Theory dislocation

In Section 3.2.3.2, the reader was introduced to dislocations (and to that 1934 paper by Geoffrey Taylor) and an account was also presented of how the sceptical response to these entities was gradually overcome by visual proofs of various kinds. However, by the time, in the late 1950s, that metallurgists and physicists alike had been won over by the principle seeing is believing , another sea-change had already taken place. 

After World War 11, dislocations had been taken up by some adventurous metallurgists, who held them responsible, in a purely handwaving (qualitative) manner and even though there was as yet no evidence for their very existence, for a variety of phenomena such as brittle fracture. They were claimed by some to explain everything imaginable, and therefore respectable scientists reckoned that they explained nothing. 

The importance of this advance is hidden in the simple words It is shown... , and furthermore in the parallel drawn with the D-H theory of electrolytes. This was 

Just recently (Wilde et al. 2000), half a century after the indirect demonstration, it has at last become possible to see carbon atmospheres around dislocations in steel directly, by means of atom-probe imaging (see Section 6.2.4). The maximum carbon concentration in such atmospheres was estimated at 8 2 at.% of carbon. 

It is worthwhile to present this episode in eonsiderable detail, beeause it eneapsulates very elearly what was new in physieal metallurgy in the middle of the eentury. The elements are an aecurate theory of the effects in question, preferably without disposable parameters and, to check the theory, the use of a technique of measurement (the Snoek pendulum) which is simple in the extreme in construction and use but subtle in its quantitative interpretation, so that theory ineluctably comes into the measurement itself. It is impossible that any handwaver could ever have conceived the use of a pendulum to measure dissolved carbon concentrations  

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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. 

Screen printing inks Screen-process inks Screens Screw dislocation theory Scrip set Scrubbers... 

The screw dislocation theory (27), often referred to as the BCE theory (after its formulators), shows that the dependence of growth rate on supersaturation can vary from a paraboHc relationship at low supersaturation to a linear relationship at high supersaturation. In the BCE theory, growth rate is given by... 

Mott played a major part, with his collaborator Frank Nabarro (b. 1917) and in consultation with Orowan, in working out the dynamics of dislocations in stressed crystals. A particularly important early paper was by Mott and Nabarro (1941), on the flow stress of a crystal hardened by solid solution or a coherent precipitate, followed by other key papers by Koehler (1941) and by Seitz and Read (1941). Nabarro has published a lively sequential account of their collaboration in the early days (Nabarro 1980). Nabarro originated many of the important concepts in dislocation theory, such as the idea that the contribution of grain boundaries to the flow stress is inversely proportional to the square root of the grain diameter, which was later experimentally confirmed by Norman Fetch and Eric Hall. 

Bridgman had strong views on the importance of empirical research, influenced as little as possible by theory, and this helped him test the influence of numerous variables that lesser mortals failed to heed. He kept clear of quantum mechanics and dislocation theory, for instance. He became deeply ensconced in the philosophy of physics research for instance, he published a famous book on dimensional analysis, and another on the logic of modern physics . When he sought to extrapolate his ideas into the domain of social science, he found himself embroiled in harsh disputes this has happened to a number of eminent scientists, for instance, J.D. Bernal. Walter s book goes into this aspect of Bridgman s life in detail. 

In 1964, two competing series of slender volumes appeared one, the Macmillan Series in Materials Science , came from Northwestern Morris Fine wrote a fine account of Phase Transformations in Comlen.ted Systems, accompanied by Marvin Wayman s Introduction to the Crystallography of Martensite Transformations and by Elementary Dislocation Theory, written by Johannes and Julia Weertman. The second series, edited at MIT by John Wulff, was entitled The Structure and Properties of Materials , and included slim volumes on Structure, Thermodynamics of Structure, Mechanical Behaviour and Electronic Properties. 

J. Weertman J. R. Weertman, Elementary Dislocation Theory, Macmillan, London, 1964. 

C. Vermilyeo, J. Chem. Phys. 28 1254 (1956). Screw dislocation theory kinetics of rotation. 

Tilt boundaries occur if the axis of rotation between the two grains is located in the boundary (interface). In contrast, if the axis of rotation is perpendicular to the boundary, the boundary is called a twist boundary and consists of a collection of screw dislocations (Fig. 3-6b). An equation similar to Eqn. (3.14) holds for twist (and mixed) boundaries. Since dislocation theory is well understood, it is possible to quantitatively treat small-angle grain boundaries [J.P. Hirth, J. Lothe (1982)]. 

A.H. Cottrell and B.A. Bilby. Dislocation theory of yielding and strain ageing of iron. Proc. Phys. Soc. A, 49 49-62, 1949. 

More detailed treatments are given in the original paper by Cottrell and Bilby [25] and in the summary in Cottrell s text on dislocation theory [22]. 

G.B. Olson and M. Cohen. Dislocation theory of martensitic transformations. In F.R.N. Nabarro, editor, Dislocations in Solids, Vol. 7, pages 295-407. North-Holland, New York, 1986. 

Different approaches were used to describe the yielding of polymers quantitatively. Some theories took into account the free volume fraction. Eyring considered thermally activated mechanisms, and Robertson s model was based on changes of chain conformations. Argon s and Bowden s models were based on a metallurgical approach and a dislocation theory. A brief summary of the existing yielding theories is presented. 

J. Weertman and Julia Weertman, Elementary Dislocation Theory, Oxford Univ. Press, New York (1992). 

The relationship of brittle fracture to plastic deformation has, of course, been elaborated in various ways with the aid of dislocation theory, e.g. nucleation of microcracks has been discussed in terms of piling-up of dislocations [124]. Davies [145] has shown that embrittlement requires the presence of islands of martensite (about 1 pm in size) and has suggested that cracks are initiated in the martensite or at the martensite-ferrite interface. 

Watanabe, T. In Erb, U., Palumbo, G., Eds. Grain Boundary Engineering, CIM, Montreal, 1993. Weertman, J. Weertman, J. R. Elementary Dislocation Theory, Oxford University Press, New York, 1992, p. 6. 

Readers familiar with rheological principles and elementary dislocation theory may wish to omit Sections 9.1, 9.2, and 9.3. 

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