Hybrid materials, which combine inorganic and molecular components, often exhibit structural flexibility that enables unusual functional responses. Among them, Prussian blue analogs (PBAs) are a promising class for post-lithium battery technologies. Here, we show that nonequilibrium transformation processes govern the charge-storage mechanism of a PBA electrode, K2Mn[Fe(CN)6]. Ostensibly, this behavior mirrors that observed in high-rate cycling of conventional cathodes such as LiFePO4 yet arises here for fundamentally different reasons-namely, low elastic moduli and cooperative distortions inherent to the hybrid framework. Using operando x-ray absorption spectroscopy with Metropolis matrix factorization and x-ray diffraction, we show that framework flexibility limits transport kinetics and promotes collective, metastable pathways. Our results not only highlight various directions for PBA cathode optimization but also suggest a broader relevance of nonequilibrium mechanisms for mass transport in hybrid materials beyond PBAs alone.

The contrasting crystal and magnetic structures of four related iron oxide chalcogenides are reported. Ae2FeO3CuCh (Ae = Ca, Sr; Ch = S, Se) all crystallize in the Sr2GaO3CuS structure with alkaline earth iron oxide layers containing double layers of linked FeO5 square pyramids containing Fe3+ ions separated by antifluorite-type [Cu2Ch2]2- layers. Structural distortions occur below room temperature when the small Ca2+ ions are present, and these involve cooperative tilting of the FeO5 square pyramids. Magnetic reflections present in the diffraction patterns can be indexed using either √2a × √2a × c or √2a × √2a × 2c expansions of the nuclear cell with nearest-neighbor Fe3+ moments coupling antiferromagnetically and with temperature-dependent orientations relative to the crystallographic directions. The magnetic structures of these compounds are subtly different in detail, partly on account of the low directional preference of the high-spin d5 Fe3+ moments.

Iron-based superconductors have attracted much attention for their high superconducting temperatures and high upper critical fields, which make them promising candidates for application as well as fundamentally important for our understanding of superconductivity. One feature of these superconductors is their ability to intercalate and deintercalate species from between their iron-containing layers, something not available in cuprate high-temperature superconductors or niobium-based conventional superconductors used in technologies. This provides an opportunity for switchable changes in the superconducting properties as a function of chemical conditions, but the resulting structures are often hard to characterize due to loss of crystallinity and sometimes the formation of multiphase products. Here, we explore both the synthesis and decomposition of potassium and ammonia-intercalated iron selenide superconductors through in situ powder X-ray diffraction. We report a complete phase diagram including two new solution-stable ammonia-rich phases and several metastable forms. We give accurate characterization of the reported ammonia-poor forms using a combination of neutron and X-ray powder diffraction, using an innovative supercell approach to describe the phase breadth within the samples. These results give rare insight into stepwise changes occurring in solids along multiple reaction pathways, which demonstrate the importance of in situ diffraction techniques.

Alkali transition-metal layered compounds usually contain only one type of alkali cation between the edge-shared octahedra layers. Herein, the ternary phase diagram A(2)Ni(2)TeO(6) (A = Li, Na, K) was explored through solid-state synthesis and new alkali-mixed compositions showing alternation of distinct alkali layers are obtained. Such intergrowth structures are synthesized either by a single high-temperature treatment from raw chemicals or through reaction between layered precursors, the latter involving a solid-state process triggered at moderate temperatures. The in-depth characterization of the multiple cationic orderings is performed by combining powder diffraction techniques (X-rays and neutrons), high-resolution transmission electron microscopy, and solid-state NMR spectroscopy. In addition to the Ni/Te honeycomb ordering, alternation of lithium layers with sodium or potassium layers is observed for compositions (Li/Na)(2)Ni2TeO6 or (Li/K)(2)Ni2TeO6, respectively. Crystal structure solving was achieved by stacking building blocks of the respective single alkali layered oxides and unveiled a complex out-of-plane ordering of honeycomb layers. Moreover, a solid-state reaction between Li2Ni2TeO6 and NaKNi2TeO6 enables preparation of the new phase Li similar to 1Na similar to 0.5K similar to 0.5Ni2TeO6, a unique example containing up to three alkali cations and exhibiting a more complex stacking with sodium and potassium cations occupying the same layer. This investigation confirms that the chemical versatility of layered alkali transition-metal compounds could also occur on the alkali layer. Following the research methodology described here, we revisit the crystal chemistry of alkali transition-metal layered materials by exploring alkali ion substitutions previously thought infeasible, in order to find new alkali-mixed compositions.

