Availableonlineatwww.sciencedirect.com Science Direct E噩≈RS ELSEVIER Journal of the European Ceramic Society 29(2009)539-550 www.elsevier.comlocate/jeurceramsoc Development of microstructure during creep of polycrystalline mullite and a nanocomposite mullite/5 vol %o sic S Gustafsson a, L K L. Falk * J.E. Pitchford, W.J. Clegg ,E. Liden, E. Carlstromc Department of Applied Physics, Chalmers University of Technology SE-412 96 Goteborg, Sweden Metallurgy, University of Cambridge, e Swedish Ceramic Institute. Swerea /VE Box 104. SE-431 22 MoIndal. Sweden Received 25 June 2008: accepted 27 June 2008 Available online 21 August 2008 The microstructures of as-sintered and creep tested polycrystalline mullite and mullite reinforced with 5 vol %o nano-sized Sic particles have been characterized by scanning and transmission electron microscopy. The dislocation densities after tensile creep testing at 1300 and 1400C were virtually unchanged as compared to the as-sintered materials which indicates diffusion-controlled deformation. Mullite matrix grain boundaries bending around intergranular Sic particles suggest that grain boundary pinning, in addition to a reduced mullite grain size, contributed to the increased creep resistance of the mullite/5 vol. SiC nanocomposite. Both materials showed pronounced cavitation at multi-grain junctions after creep testing at 1400C which suggests that unaccommodated grain boundary sliding, facilitated by softening of the intergranular glass, occurred at this temperature. This is consistent with the higher stress exponents at 1400C C 2008 Elsevier Ltd. all rights reserved. Keywords: Mullite; Nanocomposites; Grain boundaries; Electron microscopy; Creep 1. Introduction not fully understood.. 5. It has been suggested that the improved creep resistance of alumina/SiC nanocomposites is caused by The incorporation of nano-sized second-phase ceramic parti- the thermal mismatch between alumina and SiC 5 Internal com- cles into a ceramic matrix may lead to significant improvements pressive stresses are introduced at the alumina/SiC interface, and in the mechanical properties. -Ohji et al. 2 found that the this results in a stronger particle/matrix bonding and thereby an creep rate of alumina reinforced with 17 vol %o SiC nanopar- improved creep resistance. Itis,therefore, of interest toevaluate ticles was three orders of magnitude lower, and the creep life 10 different matrix materials with different thermal expansion coef- times longer, than that of single-phase alumina. Alumina rein- ficients, and to characterize particle/matrix interface structures forced with 5 vol. SiC nanoparticles, studied by Thompson and properties et al., showed an increase in creep resistance that was sim- Mullite, 3Al2O32SiO2, is one potential matrix material in ilar to Ohji's results, but the lower fraction of Sic particles nanocomposite ceramics Mullite has excellent high temperature resulted in a reduced number of intergranular creep cavities and properties, and its creep resistance is high compared to other a much longer creep life. As shown in several studies, a smaller oxide ceramics 9-5 In the work by Lessing et al. it was shown volume fraction of nanoparticles, typically around 5 vol %, is that the creep rate of polycrystalline mullite at 1450.Cwas one often sufficient in order to give a substantial improvement in the order of magnitude lower than that of polycrystalline alumina mechanical properties. .3. of the same grain size. The thermal mismatch between mullite The mechanism behind the pronounced improvements with and SiC is. however. smaller than that between alumina and smaller additions of a nano-sized second phase is, however, st sC.16.17 < s The present paper is focussed on the relationship between he fine-scale micro- and nanostructure and the creep deforma- ing author. Tel. +4631 772 3321 tion process in polycrystalline mullite and mullite reinforced ss: Iklfalk (@chalmers. se(L K.L. Falk) with 5 vol. nano-sized SiC particles. The microstructures 0955-2219/S-see front matter o 2008 Elsevier Ltd. All rights reserved. doi: 10. 1016/j-jeurceramsoc. 2008.06.036
