Hexagonally closest

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... 

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

Bil3 type hexagonal closest-packing of X atoms... 

Among hydroxides such as Mg(OH)2 (brucite) and Ca(OH)2 the packing of the O atoms deviates from an ideal hexagonal closest-packing in that the layers are somewhat flattened the bond angles M-O-M in the layer are larger than the ideal 90° for undistorted octahedra (e.g. 98.5° in Ca(OH)2). 

From Fig. 17.1 we can see how adjacent octahedra are linked in a hexagonal closest-... 

Tetrahedra in hexagonal closest-packing (a) view of the hexagonal layers (b) view parallel to the hexagonal layers (stacking direction upwards)... 

There are four spheres, four octahedral interstices and eight tetrahedral interstices per unit cell. Therefore, their numerical relations are the same as for hexagonal closest-packing, as well as for any other stacking variant of closest-packings one octahedral and two tetrahedral interstices per sphere. Moreover, the sizes of these interstices are the same in all closest-packings of spheres. 

M2C and M2N hexagonal closest-packing of M atoms, C or N atoms in half... 

Even smaller c/a ratios are observed for the more electron-rich arsenides and antimonides (e.g. 1.39 for NiAs). Since the ideal c/a ratio of hexagonal closest-packing is 1.633, there is a considerable compression in the c direction, i.e. in the direction of the closest contacts among the metal atoms. 

The structure of wurtzite corresponds to a hexagonal closest-packing of S atoms in which half of the tetrahedral interstices are occupied by Zn atoms. In addition, any other stacking variant of closest-packings can have occupied tetrahedral interstices. Polytypes of this kind are known, for example, for SiC. 

Why are the MX3 strands shown in Fig. 16.10 compatible only with a hexagonal closest-packing of the X atoms ... 

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. 

Atoms are replaced by voids or voids are occupied by atoms. For example hexagonal closest-packing -t Cdl2 type. If the voids are considered to be zero atoms , this can be considered as a substitution of voids by atoms. 

Occupation of Octahedral Interstices in Hexagonal Closest-packing... 

According to the discussion in Section 17.3, many structures can be derived from the hexagonal closest-packing of spheres by occupying a fraction of the octahedral interstices with other atoms. If the X atoms of a compound MX form the packing of spheres, then the fraction 1 fn of the octahedral interstices must be occupied. The unit cell of the... 

Section of the hexagonal closest-packing. Gray area ... 

P63/m2/m2/c, which is the space group of the hexagonal closest-packing of spheres, has only one maximal subgroup in which the position 2a is split into two independent positions, namely P 3 2/m 1. If one of these positions is occupied and the other one remains vacant, this corresponds to the Cdl2 type. 

Group-subgroup relations from hexagonal closest-packing of spheres to some MX3 and M2X3 structures. The boxes represent octahedral voids, with the coordinates as given at the top left. The positions of the octahedron centers are labeled by their Wyckoff letters. Gray boxes refer to occupied voids. The dots indicate how the atoms Ru, P and N are shifted from the octahedron centers parallel to c... 

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