Near Edge Fine Structures on Electron Energy Loss

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Near Edge Fine Structures on Electron Energy Loss

Transcript Of Near Edge Fine Structures on Electron Energy Loss

Scanning Electron Microscopy

Volume 1985 Number 2 Part II

Article 3

3-14-1985
Near Edge Fine Structures on Electron Energy Loss Spectroscopy Core Loss Edges
C. Colliex Université Paris-Sud
T. Manoubi Université Paris-Sud
M. Gasgnier C.N.R.S.
L. M. Brown Cambridge

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Recommended Citation Colliex, C.; Manoubi, T.; Gasgnier, M.; and Brown, L. M. (1985) "Near Edge Fine Structures on Electron Energy Loss Spectroscopy Core Loss Edges," Scanning Electron Microscopy: Vol. 1985 : No. 2 , Article 3. Available at: https://digitalcommons.usu.edu/electron/vol1985/iss2/3
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SCANNING ELECTRONMICROSCOP/Y1985 / II (Pag e◊ 489 - 512) SEM In c ., AMF O'Ha~ e (Chicago), IL 60666 USA

0586- 5581/8 5$ 1. 00+.05

NEAREDGEFINESTRUCTUROENSELECTROENNERGLYOSSSPECTROSCOCPOYRELOSSEDGES C. Colue x; T. Manouib ; M. GMgni~ ~ L.M. 8Jtow3n LaboM;to~e de Phy◊ique d~ So.V.d.u, M◊oue au CNRS Bat. 510, Univ~ il e P~-Sud, 91405 - OMay (F)(.QY[ce) 2 Pvuna.ennt ad~~◊ : ERA210, C.N. R.S., Be11.eveu 3 Me;tal, Phy◊iC◊ Vep~., Cavenfuh Lab., Camb~ge CB3OHE(G.B.)
(Pap e r r e ceiv e d Apri 1 16 1984, Completed manuscript received March 14 1985)

Abstrac t"
Core edges recorded in Electron Energy Loss Spectroscopy (EELS)display a large variety of profiles. Wehave investigated several specific aspect s concerning Energy Loss Near Edge Structure s (ELNE}Sand emphasize the interest in a careful edge shape analysis to obtain refined microanalytical information, such as local symmetr y. After indicating the general impact of EELS fine structure s as compared to EDXand Auger spectroscopie s we discuss the instrumental condition s required for recording satisfactory spectra and consider the theoretical problems which are involved in data interpretation. The major portion of this paper present s results for selected K, L23, M45and N45core excitations in compounsd (mainly oxides ) . In each case the phenomenagoverning the ELNESdi stribution are pointed out. In conclusion, we summarize the potential of a careful analysi s of ELNESfor studying the chemical state of the absorbing atom and the symmetyr of it s fir st coordination shell (molecular descripti on) or longer range effect s (projections of solid state densit y of states as seen by the ejected atom}.

Keywor ds

Mi croanalytical information Electron energy lo ss spectro scopy Core lo ss edge shape Atomic point of view in a solid Local densit y of state s Multiele ctron effect s

Address for correspondence :
C. Coll ie x Laboratoire de Physique des Solides Bat. 510, Universite Paris-Sud 91405 Orsay Cedex {France) Phone (6) 941.53.70

