Metavalent Bonding-Induced Phonon Hardening and Giant Anharmonicity in BeO

TL;DR

This work compares covalent zb-BeO and metavalent rs-BeO to reveal how bonding type governs lattice dynamics and heat transport. Using first-principles methods with explicit four-phonon scattering and temperature-dependent phonon renormalization, the authors show that metavalent bonding in rs-BeO markedly enhances anharmonicity and suppresses phonon transport, yielding an ultralow lattice thermal conductivity of about $\kappa_L \approx 24\ \mathrm{W\,m^{-1}\,K^{-1}}$ at 300 K, in stark contrast to zb-BeO’s $\kappa_L \approx 357\ \mathrm{W\,m^{-1}\,K^{-1}}$. They demonstrate that accurate predictions require including SCPH-renormalized phonons and off-diagonal heat-flux contributions, and they identify three indicators for discovering metavalently bonded incipient metals: a NaCl-type structure, $\gamma > 2$, and LST violation. Collectively, the results provide microscopic insight into how metavalent bonding suppresses phonon transport and offer a framework for locating promising thermoelectric and phase-change materials.

Abstract

The search for materials with intrinsically low thermal conductivity ($κ_L$) is critical for energy applications, yet conventional descriptors often fail to capture the complex interplay between bonding and lattice dynamics. Here, first-principles calculations are used to contrast the thermal transport in covalent zincblende (zb) and metavalent rocksalt (rs) BeO. We find that the metavalent bonding in rs-BeO enhances lattice anharmonicity, activating multi-phonon scattering channels and suppressing phonon transport. This results in an ultralow $κ_L$ of 24 W m$^{-1}$ K$^{-1}$ at 300 K, starkly contrasting with the zb phase (357 W m$^{-1}$ K$^{-1}$). Accurately modeling such strongly anharmonic systems requires explicit inclusion of temperature-dependent phonon renormalization and four-phonon scattering. These contributions, negligible in zb-BeO, are essential for high-precision calculations of the severely suppressed $κ_L$ in rs-BeO. Finally, we identify three key indicators to guide the discovery of metavalently bonded, incipient-metallic materials: (i) an NaCl-type crystal structure, (ii) large Grüneisen parameters ($\textgreater$2), and (iii) a breakdown of the Lyddane-Sachs-Teller relation. These findings provide microscopic insight into thermal transport suppression by metavalent bonding and offer a predictive framework for identifying promising thermoelectrics and phase-change materials.

Figures (8)

• Figure 1: The conductivity, band gap ($E_g$), Grüneisen parameter ($\gamma$), and Born effective charges of different semiconductors. The band gap can be classified as less than 1 eV, between 1 and 2 eV, between 2 and 3 eV, between 3 and 4 eV, and larger than 8 eV, respectively. Different material dots are represented by black, blue, light green, dark green, and red dots. The p-bonded metavalent materials, p-bonded (orthogonal or rocksalt-like) systems, and sp$^3$ covalent (zincblende-like) crystals are indicated by the green, yellow, and grey ellipses, respectively. Furthermore, black arrows are used to depict the crystal structures of zb-BeO and rs-BeO, with grey and blue spheres representing the Be and O atoms, respectively. All data are available in the Supplementary Material.
• Figure 2: Normalized traces of interatomic force constants (IFCs) tensors versus atomic distances and charge density disturbance of selected atom pairs and thermal conductivity in (a) zb-BeO and (d) rs-BeO, where different colors denote IFCs with a specific element chosen as the origin atom. The equilibrium electron density distributions of the Be atomic layer in zb-BeO and rs-BeO are shown in (b) and (e), respectively. the color bars show the electron charge density in space. The interatomic area in (b) and (e), where a notable difference in electron departure from the domain is displayed between zb-BeO and rs-BeO is shown by the black circles. Comparison of charge density distortions in zb-BeO and rs-BeO caused by Be atom displacement is shown in (c) and (f). Variations in electron density are shown by color bars in units of e/$\text{\AA}^3$.
• Figure 3: The electronic properties of zb-BeO and rs-BeO. (a) The electronic band and (b) density of state (DOS) of zb-BeO, where grey shading implies total DOS and yellow, blue, aqua green, and dark green represent the Be-$s$, Be-$p$, O-$s$, and O-$p$ orbitals, respectively. (c) and (f) are projected crystal orbital Hamilton population (pCOHP) analysis for the Be-O interactions in zb-BeO and rs-BeO. Negative -pCOHP values correspond to bonding states, whereas positive values denote anti-bonding states. The energy scale is referenced to the Fermi level, which is set at 0 eV. (d-e) are the same with (a-b) where total DOS and the Be-$s$, Be-$p$, O-$s$, and O-$p$ orbitals are displayed in red, pink, orange, and violet, respectively.
• Figure 4: The phonon dispersions for (a) zb-BeO and (b) rs-BeO with different temperatures, where both are dark grey for the scenario without the LO-TO splitting. In (a), the phonon dispersions at 0 K, 500 K, 1000 K, 1500 K, and 2000 K are shown by the yellow, light green, light blue, dark blue, and purple lines, respectively. In contrast, (b) shows the phonon dispersions at the aforementioned temperatures as dark green, yellow, light blue, dark blue, and pink, respectively.
• Figure 5: The potential energy surfaces (PESs), the mean square atomic displacements (MSDs) of Be and O and the Grüneisen parameter for different phonon modes of zb-BeO and rs-BeO. Calculated potential energy surfaces (PESs) of the lowest-lying TA phonon mode are presented for zb-BeO at the $L$ point and rs-BeO at the $\Gamma$ point in (a) and (c), respectively. The insets depict the corresponding atomic vibration patterns. The MSDs of Be and O for zb-BeO and rs-BeO are shown in (b) and (e), respectively. In both (b) and (e), the MSDs from the harmonic approximation (HA) and self-consistent phonon (SCPH) method are shown as solid and dashed lines, respectively, for Be and O atoms. Specifically, the HA results use light/dark blue in (b) and flesh/coffee in (e), while the SCPH results use bright blue/bright yellow in (b) and light/deep purple in (e). The Grüneisen parameter is shown in (c) and (f) for the transversal acoustic (TA), longitudinal acoustic (LA), transversal optical (TO), and longitudinal optical (LO) phonon modes at 300 K, respectively. The overall Grüneisen parameter for rs-BeO is 2.59, while that of zb-BeO is 0.94.