On a Change in the Elastic Properties with Decreasing Size of Diamond, Silicon, and Germanium Nanocrystals

The dependences of the modulus of elasticity (B) on the size (N) and the shape of the nanocrystal surface of a simple monoatomic material is studied using a model of the nanocrystal in the form of a rectangular parallelepiped with a variable surface shape. It is shown that the modulus of elasticity decreases with decreasing nanocrystal size; moreover, the dependence B(N) is less noticeable in the low-temperature range. The larger the deviation from the most stable nanocrystal shape, the more noticeable the decrease in the function B(N) as the nanocrystal size decreases along the isotherm. It is shown that the case when the function B(N) increases with decreasing nanocrystal size can occur in the low-temperature range. The dependences B(N) are calculated for diamond, Si, and Ge. It is shown that the function B(N) decreases and the Poisson coefficient increases in the case of an isomorphic decrease in the nanocrystal size. The nanocrystal is compressed at low temperatures and is stretched at high ones under the action of surface pressure. The lattice parameters of diamond, Si, and Ge nanocrystals change most noticeably at T > 1000 K.