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Stem microanalysis by transmission electron energy loss spectroscopy in crystals
Ultramicroscopy 9 (1982) 267-276 North-Holland Publishing Company
267
S T E M MICROANALYSIS BY T R A N S M I S S I O N E L E C T R O N ENERGY L O S S S P E C T R O S C O P Y IN CRYSTALS J.C.H. SPENCE and J. L Y N C H Department of Physics, Arizona State University, Tempe, Arizona 85287, USA Received 14 June 1982 (presented at Workshop January 1982)
The interpretation of microdiffraction patterns from crystals formed with a coherent electron probe which is "smaller" than the crystal unit cell is discussed, with particular reference to the problem of extracting atomic number information. Some characteristic features of the elastic microdiffraction pattern are demonstrated which allow heavy and light atom sites in the crystal to be distinguished. The formation of a STEM lattice image is also discussed. The theory of energy-filtered microdiffraction patterns from localized core-loss excitations in crystal is outlined and the characteristic features of these discussed. The form of energy-filtered characteristic loss STEM lattice images is discussed, and the effects of partial localization on these images described. Experimental microdiffraction patterns and energy loss spectra collected at symmetry points within a single unit cell of a barium alumina specimen are used, together with the results of dynamical calculations, to discuss the interpretation and usefulness of filtered microdiffraction patterns and lattice images.
1. Introduction In this paper we consider some approaches to the problem of obtaining a direct read-out of the atomic species present in a thin crystal, together with their atomic coordinates, through the use of the elastic and core-loss energy filtered lattice images obtainable on modern field-emission dedicated STEM instruments. This utopian goal is far from obtainable, chiefly due to limited instrumental resolution and the lack of a simple theory of coupled multiple elastic and inelastic scattering with which to interpret such images. While a good deal of attention has been devoted to the problem of microanalysis using the electron energy loss spectroscopy of core losses in non-crystalline materials, there has been little discussion of the application of the same method to crystals. Since localized inelastic scattering in crystals presents some novel features (such as the sensitivity of Kikuchi line intensities to the crystallographic site of the inelastic event) and since it is possible with modern instruments to form microdiffraction patterns from regions smaller than a single unit cell [1], it was felt worthwhile to undertake a study of
microanalysis by energy loss spectroscopy in crystals. In section 2 we consider some effects of atomic number variation on the elastic microdiffraction pattern as formed with an electron probe which is "smaller" than the unit cell. In section 3, experimental results are reported in which energy loss spectra (including localized losses) are collected at different symmetry points within a single unit cell. Finally, in section 4 we discuss the origins of the differences in these spectra, and the conditions under which a direct correlation between energy filtered STEM lattice images and crystal structure may be expected.
2. Atomic number information in the elastic microdiffraction pattern Since the elastic microdiffraction pattern formed with an electron probe of sub-unit cell dimensions can be used to form a STEM structure image [2], which to some extent distinguishes atoms according to their atomic number, it might be expected that this "structure factor" contrast could be used
0304-3991/82/0000-0000/$02.75 © 1982 North-Holland
J.C.H. Spence, J. Lynch / STEM rnicroanalysis by transmission EELS in crystals
268
to distinguish heavy and light atom sites by microdiffraction in a way similar to the analysis of crystal structures by X-ray diffraction. Thus the elastic microdiffraction pattern may contain at least as much "atomic number" information as energy filtered patterns, and has the advantage of higher intensity and more straightforward interpretation, due to the absence of mixed elastic-inelastic scattering. There are now several studies in the literature giving examples of crystallographic information extracted from convergent beam microdiffraction patterns obtained using a subnanometer electron probe [3,4]. We now consider the interpretation of these patterns from the point of view of distinguishing whether the probe lies over a heavy atom or a light atom in a crystal, by using the angular variation of intensity in the overlap region between adjacent convergent beam discs, rather then the spatial variation of the overlap intensity with probe position as used in a STEM lattice image. Fig. 1 suggests the experimental arrangement typically used with our modified Vacuum Generators HB5 instrument. The experimental observation of interference effects in the region of disc overlap near P3 indicates that the objective aperture OA can be taken to be coherently filled, that is that P0 be treated as a point source. Then, in the absence of lens aberrations a diffraction limited probe of "size" a will result from the use of an objective aperture semiangle OR = 0.61X/a if the probe "size" is defined as half the width between first minima. The Bragg angle for lattice planes of spacing d is 0 B = 0.5h/d, and thus the condition that the probe be "smaller" than the crystal unit cell is that the diffraction discs overlap [2]. In fact, in the more realistic case where spherical aberration must be considered the probe has very extended "tails", but is most concentrated at the optimum "dark-field" focus [5] given by A f = - 0.44(Cs)t )
1/2 .
In general it can be shown that [2]: (i) For a perfect crystal the intensity within the microdiffraction discs is independent of probe position if these do not overlap (probe "larger" than unit cell).
Po
I
oY
I
Fig. 1. The intensity at P3 in STEM microdiffraction can be calculated using reciprocity by calculating the intensity at P0 due to a fictitious source at P3-
(ii) The intensity within the overlap region is sensitive to the probe position within the unit cell, to focus and spherical aberration, and to the crystal structure. (It is this intensity which is used to form a STEM lattice image [2].) In fact, the variation of intensity across the overlap region can be used to determine whether the probe lies on a heavier or lighter atom, as follows. We consider the systematics orientation in the configuration of fig. 1. In many crystals the projection of the structure in two directions normal to the systematic line results in a set of planes of alternating high and low potential. For this common case, the intensity variation across AB can be estimated using two-beam theory and reciprocity. Experience with this simple theory applied to the similar problem of electron channelling shows that it is a useful guide to cation site determination in spinel structures [6]. For a lens with wavefront aberration X(u) (u = 0/X), specimen thickness t, and lattice period d containing alternating planes of light and heavy atoms, two-beam theory gives the intensity variation across AB as
I(c,S) = 1 + 2 Re[ b0 b exp(2 ric/d) -X(UB + a/X) + X ( u B - a/X)].
