Giant Unit Cell Research Articles

Stochastic many-body calculations of moir\xe9 states in twisted bilayer graphene at high pressures

We introduce three developments within the stochastic many-body perturbation theory: efficient evaluation of off-diagonal self-energy terms, construction of Dyson orbitals, and stochastic constrained random phase approximation. The stochastic approaches readily handle systems with thousands of atoms. We use them to explore the electronic states of twisted bilayer graphene (tBLG) characterized by giant unit cells and correlated electronic states. We document the formation of electron localization under compression; weakly correlated states are merely shifted in energy. We demonstrate how to efficiently downfold the correlated subspace on a model Hamiltonian with a screened frequency-dependent two-body interaction. For the 6° tBLG system, the onsite interactions are between 200 and 300 meV under compression. The Dyson orbitals exhibit spatial distribution similar to the mean-field single-particle states. Under pressure, the electron-electron interactions increase in the localized states; however, the dynamical screening does not fully balance the dominant bare Coulomb interaction.

Chiral columns forming a lattice with a giant unit cell.

Mesogenic materials, quinoxaline derivatives with semi-flexible cores, are reported to form a new type of 3D columnar phase with a large crystallographic unit cell and Fddd lattice below the columnar hexagonal phase. The 3D columnar structure is a result of frustration imposed by the arrangement of helical columns of opposite chiralities into a triangular lattice. The studied materials exhibit fluorescence properties that could be easily tuned by modification of the molecular structure; for compounds with the extended π electron conjugated systems the fluorescence is quenched. For molecules with a flexible structure the fluorescence quantum yield reaches 25%. On the other hand, compounds with a more rigid mesogenic core, for which the fluorescence is suppressed, show effective photogeneration of charge carriers. For some materials bi-polar hole and electron transport was observed.

Unmasking the structure of a chiral cubic thermotropic liquid crystal phase by a combination of soft and tender resonant X-ray scattering.

A resonant X-ray scattering response for two structural models of a chiral cubic phase with a giant unit cell, one composed of a continuous grid and micelles and the other with three continuous grids, is studied theoretically and compared to experimental measurements. For both structural models resonant enhancement of all the symmetry-allowed diffraction peaks is predicted, as well as the existance of several symmetry forbidden peaks (pure resonant peaks). Experimental measurements were performed at the carbon and sulphur absorption edge. Only one pure resonant peak was observed, which is predicted by both models. Two low-angle symmetry allowed peaks, not observed in non-resonant scattering, were resonantly enhanced and their intensity angular dependence can distinguish between the two structural models.

Formation of a C15 Laves Phase with a Giant Unit Cell in Salt-Doped A/B/AB Ternary Polymer Blends.

Salt-doped A/B/AB ternary polymer blends, wherein an AB copolymer acts as a surfactant to stabilize otherwise incompatible A and B homopolymers, display a wide range of nanostructured morphologies with significant tunability. Among these structures, a bicontinuous microemulsion (BμE) has been a notable target. Here, we report the surprising appearance of a robust C15 Laves phase, at compositions near where the BμE has recently been reported, in lithium bis(trifluoromethane) sulfonimide (LiTFSI)-doped low-molar-mass poly(ethylene oxide) (PEO)/polystyrene (PS)/symmetric PS-b-PEO block copolymer blends. The materials were analyzed by a combination of small-angle X-ray scattering (SAXS), 1H NMR spectroscopy, and impedance spectroscopy. The C15 phase emerges at a high total homopolymer volume fraction ϕH = 0.8 with a salt composition r = 0.06 (Li+/[EO]) and persists as a coexisting phase across a large area of the isothermal phase diagram with high PS homopolymer compositions. Notably, the structure exhibits a huge unit cell size, a = 121 nm, with an unusually high micelle core volume fraction (fcore = 0.41) and an unusually low fraction of amphiphile (20%). This unit cell dimension is at least 50% larger than any previously reported C15 phase in soft matter, despite the low molar masses used, unlocking the possibility of copolymer-based photonic crystals without compromising processability. The nanostructured phase evolution from lamellar to hexagonal to C15 along the EO60 isopleth (ϕPEO,homo-LiTFSI/ϕH = 0.6) is rationalized as a consequence of asymmetry in the homopolymer solubility limit for each block, which leads to exclusion of PS homopolymer from the PS-b-PEO brush prior to exclusion of the PEO homopolymer, driving increased interfacial curvature and favoring the emergence of the C15 Laves phase.

Chemically driven superstructural ordering leading to giant unit cells in unconventional clathrates Cs8Zn18Sb28 and Cs8Cd18Sb28.

