spectrum at a correspondingly lower resolution. With the projector lenses turned off, a range of 1690 eV is accessible at a resolution of 10 eV.The spectrometer is designed to correct for second-order spherical aberrations. Provided the spectrometer acceptance angle is < 10 mrad, the resolution is determined solely by the energy spread of the primary beam, which increases with increasing beam current from 0.25 to 0.5 eV. For recording of the near-edge fine structures, for example, high beam currents are needed, so that in these experiments a resolution of ca. 0.5 eV is used. A precise high-voltage divider and a differential voltmeter is used to measure the incident beam voltage, which can be changed continuously thus making it possible to record different regions of the spectrum. With this facility calibration of the energy on an absolute scale is easily performed, and energies may be determined with an accuracy of kO.2 eV, which is desirable for the measurement of chemical shifts.An important feature of the instrument is the parallel detection, which gives a collec- tion efficiency 500 times higher than serial detection. To underline the importance of this, a 5 min experiment with parallel detection would require 1.8 days with serial detection in order to obtain data of the same quality provided the noise performance of both detectors is the same. Uncertainties arising from the counting statistics determine the detectability limits and the accuracy of the chemical analysis, and for a given recording time an uncertainty of, say, 10% with serial detection is reduced to 0.4% with parallel detection. When beam damage is the limiting factor a parallel detection system would provide data froF an area of 50 A on a side when a serial detection system would require an area of 1100 A on a side to obtain data of the same quality.An ideal parallel detection system for EELS, in which each channel acts as a perfect electron counter, is not available at present. All systems which have been developed up to now accumulate an amplified analogue signal which is digitised and then stored in the memory of a multichannel analyser. The amplification results from a chain of quantum conversion steps beginning with the electron-to-photon conversion in the fluorescent screen which is followed by a photon-to-photoelectron conversion at the cathode of the SIT detector. The photoelectrons are then accelerated onto the target and produce electron-hole pairs which in turn cause positive charging of the elements in proportion to the number of electrons which were originally absorbed in the corresponding areas of the fluorescent screen.After an exposure of typically 30 ms, readout, amplification, digitisation and storage in the memory of the multichannel analyser take place. This procedure is then repeated the desired number of times. The action of the intensifier chain for a channel n may be expressed in terms of the average gain g , and its variance V(g,), which results from the statistical fluctuations associated with the various conversions in the chain13 and provides a figure for the noise which is introduced by these fluctuations. Fluctuations of the dark signal, ambient noise in the ground line and other noise sources which are not correlated with the signal increase the noise in the output signal.These noise sources are of minor importance for the system in use, and they are negligible in most experimental situations contributing < 1.5 counts (r.m.s.) per channel for a 30 ms exposure and one readout. The gain is620 EELS Study of Rhodizite between 1 and 10 and can be altered by changing the accelerating voltage in the SIT detector. A gain of ca. 4 counts per electron is optimal because it is the highest gain which preserves the intrinsic range of the SIT detector of 4000 : 1. To a first approximation the detective quantum efficiency, Qd, is The gain statistic is determined by the initial conversion stages and is dominated by the statistics of the electron-to-photon conversion in the fluorescent screen.In the case of a P20 powder screen, the number of photons generated follows an exponential distribution1** l5 which gives a Qd value of 0.5. Recent measurements on a system which is almost identical to the one used in this instrument gave a value of 0.4.16 The average gain g, varies from channel to channel, giving rise to the so-called fixed pattern noise. In principle this can be removed, but deviations from a linear response, instabilities and other effects prevent an exact correction. Several procedures for the removal of fixed- pattern noise have been described." The dependence