Importance of fine structure in different types of analytical signals
In the general environment of an electron microscope column, several techniques have been recently developed to combine morphological observation, structural characterization and chemical analysis of specimen areas of one to several nanometers typical extension. A new generation of instruments, generally named "analytical electron microscopes", is the result of such an association of spectroscopic devices for electron energy loss (EELS), energy dispersive X-ray (EDX)and Auger emission spectroscopies (AES).
Howeve,r "analysis" refers to several types of information content. In its simple meaning, chemical analysis consists in recognizing a given element present within the analysed volume. But it can al so concern more elaborate types of information, such as the valence state of the element (doubly or triply ionized), the environmental symmetry of it s site (tetrahedral or octahedral •• ) or its short or long range surroundings (Colliex, 1984b).
In all analytical modes considered in this paper, the useful information is derived from an inte raction process between the i ncident electron and a target electron lying originally on a core orbital {C). EELSinvestigates the excitation mechanismsbetween a core level and an unoccupied state (U) lying above the Fermi level EF : it is a spectroscopy of type CU- see Fig. la . The relevant signal is an edge,superposed over a decreasing background,which can be displayed as in Fig. 2 after background stripping. An average jump ratio at the edge is of the order of one to several units depending on the edge under consideration. For comparison, Fig. lb and Fig. le represent in a similar diagram the level s involved in EDXand AES spectroscopies : they both result from a de-excitation process in which a higher lying electron originating from a core Cora valence band V level fills the hole produced by the primary process. The first case can be called CCspectroscopy and the second CCVor CVVdepending on the type of levels involved in the decay transition. An EDX spectrum consists in lines superposed over a background of weaker intensity (average S/B ratio 10 to 50), and an Auger spectrum is made of lines or bands on a background with typical S/B ratios of

489

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the order of l, simil arly to EELS case. Detai led analytical information is conveyed in several ways. In an X-ra y emiss ion spectrum, the lines correspon-
dinq to electronic tran siti ons between core level s may-exhibit chemical shifts when the oxi dation state or the nature of ligands i s changed. The
observed shifts (LaUger, 1971) are however of the order of a few eV or le ss and their detection requires a high resolution wave length dispersive X-ray (WDX) analyser. For the standard EDXtechnique based on energy dispersion in a solid-state detector the energy resolution is too poor to
reveal such changes. More interesting are the Auger and EELScases
because a lineshape or edgeshape analysis can provide much more information about the specimen. Consider the situation in AES, as reviewed recently by Madden (1983). For a long time AESstudies

490

Near edge fine structures on EELScore loss edges

have concentrated on elemental analysis by identification of the energy position of peaks in derivative Auger spectra. Actually early work by Lander (1953) had clearly stated that AEScould be used as a valence band spectroscopy if the shape of the Auger (CCVor CVV)lines recorded in integral modewere properly analysed. A useful approach developed during the last .few years is to analyze a CVVline in terms of the sum of convolution products of independent-particle valence band density of states {DOS)components. This method has been successful for a few simple metals. However some CVVAuger spectra from surfaces exhibit lineshapes which bear no simple relationship with convolution products of DOSdistributions ; they can be termed "atomic-like" or "quasi-atomic" because they contain features too narrow to be interpreted by band density of states. The specific case of compoundsurfaces has been the subject of recent discussions (Citrin et al., 1976, Fuggle, 1981) which point out the possibility of interatomic transitions in which the valence electrons taking part in the Auger decay come not from the site on which the initial core hole was produced but from neighbouring sites. Such inter pre tative studies have therefore introduced a new dimension to Auger spectroscopy, in which one tries to extract local bonding information from detailed analysis of the relevant valence band features.
Finally, one might underline the potential importance of deriving local bonding information in solid state physics or science of materials. A classic example is the presence of embrittling layers of elements segregated to grain boundaries, where the local environment of an atom at the boundary plays a crucial role in the mechanical behaviour of the material.
Position of the problem in EELS.
Back to EELSspectroscopy, the historical story is very similar to AES. Early core-edge studies noted the close similarity between structures following characteristic edges in EELSor X-ray absorption spectra, and plots of the density of states in the unoccupied part of the conduction band (Colliex and Jouffrey, 1972). During the past decade, much more attention has been paid to the development of a quantitative microanalytical technique, for which the state of the art is reviewed by Egerton (1984). Over the last few years, however, interest in near edge fine structures has been renewed, stimulated by two general trends : 1) improvement in spectrometer technologies which combine good energy resolution (< 1 eV) with the high collection efficiency necessary for studying core-loss edges in the energy loss range 200-2000 eV (Krivanek and Swann, 1981 , Jeanguillaume et al., 1982); 2) also there is increased interest in the near edge fine structures measured by sunchrotron X-ray absorption spectroscopy and associated interpretative efforts by various groups of theoreticians. It is important to note that the extraction of fine structure information from focused electron probes demands a specimen particularly resistant to radiation damage, and that radiation damage is one of the major barriers

to the study of organic materials.
Recent review papers by Colliex (1984a) and Egerton (1983) have summarized the major contributions to the fine structure in a core-loss (or absorption) edge, which can be used to extract detailed information. The general shape of an edge is determined by atomic considerations. It depends on the symmetry of the orbitals (initial and final) which obey the well knowndipole selection rules for electronic transitions :

