Solid-state physics beginnings

The beginnings of the enormous field of solid-state physics were concisely set out in a fascinating series of recollections by some of the pioneers at a Royal Society Symposium (Mott 1980), with the participation of a number of professional historians of science, and in much greater detail in a large, impressive book by a number of historians (Hoddeson et al. 1992), dealing in depth with such histories as the roots of solid-state physics in the years before quantum mechanics, the quantum theory of metals and band theory, point defects and colour centres, magnetism, mechanical behaviour of solids, semiconductor physics and critical statistical theory. 

J. W. Mitchell, The Beginnings of Solid State Physics, Royal Society, London, 1980, pp. 140-159. 

Since the early days of quantum mechanics, the wave function theory has proven to be very successful in describing many different quantum processes and phenomena. However, in many problems of quantum chemistry and solid-state physics, where the dimensionality of the systems studied is relatively high, ab initio calculations of the structure of atoms, molecules, clusters, and crystals, and their interactions are very often prohibitive. Hence, alternative formulations based on the direct use of the probability density, gathered under what is generally known as the density matrix theory [1], were also developed since the very beginning of the new mechanics. The independent electron approximation or Thomas-Fermi model, and the Hartree and Hartree-Fock approaches are former statistical models developed in that direction [2]. These models can be considered direct predecessors of the more recent density functional theory (DFT) [3], whose principles were established by Hohenberg,... 

Since the early days of application of Mossbauer spectroscopy in solid state physics and inorganic chemistry, electronic structure calculations have been performed to rationalize and predict the Mossbauer parameters obtained. In the beginning, calculations were applied to single ions, but later semiempirical methods could be applied to small molecules, too. Early density functional theory (DFT) methods, like the self-consistent charge (SCC)-Xa method could be successfully applied to larger molecules. For more than a decade, DFT methods with all-electron basis sets have also been applied to large bioinorganic molecules. These methods allow the determination of Mossbauer parameters with impressive accuracy and have become a valuable tool for the interpretation of Mossbauer spectra. 

If in a given solid at temperature zero all one-electron levels are filled right up to the beginning of a gap and empty above it, that solid is a semiconductor otherwise it is a metal. In the latter case, the highest occupied level is called the Fermi level, and its energy is the Fermi energy f. The relation E(n, k) for all n and k is called the electronic band structure of the solid it is the central quantity in solid-state physics. For many metallic... 

A comprehensive overview of quantum mechanics is given by Cohen-Tannoudji et al. (1977), and another good book is by Levine (2000). A staple text on solid-state physics is by Ashcroft and Mermin (1976). A thorough introduction to density-functional theory is given by Parr and Yang (1989). Two good books to learn more about molecular dynamics simulations are by Allen and Tildesley (1987) and Frenkel and Smit (1996). To learn more about pseudopotential methods, two sources with which to begin are by Pickett (1989) and Bachelet et al. (1982). 

The LDA approach originated from solid-state physics where, the Hartree-Fock approximation being less useful, it is mandatory to take electron correlation from the beginning into account, and this is almost always done in the framework of density functional theory. As the non-relativistic density functional had to be changed to take relativity into account [41], the... 

Cd(OH)2 is precipitated from aqueous Cd + by addition of bases. It is colorless and soluble in acids and aqueous NH4CI, but only slightly in NaOH solutions. Cd(OH)2 is a base stronger than Zn(OH)2l its solubility product is 10 and log K for the equilibrium Cd + + OH = CdOH+ is 6.38. Cd(OH)2 begins to undergo thermal decomposition at about 150°C (at 200°C it is complete). Several basic salts are known and may be prepared from alkaline Cd + solutions or by heating CdO with solutions of Cd + salts at 200 °C. Hydroxide halides have been carefully investigated both in solution and in solid state.Physical properties of Cd(OH)2 are reported in Table 8. 

If you are surprised, remember the gemstone ruby (Al Oj Cr ) mentioned in the beginning of this chapter. Becqgerel started long ago to. study its luminescence and spectroscopy. Ruby was and is the start of several interesting phenomena in solid state physics. Probably the most important of these is the first solid state laser which was based on mhy (Maiman, I960). This illustrates the connection between luminescence and lasers. On the other hand, in more recent years it has only been possible to unravel and understand luminescence processes by using laser spectroscopy. 

We begin by noting that at some time t, all the deep states for which E > E =kT In coot have been accumulating electrons without reemitting them, since their mean time for thermal emission t = Wq cxp(E/kT) is much longer than t. It follows that the distribution of electrons in these states must parallel the density of states. Similarly, the electrons in the shallow states for which EKE have on average experienced many thermal-emission - recapture events. The end result of this statistical scrambling for the shallow states (EKE ) is well known in solid-state physics—a Boltzmann distribution results. Thus the distribution function for the electrons in the shallow states must have the Boltzmann form exp( /fc7 )iV,( ). The proportionality constant can be calculated from the requirement that the distribution of electrons in the shallow localized states be continuous with the distribution in the deep states. If the (constant) fractional occupancy of the deep states isf, then for continuity the population in the shallow states (E K E ) must be ftxv>[iE-E )/kT]N,(E). 

The above-mentioned and other early works on the electrical conductivity of organic molecular crystals and non-crystalline organic solids were continued only sporadically up to about 1960. They made essentially no contribution to the rapid development of solid-state physics during this period. The reason for this was on the one hand the widespread reluctance of solid-state physicists to become involved in chemistry. On the other hand, in the beginning, crystalline systems with only one or a few atoms in their unit cells sufficed to carry out the elucidation of the fundamental phenomena of solid-state physics, such as superconductivity and semiconductor physics. 

From its beginnings as an elegant experiment in nuclear and solid state physics Mossbauer spectroscopy has come to be applied to different problems in many areas of science and technology. The interdisciplinary nature of the technique and its numerous applications are illustrative both of the way in which science develops and of how it leads to technological progress. As a means of investigation it successfully complements other experimental methods but has several features which make it an especially powerful technique in a number of important situations and applications. 

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