We use in situ synchrotron X-ray diffraction measurements to monitor the solvothermal crystallization mechanism of the aperiodic metal-organic framework TRUMOF-1. Following an initial incubation period, TRUMOF-1 forms as a metastable intermediate that subsequently transforms into an ordered product with triclinic crystal symmetry. We determine the structure of this ordered phase, which we call msw-TRUMOF-1, and show that it is related to TRUMOF-1 through topotactic reorganization of linker occupancies. Our results imply that the connectivity of TRUMOF-1 can be reorganized, as required for data storage and manipulation applications.

We report the magnetic behaviour of the hybrid perovskites [Gua]Mn1–xFe2x/3(HCOO)3 (0 < x < 0.88), showing that vacancy ordering drives bulk ferrimagnetism for x > 0.6. The behaviour is rationalised in terms of a simple microscopic model of percolation-induced ferrimagnetism. Monte Carlo simulations driven by this model reproduce the experimental dependence of magnetic susceptibility on x and show that, at intermediate compositions, domains of short-range vacancy order lead to the emergence of local magnetisation. Our results open up a new avenue for the design of multiferroic hybrid perovskites.

Oxide ions in transition metal oxide cathodes can store charge at high voltage offering a route towards higher energy density batteries. However, upon charging these cathodes, the oxidized oxide ions condense to form molecular O2 trapped in the material. Consequently, the discharge voltage is much lower than charge, leading to undesirable voltage hysteresis. Here we capture the nature of the electron holes on O2− before O2 formation by exploiting the suppressed transition metal rearrangement in ribbon-ordered Na0.6[Li0.2Mn0.8]O2. We show that the electron holes formed are delocalized across the oxide ions coordinated to two Mn (O–Mn2) arranged in ribbons in the transition metal layers. Furthermore, we track these delocalized hole states as they gradually localize in the structure in the form of trapped molecular O2 over a period of days. Establishing the nature of hole states on oxide ions is important if truly reversible high-voltage O-redox cathodes are to be realized. The mechanism of oxygen redox in high-energy transition metal oxide cathodes is elusive. Here the authors illustrate the nature of the electron-hole states on oxide ions, offering insights for realizing reversible, high-voltage cathodes.

Tetrathiatriarylmethyl radicals (TAM or trityl) are receiving increasing attention in various fields of magnetic resonance such as imaging, dynamic nuclear polarization, spin labeling, and, more recently, molecular magnetism and quantum information technology. Here, a trityl radical attached via a phenyl bridge to a copper(II)tetraphenylporphyrin was synthesized, and its magnetic properties studied by multi-frequency continuous-wave electron paramagnetic resonance (EPR) spectroscopy and magnetic measurements. EPR revealed that the electron spin-spin coupling constant J between the trityl and Cu2+ spin centers is ferromagnetic with a magnitude of -2.3 GHz (-0.077 cm(-1), +J(sic)(1)(sic)(2) convention) and a distribution width of 1.2 GHz (0.040 cm(-1)). With the help of density functional theory (DFT) calculations, the obtained ferromagnetic exchange coupling, which is unusual for para-substituted phenyl-bridged biradicals, could be related to the almost perpendicular orientation of the phenyl linker with respect to the porphyrin and trityl ring planes in the energy minimum, while the J distribution was rationalized by the temperature weighted rotation of the phenyl bridge about the molecular axis connecting both spin centers. This study exemplifies the importance of molecular dynamics for the homogeneity (or heterogeneity) of the magnetic properties of trityl-based systems.

We revisit the problem of polytypism in layered $\textit{MX}_2$ materials, with a view to reinterpreting the phase space accessible to this family. Our starting point is to develop a simple, constructive and compact label for the most commonly observed stacking arrangements that is similar to the Glazer notation used to label tilt systems in perovskites. The key advantage of this label in the context of $\textit{MX}_2$ systems is that it contains sufficient information to generate the corresponding stacking sequences uniquely. Using a related approach, we generate a Cartesian representation of the phase space containing all possible $\textit{MX}_2$ polytypes, with the most common structures appearing as limiting cases. We argue that variation in (e.g. composition, or temperature, or pressure) may allow navigation of this phase space along continuous paths. This interpretation is shown to be consistent with the structural evolution of stacking-faulted $\textit{MX}_2$ systems as a function of temperature and composition. Our study highlights the potential for controlling composition/structure/property relationships amongst layered $\textit{MX}_2$ materials in ways that might not previously have been obvious.

