Closest packing, cubic hexagonal

Hexagonal closest packing Cubic closest packing... 

So in the body-centered cubic arrangement 68.0% of the space is actually occupied by spheres. This is somewhat less than the space occupied in the closest packed structures (74.0%). That is, in contrast to cubic closest packing and hexagonal closest packing, the body-centered cubic method of packing spheres does not represent a closest packed structure. 

I I First look at the calcium ions in Figure 69. Would you say they are approximately cubic closest-packed or hexagonal closest packed ... 

The symbols Al, A2, and A3 represent the three simple metal structures cubic closest packed, body centered, and hexagonal closest packed, respectively. 

Tc or c cubic closest-packing of spheres Th or h hexagonal closest-packing of spheres Ts stacking sequence AA... of hexagonal layers Qs stacking sequence AA... of square layers... 

Unit cells for hexagonal (left) and cubic closest-packing of spheres. Top row projections in the stacking direction. 

Table 14.2 The element structures of the metals at ambient conditions h = hexagonal closest-packing c = cubic closest-packing...

Table 17.1 Crystallographic data of the hexagonal and cubic closest-packings of spheres. +F means +(j,0), +(j,0, j), +(0, j, j) (face centering). Values given as 0 or fractional numbers are fixed by space-group symmetry (special positions)...

Relative arrangement of the octahedra in hexagonal and in cubic closest-packing in the direction of stacking of the hexagonal layers... 

As an example of the prevalence of high-symmetry structures we can take the closest packings of spheres only in the cubic and the hexagonal closest-packing of spheres are all atoms symmetry equivalent in other stacking variants of closest-packings several nonequivalent atomic positions are present, and these packings only seldom occur. 

Figure 4.17 Structure of the intercalation phase LixCo02 (a) packing of the oxygen layers in C0O2 before intercalation is hexagonal closest packing and (b) after intercalation the packing changes to cubic closest packing.

The same atom-centered polyhedra can be used to describe interstitial diffusion in all the many metal structures derived from both face-centered cubic and hexagonal closest packing of atoms. In these cases the polyhedra are centered upon a metal atom and all the tetrahedral and octahedral interstitial sites are empty. The hardening of metals by incorporation of nitrogen or carbon into the surface layers of the material via interstitial diffusion will use these pathways. 

Cl 6c +(u,u,u +m, + m, + m + w, + w, +m) w= This structure has a rhombohedral symmetry but is usually described in terms of a triple-volume hexagonal cell, which makes comparison with the idealized Cdl2 structure simpler. The idealized unit cell is adequate for the purposes of this book. In this representation the anion layers are in cubic closest packing. .. ABC ABC ABC... The metal and nonmetal stacking sequence is... 

Figure 3.35. Position of the holes in closest packing. Unit cell projections are shown for the cubic and hexagonal sphere closest packing. Coordinates of the spheres and of the tetrahedral and octahedral holes are given. The values indicated inside the drawing correspond to the third coordinate (along the vertical axis) when two values are given, these correspond to two positions along the same vertical line.

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