(1)
J.C.H. Spence,J. Lynch / STEM microanalysisby transmissionEELS in crystals Here ~k0 and ~g are the two-beam diffracted amplitudes, S = a/d is the excitation error (with a defined in fig. 1) and c/d is the fractional probe coordinate within the lattice repeat. Using
l~o=[COSg( S) -- ia~g(1 Jr-S2~2 )-l/2 sing(s )] × exp( - i~rSt), ~kg= i(1 + S2~2g)-l/2sinF(S)exp(ieSt), with F(S)=~rt(1 + S2~2g)l/2//~g and ~g the twobeam extinction distance, we obtain
I ( c , S ) = 1 + 2(1
+ S2~2)-1/2
× cos F ( S ) cos G(S) sin F ( S ) + 2S~g(1 + $ 2 ~ ) - 1 sin2F(S) sin G ( S ) ,
(2) where
G( S ) -- 2 ~ c / d - x(uB +
a/X) (3)
+ X( UB-- a/X ) - 2¢rSt.
We choose an origin on the heavier atom, making
269
the structure factor ~r/£g= o ~ positive. Then in the absence of lens aberrations (X = 0), eq. (2) predicts an approximately linear and decreasing angular dependence for I(0,s) (probe on heavy atom) in the neighborhood of P3 (s small) for t < ~g. For c/d= 1/2 (probe on lighter atom) the sign of the second and third terms is reversed, and the curve seen for old = 0 is now exactly reversed. Thus in general a negative slope in the intensity distribution at the midpoints between Bragg reflections indicates that the probe is situated over a heavy atom, while a positive slope occurs for probe on the lighter atomic site. Note that a choice of origin on the lighter atom gives consistent results, since this changes the sign of both ~g and sin G(S). Dynamical calculations which do not make the simplifying two-beam approximation support these predictions. Fig. 2 shows the results of many-beam calculations for the systematics case of a set of alternating heavy and light atomic planes. This calculation was performed using the multislice artificial superlattice technique, in which a large unit cell is chosen containing many cells of the perfect crystal and larger than the incident electron probe. Thus the first slice contains the
~~probe onOx
probe on Au
J m 4 ~
'
.r
|
I L
;
Fig. 2. Unaberratexl elastic STEM microdiffraction pattern (dynamical systematics calculation with coherent overlapping orders). The geometrical outline of the CBED discs is shown below the abscissa. Calculations are shown for two probe positions. Note interference effect, sensitive to probe position, in region of overlap.
270
J.C.H. Spence, J. Lynch / STEM microanalysis by transmission EELS in crystals
numerical Fourier transform of the aberration function H ( u ) exp [ i x ( u ) ]
( H ( u ) the objective aperture pupil function) as the boundary condition at the entrance face of the crystal. The predicted variation in the overlap region is seen to reverse as the probe moves from the heavier to the lighter atom. The introduction of lens aberrations does not destroy this reversal of the angular dependence of the intensity in the overlap region as the probe moves from the heavier to the lighter site. However, a unique association of a particular site with the slope of the intensity is now only possible if the focus setting is known. This can be done using the Ronchigram technique [7]. The focus setting which provides the least sensitivity to changes in focus and the least variation in intensity across the overlap region is the stationary phase focus
:x f, = - C s O L where the minus sign refers to a weakened lens. Fig. 3 shows the results of dynamical calculations for a lens with C, = 2 m m at A f, and otherwise
similar conditions to fig. 2. In practice the probe may be accurately centered over either of the sites by adjusting the probe position until the required center of symmetry is observed in the microdiffraction pattern. The accuracy with which A f must be determined can be estimated as 2 d 2 / X (not difficult to achieve in practice) by allowing the maximum phase change of the A f dependent term in (3) to equal qr for 0B/2. Thus, for Cs -~ 2 m m the slope of I(0, 0) will always be positive (probe on heavier atom) near A f ~ Afs. 3. Core loss spectra recorded at symmetry points within the unit cell We report here the results of experiments designed to determine whether a useful variation in the height of a core loss peak in the transmitted electron energy loss spectrum could be observed as the STEM probe is moved from one point in the unit cell to another. Unlike previous studies [8], we have used the point group symmetry elements within the cell to reveal the absolute location of the electron probe with respect to the crystal structure.
probe On Ox ~ o n Au
Cs: 2rnm
©
o
©
Au
Ox
Au
t=g6A O/;~p,5.3-I 1-~
4X_1 " ~
I
! !
J
Fig. 3. Similar to fig. 2, but for a lens with Cs = 2 mm at the stationary phase focus for the first-order reflection. Note reversal of slope near midpoint.
J.C.H, Spence, J. Lynch / STEM rnicroanalysis by transmission EELS in crystals
By considering the Born Series solution to the Schrrdinger equation for the elastic scattering of fast electrons from a parallel sided slab in the Z O L Z approximation with boundary conditions appropriate to the use of a coherent, focussed electron probe "smaller" than the crystal unit cell, it is readily shown [9] that the point plane group symmetry of sub-unit cell electron microdiffraction pattern is equal to that of the crystal as reckoned about the center of the electron probe as origin. This is true for a stigmated lens for all focus settings and assumes that the objective aperture is coherently filled and that the intensity within the region of Bragg disc overlap (which is sensitive to probe position) is considered. Since the elastic two-dimensional microdiffraction pattern can be viewed directly on the television system attached to our HB5 STEM instrument [10], the electron probe can be located over a particular symmetry element in the unit cell by adjusting the probe position controls until the corresponding symmetry is observed in the microdiffraction pattern. Energy loss spectra were then recorded at three such positions. Crushed specimens of barium aluminate (Ba0.6A1203) were used, the structure of which is shown in fig. 4. This consists of planes of barium atoms separated at 1.14 nm intervals by spinel blocks containing only aluminium and oxygen atoms. A two-fold axis falls midway between the barium atom planes in the [100] direction, while the barium atoms themselves fall on mirror planes of symmetry. By removing the objective aperture, the Ronchigrams shown in fig. 5 were obtained
271
from thin regions of sample. The patterns are aberrated point projection shadow images of the crystal lattice [7] and are sensitive to the focus setting and aberrations of the probe-forming lens. Their use for alignment, focus and spherical aberration constant determination has been discussed in detail [7]. The stationary phase points satisfying Af = -Cs 82 for the first order barium plane reflections are indicated in fig. 5 - a small detector placed at this position could be used to obtain a two-beam STEM lattice image (related by reciprocity to an inclined illumination two-beam
0'56nm
spinel
I-Nnm
1 O: Ba *: o:
AI O
Fig. 4. Simplified structure of Ba-0.6A1203.