of the gain on the channel number was measured with homogeneous electron illumination of the fluorescent screen.The remaining fixed pattern noise leads to a further reduction of Qd to between 0.1 and 0.2, based on previous measurements. The detector is not ideal, and further improvements should be possible. Nevertheless, with a Qd value of 0.2 it is still superior to a perfect serial counting system, as the dose needed to produce a given signal is reduced by a factor of 100. In the spectra discussed below an effective signal, Seff, is given which we define as where Si and So are the input and output signals, respectively, and g is the gain of the detector averaged over all the channels. It can be shown that the variance of Seff is equal to Seff, since the input signal obeys Poisson statistics. Thus the noise can simply be judged the square root of Seff (the numbers of counts given in the spectra).The Qd can then be regarded as a factor describing the devaluation of the input signal and, compared to an ideal detector, l/Qd times more electrons are needed in order to obtain the same signal-to-noise ratio at the output. To obtain Seff we note that Qd/g is equal to So/V(So), where V(So) is the variance of So and &/g is independent of So provided that So is well above the dark-current noise as is the case in our experiments. A region of the spectrum showing no apparent structure was fitted to a low-order polynomial, and the variance of the residuals was used to estimate V(So), The advantages of performing EELS in an electron microscope have been documented previo~sly,~-~ but we would like to stress two points in the context of the sample investigated in this work.The stoichiometry and structure of natural minerals often vary over microscopic distances, and the ability to analyse small areas provides an opportunity to inve$igate such variations. Furthermore, in EELS the samples should be less than ca. 1000 A thick in order to minimise problems associated with multipl? ~cattering,~ but with the aid of an electron microscope very thin areas a few hundred A across can usually be found in samples which have simply been ground with a mortar and pestle and dispersed on a holey carbon film even when it is not possible to prepare a large sample area which is sufficiently thin. In order to quantify the elemental analysis obtained using EELS it is necessary to measure the entire spectrum, extending from the zero-loss line to the last edge of interest. Since the useful dynamic range of the detector system is only three orders of magnitude, while the dynamic range of the entire spectrum is eight orders of magnitude, separate spectra were measured over sevezal overlapping energy ranges.In order to minimise specimen damage, an area of 400 A on a side was scanned during the acquisition of each spectrum. Where a complete set of overlapping spectra spanning the range 0 to 1800 eV was measured, the scanned area was shifted between the recording of each spectrumW. Engel et al. 62 1 in order to ensure that an undamaged area was analyseg in each case. The total area was then ca. pm2, and the thickness was ca. 600 A. Thus a volume of roughly 6 x g, was used to record a complete spectrum from which the cheqical analysis has been derived.The dose varied from <a. 5 x C cm-2 (3 electron AP2) at the boron K-edge to ca. 0.5 C cm-2 (300 electron AP2) at the aluminium K-edge. For each spectrum the recording time was 5 min, except in the case of the aluminium K-edge, where a 10 min measurement was made. To ensure that the sample did not suffer significant beam damage the spectra were collected at 1 min intervals and these were then added if no significant changes were observed. Three sets of data were acquired. The first set was measured at an energy resolution of 0.5 eV (0.15 eV per channel), and no attempt was made to match the spectra one to another. The second set was measured at an energy resolution of 3 eV (1 eV per channel) and the third set at an energy resolution of 10 eV (3.3 eV per channel), both of these covering the entire energy range from - 50 to 1800 eV, with significant overlaps between spectra so that the individual measurements could be matched up.To investigate the effect of the collection semi-angle the first two sets of data were acquired with a semi-angle of 5 mrad, while the third set was acquired with a semi-angle of 10 mrad. In these experiments carbon contamination proved to be quite severe. This was reduced considerably by first baking the sample at 250 "C for 3 h in a vacuum at lo-' Torr. pm, corresponding to a mass of 2 x Results and Discussion From their