Dislocations and diffusion

Clinical features include neonatal hypotonia, a tendency toward congenital hip dislocation and diffuse muscle weakness. Later on children are frequently of short stature and low body weight and often have long thin faces and high-arched palates. Respiratory difficulties, where present, occur early on and tend to improve with time. In others a virtually static clinical picture is seen. 

Fig. 23 Comparison between surface-controlled reactions (left 1= interstitial sites, 2= vacant sites, 3= screw dislocation, 4= jump dislocation, 5=step dislocation) and diffusion-controlled processes (right)...

By lowering the grain aspect ratio, the transition temperature between dislocation and diffusion creep is shifted towards lower stresses. In the low... 

The densification of the parts by HIP implies primarily three phenomena i) fragmentation of the particles and rearrangement, ii) deformation of the interparticle areas of contact and iii) elimination of the pores. The first process is transitory and hardly contributes to the overall densification, at least if the initial forming (for example, by CIC) has been correcdy carried out. The second process brings into play effects of plastic deformation by movement of dislocations and diffusion phenomena that are similar to those indicated in the case of uniaxial pressure sintering. Lastly, by considering the final reduction of porosity, we can write phenomenologically ... 

Fast diffusion paths grain boundary and dislocation core diffusion... 

By way of example, Volume 26 in Group III (Crystal and Solid State Physics) is devoted to Diffusion in Solid Metals and Alloys, this volume has an editor and 14 contributors. Their task was not only to gather numerical data on such matters as self- and chemical diffusivities, pressure dependence of diffusivities, diffusion along dislocations, surface diffusion, but also to exercise their professional judgment as to the reliability of the various numerical values available. The whole volume of about 750 pages is introduced by a chapter describing diffusion mechanisms and methods of measuring diffusivities this kind of introduction is a special feature of Landolt-Bornstein . Subsequent developments in diffusion data can then be found in a specialised journal. Defect and Diffusion Forum, which is not connected with Landolt-Bdrnstein. 

A pecuhar sohd phase, which has been discovered not too long ago [172], is the quasi-crystalline phase. Quasi-crystals are characterized by a fivefold or icosahedral symmetry which is not of crystallographic type and therefore was assumed to be forbidden. In addition to dislocations which also exist in normal crystals, quasi-crystals show new types of defects called phasons. Computer simulations of the growth of quasicrystals [173] are still somewhat scarce, but an increasing number of quasi-crystalline details are studied by simulations, including dislocations and phasons, anomalous self-diffusion, and crack propagation [174,175]. 

In addition to movement of lattice members within a crystal, it is also possible for there to be motion of members along the surface. Consequently, this type of diffusion is known as surface diffusion. Because crystals often have grain boundaries, cracks, dislocations, and pores, there can be motion of lattice members along and within these extended defects. 

The main difficulty with the first mode of oxidation mentioned above is explaining how the cation vacancies that arrive at the metal/oxide interface are accommodated. This problem has already been addressed in Section 7.2. Distinct patterns of dislocations in the metal near the metal/oxide interface and dislocation climb have been invoked to support the continuous motion of the adherent metal/oxide interface in this case [B. Pieraggi, R. A. Rapp (1988)]. If experimental rate constants are moderately larger than those predicted by the Wagner theory, one may assume that internal surfaces such as dislocations (and possibly grain boundaries) in the oxide layer contribute to the cation transport. This can formally be taken into account by defining an effective diffusion coefficient Del( = (1 -/)-DL+/-DNL, where DL is the lattice diffusion coefficient, DNL is the diffusion coefficient of the internal surfaces, and / is the site fraction of cations located on these internal surfaces. 

In contrast to fluids, crystals have a greater number of control parameters crystal structure, strain and stress, grain boundaries, line defects (dislocations), and the size and shape of crystallites, etc. These are all relevant to kinetics. Treatments that go beyond transport and diffusion in this important field of physical chemistry are scarce. 

From these considerations, Cottrell demonstrated that the rate at which solute atoms diffuse to dislocations and subsequently pin them in place is proportional to time2/3 (this time dependence is derived by an approximate method in Exercise 3.9). This provided the first quantifiable theory for the strain aging caused by solute pinning of dislocations [22]. 

Short-circuit diffusion along grain boundaries has been studied extensively via experiments and modeling. Because diffusion along dislocations and crystal surfaces is comparatively less well characterized, particular attention is paid to grainboundary transport in this chapter. However, briefer discussions of diffusion along dislocations and free surfaces are also presented. 

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