Crystalline solids lattice defects

All crystalline solids exhibit defects in and departure from the ideal lattice structure, particularly at elevated temperature. Either lattice points remain unoccupied (vacancies) or lattice elements deposit between the regular lattice points (interstitial lattice points). These point defects determine material transport in a solid. In addition, there are a number of linear and face defects, dislocations, grain boundaries, and so forth, which although of importance to the mechanical properties of a solid are less significant for material transport. 

A crystalline solid is never perfect in that all of tire lattice sites are occupied in a regular manner, except, possibly, at the absolute zero of temperature in a perfect crystal. Point defects occur at temperatures above zero, of which the principal two forms are a vacant lattice site, and an interstitial atom which... 

Crystalline solids are built up of regular arrangements of atoms in three dimensions these arrangements can be represented by a repeat unit or motif called a unit cell. A unit cell is defined as the smallest repeating unit that shows the fuU symmetry of the crystal structure. A perfect crystal may be defined as one in which all the atoms are at rest on their correct lattice positions in the crystal structure. Such a perfect crystal can be obtained, hypothetically, only at absolute zero. At all real temperatures, crystalline solids generally depart from perfect order and contain several types of defects, which are responsible for many important solid-state phenomena, such as diffusion, electrical conduction, electrochemical reactions, and so on. Various schemes have been proposed for the classification of defects. Here the size and shape of the defect are used as a basis for classification. 

When in solid solution in the solid state, an impurity will alter the crystallinity by introducing impurity defects into the crystal lattice, thereby changing the thermodynamic and other physical properties of the solid, including the solubility and dissolution rate [2,37]. Prolonged equilibration of the solid state with the saturated solution, however, usually leads to recrystallization of the solute and to a consequent return of the crystallinity and the measured solubility of the solid state to that of the pure, highly crystalline solid. 

PLASTIC DEFORMATION. When a metal or other solid is plastically deformed it suffers a permanent change of shape. The theory of plastic deformation in crystalline solids such as metals is complicated but well advanced. Metals are unique among solids in their ability to undergo severe plastic deformation. The observed yield stresses of single crystals are often 10 4 times smaller than the theoretical strengths of perfect crystals. The fact that actual metal crystals are so easily deformed has been attributed to the presence of lattice defects inside the crystals. The most important type of defect is the dislocation. See also Creep (Metals) Crystal and Hot Working. 

Lattice defects can function both as donors and as acceptors and create free electrons or electron holes. Crystalline surfaces containing unsaturated electron valences act as electron traps and capture free electrons. This leads to changes in binding conditions and in the charge state of e.g. metal ions their ability to polarize O- in a metal oxide decreases. Surface oxidation during the grinding process often causes deep alterations of the surface structure of solids (sulphides, graphite, coal). This usually leads to increases in affinity toward water and in reactivity with the surfactant. 

The examples discussed here are the simplest possible and real systems are usually more complicated. Moreover, we have used simplified models for example, v is the characteristic frequency of the interstitial ion or an ion adjacent to a vacant lattice position it will be diflerent from the characteristic lattice frequency and will not be the same for Schottky and Frenkel defects. However, the general principles of the transfer of matter through a crystalline solid are as they have been given here. 

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... 

The electronic structure of solids and surfaces is usually described in terms of band structure. To this end, a unit cell containing a given number of atoms is periodically repeated in three dimensions to account for the infinite nature of the crystalline solid and the Schrodinger equation is solved for the atoms in the unit cell subject to periodic boundary conditions [38]. This approach can also be extended to the study of adsorbates on surfaces or of bulk defects by means of the supercell approach in which an artificial periodic structure is created where the adsorbate is translationally reproduced in correspondence to a given super lattice of the host. This procedure allows the use of efficient computer programs designed for the treatment of periodic systems and has indeed been followed by several authors to study defects using either DFT and plane waves approaches [39-41] or Hartree-Fock (HF)-based methods with localized atomic orbitals [42,43]. 

All the foregoing discussion of crystalline solids has dealt with their perfect or ideal structures. Such perfect structures are seldom if ever found in real substances and, while low levels of imperfections have only small effects2 on their chemistry, the physical (i.e., electrical, magnetic, optical and mechanical) properties of many substances are often crucially affected by their imperfections. It is, therefore, appropriate to devote a few paragraphs to describing the main types of imperfection, or defect, in real crystalline solids. We shall not, however, discuss the purely mechanical imperfections such as mosaic structure, stacking faults, and dislocations, all of which are some sort of mismatch between lattice layers. 

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