Fig. 5. Ronchigrams recorded at two probe positions differing by half the crystal period in the c axis direction. Note reversal of contrast around stationary phase point P as probe is moved.
272
J.C.H. Spence, J. Lynch / S T E M microanalysis by transmission EELS in crystals
Fig. 6. Elastic STEM lattice image formed using a small axial detector and showing the 11.4 A barium atom plane periodicity. An objective aperture sufficiently large to include the first-order reflections has been used.
lattice image in TEM). The interference patterns shown in fig. 5 were obtained from two points separated by 0.57 nm in the c axis direetion (normal to the mirror plane) and show the expected reversal of contrast at the stationary phase point as the probe is moved by half the c axis (projected) repeat distance of the structure. In this way, accurate calibration of the probe translation controls can be obtained, and particular focus settings established. The use of an axial detector allowed the bright-field axial elastic three-beam lattice image shown in fig. 6 to be obtained, which clearly reveals the 1.14 nm spacing of the barium atom planes. The insertion of an objective aperture slightly larger than the Bragg angle produced the elastic
microdiffraction pattern shown in fig. 7. The c axis direction was first determined from the lattice image, and probe positions sought which produced microdiffraction patterns showing a mirror line of symmetry (figs. 7a and 7c). Energy loss spectra were recorded successively in this position over the barium atoms (shown in fig. 8a), and midway between them (figs. 7b and 8b). The distance in the c axis direction between the probe positions used to record the microdiffraction patterns is thus 0.57 nm. The spectrum of fig. 8a (probe centered on the mirror line of symmetry containing the barium atoms) shows clear evidence of the barium M 4 and M 5 edges, while that recorded with the probe midway between the barium planes (fig. 8b does not. The detector semiangle used was 10
273
...//c./ AE (~V) 7g0
5b0
2J0
6
CK
A_ AE (eV) 750
500
250
0
Fig. 8. Electron energy loss spectra recorded with the electron probe centered on the crystal mirror plane (upper spectrum) containing the barium atoms, and midway between barium planes (lower spectrum). The vertical scale has been adjusted to clarify differing regions. Note the reduction in height of the barium M 4 and M 5 edges as the probe is moved across the unit cell.
Fig. 7. Microdiffraction patterns of barium aluminate formed using a sub-unit cell electron probe located on the mirror plane of symmetry containing the barium atoms (upper pattern), midway between the mirrors (middle pattern) and on the next mirror (lower pattern). The mirror planes are separated by 11.4 ,~. These are 35 mm photographs of the television display.
mrad and the spectra were acquired over about 20 s, using a 5 V energy window. Using the digital scan generator and facilities for image subtraction [11], it would thus be possible to form a core-loss filtered lattice image using counts collected only in the neighborhood of the edge and thus greatly relaxing the requirements on thermal and mechanical stability. In the present experiments, the mechanical stability of the probe can be judged
from the Ronchigrams; however, these cannot be viewed while the energy-loss spectrum is being collected with the present instrumental design (a modified design to allow this is under development). From extended observations of Ronchigrams we judge that the probe may have moved no more than a few .~ while the spectra were being recorded.
4. Discussion
The height of the core-loss peaks in fig. 8 depends on the intensity distribution around the origin of an energy filtered microdiffraction pattern. The interpretation of these patterns must include the effects of the multiple elastic Bragg scattering of the inelastically scattered electrons. For the barium M 4 and M 5 losses at AE = 760 eV
274
J.C.H. Spence, J. Lynch / STEM microanalysis by transmission EELS in crystals
we have that #E = AE/2Eo~ 8a so that, for axial plane-wave illumination, appreciable overlap of the Lorentzian tails of the inelastic angular scattering distribution laid down around each Bragg direction is expected. In such a "point" diffraction pattern (one formed in transmission using axial plane-wave illumination), the inelastic scattering distribution is responsible for the appearance of Kikuchi lines, which, for 0B<0E "(2oa, may be thought of as arising from the interference between overlapping inelastic scattering distributions centered about each Bragg spot. As in the case of elastic STEM lattice imaging, this overlap intensity or Kikuchi lines is expected to be sensitive to the crystallographic site of the inelastic event [12]. The theory for the two cases differs only in the form of the angular distribution assumed and in the additional depth integration over inelastic sites in the inelastic scattering case, if localized losses and single inelastic scattering is assumed. For the experimental conditions used in section 3, the lattice is resolved in the elastic channel (i.e. the elastic Bragg discs overlap) and, in addition, there is overlap of the inelastic scattering distributions, which is convoluted by multiple scattering against the elastic scattering distribution. The resulting complicated intensity distribution in energy filtered microdiffraction patterns cannot be predicted in a simple way; however, its main features should include Kikuchi lines and a high sensitivity both to the STEM probe coordinates and to those of the inelastic event. In addition, the filtered intensity must be zero for a probe situated at a large distance from the inelastic site (unlike the elastic intensity, whose normalization is independent of the probe coordinate). Finally, for the modified hydrogenic inelastic wave functions used in the following calculations, the filtered patterns should preserve the symmetry of the crystal as reckoned about the probe center. For certain conditions of objective aperture semiangle 0oh and inelastic scattering angle 0E, the intensity at the midpoint between Bragg points in the filtered inelastic pattern will be independent of focus and spherical aberration (but not of probe inelastic site coordinate), but in general the entire pattern intensity will depend on the focus and aberrations of the probe-forming lens and on the probe co-ordinate
and inelastic site. It is therefore of some importance to establish the conditions under which an energy-filtered core-loss lattice image would give misleading information, such as intensity maxima for the filtered species which are not in registry with the corresponding lattice sites of the selected atoms. (This effect is commonly seen to occur in elastic lattice imaging through incorrect choice of focus.) To test this, a series of multiple elasticsingle inelastic scattering calculations have been performed using a modification of the algorithm of Doyle for localized inelastic events [13]. Inelastic scattering amplitudes were based on the modified hydrogenic model [14] and incorporated into the multislice algorithm with an incoherent addition of scattered inelastic intensities over equivalent lattice sites occurring at different depths through the crystal. The results of a typical calculation are shown in fig. 9. Here energy filtered core-loss microdiffraction patterns are shown for two probe positions - one over the filtered species and one mid-way between them. The calculations show all the features mentioned earlier - in particular the total area under the inelastic scattering distribution decreases as the probe is moved away
I
~l I
~
~probe
/ 'J , , ~
on
Be
I
CS:Af=0
II
--8~--
©
I
©t /
0robewidtn92~ between
zeros
,Hd.pAE=111 eV
" ooo,,o t =136 ~,
~
~
I 1
I
~
Bragos
! Fig. 9. Dynamical systematics single inelastic-multiple elastic scattering calculations for the beryllium core-loss filtered microdiffraction pattern formed with a unit cell sized electron probe. Note differing ordinate scales and loss of total scattered intensity as the probe is moved away from the beryllium atom. In the absence of lens aberrations, the deep minima midway between Bragg points in the continuous line may be interpreted as a dynamical Kikuchi line.
