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￿

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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). It should be noted however that if the boundary is an interphase one and the dielectric constant of the intergranular phase is intermediate between those of the adjacent grains then nvdwcan contribute to a net repulsive force.

In the absence of any information the contribution from any electrical double layer overlap is assumed to be zero leaving only the adsorption and structural components to contribute to a positive disjoining pressure. The intergranular phase in silicon nitride alloys has been found to contain not only the elements used as a sintering aid but also many impurities common to other ceramics, namely Ca,Al,Fe and Na. Thus, the possibility of preferential adsorption of one or more of these species to the surfaces of the silicon nitride grain surfaces is real, although it has yet to measured. As a consequence a contribution to the disjoining pressure might be expected. It is also expected that this will generally be the case for all polyphase ceramics since impurities in these materials are ubiquitous.

For the particular case of the silicon nitride ceramics containing a silica based intergranular phase the similarity in structural unit and chemical bonding between silicon nitride and silica suggests that a structural component may be significant. Silicon nitride is a covalently bonded material that can be considered to consist of Si-N4, tetrahedra joined at their corners, with a Si-N bond length of approximately 1.74 A. Silica glass is also a covalently bonded material and can be thought of as a network of Si-O4 tetrahedra with an average approximate Si-0 bond length of 1.62A. On the basis of the similarity of these two materials it is proposed that the Si-0, tetrahedra adjacent to the silicon nitride grains bond to the Si-N4 tetrahedra forming an epitaxial-like partially ordered monolayer of silica on the surface of each grain of silicon nitride. The principal features of this are represented schematically in figure 4. An alternative way of describing the interfacial region shown here is that it corresponds to a layer of the (known) compound Si2N20 . The silica network in the glass between the grains must then conform to the partially ordered silica at each interface. At large distances between the grains the degree of conformation will be small, but as the distance is decreased it will necessarily become greater. When the distance is reduced to values only a few times the size of the basic tetrahedhral units the conformation will become very severe, and distortion of the Si-O4 units will occur in trying to match the ordered monolayers on both grains simultaneously. This distortional energy will be manifest as a positive structural contribution to the disjoining pressure, and is believed by the author to be responsible for the observed stability and thickness constancy of the intergranular phase in hot-pressed silicon nitride ceramics.

Si3N4 GRAIN EPITAXIAL .MONOLAYER

JOINING S~OA

Figure 4. Schematic of intergranular region between two silicon nitride grains. See text for details.

One consequence of the existence of a positive disjoining pressure is that the boundary can support a normal stress, such as might be applied during a deformation experiment. There is thus no need to resort to the concepts of grains being supported by islands of crystalline material in the glass, as has been proposed by Raj (IS), in order for the boundary to withstand a normal stress component. The structural contribution to the disjoining pressure also allows a number of further predictions to be made. Firstly, there should exist, as mentioned above, a preferred orientation to the SiO, tetrahedra on the surfaces of the crystalline grains. Secondly, the glass phase should exhibit an orientational anisotropy that becomes more marked the thinner is the intergranular film. The deviation from bulk viscosity is expected to also become more marked in the same way. Thirdly, if the structural contribution to the disjoining pressure is dominant then intergranular films of constant thickness will only exist in ceramics in which there is a similarity in structure between the major phase and the intergranular phase. For instance, as the crystal structure of both silicon carbide and beryllium oxide can be considered in terms of tetrahedral units of Si-C and Be-0 respectively and the bond lengths of the two are close it is expected that the microstruture of the Sic-Be0 material recently developed by Hitachi will have intergranular films of constant thickness. If these structural considerations are not met the thickness of the intergranular film will not have a special value. This appears to be the case from observations in the majority of ceramics containing an intergranular glass phase.

2.4 De-wetting Of Grain Boundaries

The simple energy picture of figure 1 indicates that grain boundaries wet by a glass film at high temperatures may be de-wet at lower temperatures provided the energy can be lowered. Such a situation is consistent with what is intuitively expected in ceramics prepared by liquid phase sintering where the boundaries are wet during sintering but have non-wetted boundaries when examined at room temperature. Two processes are involved, one the homogeneous thinning of the intergranular phase and the other a heterogeneous process leading to the actual de-wetting.

