Electronic origin of negative thermal expansion in samarium hexaboride revealed by X-ray diffraction and total scattering.

Samarium hexaboride, SmB6, is a negative thermal expansion (NTE) material whose structure is similar to other known NTE materials such as the family of Prussian blues. In the Prussian blues, NTE is due to a phonon mechanism, but we recently showed from DFT calculations that this is unlikely in SmB6 (Li et al., Phys. Chem. Chem. Phys. 2023, 25, 10749). We now report experimental X-ray diffraction and pair distribution function analysis of this material in the temperature range 20-300 K. The interatomic distances shown by both methods are consistent with the NTE instead arising from an electronic effect, by which the samarium atoms lose electrons and thus have a smaller ionic radius as the temperature increases.

Dynamics in the ordered and disordered phases of barocaloric adamantane.

High-entropy order-disorder phase transitions can be used for efficient and eco-friendly barocaloric solid-state cooling. Here the barocaloric effect is reported in an archetypal plastic crystal, adamantane. Adamantane has a colossal isothermally reversible entropy change of 106 J K-1 kg-1. Extremely low hysteresis means that this can be accessed at pressure differences less than 200 bar. Configurational entropy can only account for about 40% of the total entropy change; the remainder is due to vibrational effects. Using neutron spectroscopy and supercell lattice dynamics calculations, it is found that this vibrational entropy change is mainly caused by softening in the high-entropy phase of acoustic modes that correspond to molecular rotations. We attribute this difference in the dynamics to the contrast between an 'interlocked' state in the low-entropy phase and sphere-like behaviour in the high-entropy phase. Although adamantane is a simple van der Waals solid with near-spherical molecules, this approach can be leveraged for the design of more complex barocaloric molecular crystals. Moreover, this study shows that supercell lattice dynamics calculations can accurately map the effect of orientational disorder on the phonon spectrum, paving the way for studying the vibrational entropy, thermal conductivity, and other thermodynamic effects in more complex materials.

Further adventures of the perovskite family.

The perovskites are an intensely studied class of materials, with a breadth of possible compositions made even wider by the possibility of incorporating molecular ions. Here the context is discussed of a newly reported metal-free perovskite with the H3O+ ion on the B site.

The ω3 scaling of the vibrational density of states in quasi-2D nanoconfined solids.

The vibrational properties of crystalline bulk materials are well described by Debye theory, which successfully predicts the quadratic ω2 low-frequency scaling of the vibrational density of states. However, the analogous framework for nanoconfined materials with fewer degrees of freedom has been far less well explored. Using inelastic neutron scattering, we characterize the vibrational density of states of amorphous ice confined inside graphene oxide membranes and we observe a crossover from the Debye ω2 scaling to an anomalous ω3 behaviour upon reducing the confinement size L. Additionally, using molecular dynamics simulations, we confirm the experimental findings and prove that such a scaling appears in both crystalline and amorphous solids under slab-confinement. We theoretically demonstrate that this low-frequency ω3 law results from the geometric constraints on the momentum phase space induced by confinement along one spatial direction. Finally, we predict that the Debye scaling reappears at a characteristic frequency ω× = vL/2π, with v the speed of sound of the material, and we confirm this quantitative estimate with simulations.

Orientational disorder in sulfur hexafluoride: a neutron total scattering and reverse Monte Carlo study.

The orientational disorder in crystalline sulfur hexafluoride, SF6, has been studied using a combination of neutron total scattering and the reverse Monte Carlo method. Analysis of the atomic configurations has shown the extent of the disorder through the evaluation of the S-F bond orientational distribution function, consistent with, but improving upon, the results of earlier neutron powder diffraction data. The correlations between orientations of neighbouring molecules have been studied through analysis of the distributions of F-F distances, showing that nearest-neighbour F-F close contacts are avoided, consistent with previous molecular dynamics simulation results. The results present a new case study of the application of neutron total scattering and the reverse Monte Carlo methods for the study of orientational disorder, where in this instance the disorder arises from orientational frustration rather than from a mismatch of molecular and site symmetries.

Neutron powder-diffraction study of phase transitions in strontium-doped bismuth ferrite: 1. Variation with chemical composition.