£ ' - £ = ti = ± 1

( 1)

Colliex (1984a) contains a tabulation of all edges of interest for pure elements in the energy range ~ 30 eV to ~ 2500 eV, classified into five main families of edge shapes as shown in Fig. 3 :

a) saw-tooth profile such as calculated in the hydrogeni c model ;
b) delayed edge with a relatively large transfer of oscillator strength to higher energies, as a consequence of an effective centrifugal barrier most important for final state s of large £ ' quantum number;
c) "white-lines" narrow and intense peaks, often exhibiting the spin-orbit splitting of the initial level ;
d) "plasmon-like" resonance peak for edges associated with inten se oscillator strengths in the low energy los s range ;
e) mixed profile combining a discrete transition to a bound state at thre shold and a delayed contribution to continuum states at energies far above threshold. These general shapes can be understood upon
a close examination of the electronic configuration of each element. The only important edges are tho se corresponding to an initial state of maximumoccupied £ for a given n shell because these have the maximumcross-section. It is however very difficult to record experimental atomic spectra ; the specimens usually consist of molecular or solid state assemblies of one or several types of atoms (compounds) . The observed edges display much more complex structures than those discussed in simplified atomic terms. Moreover, the detailed profiles depend on the allotropic variet y or compoundin which the element is found. Recent important systematic studie s have been made to obtain complete libraries of spectra (Zaluzec, 1982, Ahn and Krivanek, 1982). Many comparative studies can be extracted from such atlases. The various spectral modifications induced by the local solid state environment affect (see Figure 2) :
1) the threshold : variation of the position, of the slope and of the associated fine structures. For a long time, the displacement of an edge has been knownas a "chemical shift" in which one measures the translation along the energy scale of edges with constant profile. This approach is often a consequence of a rather poor energy resolution which averages features at the edge, so that one

491

Collie x C. et al

a
Saw-tooth profile.
b
Delayed edge.
C
"white-1 ine s ".
.6E
d
"Pl asmon-1i ke".
e
Mixed profile.
§.:_J_ - Schema,t,ci.,k epkv.,e n,ta,t,i.o,n 06 th e 6i ve main 6amu'.-tv., 06 edge 1.h,ape i nu oduce d in th e t ert.
detects only shifts in energy without noticing modifications in the edge shape. 2) "near-edge"_structures : apoearing in an energy loss range extending from typically 10 to 50 eV above the edge. The acronym XANEfSor Xray absorption near edge structure has been used in the recent literature concerning similar

structures in X-ray absorption spectra and ELNEShas been suggested by Colliex (1982) and Taft0 and Zhu (1982) to identify these features in EELSspectra. They have been mostly interpreted in terms of the conduction band density of states (DOS)and are complementary to the valence band DOSalready mentioned for Auger lineshapes interpretation.
3) "extended" oscillations : superposed on the decreasing tail of the core loss edge. The equivalent extended X-ray absorption fine structures (EXAFS)are nowwell understood and used for solving short range environment problems in many substances (Lee et al., 1981). They cover typically several hundreds of eV above the edge and their EELSequivalent are generally termed EXELFSfollowing the original work (Ritsko et al., 1974, Leapmanand Cosslett, 1976 and Colliex et al., 1976). EXELFS spectra have been published by many authors
during the last few years (Kincaid et al., 1978 Disko et al., 1982, Leapman, 1982) and reviews can be found in the papers of Leapmanet al., (1981) and of Csillag et al. (1981). EXELFS can be analyzed in the same way as EXAFSby use of the formulati on developed by Ashley and
Doniach (1975) and Lee and Pendry (1975) after the pioneering contribution due to Sayers et al. (1971). For several reasons, the potential field of
application of EXELFSappears limited. By comparison with EXAFSstudies, it offers a clear advantage because it is easily used for light elements and because it can be applied to very small volumes of material which can be characterized by other electron microscopy techniques (Batson and Craven, 1979, Batson et al., ( 1980). Howeverthe fine structure modulations on the tail of a characteristic signal are weak and superposed on an intense background. Consequently very high counting rates are required to offer a satisfactory signal of noise ratio. A second limit i s due to the fact that in EELSthe edges lie in the moderate 1000 eV energy loss range, in which the EXELFSfrom one edge often overlap another edge. The accuracy of the procedure used for the estimation of nearest neighbour distances is defined by the overall energy loss domain over which the Fourier analysis of oscillations is performed. In the EXELFSsituations, the low k truncation is determined by the necessity of avoiding multiple scattering events close to the edge while the high k truncation is imposed either by the onset of another edge or by noise. Altogether this restricted k-window degrades the capability of the method to solve local order problems. A last point worth mentioning is that the required theory
is not fully developed for situations involving more complex edges (e.g. M23, M45.. ) which are clearly observable in EELspectra, and for cases departing from the dipolar approximation when large collection angles are used.
Because of the limitations just discussed, we think that a more detailed study of the features classified above as 1) and 2) is rather
promising because it is easier to acquire spectra with an acceptable signa l to noise ratio. The
remainder of this paper describes a selection of

