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

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 $\infty$. It is found that a certain “inversion temperature” $T_i$ exists for any substance, where the temperature dependences of surface pressure for different sizes of nanocrystal intersect. When the crystal disperses in the $T < T_i$ region, the “surface” pressure increases, and in the $T > T_i$ region decreases, with decreasing size of nanocrystal: $P_{\text{sf}}(N) \sim N^{-1/3}$. The greater the deviation of the nanocrystal shape from cubic, the stronger the dependence $P_{\text{sf}}(N)$. It is demonstrated that, at some temperatures $(T < T_0)$, 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” $T_0$, which depends on the nanocrystal size and shape.