study of rhodizite, Pring et al." deduce a compositional formula which is and they conclude that the mineral is cubic (a = 7.318f0.01 A) with space group ~ 4 3 m .Fig. 1 shows the spectra recorded at 0.5 eV resolution. The beam current was increased by several orders of magnitude going from (a) to (f), so that this series of spectra does not reflect the strong decrease of the inelastic cross-section with increasing energy loss. With the exception of spectrum (f), Seff was always of the order of lo5 counts per channel. In the series of spectra which were measured at 3 eV resolution and then matched, the full dynamic range can be determined and the count rates at the peaks of the K-edges of beryllium, boron, oxygen and aluminium were 4.1 x 4.4 x lop5 and 3.0 x times the count rate at the peak of the zero-loss line, respectively. Small significant features associated with the various edges and the noise are largely hidden in fig.1 and the spectra will be shown in greater detail in Part 2, where the fine structure associated with each edge is discussed. The low loss spectrum [fig. 1 (a)], which is due mainly to the excitation of plasmons and interband transitions, is dominated by the broad plasmon peak. Immediately beyond this [fig. l(b) and (c)] the edge signals are superimposed on a very high background, which gives the dominant contribution to the noise. The signal-to-background ratio improves significantly for the edges at high energy losses [fig. l(d)-(f)J. The quantitative analysis was carried out using the second set of data (3 eV resolution). After the individual spectra had been matched the entire spectrum was deconvoluted using the ' Fourier-log ' method'* with a thickness parameter (thickness divided by the plasmon mean free path), derived from the data, of 0.64.The intensity under each edge was calculated after subtracting an appropriate background. The dependence of the background on the energy loss, AE, was assumed to obey the power law AAE-'. The exponent Y and the constant A were derived from a fit to the pre-edge region. In some cases a region far beyond the edge was used to determine the exponent 1.2 x 21 F A R 1622 EELS Study I " ' ' I " " " " ' " ' " I " ' " " ' I I ' '"I of Rhodizite l , l , l t l , l , l , I , I , l , I , 80 I00 I20 I20 I10 I 200 2 20 240 1560 1580 1600 energy/eV Fig. 1. Rhodizite EELS spectra before background subtraction, measured with a resolution of 0.5 eV.(a) The low loss, (b) the aluminium L,,,-edge, (c) the beryllium K-edge, ( d ) the boron K-edge, (e) the oxygen K-edge, (f) the aluminium K-edge. The collection semi-angle was 5 mrad for (a)-(e) and 10 mrad for 0. The incident beam energy was 60 keV. The counts give Serf (see text for explanation). r. The cross-sections for exciting the various core electrons were calculated using Egerton's SIGMA programs,5* l9 including a correction for the convergence of the incident beam. The oxygen edge at 532 eV, which is strong and well separated from the other edges, provides a useful reference edge with respect to which the others have been measured. The results are given in table 1. The presence in the sample of beryllium, boron, aluminium, oxygen, potassium and caesium is immediately confirmed, and the quantitative estimates are in good agreement with the values obtained by Pring et uLl1 However, the analysis reveals a number of difficulties which are associated with the quantification of EELS data.In the low-resolution spectrum it was difficult to extract the aluminium Ledge, and the amount of aluminium was estimated with respect to beryllium using the high- resolution spectrum, which was not deconvoluted. This spectrum (which is shown in Part 2) reveals detailed structure in the tail of the aluminium Ledge which starts atW. Engel et al. 623 Table 1. The elemental composition of rhodizite as determined by EELS and X.r.e. compared to the results of Pring et al." (Crystallography)" EELS X crystallography E,IeV O K Li K Be K B K A1 L A1 K Na K K K K L Rb L c s L cs M 28 4.9 f 0.5 11.2f0.5 4.2 f 0.4b 5.9 f 0.3' 4.1 f0.2d - - 0.37 f0.05 - 0.24 28 28 - 0.02 - 4.55 - 11.35 - 3.99 13.5 3.99 - 6.3 - e 6.6 - 0.02 0.46 0.46 0.06 0.36 0.36 532 55 111 188 73 1560 1071 3608 294 1830 5012 727 ~~ a The EELS and X.r.e.measurements were normalised with respect to the amount of oxygen, which was set to 28 atoms. * Calculated assuming 4.55 Be atoms per unit cell. ' Measured with a 5 mrad collection aperture. Eb gives the XPS binding energies to indicate the energies of the edges. The EELS edge energies are discussed in Part 2. Measured with a 10 mrad collection aperture. Detected but not quantified. 