Anisotropic thermal expansion of black phosphorus from nanoscale dynamics of phosphorene layers

Black phosphorus (bP) is a crystalline material which can be seen as an ordered stacking of two-dimensional layers, referred to as phosphorene. The knowledge of the linear thermal expansion coefficients (LTECs) of bP is of great interest in the field of 2D materials for a better understanding of the anisotropic thermal properties and exfoliation mechanism of this material. Despite several theoretical and experimental studies, important uncertainties remain in the determination of the LTECs of bP. Here, we report accurate thermal expansion measurements along the three crystallographic axes using in situ high temperature X-ray diffraction. From the progressive reduction of the diffracted intensities with temperature, we monitored the loss of the crystal structure of bP across the investigated temperature range, evidencing two thermal expansion regimes at temperature below and above 706 K. Below 706 K, a strong out-of-plane anisotropy can be observed, while at temperatures above 706 K a larger thermal expansion occurs along the a crystallographic direction. From our data and by taking advantage of ab initio optimization, we propose a detailed anisotropic thermal expansion mechanism of bP, which leads to an inter- and intra-layer destabilization. An interpretation of it, based on the high T perturbation of the stabilizing sp orbital mixing effect, is provided, consistent with the high pressure data.