Hexagonal close-packing, hep

The hexagonal-close-packed (hep) metals generally exhibit mechanical properties intermediate between those of the fee and bcc metals. For example Zn encounters a ductile-to-brittle transition whereas Zr and pure Ti do not. The latter and their alloys with a hep structure remain reasonably ductile at low temperatures and have been used for many applications where weight reduction and reduced heat leakage through the material have been important. However, small impurities of O, N, H, and C can have a detrimental effect on the low temperature ductihty properties of Ti and its alloys. 

It is well known that the 0 of a metal depends on the surface crystallographic orientation.6,65,66 In particular, it is well established that 0 increases with the surface atomic density as a consequence of an increase in the surface potential M. More specifically, for metals crystallizing in the face-centered cubic (fee) system, 0 increases in the sequence (110) <(100) <(111) for those crystallizing in the body-centered cubic (bcc) system, in the sequence (111) < (100) <(110) and for the hexagonal close-packed (hep) system, (1120) < (1010) < (0001). 

Figure 5.1. Unit cells of the face-centered cubic (fee), body-centered cubic (bcc), and hexagonally closed packed (hep) lattices.

The chemical bonding and the possible existence of non-nuclear maxima (NNM) in the EDDs of simple metals has recently been much debated [13,27-31]. The question of NNM in simple metals is a diverse topic, and the research on the topic has basically addressed three issues. First, what are the topological features of simple metals This question is interesting from a purely mathematical point of view because the number and types of critical points in the EDD have to satisfy the constraints of the crystal symmetry [32], In the case of the hexagonal-close-packed (hep) structure, a critical point network has not yet been theoretically established [28]. The second topic of interest is that if NNM exist in metals what do they mean, and are they important for the physical properties of the material The third and most heavily debated issue is about numerical methods used in the experimental determination of EDDs from Bragg X-ray diffraction data. It is in this respect that the presence of NNM in metals has been intimately tied to the reliability of MEM densities. 

The corresponding unit cells are shown in Figure 1.1 and an examination of simple ball-and-stick models (which the reader is strongly urged to carry out) shows that the face-centred cubic (fee) and hexagonal close-packed (hep) structures correspond to the only two possible ways of close-packing spheres, in which each sphere has twelve nearest neighbours. 

As a first approximation, let us consider the X atoms as rigid spheres arranged in an ideal hexagonal close-packed (hep) sublattice. On transforming the usual hexagonal unit cell (a, 6, c ) to an ortho-hexagonal cell, defined by a0 = c, bo = b —a, and Co = + b, and introducing... 

The most important metals for catalysis are those of Groups VIII and I-B of the periodic system. Three crystal structures are important, face-centered cubic (fee Ni, Cu, Rh, Pd, Ag, Ir, Pt, Au), hexagonal close-packed (hep Co, Ru, Os) and body-centered cubic (bcc Fe) [9, 10]. Before discussing the surfaces that these lattices expose, we mention a few general properties. 

Most metals active in cyclization belong to Group VIIIB and have either face-centered-cubic (fee) or hexagonal close packed (hep) crystal structure. 

It is not hard to understand why many metals favor an fee crystal structure there is no packing of hard spheres in space that creates a higher density than the fee structure. (A mathematical proof of this fact, known as the Kepler conjecture, has only been discovered in the past few years.) There is, however, one other packing that has exactly the same density as the fee packing, namely the hexagonal close-packed (hep) structure. As our third example of applying DFT to a periodic crystal structure, we will now consider the hep metals. 

Earlier, we mentioned that other crystal structures can have different Miller indices than the fee structure. In the hexagonal close-packed (hep)... 

Hexagonal close-packed (hep) materials have a sixfold symmetry axis normal to the basal plane. Using a three-axis system to define Miller indices for this structure is unsatisfactory, as is demonstrated in Fig. 4.9. The two planes highlighted in Fig. 4.9 are equivalent by symmetry, and yet their Miller indices do not show this relationship. This is unfortunate since one of the reasons Miller indices are useful is that equivalent planes have similar... 

The structural sequence dhcp — ccp was also expected to occur in the next element, curium. But the ccp phase was not observed under pressure. In contrast, the simple hexagonal close-packed (hep) and, at still higher pressure, an as yet undetermined structure is formed. If these results are confirmed by further study, curium structures will have to be considered as another intermediate stage between the lighter and the heavier actinides. ... 

Phase analysis and texture of the metal particles. Over the whole composition range, whatever the particle diameter, a face-centered cubic (fee) phase is always observed (Fig. 9.2. J 3) by x-ray diffraction (XRD) either as a single phase (Ni and CovNi) v with x < 0.35) or beside a hexagonal close-packed (hep) phase with broad lines (Co and Co,Ni (with x 2 0.35). The lattice parameter of the fee phase shows... 

The metal substrates used in the LEED experiments have either face centered cubic (fee), body centered cubic (bcc) or hexagonal closed packed (hep) crystal structures. For the cubic metals the (111), (100) and (110) planes are the low Miller index surfaces and they have threefold, fourfold and twofold rotational symmetry, respectively. 

Pure gadolinium crystallizes in the well known hexagonal close-packed (hep) structure (see fig. 4), which is described within the space group P6-ijmmc with Gd on the 2c-sites (point symmetry 6m 2). 

Ethylidyne occurs on the triangular threefold sites on fee (111) or hexagonal close-packed (hep) (0001) faces and is formed at lower temperatures on Pd(lll) and Pt(lll) in the presence of coadsorbed hydrogen. Its spectral signature also occurs on Ru(0001) at 330 K and on Ir(lll) at 300 K. Ni(lll) is exceptional in not giving spectroscopic evidence for the ethylidyne species derived from adsorbed ethyne (or from ethene, 1). 

Other features of interest in the phase diagram of 4He include triple points between various liquid and solid phases of the element. At point c in Figure 13.11, liquid I, liquid II and a body-centered cubic (bcc) solid phase are in equilibrium. The bcc solid exists over a narrow range of pressure and temperature. It converts by way of a first-order transition to a hexagonal close packed (hep) solid, or to liquid I or liquid II. At point d, liquid I and the two solids (bcc and hep) are in equilibrium liquid II and the two solids are in equilibrium at point e. 

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