Thermodynamic Study Of The Influence Of Related Parameters On Phase Transition Of Nanocrystals

Recent years, materials in nanoscale have attracted a great deal of interest in moderntechnological applications and scientific studies. As the size of materials decreases intonanometer range, the relevant optic, magnetic, electronic, catalytic and thermodynamicproperties are significantly different from those of the bulk counterparts. Thesefascinating physical and chemical properties of nanocrystals are caused by the highsurface/volume ratio and the resulting amount of coordination imperfection of surfaceatoms or molecules. Among the above properties, the thermodynamic stability seemsespecially important, which refers to the solid-liquid, solid-solid, and solid-vaportransitions. Describing the thermodynamic stability and the corresponding phasetransitions via theoretical method becomes a significant work since such investigationcan not only deepen our understanding of the nature of phase transition of nanocrystals,but also conduct experimental operations and their applications in various fields.For the ultrahigh density magnetic storage devices, the critical issue is to improvethe magnetic anisotropy of bimetallic nanocrystals to withstand thermal fluctuations ofthe direction of magnetization. This is related to an order-disorder transition, namelyfrom the low temperature CuAu I-type （L10-type） chemically ordered structure to hightemperature face-center-cubic （fcc） disordered phase. Such bimetallic alloys include FePt,CoPt, FePd, Cu3Au etc. Lots of experiments and simulations have shown that thisorder-disorder transition temperature is size-dependent and decreases as the size ofnanocrystals drops. Moreover, recent studies show that as the size decreases intonanoscale, the effects of shape and dimension cannot be neglected.Since Takagi in1954experimentally demonstrated that the melting temperature ofultrafine metallic nanocrystals is lower than that of corresponding bulk, the sizedependence of melting phenomenon becomes the research issues. Melt is the essentialphysical property of materials, which determines the stability of materials under differentconditions. Also the melting temperature can be related to other properties such as cohesive energy, glass transition temperature, ferromagnetic temperature, andferroelectric temperature etc. Therefore, understanding the melting mechanism issignificant for designing and governing materials for applications. Nowadays, thetheoretical investigations on size-dependent melting are mainly focus on metals, organicmolecules, semiconductors nanocrystals and the ones embedded in matrix. For liquidcrystal materials, which are widely used in the flat panel display, sensors andelectro-optical devises, the corresponding melting and freezing transition also exhibit sizedependence. However, using thermodynamic method to describe the size-dependentmelting and freezing of the confined liquid crystals in nanoscale is still scarce. Thesuccessful description of a thermodynamic model provided in recent years on metal,organic molecule and semiconductor stimulates us to study the size dependence ofmelting and freezing transition of liquid crystal materials via theory method.As the size drops, the thermodynamic stability of nanocrystals decreases and a phasetransition （from bulk stable phase to metastable structure） may occur. This is especiallyimportant for semiconductors and metal oxides, which would benefit to explore newexcellent physical and chemical properties and extend the application field of theirnanocrystals. Surface energy and surface stress are two important parameters to modulatethe phase transition of nanocrystals. Thus, their roles should be clarified, especially fortheir individual contributions on the Gibbs free energy of the system with two phases.Moreover, the external pressure is an important driving force to trigger the transition ofnanophase. Studies show that the critical transition pressure can increase or decrease withdrops of size. However, the underlying mechanism is still unclear now. Thecorresponding experiment and theoretical work should be developed to explore theessence of pressure-induced phase transition of nanocrystals.Based on the above considerations, in terms of a thermodynamic model recentlyproposed, the size, shape, composition and dimension effects on the order-disorder andmelting transition temperature for bimetallic nanoparticles are discussed. We extend thismodel to describe the size dependence of melting and freezing transition for confinedliquid crystal materials. The roles of surface energy and surface stress in In₂O₃nanocrystals are explored. We have also developed a unified model to predict the variation tendency of critical pressure that triggers the phase transition of semiconductornanocrystals. The concrete contents are listed below:1. In terms of size-dependent thermodynamic model for melting, the influence ofsize, shape, dimension and composition on order-disorder transition temperature andmelting temperature of bimetallic nanoparticles are discussed. Both transitiontemperatures decrease as size drops and shape factor increases. For order-disordertransition, it is found that the transition temperature with different dimensionality followsa trend of TOD[film]> TOD[plate]> TOD[wire]. This difference is induced by theirdifferent surface/volume ratio. While for the melting of AuPt nanoparticles, the increaseof component Pt enhances the melting temperature. This result can be interpreted by theatomic cohesive energy as well as the formation heat for nanoparticles.2. The size-dependent melting and freezing transition temperatures for confinedliquid crystal materials are modeled. The melting and freezing transition temperaturesboth drop as the confined pore size decreases, which attributes to the increase ofsurface/volume ratio of confined liquid crystal. We also found that the transitiontemperatures directly depend on the density of hydrogen bond at the interface region. Theintroduction of less reactive molecules at the inner walls of pore breaks the hydrogenbond at the interface and decreases its density, and thus weakens the anchoring effect ofhydrogen bond on liquid crystal molecules and lowers the corresponding phase transitiontemperatures. According to the above results, we can modulate the phase transitiontemperature for the confined liquid crystals in nanoscale by change the density ofhydrogen bond at the interface.3、The solid-solid phase transition of transparent conducting In₂O₃nanocrystal frombody-centered cubic structure （bcc） to rhombohedral structure （rh） is studied. We foundthat both the critical temperature and pressure of bcc-rh phase transition drop as sizedecreases. While the former agrees well with the experimental observation, the latterdiffers from the experimental result. We analyzed the roles of surface energy and surfacestress in phase transition, and found that as the size decreases, surface stress improves theGibbs free energy of the system, the phase transition temperature and pressure, butsurface energy inhibits all of them. The contribution of surface energy is larger than that of surface stress, which is the main factor for the decreases of phase transition pressureand temperature. Moreover, we also predicted that the critical diameter is about2.1nmfor the nanocrystals when the phase transition occurs under room temperature condition.4、 An unified model is developed to estimate the variation tendency ofsize-dependent pressure of phase transition. It is found that the size effects on thevariation trend and phase transition pressure can be estimated by surface energy, surfacestress and gram-atom volume between two phases. Moreover, the individualcontributions of surface energy and surface stress on phase transition pressure areconsidered. Results show that only surface energy or surface stress can not determine thevariation tendency of phase transition pressure, and the role of gram-atom volume can notbe neglected.