High-symmetry Lattice Research Articles

Enhanced Thermoelectric Performance and Low Thermal Conductivity in Cu2GeTe3 with Identified Localized Symmetry Breakdown

Highly efficient and eco-friendly thermoelectric generators rely on low-cost and nontoxic semiconductors with high symmetry and ultralow lattice thermal conductivity κL. We report the rational synthesis of the novel cubic (Ag, Se)-doped Cu2GeTe3 semiconductors. A localized symmetry breakdown (LSB) was found in the composition of Cu1.9Ag0.1GeTe1.5Se1.5 (i.e., CAGTS15) with an ultralow κL of 0.37 W/mK at 723 K, the lowest value outperforming all Cu2GeCh3 (Ch = S, Se, and Te). A joint investigation of synchrotron X-ray techniques identifies the LSB embedded into the cubic CAGTS15 host matrix. This LSB is an Ångström-scale orthorhombic symmetry unit, characteristic of multiple bond lengths, large anisotropic atomic displacements, and distinct local chemical coordination of anions. Computational results highlight that such an unusual orthorhombic symmetry demonstrates low-frequency phonon modes, which become softer and more predominant with increasing temperatures. This unconventional LSB promotes bond complexity and phonon scattering, highly beneficial for extraordinarily low lattice thermal conductivity.

Unconventional surface state pairs in a high-symmetry lattice with anti-ferromagnetic band-folding

Many complex magnetic structures in a high-symmetry lattice can arise from a superposition of well-defined magnetic wave vectors. These “multi-q” structures have garnered much attention because of interesting real-space spin textures such as skyrmions. However, the role multi-q structures play in the topology of electronic bands in momentum space has remained rather elusive. Here we show that the type-I anti-ferromagnetic 1q, 2q and 3q structures in an face-centered cubic sublattice with band inversion, such as NdBi, can induce unconventional surface state pairs inside the band-folding hybridization bulk gap. Our density functional theory calculations match well with the recent experimental observation of unconventional surface states with hole Fermi arc-like features and electron pockets below the Neel temperature. We further show that these multi-q structures have Dirac and Weyl nodes. Our work reveals the special role that band-folding from anti-ferromagnetism and multi-q structures can play in developing new types of surface states.

Processing of perovskite La0.9Sr0.1Ga0.8Mg0.2O3-δ electrolyte by glycine-nitrate combustion method

The doped LaGaO3 is a well-known intermediate-temperature electrolyte due to its high ionic conductivity and negligible electronic conductivity. However, the phase pure La0.9Sr0.1Ga0.8Mg0.2O3-δ (LSGM 9182) compound is not easy to be prepared because of its sensitive character with preparing process. In this work, the influence of evaporating temperature (glycine-nitrate combustion method) on the phase formation and physical property of LSGM 9182 is investigated systematically. The samples with different evaporating temperature 80 °C ≤ T ˂ 84 °C, 84 °C ≤ T ˂ 88 °C, 88 °C ≤ T ˂ 92 °C and T ≥ 92 °C was named as compound A, B, C and D. XRD results show that the phase pure compound can only be synthesized with the evaporating temperature 80 °C ≤ T ˂ 84 °C, the higher evaporating temperature, the higher content of LaSrGaO4 or LaSrGa3O7 impurity. Due to the slight change in composition, shoulders and splitting of some XRD reflections in phase pure compound A disappear for compound D, representing an transition from low-symmetry orthorhombic lattice to high-symmetry cubic lattice. Owing to the competiting contribution between crystal symmetry and impurity, the conductivity of compound D does not decrease almostly at low temperature, however, the influence of low conductive LaSrGaO4 prevails at high temperature, consequently, the conductivity of compound D decreases to a large degree at 800 °C. Above results suggest that evaporating temperature is an important parameter to prepare high quality LSGM electrolyte, suitable evaporating temperature supplies proper energy for chemical reaction and produce single perovskite phase compound finally.

Ring structure of selected two-dimensional procrystalline lattices.

