First-principles study of thermal expansion and thermomechanics of single-layer black and blue phosphorus

The linear thermal expansion coefficients (LTEC) and thermomechanics of single-layer black and blue phosphorus are systematically studied using first-principles based on quasiharmonic approximation. We find the thermal expansion of black phosphorus is very anisotropic. The LTEC along zigzag direction has a turning from negative to positive at around 138 K, while the LTEC along armchair direction is positive (except below 8 K) and about 2.5 times larger than that along zigzag direction at 300 K. For blue phosphorus, the LTEC is negative in the temperature range from 0 to 350 K. In addition, we find that the Young's modulus and Poisson's ratio of black phosphorus along zigzag direction are 4 to 5 times larger than those along armchair direction within considered temperature range, showing a remarkable anisotropic in-plane thermomechanics property. The mechanisms of these peculiar thermal properties are also explored. This work provides a theoretical understanding of the thermal expansion and thermomechanics of this single layer phosphorus family, which will be useful in nanodevices.