79 eV and runs into the beryllium K-edge at 118 eV. It also contains a weak contribution from the caesium N-edge at ca.80 eV, although this is entirely submerged in the structure associated with the aluminium Ledge. Using an approximate cross-section, based on the energy loss and the number of N-shell electrons which are excited, together with the amount of caesium determined from the caesium M,,,-edge, the contribution of the caesium N4, ,-edge to the integrated intensity under the aluminium L2, ,-edge was estimated to be 15%. An aluminium-to-beryllium ratio of 1.08 was then obtained assuming that the contribution of the aluminium and caesium signals to the integrated intensity under the beryllium K-edge is negligible. Using the deconvoluted, low- resolution data the beryllium content was found to be 4.9f0.5 atoms per unit cell (normalised to 28 oxygen atoms).Because of the overlap of these signals and the uncertainties in fitting the background we estimate that the amounts of beryllium and aluminium (derived from the L2, ,-edge) given in table 1 are reliable to within & 10 %. The boron K-edge at 188 eV is both intense and well separated from the other edges, and the amount of boron deduced from the EELS data is 1 1.2 & 0.5 atoms, which agrees well with the value of 11.35 obtained by Pring et u1.l1 The quantification of the weak Ledge of potassium at 298 eV, which Pring et a1.l1 estimate to constitute 0.9 atom%, also caused difficulties. The spectrum recorded at 3 eV resolution and the background which was obtained by smoothing the tail of the boron K-edge are shown in fig.2. The EXELFS oscillations from the boron K-edge are clearly seen, and extend into the potassium Ledge. Knowing the general form of the EXELFS oscillations, their contribution to the integrated intensity under the potassium edge was estimated to be 10 %. Further complications arise from the possible presence of carbon contamination, as the carbon K-edge occurs at 289eV. After extended irradiation of the sample the signal from the carbon K-edge increased to 4 times the signal from the potassium Ledge. Using this spectrum as a guide we were able to estimate the contribution of the carbon to the spectrum used for the analysis. This was found to be between 5 and 10% of the area under the potassium Ledge, and corresponds to one carbon monolayer, assuming that the sample was 100 unit cells thick 21-2624 EELS Study of Rhodizite 6 m 4 0 0 -2 1 3 2 , 2 2 50 300 350 400 energy/eV Fig.2. Rhodizite EELS spectrum of the potassium L2, ,-edge after subtraction of the background (solid line). The background is indicated by the dashed line. The resolution is 3 eV and the counts give S,,, (see text for explanation). (700 A) and that 10 carbon atoms on a unit cell face form a monolayer. The amount of potassium given in table 1 is then reliable to within 15%. lines at 734.0 and 747.6 eV [fig. 3(a)] show up very clearly in the EELS spectrum, although EXAFS oscillations from the oxygen K-edge also run through this edge. Their amplitude is much smaller than in the case of the potassium L,,,-edge, and to a first approximation they can be neglected in the calculation of the caesium M4, intensity.Unfortunately, the cross-sections for scattering from M-shell electrons are not available, so that the L-shell cross-section for iron at 710 eV, scaled according to the number of electrons, was used instead. The dominant factors which determine the cross-section of a given shell are the number of electrons in that shell and the corresponding energy-loss, so that this should provide a rough estimate of the M-shell cross-section. The amount of caesium is then 30% less than that obtained by Pring et a/.'' It should be borne in mind, however, that the alkali-metal content of rhodizite is quite variable, and is partly dependent on the electron dose, so that the low figure may also reflect the differences between one crystal and another as well as the con- ditions under which they were examined.In fig. 3(b) the caesium M4,,-edge measured at a resolution of 10 eV is also given in order to illustrate the importance of high resolution in detecting low concentrations of particular elements. In the 10 eV data the resolution blurs out the sharp features, which both reveal and serve to identify the edge. Of course, the degradation caused by the low resolution will be less severe in edges which have less fine structure. The analysis of the aluminium K-edge at ca. 1565 eV reveals problems which are associated with the limited collection aperture of the spectrometer. The analysis based on the data measured at 3 eV resolution