492

Near edge fine structures on EELScore loss edges

examples of experimental recording of nea~ edge fine structures together with the theo~etical problems involved in their interpretation.

Instrumental parameters

The experimental work was p~rformed with the
Scanning Transmission Electron Microscope (STEM)
VacuumGenerators VGHB501operated a~ Or~ay ov~r the past three years. Details concerning ~ts main
modes of operation for imaging and analytical purposes have been described elsewhere (Colliex
and Trebbia, 1982, Colliex and Treacy, 1983, Colliex and Mory, 1983). Hence we need only summa-
rize the major characteristics pertinent to ~he recording and study of near edge structures in

EELS.

h ·

The STEMconfiguration delivers on the tin

foil specimen a convergent bea~ of electrons within a probe of very small sized : the angle of

illumination a0 governs the dimension and the shape of the distribution of primary electrons on the

specimen entrance surfac~. In ou~ syst~m,_70 % of the incident current is contained within a

circle of radius r ~ 0.3 nm for a0 = 7.5 mrad and ~ 2 nmfor a0 = 15.0 mrad, these two conditions being the commonlyused ones. The analysed

volume can roughly be described as a cyli~der of

section set by the primary beam and of height .

imposed by the specimen_thickne~s, ~s long as it

remains sufficiently thin to maintain the beam

spread at a reason~ble level .. In most cases, the specimen properties are monitored by standard

imaging and diffraction, so that a ho~ogeneous_

area can be chosen within a characterised speci-

men grain size, and repeatedly scanned during . the recording of spectra. In most cases, the acqui-

sition area consists of a rectangular raster of

several nanometers on a side.

The spectrometer is a Gatan 607 homogeneous

field magnetic sector, whose design compensates

for second order aberrations. It has proven to be

capable of achieving an energy resolution of the

order of 1 eV on characteristic edges while collec-

ting all electrons inelastically scattered ~ithin

a collection angle S0 ~ 25 mrad at the specimen exit surface. Spectra shown below illustrate this

typical performance level.

