Electrical conductivity in solids

Suppose we have an allowed band of n electrons, the current I flowing during dt is the sum of the n electron contributions. If denotes the electric field, then  

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Dislocation theory as a portion of the subject of solid-state physics is somewhat beyond the scope of this book, but it is desirable to examine the subject briefly in terms of its implications in surface chemistry. Perhaps the most elementary type of defect is that of an extra or interstitial atom—Frenkel defect [110]—or a missing atom or vacancy—Schottky defect [111]. Such point defects play an important role in the treatment of diffusion and electrical conductivities in solids and the solubility of a salt in the host lattice of another or different valence type [112]. Point defects have a thermodynamic basis for their existence in terms of the energy and entropy of their formation, the situation is similar to the formation of isolated holes and erratic atoms on a surface. Dislocations, on the other hand, may be viewed as an organized concentration of point defects they are lattice defects and play an important role in the mechanism of the plastic deformation of solids. Lattice defects or dislocations are not thermodynamic in the sense of the point defects their formation is intimately connected with the mechanism of nucleation and crystal growth (see Section IX-4), and they constitute an important source of surface imperfection. 

Electrical conductance in solids (other than ionic conductors) depends on the availability of delocalised orbitals close enough together in energy to form bands. 

Following the introduction of basic kinetic concepts, some common kinetic situations will be discussed. These will be referred to repeatedly in later chapters and include 1) diffusion, particularly chemical diffusion in different solids (metals, semiconductors, mixed conductors, ionic crystals), 2) electrical conduction in solids (giving special attention to inhomogeneous systems), 3) matter transport across phase boundaries, in particular in electrochemical systems (solid electrode/solicl electrolyte), and 4) relaxation of structure elements. 

We begin our discussion by characterizing the electrical conduction in solid electrolytes. These are solids with predominantly ionic transference, at least over a certain range of their component activities. This means that the electronic transference number, defined as... 

In the above radical-cation salts, the crystal contains partially oxidized donors, while the electroneutrality is achieved by the presence of closed shell anions. The structural requirements necessary for electrical conductivity in solid salts can also be met upon mixing of donors and acceptors in the resulting charge-transfer (CT) complexes both the donor and acceptor exist in a partially oxidized and reduced state, respectively. Famous examples are the conducting CT complexes formed upon mixing of perylene (112) [323. 324] and iodine or of tetrathiafulvalene (TTF, 119) as donor and 7,7,8,8-tetracyanoquinodimethane (TCNQ, 120) as acceptor [325-327] the crucial structural finding for the... 

Electric Waves, Heinrich Hertz. 1.75 Principles of Mechanics, Heinrich Hertz. 2.50 Atomic Spectra and Atomic Structure, Gerhard Herzberg. 2.00 Introduction to Differential Equations of Physics, L. Hopf. 1.45 Principles of Quantum Mechanics, William V. Houston. 2.00 Electrical Conduction in Solids, H. Inokuchi. 1.35 Tables of Functions with Formulae and Curves, Eugene Jahnke and Fritz Emde. 2.25... 

Phonons Based on an analogy between crystal lattice vibrations and those of an electromagnetic field, these particles of quantized vibrational energy were used by physicists to facilitate calculations of thermal and electrical conduction in solids. 

An alternative interpretation of electric conduction in solids is based on the fact that charge transfer is possible only in non-ideal lattices. The solid must have crystallographic defects. Foreign atoms as dopants in semiconductors can be considered as a defect itself, but not as the only one. 

Ionic conductivity is electrical conductivity due to the motion of ionic charge. Elementary science introduces this phenomenon as a property of liquid electrolyte solutions. In the solid state, ionic conductivity has recently been somewhat overshadowed by electronic, but nevertheless was recognized by Faraday, who observed electrical conductivity in solid lead fluoride at high temperature. The conductivity in this case was due to the motion of fluoride anions within the structure. This type of conductivity in solids has long been of fundamental interest as well as being applied in the interpretation of corrosion. More recently, applications have been found in energy conversion devices and chemical sensors. ... 

The swelling of the adsorbent can be directly demonstrated as in the experiments of Fig. 4.27 where the solid was a compact made from coal powder and the adsorbate was n-butane. (Closely similar results were obtained with ethyl chloride.) Simultaneous measurements of linear expansion, amount adsorbed and electrical conductivity were made, and as is seen the three resultant isotherms are very similar the hysteresis in adsorption in Fig. 4.27(a), is associated with a corresponding hysteresis in swelling in (h) and in electrical conductivity in (c). The decrease in conductivity in (c) clearly points to an irreversible opening-up of interparticulate junctions this would produce narrow gaps which would function as constrictions in micropores and would thus lead to adsorption hysteresis (cf. Section 4.S). 