J. CH. Spence, J. Lynch / S T E M microanalysis by transmission EELS in crystals
from the filtered species. Since there is no "forward scattered" beam, the use of a small axial detector produces a "dark-field" energy filtered image. The entire pattern is sensitive to focus; however, calculations with Cs - - 2 mm, 0ohj = 0.01 rad around Af0 = --378 ,~ all show a decrease in total inelastic scattering as the "probe" is moved away from the filtered species. The optimum focus setting for best resolution is thus Af0 = -0.44(CsX) 1/2, as for dark-field TEM elastic imaging [5]. Under these conditions there is a direct correlation between intensity maxima in the filtered image and the sites of the selected species in the lattice, for thin specimens (t < 100,~). The effect of finite localization must also be considered. For 0 E >>0ohj (localization smaller than probe "size"), these effects are unimportant; however, for 0 E < 0 B (localization larger than the lattice spacing) it is possible for atoms other than the energy filtered species to appear in the filtered lattice image. Energy filtered lattice images have been used previously to demonstrate this point [8,15]. Fig. l0 shows the calculated image filtered for the K-shell loss of a single atom resting on a crystalline substrate. Here the fine oscillations in the image reveal those substrate atoms which fall within the localization of the inelastic event and which appear as a result of the elastic scattering in the substrate of the inelastically scattered electrons.
Be a a a t o m filtered
K-Iosl
image
A E . 1 1 1 eV t.72~ Cs • / ~ f , 0 . 0
Oob;>%
Fig. 10. Calculated core-loss filtered image of a single beryllium atom on a thin crystalline gold substrate. The oscillations in the tails reveal the periodicity of the substrate, despite filtering for the adatom. Note that a dark-field image is seen when using a n axial "bright-field" detector.
275
5. Conclusions (1) The variation of intensity with angle reverses in the overlap region midway between Bragg spots in coherent microdiffraction patterns as the probe is moved by half the lattice repeat distance. This result is exact in the presence of lens aberrations only in the two-beam dynamical approximation. (2) The symmetry points within a crystal unit cell can be used to determine the absolute location of a coherent STEM probe with respect to the crystal lattice if facilities are provided for efficient detection and convenient viewing of the elastic electron microdiffraction pattern. (3) Electron energy loss spectra have been recorded at symmetry points within a single unit cell known to fall on atomic planes of widely differing atomic number. These show the expected variation in the height of core-loss peaks due to localized inelastic scattering. (4) While the interpretation of core-loss filtered lattice images by comparison with computed images appears completely hopeless in the general case of coupled multiple elastic and multiple localized inelastic electron scattering, a direct correlation between intensity maxima in a filtered image and the positions of the selected species in the lattice can be expected under certain conditions. These are: (i) Specimen thickness less than about 100.~. (ii) Localized core losses are used, with a localization "smaller" than the unit cell (this may mean AE < 1000 eV (15)). (iii) A coherent probe is used at the optimum dark-field focus Af---- --0.44 (Cs)~)l/2 and an objective aperture sufficiently large to resolve the lattice. The use of electron Ronchigrams [7] allows this focus setting to be selected. (iv) The use of a STEM detector large enough to collect all the appreciable inelastic scattering of interest appears to have theoretical advantages; however, the influence of detector size on image resolution has not been studied in detail. In practice this will be limited by spectrometer aberrations.
Acknowledgments We are most grateful to Dr. M. O'Keefe for his advice and help with the preparation of specimens.
276
J.C.H. Spence, J. Lynch / STEM microanalysis by transmission EELS in crystals
This work was supported by ARO grant No. DAAG-29-80-C-0080, and the NSF HREM Facility at ASU.
References [1] J.M. Cowley, Ultramicroscopy 7 (1981) 19. [2] J.C.H. Spence and J.M. Cowley, Optik 50 (1978) 129. [3] J.M. Cowley and J.C.H. Spence, Ultramicroscopy 6 (1981) 359, [4] J.P. Lynch, E. Lesage, H. Dexpert and E. Freund, Inst. Phys. Conf. Ser. 61 (1982). [5] J.M. Cowley, Acta Cryst. A29 (1973) 529.
[6] J. Taft,, Acta Cryst., in press. [7] J.M. Cowley, Ultramicroscopy 4 (1979) 435. [8] A.J. Craven and C. Colliex, J. Microsc. Spectrosc. Electron. 2 (1977) 511. [9] J.M. Cowley and J.C.H. Spence, Ultramicroscopy 3, (1979) 433. [10] J.M. Cowley, in: Scanning Electron Microscopy/1980, Vol. 1, Ed. O. Johari (Scanning Electron Microscopy, AMF O'Hare, IL) p. 61. [11] M. Strahm and J.H. Butler, Rev. Sci. Instr. 52 (1981) 840. [12] J. Gjonnes and R. Hoier, Acta Cryst. A27 (1971) 166. [13] P.A. Doyle, Acta Cryst. A25 (1969) 569. [14] R.F. Egerton, Ultramicroscopy 4 (1979) 169. [15] A.J. Craven, J.M. Gibson, A. Howie and D.R. Spalding, Phil. Mag. A38 (1978) 519.