Recent work has introduced the term "procrystalline" to define systems which lack translational symmetry but have an underlying high-symmetry lattice. The properties of five such two-dimensional (2D) lattices are considered in terms of the topologies of rings which may be formed from three-coordinate sites only. Parent lattices with full coordination numbers of four, five, and six are considered, with configurations generated using a Monte Carlo algorithm. The different lattices are shown to generate configurations with varied ring distributions. The different constraints imposed by the underlying lattices are discussed. Ring size distributions are obtained analytically for two of the simpler lattices considered (the square and trihexagonal nets). In all cases, the ring size distributions are compared to those obtained via a maximum entropy method. The configurations are analyzed with respect to the near-universal Lemaître curve (which connects the fraction of six-membered rings with the width of the ring size distribution) and three lattices are highlighted as rare examples of systems which generate configurations which do not map onto this curve. The assortativities are considered, which contain information on the degree of ordering of different sized rings within a given distribution. All of the systems studied show systematically greater assortativities when compared to those generated using a standard bond-switching method. Comparison is also made to two series of crystalline motifs which shown distinctive behavior in terms of both the ring size distributions and the assortativities. Procrystalline lattices are therefore shown to have fundamentally different behavior to traditional disordered and crystalline systems, indicative of the partial ordering of the underlying lattices.

Unconventional non-uniform local lattice distortion in dilute Ti-Mo solid solution

The substitutional solute atom induced local lattice distortion (LLD) in dilute metal solid solution was believed to be uniform because the solute atom was supposed to occupy the high symmetry lattice site without breaking the point group symmetry of the crystal lattice. Contrary to this conventional picture, we report in this paper that substitutional Mo atom in Ti-Mo solid solution occupies an off-center position instead of the high symmetry lattice site and leads to highly non-uniform LLD, as evidenced by our first principles calculations. The physics underlying the off-center occupation and non-uniform LLD are shown to be the Jahn-Teller splitting of the degenerated d states of Mo atom. With which, the solid-solutions suffering from non-uniform LLD are predicted. The non-uniform LLD challenges the application of classical solid solution hardening model based on uniform LLD and spherical stress tensor assumption to this kind of solid solutions. This work also questions the traditional view that elementary substitutional solute atoms in metal solid solutions should not induce anelastic relaxation and internal friction.

Defect-induced Dzyaloshinskii–Moriya interaction in a nanocrystalline two-phase alloy

The Dzyaloshinskii–Moriya interaction (DMI) is believed to be operative in low-symmetry crystal structures lacking space-inversion symmetry. However, already in 1963, Arrott pointed out that even in a high-symmetry lattice, where the DMI would normally vanish, this interaction is present in the vicinity of any lattice defect. Based on these considerations and recent theoretical work, first experimental studies of the impact of the DMI on the spin-polarized magnetic small-angle neutron scattering (SANS) of polycrystalline magnets exhibiting a large density of microstructural defects have been performed. They demonstrated that an asymmetry in the difference between the two polarized SANS cross sections is induced by the DMI in nanocrystalline terbium and holmium as well as in mechanically-deformed microcrystalline cobalt. Here, we present a more complicated case, the nanocrystalline magnetically-textured soft magnet Vitroperm (Fe73Si16B7Nb3Cu1), where the interface between the FeSi nanoparticles and the amorphous magnetic matrix serves as the defect. The SANS cross section exhibits the polarization-dependent asymmetric term originating from the DMI. The effect has a magnetic field dependence and is less pronounced at higher fields until it eventually vanishes at full saturation. The result supports the generic relevance of the DMI for the magnetic structure of defect-rich ferromagnets. Furthermore, it shows that polarized SANS is a particularly powerful tool for investigating defect-induced DMI, which is a consequence of the unique dependence of the SANS cross section on the chiral interactions.

Unconventional Non-Uniform Local Lattice Distortion in Dilute Ti-Mo Solid Solution

The substitutional solute atom induced local lattice distortion (LLD) in dilute metal solid solution was believed to be uniform because the solute atom was supposed to occupy the high symmetry lattice site without breaking the point group symmetry of the crystal lattice. Contrary to this conventional picture, we report in this paper that substitutional Mo atom in Ti-Mo solid solution occupies an off-center position instead of the high symmetry lattice site and leads to highly non-uniform LLD, as evidenced by our first principles calculations. The physics underlying the off-center occupation and non-uniform LLD are shown to be the Jahn-Teller splitting of the degenerated d states of Mo atom. With which, the solid-solutions suffering from non-uniform LLD are predicted. The non-uniform LLD challenges the application of classical solid solution hardening model based on uniform LLD and spherical stress tensor assumption to this kind of solid solutions. This work also questions the traditional view that elementary substitutional solute atoms in metal solid solutions should not induce anelastic relaxation and internal friction.

A general strategy for tailoring upconversion luminescence in lanthanide-doped inorganic nanocrystals through local structure engineering.

