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.

The Rigid Unit Mode model: review of ideas and applications.

We review a set of ideas concerning the flexibility of network materials, broadly defined as structures in which atoms form small polyhedral units that are connected at corners. One clear example is represented by the family of silica polymorphs, with structures composed of corner-lined SiO4tetrahedra. TheRigid Unit Mode(RUM) is defined as any normal mode in which the structural polyhedra can translate and/or rotate without distortion, and since forces associated with changing the size and shape of the polyhedra are much stronger than those associated with rotations of two polyhedra around a shared vertex, the RUMs might be expected to have low frequencies compared to all other phonon modes. In this paper we discuss the flexibility of network structures, and how RUMs can arise in such structures, both in principle and in a number of specific examples of real systems. We also discuss applications of the RUM model, particularly for our understanding of phenomena such as displacive phase transitions and negative thermal expansion in network materials. .

Observation of the mixed magneto-optical Kerr effects using weak measurement.

In this paper, we use weak measurement to study the mixed magneto-optical Kerr effects (MOKEs) in a magnetic single layer of Co and in organic/Co bilayer films. The relationship between the amplified shift and the MOKE parameters is theoretically established and then experimentally observed as a function of both the magnetization intensity and the magnetization direction in magnetic thin films with an arbitrary magnetization. Furthermore, we experimentally observe a magnetic coupling at the organic/ferromagnetic interface. Due to this being a robust coupling, there is a significant dependence of the amplified shift with the thickness of the organic layer. This work has value for its application in the magnetic measurement technique for the more general case based on weak measurement.

The contribution of phonons to the thermal expansion of some simple cubic hexaboride structures: SmB6, CaB6, SrB6 and BaB6.

We have performed first-principles calculations of the structure and lattice dynamics in the metal hexaborides SmB6, CaB6, SrB6 and BaB6 using Density Functional Theory in an attempt to understand the negative thermal expansion in the first of these materials. The focus is on the role of Rigid Unit Modes involving rotations of the B6 octahedra similar to the rotations of structural polyhedra connected by bonds in Zn(CN)2, Prussian Blue and Si(NCN)2. However, it was found that there is very low flexibility of the network of connected B6 octahedra, and the lattice dynamics do not support negative thermal expansion except possibly at very low temperature. Thus the negative thermal expansion observed in SmB6 probably has an electronic origin.

Phonon mechanism for the negative thermal expansion of zirconium tungstate, ZrW2O8.

Negative thermal expansion (NTE) in ZrW2O8 was investigated using a flexibility analysis of ab initio phonons. It was shown that no previously proposed mechanism adequately describes the atomic-scale origin of NTE in this material. Instead it was found that the NTE in ZrW2O8 is driven, not by a single mechanism, but by wide bands of phonons that resemble vibrations of near-rigid WO4 units and Zr-O bonds at low frequency, with deformation of O-W-O and O-Zr-O bond angles steadily increasing with increasing NTE-phonon frequency. It is asserted that this phenomenon is likely to provide a more accurate explanation for NTE in many complex systems not yet studied.

Unique features of the structural phase transition in acetylene showing simultaneous characteristics of reconstructive, displacive and order-disorder.

We have studied the two phases of the molecular crystal acetylene, C2H2, using calculations of the lattice dynamics by Density Functional Theory methods. together with the use of classical molecular dynamics (MD) simulation methods. The two phases share the same simple face-centred cubic lattice arrangement of the molecular centres of mass, but with different molecular orientations. We show that the higher-temperature phase has lower phonon frequencies and hence higher entropy, giving thermodynamic stability at higher temperature. The calculated lattice dynamics of this phase show instabilities associated with phonons involving pure rotations of the molecules. The MD results show large amplitudes of librational motion in this phase. The MD simulations also showed a potential phase transition to a structure of tetragonal symmetry. The picture that emerges is that the phase transition in acetylene is a very rare example of one that encompasses elements of three types of transition: displacive, order-disorder and reconstructive.

Origin of Ferroelectricity in Two Prototypical Hybrid Organic-Inorganic Perovskites.

Hybrid organic-inorganic perovskite (HOIP) ferroelectrics are attracting considerable interest because of their high performance, ease of synthesis, and lightweight. However, the intrinsic thermodynamic origins of their ferroelectric transitions remain insufficiently understood. Here, we identify the nature of the ferroelectric phase transitions in displacive [(CH3)2NH2][Mn(N3)3] and order-disorder type [(CH3)2NH2][Mn(HCOO)3] via spatially resolved structural analysis and ab initio lattice dynamics calculations. Our results demonstrate that the vibrational entropy change of the extended perovskite lattice drives the ferroelectric transition in the former and also contributes importantly to that of the latter along with the rotational entropy change of the A-site. This finding not only reveals the delicate atomic dynamics in ferroelectric HOIPs but also highlights that both the local and extended fluctuation of the hybrid perovskite lattice can be manipulated for creating ferroelectricity by taking advantages of their abundant atomic, electronic, and phononic degrees of freedom.

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.

