Modelling Solid-state Defects

Materials that contain defects and impurities can exhibit some of the most scientifically interesting and economically important phenomena known. The nature of disorder in solids is a vast subject and so our discussion will necessarily be limited. The smallest degree of disorder that can be introduced into a perfect crystal is a point defect. Three common types of point defect are vacancies, interstitials and substitutionals. Vacancies form when an atom is missing from its expected lattice site. A common example is the Schottky defect, which is typically formed when one cation and one anion are removed from the bulk and placed on the surface. Schottky defects are common in the alkali halides Interstitials are due to the presence of an atom in a location that is usually unoccupied. A 

Two point defects may aggregate to give a defect pair (such as when the two vacancies diat constitute a Schottky defect come from neighbouring sites). Ousters of defects can also form. These defect clusters may ultimately give rise to a new periodic structure or to an extended defect such as a dislocation. Increasing disorder may alternatively give rise to a random, amorphous solid. As the properties of a material may be dramatically altered by the presence of defects it is obviously of great interest to be able to understand these relationships and ultimately predict them. However, we will restrict our discussion to small concentrations of defects. 

The most direct effect of defects on the properties of a material usually derive from the altered ionic conductivity and diffusion properties. So-called superionic conductors are materials which have an ionic conductivity comparable to that of molten salts. This high conductivity is due to the presence of defects, which can be introduced thermally or via the presence of impurities. Diffusion affects important processes such as corrosion and catalysis. The specific heat capacity is also affected near the melting temperature the heat capacity of a defective material is higher than for the equivalent ideal crystal. This reflects the fact that the creation of defects is enthalpically unfavourable but is more than compensated for by the increase in entropy, so leading to an overall decrease in the free energy. 

This can be used to eliminate the energy E2 from Equation (11.90), giving the following expression for the total energy  

In order to determine the energy it would thus seem that it is necessary merely to minimise with respect to the positions x and the displacements y. However, a complication arises due to the fact that the displacements in the outer region are themselves a function of the inner-region coordinates. The solution to this problem is to require that the forces on the ions in region 1 are zero, rather than that the energy should be at a minimum (for simple problems the two are synonymous, but in practice there may still be some non-zero forces present when the energy minimum is considered to have been located). An additional requirement is that the ions in region 2 need to be at equilibrium. 

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Four Challenges in IVIoSecula Modelling Free Energies, Solvation, Reactions and Solid-state Defects... 

Our work has applied these techniques to the study of the binary insulating materials including the fluorites, alkali halides, alkaline earth oxides, and perovskites. Many of these are simple materials that are commonly used as models for all solid state defect equilibria. Our work has had the goal of determining at the microscopic level the defect equilibria and dynamics that are important in understanding solid state chemistry as well as developing new tools for the studies of solid materials. 

Figure 55. Ajump within the true potential (lattice potential (top) plus defect potential (center)) requires the surmounting of a relatively high activation energy and a subsequent relaxation of the environment, before the site B takes on the original potential surroundings of A (see text). From Ref.217. (Reprinted from K. Funke, Ion transport in fast ion conductors—spectra and models , Solid State Ionics. 94, 27-33. Copyright 1997 with permission from Elsevier.)...

Amin, R. Maier, J. Effect of annealing on transport properties of LiFeP04 Towards a defect chemical model. Solid State Ionics, 178, 1831(2008). 

In this chapter we shall consider four important problems in molecular n iudelling. First, v discuss the problem of calculating free energies. We then consider continuum solve models, which enable the effects of the solvent to be incorporated into a calculation witho requiring the solvent molecules to be represented explicitly. Third, we shall consider the simi lation of chemical reactions, including the important technique of ab initio molecular dynamic Finally, we consider how to study the nature of defects in solid-state materials. 

Fig. 2 Mechanically oriented bilayer samples as a membrane model for ssNMR. (a) Illustration of the hydrated lipid bilayers with MAPs embedded, the glass supports, and the insulating wrapping, (b) A real sample consists of 15 stacked glass slides, (c) Schematic solid-state 19F-NMR lineshapes from an oriented CF3-labelled peptide (red), and the corresponding powder lineshape from a non-oriented sample (grey), (d) Illustration of typical orientational defects in real samples - the sources of powder contribution in the spectra...

