Computational Screening and Stabilization of Boron-Substituted Type-I and Type-II Carbon Clathrates.

Boron substitution represents a promising approach to stabilize carbon clathrate structures, but no thermodynamically stable substitution schemes have been identified for frameworks other than the type-VII (sodalite) structure type. To investigate the possibility for additional tetrahedral carbon-based clathrate networks, more than 5000 unique boron decoration schemes were investigated computationally for type-I and type-II carbon clathrates with a range of guest elements including Li, Na, K, Rb, Cs, Mg, Ca, Sr, and Ba. Density functional theory calculations were performed at 10 and 50 GPa, and the stability and impact of boron substitution were evaluated. The results indicate that the boron-substituted carbon clathrates are stabilized under high-pressure conditions. Full cage occupancies of intermediate-sized guest atoms (e.g., Na, Ca, and Sr) are the most favorable energetically. Clathrate stability is maximized when the boron atoms are substituted within the hexagonal rings of the large [51262]/[51264] cages. Several structures with favorable formation enthalpies <-200 meV/atom were predicted, and type-I Ca8B16C30 is on the convex hull at 50 GPa. This structure represents the first thermodynamically stable type-I clathrate identified and suggests that boron-substituted carbon clathrates may represent a large family of diamond-like framework materials with a range of structure types and guest/framework substitutions.

Electron Spin Decoherence Dynamics in Magnetic Manganese Hybrid Organic-Inorganic Crystals: The Effect of Lattice Dimensionality.

Organic-inorganic metal hybrids with their tailorable lattice dimensionality and intrinsic spin-splitting properties are interesting material platforms for spintronic applications. While the spin decoherence process is extensively studied in lead- and tin-based hybrids, these systems generally show short spin decoherence lifetimes, and their correlation with the lattice framework is still not well-understood. Herein, we synthesized magnetic manganese hybrid single crystals of (4-fluorobenzylamine)2MnCl4, ((R)-3-fluoropyrrolidinium)MnCl3, and (pyrrolidinium)2MnCl4, which represent a change in lattice dimensionality from 2D and 1D to 0D, and studied their spin decoherence processes using continuous-wave electron spin resonance spectroscopy. All manganese hybrids exhibit nanosecond-scale spin decoherence time τ2 dominated by the symmetry-directed spin exchange interaction strengths of Mn2+-Mn2+ pairs, which is much longer than lead- and tin-based metal hybrids. In contrast to the similar temperature variation laws of τ2 in 2D and 0D structures, which first increase and gradually drop afterward, the 1D structure presents a monotonous rise of τ2 with the temperatures, indicating the strong correlation of spin decoherence with the lattice rigidity of the inorganic framework. This is also rationalized on the basis that the spin decoherence is governed by the competitive contributions from motional narrowing (prolonging the τ2) and electron-phonon coupling interaction (shortening the τ2), both of which are thermally activated, with the difference that the former is more pronounced in rigid crystalline lattices.

Understanding the Behavior of the Above-Room-Temperature Molecular Ferroelectric 5,6-Dichloro-2-methylbenzimidazole Using Symmetry Adapted Distortion Mode Analysis.

The exploitable properties of many functional materials are intimately linked with symmetry-changing phase transitions. These include properties such as ferroelectricity, second harmonic generation, conductivity, magnetism and many others. We describe a new symmetry-inspired method for systematic and exhaustive evaluation of the symmetry changes possible in molecular systems using molecular distortion modes, and how different models can be automatically tested against diffraction data. The method produces a quantitative structural landscape from which the most appropriate structural description of a child phase can be chosen. It can be applied to any molecular or molecular-fragment containing material where a (semi) rigid molecule description is appropriate. We exemplify the method on 5,6-dichloro-2-methylbenzimidazole (DC-MBI), an important molecular ferroelectric. We show that DC-MBI undergoes an unusual symmetry-lowering transition on warming from orthorhombic Pca21 ( T ≲ 400 K) to monoclinic Pc. Contrary to expectations, the high temperature phase of DC-MBI remains polar.

An Exhaustive Symmetry Approach to Structure Determination: Phase Transitions in Bi2Sn2O7.

