Thermodynamics of metastable phase nucleation at the nanoscale

Chemical and physical routes under conditions of moderate not extreme temperatures and pressures are generally used to synthesize nanocrystals and nanostructures with metastable phases. However, the corresponding bulk materials with the same metastable structures are prepared under conditions of high temperatures or high pressures. The size effect of nanocrystals and nanostructures may be responsible for the formation of these metastable phases at the nanometer size. To date, there has not been a clear and detailed understanding of the effects causing the formation of the metastable structures from the viewpoint of thermodynamics. There is no a clear insight into which chemical and physical origins leading to the tendency of the metastable phases emerging at the nanoscale. We have proposed universal thermodynamic approach on nanoscale to elucidate the formation of the metastable phases taking place in the microphase growth. In this review, we first introduce the fundamental concepts and methods of the thermodynamic approach on nanoscale (so-called nanothermodynamics). Note that our nanothermodynamics, by taking into account the size-dependence of the surface tension of nanocrystals, differs from the thermodynamics of small systems proposed by Hill [T.L. Hill, J. Chem. Phys. 36 (1962) 3182; T.L. Hill, Proc. Natl. Acad. Sci. U.S.A. 93 (1996) 14328; T.L. Hill, R.V. Chamberlin, Proc. Natl. Acad. Sci. U.S.A. 95 (1998) 12779; T.L. Hill, J. Chem. Phys. 34 (1961) 1974; T.L. Hill, J. Chem. Phys. 35 (1961) 303; T.L. Hill, Nano Lett. 1 (2001) 273; T.L. Hill, R.V. Chamberlin, Nano Lett. 2 (2002) 609; T.L. Hill, Nano Lett. 1 (2001) 159]. Our thermodynamic theory emphasizes the size effect of the surface tension of nanocrystals on the stable and metastable equilibrium states during the microphase growth. Then, taking the syntheses of diamond and cubic boron nitride (c-BN) nanocrystals as examples, we summarize the applications of the nanothermodynamics to elucidate the nucleation of diamond and related materials nanocrystals in various moderate environments. Firstly, we studied diamond nucleation upon chemical vapor deposition (CVD), and found out that the capillary effect of the nanosized curvature of diamond critical nuclei could drive the metastable phase region of the nucleation of CVD diamond into a new stable phase region in the carbon thermodynamic equilibrium diagram. Consequently, the diamond nucleation is preferable to the graphite phase formation in the competing growth of diamond and graphite upon CVD. Similarly, c-BN nucleation upon CVD has been investigated. Secondly, we investigated the c-BN nucleation taking place in the high-pressure and high-temperature supercritical-fluids systems under conditions of the low-threshold-pressures (< 3.0 GPa) and low-temperatures (< 1500 K), and predicted the threshold pressure of the formation of c-BN in the high-pressure and high-temperature supercritical-fluids system. Thirdly, to gain a clear insight into the diamond nucleation upon the hydrothermal synthesis and the reduction of carbide (HSRC), we have performed the thermodynamic approach on nanoscale, in which the diamond nucleation is preferable to the graphite phase formation in the competing growth between diamond and graphite upon HSRC. We theoretically predicted that the pressure of 400 MPa should be the threshold pressure for the diamond synthesis by HSRC in the metastable phase region of diamond in the carbon phase diagram. More importantly, these theoretical results above are consistent with the experimental data. Additionally, thedeveloped nanothermodynamics was used to study the theory of nucleation and growth of diamond nanowires inside nanotubes. Accordingly, the thermodynamic approach on the nanometer size seems to provide insight into the metastable phase generation in microphase growth from the viewpoint of thermodynamics. Therefore, we expect the nanothermodynamic analysis to be a general method to understand the metastable phase formations on nanoscale. (c) 2005 Elsevier B.V. All rights reserved.