Metavalent Bonding in 2D Chalcogenides: Structural Origin and Chemical Mechanisms.

An unusual set of anomalous functional properties of rocksalt crystals of Group IV chalcogenides were recently linked to a kind of bonding termed as metavalent bonding (MVB) which involves violation of the 8-N rule. Precise mechanisms of MVB and the relevance of lone pair of Group IV cations are still debated. With restrictions of low dimensionality on the possible atomic coordination, 2D materials provide a rich platform for exploration of MVB. Here, we present first-principles theoretical analysis of the nature of bonding in five distinct 2D lattices of Group IV chalcogenides MX (M: Sn, Pb, Ge and X: S, Se, Te), in which the natural out-of-plane expression of the lone pair versus in-plane bonding can be systematically explored. While their honeycomb lattices respecting the 8-N rule are shown to exhibit covalent bonding, their square and orthorhombic structures exhibit MVB only in-plane, with cationic lone pair activating the out-of-plane structural puckering that controls their relative stability. Anomalies in Born-effective charges, dielectric constants, Grüneisen parameters occur only in their in-plane behaviour, confirming MVB is confined strictly to 2D and originates from p-p orbital interactions. Our work opens up directions for chemical design of MVB based 2D materials and their heterostructures.

Metavalent Bonding-Mediated Dual 6s2 Lone Pair Expression Leads to Intrinsic Lattice Shearing in n-Type TlBiSe2.

Metavalent bonding has attracted immense interest owing to its capacity to impart a distinct property portfolio to materials for advanced functionality. Coupling metavalent bonding to lone pair expression can be an innovative way to propagate lattice anharmonicity from lone pair-induced local symmetry-breaking via the soft p-bonding electrons to achieve long-range phonon dampening in crystalline solids. Motivated by the shared chemical design pool for topological quantum materials and thermoelectrics, we based our studies on a three-dimensional (3D) topological insulator TlBiSe2 that held prospects for 6s2 dual-cation lone pair expression and metavalent bonding to investigate if the proposed hypothesis can deliver a novel thermoelectric material. Herein, we trace the inherent phononic origin of low thermal conductivity in n-type TlBiSe2 to dual 6s2 lone pair-induced intrinsic lattice shearing that strongly suppresses the lattice thermal conductivity to a low value of 1.1-0.4 Wm-1 K-1 between 300 and 715 K. Through synchrotron X-ray pair distribution function and first-principles studies, we have established that TlBiSe2 exists not in a monomorphous R-3m structure but as a distribution of distorted configurations. Via a cooperative movement of the constituent atoms akin to a transverse shearing mode facilitated by metavalent bonding in TlBiSe2, the structure shuttles between various energetically accessible low-symmetry structures. The orbital interactions and ensuing multicentric bonding visualized through Wannier functions augment the long-range transmission of atomic displacement effects in TlBiSe2. With additional point-defect scattering, a κlatt of 0.3 Wm-1 K-1 was achieved in TlBiSeS with a maximum n-type thermoelectric figure of merit (zT) of ∼0.8 at 715 K.

Hg Doping Induced Reduction in Structural Disorder Enhances the Thermoelectric Performance in AgSbTe2.

Defect engineering, achieved by precise tuning of the atomic disorder within crystalline solids, forms a cornerstone of structural chemistry. This nuanced approach holds the potential to significantly augment thermoelectric performance by synergistically manipulating the interplay between the charge carrier and lattice dynamics. Here, the current study presents a distinctive investigation wherein the introduction of Hg doping into AgSbTe2 serves to partially curtail structural disorder. This strategic maneuver mitigates potential fluctuations originating from pronounced charge and size disparities between Ag+ and Sb3+, positioned in octahedral sites within the rock salt structure. Hg doping significantly improves the phase stability of AgSbTe2 by restricting the congenital emergence of the Ag2Te minor secondary phase and promotes partial atomic ordering in the cation sublattice. Reduction in atomic disorder coalesced with a complementary modification of electronic structure by Hg doping results in increased carrier mobility. The formation of nanoscale superstructure with sizes (2-5 nm) of the order of phonon mean free path in AgSbTe2 is further promoted by reduced partial disorder, causes enhanced scattering of heat-carrying phonons, and results in a glass-like ultralow lattice thermal conductivity (∼0.32 W m-1 K-1 at 297 K). Cumulatively, the multifaceted influence of Hg doping, in conjunction with the consequential reduction in disorder, allows achieving a high thermoelectric figure-of-merit, zT, of ∼2.4 at ∼570 K. This result defies conventional paradigms that prioritize increased disorder for optimizing zT.

