Three-Fold Coordination of Copper in Sulfides: A Blockade for Hole Carrier Delocalization but a Driving Force for Ultralow Thermal Conductivity.

Copper-rich sulfides are very promising for energy conversion applications due to their environmental compatibility, cost effectiveness, and earth abundance. Based on a comparative analysis of the structural and transport properties of Cu3BiS3 with those of tetrahedrite (Cu12Sb4S13) and other Cu-rich sulfides, we highlight the role of the cationic coordination types and networks on the electrical and thermal properties. By precession-assisted 3D electron diffraction analysis, we find very high anisotropic thermal vibration of copper attributed to its 3-fold coordination, with an anisotropic atomic displacement parameter up to 0.09 Å2. Density functional theory calculations reveal that these Cu atoms are weakly bonded and give rise to low-energy Einstein-like vibrational modes that strongly scatter heat-carrying acoustic phonons, leading to ultralow thermal conductivity. Importantly, we demonstrate that the 3-fold coordination of copper in Cu3BiS3 and in other copper-rich sulfides constituted of interconnected CuS3 networks causes a hole blockade. This phenomenon hinders the possibility of optimizing the carrier concentration and electronic properties through mixed valency Cu+/Cu2+, differently from tetrahedrite and most other copper-rich chalcogenides, where the main interconnected Cu-S network is built of CuS4 tetrahedra. The comparison with various copper-rich sulfides demonstrates that seeking for frameworks characterized by the coexistence of tetrahedral and 3-fold coordinated copper is very attractive for the discovery of efficient thermoelectric copper-rich sulfides. Considering that lattice vibrations and carrier concentration are key factors for engineering transport phenomena (electronic, phonon, ionic, etc.) in copper-rich chalcogenides for various types of applications, our findings improve the guidelines for the design of materials enabling sustainable energy solutions with wide-ranging applications.

Lone Pair Rotation and Bond Heterogeneity Leading to Ultralow Thermal Conductivity in Aikinite.

Understanding the relationship between the crystal structure, chemical bonding, and lattice dynamics is crucial for the design of materials with low thermal conductivities, which are essential in fields as diverse as thermoelectrics, thermal barrier coatings, and optoelectronics. The bismuthinite-aikinite series, Cu1-x□xPb1-xBi1+xS3 (0 ≤ x ≤ 1, where □ represents a vacancy), has recently emerged as a family of n-type semiconductors with exceptionally low lattice thermal conductivities. We present a detailed investigation of the structure, electronic properties, and the vibrational spectrum of aikinite, CuPbBiS3 (x = 0), in order to elucidate the origin of its ultralow thermal conductivity (0.48 W m-1 K-1 at 573 K), which is close to the calculated minimum for amorphous and disordered materials, despite its polycrystalline nature. Inelastic neutron scattering data reveal an anharmonic optical phonon mode at ca. 30 cm-1, attributed mainly to the motion of Pb2+ cations. Analysis of neutron diffraction data, together with ab-initio molecular dynamics simulations, shows that the Pb2+ lone pairs are rotating and that, with increasing temperature, Cu+ and Pb2+ cations, which are separated at distances of ca. 3.3 Å, exhibit significantly larger displacements from their equilibrium positions than Bi3+ cations. In addition to bond heterogeneity, a temperature-dependent interaction between Cu+ and the rotating Pb2+ lone pair is a key contributor to the scattering effects that lower the thermal conductivity in aikinite. This work demonstrates that coupling of rotating lone pairs and the vibrational motion is an effective mechanism to achieve ultralow thermal conductivity in crystalline materials.

Relaxation time approximations in PAOFLOW 2.0.

Regardless of its success, the constant relaxation time approximation has limited validity. Temperature and energy dependent effects are important to match experimental trends even in simple situations. We present the implementation of relaxation time approximation models in the calculation of Boltzmann transport in PAOFLOW 2.0 and apply those to model band-structures. In addition, using a self-consistent fitting of the model parameters to experimental conductivity data, we provide a flexible tool to extract scattering rates with high accuracy. We illustrate the approximations using simple models and then apply the method to GaAs, Si, [Formula: see text], and [Formula: see text].

A Tunable Structural Family with Ultralow Thermal Conductivity: Copper-Deficient Cu1-x□xPb1-xBi1+xS3.