gives an aluminium-to-oxygen ratio which is 50% greater than that given by Pring el al." We believe that this may be attributed to the effect of multiple Bragg-edge scattering.20 In these experiments the first Bragg spot is at 6.8 mrad, while the spectrometer collection semi-angle is 5 mrad.The characteristic angle (equal to AE/2E0 where AE is the energy loss and Eo is the incident energy), which determines the angular spread of the inelastically scattered electrons, is 13.0 mrad for the aluminium K-shell excitations, so that an electron which is scattered into a (100) Bragg beam has a high probability of being scattered back into the collection aperture. On the The caesiumW. Engel et al. 625 1.0 0 700 750 800 energ y/eV Fig. 3. Rhodizite EELS spectra of the caesium M4, ,-edge after background subtraction, measured with a resolution of: (a) 3 eV and (b) 10 eV.The counts give SePP (see text for explanation). The background decreases from 1.5 x lo5 counts to 8 x lo4 counts across the energy range shown in the figure. other hand the characteristic angle for the excitation of an oxygen K-shell electron is only 4.4 mrad, so that the probability of scattering into the (100) direction and then back into the aperture is significantly less. The effect of this will be to enhance the intensity in the aluminium K-edge as compared to the oxygen K-edge, and from results calculated in a previous paper for the silicon K- and L-shells2' this correction should be of the order of 20-30Y0, which would bring the aluminium value close to the value given by Pring et al.ll This explanation was confirmed by the analysis of deconvoluted spectra recorded with a 10 mrad collection aperture and resolution of 10 eV.This gave a figure of 4.05 aluminium atoms per unit cell, uncertainties in the A1 K-edge background indicating errors of & 5 %, and this is close to the value obtained by Pring et al.," indicating that once the collection aperture is large enough to include the first strong set of Bragg spots, the effect of elastic-inelastic scattering is relatively small. With the exception of the aluminium Ledge, all of the elemental quantification was performed on deconvoluted spectra, and the effect of this is illustrated in fig. 4, which shows the oxygen edge from the data measured at 3 eV resolution before and after deconvolution. The effect of deconvolution is to increase the calculated boron to oxygen ratio by 31 YO and to decrease the aluminium to oxygen ratio (derived from the aluminium K-edge) by 16 YO.Sodium and lithium, which are only 0.04 atom YO in the sample, were not detected. The sodium Ledge at 31 eV and the lithium K-edge at 55 eV are superimposed on626 EELS Study of Rhodizite 500 600 energy/eV 700 Fig. 4. Rhodizite EELS spectra of the oxygen K-edge after background subtraction and measured with a resolution of 3 eV. The dashed line is before and the solid line is after deconvolution. The deconvoluted data are normalised to give the same area under the edge. the very intense tail of the plasmon peak and become submerged in the statistical fluctuations of the strong plasmon signal even though the cross-sections are large.We were unable to detect the sodium K-edge or any of the core-edges of rubidium, which constitutes 0.1 atom % of the sample.'' X-Ray Emission Analysis X.r.e. spectra were also measured for rhodizite using a JEOL 200 CX microscope fitted with a windowless, lithium-drifted silicon detector, and the results are given in table 1. The presence of oxygen, aluminium, potassium, caesium and a small amount of rubidium was confirmed. With such a detector it is possible to identify elements as light as carbon or nitrogen, but it is difficult to quantify the analysis. Two complicating factors are the adosorption of the characteristic X-rays, even for samples which are only a few hundred A thick, and the fluorescent enhancement which arises when the X-rays emitted from more tightly bound electrons excite fluorescence from the less tightly bound electrons.21 The values given in table 1 were obtained without correcting for fluorescent enhancement or absorption.As the X.r.e. and the EELS measurements were carried out on different crystallites in different microscopes it was not possible to use the EELS to determine the sample thickness for the XRE measurements. However, if one calculates the sample thickness, assuming an approximate elemental composition and an absorption term proportional to exp(-pt), where p is the mass absorption coefficient and t is the thickness which reproduces the oxygen-to-aluminium ratio given by Pring et aZ.,ll the thickness was found to