SOLIDSTATE SINTERINGMODELS
ANDDENSIFICATION
Solid state sintering is usually divided into three overlapping stages — initial, intermediate and final. Figure 4.1 schematically depicts the typical densification curve of a compact through these stages over sintering time. The initial stage is characterized by the formation of necks between particles and its contribution to compact shrinkage is limited to 2–3% at most. During the intermediate stage, considerable densification, up to _93% of the relative density, occurs before isolation of the pores. The final stage involves densification from the isolated pore state to the final densification. For each of these three stages, simplified models are typically used: the two-particle model for the initial stage, the channel pore model for the intermediate stage, and the isolated pore model for the final stage. Although all models ignore grain growth during sintering, they do provide a means of analysing the densification process and evaluating the effects of various processing parameters
8.2 MECHANISMS OF SINTERING
Sintering of polycrystalline materials occurs by diffusional transport of matter along definite paths that define the mechanisms of sintering. We will recall that matter is transported from regions of higher chemical potential (referred to as the source of matter) to regions of lower chemical potential (referred to as the sink). There are at least six different mechanisms of sintering in polycrystalline materials, as shown schematically in Fig. 8.1 for a system of three sintering particles. They all lead to bonding and growth of necks between the particles, so the strength of the powder compact increases during sintering. Only certain mechanisms, however, lead to shrinkage or densification, and a distinction is commonly made between densifying and nondensifying mechanisms. Surface diffusion lattice diffusion from the particle surfaces to the neck, and vapor transport (mechanisms 1, 2, and 3) lead to neck growth without densification and are referred to as nondensifying mechanisms. Grain boundary diffusion and lattice diffusion from the grain boundary to the pore (mechanisms 4 and 5) are the most important densifying mechanisms in polycrystalline ceramics. Diffusion from the
grain boundary to the pore permits neck growth as well as densification. Plastic flow by dislocation motion (mechanism 6) also leads to neck growth and densification but is more common in the sintering of metal powders. The nondensifying mechanisms cannot simply be ignored because when they occur, they reduce the curvature of the neck surface (i.e., the driving force for sintering) and so reduce the rate of the densifying mechanisms. In addition to the alternative mechanisms, there are additional complications arising from the diffusion of the different ionic species making up the compound. As discussed in Chapter 7, the flux of the different ionic species is coupled to preserve the stoichiometry and electroneutrality of the compound. As a result, it is the slowest diffusing species along its fastest path that controls the rate of densification. For amorphous materials (glasses), which cannot have grain boundaries,
neck growth and densification occur by viscous flow involving deformation of the particles. Figure 8.2 shows as an example the sintering of two glass spheres by viscous flow. The path by which matter flows is not clearly defined. The geometrical changes that accompany viscous flow are fairly complex, and as we shall see later, severe simplifying assumptions are made in formulating the equations for matter transport. For the sintering of spheres, Fig. 8.3a shows a schematic of two possible flow fields for viscous sintering (2). While the form shown on the left-hand side may be expected in real systems, the results of recent simulations (Fig. 8.3b) show good agreement with the flow field on the right (see Sec. 8.7). Table 8.1 summarizes the sintering mechanisms in polycrystalline and amorphous solids.
8.6.1 Stages of Sintering
Sintering is normally thought to occur in three sequential stages referred to as (1) the initial stage, (2) the intermediate stage, and (3) the final stage. In some analyses of sintering, an extra stage, stage 0, is considered which describes the instantaneous contact between the particles, when they are first brought together due to elastic deformation in response to surface energy reduction at the interface (9). However, we shall not consider this refinement. A stage represents an interval of time or density over which the microstructure is considered to be reasonably well defined. For polycrystalline materials, Fig. 8.8 shows the idealized geometrical structures that were suggested by Coble (10) as representative of the three
stages. For amorphous materials, the geometrical models assumed for the intermediate
and final stages are very different from those for the polycrystalline case and will be described appropriately later.
8.6.1.1 Initial Stage
The initial stage consists of fairly rapid interparticle neck growth by diffusion, vapor transport, plastic flow, or viscous flow. The large initial differences in surface curvature are removed in this stage, and shrinkage (or densification) accompanies neck growth for the densifying mechanisms. For a powder system consisting of spherical particles, the initial stage is represented as the transition between Figs. 8.8a and 8.8b. It is assumed to last until the radius of the neck between the particles has reached a value of _0.4–0.5 of the particle radius. For a powder system with an initial density of 0.5–0.6 of the theoretical density, this
corresponds to a linear shrinkage of 3 to 5% or an increase in density to _0.65 of the theoretical when the densifying mechanisms dominate.
8.6.1.2 Intermediate Stage
The intermediate stage begins when the pores have reached their equilibrium shapes as dictated by the surface and interfacial tensions (see Sec. 8.3). The pore phase is still continuous. In the sintering models, the structure is usually idealized in terms of a spaghetti-like array of porosity sitting along the grain edges as illustrated in Fig. 8.8c. Densification is assumed to occur by the pores simply shrinking to reduce their cross section. Eventually, the pores become unstable and pinch off, leaving isolated pores; this constitutes the beginning of the final stage. The intermediate stage normally covers the major part of the sintering process, and it is taken to end when the density is _0.9 of the theoretical.
8.6.1.3 Final Stage
The microstructure in the final stage can develop in a variety of ways, and we shall consider this in detail in Chapter 9. In one of the simplest descriptions, the final stage begins when the pores pinch off and become isolated at the grain corners, as shown by the idealized structure in Fig. 8.8d. In this simple description, the pores are assumed to shrink continuously and may disappear altogether. As outlined in Chapter 1, the removal of almost all of the porosity has been achieved in the sintering of several real powder systems. Some of the main parameters associated with the three idealized stages of sintering are summarized in Table 8.4, and examples of the microstructures (planar section) of real powder compacts in the initial, intermediate, and final stages are shown in Fig. 8.9
المادة المعروضة اعلاه هي مدخل الى المحاضرة المرفوعة بواسطة استاذ(ة) المادة . وقد تبدو لك غير متكاملة . حيث يضع استاذ المادة في بعض الاحيان فقط الجزء الاول من المحاضرة من اجل الاطلاع على ما ستقوم بتحميله لاحقا . في نظام التعليم الالكتروني نوفر هذه الخدمة لكي نبقيك على اطلاع حول محتوى الملف الذي ستقوم بتحميله .
الرجوع الى لوحة التحكم
|