While the Born elastic stability criteria are well-known for cubic crystals, there is some confusion in the literature about the form it should take for lower symmetry crystal classes. We present here closed form necessary and sufficient conditions for elastic stability in all crystal classes, as a concise and pedagogical reference to stability criteria in non-cubic materials.

Throughout much of condensed matter science, correlated disorder is key to material function. While structural and compositional defects are known to exist within a variety of metal–organic frameworks, the prevailing understanding is that these defects are only ever included in a random manner. Here we show—using a combination of diffuse scattering, electron microscopy, anomalous X-ray scattering, and pair distribution function measurements—that correlations between defects can in fact be introduced and controlled within a hafnium terephthalate metal–organic framework. The nanoscale defect structures that emerge are an analogue of correlated Schottky vacancies in rocksalt-structured transition metal monoxides and have implications for storage, transport, optical and mechanical responses. Our results suggest how the diffraction behaviour of some metal–organic frameworks might be reinterpreted, and establish a strategy of exploiting correlated nanoscale disorder as a targetable and desirable motif in metal–organic framework design.

Adsorption-based phenomena are important in gas separations, such as the treatment of greenhouse-gas and toxic-gas pollutants, and in water-adsorption-based heat pumps for solar cooling systems. The ability to tune the pore size, shape and functionality of crystalline porous coordination polymers--or metal-organic frameworks (MOFs)--has made them attractive materials for such adsorption-based applications. The flexibility and guest-molecule-dependent response of MOFs give rise to unexpected and often desirable adsorption phenomena. Common to all isothermal gas adsorption phenomena, however, is increased gas uptake with increased pressure. Here we report adsorption transitions in the isotherms of a MOF (DUT-49) that exhibits a negative gas adsorption; that is, spontaneous desorption of gas (methane and n-butane) occurs during pressure increase in a defined temperature and pressure range. A combination of in situ powder X-ray diffraction, gas adsorption experiments and simulations shows that this adsorption behaviour is controlled by a sudden hysteretic structural deformation and pore contraction of the MOF, which releases guest molecules. These findings may enable technologies using frameworks capable of negative gas adsorption for pressure amplification in micro- and macroscopic system engineering. Negative gas adsorption extends the series of counterintuitive phenomena such as negative thermal expansion and negative refractive indices and may be interpreted as an adsorptive analogue of force-amplifying negative compressibility transitions proposed for metamaterials.

Metal-organic frameworks (MOFs) are a family of chemically diverse materials, with applications in a wide range of fields, covering engineering, physics, chemistry, biology and medicine. Until recently, research has focused almost entirely on crystalline structures, yet now a clear trend is emerging, shifting the emphasis onto disordered states, including 'defective by design' crystals, as well as amorphous phases such as glasses and gels. Here we introduce a strongly associated MOF liquid, obtained by melting a zeolitic imidazolate framework. We combine in situ variable temperature X-ray, ex situ neutron pair distribution function experiments, and first-principles molecular dynamics simulations to study the melting phenomenon and the nature of the liquid obtained. We demonstrate from structural, dynamical, and thermodynamical information that the chemical configuration, coordinative bonding, and porosity of the parent crystalline framework survive upon formation of the MOF liquid.

We provide a general thermodynamic framework for the understanding of guest-induced structural transitions in hybrid organic-inorganic materials. The method is based on the analysis of experimental adsorption isotherms. It allows the determination of the free energy differences between host structures involved in guest-induced transitions, especially hard to obtain experimentally. We discuss the general case of adsorption in flexible materials and show how a few key quantities, such as pore volumes and adsorption affinities, entirely determine the phenomenology of adsorption, including the occurrence of structural transitions. On the basis of adsorption thermodynamics, we then propose a taxonomy of guest-induced structural phase transitions and the corresponding isotherms. In particular, we derive generic conditions for observing a double structural transition upon adsorption, often resulting in a two-step isotherm. Finally, we show the wide applicability and the robustness of the model through three case studies of topical hybrid organic-inorganic frameworks: the hysteretic hydrogen adsorption in Co(1,4-benzenedipyrazolate), the guest-dependent gate-opening in Cu(4,4'-bipyridine)(2,5-dihydroxybenzoate)2 and the CO2-induced "breathing" of hybrid material MIL-53.

Recent years have seen a large increase of the research effort focused on framework materials, including the nowadays-ubiquitous metal−organic frameworks but also dense coordination polymers, covalent organic frameworks, and molecular frameworks. With the quickly increasing number of structures synthesized and characterized, one pattern emerging is the common occurrence of flexibility. More specifically, an important number of framework materials are stimuli-responsive: their structure can undergo changes of large amplitude in response to physical or chemical stimulation. They can display transformations induced by temperature, mechanical pressure, guest adsorption or evacuation, light absorption, etc. and are sometimes referred to as smart materials, sof t crystals, or dynamic materials. This Perspective highlights recent progress in this field, showcasing some of the most novel and unusual responses to stimuli, as well as advances in the fundamental understanding of flexible framework materials.

We report on the implementation of a tool for the analysis of second-order elastic stiffness tensors, provided with both an open-source Python module and a standalone online application allowing the visualization of anisotropic mechanical properties. After describing the software features, how we compute the conventional elastic constants and how we represent them graphically, we explain our technical choices for the implementation. In particular, we focus on why a Python module is used to generate the HTML web page with embedded Javascript for dynamical plots.

The use of the osmotic thermodynamic model, combined with a series of methane and carbon dioxide gas adsorption experiments at various temperatures, has allowed to shed some new light on the fascinating phase behavior of flexible MIL-53(Al) metal-organic frameworks. A generic temperature-loading phase diagram has been derived; it is shown that the breathing effect in MIL-53 is a very general phenomenon, which should be observed in a limited temperature range regardless of the guest molecule. In addition, the previously proposed stress model for the structural transitions of MIL-53 is shown to be transferable from xenon to methane adsorption. The stress model also provides a theoretical framework for understanding the existence of lp/np phase mixtures at pressures close to the breathing transition pressure, without having to invoke an inhomogeneous distribution of the adsorbate in the porous sample.