Thermodynamics For Nanosystems: Grain And Particle-Size Dependent Phase Diagrams

Unusual phases are often observed in nanocrystalline materials; these are often assumed to be metastable phases produced by non-equilibrium synthesis techniques. The present analysis shows that, in fact, some such phases are stable, and their presence can be rigorously predicted by thermodynamics. Using dilatometry and high temperature differential scanning calorimetry (HTDSC) on zirconia samples with varying grain sizes and yttria content, we are able to show that the tetragonal-to- monoclinic phase transformation temperature varies linearly with inverse crystallite/grain size. This shift, which traverses hundreds of degrees, obeys a simple thermodynamic model that adds an interfacial energy term to the total free energy of the system. The relevant thermodynamic parameters, such as the change in volumetric enthalpy and entropy, change in surface enthalpy and entropy, and the interfacial energy and strain energy change involved in the transformation, are calculated from experiment. The result is an ability to redraw the Y2O3 - ZrO2 phase diagram with crystallite/grain size as a third variable.