General equations for lattice contraction and surface stress of fcc nanocrystals are established based on the Laplace-Young equation and a consideration for the size-dependence of the solid-liquid interface energy. The predictions of our equations are in agreement with the experimental results on the measurement of lattice contraction and surface (interface) stress of nanoparticles and thin films and theoretical calculations.

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The failure of most rock materials is essentially a process of crack initiation and propagation. It is of great significance to study the microcrack growth characteristics of granite under ultrasonic high-frequency excitation for understanding the failure mechanism of rock under ultrasonic vibration. In this paper, the experimental and numerical simulation methods are used to study the propagation characteristics of rock cracks under ultrasonic vibration. Scanning electron microscopy (SEM) was used to observe the growth of microcracks in granite samples after ultrasonic vibration for 0 min, 2 min, and 4 min. A discrete element software PFC2D was used to simulate and solve the cracking mechanism of rock cracks under ultrasonic vibration. Also, it is found that the action of ultrasonic vibration can effectively promote the development of microcracks in the granite samples. The main three cracks causing the failure of quartz under the ultrasonic high frequency are intragranular cracks, transgranular cracks, and grain boundary cracks. The breakage of transgranular cracks usually contributes a shell-like fracture, that is, a regular curved surface with a concentric circular pattern appears on the fracture surface, which is a typical quartz brittle fracture mode. In addition, the feldspar grain failure is mainly caused by intragranular crack and transgranular crack. Microcracks are wavy expansion in feldspar grain. Mica failure is mainly caused by grain boundary crack, and the effect of lamellar cleavage on the failure of mica is significant. Moreover, it is also found that the mechanism of microcrack propagation is tensile failure. The failure of feldspar grains is mainly contributed to the failure of granite.