The unconventional clathrates, Cs8Zn18Sb28 and Cs8Cd18Sb28, were synthesized and reinvestigated. These clathrates exhibit unique and extensive superstructural ordering of the clathrate-I structure that was not initially reported. Cs8Cd18Sb28 orders in the Ia3̄d space group (no. 230) with 8 times larger volume of the unit cell in which most framework atoms segregate into distinct Cd and Sb sites. The structure of Cs8Zn18Sb28 is much more complicated, with an 18-fold increase of unit cell volume accompanied by significant reduction of symmetry down to P2 (no. 3) monoclinic space group. This structure was revealed by a combination of synchrotron X-ray diffraction and electron microscopy techniques. A full solid solution, Cs8Zn18−xCdxSb28, was also synthesized and characterized. These compounds follow Vegard's law in regard to their primitive unit cell sizes and melting points. Variable temperature in situ synchrotron powder X-ray diffraction was used to study the formation and melting of Cs8Zn18Sb28. Due to the heavy elements comprising clathrate framework and the complex structural ordering, the synthesized clathrates exhibit ultralow thermal conductivities, all under 0.8 W m−1 K−1 at room temperature. Cs8Zn9Cd9Sb28 and Cs8Zn4.5Cd13.5Sb28 both have total thermal conductivities of 0.49 W m−1 K−1 at room temperature, among the lowest reported for any clathrate. Cs8Zn18Sb28 has typical p-type semiconducting charge transport properties, while the remaining clathrates show unusual n–p transitions or sharp increases of thermopower at low temperatures. Estimations of the bandgaps as activation energy for resistivity dependences show an anomalous widening and then shrinking of the bandgap with increasing Cd-content.

A Double-Walled Thorium-Based Metal–Organic Framework as a Promising Dual-Function Absorbent for Efficiently Capturing Iodine and Dyes

We prepared a rare thorium metal–organic framework (MOF) (Th-TATAB) with a double-walled tetrahedral cage structure and giant unit cell volume of 43 513 A3, which is the largest of all reported tho...

Structure and Oxidation States of Giant Unit Cell Compound Dy117+xFe57–ySn112–z

Motivated by the complex structure and properties of giant unit cell intermetallic compounds, a new isostructural Fe analogue of the Dy117Co57Sn112 structure type was synthesized. Single crystals of Dy122Fe55Sn101 were grown at 1260 °C via a Dy–Fe eutectoid flux. The Fe analogue also adopts the space group Fm3m with lattice parameters a = 29.914(9) Å, V = 26769(23) Å3, and Z = 4. Dy122Fe55Sn101 has a large cell volume, structural complexity, and consists of seven Dy, eight Fe, and ten Sn unique crystallographic sites. There are fifteen fully occupied atomic positions, three unique pairs of alternating atomic positions with positional disorder, and seven partially occupied atomic sites. Within this complex unit cell, only approximately half the unique atomic positions are fully occupied with the remainder of the atoms either positionally or occupationally disordered. X‐ray photoelectron spectroscopy indicates that the compound contains Dy3+, Fe0, Fe2+, Sn0, and Sn4+.

On the edge of periodicity: Unconventional magnetism of Gd117Co56.4Sn114.3

Magnetization measurements reveal the onset of magnetic ordering at TC = 65 K followed by three additional magnetic anomalies at T1 = 47 K, T2 = 28 K, and T3 = 11 K in Gd117Co56.4Sn114.3 – a compound with a giant cubic unit cell that crystallizes in the Dy117Co56Sn112 structure type with space group Fm3¯m and lattice parameter a = 30.186 Å. The magnetic ordering temperature increases with applied magnetic field; however, the analysis of magnetic data indicates that antiferromagnetic interactions also play a role in the ground state. AC magnetic susceptibility confirms multiple magnetic anomalies and shows minor frequency dependence. The local magnetic ordering below 60 K is supported by the Mössbauer spectroscopy. A single broad anomaly is detected at T3 in the heat capacity; we suggest that magnetic domains form below this temperature. These data highlight unique features of magnetism in this and, potentially, other rare-earth intermetallics crystallizing with giant unit-cells where the exchange correlation lengths are much shorter when compared to the periodicity of the crystal lattice.

