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SEM based estimation of the grain boundary plane orientation in zinc oxide varistors using conductive mode microscopy
Scripta mater. 43 (2000) 529 –534 www.elsevier.com/locate/scriptamat
SEM BASED ESTIMATION OF THE GRAIN BOUNDARY PLANE ORIENTATION IN ZINC OXIDE VARISTORS USING CONDUCTIVE MODE MICROSCOPY C. Leach Manchester Materials Science Centre, University of Manchester and UMIST, Manchester M1 7HS, UK (Received April 3, 2000) (Accepted in revised form May 18, 2000) Keywords: Electroceramic; Grain boundary; Scanning electron microscopy; REBIC
Introduction The special properties of many electroceramics arise from the presence of charged grain boundary planes and the associated space-charge regions [1]. Whilst it is generally considered that these structures are enhanced by the careful and controlled addition of selected dopants, there is growing evidence that crystallographic aspects of the interface also play a role in determining details of the electrical behaviour of individual grain boundaries [2– 4]. This is potentially important in anisotropic crystal systems, such as zinc oxide (space group P63mc), where differing crystal faces presented on opposite sides of the interface may lead to abrupt changes in the electrical behaviour, affecting density of states, dielectric constant or band structure. The development of new high resolution local property measurement techniques has given new impetus to the study of factors governing functional behaviour and detailed information regarding the structure and properties of individual interfaces is now becoming available [5–7]. Remote electron beam induced current (REBIC) microscopy is a form of the conductive mode of operation of the SEM and is widely used to study electrically active grain boundaries in polycrystalline semiconductors and electroceramics [8 –11]. Figure 1 shows the experimental configuration, with the two current collecting electrodes forming ohmic contacts on either side of the grain boundary of interest. Under primary beam irradiation, electron-hole pairs that are generated within the space-charge region of the grain boundary, or (minority) carriers that can drift into the space-charge region before recombining are swept up by the electric field, giving rise to an EBIC signal. For a symmetrical, charged grain boundary, the expected EBIC contrast is bright-dark (termed type I in ref [8]) as the grain boundary is traversed since the opposed fields on either side of the interface generate charge collection currents in opposite directions [10]. However, whilst symmetrical grain boundary structures are commonly observed in cubic materials, such as silicon or gallium arsenide, it is frequently the case in non-cubic crystal systems, such as zinc oxide, that the REBIC signal is suppressed on one side of the interface and only a single bright or single dark line is present (type II contrast) [8], suggesting that the local crystal structure may affect details of the electrical characteristics. In REBIC mode microscopy, the peak EBIC current, IEBIC, collected by the electrodes is given by: 1359-6462/00/$–see front matter. © 2000 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S1359-6462(00)00463-2
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Figure 1. The sample configuration used for conductive mode microscopy.
VBIB IEBIC ⫽ CC d ⑀
(1)
where is the drift length, d the separation of the current collecting electrodes, cc the fraction of electron hole pairs generated by the incident beam that are swept up by the field, VB the beam energy, IB the beam current and ⑀ the average energy required to form an electron hole pair [12]. In zinc oxide based varistors, with electrode spacings of 20 m to 40 m, IEBIC is typically 10 –25 times the incident beam current and so can be readily resolved over background. Since many grain boundaries are curved it is key to establish the local orientation in the same region as the electrical property measurements are being made, in order to relate the electrical characteristics of a particular grain boundary to its structure. Whilst SEM based electron backscattered diffraction pattern (EBSP) analysis is now routinely used to measure grain orientation [2], it cannot be used directly to establish the slope of the grain boundary plane, and so other approaches are required. In an earlier study, depth resolved EBIC microscopy was used to estimate the orientation of electrically active varistor grain boundaries showing type I EBIC contrast, by measuring orientation dependant broadening of the EBIC signal with beam energy [13]. However, this approach was found to be of limited use, since the magnitude of the effect meant that it was only possible to measure the orientation of shallowly dipping grain boundaries accurately. Further, the method was inappropriate for characterising the majority of electrically active grain boundaries in zinc oxide, that show type II contrast. A modified approach is presented here, enabling an estimate of the slope of asymmetric electrically active grain boundaries to be made, by measuring the lateral shift in REBIC contrast with beam energy. Method Zinc oxide powder, doped with 1.0wt.% bismuth oxide and 0.5wt.% antimony oxide, was prepared by a conventional mixed oxide route, compacted and sintered at 1100°C for 2 hours, producing a varistor with a mean grain size of around 40 m. One face of the sintered pellet was ground flat and lapped with diamond paste, prior to final polishing with a water-based slurry of 0.3 m alumina powder. The sample was then mounted onto an electrically isolated stub and placed in the chamber of a Phillips 525 SEM for secondary electron and conductive mode imaging using a beam voltage of 15keV and a beam current of 2nA. Tungsten current collecting electrodes were positioned directly onto the sample surface immediately to either side of the grain boundary of interest using a micromanipulator. The signal collected under primary beam irradiation was amplified using a commercial EBIC amplifier.
