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

Phase Stability of Lead Phosphate Apatite Pb10−x_{10-x}Cux_{x}(PO4_{4})6_{6}O, Pb10−x_{10-x}Cux_{x}(PO4_{4})6_{6}(OH)2_{2}, and Pb8_{8}Cu2_{2}(PO4_{4})6_{6}

Recently, Cu-substituted lead apatite LK-99 was reported to have room-temperature ambient-pressure 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 Pb$_{10}$(PO$_4$)$_6$O and Pb$_{10}$(PO$_4$)$_6$(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, Pb$_8$Cu$_2$(PO$_4$)$_6$, 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 Pb$_9$Cu(PO$_4$)$_6$O and Pb$_8$Cu$_2$(PO$_4$)$_6$, and found that both of these two structures are likely to be synthesized under a 1:1 ratio of reactants Pb$_2$SO$_5$ and Cu$_3$P. 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

Coalescence dynamics of platinum group metal nanoparticles revealed by liquid-phase transmission electron microscopy

Summary: Coalescence, one of the major pathways observed in the growth of nanoparticles, affects the structural diversity of the synthesized nanoparticles in terms of sizes, shapes, and grain boundaries. As coalescence events occur transiently during the growth of nanoparticles and are associated with the interaction between nanoparticles, mechanistic understanding is challenging. The ideal platform to study coalescence events may require real-time tracking of nanoparticle growth trajectories with quantitative analysis for coalescence events. Herein, we track nanoparticle growth trajectories using liquid-cell transmission electron microscopy (LTEM) to investigate the role of coalescence in nanoparticle formation and their morphologies. By evaluating multiple coalescence events for different platinum group metals, we reveal that the surface energy and ligand binding energy determines the rate of the reshaping process and the resulting final morphology of coalesced nanoparticles. The coalescence mechanism, based on direct LTEM observation explains the structures of noble metal nanoparticles that emerge in colloidal synthesis