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

MCQA

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FPGA-Based Accelerator for Rank-Enhanced and Highly-Pruned Block-Circulant Neural Networks

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Complex ligand adsorption on 3D atomic surfaces of synthesized nanoparticles investigated by machine-learning accelerated ab initio calculation

Nanoparticle surfaces are passivated by surface-bound ligands, and their adsorption on synthesized nanoparticles is complicated because of intricate and low-symmetry surface structures. Thus, it is challenging to precisely investigate ligand adsorption on synthesized nanoparticles. Here, we applied a machine-learning-accelerated ab-initio calculation into experimentally resolved 3D atomic structures of Pt nanoparticles to analyze the complex adsorption behavior of polyvinylpyrrolidone (PVP) ligands on synthesized nanoparticles. Different angular configurations of the large-sized ligands are thoroughly investigated to understand adsorption behaviors onto the various surface-exposed atoms with intrinsic low-symmetry. It is revealed that long-range van der Waals interaction (EvdW) shows weak negative relationship against generalized coordination number (-CN-), in contrast to the positive relationship in short-range direct bonding (Ebind), which attenuates the correlation between ligand binding energy (Eads) and -CN-. In addition, the PVP ligands favor to adsorb at which the long-range vdW interaction with surrounding surface structure is maximized. Our results highlight the significant contribution of vdW interactions and importance of local geometry of surface atoms to adsorption behavior of large-sized ligands on synthesized nanoparticle surfaces

Complex ligand adsorption on 3D atomic surfaces of synthesized nanoparticles investigated by machine-learning accelerated ab initio calculation

Nanoparticle surfaces are passivated by surface-bound ligands, and their adsorption on synthesized nanoparticles is complicated because of the intricate and low-symmetry surface structures. Thus, it is challenging to precisely investigate ligand adsorption on synthesized nanoparticles. Here, we applied machine-learning-accelerated ab initio calculation to experimentally resolved 3D atomic structures of Pt nanoparticles to analyze the complex adsorption behavior of polyvinylpyrrolidone (PVP) ligands on synthesized nanoparticles. Different angular configurations of large-sized ligands are thoroughly investigated to understand the adsorption behavior on various surface-exposed atoms with intrinsic low-symmetry. It is revealed that the ligand binding energy (E-ads) of the large-sized ligand shows a weak positive relationship with the generalized coordination number((CN)) . This is because the strong positive relationship of short-range direct bonding (E-bind) is attenuated by the negative relationship of long-range van der Waals interaction (E-vdW). In addition, it is demonstrated that the PVP ligands prefer to adsorb where the long-range vdW interaction with the surrounding surface structure is maximized. Our results highlight the significant contribution of vdW interactions and the importance of the local geometry of surface atoms to the adsorption behavior of large-sized ligands on synthesized nanoparticle surfaces.11Nscopu

3-Dimensional Scanning of Entire Unit Cells in Single Nanoparticles.

Properties of nanomaterials such as optical, electrical, and chemical properties are strongly correlated with lattice symmetry, making characterization of lattice symmetry essential. We introduce a symmetry analysis method using 3D atomic coordinates obtained by Brownian one-particle 3D reconstruction. The method allows direct and quantitative analysis of symmetrical properties and delivers local structural characteristics of individual platinum (Pt) nanoparticles in unit-cell level. Local structural deformations of the Pt nanoparticles such as lattice distortion and internal symmetry breakage are demonstrated, revealing that the crystal structure of sub-3 nm Pt nanoparticles generally maintains FCC crystallinity and exhibits localized deviation from their bulk counterpart.11Nsciescopu