Negative/zero thermal expansion in black phosphorus nanotubes†
Black phosphorus nanotubes (BPNTs) as new 1D materials have very promising prospects in nanoelectronic devices. Taking into account that the effect of finite temperature on nanoelectronic devices is indispensable, we perform a comprehensive first-principles study of thermal expansion of BPNTs. It is surprisingly found that the thermal expansion can be tuned from positive thermal expansion (PTE) to zero thermal expansion (ZTE) and even to negative thermal expansion (NTE) by changing the diameter and bonding in the unique configurations of armchair and zigzag BPNTs. The thermal expansion of zigzag BPNTs is diameter independent, in contrast, the size effect of thermal expansion is evidently presented in the armchair BPNTs. Accordingly, it is more manageable to adjust the coefficient of thermal expansion (CTE) in the armchair BPNTs. Unusual phonon hardening with the increase of temperature can be detected in both types of nanotubes. The unique dynamical modes and different vibrational amplitudes are analyzed. Underlying physical mechanisms have been explored. This work can provide some inspiration for exploring the abnormal thermal expansion in nanotubes and how to regulate these properties.