Dependences of the specific surface energy on the size and shape of the nanocrystal under various $P$–$T$ conditions

Based on the RP model, the dependences of the specific surface energy $\sigma$ and surface pressure $P_{\mathrm{sf}}$ on the size $(N)$ and shape of the nanocrystal at different values of pressure $P$ and temperature $T$ are studied. Calculations for a gold nanocrystal have shown that at $P=0$, the $P_{\mathrm{sf}}(N)$ function lies in the negative region, i. e. the nanocrystal is stretched by surface pressure the more the temperature is higher, or the more the nanocrystal shape deviates from the most energy-optimal shape. With a decrease in $N$ value at $P=0$, the $\sigma(N)$ function decreases the more noticeably the higher the temperature, or the more the nanocrystal shape deviates from the most energy-optimal shape. Based on these results, it is shown that obtained in some articles the increase in the $\sigma(N)$ function with an isomorphically-isothermal decrease in $N$ does not correspond to the physical properties of the nanocrystal. In these articles, the nanocrystal was compressed by surface pressure, which increased with an isomorphically-isothermal decrease in $N$ value. This compression led to a corresponding increase in the $\sigma(N)$ function both with an isomorphic-isothermal decrease in size and with an isomeric (i. e., at $N$=const) increase in the temperature of the nanocrystal.