Understanding the mechanism that connects heat transport with crystal structures and order/disorder phenomena is crucial to develop materials with ultralow thermal conductivity (κ), for thermoelectric and thermal barrier applications, and requires the study of highly pure materials. We synthesized the n-type sulfide CuPbBi5S9 with an ultralow κ value of 0.6-0.4 W m-1 K-1 in the temperature range 300-700 K. In contrast to prior studies, we show that this synthetic sulfide does not exhibit the ordered gladite mineral structure but instead forms a copper-deficient disordered aikinite structure with partial Pb replacement by Bi, according to the chemical formula Cu1/3□2/3Pb1/3Bi5/3S3. By combining experiments and lattice dynamics calculations, we elucidated that the ultralow κ value of this compound is due to very low energy optical modes associated with Pb and Bi ions and, to a smaller extent, Cu. This vibrational complexity at low energy hints at substantial anharmonic effects that contribute to enhance phonon scattering. Importantly, we show that this aikinite-type sulfide, despite being a poor semiconductor, is a potential matrix for designing novel, efficient n-type thermoelectric compounds with ultralow κ values. A drastic improvement in the carrier concentration and thermoelectric figure of merit have been obtained upon Cl for S and Bi for Pb substitution. The Cu1-x□xPb1-xBi1+xS3 series provides a new, interesting structural prototype for engineering n-type thermoelectric sulfides by controlling disorder and optimizing doping.

Local-Disorder-Induced Low Thermal Conductivity in Degenerate Semiconductor Cu22Sn10S32.

S-based semiconductors are attracting attention as environmentally friendly materials for energy-conversion applications because of their structural complexity and chemical flexibility. Here, we show that the delicate interplay between the chemical composition and cationic order/disorder allows one to stabilize a new sphalerite derivative phase of cubic symmetry in the Cu-Sn-S diagram: Cu22Sn10S32. Interestingly, its crystal structure is characterized by a semiordered cationic distribution, with the Cu-Sn disorder being localized on one crystallographic site in a long-range-ordered matrix. The origin of the partial disorder and its influence on the electronic and thermal transport properties are addressed in detail using a combination of synchrotron X-ray diffraction, Mössbauer spectroscopy, transmission electron microscopy, theoretical modeling, and transport property measurements. These measurements evidence that this compound behaves as a pseudogap, degenerate p-type material with very low lattice thermal conductivity (0.5 W m-1 K-1 at 700 K). We show that localized disorder is very effective in lowering κL without compromising the integrity of the conductive framework. Substituting pentavalent Sb for tetravalent Sn is exploited to lower the hole concentration and doubles the thermoelectric figure of merit ZT to 0.55 at 700 K with respect to the pristine compound. The discovery of this semiordered cubic sphalerite derivative Cu22Sn10S32 furthers the understanding of the structure-property relationships in the Cu-Sn-S system and more generally in ternary and quaternary Cu-based systems.

OPTIMADE, an API for exchanging materials data.

The Open Databases Integration for Materials Design (OPTIMADE) consortium has designed a universal application programming interface (API) to make materials databases accessible and interoperable. We outline the first stable release of the specification, v1.0, which is already supported by many leading databases and several software packages. We illustrate the advantages of the OPTIMADE API through worked examples on each of the public materials databases that support the full API specification.

Vacancies in graphene: an application of adiabatic quantum optimization.

Quantum annealers have grown in complexity to the point that quantum computations involving a few thousand qubits are now possible. In this paper, with the intentions to show the feasibility of quantum annealing to tackle problems of physical relevance, we used a simple model, compatible with the capability of current quantum annealers, to study the relative stability of graphene vacancy defects. By mapping the crucial interactions that dominate carbon-vacancy interchange onto a quadratic unconstrained binary optimization problem, our approach exploits the ground state as well as the excited states found by the quantum annealer to extract all the possible arrangements of multiple defects on the graphene sheet together with their relative formation energies. This approach reproduces known results and provides a stepping stone towards applications of quantum annealing to problems of physical-chemical interest.

High-Throughput Computational Search for Half-Metallic Oxides.

Half metals are a peculiar class of ferromagnets that have a metallic density of states at the Fermi level in one spin channel and simultaneous semiconducting or insulating properties in the opposite one. Even though they are very desirable for spintronics applications, identification of robust half-metallic materials is by no means an easy task. Because their unusual electronic structures emerge from subtleties in the hybridization of the orbitals, there is no simple rule which permits to select a priori suitable candidate materials. Here, we have conducted a high-throughput computational search for half-metallic compounds. The analysis of calculated electronic properties of thousands of materials from the inorganic crystal structure database allowed us to identify potential half metals. Remarkably, we have found over two-hundred strong half-metallic oxides; several of them have never been reported before. Considering the fact that oxides represent an important class of prospective spintronics materials, we have discussed them in further detail. In particular, they have been classified in different families based on the number of elements, structural formula, and distribution of density of states in the spin channels. We are convinced that such a framework can help to design rules for the exploration of a vaster chemical space and enable the discovery of novel half-metallic oxides with properties on demand.

