Geometric analysis of shape transition for two-layer carbon-silicon nanotubes

The two-layer nanotubes consisted of carbon atoms on the outside layer and silicon atoms on the inside layer (CNT@SiNT) show a series of diversity in the shape transitions, for instance transforming from a circle through an oval to a rectangle. In this paper, we investigate this geometric change from three perspectives. In the first aspect, we stationary time, followed by quantize in the three-dimensional Z-axis of nanotubes. In the second aspect, we stationary Z-axis, followed by quantize in the time. Finally, we tracked distance of nanotubes flattest section and roundest section. At the stationary time, the overall image of different Z-axis distance distributions is similar to a plan view of multiple ice creams, regardless of whether CNT or SiNT are on the same Z-axis, their slice plans are circle or rectangle of the projection of the Z-axis section on the XOY plane. In the stationary Z-axis, the nanotubes periodically change from a circle to an oval, and then from an oval to a rectangle at different times. Most remarkably, the distance value of deformation which we track the flattest and roundest is a constant value, and in the same distance period, there is only one roundest circle and one longest rectangle at different section and different time. The geometric analysis provided theoretical reference for the preparation of various devices and semiconductor nano-heterojunctions.