The spectra are recorded in a sequential

mode that is, an externally driven magnet current

scan; them in front of the selection slit and the

detector located behind them. A computer is used

to govern the conditions of spectrum acquisition

by applying a step function ramp on the magnet

current. It also collects in a digital format the

signals coming from the detector analogue to digi-

tal converter (ADC)for the high counting rates

in the low energy loss part of the spectrum,

whereas a pulse counting mode is used for the low

counting rates in the high energy loss part of

the spectrum, the transition between the two

domains being a priori fixed at a given energy

loss channel. The important parameters are the

number of channels used for recording a spectrum,

the channel energy increment, the dwell time per

channel and the counting rate. Whenone is inte-

rested by a specific edge, an acquisition is made

over 1000 channels with a 0.2 eV step increment

such as shown in figure 4, whose caption lists

Countxs1000

,

10

j\

..:•I

; i (;
i :J ·---------

880

700

720

740

780

780

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the employed experimental conditions. The results can then be processed for display
in a useful way. A simple program strips the background by fitting to a model law generally
chosen as A(~E)-R, following Egerton (19'.5). The determination of the A and R parameters is made
by a least-square fit method over t ypi cally one
hundred channels before the edge, following a
Curfit program written by Trebbia (see Colliex et al., 1981). All results in the following ~ara-
graphs are shown after such a backgr?und stripping, to reveal the fine structures in a _way
similar to the illustrative diagram of figure 2. One major feature in EELSi s the occurrence
of plural scattering which becomes important when
the sample thickness approaches the total mean
free path for inelastic scattering (typicallt 50 to 100 nm for 100 kV primary electrons). It introduces sate llite edges in core edge spectra, which
are due to the possibility of core and plasmon
excitations by a single incident electron. The~e structures are shifted from the single scattering core edge by an energy equal to the plasmon energy
and can be confused with real near edge structures,
such as shown in fig. 6. for boron and nitrogen K-edges in specimens of increasing thickness.
Programs for removing plural scattering events from core edge spectra have been developed by
several authors, e.g. Johnson and Spence (1974) or Swyt and Leapman(1982). They can be classified
either as Fourier-log or Fourier-ratio method, the first one being more advantageous at the price of more computing time because it also remo-
ves plural scattering from the background (Egerton, private communication, 1984). These methods have
not been used in the present study but should be
implemented for further developments, when one wants to take into account Near Edge Structures
lying more than one plasmon energy abov~ the edge.
However, they are of less use when one is more concerned by the changes in edge shape, closer
than the first plasmon loss to the edge. . A final commentshould be made concerning the
absolute energy values in spectra reported here.
Wherepossible, features have been calibrated ~
against we11-knownedges or peaks such as the. TT" peak on the contamination carbon K-edge. Ou~ impres-
sion is that absolute energy values are reliable
to ~ 1 eV.

493

Coll iex C. et al

Theoretical considerations

Without introducing p detailed mathematical treatment, it is useful to provide some general guidelines for the interpretation of the observed spectra. Since the fir st experiments on absorption spectra, it was postulated that the inten sity was determined by the product of a probability of tran-
sition P(6E) with a density of states (DOS)for the unoccupied final states Nc(6E), such as

(2)

The first term P(6E) is governed by a matrix element between the initial and final states involved in the transition. Let us consider first a oneelectron transition in which one core-electron is excited to an unfilled ~tate : the initial state is described by Ii > = lk0+0> for an incident free electron of wave vector k and a core electron
wave function IO> = lwn 1tr) > and the final state by If > =lk,n > with a scattered free electron of
wave vector k = k0 - q and an excited electron
wave function In> = lwE 1•(r) >. In this latter case, one refers to a v~cuumstate wave function of energy E and angular momentum1 '. The tran sition matri x element

P(6E) cr ll 2 l
where H. is the Coulombinteraction is govetned by the dipolar term

( 3)
Hamiltonian,

( 4)

in the small angle limit because one approximates
eiq.r= l+i q .r . As a consequence, one obtains the wel l known selection rule s 1' = 1 ± 1, so that one deal s in an equivalent photoabsorption or a core-loss EELSmeasurement with a projection of the unoccupied density of states on a given type of momentumsymmetry. Somesuccess has been obtained with this first simplified descriotion,e specially in the case of metals (see for instance Colliex and Jouffrey (1972), or more recently Grunes (1983): the near edge structure reflects the partial density of states obtained from a band structure calculation, provided the matrix element factor is slowly varying with energy in this region .
In the case of compounds, this method i s insufficient because it neglects an important effect, which can be described as a "local density of states" such as introduced 30 years ago by Friedel (1954). A very complete review of the present state of representation of the electronic structure from the point of view of the local atomic environment can be found in Heine (1980) ; he defines
n(E,r) = n(E).l wE(r)l 2 in which the total density
of states n(E) is modulated by lwl2 fora "typical" state of energy E. Roughly speaking, a core edge spectroscopy measurement provides a picture of n(E,r) on an atom, decomposed according to different angular momenta1 with the projection operato, -s introduced by dipolar rules. There is a doubl e projection on the unoccupied density of states, one in space on the site of the core hole and one in symmetry.