Synthesis, Crystal Structure, and Magnetic Properties of Giant Unit Cell Intermetallics R117Co52+δSn112+γ (R = Y, La, Pr, Nd, Ho)

Ternary intermetallics R117Co52+δSn112+γ (R = Y, La, Pr, Nd, and Ho) have been prepared by arc-melting followed by annealing at 800 °C. All the compounds belong to the Tb117Fe52Ge112 structure type (space group Fm 3 ¯ m) characterized by a complex giant cubic unit cell with a ~ 30 Å. The single-crystal structure determination of Y- and La-containing compounds reveals a significant structural disorder. A comparison of these and earlier reported crystal structures of R117Co52+δSn112+γ suggests that more extensive disorder occurs for structures that contain larger lanthanide atoms. This observation can be explained by the need to maintain optimal bonding interactions as the size of the unit cell increases. Y117Co56Sn115 exhibits weak paramagnetism due to the Co sublattice and does not show magnetic ordering in the 1.8–300 K range. Ho117Co55Sn108 shows ferromagnetic ordering at 10.6 K. Both Pr117Co54Sn112 and Nd117Co54Sn111 exhibit antiferromagnetic ordering at 17 K and 24.7 K, respectively, followed by a spin reorientation transition at lower temperature.

Epitaxial Stabilization between Intermetallic and Carbide Domains in the Structures of Mn16SiC4 and Mn17Si2C4.

The concept of frustration between competing geometrical or bonding motifs is frequently evoked in explaining complex phenomena in the structures and properties of materials. This idea is of particular importance for metallic systems, where frustration forms the basis for the design of metallic glasses, a source of diverse magnetic phenomena, and a rationale for the existence of intermetallics with giant unit cells containing thousands of atoms. Unlike soft materials, however, where conflicts can be synthetically encoded in the molecular structure, staging frustration in the metallic state is challenging due to the ease of macroscopic segregation of incompatible components. In this Article, we illustrate one approach for inducing the intergrowth of incompatible bonding motifs with the synthesis and characterization of two new intermetallic carbides: Mn16SiC4 (mC42) and Mn17Si2C4 (mP46). Similar to the phases Mn5SiC and Mn8Si2C in the Mn-Si-C system, these compounds appear as intergrowths of Mn3C and tetrahedrally close-packed (TCP) regions reminiscent of Mn-rich Mn-Si phases. The nearly complete spatial segregation of Mn-Si (intermetallic) and Mn-C (carbide) interactions in these structures can be understood from the differing geometrical requirements of C and Si. Rather than macroscopically separating into distinct phases, though, the two bonding types are tightly interwoven, with most Mn atoms being on the interfaces. DFT chemical pressure analysis reveals a driving force stabilizing these interfaces: the major local pressures acting between the Mn atoms in the Mn-Si and Mn-C systems are of opposite signs. Joining the intermetallic and carbide domains together then provides substantial relief to these local pressures, an effect we term epitaxial stabilization.

Strain induced incommensurate structures in vicinity of reconstructive phase transitions

General conditions controlling the formation of incommensurate phases in crystals undergoing reconstructive phase transitions are analyzed in the framework of a model-free phenomenological approach. A universal trend to stabilizing such intermediate phases in the vicinity of reconstructive phase transitions stems from the fact that certain high-order improper Lifshitz invariants reduce at such transformations to ones bi-linearly coupling critical displacement gradients and strains or even to the proper Lifshitz invariant. The approach developed here introduces a universal mechanism for the formation both of premartensite incommensurate phases and complex structures with giant unit cells, as found in some elemental crystals at high pressure.

Sphericity and symmetry breaking in the formation of Frank-Kasper phases from one component materials.

Frank-Kasper phases are tetrahedrally packed structures occurring in numerous materials, from elements to intermetallics to self-assembled soft materials. They exhibit complex manifolds of Wigner-Seitz cells with many-faceted polyhedra, forming an important bridge between the simple close-packed periodic and quasiperiodic crystals. The recent discovery of the Frank-Kasper σ-phase in diblock and tetrablock polymers stimulated the experiments reported here on a poly(isoprene-b-lactide) diblock copolymer melt. Analysis of small-angle X-ray scattering and mechanical spectroscopy exposes an undiscovered competition between the tendency to form self-assembled particles with spherical symmetry, and the necessity to fill space at uniform density within the framework imposed by the lattice. We thus deduce surprising analogies between the symmetry breaking at the body-centered cubic phase to σ-phase transition in diblock copolymers, mediated by exchange of mass, and the symmetry breaking in certain metals and alloys (such as the elements Mn and U), mediated by exchange of charge. Similar connections are made between the role of sphericity in real space for polymer systems, and the role of sphericity in reciprocal space for metallic systems such as intermetallic compounds and alloys. These findings establish new links between disparate materials classes, provide opportunities to improve the understanding of complex crystallization by building on synergies between hard and soft matter, and, perhaps most significantly, challenge the view that the symmetry breaking required to form reduced symmetry structures (possibly even quasiperiodic crystals) requires particles with multiple predetermined shapes and/or sizes.

