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Grain Boundaries in Polyphase Ceramics D GRAIN BOUNDARIES IN POLYPHASE CERAMICS D. Clarke To cite this version: D. Clarke. GRAIN BOUNDARIES IN POLYPHASE CERAMICS. Journal de Physique Colloques, 1985, 46 (C4), pp.C4-51-C4-59. 10.1051/jphyscol:1985404. jpa-00224653 HAL Id: jpa-00224653 https://hal.archives-ouvertes.fr/jpa-00224653 Submitted on 1 Jan 1985 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. JOURNAL DE PHYSIQUE Colloque C4, suppl6ment au n04, Tome 46, avril 1985 page C4-5 1 GRAIN BOUNDARIES IN POLYPHASE CERAMICS D.R. Clarke Thomas J. Watson Research Center, IBM, Yorktown Heights, NY 10598, U.S.A. ABSTRACT. The majority of polyphase ceramics contain a residual glass phase at their grain boundaries. The stability of these phases, particularly at the two-grain boundaries, is of significance since they affect the properties of the material as a whole. Drawing analogies with soap films, the stability of a continuous intergranular phase is considered in terms of the balance between the capillarity and disjoining pressures. The individual components to the disjoining pressures are discussed. It is argued that a large structural component to the disjoining pressure is responsible for the observed constancy of the thickness of its intergranular phase in polyphase silicon nitride ceramics. Mechanisms for the de-wetting of a grain boundary containing an intergranular glass phase are also discussed. 1. INTRODUCTION In contrast to the voluminous literature devoted to the the structure of grain boundaries in metals, and to a lesser extent diamond cubic semiconductors, relatively few studies have been directed to elucidating the structure of grain boundaries in ceramic materials. The crystallographic studies performed have been reviewed by Balluffi and colleagues (1,Z) but, reflecting the work carried out to date, these papers have been restricted to single phase ceramics of relatively simple crystal structures and small unit cells. Much less attention has been given to the more complicated polyphase ceramics that are of interest to ceramic scientists today. These include the structural ceramics, such as the silicon nitride alloys, the multicomponent substrate ceramics and the dielectric and electrical ceramics. One of the central issues from the materials science point of view in these ceramics is the role of the intergranular glass phase. In addition key questions concern the stability and structure of the glass phase at the grain 2. GLASS PHASES AT GRAIN BOUNDARIES The majority of ceramics in use today or contemplated are in practice polyphase materials either because they are composites of two or more crystalline phases or because they are nominally single phase material but contain a remnant intergranular glass phase. Three principal origins of intergranular glass phases in ceramics can be identified. In many ceramics the phase results from the liquid phase sintering process used to densify them. Examples of these include the silicon nitride alloys, the zinc oxide varistor materials, and the alumina substrates. In others, such intergranular films are present because the materials are prepared by the controlled but incomplete crystallization of a glass (glass-ceramics). A third, but important category, is those in which the phase forms from the impurities present, for instance, ceramics for nuclear waste encapsulation and certain single phase zirconia ceramics. Much of the effort devoted to characterizing the grain boundaries in polyphase ceramics has in fact been focused on detecting the existence or otherwise of an intergranular glass phase. The techniques developed for this purpose have been fully described elsewhere (3) but these reveal a number of common findings. These include the fact that the glass phases are located at three and four grain junctions and also, in the majority of cases, as a continuous phase along the two-grain boundaries. The thickness of the glass phase at the grain boundaries varies from one batch of material to another, and from one grain to another, with the exception of grain boundaries in hot-pressed silicon nitrides. In these materials the thickness appears to be relatively constant having a value of 8-15 A. 2.1 Stability Of Intergranular Phases These observations raise a number of questions as to whether such intergranular glass phases are stable. Amongst the more prominent questions are: Why some grain boundaries appear to be wet by a glass phase whereas others are not; What dictates the thickness of the glass phase at two-grain junctions; Are the films Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985404 C4-52 JOURNAL DE PHYSIQUE thermodynamically stable; and if so why. The difficulties in discussing these questions is compounded by the fact that the observations are made at room temperature on materials cooled from the temperature at which many of the intergranular phases form and are probably liquid. In what follows it is assumed that at the relevant temperatures the intergranular phase is a liquid and that as the temperature is lowered the liquid solidifies freezing in the high temperature structure. 