Following Hayes and Boyce (1982) and

Noguera (1981), this can be expressed on a more

mathematical basis by introducing the Green func-

tion for the final state. One writes the inten sity

of the c~re loss excitation on the initial orbi-

tal lwo(r) > as :

.~

.++

won(6E)cr

(5)

where the G operator of the excited electron can be developed in terms of scattering events as

(6)

The zero order term G neglects all scattering on the surrounding atoms0 ; it represents the atomic

term, because Wn(6E) i s then equal to : 0.++

Zll 2

(7)

n o

n

using the definition of the Green function:

2

..!_ImG(r,r',6E)=Zlwn(r) >8[6E-tl2(k~-k~)l
TT

n

m

Whenone uses the expansion of the above scattering series to first order, the expression corresponds to single scattering and can be rewritten as :
. -+ -+
~l<~o(r) le 1q.r lwn(r )>l 2 (l + x(q)) (9)

where one recognize s the modulation factor x(q), introduced in EXAFStheory. It actually contains information on the neare st neighbour s in thi s
single scattering approach and detailed calcula-
tions of x(q) are found in Lee and Pendry (1975). The natural development consists of introducing higher order terms which correspond to multiple
scattering from the environmental atoms (see Fig. 5). This is the method followed by Durham
et al. (1981) and (1982) for the calculation of X-ray absorption near-edge structure (XANES).We
can check that it is formally equivalent to a
local density of states because one can rewrite

n(E,r-+) = -1 Im G(-r+,+r,E)

(10)

TT
as shown by Heine (1980) . In practice, the multiple scattering calculation is done in real space by considering a cluster of atoms surrounding the excited atom. This approach can accommodatesuch requirements as the use of an excited atom potential for the absorbing atom, which cannot be done very conveniently in a band structure calcu l ation. Within the framework of the tight-binding approximation an expansion of the sol id state wavefunctions as a linear combination of atomic orbitals greatly reduces the required computing time for
finite clusters. Disko et al. (1984) have recently performed such a simplified calculation of the p- DOSlocalized at the excited atom for both Be and Cina Be2Cstructure.
In the above description, the remaining electrons of the solid have been assumed to be unperturbed in their original states during the one-

494

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Near edge fine st ructure s on EELScore loss edges

PHOTOELECTRON

ATOMS X n ON THE FIRST

COORDINATION
I

SHELL
~

(a)
EXAFS

(b)
XANES

electron core excitation. What is the importance
of multielectron effects in XANESs, uch as the relaxation of the valence electrons to screen the core hole or the induced core-hole excited electron interaction? In the case of a metallic alloy, one can expect that the free conduction electron gas efficiently screens the hole created in the core level. The importance of many-body correlations has been the subject of several papers in the late sixties-early seventies (see for instance Mahan, 1974 and Dow, 1974) concerning the shaping of Kor Lz3 edges. Altogether, the energy width of such effects was predicted to be smaller than typically 0.3 eV and therefore inaccessible in
most EELSexperiments. The situation is however very different for
in sulator s with band gaps of a few eV between the
filled valence and unfilled conduction bands. In this case, the core-hole is poorly screened by the valence el ectrons which are involved in localized bonds, so that there generally remains a strong coulomb interaction between the core-ho le and the excited electron leading to the likely formation
of core-excitons. As pointed out by Grunes (1982) the symmetry projected final states of the transition s are not those of the unperturbed initial
solid. One must consider the influence of a partiall y screened hole and it is not expected that such a final DOSwill be equivalent for excitations on different atoms in the same solid. Even for atomic spectra, the influence of many electron effects cannot be ruled out, variou s intrashell and intershell correlations being involved in the exact description of delayed atomic spectra of type band d described above (Amusia, 1974 and Wendin, 1974). Further examples will be given in the next section.
In summary, a hierarchy of contributions can be referred to when attempting to understand features in the near edge structure :
. atomic effects, with or without multielectron correlations ;
. environmental effects, determined by the local density of states on the excited electron si te.