Vibrational spectral fingerprinting for chemical recognition of biominerals.

Pathologies associated with calcified tissue, such as osteoporosis, demand in vivo and/or in situ spectroscopic analysis to assess the role of chemical substitutions in the inorganic component. High energy X-ray or NMR spectroscopies are impractical or damaging in biomedical conditions. Low energy spectroscopies, such as IR and Raman techniques, are often the best alternative. In apatite biominerals, the vibrational signatures of the phosphate group are generally used as fingerprint of the materials although they provide only limited information. Here, we have used first principles calculations to unravel the complexity of the complete vibrational spectra of apatites. We determined the spectroscopic features of all the phonon modes of fluoroapatite, hydroxy-apatite, and carbonated fluoroapatite beyond the analysis of the phosphate groups, focusing on the effect of local corrections induced by the crystalline environment and the specific mineral composition. This provides a clear and unique reference to discriminate structural and chemical variations in biominerals, opening the way to a widespread application of non-invasive spectroscopies for in vivo diagnostics, and biomedical analysis.

Mechanical Properties of Chemically Modified Clay.

Serpentine clay minerals are found in many geological settings. The rich diversity, both in chemical composition and crystal structure, alters the elastic behavior of clay rocks significantly, thus modifying seismic and sonic responses to shaley sequences. Computation of the elastic properties is a useful tool to characterize this diversity. In this paper we use first principles methods to compare the mechanical properties of lizardite Mg3(Si2O5)(OH)4, a polymorph of serpentine family, with the new compounds derived by substituting Mg ions with isovalent elements from different chemical groups. New compounds are first selected according to chemical and geometrical stability criteria, then full elastic tensors, bulk and shear modulii, and acoustic velocities are obtained. Overall, the new compounds have a lower anisotropy and are less resistant to mechanical deformation compared to the prototype, thus providing valuable information regarding chemical composition and mechanical properties in these systems.

Copper-Rich Thermoelectric Sulfides: Size-Mismatch Effect and Chemical Disorder in the [TS4 ]Cu6 Complexes of Cu26 T2 Ge6 S32 (T=Cr, Mo, W) Colusites.

Herein, we investigate the Mo and W substitution for Cr in synthetic colusite, Cu26 Cr2 Ge6 S32 . Primarily, we elucidate the origin of extremely low electrical resistivity which does not compromise the Seebeck coefficient and leads to outstanding power factors of 1.94 mW m-1 K-2 at 700 K in Cu26 Cr2 Ge6 S32 . We demonstrate that the abnormally long iono-covalent T-S bonds competing with short metallic Cu-T interactions govern the electronic transport properties of the conductive "Cu26 S32 " framework. We address the key role of the cationic size-mismatch at the core of the mixed tetrahedral-octahedral complex over the transport properties. Two essential effects are identified: 1) only the tetrahedra that are directly bonded to the [TS4 ]Cu6 complex are significantly distorted upon substitution and 2) the major contribution to the disorder is localized at the central position of the mixed tetrahedral-octahedral complex, and is maximized for x=1, i.e. for the highest cationic size-variance, σ2 .

Machine Learning the Voltage of Electrode Materials in Metal-Ion Batteries.

Machine-learning (ML) techniques have rapidly found applications in many domains of materials chemistry and physics where large data sets are available. Aiming to accelerate the discovery of materials for battery applications, in this work, we develop a tool ( http://se.cmich.edu/batteries ) based on ML models to predict voltages of electrode materials for metal-ion batteries. To this end, we use deep neural network, support vector machine, and kernel ridge regression as ML algorithms in combination with data taken from the Materials Project database, as well as feature vectors from properties of chemical compounds and elemental properties of their constituents. We show that our ML models have predictive capabilities for different reference test sets and, as an example, we utilize them to generate a voltage profile diagram and compare it to density functional theory calculations. In addition, using our models, we propose nearly 5000 candidate electrode materials for Na- and K-ion batteries. We also make available a web-accessible tool that, within a minute, can be used to estimate the voltage of any bulk electrode material for a number of metal ions. These results show that ML is a promising alternative for computationally demanding calculations as a first screening tool of novel materials for battery applications.

High-Performance Thermoelectric Bulk Colusite by Process Controlled Structural Disordering.