267
S T E M MICROANALYSIS BY T R A N S M I S S I O N E L E C T R O N ENERGY L O S S S P E C T R O S C O P Y IN CRYSTALS J.C.H. SPENCE and J. L Y N C H Department of Physics, Arizona State University, Tempe, Arizona 85287, USA Received 14 June 1982 (presented at Workshop January 1982)
The interpretation of microdiffraction patterns from crystals formed with a coherent electron probe which is "smaller" than the crystal unit cell is discussed, with particular reference to the problem of extracting atomic number information. Some characteristic features of the elastic microdiffraction pattern are demonstrated which allow heavy and light atom sites in the crystal to be distinguished. The formation of a STEM lattice image is also discussed. The theory of energy-filtered microdiffraction patterns from localized core-loss excitations in crystal is outlined and the characteristic features of these discussed. The form of energy-filtered characteristic loss STEM lattice images is discussed, and the effects of partial localization on these images described. Experimental microdiffraction patterns and energy loss spectra collected at symmetry points within a single unit cell of a barium alumina specimen are used, together with the results of dynamical calculations, to discuss the interpretation and usefulness of filtered microdiffraction patterns and lattice images.
1. Introduction In this paper we consider some approaches to the problem of obtaining a direct read-out of the atomic species present in a thin crystal, together with their atomic coordinates, through the use of the elastic and core-loss energy filtered lattice images obtainable on modern field-emission dedicated STEM instruments. This utopian goal is far from obtainable, chiefly due to limited instrumental resolution and the lack of a simple theory of coupled multiple elastic and inelastic scattering with which to interpret such images. While a good deal of attention has been devoted to the problem of microanalysis using the electron energy loss spectroscopy of core losses in non-crystalline materials, there has been little discussion of the application of the same method to crystals. Since localized inelastic scattering in crystals presents some novel features (such as the sensitivity of Kikuchi line intensities to the crystallographic site of the inelastic event) and since it is possible with modern instruments to form microdiffraction patterns from regions smaller than a single unit cell [1], it was felt worthwhile to undertake a study of
microanalysis by energy loss spectroscopy in crystals. In section 2 we consider some effects of atomic number variation on the elastic microdiffraction pattern as formed with an electron probe which is "smaller" than the unit cell. In section 3, experimental results are reported in which energy loss spectra (including localized losses) are collected at different symmetry points within a single unit cell. Finally, in section 4 we discuss the origins of the differences in these spectra, and the conditions under which a direct correlation between energy filtered STEM lattice images and crystal structure may be expected.
2. Atomic number information in the elastic microdiffraction pattern Since the elastic microdiffraction pattern formed with an electron probe of sub-unit cell dimensions can be used to form a STEM structure image [2], which to some extent distinguishes atoms according to their atomic number, it might be expected that this "structure factor" contrast could be used
0304-3991/82/0000-0000/$02.75 © 1982 North-Holland
J.C.H. Spence, J. Lynch / STEM rnicroanalysis by transmission EELS in crystals
268
to distinguish heavy and light atom sites by microdiffraction in a way similar to the analysis of crystal structures by X-ray diffraction. Thus the elastic microdiffraction pattern may contain at least as much "atomic number" information as energy filtered patterns, and has the advantage of higher intensity and more straightforward interpretation, due to the absence of mixed elastic-inelastic scattering. There are now several studies in the literature giving examples of crystallographic information extracted from convergent beam microdiffraction patterns obtained using a subnanometer electron probe [3,4]. We now consider the interpretation of these patterns from the point of view of distinguishing whether the probe lies over a heavy atom or a light atom in a crystal, by using the angular variation of intensity in the overlap region between adjacent convergent beam discs, rather then the spatial variation of the overlap intensity with probe position as used in a STEM lattice image. Fig. 1 suggests the experimental arrangement typically used with our modified Vacuum Generators HB5 instrument. The experimental observation of interference effects in the region of disc overlap near P3 indicates that the objective aperture OA can be taken to be coherently filled, that is that P0 be treated as a point source. Then, in the absence of lens aberrations a diffraction limited probe of "size" a will result from the use of an objective aperture semiangle OR = 0.61X/a if the probe "size" is defined as half the width between first minima. The Bragg angle for lattice planes of spacing d is 0 B = 0.5h/d, and thus the condition that the probe be "smaller" than the crystal unit cell is that the diffraction discs overlap [2]. In fact, in the more realistic case where spherical aberration must be considered the probe has very extended "tails", but is most concentrated at the optimum "dark-field" focus [5] given by A f = - 0.44(Cs)t )
1/2 .
In general it can be shown that [2]: (i) For a perfect crystal the intensity within the microdiffraction discs is independent of probe position if these do not overlap (probe "larger" than unit cell).
Po
I
oY
I
Fig. 1. The intensity at P3 in STEM microdiffraction can be calculated using reciprocity by calculating the intensity at P0 due to a fictitious source at P3-
(ii) The intensity within the overlap region is sensitive to the probe position within the unit cell, to focus and spherical aberration, and to the crystal structure. (It is this intensity which is used to form a STEM lattice image [2].) In fact, the variation of intensity across the overlap region can be used to determine whether the probe lies on a heavier or lighter atom, as follows. We consider the systematics orientation in the configuration of fig. 1. In many crystals the projection of the structure in two directions normal to the systematic line results in a set of planes of alternating high and low potential. For this common case, the intensity variation across AB can be estimated using two-beam theory and reciprocity. Experience with this simple theory applied to the similar problem of electron channelling shows that it is a useful guide to cation site determination in spinel structures [6]. For a lens with wavefront aberration X(u) (u = 0/X), specimen thickness t, and lattice period d containing alternating planes of light and heavy atoms, two-beam theory gives the intensity variation across AB as
I(c,S) = 1 + 2 Re[ b0 b exp(2 ric/d) -X(UB + a/X) + X ( u B - a/X)].
