[Paper Review] Phase Stability of Lead Phosphate Apatite Pb$_{10-x}$Cu$_{x}$(PO$_{4}$)$_{6}$O, Pb$_{10-x}$Cu$_{x}$(PO$_{4}$)$_{6}$(OH)$_{2}$, and Pb$_{8}$Cu$_{2}$(PO$_{4}$)$_{6}$

Jiahong Shen, Dale Gaines+9 more|arXiv (Cornell University)|Aug 14, 2023

X-ray Diffraction in Crystallography40 references4 citations

TL;DR

This study uses density functional theory (DFT) to investigate the thermodynamic and dynamic stability of Cu-doped lead phosphate apatites, including LK-99. It proposes a new phase, Pb₈Cu₂(PO₄)₆, where Cu²⁺ substitutes for Pb²⁺ and an oxygen anion is removed, showing slightly improved dynamic stability over Pb₉Cu(PO₄)₆O. The work identifies energetically favorable synthesis pathways using Pb₂SO₅ and Cu₃P in a 1:1 ratio.

ABSTRACT

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.

Motivation & Objective

• To assess the thermodynamic and dynamic stability of Cu-substituted lead phosphate apatites, including LK-99, using first-principles DFT calculations.
• To investigate the role of Cu doping in promoting oxygen vacancy formation in apatite structures.
• To propose a new, previously unreported phase, Pb₈Cu₂(PO₄)₆, as a potential stable configuration with anion site removal.
• To evaluate multiple reaction pathways for synthesizing Pb₉Cu(PO₄)₆O and Pb₈Cu₂(PO₄)₆ using reaction convex hull analysis.
• To provide a foundation for future experimental validation of LK-99-related compounds and their synthesis routes.

Proposed method

• Density functional theory (DFT) with the PBE exchange-correlation functional and GGA+U method (U-J = 4 eV) to account for localized Cu 3d electrons.
• Structural relaxation with energy and force convergence thresholds of 10⁻⁸ eV and 10⁻³ eV/Å, respectively.
• Harmonic phonon calculations via the finite displacement method using phonopy to assess dynamic stability at T=0 K.
• Convex hull construction using the Open Quantum Materials Database (OQMD) to determine thermodynamic stability relative to competing phases.
• Reaction convex hull analysis to evaluate the relative stability of various synthesis pathways involving Pb₂SO₅ and Cu₃P as reactants.
• Oxygen vacancy formation energy calculations to quantify the tendency of Cu doping to induce anion site defects.

Experimental results

Research questions

• RQ1 Is the Cu-doped LK-99 phase, Pb₉Cu(PO₄)₆O, thermodynamically stable relative to competing phases in the Pb–P–O system?
• RQ2 What is the dynamic stability of Pb₉Cu(PO₄)₆O and Pb₈Cu₂(PO₄)₆ at T=0 K, and how do their phonon band structures compare?
• RQ3 Can a new phase, Pb₈Cu₂(PO₄)₆, be stabilized by substituting two Pb(1) sites with Cu⁺ and removing one oxygen anion, and is it more stable than the known Cu-doped phases?
• RQ4 What are the most favorable reaction pathways for synthesizing Pb₉Cu(PO₄)₆O and Pb₈Cu₂(PO₄)₆, and which reactant ratios are energetically preferred?
• RQ5 How does Cu doping affect the formation energy of oxygen vacancies in the apatite lattice?

Key findings

• Pb₁₀(PO₄)₆O and Pb₁₀(PO₄)₆(OH)₂ are thermodynamically stable, lying on the T=0 K convex hull, while their Cu-substituted counterparts, Pb₉Cu(PO₄)₆O and Pb₉Cu(PO₄)₆(OH)₂, are unstable and lie above the convex hull.
• All four apatite structures—Pb₁₀(PO₄)₆O, Pb₁₀(PO₄)₆(OH)₂, Pb₉Cu(PO₄)₆O, and Pb₈Cu₂(PO₄)₆—exhibit dynamic instability at T=0 K, as indicated by imaginary phonon modes in their dispersions.
• The oxygen vacancy formation energy is lower in Cu-doped structures, indicating that Cu doping increases the likelihood of oxygen vacancy formation on anion sites.
• The proposed phase Pb₈Cu₂(PO₄)₆, formed by substituting two Pb(1) sites with Cu⁺ and removing one O²⁻, shows slightly reduced dynamic instability compared to Pb₉Cu(PO₄)₆O, with higher-frequency imaginary phonon modes and fewer unstable modes along high-symmetry directions.
• A 1:1 molar ratio of Pb₂SO₅ and Cu₃P is identified as a promising reactant combination for synthesizing both Pb₈Cu₂(PO₄)₆ and Pb₉Cu(PO₄)₆O, based on reaction convex hull energy analysis.
• The study identifies Pb₄P₆O₁₉ as a new stable phase in the Pb–P–O system through comparison with the Ca–P–O phase diagram, completing the phase space of this system.