Valence Electron Count Research Articles

Complex Structure, Chemical Bonding, and Electrical Transport Properties of a La-Doped Zintl Phase

The La-doped ternary Zintl phase Ca10.43(3)La0.57Sb9.69(1) was successfully synthesized by arc melting, and the title compound adopted the Ho11Ge10-type structure with a tetragonal I4/mmm space group (Z = 4, Pearson code tI84). The complex crystal structure is composed of (1) the four different kinds of cationic Ca or Ca/La mixed sites surrounded by seven or nine Sb atoms and (2) the 3-dimensional cage-shaped anionic frameworks built by the other two types of Sb atoms. In particular, the La dopants preferred to occupy the Ca4 and Ca1 sites, and this specific cationic-site preference can be rationalized by both electronic and size-factor criteria. Moreover, the ca. 16% occupational deficiency observed at the Sb3 site was attributed to the energetically unfavorable antibonding character of the Sb3–Sb3 bond in the [Sb3]4 tetramers, according to a series of DFT calculations. A crystal Hamilton overlap population curve analysis also proved that the title compound Ca10.43(3)La0.57Sb9.69(1) tried to keep the valence electron count below 71.02 to remain energetically stable in the Ho11Ge10-type phase. Measurements of temperature-dependent electrical transport properties revealed that the La doping indeed enhanced the electrical conductivity of Ca10.43(3)La0.57Sb9.69(1) compared to the un-doped Ca11Sb10. However, unlike other rare earth metal (RE)-doped compounds in the Ca11−xRExSb10 (RE = Nd and Sm) system that display semiconducting behavior, the La-doped title compound showed poor metallic electrical properties. The positive values of Seebeck coefficients indicated the p-type character of the title compound despite the successful n-type La doping, and this should be attributed to Sb deficiency.

Integrated design of aluminum-enriched high-entropy refractory B2 alloys with synergy of high strength and ductility.

Refractory high-entropy alloys (RHEAs) are promising high-temperature structural materials. Their large compositional space poses great design challenges for phase control and high strength-ductility synergy. The present research pioneers using integrated high-throughput machine learning with Monte Carlo simulations supplemented by ab initio calculations to effectively navigate phase selection and mechanical property predictions, developing single-phase ordered B2 aluminum-enriched RHEAs (Al-RHEAs) demonstrating high strength and ductility. These Al-RHEAs achieve remarkable mechanical properties, including compressive yield strengths up to 1.7 gigapascals, fracture strains exceeding 50%, and notable high-temperature strength retention. They also demonstrate a tensile yield strength of 1.0 gigapascals with a ductility of 9%, albeit with B2 ordering. Furthermore, we identify valence electron count domains for alloy ductility and brittleness with the explanation from density functional theory and provide crucial insights into elemental influence on atomic ordering and mechanical performance. The work sets forth a strategic blueprint for high-throughput alloy design and reveals fundamental principles governing the mechanical properties of advanced structural alloys.

Structure and physical properties of modified Ti2MnAl compound – Ti2Fe0.5Cr0.5Al and Ti2MnAl0.5In0.5 case

Ti2MnAl was believed to be Spin Gapless Semiconducting (SGS) material, but this state can be achieved only in an inverted variant of Heusler structure. This specific structure is not realized under normal conditions, however, earlier reports suggest that substituting Al by In or Sn should make it possible. This was the motivation for studying the structural and physical properties of Ti2MnAl0.5In0.5 alloy in this paper. We also studied isoelectronic Ti2Fe0.5Cr0.5Al material, as it is well known that properties of Heusler compounds strongly depend on the valence electron count. We report a combined experimental and theoretical study, where we synthesized substituted variants and measured their diffraction patterns. Additionally we performed ab initio calculations using several methods to study the stability of the resulting compounds. We also examined the impact of disorder within Coherent Potential Approximation. Experimental XPS (X-ray Photoemission Spectroscopy) spectra, magnetic susceptibility and electrical resistivity are also discussed.

