It was recalled that polycrystals exhibited an abnormal Hall-Petch dependence when their grain size fell to the sub-micron range. One explanation given was that the scale-dependence of the yield stress of sub-micron polycrystals was governed not only by the internal energy of the dislocation patterns, but also by their configurational entropy. Two-level dislocation arrangements were explored which naturally embedded a grain size. Detailed calculations of the internal energy and the configurational entropy were facilitated by the dislocation pile-up theory and the Ashby model of geometrically necessary dislocations. It was shown that the present model was capable of explaining the abnormal Hall-Petch dependence for grain sizes in the sub-micron range.

Scale Dependence of Sub-Micron Polycrystals due to Configurational Entropy. Q.Yang, W.Yang: Applied Physics Letters, 1998, 73[23], 3384-6