A local structure around lanthanide (Ln3+) emitters in Ln3+-doped upconversion nanocrystals (UCNCs) is of fundamental importance in tailoring their upconversion luminescence (UCL) features. However, a general strategy responsible for the local-structure-dependent UCL in Ln3+-doped UCNCs has not been conclusively established to date. Herein, we report a new class of alkaline zirconium fluoride-based Yb3+/Er3+ co-doped UCNCs featuring a diversity of crystallographic structures for Ln3+ ion doping, which thereby allow us to thoroughly understand the origin underlying the local-structure-dependent UCL of the Er3+ ion for the first time. We reveal that the high-symmetry crystal lattice of Yb3+/Er3+ co-doped UCNCs may incur the large UCL red-to-green intensity ratio of Er3+ regardless of their identical elemental compositions. In combination with the first-principles calculations, we show that such local-structure-dependent UCL of Er3+ is primarily due to the varied electronic band structures induced by the Yb3+/Er3+ doping in different crystallographic structures of alkaline zirconium fluorides. These findings may open up a new avenue for constructing high-quality UCNCs with a tailored UCL profile and lifetime for diverse applications.

Predicting displacements of octahedral cations in ferroelectric perovskites using machine learning.

In ferroelectric perovskites, displacements of cations from the high-symmetry lattice positions in the paraelectric phase break the spatial inversion symmetry. Furthermore, the relative magnitude of ionic displacements correlate strongly with ferroelectric properties such as the Curie temperature. As a result, there is interest in predicting the relative displacements of cations prior to experiments. Here, machine learning is used to predict the average displacement of octahedral cations from its high-symmetry position in ferroelectric perovskites. Published octahedral cation displacements data from density functional theory (DFT) calculations are used to train machine learning models, where each cation is represented by features such as Pauling electronegativity, Martynov-Batsanov electronegativity and the ratio of valence electron number to nominal charge. Average displacements for ten new octahedral cations for which DFT data do not exist are predicted. Predictions are validated by comparing them with new DFT calculations and existing experimental data. The outcome of this work has implications in the design and discovery of novel ferroelectric perovskites.

Crystalline field effect and magnetic ordering in the heavy fermion Kondo lattice Ce6Pd12In5

Results of magnetic, specific heat, electric and thermal transport studies carried out on the novel hexagonal-type structure Ce6Pd12In5 compound, with a unique site for Ce, two sites for In and four sites for Pd are reported. The compound exhibits long-range order, probably of antiferromagnetic type, below TN=1.6K in spite of a moment reducing Kondo effect acting on the magnetic Ce3+ ions. A strong influence of magnetic field on the low temperature dependencies of susceptibility, specific heat and electrical resistivity is observed. The crystal-electric field effect, CEF, plays an influential role in the ground state of this compound. The CEF parameters have been estimated. Based upon the low-temperature specific heat we observe heavy fermion behavior with the electronic specific heat coefficient that is enhanced to the value of γ=132mJ/Ce-molK2. In the electrical resistivity, a logarithmic character ρ4f(T)∼-lnT is observed that arises from incoherent Kondo scattering. Towards low temperature this behavior evolves into Kondo lattice formation with a coherence temperature Tcoh≃5.3K, before long-range order takes place. We propose that Ce6Pd12In5 presents a new case study for competing Kondo and magnetic ordering in a high-symmetry lattice, with CEF and magnetocrystalline anisotropy further impacting upon the cooperative magnetic behavior.

Two-Dimensional Self-Assembly of a Symmetry-Reduced Tricarboxylic Acid

Investigations of the self-assembly of simple molecules at the solution/solid interface can provide useful insight into the general principles governing supramolecular chemistry in two dimensions. Here, we report on the assembly of 3,4',5-biphenyl tricarboxylic acid (H3BHTC), a small hydrogen bonding unit related to the much-studied 1,3,5-benzenetricarboxylic acid (trimesic acid, TMA), which we investigate using scanning tunneling microscopy (STM) and density functional theory (DFT) calculations. STM images show that H3BHTC assembles by itself into an offset zigzag chain structure that maximizes the surface molecular density in favor of maximizing the number density of strong cyclic hydrogen bonds between the carboxylic groups. The offset geometry creates "sticky" pores that promote solvent coadsorption. Adding coronene to the molecular solution produces a transformation to a high-symmetry host-guest lattice stabilized by a dimeric/trimeric hydrogen bonding motif similar to the TMA flower structure. Finally, we show that the H3BHTC lattice firmly immobilizes the guest coronene molecules, allowing for high-resolution imaging of the coronene structure.