Available online at www.sciencedirect.com Journal of the European Ceramic Society 29 (2009) 539–550 Development of microstructure during creep of polycrystalline mullite and a nanocomposite mullite/5 vol.% SiC S. Gustafsson a, L.K.L. Falk a,∗, J.E. Pitchford b, W.J. Clegg b, E. Lidén c, E. Carlströmc a Department of Applied Physics, Chalmers University of Technology, SE-412 96 Göteborg, Sweden b Department of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, CB2 3QZ Cambridge, UK c Swedish Ceramic Institute, Swerea IVF, Box 104, SE-431 22 Mölndal, Sweden Received 25 June 2008; accepted 27 June 2008 Available online 21 August 2008 Abstract The microstructures of as-sintered and creep tested polycrystalline mullite and mullite reinforced with 5 vol.% nano-sized SiC particles have been characterized by scanning and transmission electron microscopy. The dislocation densities after tensile creep testing at 1300 and 1400 ◦C were virtually unchanged as compared to the as-sintered materials which indicates diffusion-controlled deformation. Mullite matrix grain boundaries bending around intergranular SiC particles suggest that grain boundary pinning, in addition to a reduced mullite grain size, contributed to the increased creep resistance of the mullite/5 vol.% SiC nanocomposite. Both materials showed pronounced cavitation at multi-grain junctions after creep testing at 1400 ◦C which suggests that unaccommodated grain boundary sliding, facilitated by softening of the intergranular glass, occurred at this temperature. This is consistent with the higher stress exponents at 1400 ◦C. © 2008 Elsevier Ltd. All rights reserved. Keywords: Mullite; Nanocomposites; Grain boundaries; Electron microscopy; Creep 1. Introduction The incorporation of nano-sized second-phase ceramic particles into a ceramic matrix may lead to significant improvements in the mechanical properties.1–8 Ohji et al.2 found that the creep rate of alumina reinforced with 17 vol.% SiC nanoparticles was three orders of magnitude lower, and the creep life 10 times longer, than that of single-phase alumina. Alumina reinforced with 5 vol.% SiC nanoparticles, studied by Thompson et al.,3 showed an increase in creep resistance that was similar to Ohji’s results, but the lower fraction of SiC particles resulted in a reduced number of intergranular creep cavities and a much longer creep life. As shown in several studies, a smaller volume fraction of nanoparticles, typically around 5 vol.%, is often sufficient in order to give a substantial improvement in the mechanical properties.1,3,7,8 The mechanism behind the pronounced improvements with smaller additions of a nano-sized second phase is, however, still ∗ Corresponding author. Tel.: +46 31 772 3321. E-mail address: lklfalk@chalmers.se (L.K.L. Falk). not fully understood.3,5,8 It has been suggested that the improved creep resistance of alumina/SiC nanocomposites is caused by the thermal mismatch between alumina and SiC.5 Internal compressive stresses are introduced at the alumina/SiC interface, and this results in a stronger particle/matrix bonding and thereby an improved creep resistance.5 It is, therefore, of interest to evaluate different matrix materials with different thermal expansion coef- ficients, and to characterize particle/matrix interface structures and properties. Mullite, 3Al2O3·2SiO2, is one potential matrix material in nanocomposite ceramics. Mullite has excellent high temperature properties, and its creep resistance is high compared to other oxide ceramics.9–15 In the work by Lessing et al.9 it was shown that the creep rate of polycrystalline mullite at 1450 ◦C was one order of magnitude lower than that of polycrystalline alumina of the same grain size. The thermal mismatch between mullite and SiC is, however, smaller than that between alumina and SiC.16,17 The present paper is focussed on the relationship between the fine-scale micro- and nanostructure and the creep deformation process in polycrystalline mullite and mullite reinforced with 5 vol.% nano-sized SiC particles. The microstructures 0955-2219/$ – see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jeurceramsoc.2008.06.036
S. gi Joumal of the European Ceramic Society 29(2009 )539-550 of as-fabricated and creep tested specimens were character- zed by scanning and transmission electron microscopy (SEM. mull e TEM), and particular attention was paid to the grain bound 106 ary regions and the location and size distribution of the Sic particles. The creep tests, and theoretical modelling for the prediction of the creep behaviour of these ceramics, have uFau 1400° previously been carried out by Clegg and co-workers. 8, I9 Results from that work, relevant to the electron microscopy ivestigation presented in this paper, are reviewed shortly 1300 2. Review of creep test and modelling results 1010 STRESS(MPa) Polycrystalline mullite, and mullite reinforced with 5 vol %o SiC nanoparticles (in the following termed"the nanocompos- mu‖tesc ite"), have been subjected to tensile creep tests in air at 1300 and 1400C under stresses between 10 and 50 MPa. 18, 19 The oretical modelling of diffusion-controlled creep deformation of these two materials was also carried out. 18,19 u 2.1. Polycrystalline mullite 1300°C Creep tests of the polycrystalline mullite material at 1300C showed a stress exponent of n=1. 