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Figure 2. Secondary electron (a), and EBIC images of an electrically active grain boundary in a zinc oxide varistor, taken at a beam current of 2nA and beam voltages of; (b) 5keV; (c) 15keV, and (d) 25keV. The arrowed line shows the shift of bright EBIC contrast to the right as the beam energy is increased. (Scale bar ⫽ 10 m.)
Grain orientations were established by electron backscattered diffraction (EBSD) pattern analysis, using a JEOL JSM 6300 fitted with a Nordif CCD camera and HKL Channel⫹ software. The Gru¨n range, RG, in m, was calculated according to [14]; RG ⫽ 共0.040Eb1.75兲/
(2)
where Eb is the beam energy in keV and is the density of zinc oxide in g 䡠 cm⫺3. Results and Discussion Figure 2(a) is a secondary electron image of the area selected for study. The grain boundary is located between current collecting electrodes that are positioned on the surface 30 m apart. Figure 2(b-d) show three REBIC images of the grain boundary, at beam energies of 5keV, 15keV and 25keV respectively and a beam current of 1.9nA. The grain boundary is electrically asymmetric, with only one side of the interface showing electrical activity, resulting in bright type II contrast. At 5keV beam energy (Figure 2b), the penetration depth of the electrons is small and the EBIC signal is seen to vary in intensity along
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Figure 3. REBIC linescan of the electrically active grain boundary studied here, showing bright type II contrast. Beam energy ⫽ 15keV.
the length of the grain boundary, presumably due to local differences in surface recombination velocity. As the beam energy is increased (Figure 2(c,d)) the penetration depth increases and the grain boundary is excited deeper below the surface. The signal becomes wider due to the increased Gru¨n range and there is a small lateral shift of the EBIC signal relative to the electrodes (arrowed), that is just visible in the REBIC mode images, indicating that the grain boundary is sloping. Figure 3 shows a REBIC mode linescan of the electrically active grain boundary, using beam parameters of 15keV and 1.9nA. The curve follows the classic Gaussian profile, due to the form of the excitation volume, with exponentially decreasing tails due to the finite drift length. The precise orientation of the grain boundary immediately below the surface may be established using the simple beam interaction model shown in Figure 4. In this case the grain boundary is inclined at an angle, , to the surface and the electrically active region has width, t. As the incident electron beam rasters the surface it generates electron-hole pairs within a sphere of diameter RG, the Gru¨n range, tangential to the surface. Any electron or hole that is formed within the drift length, , of the electrically active region may be collected by the field and contribute to IEBIC. The range of incident beam positions over which this occurs is indicated, resulting in the EBIC signal having an overall width, W. For a sloping grain boundary, inclined at angle to the horizontal, W is given by:
Figure 4. The grain boundary EBIC model used in this study.
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Figure 5. Graph showing the lateral shift of the image with beam voltage, plotted against RG/2, from which the grain boundary orientation may be established.
