Phase Stability of Lead Phosphate Apatite

Recently, Cu-substituted lead apatite LK-99 was reported to have room-temperature ambientpressure superconductivity. Here we utilize density functional theory (DFT) total energy and harmonic phonon calculations to investigate the thermodynamic and dynamic stability of two lead phosphate apatites in their pure and Cu-substituted structures. Though Pb10(PO4)6O and Pb10(PO4)6(OH)2 are found to be thermodynamically stable (i.e., on the T=0K ground state convex hull), their Cu-substituted counterparts are above the convex hull. Harmonic phonon calculations reveal dynamic instabilities in all four of these structures. Oxygen vacancy formation energies demonstrate that the addition of Cu dopant substituting for Pb increases the likelihood of the formation of oxygen vacancies on the anion site. We propose a new possible phase in this system, Pb8Cu2(PO4)6, where two monovalent Cu atoms are substituted for two Pb(1) atoms and the anion oxygen is removed. We also propose several reaction pathways for Pb9Cu(PO4)6O and Pb8Cu2(PO4)6, and found that both of these two structures are likely to be synthesized under a 1:1 ratio of reactants Pb2SO5 and Cu3P. Our work provides a thorough foundation for the thermodynamic and dynamic stabilities of LK-99 related compounds and we propose several possible novel synthesis reaction pathways and a new predicted structure for future studies

Synergistic Effect of Alloying on Thermoelectric Properties of Two-Dimensional Pdpq (Q = S, Se).

Hosts of 2D materials exist, yet few allow compositional and structural tailoring as the MQ (M = Mo, W; Q = S, Se) family does, for which various structural superlattices have been synthesized. Using thorough first-principles calculations, we show how bonding hierarchy contributes to the structural resilience of 2D PdPQ and allows for full-range alloying of sulfur and selenium. Within the structural unit of PdPQ, the covalently-bonded [PQ] polyanions hold the structure together with their molecular-like P-P bonds while ionically bonded Pd-Qs allow the S/Se substitution. Here, the bonding hierarchy imparts superior electronic and structural features to the PdPQ monolayers. As such, the flat-and-dispersive valence band and the eight degenerate valleys of the conduction band benefit the p-type and n-type thermoelectricity of pristine PdPQ, which can be further enhanced by alloying. The high-entropy alloying synergistically suppresses the lattice heat transport from 75 to 30 W m K and increases the band degeneracy of PdPQ monolayers, resulting in an overall improvement in . Combining these features, in a naïve approach, results in a large approaching two for both p-type and n-type doping. However, accurate fully-fledged electron-phonon calculations rebut this promise, showing that at high temperatures, the increased electron scattering results in a stagnant power factor in the flat-and-dispersive valence band. Using a realistic first-principles scattering, we finally calculate the thermoelectric efficiency of PdPQ (Q = S, Se) and highlight the importance of an accurate estimation of electron relaxation time for thermoelectric predictions