Metavalent Bonding in GeSe Leads to High Thermoelectric Performance.

Orthorhombic GeSe is a promising thermoelectric material. However, large band gap and strong covalent bonding result in a low thermoelectric figure of merit, zT≈0.2. Here, we demonstrate a maximum zT≈1.35 at 627 K in p-type polycrystalline rhombohedral (GeSe)0.9 (AgBiTe2 )0.1 , which is the highest value reported among GeSe based materials. The rhombohedral phase is stable in ambient conditions for x=0.8-0.29 in (GeSe)1-x (AgBiTe2 )x . The structural transformation accompanies change from covalent bonding in orthorhombic GeSe to metavalent bonding in rhombohedral (GeSe)1-x (AgBiTe2 )x . (GeSe)0.9 (AgBiTe2 )0.1 has closely lying primary and secondary valence bands (within 0.25-0.30 eV), which results in high power factor 12.8 µW cm-1 K-2 at 627 K. It also exhibits intrinsically low lattice thermal conductivity (0.38 Wm-1 K-1 at 578 K). Theoretical phonon dispersion calculations reveal vicinity of a ferroelectric instability, with large anomalous Born effective charges and high optical dielectric constant, which, in concurrence with high effective coordination number, low band gap and moderate electrical conductivity, corroborate metavalent bonding in (GeSe)0.9 (AgBiTe2 )0.1 . We confirmed the presence of low energy phonon modes and local ferroelectric domains using heat capacity measurement (3-30 K) and switching spectroscopy in piezoresponse force microscopy, respectively.

Ferroelectric Instability Induced Ultralow Thermal Conductivity and High Thermoelectric Performance in Rhombohedral p-Type GeSe Crystal.

The orthorhombic phase of GeSe, a structural analogue of layered SnSe (space group: Pnma), has recently attracted attention after a theoretical prediction of high thermoelectric figure of merit, zT > 2. The experimental realization of such high performance in orthorhombic GeSe, however, is still elusive (zT ≈ 0.2). The rhombohedral phase of GeSe, a structural analogue of GeTe (space group: R3m), previously stabilized at high pressure (2 GPa) and high temperature (1600 K), is promising due to its theoretically predicted ferroelectric instability and the higher earth abundance of Se compared to Te. Here, we demonstrate high thermoelectric performance in the rhombohedral crystals of GeSe, which is stabilized at ambient conditions by alloying with 10 mol % AgBiSe2. We show ultralow lattice thermal conductivity (κL) of 0.74-0.47 W/mK in the 300-723 K range and high zT ≈ 1.25 at 723 K in the p-type rhombohedral (GeSe)0.9(AgBiSe2)0.1 crystals grown using Bridgman method. First-principles density functional theoretical analysis reveals its vicinity to a ferroelectric instability which generates large anomalous Born effective charges and strong coupling of low energy polar optical phonons with acoustic phonons. The presence of soft optical phonons and incipient ferroelectric instability in (GeSe)0.9(AgBiSe2)0.1 are directly evident in the low temperature heat capacity (Cp) and switching spectroscopy piezoresponse force microscopy (SS-PFM) experiments, respectively. Effective scattering of heat carrying acoustic phonons by ferroelectric instability induced soft transverse optical phonons significantly reduces the κL and enhances the thermoelectric performance in rhombohedral (GeSe)0.9(AgBiSe2)0.1 crystals.

Realization of Both n- and p-Type GeTe Thermoelectrics: Electronic Structure Modulation by AgBiSe2 Alloying.