Machine Learning-Based Predictions of Power Factor for Half-Heusler Phases

A support vector regression model for predictions of the thermoelectric power factor of half-Heusler phases was implemented based on elemental features of ions. The training subset was composed of 53 hH phases with 18 valence electrons. The target values were calculated within the density functional theory and Boltzmann equation. The best predictors out of over 2000 combinations regarded for the p-type power factor at room temperature are: electronegativity, the first ionization energy, and the valence electron count of constituent ions. The final results of support vector regression for 70 hH phases are compared with data available in the literature, revealing good ability to determine favorable thermoelectric materials, i.e., VRhGe, TaRhGe, VRuSb, NbRuAs, NbRuBi, LuNiAs, LuNiBi, TaFeBi, YNiAs, YNiBi, TaRuSb and NbFeSb. The results and discussion presented in this work should encourage further fusion of ab initio investigations and machine learning support, in which the elemental features of ions may be a sufficient input for reasonable predictions of intermetallics with promising thermoelectric performance.

Tunable valence tautomerism in lanthanide-organic alloys.

The inimitable electronic structures of the lanthanide (Ln) ions are key to advanced materials and technologies involving these elements. The trivalent ions are ubiquitous and are used much more widely than the divalent and tetravalent analogues, which possess vastly different optical and magnetic properties. Hence, alteration of the valence electron count by external stimuli can lead to dramatic changes in materials properties. Compounds exhibiting a temperature-induced complete Ln(III) ⇄ Ln(II) switch, referred to as a valence tautomeric (VT) transition, are rare. Here we present an abrupt and hysteretic VT transition in a lanthanide-based coordination polymer, SmI2(pyrazine)3, driven by the interconversion of Sm(II)-pyrazine(0) and Sm(III)-pyrazine(·-) redox pairs. Alloying SmI2(pyrazine)3 with Yb(II) yields isomorphous Sm1-xYbxI2(pyrazine)3 solid solutions with VT transition critical temperatures ranging widely from 200 K to ∼50 K at ambient pressure. These findings demonstrate a simple strategy to realize thermally switchable magnetic materials with chemically tunable transition temperatures.

Temperature and composition insensitivity of thermoelectric properties of high-entropy half-heusler compounds

Composition modification by doping and solid solution is a well-studied strategy in thermoelectric (TE) materials to optimize their properties. Recently, the concept of entropy stabilization has offered the possibility of forming random solid solutions that have properties that go beyond the rule of mixture. In this study, we prepared a series of high-entropy half-Heusler solid solutions (HEHHs) with varying valence electron counts (VEC), (Ti0.33Zr0.33Hf0.33)1-x(V0.33Nb0.33Ta0.33)xCoSb (x = 0.5 to 0.75). Compared to their medium- and low-entropy counterparts, the TE properties of HEHHs are less sensitive to temperature and composition variation (charge carrier concentration efficiency of ∼10 %). An ultra-low lattice thermal conductivity for half-Heusler of 1.19 W·m−1·K−1 was achieved.

A stabilization rule for metal carbido cluster bearing μ3-carbido single-atom-ligand encapsulated in carbon cage

Metal carbido complexes bearing single-carbon-atom ligand such as nitrogenase provide ideal models of adsorbed carbon atoms in heterogeneous catalysis. Trimetallic μ3-carbido clusterfullerenes found recently represent the simplest metal carbido complexes with the ligands being only carbon atoms, but only few are crystallographically characterized, and its formation prerequisite is unclear. Herein, we synthesize and isolate three vanadium-based μ3-CCFs featuring V = C double bonds and high valence state of V (+4), including VSc2C@Ih(7)-C80, VSc2C@D5h(6)-C80 and VSc2C@D3h(5)-C78. Based on a systematic theoretical study of all reported μ3-carbido clusterfullerenes, we further propose a supplemental Octet Rule, i.e., an eight-electron configuration of the μ3-carbido ligand is needed for stabilization of metal carbido clusters within μ3-carbido clusterfullerenes. Distinct from the classic Effective Atomic Number rule based on valence electron count of metal proposed in the 1920s, this rule counts the valence electrons of the single-carbon-atom ligand, and offers a general rule governing the stabilities of μ3-carbido clusterfullerenes.

