Abstract
So far, in this book we have looked at a number of different classes of crystals that had one thing in common: they were invariably dense structures. This does not necessarily mean that their components completely fill the space, i.e., to 100%. For instance, it is well-known that the densest packing of spheres, whether these are atoms or cannonballs, fills the volume to only 74%. There are two of these densest packings: the cubic face-centered (cubic closest packing, ccp) and the hexagonal closest packing (hcp). A large class of crystals that can be described with these two sphere packages forms the structures of many metals, i.e., metallic elemental crystals (► Sect. 4.2.4). With a space-filling of approx. 68%, the cubic body-centered spherical packing is already somewhat less dense. This structure is also formed by some metals, for instance, V, Nb, Ta, Cr, Mo, W, and α-Fe.
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Notes
- 1.
In all three networks, all nodes have two neighbors; node 1 is always connected to nodes 12 and 2, node 2 to 1 and 3, and so on.
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Hoffmann, F. (2020). Porous Crystals, Crystal Structures as Networks, and an Insight into Crystallographic Topology. In: Introduction to Crystallography. Springer, Cham. https://doi.org/10.1007/978-3-030-35110-6_9
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