W ⫽ 共RG ⫹ 2 ⫹ t兲/sin
(3)
Thus, the peak will show some broadening if the grain boundary plane is not parallel to the incident electron beam, and this must be allowed for in modelling beam interactions. It can easily be seen that the centre of the EBIC signal coincides with the centre of the electrically active region of the grain boundary at a depth, RG/2, below the surface. Even if the drift length differs on each side of the interface due to crystal anisotropy effects, the centre of the REBIC signal will maintain a constant offset with regard to the grain boundary plane as RG is varied. Thus, by plotting the lateral shift of the EBIC contrast against RG/2, calculated using equation (2), the grain boundary orientation can be established. Figure 5 shows this for the grain boundary studied here using beam energies in the range 10keV to 25keV. In this case the mean declination of the grain boundary in the top 1 m of the sample was found to be 42° to the horizontal. The crystal faces forming the grain boundary are defined by the orientation of the grain boundary plane with respect to the crystal axes of the zinc oxide grains on either side of the interface. Standard EBSP analysis was carried out to establish the grain orientations. The mismatch across the interface was found to be 63° about an axis 4.5° from [31.0], classifying the grain boundary as random, high angle. Figure 6a shows the crystal axes of the two grains in stereographic projection, oriented with the sample surface horizontal and the trace of the grain boundary plane running N-S. The pole to the grain
Figure 6. (a) stereographic projection showing the orientations of the grains on either side of the interface, relative to the sample surface. a1, a2, a3 and c refer to the principal crystallographic axes of the grains on the left (L) and the right (R) sides of the interface. The pole to the grain boundary plane is also indicated (b) stereogram showing the crystal planes on the left (L) and right (R) hand sides of the grain boundary plane.
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boundary plane is also shown. In Figure 6b the orientations of the planes forming the grain boundary are plotted on the hexagonal ‘standard triangle’ in [00.1] projection. Using the method adopted here has the advantage that the orientation of the grain boundary plane is determined in the same region as the electrical measurements are made. Although it cannot provide the level of accuracy afforded by TEM, the approach is non-destructive (of the SEM sample), permits any electrically active interface to be selected for study and, in cases where the grain boundaries show marked curvature, is more accurate than approaches that calculate a mean grain boundary orientation over a larger dimension, such as optical methods or serial sectioning. This technique may be used at grain boundaries showing other forms of electrical activity, where the material can be excited at various depths, for example using cathodoluminescence or resistive contrast imaging. Since the measurements are made close to the surface, this approach could be of use in correlating electrical information gained from surface analytical techniques e.g. atomic force microscopy or scanning tunnelling microscopy with interfacial crystallography. Detailed analysis of the REBIC linescan profiles and the effect of grain boundary planes on the form of the REBIC contrast are currently underway. Conclusions The orientation of an electrically active grain boundary plane has been established in the SEM using depth resolved REBIC microscopy. Combining this information with EBSP analysis has permitted the crystal faces forming the grain boundary to be identified. This technique has the advantage of measuring the local plane orientation close to the surface, allowing direct correlation of the local grain boundary crystallography with electrical property information gained from REBIC or surface analysis techniques. The grain boundary plane may be found using other SEM signals provided they can be generated at different depths below the surface by varying the beam energy. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
A. J. Moulson and J. M. Herbert, Electroceramics, Chapman and Hall, London, (1997). F. Ernst, O. Kienzle, and M. Ru¨hle. J. Eur. Ceram. Soc. 19, 665 (1999). N. Kataoka, K. Hayashi, T. Yamamoto, Y. Sugawara, Y. Ikuhara, and T. Sakuma. J. Am. Ceram. Soc. 81, 1961 (1998). J. D. Russell, D. C. Halls, and C. Leach, J. Mater. Sci. 32, 4585 (1997). B. D. Huey, D. Lisjak, and D. A. Bonnell, J. Am. Ceram. Soc. 82, 1941 (1999). E. C. Dichey, X. Fan, and S. J. Pennycock. Acta Mater. 47, 4061 (1999). J. D. Russell and C. Leach, J. Eur. Ceram. Soc. 15, 617 (1995). J. D. Russell, D. C. Halls, and C. Leach, Acta Mater. 44, 2431 (1996). G. J. Russell, M. J. Robertson, B. Vincent, and J. Woods, J. Mater. Sci. 15, 939 (1980). J. Palm and H. Alexander, J. Phys. IV Colloq. C6, supplement to J. Phys. III, 1, 101 (1991). C. Leach, Z. Ling, and R. Freer, Scripta Mater. in press. W. Ehrenberg and D. J. Gibbons, Electron Bombardment Induced Conductivity and Its Applications, Academic Press, London (1981). J. D. Russell and C. Leach, Acta Mater. 46, 6227 (1998). A. E. Gru¨n, Z. Naturforsch. 12(a), 89 (1957).