(1)
J.C.H. Spence,J. Lynch / STEM microanalysisby transmissionEELS in crystals Here ~k0 and ~g are the two-beam diffracted amplitudes, S = a/d is the excitation error (with a defined in fig. 1) and c/d is the fractional probe coordinate within the lattice repeat. Using
l~o=[COSg( S) -- ia~g(1 Jr-S2~2 )-l/2 sing(s )] × exp( - i~rSt), ~kg= i(1 + S2~2g)-l/2sinF(S)exp(ieSt), with F(S)=~rt(1 + S2~2g)l/2//~g and ~g the twobeam extinction distance, we obtain
I ( c , S ) = 1 + 2(1
+ S2~2)-1/2
× cos F ( S ) cos G(S) sin F ( S ) + 2S~g(1 + $ 2 ~ ) - 1 sin2F(S) sin G ( S ) ,
(2) where
G( S ) -- 2 ~ c / d - x(uB +
a/X) (3)
+ X( UB-- a/X ) - 2¢rSt.
We choose an origin on the heavier atom, making
269
the structure factor ~r/£g= o ~ positive. Then in the absence of lens aberrations (X = 0), eq. (2) predicts an approximately linear and decreasing angular dependence for I(0,s) (probe on heavy atom) in the neighborhood of P3 (s small) for t < ~g. For c/d= 1/2 (probe on lighter atom) the sign of the second and third terms is reversed, and the curve seen for old = 0 is now exactly reversed. Thus in general a negative slope in the intensity distribution at the midpoints between Bragg reflections indicates that the probe is situated over a heavy atom, while a positive slope occurs for probe on the lighter atomic site. Note that a choice of origin on the lighter atom gives consistent results, since this changes the sign of both ~g and sin G(S). Dynamical calculations which do not make the simplifying two-beam approximation support these predictions. Fig. 2 shows the results of many-beam calculations for the systematics case of a set of alternating heavy and light atomic planes. This calculation was performed using the multislice artificial superlattice technique, in which a large unit cell is chosen containing many cells of the perfect crystal and larger than the incident electron probe. Thus the first slice contains the
~~probe onOx
probe on Au
J m 4 ~
'
.r
|
I L
;
Fig. 2. Unaberratexl elastic STEM microdiffraction pattern (dynamical systematics calculation with coherent overlapping orders). The geometrical outline of the CBED discs is shown below the abscissa. Calculations are shown for two probe positions. Note interference effect, sensitive to probe position, in region of overlap.
270
J.C.H. Spence, J. Lynch / STEM microanalysis by transmission EELS in crystals
numerical Fourier transform of the aberration function H ( u ) exp [ i x ( u ) ]
( H ( u ) the objective aperture pupil function) as the boundary condition at the entrance face of the crystal. The predicted variation in the overlap region is seen to reverse as the probe moves from the heavier to the lighter atom. The introduction of lens aberrations does not destroy this reversal of the angular dependence of the intensity in the overlap region as the probe moves from the heavier to the lighter site. However, a unique association of a particular site with the slope of the intensity is now only possible if the focus setting is known. This can be done using the Ronchigram technique [7]. The focus setting which provides the least sensitivity to changes in focus and the least variation in intensity across the overlap region is the stationary phase focus
:x f, = - C s O L where the minus sign refers to a weakened lens. Fig. 3 shows the results of dynamical calculations for a lens with C, = 2 m m at A f, and otherwise
similar conditions to fig. 2. In practice the probe may be accurately centered over either of the sites by adjusting the probe position until the required center of symmetry is observed in the microdiffraction pattern. The accuracy with which A f must be determined can be estimated as 2 d 2 / X (not difficult to achieve in practice) by allowing the maximum phase change of the A f dependent term in (3) to equal qr for 0B/2. Thus, for Cs -~ 2 m m the slope of I(0, 0) will always be positive (probe on heavier atom) near A f ~ Afs. 3. Core loss spectra recorded at symmetry points within the unit cell We report here the results of experiments designed to determine whether a useful variation in the height of a core loss peak in the transmitted electron energy loss spectrum could be observed as the STEM probe is moved from one point in the unit cell to another. Unlike previous studies [8], we have used the point group symmetry elements within the cell to reveal the absolute location of the electron probe with respect to the crystal structure.
probe On Ox ~ o n Au
Cs: 2rnm
©
o
©
Au
Ox
Au
t=g6A O/;~p,5.3-I 1-~
4X_1 " ~
I
! !
J
Fig. 3. Similar to fig. 2, but for a lens with Cs = 2 mm at the stationary phase focus for the first-order reflection. Note reversal of slope near midpoint.
J.C.H, Spence, J. Lynch / STEM rnicroanalysis by transmission EELS in crystals
By considering the Born Series solution to the Schrrdinger equation for the elastic scattering of fast electrons from a parallel sided slab in the Z O L Z approximation with boundary conditions appropriate to the use of a coherent, focussed electron probe "smaller" than the crystal unit cell, it is readily shown [9] that the point plane group symmetry of sub-unit cell electron microdiffraction pattern is equal to that of the crystal as reckoned about the center of the electron probe as origin. This is true for a stigmated lens for all focus settings and assumes that the objective aperture is coherently filled and that the intensity within the region of Bragg disc overlap (which is sensitive to probe position) is considered. Since the elastic two-dimensional microdiffraction pattern can be viewed directly on the television system attached to our HB5 STEM instrument [10], the electron probe can be located over a particular symmetry element in the unit cell by adjusting the probe position controls until the corresponding symmetry is observed in the microdiffraction pattern. Energy loss spectra were then recorded at three such positions. Crushed specimens of barium aluminate (Ba0.6A1203) were used, the structure of which is shown in fig. 4. This consists of planes of barium atoms separated at 1.14 nm intervals by spinel blocks containing only aluminium and oxygen atoms. A two-fold axis falls midway between the barium atom planes in the [100] direction, while the barium atoms themselves fall on mirror planes of symmetry. By removing the objective aperture, the Ronchigrams shown in fig. 5 were obtained
271
from thin regions of sample. The patterns are aberrated point projection shadow images of the crystal lattice [7] and are sensitive to the focus setting and aberrations of the probe-forming lens. Their use for alignment, focus and spherical aberration constant determination has been discussed in detail [7]. The stationary phase points satisfying Af = -Cs 82 for the first order barium plane reflections are indicated in fig. 5 - a small detector placed at this position could be used to obtain a two-beam STEM lattice image (related by reciprocity to an inclined illumination two-beam
0'56nm
spinel
I-Nnm
1 O: Ba *: o:
AI O
Fig. 4. Simplified structure of Ba-0.6A1203.