Power generation from n-type NbCo1−xNixSn and p-type NbFe1−xMnxSb ternary half-Heusler compounds: from materials development to module fabrication

The thermoelectric figure of merit zT in n-type Ni-doped NbCoSn and p-type Mn-doped NbFeSb half-Heusler (HH) compounds was successfully improved using the 18 valence electron count concept, demonstrating reliable power generation in HH-based modules.

Low lattice thermal conductivity of novel NiVSn with 19 valence electron count contrasted to 18 of NiVAl and NiAlSb Half-Heusler compounds

In the current study, the novel pristine compounds of both VEC 18 (NiVAl & NiAlSb) and VEC 19 (NiVSn) materials have been synthesized employing arc-melting and hot-pressed at 1073 K. The measured carrier concentration for all the compounds was found ∿ 1020-1021 cm−3. Further, NiAlSb, NiVAl, and NiVSn half-Heusler (HH) compounds exhibited n-type semiconductor behaviour, with maximum Seebeck coefficients (S) of −50.2 μV/K, −40.5 μV/K, and −14.5 μV/K at 723 K. As a result of the measured S and electrical conductivity, the estimated power factor for NiVSn (0.20 mWm−1K−2), NiAlSb (0.41 mWm−1K−2), and NiVAl (0.65 mWm−1K−2) at 723 K. The NiVSn lattice thermal conductivity (κl) was reduced to ∿ 79.80 % and 76.71 % as compared to NiAlSb and NiVAl compounds. Despite having reduced κl, low zT exhibited for NiVSn compound mainly due to nominal S. The reduced κl was mainly attributed to weak chemical bonding results from lower group velocity of phonon, leading to a higher anharmonicity effect in the lattice. Therefore, NiVSn of VEC 19-based compound can be considered as a potential candidate material for TE applications other than traditional 18-VEC HH compounds. The thermoelectric performance of the novel HH compounds is suitably corroborated with the structural and microstructural investigations.

Rare coexistence of disorder-induced Griffiths phase and reentrant spin-glass state in a Heusler alloy Rh2FeAl with high Curie temperature

In this work, we report the synthesis of a Heusler alloy Rh2FeAl with valence electron count (VEC) 29 forming in B2-type structural disorder, where Fe atoms are distributed randomly with Al atoms between 4a and 4b Wyckoff positions (space group Fm3¯m, No: 225). Despite the structural disorder among the moment carrying Fe atoms, the compound exhibits ferromagnetic Curie temperature around TC ∼ 497 K. Nevertheless, the observation of Griffiths-phase (GP) like behaviour at TG ∼ 592 K suggests that atomic disorders brought down the bulk TC by about 95 K. The structural disorder also affects the ordered spin arrangements below TC through the development of a reentrant spin glass (RSG) state at low temperature. Both the GP like behaviour as well as RSG states are rarely observed in Heusler alloys while their coexistence is even rarer. The isothermal magnetisation as well as temperature dependence of resistivity behaviour ruled out the possibility of having half-metallic ferromagnetic characteristic in this material.

Enhanced thermoelectric performance of NbCoSb half-Heusler alloys by using an amorphous precursor

Amorphous flakes with a stoichiometric composition of NbCoSb were successfully synthesized by introducing a rapid solidification technique. The amorphous phase transformed into a nanostructured NbCoSb half-Heusler phase with a valence electron count (VEC) of 19 during spark plasma sintering. Due to the chemically homogeneous nature of amorphous phase, uniform nanostructure of NbCoSb half-Heusler phase was obtained within the disk samples without impurity phase formation as well as long term annealing treatment required in the conventional manufacturing process. Nanostructuring of NbCoSb half-Heusler phase significantly increased grain boundary area in which electron and phonon scattering occurred and was effective to enhance thermoelectric performance. Furthermore, the carrier concentration was reduced by doping with Sn causing an increased dimensionless figure-of-merit ZT value. A maximum ZT value of ∼0.78, corresponding to a two-fold improvement compared to the ZT value of the as-cast sample, was achieved at 1173 K for the sintered NbCoSb0.95Sn0.05 sample.

