| Surface and interface is two-dimension area at which material physical and chemistry character breaks, many material physical and chemistry processes take place at surface and interface, at the same time, lots of breakages and invalidations also start from surface and interface. Surface stress ? and interface energy γis one of basically quantities to research surface and interface; so, great deals of theoretic and experimental works have been carried out. Theoretically, although close results of ? and γfor elements and compounds have been obtained by first principle calculation, modified embedded atom method potential and computer simulation, these results are not general. Experimental, it has standard method to determine surface energy, but interface energy, even the most simple solid-liquid interface energy, can not been accurately ascertained because of specimen self or different transmit heat between specimen and container, measure precision can only consistent with the scalar level. Therefore, how to theoretically scientific forecast interface energy becomes very important. Crystal size directly decides the crystal performance, every kinds of nanocrystal character change with crystal size, and interface energy is just the function of temperature and size of material. As the size decreases, the energy difference and entropy difference between crystal and liquid or gas all decrease, which results in decrease of related interface energy. This strong size-dependent peculiarity is not often seen in general material, so we need to research it. Just based on above consideration, this paper has developed one simple model without any adjustable parameters for surface stress and size-dependent interface energy, and after been validated by experimental results, we extend this model to related phase transition of nano carbon and nano Ti. The contribution includes following parts: 1. Model of intrinsic surface stress. Based on the equation of solid-liquid interface energy, and according to two asymptotic limits: 1. D →∞, γsl(D) →γsl0 where D is the particle diameter and γsl0 is the bulk solid-liquid interface energy; 2. when almost all atoms of a particle are located on its surface with a diameter of D0, the particle is almost indistinguishable from the surrounding fluid, that is D →D0, γsl(D) →0, we finally obtain the formula of surface stress. To validate the universality of this expression, we calculate the surface stress of metals, multilayer films, semiconductors and ionic crystals, respectively, and find the results are consistent with the other theoretic model and experimental results. 2. Thermodynamic phase stabilities of nano-carbon It is well known that the graphite-to-diamond transition occurs at high temperature and high pressure. However, it is observed that nanodiamond is also obtained at low temperature and low pressure. Despite the intense interest in nano-carbon for a variety of engineering applications, many details of their relative thermodynamic stabilities remain a mystery. Here, we present a unified thermodynamic model for thermodynamic stabilities of nano-carbon in different polymorphes. This model is based on considerations on the energetic contributions of surface energy and surface stress on the total Gibbs free energy of the nano-carbon. Through considering thermodynamically the size dependent phase stabilities among graphite (G), diamond (D), fullerenes (F), and carbon onions (O), size-temperature phase diagram of nano-carbon is established. The equilibrium temperatures among these phases increase as their sizes decrease. The obtained results are consistent with the available experimental and theoretical results. Moreover, related phase stabilities of bulky diamond (B) and nanotubes (T) in comparison with the above phases are also discussed. 3. Phase stabilities of fcc Ti nanocrystals...
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