High-performance thermoelectric bulk sulfide with the colusite structure is achieved by controlling the densification process and forming short-to-medium range structural defects. A simple and powerful way to adjust carrier concentration combined with enhanced phonon scattering through point defects and disordered regions is described. By combining experiments with band structure and phonons calculations, we elucidate, for the first time, the underlying mechanism at the origin of intrinsically low thermal conductivity in colusite samples as well as the effect of S vacancies and antisite defects on the carrier concentration. Our approach provides a controlled and scalable method to engineer high power factors and remarkable figures of merit near the unity in complex bulk sulfide such as Cu26V2Sn6S32 colusites.

Improved electronic structure and magnetic exchange interactions in transition metal oxides.

We discuss the application of the Agapito Curtarolo and Buongiorno Nardelli (ACBN0) pseudo-hybrid Hubbard density functional to several transition metal oxides. For simple binary metal oxides, ACBN0 is found to be a fast, reasonably accurate and parameter-free alternative to traditional DFT + U and hybrid exact exchange methods. In ACBN0, the Hubbard energy of DFT + U is calculated via the direct evaluation of the local Coulomb and exchange integrals in which the screening of the bare Coulomb potential is accounted for by a renormalization of the density matrix. We demonstrate the success of the ACBN0 approach for the electronic properties of a series technologically relevant mono-oxides (MnO, CoO, NiO, FeO, both at equilibrium and under pressure). We also present results on two mixed valence compounds, Co3O4 and Mn3O4. Our results for these binary oxides and all the materials we have investigated, obtained at the computational cost of a standard LDA/PBE calculation, are in excellent agreement with hybrid functionals, the GW approximation and experimental measurements.

Density of States for Warped Energy Bands.

Warping of energy bands can affect the density of states (DOS) in ways that can be large or subtle. Despite their potential for significant practical impacts on materials properties, these effects have not been rigorously demonstrated previously. Here we rectify this using an angular effective mass formalism that we have developed. To clarify the often confusing terminology in this field, "band warping" is precisely defined as pertaining to any multivariate energy function E(k) that does not admit a second-order differential at an isolated critical point in k-space, which we clearly distinguish from band non-parabolicity. We further describe band "corrugation" as a qualitative form of band warping that increasingly deviates from being twice differentiable at an isolated critical point. These features affect the density-of-states and other parameters ascribed to band warping in various ways. We demonstrate these effects, providing explicit calculations of DOS and their effective masses for warped energy dispersions originally derived by Kittel and others. Other physical and mathematical examples are provided to demonstrate fundamental distinctions that must be drawn between DOS contributions that originate from band warping and contributions that derive from band non-parabolicity. For some non-degenerate bands in thermoelectric materials, this may have profound consequences of practical interest.

First principles thermodynamical modeling of the binodal and spinodal curves in lead chalcogenides.

High-throughput ab initio calculations, cluster expansion techniques, and thermodynamic modeling have been synergistically combined to characterize the binodal and the spinodal decompositions features in the pseudo-binary lead chalcogenides PbSe-PbTe, PbS-PbTe, and PbS-PbSe. While our results agree with the available experimental data, our consolute temperatures substantially improve with respect to previous computational modeling. The computed phase diagrams corroborate that in ad hoc synthesis conditions the formation of nanostructure may occur justifying the low thermal conductivities in these alloys. The presented approach, making a rational use of online quantum repositories, can be extended to study thermodynamical and kinetic properties of materials of technological interest.

First principles NMR study of fluorapatite under pressure.

NMR is the technique of election to probe the local properties of materials. Herein we present the results of density functional theory (DFT) ab initio calculations of the NMR parameters for fluorapatite (FAp), a calcium orthophosphate mineral belonging to the apatite family, by using the GIPAW method (Pickard and Mauri, 2001). Understanding the local effects of pressure on apatites is particularly relevant because of their important role in many solid state and biomedical applications. Apatites are open structures, which can undergo complex anisotropic deformations, and the response of NMR can elucidate the microscopic changes induced by an applied pressure. The computed NMR parameters proved to be in good agreement with the available experimental data. The structural evaluation of the material behavior under hydrostatic pressure (from -5 to +100 kbar) indicated a shrinkage of the diameter of the apatitic channel, and a strong correlation between NMR shielding and pressure, proving the sensitivity of this technique to even small changes in the chemical environment around the nuclei. This theoretical approach allows the exploration of all the different nuclei composing the material, thus providing a very useful guidance in the interpretation of experimental results, particularly valuable for the more challenging nuclei such as (43)Ca and (17)O.