The exploitable properties of many materials are intimately linked to symmetry-lowering structural phase transitions. We present an automated and exhaustive symmetry-mode method for systematically exploring and solving such structures which will be widely applicable to a range of functional materials. We exemplify the method with an investigation of the Bi2Sn2O7 pyrochlore, which has been shown to undergo transitions from a parent γ cubic phase to ß and α structures on cooling. The results include the first reliable structural model for ß-Bi2Sn2O7 (orthorhombic Aba2, a = 7.571833(8), b = 21.41262(2), and c = 15.132459(14) Å) and a much simpler description of α-Bi2Sn2O7 (monoclinic Cc, a = 13.15493(6), b = 7.54118(4), and c = 15.07672(7) Å, ß = 125.0120(3)°) than has been presented previously. We use the symmetry-mode basis to describe the phase transition in terms of coupled rotations of the Bi2O' anti-cristobalite framework, which allow Bi atoms to adopt low-symmetry coordination environments favored by lone-pair cations.

Chiral multiferroicity in two-dimensional hybrid organic-inorganic perovskites.

Chiral multiferroics offer remarkable capabilities for controlling quantum devices at multiple levels. However, these materials are rare due to the competing requirements of long-range orders and strict symmetry constraints. In this study, we present experimental evidence that the coexistence of ferroelectric, magnetic orders, and crystallographic chirality is achievable in hybrid organic-inorganic perovskites [(R/S)-ß-methylphenethylamine]2CuCl4. By employing Landau symmetry mode analysis, we investigate the interplay between chirality and ferroic orders and propose a novel mechanism for chirality transfer in hybrid systems. This mechanism involves the coupling of non-chiral distortions, characterized by defining a pseudo-scalar quantity, ξ = p ⋅ r ( p represents the ferroelectric displacement vector and r denotes the ferro-rotational vector), which distinguishes between (R)- and (S)-chirality based on its sign. Moreover, the reversal of this descriptor's sign can be associated with coordinated transitions in ferroelectric distortions, Jahn-Teller antiferro-distortions, and Dzyaloshinskii-Moriya vectors, indicating the mediating role of crystallographic chirality in magnetoelectric correlations.

Phase progression of γ-Al2O3 nanoparticles synthesized in a solvent-deficient environment.

Our simple and uniquely cost-effective solvent-deficient synthetic method produces 3-5 nm Al2O3 nanoparticles which show promise as improved industrial catalyst-supports. While catalytic applications are sensitive to the details of the atomic structure, a diffraction analysis of alumina nanoparticles is challenging because of extreme size/microstrain-related peak broadening and the similarity of the diffraction patterns of various transitional Al2O3 phases. Here, we employ a combination of X-ray pair-distribution function (PDF) and Rietveld methods, together with solid-state NMR and thermogravimetry/differential thermal analysis-mass spectrometry (TG/DTA-MS), to characterize the alumina phase-progression in our nanoparticles as a function of calcination temperature between 300 and 1200 °C. In the solvent-deficient synthetic environment, a boehmite precursor phase forms which transitions to γ-Al2O3 at an extraordinarily low temperature (below 300 °C), but this γ-Al2O3 is initially riddled with boehmite-like stacking-fault defects that steadily disappear during calcination in the range from 300 to 950 °C. The healing of these defects accounts for many of the most interesting and widely reported properties of the γ-phase.

Novel synthesis and structural analysis of ferrihydrite.

Naturally occurring ferrihydrite is both impure and difficult to isolate, so the numerous applications and interesting properties of ferrihydrite have spurred the development of various synthetic techniques. Nearly all techniques are based on the hydrolysis of an iron salt and require careful control of temperature, pH, and concentration. In this Article, we report a new synthetic method which does not require such control and is perhaps the fastest and simplest route to synthesizing ferrhydrite. XRD, TEM, BET, and chemical purity characterizations show that the chemically pure, 2-line ferrihydrite product consists of crystallites 2-6 nm in diameter which aggregate to form mesoporous, high surface area agglomerates that are attractive candidates for the many adsorption applications of ferrihydrite. X-ray PDF data were also collected for the ferrihydrite product and refined against the hexagonal structural model recently proposed by Michel et al. These analyses suggest that ferrihydrite has a consistent, repeatable structure independent of variation in the synthetic method, water content of the sample, or particle size of the crystallites, and this structure can be adequately described by the proposed hexagonal model.

Enumeration and tabulation of magnetic (3+d)-dimensional superspace groups.