2 which implies that diffu sion processes(n=1)are controlling the creep deformation at this temperature, see Fig. la Creep tests performed at 1400C resulted in a higher stress exponent of n=2(Fig. la), which STRESS(MPa suggests that, in addition to diffusion processes, other creep Fig. 1. Experimentally determined steady-state creep rates of(a)the polycrys mechanisms become active at this temperature. talline mullite and(b) the mullite/5 vol %o SiC at 1300 and 1400C plotted The experimentally determined creep rates were compared as function of stress. The testing conditions for the specimens subjected to with creep rates expected for diffusion-controlled creep as the microstructural characterization are marked by circles. Diffusional creep experimental materials, are also shown plotted. Data taken from Pitchtordto 1402 from mullite creep data presented in the literature. 9, 12, 13, 20These where o is the applied stress, s2 the volume of the rate- values were then used in an estimate of the creep rate interval of ontrolling diffusing species, k the Boltzmann constant and d is the mullite ceramic in the present investigation(d=1.5 um). 18 the grain size. Deff is the effective diffusion coefficient. related The plots in Fig. la, based on data taken from Pitchford, show to the diffusion coefficients for lattice diffusion Di and grain that the experimentally determined creep rates at 1300 C, and at boundary diffusion Db according to Deff= DI (2) 2.2. Mullite reinforced with 5 vol %o SiC nanoparticles where 8 is the grain boundary width. Maximum and minimum The experimental creep rates of the nanocomposite at 1300 values of Defm S2 at the two test temperatures were calculated and 1400C are plotted in Fig. Ib. The creep tests at 1400C Table I The as-sintered and creep tested materials Material Test temperature(°C) Stress(MPa) Steady-state creep rate(s-) Grain size(um) Polycrystalline mullite 15 15x 1400 1.2×10 5 1300 9.5×10-9 Mullite/SiC nanocomposite As-sintered 1.9x 1400 2.9×10 3.2×10 0.8
540 S. Gustafsson et al. / Journal of the European Ceramic Society 29 (2009) 539–550 of as-fabricated and creep tested specimens were characterized by scanning and transmission electron microscopy (SEM, TEM), and particular attention was paid to the grain boundary regions and the location and size distribution of the SiC particles. The creep tests, and theoretical modelling for the prediction of the creep behaviour of these ceramics, have previously been carried out by Clegg and co-workers.18,19 Results from that work, relevant to the electron microscopy investigation presented in this paper, are reviewed shortly below. 2. Review of creep test and modelling results Polycrystalline mullite, and mullite reinforced with 5 vol.% SiC nanoparticles (in the following termed “the nanocomposite”), have been subjected to tensile creep tests in air at 1300 and 1400 ◦C under stresses between 10 and 50 MPa.18,19 Theoretical modelling of diffusion-controlled creep deformation of these two materials was also carried out.18,19 2.1. Polycrystalline mullite Creep tests of the polycrystalline mullite material at 1300 ◦C showed a stress exponent of n = 1.2 which implies that diffusion processes (n = 1) are controlling the creep deformation at this temperature, see Fig. 1a. Creep tests performed at 1400 ◦C resulted in a higher stress exponent of n =2 (Fig. 1a), which suggests that, in addition to diffusion processes, other creep mechanisms become active at this temperature. The experimentally determined creep rates were compared with creep rates expected for diffusion-controlled creep as given by ε˙ = 14σΩ kTd2 Deff (1) where σ is the applied stress, Ω the volume of the ratecontrolling diffusing species, k the Boltzmann constant and d is the grain size. Deff is the effective diffusion coefficient, related to the diffusion coefficients for lattice diffusion Dl and grain boundary diffusion Db according to Deff = Dl + πδ d Db (2) where δ is the grain boundary width. Maximum and minimum values of DeffΩ at the two test temperatures were calculated Fig. 1. Experimentally determined steady-state creep rates of (a) the polycrystalline mullite and (b) the mullite/5 vol.