Anisotropic intrinsic lattice thermal conductivity of phosphorene from first principles

Phosphorene, the single layer counterpart of black phosphorus, is a novel two-dimensional semiconductor with high carrier mobility and a large fundamental direct band gap, which has attracted tremendous interest recently. Its potential applications in nano-electronics and thermoelectrics call for a fundamental study of the phonon transport. Here, we calculate the intrinsic lattice thermal conductivity of phosphorene by solving the phonon Boltzmann transport equation (BTE) based on first-principles calculations. The thermal conductivity of phosphorene at $300\,\mathrm{K}$ is $30.15\,\mathrm{Wm^{-1}K^{-1}}$ (zigzag) and $13.65\,\mathrm{Wm^{-1}K^{-1}}$ (armchair), showing an obvious anisotropy along different directions. The calculated thermal conductivity fits perfectly to the inverse relation with temperature when the temperature is higher than Debye temperature ($\Theta_D = 278.66\,\mathrm{K}$). In comparison to graphene, the minor contribution around $5\%$ of the ZA mode is responsible for the low thermal conductivity of phosphorene. In addition, the representative mean free path (MFP), a critical size for phonon transport, is also obtained.Comment: 5 pages and 6 figures, Supplemental Material available as http://www.rsc.org/suppdata/cp/c4/c4cp04858j/c4cp04858j1.pd

Denotational engineering

AbstractThis paper is devoted to the methodology of using denotational techniques in software design. Since denotations describe the essential components comprising a system and syntax provides ways for the user to access and communicate with these components, we suggest that denotations be developed in the first place and that syntax be derived from them later. That viewpoint is opposite to the traditional (descriptive) style where denotational techniques are used in assigning a meaning to some earlier defined syntax. Our methodology is discussed on an algebraic ground where both denotations and syntax constitute many-sorted algebras and where denotational semantics is a homomorphism between them. On that ground the construction of a denotational model of a software system may be regarded as a derivation of a sequence of algebras. We discuss some mathematical techniques which may support that process especially this part where syntax is derived from denotations. The suggested methodology is illustrated on two small examples