The Defect Solid

Consider the surface of a solid. In the interior, we see a certain S5Tnmetry which depends upon the structure of the solid. As we approach the surface from the interior, the symmetry begins to change. At the very surface, the surface atoms see only half the symmetry that the interior atoms do (and half of the bonding as well). Reactions between solids take place at the surface. If there were some way to complete the symmetry of the surface atoms, then they too would likely be nearly non-reactive. 

In a three-dimensional solid, we can conceive of three major types of defects, one-, two- and three- dimensional in nature. These are called point, line (edge) and volume (plane), respectively. Point defects are changes at atomistic levels, while line and volume defects are changes in stacking of groups of atoms (molecules). An easy way to visualize point defects is shown in the following  

BUBBLE RAFT SHOWING EFFECTS OF VACANCY AND IMPURITY ON HEXAGONAL CLOSE-PACKING 

A bubble raft is made by creating bubbles in a soap solution which float to the surface of the liquid (in this case, water) to create a raft. The trick is 

In this diagram, we see three types of point defects. In addition to the vacancy, we also see two types of substitutional defects. Both are direct substitutions in the lattice , or arrangement of the atoms. One is a smaller atom, while the other is larger than the atoms comprising the lattice. Note the difference, due to size of the impurity, upon the ordering 

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We can be qualitatively certain that the fluidlike flow of shock deformation is a consequence of motion of defects. We cannot be quantitatively certain as to the significant, detailed descriptions and consequences of these defects. Indeed, the principal unfinished business of shock-compression science is the scientific description of the defective solid in all its manifestations. 

In large measure the paradigm within which work is carried out is strongly influenced by the objectives of the work, the background of the investigator, and the particular materials model under study. From a strictly fluid mechanics, hydrodynamic, or continuum framework, defect issues are not overtly at issue. From a strictly mechanical framework, the defective solid... 

We can anticipate that the highly defective lattice and heterogeneities within which the transformations are nucleated and grow will play a dominant role. We expect that nucleation will occur at localized defect sites. If the nucleation site density is high (which we expect) the bulk sample will transform rapidly. Furthermore, as Dremin and Breusov have pointed out [68D01], the relative material motion of lattice defects and nucleation sites provides an environment in which material is mechanically forced to the nucleus at high velocity. Such behavior was termed a roller model and is depicted in Fig. 2.14. In these catastrophic shock situations, the transformation kinetics and perhaps structure must be controlled by the defective solid considerations. In this case perhaps the best published succinct statement... 

There is a scarcity of oxygen-transport data for oxygen-deficient actinide oxide systems. Because of this, our understanding and predictive capabilities of the effect of the defect solid state on the properties of reactor fuel systems, as well as on the chemical state of fission products in these systems, are limited. 

Rees, A. L. G., Chemistry of the Defect Solid State, Methuen, London, 1954. 

The usefulness of quadrupolar effects on the nuclear magnetic resonance c I 7 yi nuclei in the defect solid state arises from the fact that point defects, dislocations, etc., give rise to electric field gradients, which in cubic ciystals produce a large effect on the nuclear resonance line. In noncubic crystals defects of course produce an effect, but it may be masked by the already present quadrupole interaction. Considerable experimental data have been obtained by Reif (96,97) on the NMR of nuclei in doped, cubic, polycrystalline solids. The effect of defect-producing impurities is quite... 

Most metals acquire an oxide film or scale on their surfaces on exposure to oxygen or air, especially at elevated temperatures.5-7 The kinetics and mechanism of formation of such films provide examples of applications of the concepts of the defect solid state outlined above, and indeed of solid-state kinetics in general.8... 

To our knowledge there have been no reported measurements of equilibrium defect concentrations in soft-sphere models. Similarly, relatively few measurements have been reported of defect free energies in models for real systems. Those that exist rely on integration methods to connect the defective solid to the perfect solid. In ab initio studies the computational cost of this procedure can be high, although results have recently started to appear, most notably for vacancies and interstitial defects in silicon. For a review see Ref. 109. 

Each of the four cases delineated [(ci), (cv), (ai), and (av)] is developed individually in such a way that it is self-contained. Each theoretical development is preceded by a formulation of the relevant equations for the defect solid-state reactions [63, 64] occurring at the phase boundaries separating the oxides. That is, balanced chemical equations involving... 

A thermodynamic description of the defect solid state of linear high polymers. Polymer 5, 125—134 (1964). 

Until recently very little was understood as to the factors which determine whether point or extended defects are formed in a non-stoicheiometric phase, although interesting empirical correlations between shear-plane formation and both dielectric and lattice dynamical properties of the defective solid had been noted. Theoretical techniques have, however, provided valuable insight into this problem and into the related one of the relative stabilities of extended and point defect structures. The role of these techniques is emphasized in this article. 

The properties of the defect solid state are fundamental to our understanding of all reacting systems involving a solid in fact, there is little of the metallurgical and chemical industries which is not based on the chemical properties of defect solids. A little reflection will make this so obvious that there is no necessity to enumerate specific examples even the electrical industry depends on the ability to produce materials having controllable defect properties, e.g. luminescent materials for fluorescent lamps and cathode-ray tube screens, oxide materials for cathode coatings, a variety of semi-conductors for resistors, rectifiers, detectors and photoelectric devices. 

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