Multi-scale chemo-mechanical evolution during crystallization of mixed conducting SrTi[subscript 0.6
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Buckner, Haley B.↗
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Results for “Polyhedra”
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Lipid vesicles induced ordered nanoassemblies of Janus nanoparticles
Since many advanced applications require specific assemblies of nanoparticles (NPs), considerable efforts have been made to fabricate nanoassemblies with specific geometries. Although nanoassemblies can be fabricated through top-down approaches, recent advances show that intricate nanoassemblies can also be obtained through self-assembly, mediated for example by DNA strands. Here, we show, through extensive molecular dynamics simulations, that highly ordered self-assemblies of NPs can be mediated by their adhesion to lipid vesicles (LVs). Specifically, Janus NPs are considered so that the amount by which they are wrapped by the LV is controlled. The specific geometry of the nanoassembly is the result of effective curvature-mediated repulsion between the NPs and the number of NPs adhering to the LV. Further, the NPs are arranged on the LV into polyhedra which satisfy the upper limit of Euler's polyhedral formula, including several deltahedra and three Platonic solids, corresponding to the tetrahedron, octahedron, and icosahedron.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Systematic study of short- and long-range correlations in RE 3 TaO 7 weberite-type compounds by neutron total scattering and X-ray diffraction
The atomic structures of the lanthanide tantalates, Ln 3 TaO 7 , series (Ln = Pr, Tb, Dy, Ho, Tm, Yb) were systematically investigated using total scattering techniques. High-energy X-ray and neutron diffraction analysis revealed that the long-range structures can be grouped into three distinct families: (1) ordered Cmcm (Ln = Pr), (2) ordered Ccmm (Ln = Tb, Dy, Ho), and (3) disordered, defect-fluorite Fm$\bar{3}$m (Ln = Ho, Tm, Yb). These findings help to clarify the symmetry discrepancy for the already reported long-range structures in the literature. The short-range analysis of neutron total scattering data via pair distribution functions reveals a high degree of structural heterogeneity across length scales for all compounds, with distinct local atomic arrangements that are not fully captured by the average, long-range structure. The short-range structures at the level of coordination polyhedra are better captured by a set of alternative non-centrosymmetric structural models: (1) C2cm, (2) C222 1 , and (3) C2mm. This establishes a short-range multiferroic character for weberite-type tantalates because ferroelectric interactions compete with magnetic correlations. These ferroelectric interactions are particularly pronounced for the disordered compounds Tm 3 TaO 7 and Yb 3 TaO 7 . In conclusion, the structural differences among the three families are the result of changes in TaO 6 polyhedral tilt (transition between families 1 and 2) and dipolar interactions of off-centered Ta cations (transition between families 2 and 3).
36 MATERIALS SCIENCE↗
Synthesis of a series of rare-earth-based multi-anion chalcogenide iodides RE 3 Si 2 Se x S 8− x I (RE = La, Ce, Pr, and Nd) using the flux-assisted boron–chalcogen mixture method
Single crystals and polycrystalline powders of rare earth mixed chalcogenide iodides La 3 Si 2 Se 1.21 S 6.79 I, Ce 3 Si 2 Se 1.39 S 6.61 I, Pr 3 Si 2 Se 1.22 S 6.78 I, and Nd 3 Si 2 Se 1.18 S 6.82 I were prepared using the reactive flux-assisted boron–chalcogen mixture (BCM) method at 850 °C. All compounds crystallized in the monoclinic crystal system, space group C2/c (space group number 15). The series adopts the La 3 Si 2 O 8 Cl structure type, containing isolated SiQ 4 tetrahedra connected by REQ 8 (RE = La, Ce, Pr and Nd) polyhedra; this arrangement creates tunnels that are filled by I atoms. The partial substitution of S by Se was carried out to modulate the optical properties. Phase pure samples and uniform solid solutions were obtained for all compositions as determined using powder X-ray diffraction patterns. Polycrystalline powders were used for physical property measurements, including magnetic susceptibility and UV-Vis diffuse reflectance. The solid-state UV-Vis data for the polycrystalline La 3 Si 2 Se 1.21 S 6.79 I, Ce 3 Si 2 Se 1.39 S 6.61 I, and Pr 3 Si 2 Se 1.22 S 6.78 I samples revealed band gaps of E g = 2.5(1), 2.2(1), and 2.3(1) eV, typical of semiconductors. Magnetic measurements indicated that Ce 3 Si 2 Se 1.39 S 6.61 I and Nd 3 Si 2 Se 1.18 S 6.82 I exhibit paramagnetic behavior with slightly negative Weiss constants θ = −25 and −38. The photoluminescence spectrum of Ce 3 Si 2 Se 1.39 S 6.61 I exhibits a broad emission band around ∼493 nm.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
