Metallic bonding band theory

The band of molecular orbitals formed by the 2s orbitals of the lithium atoms, described above, is half filled by the available electrons. Metallic beryllium, with twice the number of electrons, might be expected to have a full 2s band . If that were so the material would not exist, since the anti-bonding half of the band would be fully occupied. Metallic beryllium exists because the band of MOs produced from the 2p atomic orbitals overlaps (in terms of energy) the 2s band. This makes possible the partial filling of both the 2s and the 2p bands, giving metallic beryllium a greater cohesiveness and a higher electrical conductivity than lithium. 

The cohesiveness of metallic structures (equivalent to their bond strengths) is demonstrated by their enthalpies of atomization, Aa//e. The values for lithium and beryllium are 161 and 321 kJ mol, respectively. For comparison, the values for iron and tungsten metals are 418 and 844 kJ mol 

The participation of the 2p band in the bonding of metallic beryllium explains the greater cohesiveness (bond strength) of the metal when compared to that of lithium, and also why the enthalpies of atomization and the melting temperatures of the two metals are different, as shown by the data in Table 7.2. 

If overlap between bands does not occur, the size of the band gap (between the lowest level of the vacant band and the highest level of the 

The colour of gold adds to the attractiveness of the metal, and the liquid state of mercury allows the metal to be used over a wide range of temperatures in thermometers and electrical contact switches. These unusual properties are explicable in terms of relativistic effects. The relativistic effects on the 6s orbital are at a maximum in gold and are considerable in mercury. 

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Bonding in Solids Metals, Insulators, and Semiconductors Models of Metallic Bonding Band Theory and Conductivity Semiconductors... 

In this chapter, the basic types of chemical bonds existing in condensed phases are discussed. These interactions include ionic bonds, metallic bonds, covalent bonding (band theory), and intermolecular forces. In Chapter 10, the structures of some inorganic crystalline materials will be presented. 

Metals share several common properties. All metals are opaque (we cannot see through them), and they are good conductors of heat and electricity. They generally have high malleability (the ability to be bent or hammered into desired forms) and ductihty (the ability to be drawn into wires). We can explain these properties by the bonding theories that we have already examined for metals the electron sea model and band theory. In the electron sea model, discussed in Section 9.11, each metal atom within a metal sample donates one or more electrons to an electron sea, which flows within the metal. In band theory, discussed in Section 11.13, the atomic orbitals of the metal atoms are combined, forming bands that are delocalized over the entire crystalline solid electrons move freely within these bands. The mobile electrons in both of these models endow metals with many of their shared properties. 

In Chapter 9, we considered a simple picture of metallic bonding, the electron-sea model The molecular orbital approach leads to a refinement of this model known as band theory. Here, a crystal of a metal is considered to be one huge molecule. Valence electrons of the metal are fed into delocalized molecular orbitals, formed in the usual way from atomic... 

It was pointed out in my 1949 paper (5) that resonance of electron-pair bonds among the bond positions gives energy bands similar to those obtained in the usual band theory by formation of Bloch functions of the atomic orbitals. There is no incompatibility between the two descriptions, which may be described as complementary. It is accordingly to be expected that the 0.72 metallic orbital per atom would make itself clearly visible in the band-theory calculations for the metals from Co to Ge, Rh to Sn, and Pt to Pb for example, the decrease in the number of bonding electrons from 4 for gray tin to 2.56 for white tin should result from these calculations. So far as I know, however, no such interpretation of the band-theory calculations has been reported. 

All these properties of metals are consistent with a bonding description that places the valence electrons in delocalized orbitals. This section describes the band theory of solids, an extension of the delocalized orbital ideas... 

Further studies were carried out on the Pd/Mo(l 1 0), Pd/Ru(0001), and Cu/Mo(l 10) systems. The shifts in core-level binding energies indicate that adatoms in a monolayer of Cu or Pd are electronically perturbed with respect to surface atoms of Cu(lOO) or Pd(lOO). By comparing these results with those previously presented in the literature for adlayers of Pd or Cu, a simple theory is developed that explains the nature of electron donor-electron acceptor interactions in metal overlayer formation of surface metal-metal bonds leads to a gain in electrons by the element initially having the larger fraction of empty states in its valence band. This behavior indicates that the electro-negativities of the surface atoms are substantially different from those of the bulk [65]. 

The free-electron model is a simplified representation of metallic bonding. While it is helpful for visualizing metals at the atomic level, this model cannot sufficiently explain the properties of all metals. Quantum mechanics offers a more comprehensive model for metallic bonding. Go to the web site above, and click on Web Links. This will launch you into the world of molecular orbitals and band theory. Use a graphic organizer or write a brief report that compares the free-electron and band-theory models of metallic bonding. 

Bonding in metals involves delocalization of electrons over the whole metal crystal, rather like the n electrons in graphite (Section 3.2) except that the delocalization, and hence also the high electrical conductivity, is three dimensional rather than two dimensional. Metallic bonding is best described in terms of band theory, which is in essence an extension of molecular orbital (MO) theory (widely used to represent bonding in small molecules) to arrays of atoms of quasi-infinite extent. 

As the name implies, the phenomenon is based on coating a solid metal with a liquid metal. In our theory, liquid metal (being above its melting temperature) has no covalent bonds and the free electrons essentially provide the cohesive energy. It can be recalled that this was the basis for obtaining the correlation (Fig. 11). Thus, by coating a metal that has a distinct ratio of covalent bond over free electron band with a liquid metal that has only free electrons (no covalent bond) can have no effect whatsoever in the AEi (for these notations refer to Fig. 9) which has to do only with covalent bond. This is the observation of 4.1.3. 

Molecular orbital (MO) theory has been used to explain the bonding in metallic crystals, such as pure sodium or pure aluminum. Each MO, instead of dealing with a few atoms in a typical molecule, must cover the entire crystal (might be 1020 or more atoms ). Following the rule that the number of MOs must equal the number of atomic orbitals (AOs) combined, this many MOs must be so close on an energy level diagram that they form a continuous band of energies. Because of this factor, the theory is known as band theory. 

A simple alternative model, consistent with band theory, is the electron sea concept illustrated in Fig. 9-22 for sodium. The circles represent the sodium ions which occupy regular lattice positions (the second and fourth lines of atoms are in a plane below the first and third). The eleventh electron from each atom is broadly delocalized so that the space between sodium ions is filled with an electron sea of sufficient density to keep the crystal electrically neutral. The massive ions vibrate about the nominal positions in the electron sea, which holds them in place something like cherries in a bowl of gelatin. This model successfully accounts for the unusual properties of metals, such as the electrical conductivity and mechanical toughness. In many metals, particularly the transition elements, the picture is more complicated, with some electrons participating in local bonding in addition to the delocalized electrons. 

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