The thinning process can occur by a variety of mechanisms. One is by viscous flow of the liquid in response to the difference between the capillarity and disjoining pressures. For a thick film (where bulk diffusion dominates) the rate of thinning is given by Reynolds equation:

The implications of this equation are that thinning will only stop when the capillary force equals the disjoining pressure, as indicated in the previous section and that, for a given driving force, will be temperature dependent. At smaller thicknesses of the film, where appreciable mass transport by surface diffusion processes become significant the rate of thinning can be written:

where D, is the surface diffusivity Db is the bulk diffusivity c, is the concentration of the adsorbing species r, is the surface excess concentration

Thinning by viscous flow in both the thick and thin film approximations requires that the grain centers-move closer together implying that if the grains do not change shape the displaced liquid will extrude to the surface.

An additional mechanism that can contribute to the thinning of the film is solution-reprecipitation (or pressure solution as it is sometimes referred to). This does not require that the grain centers approach one another but leads to a change in shape of the grains. The governing equation for solution-reprecipitation thinning may be expressed as:

In practice it is likely that viscous flow and solution-reprecipitation will act concurrently. JOURNAL DE PHYSIQUE

LOCALLY ENHANCED SOW1ION -REPRECIPITATION

Figure 5. Possible mechanisms by which an intergranular phase may retract from a boundary when wetting is no longer energetically favourable. Schematic.

The withdrawal of the glass phase from a grain boundary as its energy is lowered requires either that the phase uniformly thins until it is of a monolayer thickness (and is no longer a distinguishable phase) or a heterogeneous process in which the adjacent grains contact at one point and the liquid then retracts. On the basis of the relatively few observations made by the author to date and occasional pictures in the literature a heterogeneous mechanism appears to be more common. The mechanisms, sketched schematically in figure 5 might be classified as ledge growth, "dimpling", and faceting. Nucleation and advance of a ledge across the grain implies crystal growth with a consequent increase in the grain volume. This is feasible if the solubility of the material decreases as the temperature is lowered. The "dimpling" requires that a perturbation occur which causes the glass to pinch off and form a region of crystal-crystal contact. This is illustrated by the micrograph of figure 6 of a zinc oxide varistor material. The bismuth-rich intergranular phase, appearing darker than the adjacent grains, is known from observations of quenched material to encompass the zinc oxide grains at the sintering temperatures. (In examining microstructures such as in this micrograph it is tempting to measure the observed contact angle and use it in subsequent analysis. Before doing so it is important to know whether the material is in equilibrium ; studies of wetting of liquids on substrates demonstrate that the contact angles of advancing and retracting interfaces can be markedly different.) After pinching off, the intergranular phase can then retract back along the grain boundary to the three-grain junction.

One method in which the phase may pinch off is by faceting of one of the two grains, as shown schematically in figure 5. This requires nucleation of a preferred facet and subsequently its growth by surface diffusion accommodated by local diffusion of the glass phase. What is believed to be an example of this process is shown in figure 7 taken of a boundary in a complex magnesium- Sialon. Such a mechanism will clearly not be expected to occur when the surface of the grain is already the low energy plane. Figure 6. Partially retracted intergranular phase in a zinc oxide varistor. The bismuth rich intergranular phase, appearing dark in this photomicrograph, is seen to completely wet the boundaries when quenched from above about 100O0C,but on slow cooling is found principally at three grain junctions.

Figure 7. An example of facetting, P, across an intergranular glass phase in a magnesium-Sialon. The formation of more than one facet protrusion per grain boundary leaves behind a prism or pocket of intergran- ular phase as here at R. The lattice fringes have a spacing of 2.2nm. JOURNAL DE PHYSIQUE

CONCLUDING REMARKS

By using some of the concepts normally employed in the colloid sciences I have attempted to argue for the thermodynamic stability of intergranular glass phases in certain ceramics. The forces required to balance the capilarity pressure are those due to the dispersion interactions across the grain boundaries, the overlap of electrical double layers, the excess energy associated with surface adsorption and those due to structural units of the liquid phase. None of these forces can presently be measured for the material systems of interest. Nevertheless, consideration of these forces allows a number of predictions to be made for the specific system of glass at grain boundaries in silicon nitride ceramics. When the intergranular phase is not stable at a boundary it must retract; some of the important parameters are emphasized and plausible mechanisms illustrated with examples.