A magnetic superspace group (MSSG) simultaneously constrains both the magnetic and non-magnetic (e.g. displacive, occupational, rotation and strain) degrees of freedom of an incommensurately modulated magnetic crystal. We present the first enumeration and tabulation of all non-equivalent (3+d)-dimensional magnetic superspace groups for d = 1, 2 and 3 independent incommensurate modulations, along with a number, symbol and reference setting for each group. We explain the process for generating an exhaustive set of inequivalent magnetic superspace groups, describe several examples, and show how the tables can be accessed via the ISO(3+d)D interface within the ISOTROPY Software Suite. We recommend that published incommensurate magnetic structures indicate a magnetic superspace-group number and symbol from these tables, as well as the transformation matrix from the published group setting to the reference setting used in these tables.

Introducing a unified magnetic space-group symbol.

The two commonly used systems of magnetic space-group (MSG) symbols, with accompanying numbers and settings, are those of Belov-Neronova-Smirnova (BNS) and Opechowski-Guccione (OG). The symbols from both systems have been used for several decades now. Both have advantages and disadvantages. Both present challenges of interpretation to novice and expert users alike, which can inhibit understanding and lead to errors in published magnetic structures. To address each of these challenges going forward, a new unified (UNI) MSG symbol is introduced, which combines a modified BNS symbol with essential information from the OG symbol.

The ISOTILT software for discovering cooperative rigid-unit rotations in networks of interconnected rigid units.

A user-friendly web-based software tool called 'ISOTILT' is introduced for detecting cooperative rigid-unit modes (RUMs) in networks of interconnected rigid units (e.g. molecules, clusters or polyhedral units). This tool implements a recently described algorithm in which symmetry-mode patterns of pivot-atom rotation and displacement vectors are used to construct a linear system of equations whose null space consists entirely of RUMs. The symmetry modes are first separated into independent symmetry-mode blocks and the set of equations for each block is solved separately by singular value decomposition. ISOTILT is the newest member of the ISOTROPY Software Suite. Here, it is shown how to prepare structural and symmetry-mode information for use in ISOTILT, how to use each of ISOTILT's input fields and options, and how to use and interpret ISOTILT output.

Normally supportive sublattices of crystallographic space groups.

The tabulation of normal subgroups of 3D crystallographic space groups that are themselves 3D crystallographic space groups (csg's) is an ambitious goal, but would have a variety of applications. For convenience, such subgroups are referred to as `csg-normal' while normal subgroups of the crystallographic point group (cpg) of a crystallographic space group are referred to as `cpg-normal'. The point group of a csg-normal subgroup must be a cpg-normal subgroup. The present work takes a significant step towards that goal by tabulating the translational subgroups (a.k.a. sublattices) that are capable of supporting csg-normal subgroups. Two necessary conditions are identified on the relative sublattice basis that must be met in order for the sublattice to support csg-normal subgroups: one depends on the operations of the point group of the space group, while the other depends on the operations of the cpg-normal subgroup. Sublattices that meet these conditions are referred to as `normally supportive'. For each cpg-normal subgroup (excluding the identity subgroup 1) of each of the arithmetic crystal classes of 3D space groups, all of the normally supportive sublattices have been tabulated in symbolic form, such that most of the entries in the table contain one or more integer variables of infinite range; thus it could be more accurately described as a table of the infinite families of normally supportive sublattices. For a given pair of cpg-normal subgroup and normally supportive sublattice, csg-normal subgroups of the space groups of the parent arithmetic crystal class can be constructed via group extension, though in general such a pair does not guarantee the existence of a corresponding csg-normal subgroup.

High-pressure polymorphism in pyridine.

Single crystals of the high-pressure phases II and III of pyridine have been obtained by in situ crystallization at 1.09 and 1.69 GPa, revealing the crystal structure of phase III for the first time using X-ray diffraction. Phase II crystallizes in P212121 with Z' = 1 and phase III in P41212 with Z' = ½. Neutron powder diffraction experiments using pyridine-d5 establish approximate equations of state of both phases. The space group and unit-cell dimensions of phase III are similar to the structures of other simple compounds with C 2v molecular symmetry, and the phase becomes stable at high pressure because it is topologically close-packed, resulting in a lower molar volume than the topologically body-centred cubic phase II. Phases II and III have been observed previously by Raman spectroscopy, but have been mis-identified or inconsistently named. Raman spectra collected on the same samples as used in the X-ray experiments establish the vibrational characteristics of both phases unambiguously. The pyridine molecules interact in both phases through CH⋯π and CH⋯N interactions. The nature of individual contacts is preserved through the phase transition between phases III and II, which occurs on decompression. A combination of rigid-body symmetry mode analysis and density functional theory calculations enables the soft vibrational lattice mode which governs the transformation to be identified.