Spin-glass behavior in a giant unit cell compound Tb117Fe52Ge113.8(1)

In this paper we demonstrate evidence of a cluster spin glass in Tb117Fe52Ge113.8(1) (a compound with a giant cubic unit cell) via ac and dc magnetic susceptibility, magnetization, magnetic relaxation and heat capacity measurements. The results clearly show that Tb117Fe52Ge113.8(1) undergoes a spin glass phase transition at the freezing temperature, ~38 K. The good fit of the frequency dependence of the freezing temperature to the critical slowing down model and Vogel-Fulcher law strongly suggest the formation of cluster glass in the Tb117Fe52Ge113.8(1) system. The heat capacity data exhibit no evidence for long-range magnetic order, and yield a large value of Sommerfeld coefficient. The spin glass behavior of Tb117Fe52Ge113.8(1) may be understood by assuming the presence of competing interactions among multiple non-equivalent Tb sites present in the highly complex unit cell.

New intermetallic La117Ru57Sn112.

The new ternary compound with giant unit cell La117Ru57Sn112 has been yielded by interaction between pure components lanthanum, ruthenium and tin and investigated by X-ray diffraction and scanning electron microscopy (SEM) in combination with energy dispersive X-ray spectroscopy (EDX) means. Previously, intermetallics with cobalt of similar composition and structure were found in the ternary systems and Dy-Co-Sn and Pr-Co-Sn – Dy117Co57Sn112 and Pr117Co57Sn112 respectively [1, 2]. The intermetallic La117Ru57Sn112 crystallizes in a cubic Dy117Co57Sn112 type structure with space group Fm-3m (No. 225) and lattice parameter a = 31.529(5). A single-crystal suitable for the X-ray measurements was isolated from the of the equiatomic alloy La33.3Ru33.3Sn33.4. The structure was solved by means of direct methods and refined using the SHELXS-97 and SHELXL-97 programs (R1 = 0.033 for 1042 Fo > 4σ(Fo) and 0.061 for all collected data). The additional sample of the La40.2Ru19.9Sn39.9 composition was prepared and investigated X-ray by powder diffraction technique (CuKα1 radiation, 5 < 2Θ < 900). The collected intensities data were refined by the Rietveld method using the La117Ru57Sn112 single crystal model and FullProf program. Based on a minimum of differences between the observed and calculated theoretically intensities one can judge the good convergence results.

Study of intermetallics and phase equilibria of Mg–Zn–La system in Mg-rich corner at 345 °C

Phase compositions, lattice structures and phase equilibria of Mg–Zn–La system in Mg-rich corner at 345°C have been investigated by equilibrated alloy method and diffusion couple technique. The results show that a binary solid solution of Mg12La is confirmed as (Mg,Zn)12La with 0–4.96at.% Zn. It has a body-centred tetragonal lattice structure with giant unit cell of a=b≈1.032nm and c≈7.748nm. Another linear ternary intermetallic (Mg,Zn)11La (Zn≈8.66–43.39at.%) has been identified too. (Mg,Zn)11La has a C-centred orthorhombic structure, and the unit cell of which becomes smaller with the increase of Zn content. The smallest lattice parameters of it are a≈1.1191nm, b≈0.9701nm and c≈0.9498nm. Both (Mg,Zn)12La and (Mg,Zn)11La are in equilibrium with Mg solid solution in their composition range. A three-phase equilibrium of Mg+(Mg,Zn)12La+(Mg,Zn)11La is also ascertained. In addition, MgZn phase containing about 1.53at.% La is confirmed, which is in equilibrium with Mg solid solution and (Mg,Zn)11La at 345°C. This result indicates that it is impossible for Mg17Zn21La2 reported in literature to be in equilibrium with Mg solid solution as a stable phase at this temperature.

