Lattices defects

Physical properties of solid materials which are greatly influenced by the presence of defects of lattice order in real single crystals are called structural-sensitive properties, and are distinguished from intrinsic properties, which are determined by the elements constituting the crystal, for example the chemical bonds, the structure, etc. Color, plasticity, glide, and semiconductor properties are structural-sensitive properties, whereas density, hardness, elasticity, and optical, thermal, and magnetic properties are the intrinsic properties. Structural-sensitive 

The lattice defects are classified as (i) point defects, such as vacancies, interstitial atoms, substitutional impurity atoms, and interstitial impurity atoms, (ii) line defects, such as edge, screw, and mixed dislocations, and (iii) planar defects, such as stacking faults, twin planes, and grain boundaries. 

Within these three categories, the earliest attention was paid to point defects this arose from intellectual curiosity about the origin of the deep blue color seen in large colorless single crystals of NaCl occurring in salt deposits. From this starting point, the idea of color centers was developed. Since the color centers are point defects, they modify the electronic states around the defects and affect the heat and electronic conductivity consequently, they have become directly connected to the development of the semiconductor industry. 

If we assume that gliding occurs on the glide plane in the direction of and by the amount indicated by the solid arrow, we see that the lattice is distorted along the front of the glide, SVWE. The mode of distortion of the lattice plane is different 

The concept of dislocations was theoretically introduced in the 1930s by E. Orowan and G. I. Taylor, and it immediately played an essential role in the understanding of the plastic properties of crystalline materials, but it took a further twenty years to understand fully the importance of dislocations in crystal growth. As will be described in Section 3.9, it was only in 1949 that the spiral growth theory, in which the growth of a smooth interface is assumed to proceed in a spiral step manner, with the step serving as a self-perpetuating step source, was put forward [7]. 

The importance of dislocations becomes evident when we consider the strain on the microstructure of a simple crystal. The atoms or ions in a crystal are in symmetric energy wells and so vibrate around their lattice site. When we track across a crystal plane, the potential energy increases and decreases in a regular fashion with the minima at the lattice points 

Work hardening of our crystal system occurs as the dislocations move and eventually meet and lock. However these are still potential weaknesses and increasing applied stress or strain will again produce motion. Eventually catastrophic failure occurs as the material fractures. Here dislocations can come together to produce a crack. 

This is, of course, the reciprocal of the time taken for an atom to move a lattice site distance into a vacancy. um can be estimated from the heat capacity of the crystalline material using the Einstein or Debye models6 of atoms as harmonic oscillators in a lattice. Combining Equations (2.30) and (2.31) gives the number of atoms moving per second as 

The diffusion constant, D, is given by the square of the distance moved per second and so 

Annealing the system at temperatures close to its softening point allows recrystallisation to occur and the grain size to increase. This process again progresses by diffusion of holes through the structure and it is quite clear from Equation (2.33) that this process will be assisted by elevated temperatures. 

Zn2 + ions occupy half of the tetrahedral holes. The substances ZnO and CdS also show both the zinc blende and wurtzite structures. 

The structure of the compound CaF2 can be described as a face-centered cubic array of Ca2+ ions with the F ions in all the tetrahedral holes. This gives the required 1 2 ratio of Ca2+ and F ions. This structure is called the fluorite structure [see Fig. 16.41(d)] and is also observed in the compounds SrF2, BaCl2, PbF2, and CdF2, among others. 

So far we have assumed that crystalline compounds are perfect—that is, that all the atoms, ions, or molecules are present and occupy the correct sites. Although crystalline materials are highly ordered and most of the components are where they are expected to be, all real crystals have imperfections called lattice defects. 

Point defects refer to totally missing particles (atoms, ions, or molecules) or to cases where the particle is in a nonstandard location. A crystal with missing particles is said to have Schottky defects [see Fig. 16.43(a)]. When ions are missing from an ionic compound, they must be missing in a way that preserves the overall electrical neutrality of the substance. For example, for every missing Ca2+ ion in CaF2, there must be two missing F ions. 

Crystals in which particles have migrated to nonstandard positions are said to exhibit Frenkel defects [see Fig. 16.43(b)]. One group of compounds where Frenkel defects are present to the extreme is the silver halides—AgCl, AgBr, and Agl. In these compounds the anion positions are mostly those expected from closest packing ideas however, the silver ions are distributed almost randomly in the various holes and can easily travel within the solid structure. This property is a major reason that the silver halides are so useful in photographic films. 

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Cd(OH) j. The hydroxide is precipitated from aqueous solution by OH", it does not dissolve in excess OH". Ignition of Cd(OH)2 or CdCO, gives CdO which varies in colour from red-brown to black because of lattice defects. 

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. 

Lutsko J F ef a/1989 Molecular-dynamic study of lattice-defect-nucleated melting in metals using an embedded-atom-method potential Phys. Rev. B 40 2841... 

An additional problem is encountered when the isolated solid is non-stoichiometric. For example, precipitating Mn + as Mn(OH)2, followed by heating to produce the oxide, frequently produces a solid with a stoichiometry of MnO ) where x varies between 1 and 2. In this case the nonstoichiometric product results from the formation of a mixture of several oxides that differ in the oxidation state of manganese. Other nonstoichiometric compounds form as a result of lattice defects in the crystal structure. ... 

Fig. 7. Bombardment processes at the surface and in the near-surface region of a sputtering target, where represents the energetic particle used for bombarding the surface <), an adsorbed surface species 0> atoms and x, lattice defects.

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... 

In principle, we could find the minimum-energy crystal lattice from electronic structure calculations, determine the appropriate A-body interaction potential in the presence of lattice defects, and use molecular dynamics methods to calculate ab initio dynamic macroscale material properties. Some of the problems associated with this approach are considered by Wallace [1]. Because of these problems it is useful to establish a bridge between the micro-... 

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... 

N. N. Greenwood, Ionic Crystals. Lattice Defects and Nonstoichiometry, Butterworths, London, 1968, 194 pp. 

CdO is produced from the elements and, depending on its thermal history, may be greenish-yellow, brown, red or nearly black. This is partly due to particle size but more importantly, as with ZnO, is a result of lattice defects — this time in an NaCl lattice. It is more basic than ZnO, dissolving readily in acids but hardly at all in alkalis. White Cd(OH)2 is precipitated from... 

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