Line defect

Line defects in a crystalline material are known as dislocations. Dislocations are formed due to nonequilibrium conditions such as ion implantation and thermal processing. Under equilibrium conditions, there is no requirement for the presence of dislocations or any other defect (except native point defects) in the crystal. An edge dislocation may be viewed also as having an extra half-plane inserted into the crystal (see Fig. 9.9). 

Line defects are dislocations around which some of the atoms of the crystal lattice are misaligned. There are two types of dislocations the edge dislocation and the screw dislocation. Dislocations are caused by the termination of a plane of atoms in the middle of a crystal. In such a case, the surrounding planes are not straight, but instead bend around the edge of the terminating plane so that the crystal structure is perfectly ordered on either side. 

Things of particular note about dislocations are as follows. First, in the case of both the screw and edge dislocations, virtually aU of the distortion of the crystal due to the defect is accommodated within the first few atom spacings around the dislocation line (see Figs 7.9 and 7.10). The magnitude of the distortion decreases as 1/r, where r is the distance from the dislocation hne. 

dislocations may be of mixed character — partially screw-like and partially edge-like. In this case the Burger s vector is neither perpendicular to nor parallel to the dislocation line. One can see how this can happen as follows. Slicing the sohd and moving an irregularly-shaped plane of atoms to form a dislocation has the same displacement, and hence the same Burger s vector across its entire surface. However, the line of the dislocation is forced to follow the edges of the plane, wherever they 

The energy to form a dislocation is significant in most materials but is particularly large in strongly bound materials. As a consequence, these materials are brittle. The energy per unit length of a screw dislocation can be shown to be  

One of the more important aspects of edge and screw dislocations is their strain field. This is crucial to accommodating differences in lattice constants in heterostructures. Strain is the distortion of the lattice caused by stretching, bending, or shearing it. An edge dislocation includes a hydrostatic component of strain, which means that the lattice is to some extent uniformly expanded or compressed by the dislocation. The stress, 7, on a material is the force per unit area and is linearly related to the strain, 8. 

where Y is the elastic or Young s modulus. Looking at the drawing of the edge dislocation, one can see that the lattice is compressed relative to its normal spacing on the side of the line where the partial plane ends. On the other side of the dislocation core the lattice is expanded (it is in tension). In the plane perpendicular to the extra half plane running through the core the strain is zero. 

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A Novel Method for Off-Line Defect Characterization and Sizing from Standard b-Scan Data. 

As in crystals, defects in liquid crystals can be classified as point, line or wall defects. Dislocations are a feature of liquid crystal phases where tliere is translational order, since tliese are line defects in tliis lattice order. Unlike crystals, tliere is a type of line defect unique to liquid crystals tenned disclination [39]. A disclination is a discontinuity of orientation of tire director field. 

Common teniiinology used to characterize impurities and defects in semiconductors includes point and line defects, complexes, precipitates and extended defects. These teniis are somewhat loosely defined, and examples follow. 

When plastic deformation occurs, crystallographic planes sHp past each other. SHp is fackitated by the unique atomic stmcture of metals, which consists of an electron cloud surrounding positive nuclei. This stmcture permits shifting of atomic position without separation of atomic planes and resultant fracture. The stress requked to sHp an atomic plane past an adjacent plane is extremely high if the entire plane moves at the same time. Therefore, the plane moves locally, which gives rise to line defects called dislocations. These dislocations explain strain hardening and many other phenomena. 

The other major defects in solids occupy much more volume in the lattice of a crystal and are refeiTed to as line defects. There are two types of line defects, the edge and screw defects which are also known as dislocations. These play an important part, primarily, in the plastic non-Hookeian extension of metals under a tensile stress. This process causes the translation of dislocations in the direction of the plastic extension. Dislocations become mobile in solids at elevated temperamres due to the diffusive place exchange of atoms with vacancies at the core, a process described as dislocation climb. The direction of climb is such that the vacancies move along any stress gradient, such as that around an inclusion of oxide in a metal, or when a metal is placed under compression. 

In a detailed study the dissolution kinetics of shock-modified rutile in hydrofluoric acid were carefully studied by Casey and co-workers [88C01], Based on the defect studies of the previous sections in which quantitative measures of point and line defects were obtained, dissolution rates were measured on the as-shocked as well as on shocked and subsequently annealed powders. At each of the annealing temperatures of 200, 245, 330, 475, 675, 850, and 1000 °C, the defects were characterized. It was observed that the dissolution rates varied by only a factor of 2 in the most extreme case. Such a small effect was surprising given the very large dislocation densities in the samples. It was concluded that the dissolution rates were not controlled by the dislocations as had been previously proposed. 

The simplest type of line defect is the edge dislocation, which consists of an extra half plane of atoms in the crystal, as illustrated schematically in Fig. 20.30a edge dislocations are often denoted by 1 if the extra half plane ab is above the plane sp, or by T if it is below. 