We report results from a study of the crystal and magnetic structures of strontium-doped BiFeO3using neutron powder diffraction and the Rietveld method. Measurements were obtained over a wide range of temperatures from 300-800 K for compositions between 10%-16% replacement of bismuth by strontium. The results show a clear variation of the two main structural deformations-symmetry-breaking rotations of the FeO6octahedra and polar ionic displacements that give ferroelectricity-with chemical composition, but relatively little variation with temperature. On the other hand, the antiferromagnetic order shows a variation with temperature and a second-order phase transition consistent with the classical Heisenberg model. There is, however, very little variation in the behaviour of the antiferromagnetism with chemical composition, and hence with the degree of the structural symmetry-breaking distortions. We therefore conclude that there is no significant coupling between antiferromagnetism and ferroelectricity in Sr-doped BiFeO3and, by extension, in pure BiFeO3.

Neutron powder diffraction study of the phase transitions in deuterated methylammonium lead iodide.

We report the results of a neutron powder diffraction study of the phase transitions in deuterated methylammonium lead iodide, with a focus on the system of orientational distortions of the framework of PbI6octahedra. The results are analysed in terms of symmetry-adapted lattice strains and normal mode distortions. The higher-temperature cubic-tetragonal phase transition at 327 K is weakly discontinuous and nearly tricritical. The variations of rotation angles and spontaneous strains with temperature are consistent with a standard Landau theory treatment. The lower-temperature transition to the orthorhombic phase at 165 K is discontinuous, with two systems of octahedral rotations and internal distortions that together can be described by 5 order parameters of different symmetry. In this paper we quantify the various symmetry-breaking distortions and their variation with temperature, together with their relationship to the spontaneous strains, within the formalism of Landau theory. A number of curious results in the low-temperature phase are identified, particularly regarding distortion amplitudes that decrease rather than increase with lowering temperature.

Orientational order and phase transitions in deuterated methane: a neutron total scattering and reverse Monte Carlo study.

We report a study of the orientational order and phase transitions in crystalline deuterated methane, carried out using neutron total scattering and the reverse Monte Carlo method. The resultant atomic configurations are consistent with the average structures obtained from Rietveld refinement of the powder diffraction data, but additionally enable us to determine the C-D bond orientational distribution functions (ODF) for the disordered molecules in the high-temperature phase, and for both ordered and disordered molecules in the intermediate-temperature phase. We show that this approach gives more accurate information than can been obtained from fitting a bond ODF to diffraction data. Given the resurgence of interest in orientationally-disordered crystals, we argue that the approach of total scattering with the RMC method provides a unique quantification of orientational order and disorder.

Rotational dynamics of the imidazolium ion in cyanide-bridged dielectric framework materials.

Reorientation of organic cations in the cubic interstices of cyanoelpasolite molecular perovskites results in a variety of structural phase transitions, but far less is known about these cations' dynamics. We report quasielastic neutron scattering from the materials (C3H5N2)2K[MIII(CN)6], M = Fe,Co, which is directly sensitive to the rotation of the imidazolium ion. The motion is well described by a circular three-site hopping model, with the ion rotating within its plane in the intermediate-temperature phase, but tilting permanently in the high-temperature phase. Thus the two rhombohedral phases, which are crystallographically rather similar, have markedly different dynamics. The activation energy of rotation is about 10 kJ mol-1 and the barrier between orientations is 6 kJ mol-1. Our results explain two anomalous features in these materials' dielectric constants.

Colossal Pressure-Induced Softening in Scandium Fluoride.

The counterintuitive phenomenon of pressure-induced softening in materials is likely to be caused by the same dynamical behavior that produces negative thermal expansion. Through a combination of molecular dynamics simulation on an idealized model and neutron diffraction at variable temperature and pressure, we show the existence of extraordinary and unprecedented pressure-induced softening in the negative thermal expansion material scandium fluoride ScF_{3}. The pressure derivative of the bulk modulus B, B^{'}=(∂B/∂P)_{P=0}, reaches values as low as -220±30 at 50 K, and is constant at -50 between 150 and 250 K.

Neutron scattering study of the orientational disorder and phase transitions in barium carbonate.

Orientational disorder of the molecular [Formula: see text] anions in BaCO3, which occurs naturally as the mineral witherite, has been studied using a combination of neutron total scattering analysed by the reverse Monte Carlo method and molecular dynamics simulations. The primary focus is on the phase transition to the cubic phase, which assumes a rocksalt structure (Strukturbericht type B1) with highly disordered orientations consistent with the mismatch between the site ([Formula: see text]) and molecular (3/m) symmetries. Both experiment and simulation show a high degree of disorder, with the C-O bond orientation distribution never exceeding 25% variation from that of a completely uniform distribution, although there are differences between the two methods regarding the nature of these variations. Molecular dynamics simulations are also reported for the analogous phase transitions in the very important mineral calcite, CaCO3. The combination of the simulations and comparison with BaCO3 shows that the properties of calcite at all temperatures within its stability field are affected mostly by the onset of orientational disorder associated with the high-temperature cubic phase, even though this lies outside the stability field of calcite. This is a new understanding of calcite, which previously had been interpreted purely in terms of the phase transition to an intermediate partially-disordered phase. Finally, we also found that witherite itself appears to support the development of orientational disorder on heating, with the simulations showing a sequence of phase transitions that explain the much larger thermal expansion of one axis.