Revised Bismuth Chloroselenite System: Evidence of a Noncentrosymmmetric Structure with a Giant Unit Cell

The reactions between PbO, Bi2O3 (or BiOCl), and SeO2 by the chemical vapor transport method using HCl as a transporting agent afforded three novel bismuth/lead chloroselenites, namely, β-BiSeO3Cl (1), Bi6(SeO3)4Cl10 (2), and PbBi10(SeO3)12Cl8 (3). Compound 1 is noncentrosymmetric (space group Cc, SHG active) and has a giant unit cell (V = 19792(2) A3). In the context of the complex BiSeO3Cl phase diagram reported by Oppermann et al., it was assigned to the undescribed β-form on the basis of its IR spectra and powder X-ray diffraction pattern. The comparison between the α-, β-, and γ-forms suggests their formation via the condensation of volatile Bi(SeO3)Cl molecules. Analysis of the structures of the α-, β-, and γ-forms indicates that the α → β → γ phase transitions are associated with a dramatic fluctuation of structural complexity together with the transitional character of the β phase. Compounds 1 and 3 are layered compounds with identical ([M8Cl16]8+ and [M14(SeO3)24]6−) layers, where M stands for Bi...

Antiferromagnetic cluster spin-glass behavior in Pr117Co54.5Sn115.2 – A compound with a giant unit cell

The magnetic properties of Pr117Co54.5Sn115.2 – a member of a family of materials with a giant unit cell – have been investigated by dc magnetization, ac magnetic susceptibility, specific heat, and electrical resistivity measurements. A magnetic glassy state at freezing temperature of ∼11K was determined from the magnetic susceptibility and specific heat data. The glassy state in Pr117Co54.5Sn115.2 is not the conventional spin glass with randomly oriented magnetic moments, but it is related to clusters of atoms that exist in the complex crystal lattice of the material. Furthermore, the glassy state coexists with short range antiferromagnetic order, leading to the development of antiferromagnetic clusters. A weak anomaly in the specific heat data centered around 11K supports the formation of magnetic cluster glass state in Pr117Co54.5Sn115.2. Semiconductor-like resistivity with a negative temperature coefficient from 2 to 300K is also observed in Pr117Co54.5Sn115.2.

Electrical Resistivity and Magnetoresistance of the δ-FeZn10 Complex Intermetallic Phase

ABSTRACTThe δ-FeZn10 phase possesses high structural complexity typical of complex metallic alloys: a giant unit cell comprising 556 atoms, polyhedral atomic order with icosahedrally-coordinated environments, fractionally occupied lattice sites and statistically disordered atomic clusters that introduce intrinsic disorder into the structure. The electrical resistivity is large and exhibits a maximum at about 220 K. The magnetoresistance is sizeable, amounting to 1.5 % at 2 K in 9 T field. The temperature–dependent resistivity is discussed within the frame of the theory of slow charge carriers, applicable to metallic systems with weak dispersion of the electronic bands, where the electron motion changes from ballistic to diffusive upon heating. A comparison to the theory of weak localization is also made.

On the Symmetry and Composition of Complex Intermetallics

ABSTRACTComplex intermetallic structures can be found in many intermetallic systems and exhibit giant unit cells. They feature quite a number of peculiar structural and physical properties and have, until now, barely been treated in a unifying matter. We are following an integrated approach towards their description and categorization and are thereby formulating a fundamental definition of these very interesting and rather diverse compounds.

Electrical, magnetic, and thermal properties of theδ-FeZn10complex intermetallic phase

We report the electrical, magnetic, and thermal properties of the \ensuremath{\delta}-FeZn${}_{10}$ phase in the zinc-rich domain of the Fe-Zn system. The \ensuremath{\delta}-FeZn${}_{10}$ phase possesses high structural complexity typical of complex metallic alloys: a giant unit cell comprising 556 atoms, polyhedral atomic order with icosahedrally coordinated environments, fractionally occupied lattice sites, and statistically disordered atomic clusters that introduce intrinsic disorder into the structure. Structural disorder results in suppression of the electrical and heat transport phenomena, making \ensuremath{\delta}-FeZn${}_{10}$ a poor electrical and thermal conductor. Structural complexity results in a complex electronic structure that is reflected in the opposite signs of the thermoelectric power and the Hall coefficient. The \ensuremath{\delta}-FeZn${}_{10}$ phase is paramagnetic down to the lowest investigated temperature of 2 K with a significant interspin coupling of antiferromagnetic type. Specific heat indicates the formation of short-range-ordered spin clusters at low temperatures, very likely a precursor of a phase transition to a collective magnetic state that would take place below 2 K. The magnetoresistance of \ensuremath{\delta}-FeZn${}_{10}$ is sizeable, amounting to 1.5$%$ at 2 K in a 9-T field. The electrical resistivity exhibits a maximum at about 220 K, and its temperature dependence could be explained by the theory of slow charge carriers, applicable to metallic systems with weak dispersion of the electronic bands, where the electron motion changes from ballistic to diffusive upon heating.