These are governed mainly by spatial site and angular momentumsymmetries and can (or cannot) be accompanied by multielectron rearrangements. A description in terms of molecular orbitals naturally constitutes a first step for describing this environmental contribution because the neare st neighbour bonding largely defines the symmetry of the unoccupied wave functions on the core-hole site.
Results and discu ssion
GeneAaf c.ommen;t,!,. The number of accessible edges in EELSis
very large as shown by the great number of spectra displayed in libraries such as the one edited by Ahn and Krivanek ( 1982) . It becomes enormous as soon as one is concerned about fine structure changes in different chemical environments and crystallographic structures (for instance, there are twelve forms of sili ca structures ! !). The present work remaining limited, it contains a subjective choice of compounds. Weconcentrate on oxides, because apart from their natural abundance, the oxygen K edge cannot be easily studied with synchrotron techniques. Wehave added some other edges for low Z elements and have decided to clas sif y them in the following section, as a function of their angular momentumsymmetry, since the dipolar approximation constitutes a major rule for interpreting lineshapes.
In all cases, an effort has been made to record spectra from well defined specimen areas and crysta llographic structures, checked by standard imaging and diffraction techniques.
Bo~on K- ed, e. (Fig. 6) For a 1 K edges stud ied here, the genera l
atomic profile is hydrogenic consisting of a sawtooth shape with a steep edge followed by a monotically decreasing tail.

495

Coll iex C. et al

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Hg . 6. (a,c.) NeaJLEdge Hne SVLuuWLe 06 B-K edge in a hexagonal BoAon-N~e.
(b,d) NeM Edge Fine SVLuUWLe06 N-K edge in a hexagonal BoAon-NiVl.ide. (el Lowlo~~ ~pec.VLwn06 hexagonal BoAon-NiVLide. (6) B-K edge in an amoAphoMBoAon.

Bo~on-NiVl.ide (BN). The specimen consists of thin flakes of
hexagonal graphitic BNdeposited on a holey carbon film. One choses protruding areas to get rid
of the carbon K edge contribution. Thickness ranges from typically 10 to 50 nmand the influence of multiple scattering i s illustrated by comparison of the Band N-Kedges for thin and thicker areas {Figs. 6a, 6b, 6c and 6d) : the relative intensity of peaks marked d and e with respect to oeaks a, band c closer to the edge clearly depends on specimen thickness . For interpretation, a low loss spectrum is shown in Fig. 6e which
exhibits two main features all and bll · It seems reasonable to assume that in the BN-nitrogen K
edge, peaks dN and eN correspond to multiple scat-

' ·....

380

400

420

Counts-1000

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460 ti.E(eV)

BN N-K edge

@)

.:-•,.:

.·.

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400

420

440

460

ti.E(eV)

Counts~ 1000

a Amorphous Boron K edge b
3 •,
.. CD .I/\ • ...
~- .:·~,/

.. ;

180

200

220

ti.E(eV)

tering events involving the all and bll low loss

features. Table 1 summarizes the energy positions of all peaks appearing in Figure 6.
Whenone considers the relative energy separation of the main three peaks a, band c in both boron and nitrogen K edges, it is clear that they coincide to within 1 eV although their relative intensity varies . This observation maybe taken as evidence that both transitions, originating from similar 1 s orbitals localized either on boron or on nitrogen atoms, go to the same £ = 1 type of final state. Moreover both sites have the same co-ordinate geometry comprised of atoms of the other species, in the graphitic structure
(a= 2.51 ~. C = 6.66 ~). Our experimental results provide high resolu-
tion spectra which confirm previous ones (Colliex, 1984a, Hosoi et al., 1982, leapman et al., 1983, Stephens and Brown, 1981). The interpretation of these data has been formulated from the beginning in terms of unperturbed DOSof unfilled conduction states, following several band calculations such

496

Near edge fine structures on EELScore loss edges

TABLE1 *

Energy position of all peaks appearing in Fig. 6.