Fig. 5. Ronchigrams recorded at two probe positions differing by half the crystal period in the c axis direction. Note reversal of contrast around stationary phase point P as probe is moved.
272
J.C.H. Spence, J. Lynch / S T E M microanalysis by transmission EELS in crystals
Fig. 6. Elastic STEM lattice image formed using a small axial detector and showing the 11.4 A barium atom plane periodicity. An objective aperture sufficiently large to include the first-order reflections has been used.
lattice image in TEM). The interference patterns shown in fig. 5 were obtained from two points separated by 0.57 nm in the c axis direetion (normal to the mirror plane) and show the expected reversal of contrast at the stationary phase point as the probe is moved by half the c axis (projected) repeat distance of the structure. In this way, accurate calibration of the probe translation controls can be obtained, and particular focus settings established. The use of an axial detector allowed the bright-field axial elastic three-beam lattice image shown in fig. 6 to be obtained, which clearly reveals the 1.14 nm spacing of the barium atom planes. The insertion of an objective aperture slightly larger than the Bragg angle produced the elastic
microdiffraction pattern shown in fig. 7. The c axis direction was first determined from the lattice image, and probe positions sought which produced microdiffraction patterns showing a mirror line of symmetry (figs. 7a and 7c). Energy loss spectra were recorded successively in this position over the barium atoms (shown in fig. 8a), and midway between them (figs. 7b and 8b). The distance in the c axis direction between the probe positions used to record the microdiffraction patterns is thus 0.57 nm. The spectrum of fig. 8a (probe centered on the mirror line of symmetry containing the barium atoms) shows clear evidence of the barium M 4 and M 5 edges, while that recorded with the probe midway between the barium planes (fig. 8b does not. The detector semiangle used was 10
273
...//c./ AE (~V) 7g0
5b0
2J0
6
CK
A_ AE (eV) 750
500
250
0
Fig. 8. Electron energy loss spectra recorded with the electron probe centered on the crystal mirror plane (upper spectrum) containing the barium atoms, and midway between barium planes (lower spectrum). The vertical scale has been adjusted to clarify differing regions. Note the reduction in height of the barium M 4 and M 5 edges as the probe is moved across the unit cell.
Fig. 7. Microdiffraction patterns of barium aluminate formed using a sub-unit cell electron probe located on the mirror plane of symmetry containing the barium atoms (upper pattern), midway between the mirrors (middle pattern) and on the next mirror (lower pattern). The mirror planes are separated by 11.4 ,~. These are 35 mm photographs of the television display.
mrad and the spectra were acquired over about 20 s, using a 5 V energy window. Using the digital scan generator and facilities for image subtraction [11], it would thus be possible to form a core-loss filtered lattice image using counts collected only in the neighborhood of the edge and thus greatly relaxing the requirements on thermal and mechanical stability. In the present experiments, the mechanical stability of the probe can be judged
from the Ronchigrams; however, these cannot be viewed while the energy-loss spectrum is being collected with the present instrumental design (a modified design to allow this is under development). From extended observations of Ronchigrams we judge that the probe may have moved no more than a few .~ while the spectra were being recorded.
4. Discussion
The height of the core-loss peaks in fig. 8 depends on the intensity distribution around the origin of an energy filtered microdiffraction pattern. The interpretation of these patterns must include the effects of the multiple elastic Bragg scattering of the inelastically scattered electrons. For the barium M 4 and M 5 losses at AE = 760 eV
274
J.C.H. Spence, J. Lynch / STEM microanalysis by transmission EELS in crystals
we have that #E = AE/2Eo~ 8a so that, for axial plane-wave illumination, appreciable overlap of the Lorentzian tails of the inelastic angular scattering distribution laid down around each Bragg direction is expected. In such a "point" diffraction pattern (one formed in transmission using axial plane-wave illumination), the inelastic scattering distribution is responsible for the appearance of Kikuchi lines, which, for 0B<0E "(2oa, may be thought of as arising from the interference between overlapping inelastic scattering distributions centered about each Bragg spot. As in the case of elastic STEM lattice imaging, this overlap intensity or Kikuchi lines is expected to be sensitive to the crystallographic site of the inelastic event [12]. The theory for the two cases differs only in the form of the angular distribution assumed and in the additional depth integration over inelastic sites in the inelastic scattering case, if localized losses and single inelastic scattering is assumed. For the experimental conditions used in section 3, the lattice is resolved in the elastic channel (i.e. the elastic Bragg discs overlap) and, in addition, there is overlap of the inelastic scattering distributions, which is convoluted by multiple scattering against the elastic scattering distribution. The resulting complicated intensity distribution in energy filtered microdiffraction patterns cannot be predicted in a simple way; however, its main features should include Kikuchi lines and a high sensitivity both to the STEM probe coordinates and to those of the inelastic event. In addition, the filtered intensity must be zero for a probe situated at a large distance from the inelastic site (unlike the elastic intensity, whose normalization is independent of the probe coordinate). Finally, for the modified hydrogenic inelastic wave functions used in the following calculations, the filtered patterns should preserve the symmetry of the crystal as reckoned about the probe center. For certain conditions of objective aperture semiangle 0oh and inelastic scattering angle 0E, the intensity at the midpoint between Bragg points in the filtered inelastic pattern will be independent of focus and spherical aberration (but not of probe inelastic site coordinate), but in general the entire pattern intensity will depend on the focus and aberrations of the probe-forming lens and on the probe co-ordinate
and inelastic site. It is therefore of some importance to establish the conditions under which an energy-filtered core-loss lattice image would give misleading information, such as intensity maxima for the filtered species which are not in registry with the corresponding lattice sites of the selected atoms. (This effect is commonly seen to occur in elastic lattice imaging through incorrect choice of focus.) To test this, a series of multiple elasticsingle inelastic scattering calculations have been performed using a modification of the algorithm of Doyle for localized inelastic events [13]. Inelastic scattering amplitudes were based on the modified hydrogenic model [14] and incorporated into the multislice algorithm with an incoherent addition of scattered inelastic intensities over equivalent lattice sites occurring at different depths through the crystal. The results of a typical calculation are shown in fig. 9. Here energy filtered core-loss microdiffraction patterns are shown for two probe positions - one over the filtered species and one mid-way between them. The calculations show all the features mentioned earlier - in particular the total area under the inelastic scattering distribution decreases as the probe is moved away
I
~l I
~
~probe
/ 'J , , ~
on
Be
I
CS:Af=0
II
--8~--
©
I
©t /
0robewidtn92~ between
zeros
,Hd.pAE=111 eV
" ooo,,o t =136 ~,
~
~
I 1
I
~
Bragos
! Fig. 9. Dynamical systematics single inelastic-multiple elastic scattering calculations for the beryllium core-loss filtered microdiffraction pattern formed with a unit cell sized electron probe. Note differing ordinate scales and loss of total scattered intensity as the probe is moved away from the beryllium atom. In the absence of lens aberrations, the deep minima midway between Bragg points in the continuous line may be interpreted as a dynamical Kikuchi line.