be 1600 A assuming that the fluorescence yields of the oxygen and aluminium K, lines are approximately equal.If this thickness is then used to calculate an absorption correction for the potassium K,-to-aluminium K, ratio, allowing for the fluorescence yields of the two K-shells, a value for the potassium-to-aluminium ratio is obtained which is within 10 YO of the value given by Pring et a2." This procedure was also applied to the caesium-to-aluminium ratio, but in this case it gave a value 40% too high.W. Engel et al. 627 Statistical Accuracy and Detection Limits The discussion in this section is based on the high-resolution data (0.5 eV), although the chemical analysis was performed using the data measured at lower resolution. The intention is to demonstrate the statistical quality of the high-resolution data which can be achieved using parallel detection.The statistical errors affect the accuracy with which the intensity under an edge can be measured in two ways. If, in a given energy window, the background is B and the signal is S, the standard error in the estimated value of S is (S+B)t. For the data shown in fig. 1 (b) the number of counts in the aluminium edge can be estimated with an accuracy of 0.15 Yo. In addition, statistical fluctuations in the data affect the accuracy of the background fit, and since the background must be extrapolated over a large range, small variations in the fit may lead to large variations in the background subtraction. To ascertain the importance of this, a confidence band for the whole of the fitted line was determined and the upper and lower bounds of this confidence band were used to estimate the uncertainty associated with the fit.The uncertainty deduced in this way was 0.17 Yo so that the two sources of error combine to give an overall figure of 0.23 '/O or 0.5 Yo for a 95 Yo confidence interval. Using these data it is therefore possible to estimate the intensity under the aluminium edge with an accuracy of A second, related parameter is the detection limit for a given element.22 In endeavouring to detect very small amounts of any element it is important to use the best possible resolution, as this avoids smearing out the structure which reveals the presence of an edge. If the entire background could be reduced to a single point and the same could be done for the signal, the detection limit for aluminium in rhodizite would be 0.5% of the amount which is actually present.In practice, an edge must be measured over a range of channels, the edge must be apparent and only then can one proceed as above. To determine a realistic figure for the detection limit, the observed edge has been divided by 10, added to the fitted background, and normally distributed random numbers have been added to this pseudo-signal with variance equal to the number of counts at each point. By fitting and then subtracting a background and smoothing by convoluting with a Gaussian of f.w.h.m. = 0.3 eV, the edge shown in fig. 5 is obtained. Estimating the number of counts under the edge gives a value of (1.02 _+ 0.02) x lo6. The original value divided by 10 is 0.96 x lo6, which is 3 standard deviations from the estimated value.In other words, with data of this quality, the amount of aluminium in the sample could be estimated with an accuracy of f0.5 YO, the detection limit is ca. 5 to 10% of the amount which is actually present (0.5-1 atom YO), and this amount of aluminium could be measured to an accuracy of ca. 5 YO. It is important to remember that it is not possible at the present time to calculate the cross-sections and to allow for systematic errors in the measurements with anything like this precision. In practice, on the other hand, it is sometimes possible to prepare standard samples, from which accurate calibration cross-sections can be obtained. Alternatively, in experiments to determine variations in composition within one sample, the high accuracy would be invaluable.The same approach has been applied to the other edges with the following results. The intensity under the beryllium edge can be measured to an accuracy of 0.2 YO and the detectability limit is ca. 5 YO of the amount present (0.5 atom %). For boron the intensity under the edge can be measured with an accuracy of +0.03%, the detectability limit is 0.5 YO of the amount which is present (0.1 atom YO), and this amount of boron could be measured to an accuracy of +6%. The intensity under the oxygen edge can be measured to an accuracy of rt 0.02 O/O ; the detectability limit is 1 O/O of the amount present (0.6 atom "lo), and this could be measured to an accuracy of ca. f 10 