Successful applications of a thermoelectric material require simultaneous development of compatible n- and p-type counterparts. While the thermoelectric performance of p-type GeTe has been improved tremendously in recent years, it has been a challenge to find a compatible n-type GeTe counterpart due to the prevalence of intrinsic Ge vacancies. Herein, we have shown that alloying of AgBiSe2 with GeTe results in an intriguing evolution in its crystal and electronic structures, resulting in n-type thermoelectric properties. We have demonstrated that the ambient rhombohedral structure of pristine GeTe transforms into cubic phase in (GeTe)100-x(AgBiSe2)x for x ≥ 25, with concurrent change from its p-type electronic character to n-type character in electronic transport properties. Such change in structural and electronic properties is confirmed from the nonmonotonic variation of band gap, unit cell volume, electrical conductivity, and Seebeck coefficient, all of which show an inflection point around x ∼ 20, as well as from the temperature variations of synchrotron powder X-ray diffractions and differential scanning calorimetry. First-principles density functional theoretical (DFT) calculations explain that the shift toward n-type electronic character with increasing AgBiSe2 concentration arises due to increasing contribution of Bi p orbitals in the conduction band edge of (GeTe)100-x(AgBiSe2)x. This cubic n-type phase has promising thermoelectric properties with a band gap of ∼0.25 eV and ultralow lattice thermal conductivity that ranges between 0.3 and 0.6 W/mK. Further, we have shown that (GeTe)100-x(AgBiSe2)x has promising thermoelectric performance in the mid-temperature range (400-500 K) with maximum thermoelectric figure of merit, zT, reaching ∼1.3 in p-type (GeTe)80(AgBiSe2)20 at 467 K and ∼0.6 in n-type (GeTe)50(AgBiSe2)50 at 500 K.

Stabilizing n-Type Cubic GeSe by Entropy-Driven Alloying of AgBiSe2 : Ultralow Thermal Conductivity and Promising Thermoelectric Performance.

The realization of n-type Ge chalcogenides is elusive owing to intrinsic Ge vacancies that make them p-type semiconductors. GeSe crystallizes into a layered orthorhombic structure similar to SnSe at ambient conditions. The high-symmetry cubic phase of GeSe is predicted to be stabilized by applying 7 GPa external pressure or by enhancing the entropy by increasing to temperature to 920 K. Stabilization of the n-type cubic phase of GeSe at ambient conditions was achieved by alloying with AgBiSe2 (30-50 mol %), enhancing the entropy through solid solution mixing. The interplay of positive and negative chemical pressure anomalously changes the band gap of GeSe with increasing the AgBiSe2 concentration. The band gap of n-type cubic (GeSe)1-x (AgBiSe2 )x (0.30≤x≤0.50) has a value in the 0.3-0.4 eV range, which is significantly lower than orthorhombic GeSe (1.1 eV). Cubic (GeSe)1-x (AgBiSe2 )x exhibits an ultralow lattice thermal conductivity (κL ≈0.43 W m-1 K-1 ) in the 300-723 K range. The low κL is attributed to significant phonon scattering by entropy-driven enhanced solid-solution point defects.

Metavalent or Hypervalent Bonding: Is There a Chance for Reconciliation?

A family of solids including crystalline phase change materials such as GeTe and Sb2 Te3 , topological insulators like Bi2 Se3, and halide perovskites such as CsPbI3 possesses an unconventional property portfolio that seems incompatible with ionic, metallic, or covalent bonding. Instead, evidence is found for a bonding mechanism characterized by half-filled p-bands and a competition between electron localization and delocalization. Different bonding concepts have recently been suggested based on quantum chemical bonding descriptors which either define the bonds in these solids as electron-deficient (metavalent) or electron-rich (hypervalent). This disagreement raises concerns about the accuracy of quantum-chemical bonding descriptors is showed. Here independent of the approach chosen, electron-deficient bonds govern the materials mentioned above is showed. A detailed analysis of bonding in electron-rich XeF2 and electron-deficient GeTe shows that in both cases p-electrons govern bonding, while s-electrons only play a minor role. Yet, the properties of the electron-deficient crystals are very different from molecular crystals of electron-rich XeF2 or electron-deficient B2 H6 . The unique properties of phase change materials and related solids can be attributed to an extended system of half-filled bonds, providing further arguments as to why a distinct nomenclature such as metavalent bonding is adequate and appropriate for these solids.

