A model of size-dependent melting of small spherical particles (with diameter larger than 2-4 nm) is used to estimate the variation of their melting temperature, when their size is varied. This variation depends on two bulk parameters: the bulk melting temperature and the energy of formation of intrinsic defects. It is estimated for 71 elements. A comparison with available experimental data shows a good or satisfactory agreement.

The influences of the size, thermodynamic quantities and depletion of the parent phase on the separation thermodynamics of nanosized supersaturated binary solid solutions are studied theoretically. A quantitative analysis of the nucleation of one nucleus and of the decomposition in small isolated nanoparticles is presented. It is shown that three possibilities exist: phase separation, prohibition of decomposition, and formation of the metastable state of the nanoalloy. The conservation of matter leads to constraints on nucleation and growth of new phases. The case of solid–solid transition phenomena in a nanosystem is studied for regular solutions. This model leads to the existence of multiple equilibrium configurations for the same sets of initial parameters. Phase diagrams of small particles, i.e. probability-size, nucleation barrier-solubility, temperature-composition, are plotted within a regular solution model.

Using a top-down approach, we report a theoretical investigation of the melting temperature at the nanoscale, T m , for different shapes of "free-standing" nanostructures. To easily calculate the nanoscale melting temperature for a wide range of metals and semiconductors, a convenient shape parameter called R shape is defined. Considering this parameter, we argue why smaller size effects are observed in high bulk melting temperature materials. Using T m , a phase transition stress model is proposed to evaluate the intrinsic strain and stress during the first steps of solidification. Then, the size effect on the Thornton & Hoffman's criterion at the nanoscale is discussed and the intrinsic residual stress determination in nanostructures is found to be essential for sizes below 100 nm. Furthermore, the inverse Hall-Petch effect, for sizes below ∼15 nm, can be understood by this model. Finally, the residual strain in hexagonal zinc oxide nanowires is calculated as a function of the wire dimensions.

The microworld and the nanoworld are now of interest to the public, scientists, engineers and industrialists. Effects negligible at the macroscopic level become important at the micrometre scale, and vice versa. Moreover, at the nanoscale, quantum effects may become dominant. Scaling laws are useful for an understanding of the origin of such differences and/or to generalize results obtained at various scales. It is the aim of this paper to examine scaling laws relevant to mechanics, fluids, electromagnetism, thermodynamics, optics and quantum mechanics. Examples related to biology, micromachines and nanotechnologies are treated to show the usefulness of the scaling laws.