K–Co–Mo–S x chalcogel: high-capacity removal of Pb 2+ and Ag + and the underlying mechanisms
Chalcogenide-based aerogels, known as chalcogels, represent a novel class of nanoparticle-based porous amorphous materials characterized by high surface polarizability and Lewis base properties, exhibiting promising applications in clean energy and separation science. This work presents a K–Co–Mo–S x (KCMS) chalcogel as a highly efficient sorbent for heavy metal ions and details its sorption mechanisms. Its incoherent structure comprises Mo 2 V (S 2 ) 6 and Mo 3 IV S(S 6 ) 2 anion-like clusters with four- and six-coordinated Co–S polyhedra, forming a Co–Mo–S covalent network that hosts K + ions through electrostatic attraction. The interactions of KCMS with heavy metal ions, particularly Pb 2+ and Ag + , reveal that KCMS is exceptionally effective in removing these ions from ppm concentrations down to trace levels (≤5 ppb). KCMS rapidly removes Ag + (≈81.7%) and Pb 2+ (≈99.5%) within five minutes, achieving >99.9% removal within an hour, with a distribution constant K d ≥10 8 mL g -1 . KCMS exhibits an impressive removal capacity of 1378 mg g -1 for Ag + and 1146 mg g -1 for Pb 2+ , establishing it as one of the most effective materials known to date for heavy metal removal. This material is also effective for the removal of Ag + and Pb 2+ along with Hg 2+ , Ni 2+ , Cu 2+ , and Cd 2+ from various water sources even in the presence of highly concentrated and chemically diverse cations, anions, and organic species. Analysis of the post-interacted KCMS by synchrotron X-ray pair distribution function (PDF), X-ray photoelectron spectroscopy (XPS) and energy dispersive X-ray spectroscopy (EDS) revealed that the sorption of Pb 2+ , Ag + , and Hg 2+ mainly occurs by the exchange of K + and Co 2+ . Despite being amorphous, this material exhibits unprecedented ion-exchange mechanisms both for the ionically and covalently bound K + and Co 2+ , respectively. In conclusion, this discovery advances our knowledge of amorphous gels and guides material synthesis principles for the highly selective and efficient removal of heavy metal ions from water.
54 ENVIRONMENTAL SCIENCES↗
Resolving local ordering and structure in Mn x Ge 1- x Te alloys through thermodynamic ensembles of pair distribution functions
Characterizing local bonding environments in complex materials is essential for understanding and optimizing their properties. Equally as important is the ability to predict local motifs as a function of synthesis conditions, enhancing chemists’ ability to design properties into materials. In this study, we present an approach to leverage statistical mechanics to generate temperature- and energy-informed ensemble averaged pair distribution functions (PDFs). This method, which we have named Thermodynamic Ensemble Averages of PDFs for Ordering and Transformations (TEAPOT), utilizes density functional theory (DFT) to relax supercells while incorporating energetic penalties for local order, enabling accurate and computationally efficient analysis of local structure. We apply this method to the neutron PDF measurements of the pseudobinary MnTe–GeTe (MGT) alloy, demonstrating its capability to resolve complex local distortions and chemical ordering. Our results reveal detailed insights into phase transformations and local distortions driven by Mn substitution. For compositions that globally present as rock salt, our analysis reveals that Ge coordination geometry is heavily impacted by synthesis temperature. We propose that high temperature synthesis conditions promote a lowered Ge polyhedra distortion, promoting high charge carrier mobility due to the alignment of local and global structure. Incorporating statistical mechanics and computation into experimental analysis thus guides synthesis of tailored local structure.