BN-Boron K edge

a
eV
190.90
± I .o

b eV 197.70 ± 1.0

C
eV 203.20 ± 1.0

d eV 206.30 ± I. 0

e eV 214.10 ± 1.0

BN-Nitrogen K
edge

400.30 ± 1,0

406.70 ± 1.0

413.70 ± 1.0

425.40 ± 1.0

438 , I 0 ± I. 0

BN-Low Loss Spectnnn

8.70 ± 1,0

26.30 ± 1.0

Amorphoui;

Boron K 192

edge

± 1,0

200,6 ± 1.0

:: Note that al though the full

resolution

of the spectrometer

1 eV, the maximum in a spectral

very much more accurately.

width half is of the peak can

maximum order of be located

as Nakhmansonand Smirnov (1972). The peak labelled a is associated with a n:: type final orbital
(in the direction perpendicular to the hexagon~l lattice planes) while peaks band c refer to a" type final orbitals in the hexagonal plane. This model is supported by the detailed work of Leapman et al. (1983) who have investigated the orienta-
tion dependence of these core edges. If a configuration of crystal and collector aperture is chosen which favours momentumtransfer parallel to the n bond, the corresponding n:: peak is more intense
and, for momentumtransfer in the hexagonal plane, it vanishes with respect to the a:: peaks. In our experimental conditions, the large acceptance angle of the spectrometer mixes both contributions and the recorded spectrum gives a rather good representation of the total DOSof unoccupied states, including both TT and a type molecular orbitals. It is not yet clear whether the exact absolute position and intensity distribution in these three peaks has to be attributed to core-exciton features or to local density of states effects. Finally we note that Hosoi et al. (1982) have compared these characteristic Band N-Kedges in several types of crystalline structures, including hexagonal type as above, cubic type and wurtzite type. There again a rough agreement with DOS-calculations seems to exist.
Amo1tphoU/2bOJton.
The last spectrum (Fig. 6f) corresponds to a thin
foil , typically a few nm thick of amorphous boron as prepared by Dorignac et al. (1979) . The fine
structure is much poorer : it only consists of a narrow peak followed by a broader and less intense one at 8eV higher energy. Similar features will be described below in molecular systems. It seems reasonable to think that since there is no well organized order around any of the excited atoms, one has to assign a fundamental Rydberg final state for peak a followed by transition to the continuum for peak b.
Ca1tbon K-e.dge.. (Fig. 7 to 11)
In solid samples, the carbon K edge is the most frequently studied case. Fig. 7 shows the spectra recorded in the three main types of carbon specimen : amorphous carbon (7a), graphite carbon (7b),
diamond carbon (7c) plotted on the same energy
scale. There exist strong similarities between Figs.

Counts .1000

Amorphous Carbon K edge 10
5 -~· ·1'~-'-----®----
2

280

320

360

400

llE(eV)

Counts .1000

30
20 .•··..".\,._,.
i \
10 5

Graphite K edge
@

280

320

360

400

Counts. 1000

liE(eV)

100

Diamond K edge

.,. © . :.; •.::
50 .'\J~

10

280

320

360

400

liE(eV)

~ - Ne.M Edge Fine ◊V!.UctuJte. 06 C-K edr;ie_in
(a) amo1tphoU/2eMbon; (b) g1tapWe. eMbon; (e) d,<,amond.

7a and 7b with the presence of a narrow peak typically 1.5 eV wide at the edge, followed by a maximumlying 6 or 7 eV above. In the graphite case the structure ranging from about 6 to 40 eV above the edge displays clearer modulations o Following earlier work, one can attri~ute the origin of the peak at the edge to a TT" molecu)_ar orbital and those in the subsequent band to a" unoccupied states, as has been confirmed by the orientation dependence experiments of Leapman et al. (1983). The general agreement with unperturbed DOScurves must not prevent one from pointing out the fact that the TT:: peak lies at an
energy typically 2 eV below the predictions of the theory while the agreement is better for the a~ peak. This effect has been more thoroughly considered by Mele and Ritsko (1979) in a study
of the ls-carbon fine structure in intercalated graphite. They have clearly shown that the TT::
line shape and position differ from a ground state calculation. They have developed a scattering theory formalism similar to the one mentioned

497
EdgeStructuresFigSpectraDensity