YO. For comparison with the EELS detectability limits, we estimated the X.r.e.detectability limits for the oxygen K3, and aluminium K, peaks. An element may be 0.5 YO.628 EELS Study of Rhodizite r 1 1 1 1 1 1 1 1 I l I I I I I I I I I I l I 1 I I 1 1 1 1 1 1 1 1 1 60 80 100 I20 energy/eV Fig. 5. The aluminium L-edge in rhodizite reconstructed to represent a sample containing 10 % of the amount of aluminium actually present. The spectrum consists of the fitted background plus the observed edge divided by ten to which has been added normally distributed random numbers to simulate the counting statistics. This reconstructed spectrum has then been smoothed with a Gaussian of f.w.h.m. = 0.3 eV and a background has been fitted and subtracted. The edge at 118 eV is the beryllium K-edge. regarded as present if the number of counts in the peak exceeds three times the standard deviation of the counts in the background.2' Applying this to the peaks used for the X.r.e.analysis in table 1 gives the detection limit for oxygen K, as 2 YO (1 atom YO) and for aluminium 6% (0.5 atom %). Conclusions From the spectra of rhodizite, which is a complex and rather beam-sensitive mineral, it is clear that the use of parallel detection to record EELS spectra makes it possible to obtain data which are significantly better than those obtained using serial detection. The most important disadvantage associated with parallel detection systems currently available arises from the limited dynamic range, so that if a complete spectrum is needed in order to quantify the analysis, it is necessary to measure several spectra over small energy ranges and then to match them up.It is also necessary to correct for the effects of the fixed pattern noise. For well separated edges their areas can be determined to better than 1 O h , even in a material as complex as rhodizite, and the accuracy of the quantitative elemental analysis is limited by the systematic errors in the theoretical cross-sections and the power-law fit for the background, For edges which are widely separated in energy, Bragg-edge multiple scattering events may also introduce a significant error unless the spectrometer collection aperture is sufficiently large to include at least the lowest order Bragg beams, as is seen in the analysis using the aluminium K-edge. For the light elements considered in this paper EELS is significantly better than X.r.e.and provides elemental ratios for beryllium, boron and aluminium, calculated with respect to the oxygen, which are in good agreement with the analysis given Pring et d.ll using wet chemistry and crystallographic techniques. The detection limits for these light elements are estimated to be between 0.1 and 1 atom %. Using X.r.e. we were unable to detect either beryllium or boron, and the analysis of the aluminium and potassium were both significantly in error because of the difficulties associated with the effects of X-ray absorption andW. Engel et al. 629 fluorescent enhancement. Of course, for heavier elements beyond the second row of the periodic table X.r.e. analysis using the K-shell X-rays is superior to that which can be obtained from EELS.Even with the high resolution obtainable using EELS as compared to X.r.e. the extended nature of the signals can lead to problems when two edges are close together, and this is seen in the difficulty of separating the aluminium Ledge from the beryllium K-edge, the pottasium Ledge from the boron K-edge, and even more so in the problem of separating the carbon K-edge from the potassium Ledge. It is clear that with the benefit of parallel detection, EELS provides a powerful analytical tool for the analysis of light elements in microscopic volumes, and it is to be expected that the use of EELS in this way will become much more widespread in the future. We thank Dr D. A. Jefferson for his invaluable advice and help in this work.We also thank the Fritz-Haber Institute for financial support, the S.E.R.C. for a studentship (to R.B.) and the Royal Society for a Senior Research Fellowship (to B.G.W.). The rhodizite used for the EELS measurements was from Ambatofinandrahana in the Ankaratara mountains, Malagasy Republic (British Museum reference BM 1984,495). We thank the Keeper of Mineralogy, British Museum for Natural History for providing the samples. References 1 P. B. Hirsch, A. Howie, R. B. Nicholson, D. W. Pashley and M. J. Whelan, Electron Microscopy of 2 C. Colliex, in Advances in Optical and Electron Microscopy, ed. R. Barer and V. E. Cosslett (Academic 3 R. D. 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Paper 7/821; Received 11th May, 1987