Crystal structures close-packed, ceramics

It may be recalled (Section 3.12) that for metals, close-packed planes of atoms stacked on one another generate both FCC and HCP crystal structures. Similarly, a number of ceramic crystal structures may be considered in terms of close-packed planes of ions, as well as unit cells. Ordinarily, the close-packed planes are composed of the large anions. As these planes are stacked atop each other, small interstitial sites are created between them in which the cations may reside. 

Ceramic crystal structures of this type depend on two factors (1) the stacking of the close-packed anion layers (both FCC and HCP arrangements are possible, which correspond to ABCABC. .. and ABABAB. .. sequences, respectively), and (2) the manner in which the interstitial sites are filled with cations. For example, consider the rock salt crystal structure discussed earlier. The unit cell has cubic symmetry, and each cation (Na ion) has six Cl ion nearest neighbors, as may be verified from Figure 12.2. That is, the Na ion at the center has as nearest neighbors the six Cl ions that reside at the centers of each of the cube faces. The crystal... 

Figure 6.1 Common crystal structures in ceramics (a) Simple cubic (or CsCl) structure (b) close-packed cubic (or NaCl), a variant of the face centered cubic (FCC) structure (c) hexagonal close-packed (HCP).

Three-dimensionally ordered macroporous ceramic with high LR ion conductivity was prepared by colloidal crystal templating method using monodispersed polystyrene beads [12]. Monodispersed polystyrene beads with 3 pm diameter were dispersed in water and then filtrated by using a membrane filter under a small pressure difference. After this treatment, polystyrene beads were accumulated on the membrane filter with closed pack structure, as shown in Fig. 4.2. Then, the membrane consisting of accumulated polystyrene beads was removed from the membrane filter and put on a glass substrate. After drying at room temperature, the... 

A majority of the important oxide ceramics fall into a few particular structure types. One omission from this review is the structure of silicates, which can be found in many ceramics [1, 26] or mineralogy [19, 20] texts. Silicate structures are composed of silicon-oxygen tetrahedral that form a variety of chain and network type structures depending on whether the tetrahedra share comers, edges, or faces. For most nonsilicate ceramics, the crystal structures are variations of either the face-centered cubic (FCC) lattice or a hexagonal close-packed (HCP) lattice with different cation and anion occupancies of the available sites [25]. Common structure names, examples of compounds with those structures, site occupancies, and coordination numbers are summarized in Tables 9 and 10 for FCC and HCP-based structures [13,25], The FCC-based structures are rock salt, fluorite, anti-fluorite, perovskite, and spinel. The HCP-based structures are wurtzite, rutile, and corundum. 

Ceramics, by definition, are composed of at least two elements, and consequently their structures are, in general, more complicated than those of metals. While most metals are face-centered cubic (FCC), body-centered cubic (BCC), or hexagonal close-packed (HCP), ceramics exhibit a much wider variety of structures. Furthermore, and in contrast to metals where the structure is descriptive of the atomic arrangement, ceramic structures are named after the mineral for which the structure was first decoded. For example, compounds where the anions and cations are arranged as they are in the rock salt structure, such as NiO and FeO, are described to have the rock salt structure. Similarly, any compound that crystallizes in the arrangement shown by corundum (the mineral name for AI2O3) has the corundum structure, and so forth. 

In some approaches, the empirical repulsive term is written in other mathematical forms, such as an exp(—r/A) dependence, where A is an empirical constant. For many ceramics, in which the cation to anion ratio is less than 0.414, the structures are considered as close-packed anions with the cations in the interstices. In these structures, the spacing between the anions becomes important and the potential must account for the anion-anion repulsion. In many situations the above approach, which links the interatomic potential to the elastic constants, is used in reverse. That is, the elastic constants are used to determine the unknown constants in the interatomic potential, e.g., n in Eq. (3.1). Equation (3.9) is also useful in estimating the elastic constants of newly studied materials using values measured from other materials with the same crystal structure. 

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