Metavalent Bonding Origins of Unusual Properties of Group IV Chalcogenides.

A distinct type of metavalent bonding (MVB) is recently proposed to explain an unusual combination of anomalous functional properties of group IV chalcogenide crystals, whose electronic mechanisms and origin remain controversial. Through theoretical analysis of evolution of bonding along continuous paths in structural and chemical composition space, emergence of MVB in rocksalt chalcogenides is demonstrated as a consequence of weakly broken symmetry of parent simple-cubic crystals of Group V metalloids. High electronic degeneracy at the nested Fermi surface of parent metal drives spontaneous breaking of its translational symmetry with structural and chemical fields, which open up a small energy gap and mediate strong coupling between conduction and valence bands making metavalent crystals highly polarizable, conductive, and sensitive to bond-lengths. Stronger symmetry-breaking structural and chemical fields, however, transform them discontinuously to covalent and ionic semiconducting states. MVB involves bonding-antibonding pairwise interactions alternating along linear chains of at least five atoms, which facilitate long-range electron transfer in response to polar fields causing unusual properties. The precise picture of MVB predicts anomalous second-order Raman scattering as an addition to set off their unusual properties, and will guide in design of new metavalent materials with improved thermoelectric, ferroelectric and nontrivial electronic topological properties.

Modulation of the electronic structure and thermoelectric properties of orthorhombic and cubic SnSe by AgBiSe2 alloying.

Recently, single-crystals of tin selenide (SnSe) have drawn immense attention in the field of thermoelectrics due to their anisotropic layered crystal structure and ultra-low lattice thermal conductivity. Layered SnSe has an orthorhombic crystal structure (Pnma) at ambient conditions. However, the cubic rock-salt phase (Fm3̄m) of SnSe can only be stabilized at very high pressure and thus, the experimental realization of the cubic phase remains elusive. Herein, we have successfully stabilized the high-pressure cubic rock-salt phase of SnSe by alloying with AgBiSe2 (0.30 ≤ x ≤ 0.80) at ambient temperature and pressure. The orthorhombic polycrystalline phase is stable in (SnSe)1-x (AgBiSe2) x in the composition range of 0.00 ≤ x < 0.28, which corresponds to narrow band gap semiconductors, whereas the band gap closes upon increasing the concentration of AgBiSe2 (0.30 ≤ x < 0.70) leading to the cubic rock-salt structure. We confirmed the stabilization of the cubic structure at x = 0.30 and associated changes in the electronic structure using first-principles theoretical calculations. The pristine cubic SnSe exhibited the topological crystalline insulator (TCI) quantum phase, but the cubic (SnSe)1-x (AgBiSe2) x (x = 0.33) showed a semi-metallic electronic structure with overlapping conduction and valence bands. The cubic polycrystalline (SnSe)1-x (AgBiSe2) x (x = 0.30) sample showed n-type conduction at room temperature, while the orthorhombic (SnSe)1-x (AgBiSe2) x (0.00 ≤ x < 0.28) samples retained p-type character. Thus, by optimizing the electronic structure and the thermoelectric properties of polycrystalline SnSe, a high zT of 1.3 at 823 K has been achieved in (SnSe)0.78(AgBiSe2)0.22.

Enhanced atomic ordering leads to high thermoelectric performance in AgSbTe2.

High thermoelectric performance is generally achieved through either electronic structure modulations or phonon scattering enhancements, which often counteract each other. A leap in performance requires innovative strategies that simultaneously optimize electronic and phonon transports. We demonstrate high thermoelectric performance with a near room-temperature figure of merit, ZT ~ 1.5, and a maximum ZT ~ 2.6 at 573 kelvin, by optimizing atomic disorder in cadmium-doped polycrystalline silver antimony telluride (AgSbTe2). Cadmium doping in AgSbTe2 enhances cationic ordering, which simultaneously improves electronic properties by tuning disorder-induced localization of electronic states and reduces lattice thermal conductivity through spontaneous formation of nanoscale (~2 to 4 nanometers) superstructures and coupling of soft vibrations localized within ~1 nanometer around cadmium sites with local strain modulation. The strategy is applicable to most other thermoelectric materials that exhibit inherent atomic disorder.