Introduction: minerals to metal-organic frameworks.

Mineralogy and materials design have always been closely intertwined. Here, I review some of the earliest work in modern materials chemistry to explicitly take inspiration from mineral structures and properties, and introduce the invited contributions to this theme issue. This article is part of the theme issue 'Mineralomimesis: natural and synthetic frameworks in science and technology'.

Hydrogen-bond-mediated structural variation of metal guanidinium formate hybrid perovskites under pressure.

The hybrid perovskites are coordination frameworks with the same topology as the inorganic perovskites, but with properties driven by different chemistry, including host-framework hydrogen bonding. Like the inorganic perovskites, these materials exhibit many different phases, including structures with potentially exploitable functionality. However, their phase transformations under pressure are more complex and less well understood. We have studied the structures of manganese and cobalt guanidinium formate under pressure using single-crystal X-ray and powder neutron diffraction. Under pressure, these materials transform to a rhombohedral phase isostructural to cadmium guanidinium formate. This transformation accommodates the reduced cell volume while preserving the perovskite topology of the framework. Using density-functional theory calculations, we show that this behaviour is a consequence of the hydrogen-bonded network of guanidinium ions, which act as struts protecting the metal formate framework against compression within their plane. Our results demonstrate more generally that identifying suitable host-guest hydrogen-bonding geometries may provide a route to engineering hybrid perovskite phases with desirable crystal structures. This article is part of the theme issue 'Mineralomimesis: natural and synthetic frameworks in science and technology'.

Crossover between Tilt Families and Zero Area Thermal Expansion in Hybrid Prussian Blue Analogues.

Materials in the family of Prussian blue analogues (C3 H5 N2 )2 K[M(CN)6 ], where C3 H5 N2 is the imidazolium ion and M=Fe, Co, undergo two phase transitions with temperature; at low temperatures the imidazolium cations have an ordered configuration (C2/c), while in the intermediate- and high-temperature phases (both previously reported as R3‾m ) they are dynamically disordered. We show from high-resolution powder neutron diffraction data that the high-temperature phase has zero area thermal expansion in the ab-plane. Supported by Landau theory and single-crystal X-ray diffraction data, we re-evaluate the space group symmetry of the intermediate-temperature phase to R3‾ . This reveals that the low-to-intermediate temperature transition is due to competition between two different tilt patterns of the [M(CN)6 ]3- ions. Controlling the relative stabilities of these tilt patterns offers a potential means to tune the exploitable electric behaviour that arises from motion of the imidazolium guest.

Orientational Disorder in Adamantane and Adamantanecarboxylic Acid.

The molecular crystals adamantane, C10 H16 , and adamantanecarboxylic acid, C10 H15 COOH, undergo order-disorder phase transitions at 208 and 250 K, respectively. Reverse Monte Carlo refinement of total neutron scattering data collected from deuterated samples immediately above these phase transitions shows that the high-temperature phases are well described by models in which the adamantyl groups are disordered over two sites. No correlation between the orientations of neighbouring molecules is observed. These results demonstrate that the intermolecular potential energy of these materials depends strongly on the orientation of the reference molecule but only very weakly on the orientations of its neighbours.

Control of Multipolar and Orbital Order in Perovskite-like [C(NH2)3]CuxCd1-x(HCOO)3 Metal-Organic Frameworks.

We study the compositional dependence of molecular orientation (multipolar) and orbital (quadrupolar) order in the perovskite-like metal-organic frameworks [C(NH2)3]CuxCd1-x(HCOO)3. Upon increasing the fraction x of Jahn-Teller-active Cu(2+), we observe an orbital disorder/order transition and a multipolar reorientation transition, each occurring at distinct critical compositions xo = 0.45(5) and xm = 0.55(5). We attribute these transitions to a combination of size, charge distribution, and percolation effects. Our results establish the accessibility in formate perovskites of novel structural degrees of freedom beyond the familiar dipolar terms responsible for (anti)ferroelectric order. We discuss the implications of cooperative quadrupolar and multipolar states for the design of relaxor-like hybrid perovskites.