J. CH. Spence, J. Lynch / S T E M microanalysis by transmission EELS in crystals
from the filtered species. Since there is no "forward scattered" beam, the use of a small axial detector produces a "dark-field" energy filtered image. The entire pattern is sensitive to focus; however, calculations with Cs - - 2 mm, 0ohj = 0.01 rad around Af0 = --378 ,~ all show a decrease in total inelastic scattering as the "probe" is moved away from the filtered species. The optimum focus setting for best resolution is thus Af0 = -0.44(CsX) 1/2, as for dark-field TEM elastic imaging [5]. Under these conditions there is a direct correlation between intensity maxima in the filtered image and the sites of the selected species in the lattice, for thin specimens (t < 100,~). The effect of finite localization must also be considered. For 0 E >>0ohj (localization smaller than probe "size"), these effects are unimportant; however, for 0 E < 0 B (localization larger than the lattice spacing) it is possible for atoms other than the energy filtered species to appear in the filtered lattice image. Energy filtered lattice images have been used previously to demonstrate this point [8,15]. Fig. l0 shows the calculated image filtered for the K-shell loss of a single atom resting on a crystalline substrate. Here the fine oscillations in the image reveal those substrate atoms which fall within the localization of the inelastic event and which appear as a result of the elastic scattering in the substrate of the inelastically scattered electrons.
Be a a a t o m filtered
K-Iosl
image
A E . 1 1 1 eV t.72~ Cs • / ~ f , 0 . 0
Oob;>%
Fig. 10. Calculated core-loss filtered image of a single beryllium atom on a thin crystalline gold substrate. The oscillations in the tails reveal the periodicity of the substrate, despite filtering for the adatom. Note that a dark-field image is seen when using a n axial "bright-field" detector.
275
5. Conclusions (1) The variation of intensity with angle reverses in the overlap region midway between Bragg spots in coherent microdiffraction patterns as the probe is moved by half the lattice repeat distance. This result is exact in the presence of lens aberrations only in the two-beam dynamical approximation. (2) The symmetry points within a crystal unit cell can be used to determine the absolute location of a coherent STEM probe with respect to the crystal lattice if facilities are provided for efficient detection and convenient viewing of the elastic electron microdiffraction pattern. (3) Electron energy loss spectra have been recorded at symmetry points within a single unit cell known to fall on atomic planes of widely differing atomic number. These show the expected variation in the height of core-loss peaks due to localized inelastic scattering. (4) While the interpretation of core-loss filtered lattice images by comparison with computed images appears completely hopeless in the general case of coupled multiple elastic and multiple localized inelastic electron scattering, a direct correlation between intensity maxima in a filtered image and the positions of the selected species in the lattice can be expected under certain conditions. These are: (i) Specimen thickness less than about 100.~. (ii) Localized core losses are used, with a localization "smaller" than the unit cell (this may mean AE < 1000 eV (15)). (iii) A coherent probe is used at the optimum dark-field focus Af---- --0.44 (Cs)~)l/2 and an objective aperture sufficiently large to resolve the lattice. The use of electron Ronchigrams [7] allows this focus setting to be selected. (iv) The use of a STEM detector large enough to collect all the appreciable inelastic scattering of interest appears to have theoretical advantages; however, the influence of detector size on image resolution has not been studied in detail. In practice this will be limited by spectrometer aberrations.
Acknowledgments We are most grateful to Dr. M. O'Keefe for his advice and help with the preparation of specimens.
276
J.C.H. Spence, J. Lynch / STEM microanalysis by transmission EELS in crystals
This work was supported by ARO grant No. DAAG-29-80-C-0080, and the NSF HREM Facility at ASU.
References [1] J.M. Cowley, Ultramicroscopy 7 (1981) 19. [2] J.C.H. Spence and J.M. Cowley, Optik 50 (1978) 129. [3] J.M. Cowley and J.C.H. Spence, Ultramicroscopy 6 (1981) 359, [4] J.P. Lynch, E. Lesage, H. Dexpert and E. Freund, Inst. Phys. Conf. Ser. 61 (1982). [5] J.M. Cowley, Acta Cryst. A29 (1973) 529.
[6] J. Taft,, Acta Cryst., in press. [7] J.M. Cowley, Ultramicroscopy 4 (1979) 435. [8] A.J. Craven and C. Colliex, J. Microsc. Spectrosc. Electron. 2 (1977) 511. [9] J.M. Cowley and J.C.H. Spence, Ultramicroscopy 3, (1979) 433. [10] J.M. Cowley, in: Scanning Electron Microscopy/1980, Vol. 1, Ed. O. Johari (Scanning Electron Microscopy, AMF O'Hare, IL) p. 61. [11] M. Strahm and J.H. Butler, Rev. Sci. Instr. 52 (1981) 840. [12] J. Gjonnes and R. Hoier, Acta Cryst. A27 (1971) 166. [13] P.A. Doyle, Acta Cryst. A25 (1969) 569. [14] R.F. Egerton, Ultramicroscopy 4 (1979) 169. [15] A.J. Craven, J.M. Gibson, A. Howie and D.R. Spalding, Phil. Mag. A38 (1978) 519.