Flexibility of network materials and the Rigid Unit Mode model: a personal perspective.

The Rigid Unit Mode model was initially developed to understand the origin of displacive phase transitions in network silicate structures. Here, we review the successes of the model, and consider how it might apply to a wider range of network structures. 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'.

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.

Negative thermal expansion and associated anomalous physical properties: review of the lattice dynamics theoretical foundation.

Negative thermal expansion (NTE) is the phenomenon in which materials shrink rather than expand on heating. Although NTE had been previously observed in a few simple materials at low temperature, it was the realisation in 1996 that some materials have NTE over very wide ranges of temperature that kick-started current interest in this phenomenon. Now, nearly two decades later, a number of families of ceramic NTE materials have been identified. Increasingly quantitative studies focus on the mechanism of NTE, through techniques such as high-pressure diffraction, local structure probes, inelastic neutron scattering and atomistic simulation. In this paper we review our understanding of vibrational mechanisms of NTE for a range of materials. We identify a number of different cases, some of which involve a small number of phonons that can be described as involving rotations of rigid polyhedral groups of atoms, others where there are large bands of phonons involved, and some where the transverse acoustic modes provide the main contribution to NTE. In a few cases the elasticity of NTE materials has been studied under pressure, identifying an elastic softening under pressure. We propose that this property, called pressure-induced softening, is closely linked to NTE, which we can demonstrate using a simple model to describe NTE materials. There has also been recent interest in the role of intrinsic anharmonic interactions on NTE, particularly guided by calculations of the potential energy wells for relevant phonons. We review these effects, and show how anhamonicity affects the response of the properties of NTE materials to pressure.

In situ studies of materials for high temperature CO2 capture and storage.

Carbon capture and storage (CCS) offers a possible solution to curb the CO2 emissions from stationary sources in the coming decades, considering the delays in shifting energy generation to carbon neutral sources such as wind, solar and biomass. The most mature technology for post-combustion capture uses a liquid sorbent, amine scrubbing. However, with the existing technology, a large amount of heat is required for the regeneration of the liquid sorbent, which introduces a substantial energy penalty. The use of alternative sorbents for CO2 capture, such as the CaO-CaCO3 system, has been investigated extensively in recent years. However there are significant problems associated with the use of CaO based sorbents, the most challenging one being the deactivation of the sorbent material. When sorbents such as natural limestone are used, the capture capacity of the solid sorbent can fall by as much as 90 mol% after the first 20 carbonation-regeneration cycles. In this study a variety of techniques were employed to understand better the cause of this deterioration from both a structural and morphological standpoint. X-ray and neutron PDF studies were employed to understand better the local surface and interfacial structures formed upon reaction, finding that after carbonation the surface roughness is decreased for CaO. In situ synchrotron X-ray diffraction studies showed that carbonation with added steam leads to a faster and more complete conversion of CaO than under conditions without steam, as evidenced by the phases seen at different depths within the sample. Finally, in situ X-ray tomography experiments were employed to track the morphological changes in the sorbents during carbonation, observing directly the reduction in porosity and increase in tortuosity of the pore network over multiple calcination reactions.

Acoustic phonons and negative thermal expansion in MOF-5.

The mechanism of negative thermal expansion (NTE) in MOF-5 has been studied using a rigid unit mode analysis of the phonons responsible for NTE. In addition to confirming the role of the previously proposed optic 'trampoline mode' mechanism [Lock et al., Dalton Trans., 2013, 42, 1933-2320], we have identified a new acoustic mode mechanism that makes a major contribution to the macroscopic NTE of this framework.

Melt-quenched glass formation of a family of metal-carboxylate frameworks.

Metal-organic framework (MOF) glasses are an emerging class of glasses which complement traditional inorganic, organic and metallic counterparts due to their hybrid nature. Although a few zeolitic imidazolate frameworks have been made into glasses, how to melt and quench the largest subclass of MOFs, metal carboxylate frameworks, into glasses remains challenging. Here, we develop a strategy by grafting the zwitterions on the carboxylate ligands and incorporating organic acids in the framework channels to enable the glass formation. The charge delocalization of zwitterion-acid subsystem and the densely filled channels facilitate the coordination bonding mismatch and thus reduce the melting temperature. Following melt-quenching realizes the glass formation of a family of carboxylate MOFs (UiO-67, UiO-68 and DUT-5), which are usually believed to be un-meltable. Our work opens up an avenue for melt-quenching porous molecular solids into glasses.

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 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.

The ferroelastic phase transition in hydrogen cyanide studied by density functional theory.

We report calculations of the crystal structures and lattice dynamics of the tetragonal and orthorhombic phases of the molecular crystal hydrogen cyanide, HCN, using density functional theory methods. By treating negative pressure as a proxy for raising temperature we show that the ferroelastic phase transition involves softening of a transverse acoustic mode, and confirm that the phase transition is discontinuous. Analysis of the complete phonon spectrum shows that the acoustic modes are responsible both for the very large thermal expansion seen in HCN and also for the thermodynamic driving force for the phase transition.

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.