The second type of line defect is the screw dislocation, which is rather less easy to visualise. Consider, however, a block of material, half of which is sheared one interatomic distance with respect to the other half, as shown in Fig. 20.306. The line cdthen constitutes a screw dislocation the arrangement of atoms around a screw dislocation is shown in Fig. 20.30c. 

To a good approximation, only atoms within the dotted circles in Figs. 20.30a and b are displaced from their equilibrium position in a real, three-dimensional crystal the diameter d of these circles would be very much less than the length / of the dislocation, i.e. the length, perpendicular to the page, of the extra half plane of atoms ab in Fig. 20.30a, or of the line cd in Fig. 20.306. Dislocations strictly, therefore, are cylindrical defects of diameter d and length / however, since I d they are referred to as line defects. 

Additionally, we have Illustrated another type of defect that can arise within the homogeneous lattice of 3.1.2. (in addition to the vacancy and substitutional impurities that are bound to arise). This is called the "selfinterstitial". Note that it has a decisive effect on the structure at the defect. Since the atoms are all the same size, the self-interstitial introduces a line-defect in the overall structure. It should be evident that the line-defect introduces a difference in packing order since the close packing at the arrows has changed to cubic and then reverts to hexagonal in both lower and upper rows of atoms. 

On the right are the t5rpes of point defects that could occur for the same sized atoms in the lattice. That is, given an array of atoms in a three dimensional lattice, only these two types of lattice point defects could occur where the size of the atoms are the same. The term vacancy is self-explanatory but self-interstitial means that one atom has slipped into a space between the rows of atoms (ions). In a lattice where the atoms are all of the same size, such behavior is energetically very difficult unless a severe disruption of the lattice occurs (usually a "line-defect" results. This behavior is quite common in certain types of homogeneous solids. In a like manner, if the metal-atom were to have become misplaced in the lattice cuid were to have occupied one of the interstitial... 

In a three-dimensional lattice, we have observed planes of atoms (or ions) composing the lattice. Up to now, we have assumed that these planes maintain a certain relation to one another. That is. we have shown that there are a set of planes as defined by the hkl values, which in turn depends upon the type of Bravais lattice that is present. However, we find that it is possible for these rows of atoms to "slip" from their equilibrium positions. Hiis gives rise to another type of lattice defect called "line defects". In the following diagram, we present a hexagonal lattice in which a line defect is present ... 

It should be clear that the presence of line defects in a crystal lattice leads to a disruption of the continuity of the lattice just as the presence of point defects affects the packing of a given lattice. The line defect. 

The volume defect is somewhat more difficult to visualize in two dimensions. Let us suppose that a line defect has appeared while the crystal structure was forming. This would be a situation similar to that already shown in 3.1.3. where aline defect was shown. The compression-tension area of the defect has a definitive effect upon the growing crystal and causes it to deform around the line defect. This is shown in the following diagram ... 

This type of volume defect in the crystal is known as a "screw dislocation", so-called because of its topography. Note that the spiral dislocation of the growing lattice deposits around the Une defect at right angles to the line defect. 

In the following diagram, given as 3.1.12. on the next page, amother representation is shown, detailing how the dislocation line (line defect) becomes a screw-dislocation. 

Grain boundaries form junctions between grains within the particle, due to vacancy and line-defect formation. This situation arises because of the 2nd Law of Thermodjmamics (Entropy). Thus, if crystallites are formed by precipitation from solution, the product will be a powder consisting of many small particles. Their actual size will depend upon the methods used to form them. Note that each crystallite can be a single-crystal but, of necessity, will be limited in size. 

This equation arises because both of these extrinsic defects affect the energy of the crystal. We can also have grain boundaries which may be clustering of line defects or mosaic blocks. The latter may be regarded as very large grains in a crystallite. 

Fig.1 Schematic representation of the different nucleation sites on the alumina film Mid nucleation at line defects, Mpd nucleation at point defects, Mrs nucleation at regular surface sites...

The nucleation behavior of transition metal particles is determined by the ratio between the thermal energy of the diffusing atoms and the interaction of the metal atoms at the various nucleation sites. To create very small particles or even single atoms, low temperatures and metal exposures have to be used. The metal was deposited as metal atoms impinging on the surface. The metal exposure is given as the thickness (in monolayer ML) of a hypothetical, uniform, close-packed metal layer. The interaction strength of the metals discussed here was found to rise in the series from Pd < Rh < Co ( Ir) < V [17,32]. Whereas Pd and Rh nucleate preferentially at line defects at 300 K and decorate the point defects at 90 K, point defects are the predominant nucleation center for Co and V at 300 K. At 60 K, Rh nucleates at surface sites between point defects [16,33]. 

It is remarkable that the feature at 2097 cm which was observed for a preparation at 90 K is missing at 60 K. The peak shows the characteristics of a monocarbonyl in mixing experiments. Furthermore, thermal treatment of the deposit as shown in Fig. 3a reveals a slightly increased thermal stability of this species as compared to the dicarbonyl at point defects. From this information it was suggested that the monocarbonyl is located at line defects of the alumina film [15]. 

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