ACKNOWLEDGEMENTS

It is a pleasure to thank T.M. Shaw and 'B.R. Stephenson for many stimulating discussions.

REFERENCES

1. R.W. Balluffi, P.D. Bristowe and C.P. Sun, J. Am. Cer. Soc. 64 (1981) 2. R.W. Balluffi, P.D. Bristowe and A. Brokman, Adv. Ceram. 6 (1983) 15 3. D. R. Clarke, Ultramicroscopy, 4 (1979) 33. 4. D.S. Phillips and S.C. Hansen, Phil. Mag. A47 (1983) 209 5. D.R. Clarke, J. Mater. Sci. (1984) In Press. 6. D.R. Clarke and G. Thomas, J. Am. Ceram. Soc. 60 (1977) 491 7. D.R. Clarke, N.J. Zaluzec and R.W. Carpenter 64 (1981) 601. 8. D.R. Clarke, J. Appl. Phys. 49 (1978) 2407. 9. W.D. Kingery and T. Mitamura, J. Am. Ceram. Soc. 62 (1979) 221. 10. H. Schmid and M. Ruhle, J. Mater. Sci. 19 (1984) 615. 11. J. Gambino, Phd Thesis, M.I.T. 1984. 12. D.R. Clarke and E.F. Lange, J. Am. Ceram. Soc. 65 (1982) 502. 13. R. Raj, J. Am. Ceram. Soc. 64 (1981) 245. 14. B.V. Derjaguin, Y.I. Rabinovich, N.Y. Churnaev, Nature 272 (1978) 313 15. R. Raj and C.K. Chyung, Acta. Metall. 29 (1981) 159.

DISCUSSION

J.T. Klom~: Should facetting not be considered as an intermediate state rather than a stable state for reasons of energy content of the system because two liquid-solid interfaces represent more energy than a single phase grain boundary. The final configuration will be the single phase GB - can you comnent on that?

D.R. Clarke: In the case when the grain boundary energies rbfall below the value of 2 yl (due to say a decrease in temperature) then facetting will occur as an intermediate state as the liquid retracts from the boundary to form a crystal-crystal boundary.

9. Atkinson: In your micrograph showing the elimination of glass from a boundary with facets it appears that when the facet touches the plane boundary a pocket of glass is trapped (in two dimensions). Are these pockets trapped in 3 dimensions? D.R. Clarke: Yes. Observations by TEM and optical microscopy of boundaries show that they are indeed trapped as you suggest. These are particularly clearly seen, for instance, in a recent paper by Lange and myseif (published in J. Am. Ceram. Soc. ) in a liquid phase sintered spinel.

J. Vitek; Is there any reason why the observation of amorphous wetting layers should be restricted to only ceramic systems?

D.R. Clarke: No.

A.G. Evans: The structural units invoked to account for the constancy of the film layer in Si3N4 presumably implies a film with different properties than the bulk glass. Yet, internal friction data obtained by Mosher and Raj indicate viscosities within the range expected for the bulk material, notwithstanding uncertainties in chemical compositions. Furthermore, internal friction measurements on other systems have generally provided consistent estimates of the grain boundary viscosities. Can you comment of this paradox?

D.R. Clarke: As we do not know the actual chemical composition of the intergranular glass phases in these materials, we cannot really know the bulk viscosity of them, and hence know whether this is a paradox or not. I'm not aware of the experiments other than those of Mosher and Raj. I would say that if there exists a monolayer of epitaxed Si04 monomers on the surfaces of the grains, their presence may be detectable by a sliding experiment, such as in internal friction measurements, since their contribution to the thickness of the grain boundary (a parameter used in calculating viscosity) will not be large.

R. Coble: Does the thickness of the liquid films in the Si3N4 based systems which you stated to be constant at the grain: grain facets depend at all on composition (MgO vs Y203 vs other doping), content of liquid (at constant composition and temperature) the temperature, or the quench rate?

D.R. Clarke: Yes. Although rather poorly and incompletely characterized, all these parameters do affect the observed thickness. However, in each case the thickness remains approximately constant in identically treated samples; it just varies from one treatment to another. This is to be expected since the thickness observed is that at which the capillary pressure is balanced by the disjoining pressure and it is the latter that will be particularly affected by the parameters you mentioned.