Dislocations—Linear Defects

How to Convert from Atom Percent to Weight Percent 

Most dislocations found in crystalline materials are probably neither pnre edge nor pure screw but exhibit components of both types these are termed mixed dislocations. All three dislocation types are represented schematically in Fignre 4.6 the lattice distortion that is produced away from the two faces is mixed, having varying degrees of screw and edge character. 

Dislocations in Crystals, McGraw-Hill Book Company, 

As we note in Section 7.2, the permanent deformation of most crystalline materials is by the motion of dislocations. In addition, the Burgers vector is an element of the theory that has been developed to explain this type of deformation. 

Virtually all crystalline materials contain some dislocations that were introduced during solidification, during plastic deformation, and as a consequence of thermal stresses that result from rapid cooling. Dislocations are involved in the plastic deformation of crystalline materials, both metals and ceramics, as discussed in Chapters 7 and 12. They have also been observed in pol5meric materials and are discussed in Section 14.13. 

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Slip from the motion of dislocations (linear defects in the crystal structure)... 

The concept of defects came about from crystallography. Defects are dismptions of ideal crystal lattice such as vacancies (point defects) or dislocations (linear defects). In numerous liquid crystalline phases, there is variety of defects and many of them are not observed in the solid crystals. A study of defects in liquid crystals is very important from both the academic and practical points of view [7,8]. Defects in liquid crystals are very useful for (i) identification of different phases by microscopic observation of the characteristic defects (ii) study of the elastic properties by observation of defect interactions (iii) understanding of the three-dimensional periodic structures (e.g., the blue phase in cholesterics) using a new concept of lattices of defects (iv) modelling of fundamental physical phenomena such as magnetic monopoles, interaction of quarks, etc. In the optical technology, defects usually play the detrimental role examples are defect walls in the twist nematic cells, shock instability in ferroelectric smectics, Grandjean disclinations in cholesteric cells used in dye microlasers, etc. However, more recently, defect structures find their applications in three-dimensional photonic crystals (e.g. blue phases), the bistable displays and smart memory cards. 

Figure 1.1 Defects in crystalline solids (a) point defects (interstitials) (b) a linear defect (edge dislocation) (c) a planar defect (antiphase boundary) (d) a volume defect (precipitate) (e) unit cell (filled) of a structure containing point defects (vacancies) and (/) unit cell (filled) of a defect-free structure containing ordered vacancies. ...

The introduction to this chapter mentions that crystals often contain extended defects as well as point defects. The simplest linear defect is a dislocation where there is a fault in the arrangement of the atoms in a line through the crystal lattice. There are many different types of planar defects, most of which we are not able to discuss here either for reasons of space or of complexity, such as grain boundaries, which are of more relevance to materials scientists, and chemical twinning, which can contain unit cells mirrored about the twin plane through the crystal. However,... 

Dislocations are linear defects and were first invoked to account for the mechanical properties of solids, particularly the shear strengths. Dislocations play an important role in a variety of solid state phenomena from phase transitions to chemical reactions and the subject has been investigated and reviewed widely (Fine, 1973 Nembach, 1974). The effect of dislocations on the transformations and properties of organic solids has been recognized in recent years (Thomas Williams, 1971 Jones Thomas, 1979). 

In nearly all metal-forming operations, slip is the dominant method of deformation, although twinning can be significant in some materials. Slip occurs when the shear stress is high enough to cause layers of atoms to move relative to one another. The critical resolved shear stress is lowered when the crystalline lattice is not perfect but contains linear defects called dislocations. Slip-induced plasticity was covered in Chapter 9 of the companion to this text (Lalena and Cleary, 2005) and is reviewed here only briefly. The interested reader is advised to consult Lalena and Cleary (2005), Honeycombe (1984), or Dieter (1976). 

The concept of a defect has undergone considerable evolution over the course of the last century. The simplest notion of a defect is a mistake at normal atom site in a solid. These stmcturally simple defects are called point defects. Not long after the recognition of point defects, the concept of linear defects, dislocations, was invoked to explain the mechanical properties of metals. In later years, it became apparent that planar defects, including surfaces, and volume defects such as rods, tubes, or precipitates, also have important roles to play in influencing the physical and chemical properties of the host matrix. More recently, it has become apparent that interactions between point defects are of considerable importance, and the simple model of isolated point defects is often inadequate with... 

During the last decade, numerous reports have appeared of linear defects in GBs in metals observed by TEM. The observed variation in geometry as well as the variation of contrast for various diffracting conditions indicate that a single type of defect cannot account for all the observations. Among the numerous interpretations that have been suggested for the linear defects are (i) absorbed lattice dislocations (ii) steps, at least a few unit cells high, in the boundary plane (iii) structural dislocations in the boundary that accommodate small deviations from the special orien-... 

Generally speaking, microstrains correspond to atom displacements with respect to their position in crystals which are free of any defects. The presence of dislocations causes this type of displacement, but in this specific case, which we detailed previously, atomic displacements are local, and related to the presence of a linear defect We will now discuss the general case of displacements that are completely independent of one another. 

The nature of plasticity is rupture and rearrangements of interatomic bonds which in crystalline objects involve peculiar mobile linear defects, referred to as dislocations. Temperature dependence of plasticity may significantly differ from that of Newtonian fluids. Under certain conditions (including the thermal ones) various molecular and ionic crystals, such as NaCl, AgCl, naphthalene, etc., reveal a behavior close to the plastic one. The values of x typically fall into the range between 10s and 109 N m 2. At the same time, plastic behavior is typical for various disperse structures, namely powders and pastes, including dry snow and sand. In this case the mechanism of plastic flow is a combination of acts involving the establishment and rupture of contacts between dispersed particles. Plastic object, in contrast to a liquid, maintains the acquired shape after removal of the stress. It is worth... 

Fig. 4.9 X-ray topography to allow the visualisation of dislocations here, defects in a benzile crystal which was grown from solution. In the centre, one can recognise the loop of a platinum wire which suspended the seed crystal platelet in the solution. Many linear dislocations start at inclusions in the surface of...

Other types of disorder partially destroy the long-range order and the structure approaches that of a liquid. Vacancies and interstitial atoms are point defects. Dislocations are linear defects of fundamental importance for the mechanical properties of materials. The interface between crystal regions with different... 

Defects in crystalline solids are important because they modify important properties. For example, just a trace of chromium impurity changes colourless aluminium oxide into ruby. Metals are ductile when linear defects called dislocations are free to move. Crystals dissolve and react at increased rates at points where dislocations intersect the surface of the crystal. Thus, it is necessary to have an idea of the types of defect that form and the role that they play in the control of properties in order to understand the behaviour of solids. 

It has long been known that the theoretical strength of a metal crystal is far greater than the strength normally observed. Moreover, metals can be deformed easily and retain the new shape, a process called plastic deformation, whereas ceramic solids fracture under the same conditions. The typical mechanical properties of metals are due to the presence of linear defects called dislocations. 

Extended defects, on the other hand, correspond to structural imperfections in the assembly of either lattice planes (planar defects), as stacking faults in layer structures, or lattice directions (linear defects), as dislocations. 

Micro-level structure has the size of atoms. At this level there are point and linear defects. The viscosity at this level is closely related to the dynamic impendence of dislocations, and can be expressed as following (Alshin and Indebom, 1975)... 

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