2.2 Why Are Not All Boundaries Wet ? Transmission electron microscopy observations of grain boundaries in debased aluminas (4,5), in hot-pressed silicon nitrides (6,7), zinc oxide varistors (8,9), and recently in a Sialon material by Schmid and Ruhle (10) indicate that whilst the majority of grain boundaries in these materials contain an intergranular phase some do not. The suggestion made by these authors has invariably been that the boundaries are crystallographically "special", although the detailed crystallography of the boundaries has not always been presented. One way of rationalizing the observations is shown schematically in figure 1 in which the energy of a grain boundary is plotted as a function of its misorientation for both a crystalline boundary and for one wet by a glass film. The former curve has the shape generally used in the literature to indicate the angular dependence of low angle grain boundaries and the existence of "special" orientations whereas the latter curve assumes that due to the isotropic nature of glass the energy is independent of orientation. (In drawing both these curves it is assumed that the crystalline phase is isotropic). On the basis of such a description low angle grain boundaries, with angles up to O, will be free of glass whereas all high angle boundaries with the exception of deep "cusp" orientations, will contain an intergranular glass phase. It is to be expected that the curve for the glass-wet boundaries will be more temperature dependent of the two and that as the temperature is reduced from, say, the sintering temperature it will rise relative to that of the purely crystalline boundary. The result will be that over a range of orientations it will no longer be energetically favorable for the boundary to be coated with a glass film and it will proceed to de-wet. (See section 2.4). Such a behavior has been seen in zinc oxide varistor materials (1 1) and in a Lii liquid phase sintered spinel (12). MISORIENTATION, 8 Figure 1. Grain boundaries will only be free of an intergranular film if their energy is lower than that of a wetted boundary, ie for misorientations for which the crystal-crystal boundary energy (full line) is lower than that of the wetted boundary (dashed line). 2.3 Thermodynamic Stability And Film Thickness The rationalization presented in figure 1 implies that continuous intergranular glass phases can be thermody- namically stable. Raj (13) has argued by comparing the energies of the two end-point conditions shown in figure 2 that a continuous intergranular glass phase is stable provided that it lowers the energy of the grain boundary, viz. 2yl < yb . Such a comparison does not however address the question as to what thickness a wetting glass film will adopt at equilibrium or provide any understanding of why, for instance the thickness of the intergranular phase in hot-pressed silicon nitrides is apparently constant at approximately 12A. In addressing these aspects of the question the approach taken here is to consider the force balance on an intergranular liquid glass film that is stable at high temperature and shown schematically in figure 3. The force acting to draw the two adjacent grains closer together and thin the film is the capillarity force due to the concave curvature at the three and four-grain junctions. At equilibrium this force is balanced by an equal force, which following Derjaguin (14), may be termed the disjoining pressure: STATE I STATE I1 Figure 2. End point configurations for comparing the energies of boundaries wet (state I) and not wet (state 11) by an intergranular phase. Redrawn after Raj (13). This force, which is everywhere normal to the glass phase, is in reality a combiqation of forces given by: where IIVd,results from the London-Van Der Waals interaction energy between the grains lTedlis due to any electrical double-layer interactions IIad is a measure of the adsorption on the grain surfaces II,, is due to structural interactions of the molecules between the grains (a steric effect). Figure 3. Schematic diagram of the force balance on an intergranular liquid glass film. PC is the capillary force and II the disjoining pressure. C4-54 JOURNAL DE PHYSIQUE As the material of the two grains is assumed to be the same the dispersion force contribution to the disjoining pressure, IIvd, , will always be negative (meaning an attractive force).
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