% SiC at 1300 and 1400 ◦C plotted as function of stress. The testing conditions for the specimens subjected to the microstructural characterization are marked by circles. Diffusional creep rate intervals of polycrystalline mullite, predicted for the grain sizes of the two experimental materials, are also shown plotted. Data taken from Pitchford18. from mullite creep data presented in the literature.9,12,13,20 These values were then used in an estimate of the creep rate interval of the mullite ceramic in the present investigation (d = 1.5m).18 The plots in Fig. 1a, based on data taken from Pitchford,18 show that the experimentally determined creep rates at 1300 ◦C, and at higher stresses at 1400 ◦C, were higher than the predicted values. 2.2. Mullite reinforced with 5 vol.% SiC nanoparticles The experimental creep rates of the nanocomposite at 1300 and 1400 ◦C are plotted in Fig. 1b. The creep tests at 1400 ◦C Table 1 The as-sintered and creep tested materials Material Test temperature (◦C) Stress (MPa) Steady-state creep rate (s−1) Grain size (m) Polycrystalline mullite As-sintered 1.5 1400 48.6 1.5 × 10−6 1.3 1400 13.0 1.2 × 10−7 1.5 1300 14.9 9.5 × 10−9 1.5 Mullite/SiC nanocomposite As-sintered 0.7 1400 50.0 1.9 × 10−6 0.7 1400 12.1 2.9 × 10−8 0.8 1300 14.4 3.2 × 10−9 0.8
S Gustafsson et al. /Joumal of the European Ceramic Sociery 29(2009)539-550 8 gm( 2um Fig. 2. Thermally etched surfaces of the polycrystalline mullite in the(a)as-sintered condition, and after creep testing under a stress of ( b)48.6 MPa at 1400C,(c) 130MPat1400°C,and(d)149 MPa at1300°C showed that the stress exponent increased with increasing stress; 3. Experimental procedures om around n=1.5 at stresses under 25 MPa to around n=4 at stresses above 25 MPa. This implies that the total strain was not 3.1. Materials caused by one single creep mechanism The creep rate intervals for diffusion-controlled creep of 3.1.1. Polycrystalline mullite polycrystalline mullite with a reduced average grain size The polycrystalline mullite material was produced by mxIn =0.7 um, corresponding to the average matrix grain size commercially available 3: 2 mullite powder(KM-10l, Kyoritsu, of the nanocomposite)were calculated as described in Sec- Japan) and an ammonium polyacrylate dispersant (Dispex tion 2. 1. 8,9 This was done in order to better assess the Allied Colloids, England) in water. The slurry was ball milled effect of the SiC particles, and these creep rate intervals for 24 h using zirconia ball milling beads. Green bodies were re also shown in Fig. 1b. As illustrated in Fig. Ib, the produced by slip casting and pressureless sintered in air at experimental creep rates of the nanocomposite tested at low 1650C for 3 h. The material was 97% dense as measured by stresses(<30 MPa)at 1400C were lower than the pre- Archimedean densitometry dicted diffusion creep rates of polycrystalline mullite with this grain size. At higher stresses, however, the creep rate of the 3. 1.2. Mullite/Sic nanocomposite predicted by the diffusion- The a-SiC starting powder (UF-45, H.C. Starck, Germany) controlled creep model. The two data points from creep tests had a specific surface area of around 45 m-/g. The larger particles at 1300C were within the predicted diffusion creep rate inter- and agglomerates that were difficult to break down by milling powder were removed by sedimentation. This resulted in nanocomposite was determined not only by the reduced mullite particle size(dso)of 0.22 will starting powder that had a mean drive self-diffusion in the low diffusivity SiC particles, so that aqueous suspension containing 95 vol. of the mullite pm grain size. It has been suggested that the extra work required to The nanocomposite material was then produced from they can move with the grain boundaries during creep, will lead der, 5 vol. of the milled and fractionated a-SiC powder, to a reduced creep rate as compared to polycrystalline mullite and 0.3 wt% of an ammonium polyacrylate dispersant(Dura of the same grain size max 3021, Rohm and Haas, Sweden). The suspension was
