Nabarro-Herring volume diffusion

An account of the mechanism for creep in solids placed under a compressive hydrostatic stress which involves atom-vacancy diffusion only is considered in Nabarro and Herring s (1950) volume diffusion model. The counter-movement of atoms and vacancies tends to relieve the effects of applied pressure, causing extension normal to the applied stress, and shrinkage in the direction of the applied stress, as might be anticipated from Le Chatelier s principle. The opposite movement occurs in the case of a tensile stress. The analysis yields the relationship... 

Let us finally mention that in polycrystalline samples, Nabarro-Herring(-Coble) creep occurs as already introduced in Section 14.3.2. The Nabarro-Herring creep rate is inversely proportional to the square of the average grain size, l2, if volume diffusion of point defects prevails. It is inversely proportional to /3 if grain boundary diffusion determines the transport. 

Here, Anh is a material parameter, a the external stress, fl the volume of a vacancy, d the grain size, and Dy the diffusion coefficient for self-diffusion through the bulk material. This process is called Nabarro-Herring creep. Since the stress dependence is linear, Nabarro-Herring creep is most important at low stresses, whereas dislocation creep is more important at high stresses. 

While combining, the product of the concentration and the atomic volume was noted to be 1. Equation 15.36 follows what is called the Nabarro-Herring creep. This mechanism of creep is predominant at higher temperatures where volume diffusion is fasfer fhan grain boundary diffusion. At lower temperatures, grain boundary diffusion predominates. Hence, Equation 15.36 is modified as ... 

In most cases, the use of fine grained ceramics on the one hand, and the high level of plastic flow required by iono-covalent crystals on the other, are such that the diffusion terms (Nabarro-Herring or Coble) override the plastic flow. Grain boundary diffusion dominates over volume diffusion all the more when the grains are finer and the temperature lower, because the volume exponent of the former is 3 whereas that of the latter is only 2, and the activation enthalpy of Dj is in general lower than that of Dy. 

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