Superconductivity in the bcc‐Type High‐Entropy Alloy TiHfNbTaMo

AbstractX‐ray powder diffraction, electrical resistivity, magnetization, and thermodynamic measurements are conducted to investigate the structure and superconducting properties of TiHfNbTaMo, a novel high‐entropy alloy possessing a valence electron count (VEC) of 4.8. The TiHfNbTaMo HEA is discovered to have a body‐centered cubic structure (space group ) with lattice parameters a = 3.445 (1) Å and a microscopically homogeneous distribution of the constituent elements. This material shows type‐II superconductivity with Tc = 3.42 K, lower critical field µ0Hc1(0) = 22.8 mT, and upper critical field µ0Hc2(0) = 3.95 T. Low‐temperature specific heat measurements show that the alloy is a conventional s‐wave type with a moderately coupled superconductor. First‐principles calculations show that the density of states (DOS) of the TiHfNbTaMo alloy is dominated by hybrid d orbitals of these five metal elements. Additionally, the TiHfNbTaMo HEA exhibits three van Hove singularities. Furthermore, the VEC and the composition of the elements (especially the Nb elemental content) affect the Tc of the bcc‐type HEA.

A ductility metric for refractory-based multi-principal-element alloys

We propose a quantum-mechanical dimensionless metric, the local-lattice distortion (LLD), as a reliable predictor of ductility in refractory multi-principal-element alloys (RMPEAs). The LLD metric is based on electronegativity differences in localized chemical environments and combines atomic-scale displacements due to local lattice distortions with a weighted average of valence-electron count. To evaluate the effectiveness of this metric, we examined body-centered cubic (bcc) refractory alloys that exhibit ductile-to-brittle behavior. Our findings demonstrate that local-charge behavior can be tuned via composition to enhance ductility in RMPEAs. With finite-sized cell effects eliminated, the LLD metric accurately predicted the ductility of arbitrary alloys, which compares well with existing tensile-elongation experiments. To validate further, we qualitatively evaluated the ductility of two refractory RMPEAs, i.e., NbTaMoW and Mo72W13Ta10Ti2.5Zr2.5, through the observation of crack formation under indentation, again showing excellent agreement with LLD predictions. A comparative study of three refractory alloys provides further insights into the electronic-structure origin of ductility in refractory RMPEAs. This proposed metric enables rapid and accurate assessment of ductility behavior in the vast RMPEA composition space.

Magnetic and transport properties in metallic and disordered Ru2VAl and Ru2VGa

In this work, we report an elaborate study on the structural, magnetic and thermoelectric properties of two Ru-based Heusler alloys, viz., Ru2VAl and Ru2VGa, having valence electron count 24. While Ru2VGa exhibits a nonmagnetic ground state, in Ru2VAl a short range ferromagnetic interaction is developed below 10 K due to the structural antisite defects and disorder, that also manifests its signature in the specific heat and electrical resistivity measurements at low temperatures. Both the Seebeck coefficient (S) and Hall measurements suggest the dominance of hole-type carrier for electronic transport in Ru2VAl whereas Ru2VGa is found to be a n-type material. The linear nature and small absolute values of S, as well as non-zero values of electronic contribution to specific heat γS (γSRu2VAl = 4.9 mJ/mol-K2 and γSRu2VGa = 5.5 mJ/mol-K2) point towards a metallic ground state for both these alloys. Both the compounds exhibit lower thermal conductivity at room temperature in comparison to Fe-based Heusler alloys due to the presence of heavier element Ru.

Recent trends of ternary, quaternary half-Heusler thermoelectric materials and contact resistance effect on their power output efficiency

Climate change isone of the most pressing global issues, owing to the high carbon footprint generated during conventional power generation via coal consumption and gasoline-fuelled exhaust. Furthermore, nearly half of thetotal energy is lost as heat. Suitable thermoelectric (TE) devices can convert waste heat into green/clean energy. Moreover, these devices have no moving parts, require no maintenance, and are environmentally friendly. A better TE device's thermoelectric performance (zT) should be highly cost-effective for process scaling. Because of their low cost, narrow band gap, better contact engineering, decent electrical properties, and high mechanical performance, Half-Heusler (HH) compounds (space group Fm-3 m) have been considered the best candidate materials worldwide. However, these materials have a high thermal conductivity. The high thermoelectric performance of HH compounds was achieved through iso-electronic doping and nanostructuring, which reduced thermal conductivity significantly. The current report briefly overviews17, 18, 19, and 21 valence electron count (VEC) HH materials and their effects on thermal conductivity and zT. Finally, using cumulative temperature dependence (CTD) and constant property models (CPM), the theoretical estimation of power density and efficiency was calculated by considering the materials' thermoelectric performanceand contact resistance.

