Dislocations Frank

Sir Frederick Charles Frank (1911-1998) received his Ph.D. in 1937 from Oxford University, followed by a postdoctoral position at the Kaiser Wilhelm Institut fiir Physik in Berlin. During World War II, Frank was involved with the British Chemical Defense Research Establishment, and because of his keen powers of observation and interpretation, he was later transferred to Scientific Intelligence at the British Air Ministry. In 1946, Frank joined the H. H. Wills Physics Laboratory at the University of Bristol under its director, Nevill Mott, who encouraged him to look into problems concerned with crystal growth and the plastic deformation of metallic crystals. A stream of successes followed, establishing his scientific fame, as evidenced by many eponyms the Frank-Read source, the Frank dislocation, Frank s rule, Frank-Kasper phases. His theoretical work has been the foundation of research by innumerable scientists from around the world. Frank was awarded the Order of the British Empire (OBE) Medal in 1946, elected a Fellow of the Royal Society (FRS) in 1954, and was knighted in 1977. 

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. 

Frank, F.C. (1985) Some personal reminiscences of the early days of crystal dislocations, in Dislocations and Properties of Rea Materials (The Institute of Metals, London) p. 9. 

Charles Frank and his recognition, in 1949, that the observation of ready crystal growth at small supersaturations required the participation of screw dislocations emerging from the crystal surface (Section 3.2.3.3) in this way the severe mismatch with theoretical estimates of the required supersaturation could be resolved. 

Frank, F.C., 1949. The influence of dislocations on crystal growth. Discussions of the Faraday Society. 5, 48-54. 

Although this sometimes occurs through the operation of Frank-Read sources it is not generally observed. What does generally occur is similar, but more complex. The process is called multiple-cross-glide, and was proposed by Koehler (1952). Its importance was hrst demonstrated experimentally by Johnston and Gilman (1959). In addition to its existence, they showed that the process produces copious dislocation dipoles which are responsible for deformation-hardening. 

Screw dislocations play an important part in crystal growth. The theoretical background to this fact was first developed in 1949 by Frank and colleagues. It was apparent that crystal growth was rapid as long as ledges and similar sites existed on the face of a crystal because these form low-energy positions for the addition of new atoms or... 

The partial dislocations described in copper and similar materials are not the only ones that can be described, and a number of other types are well known, including Frank partial dislocations, which mediate in a different slip process. 

Figure 3.15 Change of stacking across a dislocation loop in a face-centered cubic structure. The structure is that of a Frank sessile dislocation loop.

The classical crystal growth theory goes back to Burton, Cabrera and Frank (BCF) (1951). The BCF theory presents a physical picture of the interface (Fig. 6.9c) where at kinks on a surface step - at the outcrop of a screw dislocation-adsorbed crystal constituents are sequentially incorporated into the growing lattice. 

Surface Spiral Step Control. Many crystals grow faster at small supersaturation than allowed by Equation 7. This lead Frank (17) to suggest that steps may also originate from the presence of a screw dislocation, and that this kind of steps is not destroyed by spreading to the crystal edge, but continues infinitely. The rate law according to this theory is parabolic (7). We shall use the following version of the kinetic equation (10)... 

Under conditions of low supersaturation (low driving force conditions) nuclea-tion/growth proceeds via dislocations (Burton-Cabrera-Frank (BCF) mechanism). With moderate supersaturation growth results from a two dimensional nucleation/ spreading mechanism nucleation on a flat face is fairly likely, but still rate limiting. At high levels of supersaturation, there is abundant nucleation on the crystal surface and the rate of growth is limited by the rate of diffusion of new material to the crystal surface. 

As mentioned before and assuming the vahdity of the continuum elasticity theory at the dislocation core, F. C. Frank derived the expression for the characteristic radius of a hollow core (Frank, 1951) ... 

In extended defects, the displacement vector b (or R) associated with them can be defined from the Burgers Circuit shown in figure 2.4(a), for a simple cubic system (Frank 1951, Cottrell 1971, Amelinckx et al 1978). In the defective crystal (A), a sequence of lattice vectors forms a clockwise ring around the dislocation precisely the same set of lattice vectors is then used to make a second... 

Strain is concentrated along dislocation cores, and it increases as the Burgers vector of dislocations increases. It was Frank who predicted that above a critical value a dislocation is energetically more stable if a free surface is created along the dislocation core. This critical value is expressed by... 

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