36 MATERIALS SCIENCE↗
Mechanochemical α to β phase transition of U 3 O 8
Recognized as the most stable phase of uranium oxide, α-U 3 O 8 is widely used throughout the nuclear fuel cycle for safe storage and transportation. There is, however, a lack of understanding of the thermodynamic relationship between α-U 3 O 8 and its polymorph, β-U 3 O 8 . This research contributes new knowledge regarding the kinetics and mechanism of a previously described mechanochemical phase transition between the α- and β-U 3 O 8 polymorphs to improve the understanding of their thermodynamic relationship. In this work, tumble milling of α-U 3 O 8 using different milling media shows an ingrowth of the β-phase over time, with an observed correlation between media density, percent conversion and lattice strain. Anisotropic peak broadening observed within collected X-ray diffraction powder patterns suggests the preservation of uranium polyhedral layered sheets throughout the milling process. Preservation of the sheets implies a shear-induced slip mechanism occurring through in-plane shifting of uranium polyhedra along lattice planes perpendicular to the polyhedral sheets.
Roach, Jordan M. [Oak Ridge National Laboratory (O↗
ReaxFF molecular dynamics simulations of electrolyte–water systems at supercritical temperature
We have performed ReaxFF molecular dynamics simulations of alkali metal–chlorine pairs in different water densities at supercritical temperature (700 K) to elucidate the structural and dynamical properties of the system. The radial distribution function and the angular distribution function explain the inter-ionic structural and orientational arrangements of atoms during the simulation. The coordination number of water molecules in the solvation shell of ions increases with an increase in the radius of ions. We find that the self-diffusion coefficient of metal ions increases with a decrease in density under supercritical conditions due to the formation of voids within the system. The hydrogen bond dynamics has been interpreted by the residence time distribution of various ions, which shows Li+ having the highest water retaining capability. The void distribution within the system has been analyzed by using the Voronoi polyhedra algorithm providing an estimation of void formation within the system at high temperatures. We observe the formation of salt clusters of Na+ and K+ at low densities due to the loss of dielectric constants of ions. The diffusion of ions gets altered dramatically due to the formation of voids and nucleation of ions in the system.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Structure–property relations of binary ferrite melts
Molten ferrite systems are used in the smelting and refining processes in steelmaking, to reduce the loss of metals in slags and to accelerate reaction rates. Here, high-energy x-ray diffraction experiments have been performed on aerodynamically levitated molten spheres of 43BaO–57FeO X and 43SrO–57FeO X at 1873 K using laser beam heating. The composition was varied within the range of x = 1–1.5 by changing the oxygen partial pressure of the levitation gas. The corresponding x-ray pair distribution functions have been interpreted using empirical potential structure refinement (EPSR) modeling. In oxygen-rich melts (x = 1.5), our EPSR models indicate very similar structures for the different alkaline-earth liquids, with both the Ba–O and Sr–O coordination numbers to be ∼8.4 and the total Fe–O coordination numbers ∼5.7. However, our models show that in reducing environments, the Fe 3+ and Fe 2+ ions exhibit very different behaviors in the Ba- and Sr-ferrite liquids. In the Ba-ferrite melt, the Fe 3+ –O coordination number decreases from 5.7 (at x = 1.5) to 5.2 (at x = 1.07), whereas Fe 2+ –O remains constant at ∼5.0 across the same compositional range. In the Sr melts, both the Fe 2+ –O and Fe 3+ –O coordination numbers rise from ∼5.7 (at x = 1.5) to 6.3 (at x = 1.07). All models show the structures to be heterogeneous with intertwined nanometer sized clusters or channels of Ba/Sr–O and Fe–O polyhedra that grow as oxygen content is reduced. Changes in the viscosity and electrical properties are interpreted in terms of the number of bridging and non-bridging oxygens associated with FeO 4 tetrahedra and concentration of charge carriers, respectively.