SEM BASED ESTIMATION OF THE GRAIN BOUNDARY PLANE ORIENTATION IN ZINC OXIDE VARISTORS USING CONDUCTIVE MODE MICROSCOPY C. Leach Manchester Materials Science Centre, University of Manchester and UMIST, Manchester M1 7HS, UK (Received April 3, 2000) (Accepted in revised form May 18, 2000) Keywords: Electroceramic; Grain boundary; Scanning electron microscopy; REBIC
Introduction The special properties of many electroceramics arise from the presence of charged grain boundary planes and the associated space-charge regions [1]. Whilst it is generally considered that these structures are enhanced by the careful and controlled addition of selected dopants, there is growing evidence that crystallographic aspects of the interface also play a role in determining details of the electrical behaviour of individual grain boundaries [2– 4]. This is potentially important in anisotropic crystal systems, such as zinc oxide (space group P63mc), where differing crystal faces presented on opposite sides of the interface may lead to abrupt changes in the electrical behaviour, affecting density of states, dielectric constant or band structure. The development of new high resolution local property measurement techniques has given new impetus to the study of factors governing functional behaviour and detailed information regarding the structure and properties of individual interfaces is now becoming available [5–7]. Remote electron beam induced current (REBIC) microscopy is a form of the conductive mode of operation of the SEM and is widely used to study electrically active grain boundaries in polycrystalline semiconductors and electroceramics [8 –11]. Figure 1 shows the experimental configuration, with the two current collecting electrodes forming ohmic contacts on either side of the grain boundary of interest. Under primary beam irradiation, electron-hole pairs that are generated within the space-charge region of the grain boundary, or (minority) carriers that can drift into the space-charge region before recombining are swept up by the electric field, giving rise to an EBIC signal. For a symmetrical, charged grain boundary, the expected EBIC contrast is bright-dark (termed type I in ref [8]) as the grain boundary is traversed since the opposed fields on either side of the interface generate charge collection currents in opposite directions [10]. However, whilst symmetrical grain boundary structures are commonly observed in cubic materials, such as silicon or gallium arsenide, it is frequently the case in non-cubic crystal systems, such as zinc oxide, that the REBIC signal is suppressed on one side of the interface and only a single bright or single dark line is present (type II contrast) [8], suggesting that the local crystal structure may affect details of the electrical characteristics. In REBIC mode microscopy, the peak EBIC current, IEBIC, collected by the electrodes is given by: 1359-6462/00/$–see front matter. © 2000 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S1359-6462(00)00463-2
530
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Vol. 43, No. 6
Figure 1. The sample configuration used for conductive mode microscopy.
VBIB IEBIC ⫽ CC d ⑀
(1)
where is the drift length, d the separation of the current collecting electrodes, cc the fraction of electron hole pairs generated by the incident beam that are swept up by the field, VB the beam energy, IB the beam current and ⑀ the average energy required to form an electron hole pair [12]. In zinc oxide based varistors, with electrode spacings of 20 m to 40 m, IEBIC is typically 10 –25 times the incident beam current and so can be readily resolved over background. Since many grain boundaries are curved it is key to establish the local orientation in the same region as the electrical property measurements are being made, in order to relate the electrical characteristics of a particular grain boundary to its structure. Whilst SEM based electron backscattered diffraction pattern (EBSP) analysis is now routinely used to measure grain orientation [2], it cannot be used directly to establish the slope of the grain boundary plane, and so other approaches are required. In an earlier study, depth resolved EBIC microscopy was used to estimate the orientation of electrically active varistor grain boundaries showing type I EBIC contrast, by measuring orientation dependant broadening of the EBIC signal with beam energy [13]. However, this approach was found to be of limited use, since the magnitude of the effect meant that it was only possible to measure the orientation of shallowly dipping grain boundaries accurately. Further, the method was inappropriate for characterising the majority of electrically active grain boundaries in zinc oxide, that show type II contrast. A modified approach is presented here, enabling an estimate of the slope of asymmetric electrically active grain boundaries to be made, by measuring the lateral shift in REBIC contrast with beam energy. Method Zinc oxide powder, doped with 1.0wt.% bismuth oxide and 0.5wt.% antimony oxide, was prepared by a conventional mixed oxide route, compacted and sintered at 1100°C for 2 hours, producing a varistor with a mean grain size of around 40 m. One face of the sintered pellet was ground flat and lapped with diamond paste, prior to final polishing with a water-based slurry of 0.3 m alumina powder. The sample was then mounted onto an electrically isolated stub and placed in the chamber of a Phillips 525 SEM for secondary electron and conductive mode imaging using a beam voltage of 15keV and a beam current of 2nA. Tungsten current collecting electrodes were positioned directly onto the sample surface immediately to either side of the grain boundary of interest using a micromanipulator. The signal collected under primary beam irradiation was amplified using a commercial EBIC amplifier.