Gd(5)Si(4-x)Bi(x) structures: novel slab sequences achieved by turning off the directionality of nearest-slab interactions.

Substitution of Bi for Si leads to the complete cleavage of the interslab dimers T-T in the Gd(5)Si(4-x)Bi(x) system with x = 1.58 - 2.42 (T is a mixture of Si and Bi). Equivalence of the interslab T...T contacts, achieved through combination of the electronic and geometrical parameters, removes directionality of nearest-slab interactions and allows for a novel slab stacking. Two new slab sequences, ABCDABCD (x = 2.07, I4(1)/acd space group) and ABADABAD (x = 2.42, P4(2)bc), have been discovered in Gd(5)Si(4-x)Bi(x) in addition to the known one, ABAB, that is dominant among the RE(5)X(4) phases (RE is a rare-earth element, X is a p-element). The slab stacking for x = 2.07 and x = 2.42 is dictated by the second-nearest slab interactions which promote an origin shift either for the entire slab sequence as in ABCDABCD or for every other second-nearest slab pair as in ABADABAD. The loss of the directionality of the nearest-slab bonding allows for extensive stacking faults and leads to diffuse scattering.

Topotactic, pressure-driven, diffusion-less phase transition of layered CsCoO2 to a stuffed cristobalite-type configuration.

CsCoO2, featuring a two-dimensional layered architecture of edge- and vertex-linked CoO4 tetrahedra, is subjected to a temperature-driven reversible second-order phase transformation (α → ß) at 100 K, which corresponds to a structural relaxation with concurrent tilting and breathing modes of edge-sharing CoO4 tetrahedra. In the present investigation, it was found that pressure induces a phase transition, which encompasses a dramatic change in the connectivity of the tetrahedra. At 923 K and 2 GPa, ß-CsCoO2 undergoes a first-order phase transition to a new quenchable high-pressure polymorph, γ-CsCoO2. It is built up of a three-dimensional cristobalite-type network of vertex-sharing CoO4 tetrahedra. According to a Rietveld refinement of high-resolution powder diffraction data, the new high-pressure polymorph γ-CsCoO2 crystallizes in the tetragonal space group I41/amd:2 (Z = 4) with the lattice constants a = 5.8711 (1) and c = 8.3214 (2) Å, corresponding to a shrinkage in volume by 5.7% compared with the ambient-temperature and atmospheric pressure ß-CsCoO2 polymorph. The pressure-induced transition (ß â†’ γ) is reversible; γ-CsCoO2 stays metastable under ambient conditions, but transforms back to the ß-CsCoO2 structure upon heating to 573 K. The transformation pathway revealed is remarkable in that it is topotactic, as is demonstrated through a clean displacive transformation track between the two phases that employs the symmetry of their common subgroup Pb21a (alternative setting of space group No. 29 that matches the conventional ß-phase cell).

Order parameters for phase transitions to structures with one-dimensional incommensurate modulations.

Phase transitions that result in incommensurate structural modulations are widely observed in crystalline solids and are relevant to a broad range of physical phenomena in magnetic, electronic, optical and structural materials. While the (3+1)-dimensional superspace-group symmetries associated with one-dimensional modulations have been tabulated, the order parameters that produce these modulations have not been explored in detail. Here, using group-theoretical methods, we present a unique and exhaustive enumeration of the isotropy subgroups (and their corresponding order-parameter directions) belonging to irreducible representations of the (3+1)-dimensional superspace extensions of the 230 crystallographic space groups at all incommensurate k points. The vast majority of experimentally observed incommensurately modulated structures have order parameters belonging to one of these subgroups.

A general algorithm for generating isotropy subgroups in superspace.

This paper presents a general algorithm for generating the isotropy subgroups of superspace extensions of crystallographic space groups involving arbitrary superpositions of multi-k order parameters from incommensurate and commensurate k vectors. Several examples are presented in detail in order to illuminate each step of the algorithm. The practical outcome is that one can now start with any commensurate parent crystal structure and generate a structure model for any conceivable incommensurate modulation of that parent, fully parameterized in terms of order parameters of irreducible representations at the relevant wavevectors. The resulting modulated structures have (3 + d)-dimensional superspace-group symmetry. Because incommensurate structures are now commonly encountered in the context of many scientifically and technologically important functional materials, the opportunity to apply the powerful methods of group representation theory to this broader class of structural distortions is very timely.

