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We review well-known signatures of disorder in crystallographic and inelastic neutron scattering data. We show that these can arise from different types of disorder, corresponding to different values of the system entropy. Correlating the entropy of a material with its atomistic structure and dynamics is in general a difficult problem that requires correlating information between multiple experimental techniques including crystallography, spectroscopy, and calorimetry. These comments are illustrated with particular reference to barocalorics, but are relevant to a broad range of calorics and other disordered crystalline materials., Comment: 11 pages, 3 figures

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 behaviour 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., Comment: 14 pages, 6 figures

Ammonium sulfate is a giant inverse barocaloric material that is cheaply and commercially available. Exploiting its potential for cooling applications requires an understanding of the mechanism driving the entropy change. Here we report an investigation by inelastic neutron scattering and density functional theory of the phonons under working conditions of temperature and pressure. We find excellent agreement between the experimental and calculated results. The ammonium librational modes that are crucial to the entropy change are identifiable by their negative Gr\"{u}neisen parameter. Our results connect the differences in structure across the phase transition to those in the atomic dynamics, suggesting a route towards designing new caloric materials., Comment: This manuscript has now been incorporated into 2201.02548. Please check there for the latest version

Solid-state cooling using barocaloric materials is a promising avenue for eco-friendly, inexpensive and highly efficient cooling. To design barocaloric compounds ready for deployment, it is essential to understand their thermodynamic behaviour under working conditions. To this end, we have studied the rotational dynamics in the molecular-ionic crystal ammonium sulfate under pressure, providing detailed insight into the origin of its large barocaloric effect. Using quasielastic neutron scattering experiments, we show that rotation of the ammonium cations is facilitated by pressure in the low-entropy phase, with the rotational "hopping" motion increasing in frequency as the pressure-induced phase transition is approached. We explain this unusual behaviour in terms of the competing hydrogen-bond networks represented by the two phases. This work includes the first results of a recently developed low-background, high-pressure gas cell for neutron scattering, showcasing its power in obtaining high-precision measurements of molecular dynamics under pressure., Comment: 8 pages, 5 figures

The deceptively simple inorganic salt ammonium sulfate undergoes a ferroelectric phase transition associated with a very large entropy change and both electrocaloric and barocaloric functionality. While the structural origins of the electrical polarisation are now well established, those of the entropy change have been controversial for over fifty years. This question is resolved here using a combination of DFT phonon calculations with inelastic neutron scattering under variable temperature and pressure, supported by complementary total and quasielastic neutron scattering experiments. A simple model of the entropy in which each molecular ion is disordered across the mirror plane in the high symmetry phase, although widely used in the literature, proves to be untenable. Instead, the entropy arises from low-frequency librations of ammonium ions in this phase, with harmonic terms that are very small or even negative. These results suggest that, in the search for molecular materials with functionality derived from large entropy changes, vibrational entropy arising from broad energy minima is likely to be just as important as configurational entropy arising from crystallographic disorder., Comment: 18 pages, 6 figures

Atomic vibrations play a vital role in the functions of various physical, chemical, and biological systems. The vibrational properties and the specific heat of crystalline bulk materials are well described by Debye theory, which successfully predicts the quadratic $\omega^{2}$ low-frequency scaling of the vibrational density of states (VDOS) in bulk ordered solids from few fundamental assumptions. 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 VDOS of amorphous ice confined to a thickness of $\approx 1$ nm inside graphene oxide membranes and we observe a crossover from the Debye $\omega^2$ scaling to an anomalous $\omega^3$ behaviour upon reducing the confinement size $L$. Additionally, using molecular dynamics simulations, we confirm the experimental findings and also prove that such a scaling of the VDOS appears in both crystalline and amorphous solids under slab-confinement. We theoretically demonstrate that this low-frequency $\omega^3$ 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 $\omega_\times= v L/2\pi$, with $v$ the speed of sound of the material, and we confirm this quantitative estimate with simulations. This new physical phenomenon, revealed by combining theoretical, experimental and simulations results, is relevant to a myriad of systems both in synthetic and biological contexts and it could impact various technological applications for systems under confinement such as nano-devices or thin films., Comment: v2: revised manuscript, matching the published version

We demonstrate that the amorphous material PAF-1, C[(C6H4)2]2, forms a continuous random network in which tetrahedral carbon sites are connected by 4,4'-biphenyl linkers. Experimental neutron total scattering measurements on deuterated, hydrogenous, and null-scattering samples agree with molecular dynamics simulations based on this model. From the MD model, we are able for the first time to interrogate the atomistic structure. The small-angle scattering is consistent with Porod scattering from particle surfaces, of the form Q^{-4}, where Q is the scattering vector. We measure a distinct peak in the scattering at Q = 0.45 {\AA}^{-1}, corresponding to the first sharp diffraction peak in amorphous silica, which indicates the structural analogy between these two amorphous tetrahedral networks., Comment: 17 pages

We use a symmetry-motivated approach to analyse neutron pair distribution function data to investigate the mechanism of negative thermal expansion (NTE) in ReO$_3$. This analysis shows that the local structure of ReO$_3$ is dominated by an in-phase octahedral tilting mode and that the octahedral units are far less flexible to scissoring type deformations than the octahedra in the related compound ScF$_3$. These results support the idea that structural flexibility is an important factor in NTE materials, allowing the phonon modes that drive a volume contraction of the lattice to occupy a greater volume in reciprocal space. The lack of flexibility in ReO$_3$ restricts the NTE-driving phonons to a smaller region of reciprocal space, limiting the magnitude and temperature range of NTE. In addition, we investigate the thermal expansion properties of the material at high temperature and do not find the reported second NTE region. Finally, we show that the local fluctuations, even at elevated temperatures, respect the symmetry and order parameter direction of the observed $P4/mbm$ high pressure phase of ReO$_3$. The result indicates that the motions associated with rigid unit modes are highly anisotropic in these systems., Comment: 9 pages, 6 figures