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Figure 2. Secondary electron (a), and EBIC images of an electrically active grain boundary in a zinc oxide varistor, taken at a beam current of 2nA and beam voltages of; (b) 5keV; (c) 15keV, and (d) 25keV. The arrowed line shows the shift of bright EBIC contrast to the right as the beam energy is increased. (Scale bar ⫽ 10 m.)
Grain orientations were established by electron backscattered diffraction (EBSD) pattern analysis, using a JEOL JSM 6300 fitted with a Nordif CCD camera and HKL Channel⫹ software. The Gru¨n range, RG, in m, was calculated according to [14]; RG ⫽ 共0.040Eb1.75兲/
(2)
where Eb is the beam energy in keV and is the density of zinc oxide in g 䡠 cm⫺3. Results and Discussion Figure 2(a) is a secondary electron image of the area selected for study. The grain boundary is located between current collecting electrodes that are positioned on the surface 30 m apart. Figure 2(b-d) show three REBIC images of the grain boundary, at beam energies of 5keV, 15keV and 25keV respectively and a beam current of 1.9nA. The grain boundary is electrically asymmetric, with only one side of the interface showing electrical activity, resulting in bright type II contrast. At 5keV beam energy (Figure 2b), the penetration depth of the electrons is small and the EBIC signal is seen to vary in intensity along
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Figure 3. REBIC linescan of the electrically active grain boundary studied here, showing bright type II contrast. Beam energy ⫽ 15keV.
the length of the grain boundary, presumably due to local differences in surface recombination velocity. As the beam energy is increased (Figure 2(c,d)) the penetration depth increases and the grain boundary is excited deeper below the surface. The signal becomes wider due to the increased Gru¨n range and there is a small lateral shift of the EBIC signal relative to the electrodes (arrowed), that is just visible in the REBIC mode images, indicating that the grain boundary is sloping. Figure 3 shows a REBIC mode linescan of the electrically active grain boundary, using beam parameters of 15keV and 1.9nA. The curve follows the classic Gaussian profile, due to the form of the excitation volume, with exponentially decreasing tails due to the finite drift length. The precise orientation of the grain boundary immediately below the surface may be established using the simple beam interaction model shown in Figure 4. In this case the grain boundary is inclined at an angle, , to the surface and the electrically active region has width, t. As the incident electron beam rasters the surface it generates electron-hole pairs within a sphere of diameter RG, the Gru¨n range, tangential to the surface. Any electron or hole that is formed within the drift length, , of the electrically active region may be collected by the field and contribute to IEBIC. The range of incident beam positions over which this occurs is indicated, resulting in the EBIC signal having an overall width, W. For a sloping grain boundary, inclined at angle to the horizontal, W is given by:
Figure 4. The grain boundary EBIC model used in this study.
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Figure 5. Graph showing the lateral shift of the image with beam voltage, plotted against RG/2, from which the grain boundary orientation may be established.
