Pressure-Driven Evolution of the Physical Properties of Layered Y2GaB and Y2InB MAB Phases: A Comparative First-Principles Study

Technical Summary: Pressure-Driven Evolution of the Physical Properties of Layered Y2GaB and Y2InB MAB Phases

Problem Statement
Layered ternary borides known as MAB phases exhibit a unique combination of metallic electronic behavior and ceramic-like stiffness due to their nanolaminated structure, where strong in-plane metal-boron bonds coexist with weaker interlayer interactions. While previous studies have characterized specific MAB compounds at ambient pressure, there is a lack of unified understanding regarding how hydrostatic pressure and A-site substitution (specifically Ga vs. In) influence their structural stability, mechanical anisotropy, electronic topology, and thermophysical properties. Furthermore, previous computational work on Y2GaB and Y2InB reported negative-frequency phonon modes, raising questions about their dynamical stability and the sensitivity of these assessments to computational parameters (unit-cell vs. supercell treatments). This study addresses these gaps by systematically comparing the pressure-dependent evolution of Y2GaB and Y2InB from 0 to 20 GPa to establish mechanically viable pressure windows and clarify structure-property relationships.

Methodology
The study employs first-principles calculations based on Kohn-Sham density-functional theory (DFT) using the CASTEP code with the Perdew-Burke-Ernzerhof (PBE) generalized-gradient approximation (GGA). Key methodological features include:

• Structural Optimization: Hexagonal $P6_3/mmc$ structures were optimized under hydrostatic pressures (0, 5, 10, 15, and 20 GPa) using the BFGS algorithm.
• Elastic Stability: Elastic constants were derived via the finite stress-strain method. Stability was assessed using pressure-corrected criteria for hexagonal symmetry, distinguishing between homogeneous strain stability and phonon stability.
• Property Derivation: Polycrystalline moduli (Voigt-Reuss-Hill averages), acoustic velocities, Debye temperatures, and thermal conductivity estimates (Clarke and Slack models) were calculated for elastically stable states.
• Electronic and Optical Analysis: Band structures, densities of states (DOS), and Fermi surfaces were computed with and without spin-orbit coupling (SOC) using Quantum ESPRESSO. Optical properties were resolved for electric field polarizations along [100] and [001].
• Bonding and Dynamics: Electron-density difference maps, Mulliken/Hirshfeld charge analysis, and bond-overlap populations were used to characterize bonding. Phonon dispersions were calculated using the finite-displacement method for both unit-cell and expanded-supercell configurations to assess dynamical stability and numerical sensitivity.

Key Results

• Structural Evolution: Both compounds retain the $P6_3/mmc$ structure under pressure. Compression is anisotropic, with the basal lattice parameter ($a$) contracting more significantly than the axial parameter ($c$). Consequently, the $c/a$ ratio increases for both, and unit-cell volume decreases monotonically (approx. 21.8% for Y2GaB and 20.3% for Y2InB over 0–20 GPa).
• Elastic Stability and Mechanical Properties:
  • Stability Windows: Y2GaB satisfies pressure-corrected elastic stability criteria at 0, 5, and 10 GPa but becomes unstable at 15 and 20 GPa. Y2InB is elastically stable only at ambient pressure (0 GPa).
  • Mechanical Response: Within its stable range, Y2GaB exhibits increased bulk, shear, and Young's moduli with pressure. Both compounds are predicted to be ductile (Pugh ratio $G/B < 0.57$). Y2GaB shows high elastic anisotropy at 0 GPa ($A^U = 5.25$), which decreases with pressure, while Y2InB is less anisotropic at ambient pressure.
  • Thermophysical Properties: For stable Y2GaB, compression increases sound velocities, Debye temperature, and estimated melting temperatures. The Slack-estimated lattice thermal conductivity at 300 K rises from 0.605 W m⁻¹ K⁻¹ (0 GPa) to 1.543 W m⁻¹ K⁻¹ (10 GPa). Both compounds exhibit very low minimum thermal conductivities, suggesting potential for thermal barrier applications at low temperatures, limited by their relatively low melting points.
• Electronic Structure: Both materials are multiband metals. Y2GaB has nine Fermi-surface sheets, and Y2InB has eight at ambient pressure. Spin-orbit coupling (SOC) modifies local band dispersions but does not open a gap or alter the number of Fermi-surface crossings. No Lifshitz transition (topological reconstruction of the Fermi surface) is observed between 0 and 10 GPa for Y2GaB, though the central pocket shrinks significantly. The electronic states near the Fermi level are dominated by Y-4d orbitals, with secondary contributions from B-2p and A-site p-orbitals.
• Bonding Character: Analysis reveals mixed ionic-covalent bonding between Y and B, characterized by charge accumulation around B and depletion around Y. The A-site elements (Ga/In) exhibit more diffuse, metallic bonding.
• Optical Properties: Both compounds display metallic Drude responses and strong optical anisotropy between [100] and [001] polarizations. They act as efficient reflectors in the visible region and absorbers in the ultraviolet. Pressure induces non-uniform shifts in optical features, generally raising characteristic energies for Y2GaB.
• Phonon Dynamics: Unit-cell phonon calculations show positive frequencies for both compounds at 0 and 10 GPa, indicating dynamical stability within this restricted treatment. However, expanded-supercell calculations reveal imaginary modes, highlighting a sensitivity of low-frequency phonon stability to cell size and force-constant treatment. Notably, Y2InB remains elastically unstable at 10 GPa despite showing positive frequencies in the unit-cell phonon spectrum, underscoring the distinction between elastic and dynamical stability criteria.

Significance and Claims
The paper establishes a comparative framework for understanding how A-site substitution (Ga vs. In) and hydrostatic pressure modulate the properties of MAB phases. Its primary contributions are:

1. Defining Stability Windows: It identifies specific pressure ranges where Y2GaB is mechanically viable (0–10 GPa) and clarifies that Y2InB is stable only at ambient pressure under the adopted criteria.
2. Decoupling Stability Types: The study explicitly demonstrates that elastic stability (resistance to homogeneous strain) and dynamical stability (resistance to atomic displacements) are distinct and must be assessed separately, particularly noting the sensitivity of phonon calculations to supercell size.
3. Structure-Property Relationships: It details how pressure systematically enhances stiffness, thermal transport, and optical response in Y2GaB while reducing elastic anisotropy, providing a baseline for future experimental validation.
4. Modest Scope: The authors explicitly state that no experimentally established MABene derivatives of these compounds exist; the study focuses on the parent phases as a necessary foundation for any future assessment of reduced-dimensional derivatives. The thermal conductivity values are presented as model estimates (Slack/Clarke) rather than precise transport predictions, acknowledging the absence of explicit electron-phonon and anharmonic scattering calculations.