These ideas developed by chemists resemble the bipolaron model, which presents the solid-state physicist s view of the electronic properties of doped conducting polymers [96]. The model was originally constructed to characterize defects in inorganic solids. In chemical terminology, bipolarons are equivalent to diionic states of a system (S = 0) after oxidation or reduction from the neutral state. The transition from the neutral state to the bipolaron takes place via the polaron state (= monoion, S = 1/2,... 

The different responses of the NXL and XL bands would not occur if the NXL material were present as defects within tire XL phase. These data support a two-phase model of solid state structure in semicrystalline PTLE. Of course, the precise location of the two phases is difficult to specify, but for the XL phase we have good data on its initial morphology and subsequent changes based upon microscopy and X-ray diffraction. 

A force field for solid state modeling of fluoropolymers predicted a suitable helical conformation but required further improvement in describing intermole-cular effects. Though victory cannot yet be declared, the derived force fields improve substantially on those previously available. Preliminary molecular dynamics simulations with the interim force field indicate that modeling of PTFE chain behavior can now be done in an all-inclusive manner instead of the piecemeal focus on isolated motions and defects required previously. Further refinement of the force field with a backbone dihedral term capable of reproducing the complex torsional profile of perfluorocarbons has provided a parameterization that promises both qualitative and quantitative modeling of fluoropolymer behavior in the near future. 

So far, most of the quantum-chemical computations of solid compounds have assumed a free molecular model that is the intermolecular effects are initially not considered. Although these second-order effects are minor in many cases and do not cause much disagreement with solid-state NMR measurements, they might become significant and should not be neglected. Recently a series of publications has addressed this problem, based on a supercell technique.38-41 The appealing feature of this new method is that it can deal not only with free molecules but also with crystals, amorphous materials or materials with defects. 

A second important event was the development by Hosemann (1950) of a theory by which the X-ray patterns are explained in a completely different way, namely, in terms of statistical disorder. In this concept, the paracrystallinity model (Fig. 2.11), the so-called amorphous regions appear to be the same as small defect sites. A randomised amorphous phase is not required to explain polymer behaviour. Several phenomena, such as creep, recrystallisation and fracture, are better explained by motions of dislocations (as in solid state physics) than by the traditional fringed micelle model. 

Bipolaron — Bipolarons are double-charged, spinless quasiparticles introduced in solid state physics [i]. A bipolaron is formed from two -> polarons (charged defects in the solid). For chemists the double-charged states mean dications or dianions, however, bipolarons are not localized sites, they alter and move together with their environment. By the help of the polaron-bipolaron model the high conductivity of -> conducting polymers can be explained. 

A new book by von Sonntag, Free-Radical Induced DNA Damage and Its Repair has just appeared [7], This new book provides thorough updates on what is currently known about the free radical chemistry of nucleic acids. This book also contains a section on irradiation in the solid-state. Since there is no need to repeat what has already been so adequately covered, the present work will focus on the experimental techniques used to obtain the detailed structure of the primary radiation induced defects in DNA model systems, and to consider the subsequent transformations these primary radical undergo. 

In the shell model, as mentioned above, the short-range repulsion and van der Waals interactions are taken to act between the shell particles. This finding has the effect of coupling the electrostatic and steric interactions in the system in a solid-state system where the nuclei are fixed at the lattice positions, polarization can occur not only from the electric field generated by neighboring atoms, but also from the short-range interactions with close neighbors (as, e.g., in the case of defects, substitutions, or surfaces). This ability to model both electrical and mechanical polarizability is one reason for the success of shell models in solid-state ionic materials. 

Defects in Solids Dielectric Polarizabilities of Oxides Fluorides Diffraction Methods in Inorganic Chemistry Electronic Stmcture of Solids Fluorides Solid-state Chemistry Halides Solid-state Chemistry Intercalation Chemistry Non-crystalUne Solids Oxides Solid-state Chemistry Phosphates Solid-state Chemistry Polyphosphazenes Sol-Gel Synthesis of Solids Solids Computer Modeling Stmcture Property Maps for Inorganic Solids Zeolites. 

Combined quantum mechanical/molecular mechanics calculations have become popular over the last decade or so in solid state modelling. Typically a molecule attaching to a surface or the side of a cage structure or an isolated defect is treated quantum mechanically as a cluster embedded in a bulk solid described by an interatomic potential method. One of the earliest examples of this approach was Vail s work on F-centres which began in 1983" " and which treated a cluster around the F-centre quantum-mechanically and the rest of the solid via an interatomic potential method. 

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