Optimization of Chemical Bonding through Defect Formation and Ordering─The Case of Mg7Pt4Ge4.

The new phase Mg7Pt4Ge4 (≡Mg8□1Pt4Ge4; □ = vacancy) was prepared by reacting a mixture of the corresponding elements at high temperatures. According to single crystal X-ray diffraction data, it adopts a defect variant of the lighter analogue Mg2PtSi (≡Mg8Pt4Si4), reported in the Li2CuAs structure. An ordering of the Mg vacancies results in a stoichiometric phase, Mg7Pt4Ge4. However, the high content of Mg vacancies results in a violation of the 18-valence electron rule, which appears to hold for Mg2PtSi. First principle density functional theory calculations on a hypothetical, vacancy-free "Mg2PtGe" reveal potential electronic instabilities at EF in the band structure and significant occupancy of states with an antibonding character resulting from unfavorable Pt-Ge interactions. These antibonding interactions can be eliminated through introduction of Mg defects, which reduce the valence electron count, leaving the antibonding states empty. Mg itself does not participate in these interactions. Instead, the Mg contribution to the overall bonding comes from electron back-donation from the (Pt, Ge) anionic network to Mg cations. These findings may help to understand how the interplay of structural and electronic factors leads to the "hydrogen pump effect" observed in the closely related Mg3Pt, for which the electronic band structure shows a significant amount of unoccupied bonding states, indicating an electron deficient system.

Equiatomic intermetallic barium compounds BaTX (T=Pd, Pt, Au; X=Mg, Zn, Cd) with TiNiSi and ZrBeSi type structure

AbstractThe equiatomic ternary BaTX (T=Pd, Pt, Au; X=Mg, Zn, Cd) phases were obtained by reaction of the elements in sealed tantalum ampoules. The compounds were characterized through their X‐ray powder patterns. BaAuMg and BaTCd (T=Pd, Pt, Au) crystallize with the TiNiSi type structure, while the compounds BaTZn (T=Pd, Pt) adopt the ZrBeSi type. The structures of BaAuMg and BaPdZn were refined from single crystal X‐ray diffractometer data: Pnma, a=801.34(5), b=467.71(8), c=924.07(10) pm, wR2=0.0955, 736 F2 values, 20 variables for BaAuMg and P63/mmc, a=449.68(2), c=901.62(4) pm, wR2=0.1172, 145 F2 values, 8 variables for BaPdZn. The structures derive from the aristotype AlB2. The gold and magnesium atoms form puckered Au3Mg3 hexagons with 284–328 pm Au−Mg while the Pd3Zn3 hexagons in BaPdZn are planar (260 pm Pd−Zn). Comparison of all known BaTX phases shows a range of the valence electron count (VEC) from 13 (BaMnGe) to 18 (BaAuP). The BaTX phases crystallize with seven different structure types and there is no obvious correlation with VEC.

Lewis Structures and the Bonding Classification of End-on Bridging Dinitrogen Transition Metal Complexes.

