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Reverse Hall-Petch Relationship of Metals in Nanometer Size

The effect of melting temperature on Hall-Petch relationship has been studied. As grain size decreases, the melting temperature of the nano-structured crystals decreases, the Hall-Petch relationship is no longer sufficient. When the yield strength or hardness is taken as a function of reciprocal of the square root of the grain size, it has a numerical maximum whose location depends on the size of the bulk melting enthalpy of the crystals. Experimental results agree well with the modification induced by the size-dependence.