Mechanical properties of pristine and defective carbon-phosphide monolayers: a density functional tight-binding study

Using density functional tight-binding theory, we investigated the elastic properties and deformation and failure behaviors of pristine and defective carbon–phosphide (CP) monolayers subjected to uniform uniaxial tensile strain along arm-chair (AC) and zig-zag (ZZ) directions. Two variants of CP (α-CP and β-CP) were studied and two types of carbon and phosphorous vacancies (single and double) were considered. It was found that carbon monovacancies have the lowest formation energy, while phosphorous divacancies have the highest one in both CP allotropes. A strong mechanical anisotropy for CP was found with the Young's modulus and the failure stress along ZZ direction being an order of magnitude larger than those along AC direction. In both allotropes, the Young's modulus, failure stress and strain are considerably affected by vacancies, especially along AC direction. Fracture of pristine CP monolayer occurred via the rupture of phosphorous–phosphorous bonds when CP monolayer is stretched along AC direction, while via the rupture of carbon–phosphorous bonds when stretched along ZZ direction. Defective α-CP and β-CP monolayers both undergo a brittle-like failure initiated around the hosted vacancies at a lower critical strain. The failure strain and stress along the AC direction are affected only by phosphorous vacancies, while along the ZZ direction, they are almost equally affected by both phosphorous and carbon vacancies. These understandings may provide useful guidelines for potential applications of CP monolayers in nanoelectromechanical systems.