W ⫽ 共RG ⫹ 2 ⫹ t兲/sin
(3)
Thus, the peak will show some broadening if the grain boundary plane is not parallel to the incident electron beam, and this must be allowed for in modelling beam interactions. It can easily be seen that the centre of the EBIC signal coincides with the centre of the electrically active region of the grain boundary at a depth, RG/2, below the surface. Even if the drift length differs on each side of the interface due to crystal anisotropy effects, the centre of the REBIC signal will maintain a constant offset with regard to the grain boundary plane as RG is varied. Thus, by plotting the lateral shift of the EBIC contrast against RG/2, calculated using equation (2), the grain boundary orientation can be established. Figure 5 shows this for the grain boundary studied here using beam energies in the range 10keV to 25keV. In this case the mean declination of the grain boundary in the top 1 m of the sample was found to be 42° to the horizontal. The crystal faces forming the grain boundary are defined by the orientation of the grain boundary plane with respect to the crystal axes of the zinc oxide grains on either side of the interface. Standard EBSP analysis was carried out to establish the grain orientations. The mismatch across the interface was found to be 63° about an axis 4.5° from [31.0], classifying the grain boundary as random, high angle. Figure 6a shows the crystal axes of the two grains in stereographic projection, oriented with the sample surface horizontal and the trace of the grain boundary plane running N-S. The pole to the grain
Figure 6. (a) stereographic projection showing the orientations of the grains on either side of the interface, relative to the sample surface. a1, a2, a3 and c refer to the principal crystallographic axes of the grains on the left (L) and the right (R) sides of the interface. The pole to the grain boundary plane is also indicated (b) stereogram showing the crystal planes on the left (L) and right (R) hand sides of the grain boundary plane.
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boundary plane is also shown. In Figure 6b the orientations of the planes forming the grain boundary are plotted on the hexagonal ‘standard triangle’ in [00.1] projection. Using the method adopted here has the advantage that the orientation of the grain boundary plane is determined in the same region as the electrical measurements are made. Although it cannot provide the level of accuracy afforded by TEM, the approach is non-destructive (of the SEM sample), permits any electrically active interface to be selected for study and, in cases where the grain boundaries show marked curvature, is more accurate than approaches that calculate a mean grain boundary orientation over a larger dimension, such as optical methods or serial sectioning. This technique may be used at grain boundaries showing other forms of electrical activity, where the material can be excited at various depths, for example using cathodoluminescence or resistive contrast imaging. Since the measurements are made close to the surface, this approach could be of use in correlating electrical information gained from surface analytical techniques e.g. atomic force microscopy or scanning tunnelling microscopy with interfacial crystallography. Detailed analysis of the REBIC linescan profiles and the effect of grain boundary planes on the form of the REBIC contrast are currently underway. Conclusions The orientation of an electrically active grain boundary plane has been established in the SEM using depth resolved REBIC microscopy. Combining this information with EBSP analysis has permitted the crystal faces forming the grain boundary to be identified. This technique has the advantage of measuring the local plane orientation close to the surface, allowing direct correlation of the local grain boundary crystallography with electrical property information gained from REBIC or surface analysis techniques. The grain boundary plane may be found using other SEM signals provided they can be generated at different depths below the surface by varying the beam energy. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
A. J. Moulson and J. M. Herbert, Electroceramics, Chapman and Hall, London, (1997). F. Ernst, O. Kienzle, and M. Ru¨hle. J. Eur. Ceram. Soc. 19, 665 (1999). N. Kataoka, K. Hayashi, T. Yamamoto, Y. Sugawara, Y. Ikuhara, and T. Sakuma. J. Am. Ceram. Soc. 81, 1961 (1998). J. D. Russell, D. C. Halls, and C. Leach, J. Mater. Sci. 32, 4585 (1997). B. D. Huey, D. Lisjak, and D. A. Bonnell, J. Am. Ceram. Soc. 82, 1941 (1999). E. C. Dichey, X. Fan, and S. J. Pennycock. Acta Mater. 47, 4061 (1999). J. D. Russell and C. Leach, J. Eur. Ceram. Soc. 15, 617 (1995). J. D. Russell, D. C. Halls, and C. Leach, Acta Mater. 44, 2431 (1996). G. J. Russell, M. J. Robertson, B. Vincent, and J. Woods, J. Mater. Sci. 15, 939 (1980). J. Palm and H. Alexander, J. Phys. IV Colloq. C6, supplement to J. Phys. III, 1, 101 (1991). C. Leach, Z. Ling, and R. Freer, Scripta Mater. in press. W. Ehrenberg and D. J. Gibbons, Electron Bombardment Induced Conductivity and Its Applications, Academic Press, London (1981). J. D. Russell and C. Leach, Acta Mater. 46, 6227 (1998). A. E. Gru¨n, Z. Naturforsch. 12(a), 89 (1957).