Polymorphism in Halogen–Ethane Derivatives: CCl3–CF2Cl and CF3–CF2Cl

Molecular crystals of halogen–ethane derivatives C2X6–nYn (X = Cl, Y = F) are known to display order–disorder phase transitions involving changes of the translational, orientational, and conformational order. The appearance of a high-temperature orientationally disordered phase with a high symmetry lattice is expected for this set of compounds in view of their “pseudospherical” molecular geometry. In this work, we present a study of polymorphism of the compounds 1,1,1,2-tetrachloro-2,2-difluoroethane (CCl3–CF2Cl) and 1-chloro-1,1,2,2,2-pentafluoroethane (CF3–CF2Cl), in which conformational disorder is not present, by combining neutron (D2B and D1B instruments at the Laue-Langevin Institute) and X-ray scattering experiments. We show that despite the close molecular shapes and molecular structures of both compounds, strong differences concerning the disorder appear in the low-temperature phase. The low-temperature phase for CF3–CF2Cl is found to be fully ordered, with a monoclinic P21/n structure (Z = 4), while that of CCl3–CF2Cl is found to be orthorhombic Pmna (Z = 4) with a disorder concerning one Cl and one F sites, each one with a fractional occupancy of 50%. Details related to the high-temperature orientationally disordered phases (both body-centered-cubic) are also given.

Probing the Out-of-Plane Distortion of Single Point Defects in Atomically Thin Hexagonal Boron Nitride at the Picometer Scale

Crystalline systems often lower their energy by atom displacements from regular high-symmetry lattice sites. We demonstrate that such symmetry lowering distortions can be visualized by ultrahigh resolution transmission electron microscopy even at single point defects. Experimental investigation of structural distortions at the monovacancy defects in suspended bilayers of hexagonal boron nitride (h-BN) accompanied by first-principles calculations reveals a characteristic charge-induced pm symmetry configuration of boron vacancies. This symmetry breaking is caused by interlayer bond reconstruction across the bilayer h-BN at the negatively charged boron vacancy defects and results in local membrane bending at the defect site. This study confirms that boron vacancies are dominantly present in the h-BN membrane.

Effect of impurities in high-symmetry lattice positions on the local density of states and conductivity of graphene

Motivated by quantum chemistry calculations, showing that molecular adsorption in graphene takes place on preferential sites of the honeycomb lattice, we study the effect of an isolated impurity on the local electronic properties of a graphene monolayer, when the impurity is located on a sitelike, bondlike, or hollowlike position. We evaluate the local density of states (LDOS) as a function of energy on the impurity and on its neighboring sites, as well as in reciprocal space, at an energy corresponding to a bound state, in the three cases of interest. The latter study may be relevant to interpret the results of Fourier-transformed scanning tunneling spectroscopy, as they show which states mostly contribute to impurity-induced variations in the LDOS. We also estimate, semianalytically, the dependence of the condition for having a low-energy bound state on the impurity potential strength and width. Such results are then exploited to obtain the quasiparticle lifetime and the static conductivity in graphene in the dilute impurity limit. In particular, we recover a sublinear dependence of the conductivity on the carrier concentration as a generic impurity effect.

Incorporating anisotropic electronic structure in crystallographic determination of complex metals: iron and plutonium

Anisotropic electronic structure is incorporated in crystallographic determination of the structure of ferromagnetic Fe, δ-Pu and a Pu–3.7 at% Ga alloy. This is achieved by using anisotropic aspects of the inter-atomic bonds as a motif in combination with the high-symmetry cubic lattice. In the case of Fe, it is shown that ferromagnetic ordering reduces the symmetry of the structure from body centred cubic to body centred tetragonal with an associated effect on elasticity. Thus, the ferromagnetic α- and paramagnetic β-phase are separate and unique phases that should both be addressed on the Fe phase diagrams. In the case of Pu, first-principles density-functional theory calculations are used to show that the bond strengths between the 12 nearest neighbours in δ-plutonium vary greatly. Employing the calculated bond strengths as a motif in crystallographic determination yields a structure with the monoclinic space group Cm for δ-Pu rather than face-centred cubic . The reduced space group for δ-Pu illuminates why it is the only metal with a monoclinic ground state, why lattice distortions of the metal are viable and has implications for the behaviour of the material as it ages due to self-irradiation. Results for a Pu–3.7 at% Ga alloy show that the nearest neighbour bond strengths around a Ga atom are more uniform – a result that explains why Ga stabilizes face-centred cubic δ-Pu. This paper illustrates how an expansion of classical crystallography, which accounts for anisotropic electronic and magnetic structure, can explain complex materials in a novel way.