Benmore, Chris J. [Argonne National Laboratory (AN↗
The origin of the Stokes–Einstein relation in simple dense liquids
Here, we investigate the origin of the universal relation between structural relaxation and diffusion in simple dense liquids, known as the Stokes–Einstein (SE) relation. The fact that this relation, originally derived from a hydrodynamic model of a macroscopic particle in a viscous medium, can describe the microscopic-scale liquid dynamics still eludes understanding. We introduce a new universal measure of structural relaxation in a system of N identical particles based on an explicit decomposition of the configuration space into N! congruent convex polyhedra. This measure makes it possible to quantify the correlation between two distinct particle configurations in terms of their minimal Euclidean distance, optimized with respect to particle permutations. Using this measure alongside a model of independent random walkers under the single-occupancy constraint, we derive a master equation that quantifies the SE relation. It allows us to demonstrate that the universal relation between structural relaxation and diffusion in simple dense liquids is caused by two conditions: (a) the confinement of the dominant density fluctuations to the first coordination shell, manifested by de Gennes narrowing, and (b) Gaussianity of the diffusion process; the former is shown to be violated in low-density fluids, and the latter is known to be violated in supercooled liquids.
Physics - Condensed matter physics↗
A survey of nonlinear robust optimization
Robust optimization (RO) has attracted great attention from the optimization community over the past decade. RO is dedicated to solving optimization problems subject to uncertainty: design constraints must be satisfied for all the values of the uncertain parameters within a given uncertainty set. Uncertainty sets may be modeled as deterministic sets (boxes, polyhedra, ellipsoids), in which case the RO problem may be reformulated via worst-case analysis, or as families of distributions. The challenge of RO is to reformulate or approximate robust constraints so that the uncertain optimization problem is transformed into a tractable deterministic optimization problem. Most reformulation methods assume linearity of the robust constraints or uncertainty sets of favorable shape, which represents only a fraction of real-world applications. This survey addresses nonlinear RO and includes problem formulations and applications, solution approaches, and available software with code samples.
97 MATHEMATICS AND COMPUTING↗
Hard x-ray methods for studying the structure of amorphous thin films and bulk glassy oxides
High-energy photon diffraction minimizes many of the corrections associated with laboratory x-ray diffractometers, and enables structure factor measurements to be made over a wide range of momentum transfers. The method edges us closer toward an ideal experiment, in which coordination numbers can be extracted without knowledge of the sample density. Three case studies are presented that demonstrate new hard x-ray methods for studying the structure of glassy and amorphous materials. First, the methodology and analysis of high-energy grazing incidence on thin films is discussed for the case of amorphous In 2 O 3 . Additionally, the connectivity of irregular InO 6 polyhedra are shown to exist in face-, edge- and corner-shared configurations in the approximate ratio of 1:2:3. Secondly, the technique of high-energy small and wide angle scattering has been carried out on laser heated and aerodynamically levitated samples of silica-rich barium silicate (20BaO:80SiO 2 ), from the single phase melt at 1500 C-o to the phase separated glass at room temperature. Based on Ba-O coordination numbers of 6 to 7, it is argued that the although the potential of Ba is ionic, it is weak enough to cause the liquid-liquid immiscibility to become metastable. Lastly, high-energy small and wide angle scattering has also been applied to high water content (up to 12 wt.%) samples of hydrous SiO 2 glass quenched from 1500 C-o at 4 GPa. An increase of Si 1 O 2 correlations at 4.3 angstrom is found to be consistent with an increase in the population of three-membered SiO 4 rings at the expense of larger rings.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Rapid prototyping of arbitrary 2D and 3D wireframe DNA origami
