Phase instabilities in small particles

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Abstract
In this review we consider the existing theories for the structure of small particles and the nature of morphological instabilities as the size is reduced. The various electron microscopic observations confirming the stability of a new phase, the so called ‘Multiply twinned structure’, in small particles is discussed. A theoretical model is presented to calculate the free energy surfaces for a series of asymmetric and single crystal structures using a modified Curie-Wulff construction for the surface energy, and a disclination model for the elastic strain energy. Depending on the activation barrier heights and the Boltzmann occupancy factors for the various local minima on the energy surface, the idea of ‘quasi-melting’ is introduced and compared with the structural instabilities in molecular clusters seen recently by various authors using computer simulations. A phase diagram for small particles as a function of size and temperature is presented and the effect of statistical fluctuations on stability is discussed. Finally a phenomenological discussion relating the phase instabilities to various melting and related phase transitions is given.