Close-packed metals

The wave function T i oo ( = 11 / = 0, w = 0) corresponds to a spherical electronic distribution around the nucleus and is an example of an s orbital. Solutions of other wave functions may be described in terms of p and d orbitals, atomic radii Half the closest distance of approach of atoms in the structure of the elements. This is easily defined for regular structures, e.g. close-packed metals, but is less easy to define in elements with irregular structures, e.g. As. The values may differ between allo-tropes (e.g. C-C 1 -54 A in diamond and 1 -42 A in planes of graphite). Atomic radii are very different from ionic and covalent radii. 

The metals are silvery in appearance (except for Eu and Yb which are pale yellow, see p. 112 and below) and are rather soft, but become harder across the series. Most of them exist in more than one crystallographic form, of which hep is the most common all are based on typically metallic close-packed arrangements, but their conductivities are appreciably lower than those of other close-packed metals. 

The nucleation behavior of transition metal particles is determined by the ratio between the thermal energy of the diffusing atoms and the interaction of the metal atoms at the various nucleation sites. To create very small particles or even single atoms, low temperatures and metal exposures have to be used. The metal was deposited as metal atoms impinging on the surface. The metal exposure is given as the thickness (in monolayer ML) of a hypothetical, uniform, close-packed metal layer. The interaction strength of the metals discussed here was found to rise in the series from Pd < Rh < Co ( Ir) < V [17,32]. Whereas Pd and Rh nucleate preferentially at line defects at 300 K and decorate the point defects at 90 K, point defects are the predominant nucleation center for Co and V at 300 K. At 60 K, Rh nucleates at surface sites between point defects [16,33]. 

Accordingly, Neurock and co-workers have developed models for the electrochemical interface that retain this concept of hexagonal stmcture over close-packed metal surfaces [FiUiol and Neurock, 2006 Taylor et al., 2006c]. With the use of a screening charge as described in Section 4.3, the sensitivity of the stmctural parameters of water with respect to the electrochemical environment were explored [Taylor et al., 2006a]. The predominant effect stems from the polar nature of the water molecule, in which the water molecules are observed to rotate as a function of the applied potential. 

Non-nuclear maxima in hexagonal-close-packed metals... 

The hardest of the transition-metal borides are the diborides. Their characteristic crystal structure (Figure 10.6) consists of plane layers of close-packed metal atoms separated by plane openly-patterned layers of boron atoms ( chicken-wire pattern). If the metal atoms in the hexagonal close-packed layer have a spacing, d, then the boron atoms have a spacing of d/V3. 

Similar antiphase boundaries form in metals with structures based upon a hexagonal close-packed array of metal atoms, such as magnesium. Condensation of vacancies upon one of the close-packed metal atom planes to form a vacancy loop, followed by subsequent collapse, will result in a hypothetical sequence. . ABABBABAB This arrangement will be unstable because of the juxtaposition... 

It is not possible to establish directly the value of the M-M distance corresponding to bond order of 1. Methods so easily applied to organic systems cannot be so readily applied here. First, the metallic radius for 12-coordinate metal is an average value, and second, as mentioned, the M-M distance (average) established for close-packed metals generally corresponds to a bond-order value of less than 1. At best only, the distance taken to correspond to a bond order of 1 is a crude approximation. Clearly, such arguments are enforced in any attempt to establish which correspond to bond orders of 2 or more. 

According to the Frank-Kasper definition, the coordination number is unambiguously 12 in the hexagonal close-packed metals and assumes the value 14 in a body-centred cubic metal. Generally in several complex metallic structures this definition yields reasonable values such as 14, even when the nearest-neighbour definition would give 1 or 2. 

Close-packed element structure types. The structures of the close-packed metals are a simple well-known example of homeotect structure types. We have seen that the following metals can be considered as reference types. 

Mueller R. F. (1972). Stability of biotite A discussion. Amer. Mineral., 57 300-316. Mukherjee K. (1965). Monovacancy formation energy and Debye temperature of close-packed metals. Phil. Mag., 12 915-918. 

Fig. 5.5. Geometrical structure of a close-packed metal surface. Left, the second-layer atoms (circles) and third-layer atoms (small dots) have little influence on the surface charge density, which is dominated by the top-layer atoms (large dots). The top layer exhibits sixfold symmetry, which is invariant with respect to the plane group p6mm (that is, point group Q, together with the translational symmetry.). Right, the corresponding surface Brillouin zone. The lowest nontrivial Fourier components of the LDOS arise from Bloch functions near the T and K points. (The symbols for plane groups are explained in Appendix E.)...

Fig. 6.9. Corrugation amplitudes of a hexagonal close-packed surface. Solid curve, theoretical corrugation amplitude for an s and a d,- tip state, on a close-packed metal surface with a=2.88 A and 4>=3.5 eV. The orbitals on each metal atom on the sample is assumed to be 1 i-type. Measured STM corrugation amplitudes are from the data of Wintterlin et al. (1989). The first-principle calculation of Al(lll) is taken from Mednick and Kleinman (1980). The corrugation amplitude for a 4-wave tip state is more than one order of magnitude smaller then the experimental corrugation. (Reproduced from Chen, 1991, with permission.)...

Bemdt, R., Gimzewski, J. K., and Schlittler, R. R. (1992). Tunneling characteristics at atomic resolution on close-packed metal surfaces. Ultramicroscopy, 42-44, 528-532. 

Wintterlin, J., Wiechers, J., Brune, H., Giitsch, T., Hofer, H., and Behm, R. J. (1989). Atomic-resolution imaging of close-packed metal surfaces by scanning tunneling microscopy. Phys. Rev. Lett. 62, 59-62. 

Nitrides can be sub-divided into ionic, covalent and interstitial types.An alternate general classification of nitrides, based on bonding classification, as ionic, covalent and metallic has also been applied. Ionic or salt-like nitrides are formed by electropositive elements such as Li, Mg, Ca, Sr, Ba, Cu, Zn, Cd and Hg and possess formulae which correspond to those expected on the basis of the combination of the metal ion with ions. A range of covalent nitrides are known and are exhibited by less electropositive elements such as B, S, P, C and Si. Interstitial nitrides are formed by some transition metals and refer to compounds which can be described in terms of the occupancy of interstitial sites in close packed metallic structures by nitrogen atoms. Oxygen can also be accommodated within these structures and a range of oxynitrides are known to... 

DFT calculations of the structure of the molecularly adsorbed NO are in reasonable agreement with experiments, but overestimate the binding energy [197,198]. A barrier of 2.1 eV to dissociation is predicted by DFT, with the NO at the transition state nearly parallel to the surface and N and atoms in bridge sites [199]. This transition state geometry is similar to that of NO dissociation on other close-packed metal surfaces [200]. There is no global DFT PES so that all theoretical dynamics is based only on empirical model PES. 

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