B1-B2 phase transition mechanism and pathway of PbS under pressure

Experimental studies at finite Pressure-Temperature (P-T) conditions and a theoretical study at 0 K of the phase transition in lead sulphide (PbS) have been inconclusive. Many studies that have been done to understand structural transformation in PbS can broadly be classified into two main ideological streams—one with Pnma and another with Cmcm orthorhombic intermediate phase. To foster better understanding of this phenomenon, we present the result of the first-principles study of phase transition in PbS at finite temperature. We employed the particle swarm-intelligence optimization algorithm for the 0 K structure search and first-principles metadynamics simulations to study the phase transition pathway of PbS from the ambient pressure, 0 K Fm-3m structure to the high-pressure Pm-3m phase under experimentally achievable P-T conditions. Significantly, our calculation shows that both streams are achievable under specific P-T conditions. We further uncover new tetragonal and monoclinic structures of PbS with space group P2₁/c and I4₁/amd, respectively. We propose the P2₁/c and I4₁/amd as a precursor phase to the Pnma and Cmcm phases, respectively. We investigated the stability of the new structures and found them to be dynamically stable at their stability pressure range. Electronic structure calculations reveal that both P2₁/c and I4₁/amd phases are semiconducting with direct and indirect bandgap energies of 0.69(5) eV and 0.97(3) eV, respectively. In general, both P2₁/c and I4₁/amd phases were found to be energetically competitive with their respective orthorhombic successors.