SIZE DEPENDENT INTERFACE ENERGY - Energy Research Developments: Tidal Energy, Energy Efficiency and Solar Energy - page 244

Summary and Further Prospects
Several analytical models based on classic thermodynamics, free of adjustable
parameters, are presented to quantitatively determine the bulk and size dependent interface
energies as well as related interface stresses. The establishments of these models are of vital
importance in quantitatively studying some basic problems of materials, such as solidification
[92] and epitaxial growth [220]. With the high-speed developments of nanomaterials and
nanotechnology, the models for the size dependences of interface energetic terms provide the
clue to explore the fantastic properties of nanomaterials and, in particular, the continuous
changes of thermodynamic properties in larger size range (consisting of 10 2 ~10 23 atoms),
which is beyond the reach of the computer simulations. Moreover, the size range of material
referred in these works is the focus of the study in current or forthcoming nanotechnology,
such as so-called ″65 nm technique″ where 65 nm denotes the line width of the integrate
circuit.
The successes of the above classic thermodynamics in the mesoscopic and microscopic
size ranges of materials not only further enrich the classical thermodynamic theory, but also
offer powerful, irreplaceable and unfailing theoretical guidance for the development of
materials science under the condition that the computer simulations play more and more
important role.
However, since thermodynamics can only describe the statistical behavior of large
numbers of molecules, it cannot depict the action of single molecule. When the size of low-
dimensional materials decreases to a certain value, namely D 0 or D ′ 0 , quantum effect becomes
prominent and the classical thermodynamics is helpless. In addition, when clusters are small
enough, the crystalline structure of bulk materials failed while new structures arise. Thus, the
energy band theory and the electron theory should be included to discuss the limit cases, and
this combination will provide new approaches for the classical thermodynamics to investigate
the problems of nanomaterials.
The models considered in this work for surface energies and surface tension only are
applicable for the elements. When they are extended to compounds, electronic structures are
different in different surfaces. If the models are further used to predict the solid solutions and
different substances, the chemical interaction parameters must be considered although it is
known that these parameters are also size-dependent [221]. All of these are future works,
which are important for establishments of binary nano-alloy phase diagrams.
Acknowledgement
The financial supports from the NNSFC under Grants Nos. 59671010, 59931030,
50071023, 50025101, from the Trans-Century Training Program Foundation for the Talents
by the Ministry of Education of China, from National Key Basic Research and Development
Program under Grant No. 2004CB619301, and from Project 985-Automotive Engineering of
Jilin University are acknowledged.