The Variation of “Surface” Pressure in a Nanocrystal as a Function of Temperature

Abstract

The Mie-Lennard-Jones potential of interatomic interaction is used to derive an expression for “surface” pressure in a nanocrystal with free surface. The nanocrystal has the form of a parallelepiped with a square base. The number of atoms N may vary from eight to ∞. It is found that a certain “inversion temperature” Ti exists for any substance, where the temperature dependences of surface pressure for different sizes of nanocrystal intersect. When the crystal disperses in the T Ti region decreases, with decreasing size of nanocrystal: Psf(N) ∼ N−1/3. The greater the deviation of the nanocrystal shape from cubic, the stronger the dependence Psf(N). It is demonstrated that, at some temperatures (T < T0), the “surface” pressure compresses the nanocrystal, and at other temperatures-stretches this nanocrystal, as its size decreases. The more clearly the quantum effects are defined in the crystal, the lower the value of the “temperature of zero surface pressure” T0, which depends on the nanocrystal size and shape.