Pore coordination

Figure 3. Pore stability is determined by the dihedral angle and the pore coordination number, (a) The pore with concave surfaces will shrink while (b) the pore with convex surfaces will grow (or become metastable).

The term morphology is used in a general sense to include any parameter that quantifies pore-scale structure pore geometry, pore coordination number, grain shape, porosity, spatial correlations in pore size, etc. Pore morphology varies dramatically from one material to another and has a very strong influence on continuum-scale behavior. 

The Delaunay tessellation is particularly important because it provides a tool to decompose the continuum void space into discrete pores, which is essential for pore-scale modeling. An important drawback to using the Delaunay tessellation for extracting pore structure is that it leads to a fixed pore coordination number of 4, which is a geometric artifact in a real packing, not all voids conform to the tessellation s tetrahedral structure. Experimentally, the average... 

Matrix structure. The size, dimensionality, pore coordinate number, and topology of the matrix influence the phase distributions significantly. 

Figure 10.16 Effect of pore coordination on pore shrinkage for a system for which the dihedral angle o = tt/2. (a) Intersection of four grains around a pore, (h) Intersection of six grains that is, = 120 Note that to maintain the equilibrium dihedral angle, the surfaces of the grains surrounding the pore have to be convex, (c) Same system with = 60. Here the pore surface has to be concave in order to maintain the equilibrium dihedral angle.

In two dimensions, a pore can have a dihedral angle y/ = 120°, which is surrounded by N other grains. The number N is called the pore coordination number (CN). Similar to the case of a grain surrounded by other grains, if IV = 6, the pore has straight sides otherwise, it has convex sides for A < 6 and concave sides for IV > 6, as shown in Fig. 8.28. The surface of the pore will move toward its center of curvature, so the pore with < 6 will shrink, whereas the one with N>6 will expand. The pore is metastable for N = 6, so that the number is called critical pore CN, or Nc-Accordingly, if the pores have convex sides, i.e., N < 6, the decrease in the pore... 

Figure 9.40 Conditions for pore stability in three dimensions as a function of pore coordination number. (From Ref. 78.)...

Figure 11.8 Schematic diagram illustrating the reduction in the pore coordination number as a result of normal grain growth.

To further address the effect of particle packing on sintering behaviour and to develop a more general relationship between pore coordination number... 

Closed arrays that contain a single pore better represent conditions within a powder compact. The pore within the array is defined by the number of coordinating particles (pore coordination number, n) and its size (Rp) defined as the radius of the circumscribed circle (or sphere) as shown in Figure 4. 

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