Metallic bonding free-electron theory

A theory for the metallic state proposed by Drude at the turn of this century explained many characteristic features of metals. In this model, called the free-electron theory, all the atoms in a metallic crystal are assumed to take part collectively in bonding, each atom providing a certain number of (valence) electrons to the bond. These free electrons belong to the crystal as a whole. The crystal is considered to be... 

A simple explanation for the many characteristic features of the metallic state is given by free-electron theory. In metallic crystals the atoms are assumed to take part collectively in bonding, where each atom provides electrons from outer electron energy levels to the bond. The crystal... 

The three most prominent theories to date to explain metal bonding include free-electron theory, the valence bond theory, and band theory. They represent a progression in scientists understanding of metals over time. 

The occupancy of the free-electron valence band, built mainly from s- and p-valence atomic orbitals can be considered close to constant with one electron per metal atom. This is due to hybridization of the atomic orbitals by formation of the metal atom-metal atom bonds. Within free electron theory, its energy is mainly determined by the density of the metal atoms [25], When an adatom adsorbs, the charge density on the adatom adjusts so that the chemical potential on the adatom becomes equal to that at the surface. When the adatom orbital is half occupied, this results in an attractive interaction because of electron transfer to the adsorbate. When the adatom orbital is doubly occupied, the interaction becomes repulsive, because of the increase in electron kinetic energy due to the PauH electron exclusion rule [25], The interaction with adatoms is rather independent of the coordination of the adatom with the surface. 

This molecular-orbital model of metallic bonding (or band theory, as it is also called) is not so different in some respects from the electron-sea model. In both models Ihe electrons are free to move about in the solid. The molecular-orbital model is more quantitative than the simple electron-sea model, however, so many properties of metals can be accounted for by quantum mechanical calculations using molecular-orbital theory. 

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. 

Models for the electronic structure of polynuclear systems were also developed. Except for metals, where a free electron model of the valence electrons was used, all methods were based on a description of the electronic structure in terms of atomic orbitals. Direct numerical solutions of the Hartree-Fock equations were not feasible and the Thomas-Fermi density model gave ridiculous results. Instead, two different models were introduced. The valence bond formulation (5) followed closely the concepts of chemical bonds between atoms which predated quantum theory (and even the discovery of the electron). In this formulation certain reasonable "configurations" were constructed by drawing bonds between unpaired electrons on different atoms. A mathematical function formed from a sum of products of atomic orbitals was used to represent each configuration. The energy and electronic structure was then... 

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. 

It is well known through our experience that material with conduction electrons suffer from the phenomenon called corrosion i.e., metals turning into metallic oxides in time in air. On the other hand, the materials without conduction electrons do not suffer from corrosion. Technically, the presence of conduction electrons implies the existence of free electrons and conduction band. As pointed out in the mechanical property section these two distinct properties exhibit themselves also in term of plasticity . That is, the existence of free electron band allows plastic deformation whereas in the absence of free electron band the plasticity is nonexistent. It is recalled that the theory we are proposing for metals and alloys requires not only the coexistence of covalent bond and free electron band but also that the ratio of the number of these two type of electrons be maintained at a constant value for a given metal. Within such understanding, we now construct corrosion process in steps ... 

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