S. Gustafsson et al. / Journal of the European Ceramic Society 29 (2009) 539–550 541 Fig. 2. Thermally etched surfaces of the polycrystalline mullite in the (a) as-sintered condition, and after creep testing under a stress of (b) 48.6 MPa at 1400 ◦C, (c) 13.0 MPa at 1400 ◦C, and (d) 14.9 MPa at 1300 ◦C. showed that the stress exponent increased with increasing stress; from around n = 1.5 at stresses under 25 MPa to around n = 4 at stresses above 25 MPa. This implies that the total strain was not caused by one single creep mechanism. The creep rate intervals for diffusion-controlled creep of polycrystalline mullite with a reduced average grain size (d = 0.7m, corresponding to the average matrix grain size of the nanocomposite) were calculated as described in Section 2.1. 18,19 This was done in order to better assess the effect of the SiC particles, and these creep rate intervals are also shown in Fig. 1b. As illustrated in Fig. 1b, the experimental creep rates of the nanocomposite tested at low stresses (<30 MPa) at 1400 ◦C were lower than the predicted diffusion creep rates of polycrystalline mullite with this grain size. At higher stresses, however, the creep rate of the nanocomposite was in the range predicted by the diffusioncontrolled creep model. The two data points from creep tests at 1300 ◦C were within the predicted diffusion creep rate interval. The data presented in Fig. 1b indicate that the creep rate of the nanocomposite was determined not only by the reduced mullite grain size. It has been suggested that the extra work required to drive self-diffusion in the low diffusivity SiC particles, so that they can move with the grain boundaries during creep, will lead to a reduced creep rate as compared to polycrystalline mullite of the same grain size.19 3. Experimental procedures 3.1. Materials 3.1.1. Polycrystalline mullite The polycrystalline mullite material was produced by mixing commercially available 3:2 mullite powder (KM-101, Kyoritsu, Japan) and an ammonium polyacrylate dispersant (Dispex, Allied Colloids, England) in water. The slurry was ball milled for 24 h using zirconia ball milling beads. Green bodies were produced by slip casting and pressureless sintered in air at 1650 ◦C for 3 h. The material was 97% dense as measured by Archimedean densitometry. 3.1.2. Mullite/SiC nanocomposite The -SiC starting powder (UF-45, H.C. Starck, Germany) had a specific surface area of around 45 m2/g. The larger particles and agglomerates that were difficult to break down by milling the powder were removed by sedimentation. This resulted in a milled and fractionated SiC starting powder that had a mean particle size (d50) of 0.22m. The nanocomposite material was then produced from an aqueous suspension containing 95 vol.% of the mullite powder, 5 vol.% of the milled and fractionated -SiC powder, and 0.3 wt% of an ammonium polyacrylate dispersant (Duramax 3021, Rohm and Haas, Sweden). The suspension was
S Gustafsson et al. / Journal of the European Ceramic Society 29(2009)539-550 P (ah 500nm 200nm 500nm Fig. 3. The microstructure of the as-sintered polycrystalline mullite (TEM). a) Intergranular porosity(P), and a dislocation pile-up at a grain boundary (arrowed ).(b) Dislocation network(arrowed) associated with cavities on a larger 25 nm homogenised by milling for I h in a planetary mill using Si3N4 balls whereafter 3 wt% of a polyethylene glycol binder was added to the slip. In order to retain a homogeneous distribution of(c) the Sic nanoparticles, the slip was freeze granulated by sprayin into liquid nitrogen. The ice was removed by sublimation using a freeze dryer and the resulting granules were hot pressed into plates at 1600C for I h in an argon atmosphere at a maximum pressure of 40 MPa. Hot pressing has been widely used for pro- ducing dense nanocomposite materials since the nanoparticles may suppress full densification 24.6 The nanocomposite mate- rial in the present study reached nearly full density, 99.8%,as measured by a helium pycnometer. 3. 2. Microstructural characterization and instrumentation 20nm The as-sintered and creep tested materials included in the microstructural characterization are shown in Table 1. Polished Fig. 4. Amorphous pockets at triple grain junctions and glassy grain bound- and thermally etched (45 min at 1300C in argon)specimens ary films in the as-sintered polycrystalline mullite (TEM).(a) Glass containing were imaged in a SEM(Leo ULTRA 55)equipped with a field triple grain junctions(arrowed).(b)Diffuse dark field image of a thin glassy emission gun(FEG)in order to assess grain size and overall grain boundary film(arrowed) merging into an amorphous pocket. The glass homogeneity. The average grain size was determined by the tion Fresnel fringes(arrowed) extending along the grain boundaries reveal the mean linear intercept method, and the average intercept length presence of thin intergranular films merging into a pocket at the triple grain was multiplied by a factor of 1.5