The activation of dinitrogen by coordination to transition metal ions is a widely used and promising approach to the utilization of Earth's most abundant nitrogen source for chemical synthesis. End-on bridging N2 complexes (μ-η1:η1-N2) are key species in nitrogen fixation chemistry, but a lack of consensus on the seemingly simple task of assigning a Lewis structure for such complexes has prevented application of valence electron counting and other tools for understanding and predicting reactivity trends. The Lewis structures of bridging N2 complexes have traditionally been determined by comparing the experimentally observed NN distance to the bond lengths of free N2, diazene, and hydrazine. We introduce an alternative approach here and argue that the Lewis structure should be assigned based on the total π-bond order in the MNNM core (number of π-bonds), which derives from the character (bonding or antibonding) and occupancy of the delocalized π-symmetry molecular orbitals (π-MOs) in MNNM. To illustrate this approach, the complexes cis,cis-[(iPr4PONOP)MCl2]2(μ-N2) (M = W, Re, and Os) are examined in detail. Each complex is shown to have a different number of nitrogen-nitrogen and metal-nitrogen π-bonds, indicated as, respectively: W≡N-N≡W, Re═N═N═Re, and Os-N≡N-Os. It follows that each of these Lewis structures represents a distinct class of complexes (diazanyl, diazenyl, and dinitrogen, respectively), in which the μ-N2 ligand has a different electron donor number (total of 8e-, 6e-, or 4e-, respectively). We show how this classification can greatly aid in understanding and predicting the properties and reactivity patterns of μ-N2 complexes.

A family of edge-sharing bi-octahedral diruthenium(III,III) compounds containing Ru-Ru single bonds.

From paddlewheel starting reactants Ru2(R'CO2)4+, a family of edge-sharing bi-octahedral (ESBO) diruthenium(III,III) compounds has been prepared, formulated as Ru2(μ-O2CR')2(μ-OR)2(η-L)2 (1-10) [R' = CH3, R = CH3, L = acac (1), tfac (2); R' = CH3, R = CH2CH3, L = hfac (3); R' = CH2CH3, R = CH3, L = acac (4), tfac (5); R' = CH2CH3, R = CH2CH3, L = hfac (6); R' = CH2Cl, R = CH3, L = tfac (7); R' = CH2Cl, R = CH2CH3, L = hfac (8); R' = C6H5, R = CH3, L = tfac (9); and R' = H, R = CH3, L = acac (10); here, acac, tfac and hfac represent acetylacetone, trifluoroacetylacetone and hexafluoroacetylacetone, respectively]. Compounds 1-10 have a similar ESBO coordination geometry of the Ru(μ-O2CR')2(μ-OR)2Ru core with a Ru-Ru center chelated and bridged by two μ-O2CR' and two μ-OR in a trans manner, and each Ru center is also coordinated with a η2-L bidentate ligand. The Ru-Ru distances fall in the range of 2.4560(9)-2.4771(4) Å. The investigation of the electronic spectra and vibrational frequencies as well as theoretical studies with density functional theory (DFT) reveal that compounds 1-10 are ESBO bimetallic species of d5-d5 valence electron counts showing a σ2π2δ2δ*2π*2 electronic configuration. Varying -CH3 to -CF3 groups on the η2-L bidentate ligands coordinating to the Ru(μ-O2CR')2(μ-OR)2Ru core, and according to Raman spectrum measurements combined with theoretical calculations, the intense bands of compounds 1-10 appearing at ∼345 cm-1 in the small-wavenumber region can be assigned to the stretching of the Ru-Ru single bond.

Periodic Trends in the Infrared and Optical Absorption Spectra of Metal Chalcogenide Clusters.

We have investigated the optical absorption, infrared spectra, binding energies, and other cluster properties to investigate whether periodic trends can be observed in the electronic structure of transition metal chalcogenide clusters ligated with CO ligands. Our studies demonstrate the existence of several periodic trends in the properties of pure and mixed octahedral metal chalcogenide clusters, TM6Se8(CO)6 (TM = W-Pt). We find that octahedral metal chalcogenide clusters with 96, 100, and 114 valence electrons have larger excitation energies, consistent with these clusters having closed electronic shells. Periodic trends were observed in the infrared spectra, with the CO bond stretch having the highest energy at 100 and 114 valence electrons due to the closed electronic shell minimizing back-bonding with the CO molecule. A periodic trend in the antisymmetric TM-C stretch was also observed, with the vibrational energy increasing as the valence electron count increased. This is due to decrease in the TM-C bond length, resulting in a larger force constant. These results reveal that periodic trends seen earlier in simple or noble-metal clusters can be observed in symmetric transition metal chalcogenide clusters, showing that the superatom concept in metal chalcogenide clusters goes beyond electronic excitations, and can be seen in other observable properties.