Lattice defects vacancies: thermal

Theoretical explanations which have been advanced to account for the decrease in order occurring at the temperature of fusion of a crystalline solid include an increase in the amplitude of thermal vibrations so that the stabilizing forces of the crystal are overcome, and/or that there is a marked increase in the concentrations of lattice defects (vacancies) or dislocations. Within a few degrees of the melting point, the... 

In pure and stoichiometric compounds, intrinsic defects are formed for energetic reasons. Intrinsic ionic conduction, or creation of thermal vacancies by Frenkel, ie, vacancy plus interstitial lattice defects, or by Schottky, cation and anion vacancies, mechanisms can be expressed in terms of an equilibrium constant and, therefore, as a free energy for the formation of defects, If the ion is to jump into a normally occupied lattice site, a term for... 

The lattice may be distorted because of several reasons as vacancies, interstitials, dislocations and impurities. These lattice defects cause the so-called impurity scattering which produces the term i ei. At low temperatures, i ei is the constant electronic thermal resistance typical of metals. 

At small radiation doses (the number of radiation-produced defects), the mean distance l between components of such geminate pairs (the vacancy and an interstitial atom) is much less than the mean distance between different pairs Iq = n-1/3, where n is defect concentration. The initial defect distribution is described by the distribution function f(r). Below a certain temperature (typically < 30 K for interstitial atoms and 200 K for vacancies in alkali halides), defects are immobile. With a temperature increase, the defects perform thermally activated random hops between the nearest lattice sites. This is usually considered to be continuous diffusion. 

One of the causes of point defects is a temperature increase which results in an increased thermal movement of the atoms which can subsequently lead to the atoms escaping from their place in the lattice. Other causes are the effects of radiation and inbuilt, foreign atoms. In an atomic lattice a vacancy can occur due to the movement of an atom, an absence of an atom or molecule from a point which it would normally occupy in a crystal. In addition to this vacancy an atomic will form elsewhere. This combination of an atomic pair and a vacancy is called the Frenkel defect. In ionic crystals an anion and a cation have to leave the lattice simultaneously due to the charge balance. As a result a vacancy pair remains and this is called the Schottky defect. Both defects can be seen in figure 4.8. 

All real crystals above 0 K contain point defects which are thermodynamically inherent [21,22]. In a monatomic crystal, the simplest defects are the vacancy, a lattice site that is empty, and the interstitial atom, an atom on an interstitial site in the lattice. The equilibrium concentration of these defects is thermally controlled and has an exponential dependence on temperature. For example, the site fraction of vacancies, c in a pure monatomic crystal is given by ... 

The formation of hot spots is generally attributed to the presence of lattice defects [11,17,19-23], which could include vacancies, voids, dislocations, misalignments, cracks, impurities, etc. One explanation is that defects induce strain in the lattice, which is relieved, via structural relaxation, by the externally-introduced energy this results in a disproportionate localization of energy in the neighborhood of the defect, a portion of it being in lattice vibrations [21,22]. The thermal energy of hot spots must be efficiently transferred to appropriate molecular vibrational... 

Crystal lattice defects and distortions, such as vacancies, dislocations, substitutions, and so on, can play a fundamental part in determining the achievable properties of any fabricated metal product. These defects may be present, to some degree, before any final thermal, mechanical or other processing treatments are undertaken. 

The electrical resistivity is the summation of two contributions the contribution of the lattice or the thermal resistivity, i.e., the thermal scattering of conduction electrons due to atomic vibrations of the material crystal lattice (i.e., phonons), and the residual resistivity, which comes from the scattering of electrons by crystal lattice defects (e.g., vacancies, dislocations, and voids), solid solutes, and chemical impurities (i.e., interstitials). Therefore, the overall resistivity can be described by the Matthiessen s equation as follows ... 

The third term in Eq. 7, K, is the contribution to the basal plane thermal resistance due to defect scattering. Neutron irradiation causes various types of defects to be produced depending on the irradiation temperature. These defects are very effective in scattering phonons, even at flux levels which would be considered modest for most nuclear applications, and quickly dominate the other terms in Eq. 7. Several types of in-adiation-induced defects have been identified in graphite. For irradiation temperatures lower than 650°C, simple point defects in the form of vacancies or interstitials, along with small interstitial clusters, are the predominant defects. Moreover, at an irradiation temperatui-e near 150°C [17] the defect which dominates the thermal resistance is the lattice vacancy. 

In addition to the thermal vacancies, impurity-related vacancies will develop in ionic crystals. When impurity ions have a charge different from ions of like charge which are the crystal s main constituents, part of the lattice sites must remain vacant in order to preserve electroneutrality. Such impurity-type defects depend little on temperature, and their major effects are apparent at low temperatures when few thermal vacancies exist. 

The kinds of substitution mechanisms that may be relevant to super-low concentration elements such as Pa involve intrinsic defects, such as lattice vacancies or interstitials. Vacancy defects can potentially provide a low energy mechanism for heterovalent cation substitution, in that they remove or minimise the need for additional charge balancing substitutions. Formation of a vacancy per se is energetically unfavourable (e.g., Purton et al. 1997), and the trace element must rely instead on the thermal defect concentration in the mineral of interest, at the conditions of interest. Extended defects, such as dislocations or grain boundaries, may also play a key role, but as these are essentially non-equilibrium features, they will not be considered further here. 

Chemical solid state processes are dependent upon the mobility of the individual atomic structure elements. In a solid which is in thermal equilibrium, this mobility is normally attained by the exchange of atoms (ions) with vacant lattice sites (i.e., vacancies). Vacancies are point defects which exist in well defined concentrations in thermal equilibrium, as do other kinds of point defects such as interstitial atoms. We refer to them as irregular structure elements. Kinetic parameters such as rate constants and transport coefficients are thus directly related to the number and kind of irregular structure elements (point defects) or, in more general terms, to atomic disorder. A quantitative kinetic theory therefore requires a quantitative understanding of the behavior of point defects as a function of the (local) thermodynamic parameters of the system (such as T, P, and composition, i.e., the fraction of chemical components). This understanding is provided by statistical thermodynamics and has been cast in a useful form for application to solid state chemical kinetics as the so-called point defect thermodynamics. 

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