Electronic states in crystals

See for example H. Jones, The Theory of BriUouin Zones and Electronic States in Crystals, Chaps. 1 and 2, North-Holland Publishing Company, Amsterdam, I960. 

Jones, H. (1960) The Theory of Brillouirt Zones and Electronic States in Crystals. North-Holland, Amsterdam [2nd edn 1971]. 

Within the adiabatic and one-electron approximations, when electron spin is neglected, electron states in crystals are described by the eigenfunctions and their corresponding eigenvalues, which are the solutions of the Schrodinger equation,... 

Kucherenko, Yu. N. (1989a). X-Ray electron and Auger spectroscopy as methods for investigation of local partial electronic states in crystals. Doctor of Philosophy Thesis, Institute of Metal Physics, Kiev. 

Our intention is to give a brief survey of advanced theoretical methods used to detennine the electronic and geometric stmcture of solids and surfaces. The electronic stmcture encompasses the energies and wavefunctions (and other properties derived from them) of the electronic states in solids, while the geometric stmcture refers to the equilibrium atomic positions. Quantities that can be derived from the electronic stmcture calculations include the electronic (electron energies, charge densities), vibrational (phonon spectra), stmctiiral (lattice constants, equilibrium stmctiires), mechanical (bulk moduli, elastic constants) and optical (absorption, transmission) properties of crystals. We will also report on teclmiques used to study solid surfaces, with particular examples drawn from chemisorption on transition metal surfaces. 

We will limit ourselves here to transition metals. It is well known that in these metals, the cohesive properties are largely dominated by the valence d electrons, and consequently, sp electrons can be neglected save for the elements with an almost empty or filled d valence shelP. Since the valence d atomic orbitals are rather localized, the d electronic states in the solid are well described in the tight-binding approximation. In this approximation, the cohesive energy of a bulk crystal is usually written as ... 

Our discussion of electronic structure has been in terms of band filling only. Of course, there is a lot more to know about band structures. The density of states represents only a highly simplified representation of the actual electronic structure, which ignores the three-dimensional structure of electron states in the crystal lattice. Angle-dependent photoemission gives information on this property of the electrons. The interested reader is referred to standard books on solid state physics [9,10] and photoemission [16,17]. The interpretation of photoemission and X-ray absorption spectra of catalysis-oriented questions, however, is usually done in terms of the electron density of states only. 

An important aspect of semiconductor films in general with regard to electronic properties is the effect of intrabandgap states, and particularly surface states, on these properties. Surface states are electronic states in the forbidden gap that exist because the perfect periodicity of the semiconductor crystal, on which band theory is based, is broken at the surface. Change of chemistry due to bonding of various adsorbates at the surface is often an important factor in this respect. For CD semiconductor films, which are usually nanocrystalline, the surface-to-volume ratio may be very high (several tens of percent of all the atoms may be situated at the surface for 5 mn crystals), and the effects of such surface states are expected to be particularly high. Some aspects of surface states probed by photoluminescence studies are discussed in the previous section. 

Gurney then collaborated with the eminent Cambridge (U.K.) physicist. Nevil Mott, to co-author a book. Electronic Processes in Crystals (1936), which provided the foundation of solid state physics. Some years later there followed Ions in Solution, the first book to treat solution J electrochemistry at a quantum level. 

The crystal lattice and the reciprocal lattice representations have different purposes. The crystal lattice describes, and enables us to visualize, the crystal structure. The reciprocal lattice will provide a means of describing electron states and phonon states in crystals. 

Tables of compatibility relations for the simple cubic structure have been given by Jones (1962, 1975), and similar tables can be compiled for other structures, as shown by the examples in Tables 17.2 and 17.5. Compatibility relations are extremely useful in assigning the symmetry of electronic states in band structures. Their use in correlation diagrams in crystal-field theory was emphasized in Chapters 7 and 8, although there it is not so common to use B SW notation, which was invented to help describe the symmetry of electronic states in energy bands in crystals (Bouckaert el al. (1936)).

---