Spheres, close-packing, equivalent size

For charged latex particles in water above a critical volume fraction (often about 15%) the dispersion behaves as a viscoelastic solid, being able to support a shear stress. The transition from liquid to solid is found to correspond to the volume fraction of equivalent hard spheres being randomly close packed. The size of the equivalent sphere is the particle radius plus the effective size of the electrostatic interaction. 

It is evident that event the simplest model for the packing of spheres of equivalent size permits the possibility of polymorphism. Most of the metals of the lanthanide series exist in the hexagonal close-packed structure at room temperature but transform into the body-centered cubic from at temperatures exceeding 800°C [9]. For the most part, these transitions appear to be enantiotropic in nature. 

Figure 2.19c illustrates a hep unit cell defined by lattice species at (0, 0, 0) and (2/3, 1/3, 1/2). There are four tetrahedral sites and two octahedral sites per unit cell. The sizes of tetrahedral or octahedral holes within a hep and fee array are equivalent, respectively accommodating a sphere with dimensions of 0.225 or 0.414 times (or slightly larger) the size of a close-packed lattice atom/ion. 

Colloidal crystals can have a large variety of structures that depend on the nature of the colloids (hard sphere, charged, mixed sizes, and charges) [23]. The equilibrium crystalline phase of single-sized hard spheres has the face-centered cubic structure. Its energy is only about 10 k T lower than that of the hexagonal close-packed crystal [24]. Equivalently, the stacking faults on the close-packed planes in both... 

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