Local Spectroscopy and Atomic Imaging of Tunneling Current, Forces, and Dissipation on Graphite

Theory predicts that the currents in scanning tunneling microscopy (STM) and the attractive forces measured in atomic force microscopy (AFM) are directly related. Atomic images obtained in an attractive AFM mode should therefore be redundant because they should be similar to STM. Here, we show that while the distance dependence of current and force is similar for graphite, constant-height AFM and STM images differ substantially depending on the distance and bias voltage. We perform spectroscopy of the tunneling current, the frequency shift, and the damping signal at high-symmetry lattice sites of the graphite (0001) surface. The dissipation signal is about twice as sensitive to distance as the frequency shift, explained by the Prandtl-Tomlinson model of atomic friction.

Nonorthogonal tight-binding model for germanium

We present a pair of nonorthogonal tight-binding (TB) models for germanium within the NRL-TB approach. One uses an ${\mathrm{sp}}^{3}$ basis, and is optimized for total-energy calculations by fitting to the total energy and band structures of several high-symmetry lattice structures. The other uses an ${\mathrm{sp}}^{3}{d}^{5}$ basis to accurately reproduce the diamond lattice band structure, including three conduction bands. We present tests of the ${\mathrm{sp}}^{3}$ TB model on bulk properties, including high-symmetry lattice structure energies and volumes and the diamond lattice elastic constants, phonons, and band structure. We also present results for point defect formation and relaxation energies and low index surface energies and stresses, many of which have not been calculated using the density-functional theory (DFT), as well as some medium size clusters. Taking advantage of the computational efficiency of the TB approach, we go beyond the capabilities of standard density-functional theory, combining it with molecular dynamics to simulate finite temperature properties of Ge. We get good agreement with experiment for the atomic mean-squared displacement and the melting point approximated using the Lindemann criterion, as well as the linear thermal-expansion coefficient. In another demonstration of the efficiency of the TB approach, we present results for the structure and electronic properties of a high angle twist grain boundary (GB). In agreement with DFT simulation we see a range of structures with comparable energies, all with electronic states deep in the band gap. In contrast to previous work we find some different geometries with perfect fourfold coordination of all atoms in the GB. Despite the perfect coordination, these structures also have deep electronic states in the gap, indicating that the GB will be electrically active.

The [Cu(8)Br(15)](6)(-) Ion, A Crystal-Stabilized High-Symmetry Mixed-Valence Copper Complex with a Linear Halogen Bridge.

The [Cu8Br15]6- ion in green crystalline (MePh3P)6[Cu8Br15] is shown by X-ray crystallography to have the structure [Br3(μ3-Br4Cu4)(μ2-Br)(μ3-Br4Cu4)Br3]6- derived from two Cu4Br8 cubane units. The unusual geometry and charge of the anion are determined by the high-symmetry (space group Pa3) lattice of cations, maintained by phenyl···phenyl interactions, and interacting with the anion by C−H···Br hydrogen bonds.

REVIEW: THE CONCEPT OF VIBRONIC INTERACTIONS IN CRYSTAL STEREOCHEMISTRY OF TRANSITION METAL COMPOUNDS

Abstract A review of recent achievements in the application of the theory of vibronic coupling to stereochemical problems of transition metal compounds is given. After the formulation of the concept of vibronic interactions relevant to stereochemistry, its general validity is discussed, and it is shown that in the crystal state long-range forces alone cannot produce distortions of high-symmetry lattice configurations. The latter may become unstable due to the vibronic coupling which is of local origin. For ferroelectric distortions in perovskite-type crystals this result is confirmed by quite a number of different experimental data; it casts heavy doubts on the very existence of displacive phase transitions. Among other stereochemical problems solved by means of the vibronic approach, the following are briefly considered: local distortions produced by d electrons using the CuCl5 3- vs ZnCl5 3- polyhedra in similar crystals; crystal implications in the effects of plasticity, distortion isomers, and tempera...

Experimental and theoretical evidence for a new universality class in FeF3: A 3D lattice with frustrated Heisenberg spins (abstract)

The pyrochlore form of FeF3 is a Heisenberg antiferromagnet [TN=15.2(1)K], in which the Fe3+ atoms form a high-symmetry lattice of corner-sharing tetrahedra. The low-temperature magnetic structure is noncollinear with four sublattices oriented 109° from each other. Neutron diffraction was used to determine the critical exponent, β=0.17(2), which does not correspond to any known universality class. Monte Carlo simulations with finite-size scaling analysis confirm the measured value of β and also provide the exponent ν=0.34(4). The existence of this new universality class supports Kawamura’s hypothesis that critical properties of a system depend on the symmetry properties (and not just the dimensionality) of the order parameter.