542 S. Gustafsson et al. / Journal of the European Ceramic Society 29 (2009) 539–550 Fig. 3. The microstructure of the as-sintered polycrystalline mullite (TEM). (a) Intergranular porosity (P), and a dislocation pile-up at a grain boundary (arrowed). (b) Dislocation network (arrowed) associated with cavities on a larger elongated grain section. homogenised by milling for 1 h in a planetary mill using Si3N4 balls whereafter 3 wt% of a polyethylene glycol binder was added to the slip. In order to retain a homogeneous distribution of the SiC nanoparticles, the slip was freeze granulated by spraying into liquid nitrogen. The ice was removed by sublimation using a freeze dryer and the resulting granules were hot pressed into plates at 1600 ◦C for 1 h in an argon atmosphere at a maximum pressure of 40 MPa. Hot pressing has been widely used for producing dense nanocomposite materials since the nanoparticles may suppress full densification.2–4,6 The nanocomposite material in the present study reached nearly full density, 99.8%, as measured by a helium pycnometer. 3.2. Microstructural characterization and instrumentation The as-sintered and creep tested materials included in the microstructural characterization are shown in Table 1. Polished and thermally etched (45 min at 1300 ◦C in argon) specimens were imaged in a SEM (Leo ULTRA 55) equipped with a field emission gun (FEG) in order to assess grain size and overall homogeneity. The average grain size was determined by the mean linear intercept method, and the average intercept length was multiplied by a factor of 1.5. Fig. 4. Amorphous pockets at triple grain junctions and glassy grain boundary films in the as-sintered polycrystalline mullite (TEM). (a) Glass containing triple grain junctions (arrowed). (b) Diffuse dark field image of a thin glassy grain boundary film (arrowed) merging into an amorphous pocket. The glass appears with bright contrast. (c) Defocus Fresnel image of a triple grain junction. Fresnel fringes (arrowed) extending along the grain boundaries reveal the presence of thin intergranular films merging into a pocket at the triple grain junction
S Gustafsson et al. /Joumal of the European Ceramic Sociery 29(2009)539-550 Thin-foil specimens for TEM were prepared by standard composition of mullite grains and amorphous grain boundary pecimen preparation techniques; mechanical grinding and pol- regions was determined by fine probe eDX point analysis. Ele ishing, dimpling and final ion milling to electron transparency. mental profiles acquired by the EDX system attached to the The microstructures were characterized in a Philips CM200 FEGTEM were used for the evaluation of peak areas in the FEGTEM equipped with a Link ISis energy dispersive X-ray quantification of the EDX spectra Due to the uncertainty in (EDX) system and a Gatan Imaging Filter(GIF). The chemical oxygen quantification, only the relative amounts of aluminum -600nm 0 nm nm 3 nn +600nm 3.5 1.5 1000 3 nI Defocus(nm) Fig. 5. Assessment of grain film thickness in the as-sintered polycrystalline mullite using the defocus Fresnel imaging technique. (a) The underfocussed mage shows a set of dark frin to the grain boundary.(b)At Gaussian focus there are no fringes. (c)The fringe contrast is reversed in the overfocussed image so that two the boundary. (d) By plotting the fringe spacing as a function of defocus and extrapolating the data to Gaussian focus, it is possible to estimate the film thickness to, in this case, approximately 0.75 nm
S. Gustafsson et al. / Journal of the European Ceramic Society 29 (2009) 539–550 543 Thin-foil specimens for TEM were prepared by standard specimen preparation techniques; mechanical grinding and polishing, dimpling and final ion milling to electron transparency. The microstructures were characterized in a Philips CM200 FEGTEM equipped with a Link ISIS energy dispersive X-ray (EDX) system and a Gatan Imaging Filter (GIF). The chemical composition of mullite grains and amorphous grain boundary regions was determined by fine probe EDX point analysis. Elemental profiles acquired by the EDX system attached to the FEGTEM were used for the evaluation of peak areas in the quantification of the EDX spectra. Due to the uncertainty in oxygen quantification, only the relative amounts of aluminum Fig. 5. Assessment of grain boundary film thickness in the as-sintered polycrystalline mullite using the defocus Fresnel imaging technique. (a) The underfocussed image shows a set of dark fringes parallel to the grain boundary. (b) At Gaussian focus there are no fringes. (c) The fringe contrast is reversed in the overfocussed image so that two bright lines delineate the boundary. (d) By plotting the fringe spacing as a function of defocus and extrapolating the data to Gaussian focus, it is possible to estimate the film thickness to, in this case, approximately 0.75 nm