Imaging and thickness measurement of amorphous intergranular films using TEM
Introduction
The presence of thin amorphous films at grain boundaries in ceramics was first demonstrated in Si3N4 by Clarke and Thomas [1] and these have since been found in many different materials, especially ceramics such as Si3N4-derivatives, ZnO varistors [2], ZrO2 [3] and Al2O3[3], [4]. Three main methods have been developed for the imaging of such films in transmission electron microscopy (TEM). Firstly, a dark field image may be created using the objective aperture to select part of the first diffuse diffraction ring for the amorphous material, the so-called diffuse dark field (DDF) method. If care is taken to ensure that no crystalline reflections come within the aperture then the only regions to show bright contrast are those which are amorphous [5]. Secondly, the difference in atomic density or composition at the grain boundary leads to a change in inner potential. When imaged in the TEM this leads to the appearance of Fresnel fringes at the boundary in over- or underfocus conditions. The fringe spacing can be measured for various defocus values, plotted on a graph and extrapolated to Gaussian focus, giving a value for the film thickness [6]. Finally, films can be imaged using high resolution TEM (HRTEM) and the thickness directly measured from the micrograph [1], [5], [6]. In the latter two cases, the boundary must be oriented edge-on to the electron beam. Even for the dark field imaging method, one finds better contrast when the boundary is approximately edge-on, and this condition must be fulfilled if measurements of film thickness are to be made. In the case of HRTEM there is the additional and more exacting requirement that the specimen must be so oriented that lattice planes in both crystals are also edge on, so as to give a clear high resolution lattice image of both grains.
These three methods have been compared by Cinibulk et al. [7]. It was shown that the HRTEM method gave the smallest thickness, that the Fresnel fringe method gave a thickness about 20% larger, and that the diffuse dark field method gave a thickness 50–100% larger than the HRTEM method. It was concluded that the DDF method is good for revealing amorphous films, but unsuited for thickness measurements, the Fresnel method is widely applicable but may overestimate the thickness slightly (although see Ref. [8]), and the HRTEM method is the most accurate for thickness measurements, but is also very exacting and therefore time consuming.
Jin et al. [9] showed widespread applicability of the Fresnel fringe method for grain boundaries and noted less of a discrepancy with HRTEM measurements. Nevertheless, the Fresnel fringe spacing does not always obey the proposed functional dependence on defocuswhereW is the observed fringe spacing, W0 is the film thickness, Δf is the defocus, and λ the electron wavelength [10]. Jin et al. [8] found that the constant of proportionality, c, was often smaller than expected; however, no explanation was given for this discrepancy. Moreover, an anisotropy is typically observed between the under- and overfocus plots [7], [8], [11], [12].
More detailed studies of Fresnel fringe formation at interfaces including detailed mathematical and computational calculations have been performed by other workers [12], [13], [14], [15], [16]. It is clear from these studies that the amorphous-crystalline interface and thus the change in internal potential is rarely atomically sharp, and that grain boundary grooving as a result of preferential etching during specimen preparation is common; both of these effects affect the form of the fringes. Moreover, space charge has also been shown to affect the form of the fringes [15], [16]. It is therefore no great surprise if the functional form of the dependence of the fringe spacing on defocus is not always as simple as first derived by Clarke on the assumption of sharp interfaces [6]. What is perhaps more worrying, however, is that the boundary region can have a reduced atomic density even when fully crystalline, resulting in the appearance of Fresnel fringes even in the absence of any amorphous film [3], [17], [18].
Fourier filtering has been used for the processing of HRTEM images almost ever since computers became powerful enough to perform fast Fourier transforms in a reasonable time period. For example, the group of van Dyck at the University of Antwerp were among the first to demonstrate the wide variety of possibilities of such an approach in image processing. This included noise removal from HRTEM images, observation of small deviations from periodicity at stacking faults, epitaxial interfaces, and antiphase boundaries, and the imaging of short range order in Au4Cr [19], [20]. Since then it has been used for a wide variety of applications. For example, improvement of the visibility of small crystalline clusters or small particles [21], [22], [23], imaging displacement and strain in HRTEM images [24], [25], [26], generation of thickness maps in certain special cases [27], characterisation of antiphase domains and domain boundaries [28] and the localisation of dislocations in HRTEM images [25], [29], [30].
Whilst the periodic information or small deviations from periodicity at defects, steps etc. have been widely used in Fourier filtering, the non-periodic information has generally been thrown away. In the present work, use is made of a somewhat neglected suggestion of Coene et al. [19] where Fourier filtering is used to do the opposite and remove the periodic information from HRTEM micrographs in order to allow the better observation of non-periodic information. In that case, it was used for the imaging of Pt particles on a crystalline support. In the current work, a similar procedure is used for the imaging of thin amorphous films at grain boundaries. The results of this approach are compared with those of standard TEM techniques for analysis of such grain boundary films.
Section snippets
Experimental procedure
An alumina ceramic doped with 500 wt ppm Y2O3 was prepared as described previously [31], [32], [33] and was sintered at 1450°C for 96 h and then annealed at 1650°C for 12 h. As a result, abnormal growth of some grains was observed as has been reported in detail elsewhere [33].
TEM specimens were prepared using a standard procedure of slicing, disc cutting, mechanical polishing, dimpling and ion milling. A final treatment of 30 min low energy ion-beam polishing using Ar+ ions accelerated by just 500 V
Fresnel fringe analyses of grain boundaries in Y-doped alumina
A grain boundary was tilted to an essentially non-diffracting orientation and a defocal series recorded to produce Fresnel fringe images. Three images from this series are shown in Fig. 1: −480 nm, Gaussian focus, and +480 nm, together with an intensity profile across the boundary for each image (averaged in each case from 500 pixels along the length of the boundary). As is normal, a bright central fringe surrounded by two dark fringes is seen in underfocus, and a dark central fringe surrounded
Conclusions
It is shown that for the alumina specimens of this study, Fresnel fringe analysis gives confusing results, showing fringes both for boundaries having amorphous films, and for film-free boundaries. Those at film-free boundaries probably arose as a result of a Y-doping induced expansion of the boundary resulting in a reduced density and reduced inner potential at the boundary. It should therefore be stressed that the film thickness determined by the indirect method of Fresnel fringe analysis
Acknowledgements
Helpful discussions with Profs. M. Rühle, R.M. Cannon and H. Fuess, and Drs. M.A. Gülgün and G. Miehe are gratefully acknowledged. Of particular help in the preparation of this manuscript were the detailed and constructive criticisms of one of the reviewers, to whom I am greatly indebted. The author is very thankful to Dr. R. Voytovych for the preparation of the alumina ceramic used in this work and to Mrs. M. Sycha for preparing TEM specimens from the ceramic. The continuing support of the
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