Equivalence of superspace groups.

An algorithm is presented which determines the equivalence of two settings of a (3 + d)-dimensional superspace group (d = 1, 2, 3). The algorithm has been implemented as a web tool findssg on SSG(3+d)D, providing the transformation of any user-given superspace group to the standard setting of this superspace group in SSG(3+d)D. It is shown how the standard setting of a superspace group can be directly obtained by an appropriate transformation of the external-space lattice vectors (the basic structure unit cell) and a transformation of the internal-space lattice vectors (new modulation wavevectors are linear combinations of old modulation wavevectors plus a three-dimensional reciprocal-lattice vector). The need for non-standard settings in some cases and the desirability of employing standard settings of superspace groups in other cases are illustrated by an analysis of the symmetries of a series of compounds, comparing published and standard settings and the transformations between them. A compilation is provided of standard settings of compounds with two- and three-dimensional modulations. The problem of settings of superspace groups is discussed for incommensurate composite crystals and for chiral superspace groups.

Tabulation of irreducible representations of the crystallographic space groups and their superspace extensions.

New tables of irreducible representations (IRs) are introduced for the 230 crystallographic space groups (SGs) in three-dimensional space, at both special and non-special k vectors, and for their extensions to (3 + d)-dimensional superspace (`superspace-extended SGs' or SSESGs). Neither a tabulation of SG IR matrices for non-special k vectors nor a tabulation of SSESG IR matrices for d > 1 have been previously published. These tabulations are made possible by a new form in which the IR matrices of SGs are separated as a product of a translation part T and a point-operation part P, and where the IR matrices of SSESGs are separated as a product of a phase-shift part Q and a point-operation part P(s). Both T and Q have a simple prescribed form that does not need to be tabulated. Also, the new IR matrices are in a convenient block form which allows one to see by inspection which parts of the matrices and the associated order parameters belong to which arm of the star of k. In addition to complex IR matrices, real physically irreducible representation (PIR) matrices are tabulated. The new IR and PIR tables are available on the ISO-IR website (http://stokes.byu.edu/iso/irtables.php) in both convenient human-readable and computer-readable forms.

Crystal and magnetic structures of hexagonal YMnO3.

The available data on the structural and magnetic transitions in multiferroic hexagonal YMnO3 have been reviewed, first making use of the computer programs from the group theoretical ISOTROPY software suite to list possible crystal and magnetic structures, then taking into account the capability of neutron diffraction and other physical methods to distinguish them. This leads to a clear view of the transformation sequence, as follows. Hexagonal YMnO3 is paraelectric in P63/mmc at elevated temperatures, and undergoes a single structural transition on cooling through 1250 K to a ferrielectric phase in P63cm that is retained through room temperature. At a much lower temperature, 70 K, there is a magnetic transition from paramagnetic to a triangular antiferromagnetic arrangement, most likely with symmetry P63'cm'. Comment is made on the unusual coupling of ferroelectric and magnetic domains reported to occur in this material, as well as on the so-called `giant magneto-elastic' effect.

The superstructure determination of displacive distortions via symmetry-mode analysis.

For any crystal structure that can be viewed as a low-symmetry distortion of some higher-symmetry parent structure, one can represent the details of the distorted structure in terms of symmetry-adapted distortion modes of the parent structure rather than the traditional list of atomic xyz coordinates. Because most symmetry modes tend to be inactive, and only a relatively small number of mode amplitudes are dominant in producing the observed distortion, symmetry-mode analysis can greatly simplify the determination of a displacively distorted structure from powder diffraction data. This is an important capability when peak splittings are small, superlattice intensities are weak or systematic absences fail to distinguish between candidate symmetries. Here, the symmetry-mode basis is treated as a binary (on/off) parameter set that spans the space of all possible P1 symmetry distortions within the experimentally determined supercell. Using the average R(wp) over repeated local minimizations from random starting points as a cost function for a given mode set, global search strategies are employed to identify the active modes of the distortion. This procedure automatically yields the amplitudes of the active modes and the associated atomic coordinates. The active modes are then used to detect the space-group symmetry of the distorted phase (i.e. the type and location of each of the parent symmetry elements that remain within the distorted supercell). Once a handful of active modes are identified, traditional refinement methods readily yield their amplitudes and the resulting atomic coordinates. A final symmetry-mode refinement is then performed in the correct space-group symmetry to improve the sensitivity to any secondary modes present.