See 2-3.1. Electrical conduction through solids takes place both through the bulk material and over the surface. In most cases surfaces have different physical and chemical properties than the bulk, for example due to contamination or moisture. Volume and surface resistivity can be separately measured for solid materials such as antistatic plastic sheet. Powders represent a special case since although both surface and bulk conduction occur, their contributions cannot be individually measured and the volume or bulk resistivity of a powder includes surface effects. 

The electrical conductivity in the solid state is determined by the product of the carrier concentration and the carrier mobility. In conjugated polymers both entities are material dependent and, i.e., are different for electrons and holes. Electrons or holes placed on a conjugated polymer lead to a relaxation of the surrounding lattice, forming so-called polarons which can be positive or negative. Therefore, the conductivity, o, is the sum of both the conductivity of positive (P+) and negative polarons (P ) ... 

The great variations among solids make it desirable to And useful classification schemes. Though this topic is taken up much later in the course (Chapter 17), a beginning is provided by a look at the electrical conductivity of solids. 

Electrical conduction in metals can be explained in terms of molecular orbitals that spread throughout the solid. We have already seen that, when N atomic orbitals merge together in a molecule, they form N molecular orbitals. The same is true of a metal but, for a metal, N is enormous (about 1023 for 10 g of copper, for example). Instead of the few molecular orbitals with widely spaced energies typical of small molecules, the huge number of molecular orbitals in a metal are so close together in energy that they form a nearly continuous band (Fig. 3.43). 

This equation is identical to the Maxwell [236,237] solution originally derived for electrical conductivity in a dilute suspension of spheres. Hashin and Shtrikman [149] using variational theory showed that Maxwell s equation is in fact an upper bound for the relative diffusion coefficients in isotropic medium for any concentration of suspended spheres and even for cases where the solid portions of the medium are not spheres. However, they also noted that a reduced upper bound may be obtained if one includes additional statistical descriptions of the medium other than the void fraction. Weissberg [419] demonstrated that this was indeed true when additional geometrical parameters are included in the calculations. Batchelor and O Brien [34] further extended the Maxwell approach. 

Atoms of metals are more interesting tiian hydrogen atoms, because they can form not only dimers Ag2, but also particles with larger number of atoms. What are the electric properties of these particles on surfaces of solids The answer to this question can be most easily obtained by using a semiconductor sensor which plays simultaneously the role of a sorbent target and is used as a detector of silver adatoms. The initial concentration of silver adatoms must be sufficiently small, so that growth of multiatomic aggregates of silver particles (clusters) could be traced by variation of an electric conductivity in time (after atomic beam was terminated), provided the assumption of small electric activity of clusters on a semiconductor surface [42] compared to that of atomic particles is true. 

The description of the properties of this region is based on the solution of the Poisson equation (Eqs 4.3.2 and 4.3.3). For an intrinsic semiconductor where the only charge carriers are electrons and holes present in the conductivity or valence band, respectively, the result is given directly by Eq. (4.3.11) with the electrolyte concentration c replaced by the ratio n°/NA, where n is the concentration of electrons in 1 cm3 of the semiconductor in a region without an electric field (in solid-state physics, concentrations are expressed in terms of the number of particles per unit volume). 

Effective charge and transition-state structure in solution, 27, 1 Effective molarities of intramolecular reactions, 17,183 Electrical conduction in organic solids, 16,159 Electrochemical methods, study of reactive intermediates by, 19, 131 Electrochemical recognition of charged and neutral guest species by redox-active receptor molecules, 31, 1... 

Tintinelli A, Rizzo C, and Giunta G. Ni-YSZ porous cermets microstructure and electrical conductivity. In Bossel U, editor. Proceedings of the first European Solid Oxide Fuel Cells Forum. Lucerne, Switzerland European Fuel Cell Forum, 1994 455 164. 

Type of Crystalline Solid Particles Involved Primary Forces of Attraction Between Particles Boiling Point Electrical Conductivity in Liquid State Other Physical Properties of Crystals Conditions Necessary for Formation Examples... 

Megnamisi-Belombe M (1977) Evidence for intrinsic electrical conduction in the linear metal-chain semiconductor bis(l,2-benzoquinonedioximato)platinum(II), Pt(bqd)2. J Solid State Chem 22 151-156... 

This improvement made it possible to resolve micron distances behind the front. The value of the peak conductivity was found to correlate so strongly with the amount of solid carbon present in the detonation products, as to suggest that the principal path of electrical conduction in that region is thru a con-tinous network of solid carbon... 

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