Wireframe DNA origami assemblies can now be programmed automatically from the top-down using simple wireframe target geometries, or meshes, in 2D and 3D, using either rigid, six-helix bundle (6HB) or more compliant, two-helix bundle (DX) edges. While these assemblies have numerous applications in nanoscale materials fabrication due to their nanoscale spatial addressability and high degree of customization, no easy-to-use graphical user interface software yet exists to deploy these algorithmic approaches within a single, standalone interface. Further, top-down sequence design of 3D DX-based objects previously enabled by DAEDALUS was limited to discrete edge lengths and uniform vertex angles, limiting the scope of objects that can be designed. Here, we introduce the open-source software package ATHENA with a graphical user interface that automatically renders single-stranded DNA scaffold routing and staple strand sequences for any target wireframe DNA origami using DX or 6HB edges, including irregular, asymmetric DX-based polyhedra with variable edge lengths and vertices demonstrated experimentally, which significantly expands the set of possible 3D DNA-based assemblies that can be designed. ATHENA also enables external editing of sequences using caDNAno, demonstrated using asymmetric nanoscale positioning of gold nanoparticles, as well as providing atomic-level models for molecular dynamics, coarse-grained dynamics with oxDNA, and other computational chemistry simulation approaches.
59 BASIC BIOLOGICAL SCIENCES↗
Hierarchy among the crystal lattice, charge density wave, and superconducting orders in transition metal dichalcogenides
Using high-energy x-ray scattering and large-scale three-dimensional (3D) structure modeling, in this study we investigate the relationship between the crystal lattice, charge density wave (CDW), and superconducting (SC) orders in transition metal dichalcogenides (TMDs). In particular, we systematically substitute Te for Se in Ta-Se-Te solid solutions, determine changes in their crystal lattice, and relate them to changes in the CDW transition temperature, $T_{CDW}$, and SC critical temperature, $T_c$ . We find that strong lattice distortions such as buckling of Ta layers are detrimental to the CDW and SC orders. The presence of a perfect lattice order in two dimensions is a prerequisite to the emergence of CDWs but insufficient to achieve a SC ordered state. For the SC order to emerge, the Ta sublattice should also appear periodic in 3D. Local chemical disorder may promote the SC order, and the perfectness of Ta coordination polyhedra is a factor contributing to its strength. A hierarchical relationship among the crystal lattice, CDW, and SC orders thus appears to exist in TMDs in a sense that different degrees of crystal lattice order-disorder promote and maintain the CDW and SC orders to a different extent, offering an opportunity to control the latter through modifying the former by rational design. Our findings are a step towards a better understanding of the correlation between lattice and electronic degrees of freedom in TMDs. We also demonstrate an efficient experimental approach to study them in fine detail.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Motif magnetism and quantum many-body scars
In this work, we generally expect quantum systems to thermalize and satisfy the eigenstate thermalization hypothesis (ETH), which states that finite-energy-density eigenstates are thermal. However, some systems, such as many-body localized systems and systems with quantum many-body scars, violate ETH and have high-energy athermal eigenstates. In systems with scars, most eigenstates thermalize, but a few atypical scar states do not. Scar states can give rise to a periodic revival when time-evolving particular initial product states, which can be detected experimentally. Recently, a family of spin Hamiltonians was found with magnetically ordered three-colored eigenstates that are quantum many-body scars [Lee et al., Phys. Rev. B 101, 241111(R) (2020)]. These models can be realized in any lattice that can be tiled by triangles, such as the triangular or kagome lattices, and have been shown to have close connections to the physics of quantum spin liquids in the Heisenberg kagome antiferromagnet. In this paper, we introduce a generalized family of n-colored Hamiltonians with “spiral colored” eigenstates made from n-spin motifs such as polygons or polyhedra. We show how these models can be realized in many different lattice geometries and provide numerical evidence that they can exhibit quantum many-body scars with periodic revivals that can be observed by time-evolving simple product states. The simple structure of these Hamiltonians makes them promising candidates for future experimental studies of quantum many-body scars.
