Vacancy effect on the elastic constants of layer-structured nanomaterials

Layer-structured nanomaterials where alternating layers of nanocrystallites meet along high angle grain boundaries constitute a special category of nanomaterials. In the present study we investigated the effect of the presence of a vacancy on the elastic constants of such materials by the use of atomistic simulation methods. The calculations were performed on a model system where atoms interact via a Lennard–Jones potential and the elastic constants were obtained in the frame of homogeneous deformations, for nanocrystallite layer widths ranging from 2.24 up to 37.12 nm. The results show that the favoured position of the vacancy is located in the GB core. The state of relaxation of the structure is an important factor that affects the obtained results. In both the unrelaxed and relaxed structures results converge to a given value after the 5th (3 1 0) layer. This value seems to depend on the size of the nanocrystallite L and approaches the bulk value above a given size L. It is also concluded that in the case of a relaxed system there is a smoother variation of the system energy and elastic constant as a function of the distance of the vacancy from the GB plane when the size L increases. The way that external stresses are applied on the system affects the values of the obtained elastic properties, with the elastic constants related to the characteristic directions of the grain boundary being the most affected ones. These findings are of particular interest for fabrication methods of nanostructured materials, experimental methods for the measurement of their elastic properties as well as multiscale modelling schemes.