The counter-intuitive phenomenon of pressure-induced softening in materials is likely to be caused by the same dynamical behaviour that produces negative thermal expansion. Through a combination of molecular dynamics simulation on an idealised 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$_3$, with values of the pressure-derivative of the bulk modulus $B$, $B^\prime = \partial B / \partial P$, reaching as low as $-40 \pm 1$.

Negative thermal expansion (NTE) - the phenomenon where some materials shrink rather than expand when heated - is both intriguing and useful, but remains poorly understood. Current understanding hinges on the role of specific vibrational modes, but in fact thermal expansion is a weighted sum of contributions from every possible mode. Here we overcome this difficulty by deriving a real-space model of atomic motion in the prototypical NTE material scandium trifluoride, ScF3, from total neutron scattering data. We show that NTE in this material depends not only on rigid unit modes - the vibrations in which the scandium coordination octahedra remain undistorted - but also on modes that distort these octahedra. Furthermore, in contrast with previous predictions, we show that the quasiharmonic approximation coupled with renormalisation through anharmonic interactions describes this behaviour well. Our results point the way towards a new understanding of how NTE is manifested in real materials., Comment: 13 pages, 6 figures; version 4

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, far less is known about their behaviour under pressure. We have studied the structures of of manganese and cobalt guanidinium formate under pressure using single-crystal X-ray and powder neutron diffraction. Remarkably, when pressure reduces these materials' volume, they transform to a phase isostructural to cadmium guanidinium formate, which has an larger volume. Using DFT calculations, we show that this counterintuitive behaviour depends on the hydrogen-bonded network of guanidinium ions, which act as struts protecting the metal formate framework against compression. Our results demonstrate more generally that engineering desirable crystal structures in the hybrid perovskites will depend on achieving suitable host-guest hydrogen-bonding geometries., Comment: 9 pages, 3 figures

We use a combination of neutron and X-ray total scattering measurements together with pair distribution function (PDF) analysis to characterise the variation in local structure across the orbital order--disorder transition in LaMnO$_3$. Our experimental data are inconsistent with a conventional order--disorder description of the transition, and reflect instead the existence of a discontinuous change in local structure between ordered and disordered states. Within the orbital-ordered regime, the neutron and X-ray PDFs are best described by a local structure model with the same local orbital arrangements as those observed in the average (long-range) crystal structure. We show that a variety of meaningfully-different local orbital arrangement models can give fits of comparable quality to the experimental PDFs collected within the disordered regime; nevertheless, our data show a subtle but consistent preference for the anisotropic Potts model proposed in \emph{Phys Rev.\ B} {\bf 79}, 174106 (2009). The key implications of this model are electronic and magnetic isotropy together with the loss of local inversion symmetry at the Mn site. We conclude with a critical assessment of the interpretation of PDF measurements when characterising local symmetry breaking in functional materials., Comment: 14 pages, 8 figures, 3 tables

Many ceramic and hybrid metal-organic framework materials show negative thermal expansion (NTE): they \textit{contract} instead of expanding on heating \cite{Barrera_Miller_Lind_Romao 2005}. Their structures are invariably characterised as a network of polyhedral groups of atoms that are connected through sharing of corner atoms or by shared ligands. Empirically, NTE materials tend to show pressure-induced softening, pressure enhancement of NTE, and the reduction of NTE on heating. But such effects have only been investigated in a small number of materials \cite{Pantea 2006,Chapman 2005,Chapman 2007,Fangexp 2013}, and as yet there is no general framework for understanding the whole suite of properties together. By studying models with Hamiltonians chosen to reflect the physical picture generally accepted as responsible for NTE in framework materials, we demonstrate that NTE, pressure-enhanced NTE, and pressure-induced softening naturally emerge together. We then show how anharmonic interactions lead to structural warm hardening---something that has only previously been seen in laser-excited warm-dense matter \cite{Ernstorfer 2009}---as well as to the transition from NTE to positive thermal expansion and the disappearing of the pressure-induced softening at high temperatures.

We investigate the temperature dependence of the pressure-induced softening in the negative thermal expansion material Zn(CN)$_2$ using neutron powder diffraction and molecular dynamics simulations. Both the simulation and experiment show that the pressure-induced softening only occurs above a minimum temperature and also weakens at high temperatures.

We report photoexcited-state crystal structures for two new members of the [Ru(SO_2)(NH_3)_4X]Y family: 1:X=H2O, Y=(+/-)-camphorsulfonate_2; 2:X=isonicotinamide, Y=tosylate_2. The excited states are metastable at 100 K, with a photoconversion fraction of 11.1(7)% achieved in 1, and 22.1(10)% and 26.9(10)% at the two distinct sites in 2.We further show using solid-state density-functional-theory calculations that the excited-state geometries achieved are strongly influenced by the local crystal environment. This result is relevant to attempts to rationally design related photoexcitation systems for optical data-storage applications., Comment: 6 pages, 5 figures