36 MATERIALS SCIENCE↗
Full-potential KKR within the removed-sphere method: A practical and accurate solution to the Poisson equation
Here an efficient and accurate generalization of the removed-sphere method (RSM) to solve the Poisson equation for total charge density in a solid with space-filling convex Voronoi polyhedra (VPs) and any symmetry is presented. The generalized RSM avoids the use of multipoles and VP shape functions for cellular integrals, which have associated ill-convergent large, double-internal L sums in spherical-harmonic expansions, so that fast convergence in single-L sums is reached. Our RSM adopts full Ewald formulation to work for all configurations or when symmetry breaking occurs, such as for atomic displacements or elastic constant calculations. The structure-dependent coefficients A L that define RSM can be calculated once for a fixed structure and speed up the whole self-consistent-field procedure. The accuracy and rapid convergence properties are confirmed using two analytic models, including the Coulomb potential and energy. We then implement the full-potential RSM using the Green's function Korringa-Kohn-Rostoker (KKR) method for real applications and compare the results with other first-principle methods and experimental data, showing that they are equally as accurate.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Patterning of multicomponent elastic shells by gaussian curvature
Recent findings suggest that shell protein distribution and the morphology of bacterial microcompartments regulate the chemical fluxes facilitating reactions which dictate their biological function. Here, we explore how the morphology and component patterning are coupled through the competition of mean and gaussian bending energies in multicomponent elastic shells that form three-component irregular polyhedra. We observe two softer components with lower bending rigidities allocated on the edges and vertices while the harder component occupies the faces. When subjected to a nonzero interfacial line tension, the two softer components further separate and pattern into subdomains that are mediated by the gaussian curvature. We find that this degree of fractionation is maximized when there is a weaker line tension and when the ratio of bending rigidities between the two softer domains ≈2. Our results reveal a patterning mechanism in multicomponent shells that can capture the observed morphologies of bacterial microcompartments, and moreover, can be realized in synthetic vesicles.
Monte Carlo methods↗
Optimized in situ crystal growth and disordered quasi-one-dimensional magnetism in Li 2 Mn 2 ( MoO 4 ) 3
We present that the quasi-one-dimensional structure of Li 2 Mn 2 ( MoO 4 ) 3 consists of three mutually distinct chains of Li 1 - x Mn x -centered polyhedra in which Mn ostensibly adopts a J = 5 / 2 Mn 2 + configuration. In situ x-ray scattering experiments carried out as crystallites emerge from a molten oxide solution facilitate the synthesis of large single crystals. Ex situ x-ray diffraction finds no evidence of long-range Li/Mn occupancy ordering, suggesting that the structure is effectively composed of finite chains of Mn moments of statistically varying lengths. UV/visible diffuse reflectance spectroscopy measurements establish a wide 3.43(12)-eV direct charge gap consistent with the local polyhedral coordination of the nominally Mn 2 + species. The temperature T dependence of the DC magnetic susceptibility χ reveals a fluctuating moment of only 2.74 μ B ± 0.01 μ B /Mn, dramatically reduced from the 5.9 μ B /Mn expected for Mn 2 + . Meanwhile, the Weiss temperature Θ W = - 89 ± 1 K reveals antiferromagnetic fluctuations that are stymied from reaching an ordered state apparently by the chemical disorder intrinsic to the polyhedral chains. Measurements of magnetization vs field H at T ≤ 10 K are far from saturation even at H = 5 T and are strongly non-Brillouin-like, instead scaling as H / T 0.24 ( 3 ) and suggesting the presence of quantum fluctuations associated with an eventual quasi-one-dimensional, disordered magnetic phase.
1-dimensional systems↗