We revisit the problem of polytypism in layered ${MX}_{2}$ materials, with a view to reinterpreting the phase space accessible to this family. Our starting point is to develop a simple, constructive, and compact label for the most commonly observed stacking arrangements, similar to the Glazer notation used to label tilt systems in perovskites. The key advantage of this label in the context of ${MX}_{2}$ systems is that it contains sufficient information to generate the corresponding stacking sequences uniquely. Using a related approach, we generate a Cartesian representation of the phase space containing all possible ${MX}_{2}$ polytypes, with the most common structures appearing as limiting cases. We argue that variation in, e.g., composition, temperature, or pressure may allow navigation of this phase space along continuous paths. This interpretation is shown to be consistent with the structural evolution of stacking-faulted ${MX}_{2}$ systems as a function in temperature and pressure. In this way, our study highlights the potential for controlling composition/structure/property relationships among layered ${MX}_{2}$ materials in ways that might not previously have been obvious.

A new reduced phase derived from the excitonic insulator candidate Ta2NiSe5 has been synthesized via the intercalation of lithium. LiTa2NiSe5 crystallizes in the orthorhombic space group Pmnb (no. 62) with lattice parameters a = 3.50247(3) Å, b = 13.4053(4) Å, c = 15.7396(2) Å, and Z = 4, with an increase of the unit cell volume by 5.44(1)% compared with Ta2NiSe5. Significant rearrangement of the Ta-Ni-Se layers is observed, in particular a very significant relative displacement of the layers compared to the parent phase, similar to that which occurs under hydrostatic pressure. Neutron powder diffraction experiments and computational analysis confirm that Li occupies a distorted triangular prismatic site formed by Se atoms of adjacent Ta2NiSe5 layers with an average Li-Se bond length of 2.724(2) Å. Li-NMR experiments show a single Li environment at ambient temperature. Intercalation suppresses the distortion to monoclinic symmetry that occurs in Ta2NiSe5 at 328 K and that is believed to be driven by the formation of an excitonic insulating state. Magnetometry data show that the reduced phase has a smaller net diamagnetic susceptibility than Ta2NiSe5 due to the enhancement of the temperature-independent Pauli paramagnetism caused by the increased density of states at the Fermi level evident also from the calculations, consistent with the injection of electrons during intercalation and formation of a metallic phase.

We study the phenomenology of cooperative off-centering of K+ ions in potassiated Prussian blue analogues (PBAs). The principal distortion mechanism by which this off-centering occurs is termed a "K-ion slide", and its origin is shown to lie in the interaction between local electrostatic dipoles that couple through a combination of electrostatics and elastic strain. Using synchrotron powder X-ray diffraction measurements, we determine the crystal structures of a range of low-vacancy K2M[Fe(CN)6] PBAs (M = Ni, Co, Fe, Mn, Cd) and establish an empirical link between composition, temperature, and slide-distortion magnitude. Our results reflect the common underlying physics responsible for K-ion slides and their evolution with temperature and composition. Monte Carlo simulations driven by a simple model of dipolar interactions and strain coupling reproduce the general features of the experimental phase behavior. We discuss the implications of our study for optimizing the performance of PBA K-ion battery cathode materials and also its relevance to distortions in other, conceptually related, hybrid perovskites.

Topochemistry enables step-by-step conversions of solid-state materials often leading to metastable structures that retain initial structural motifs. Recent advances in this field revealed many examples where relatively bulky anionic constituents were actively involved in redox reactions during (de)intercalation processes. Such reactions are often accompanied by anion-anion bond formation, which heralds possibilities to design novel structure types disparate from known precursors, in a controlled manner. Here multistep conversion is presented of layered oxychalcogenides Sr2MnO2Cu1.5Ch2 (Ch = S, Se) into Cu-deintercalated phases where antifluorite type (Cu1.5Ch2)2.5- slabs collapsed into 2D arrays of chalcogen dimers. The collapse of the sulphide layers on deintercalation led to various stacking types of Sr2MnO2Ch2 slabs, which formed unprecedented polychalcogenide structures unattainable by conventional high-temperature syntheses. Anion-redox topochemistry is demonstrated to be of interest not only for electrochemical applications but also to design of complex novel layered architectures.

Intercalation of alkali and alkaline earth metals into ZrSe3 via soft chemical routes injects electrons and has a significant effect on the selenide-selenide bonding. K, Rb and Cs intercalates of ZrSe3 prepared at low temperatures (-78 degrees C) from metal ammonia solutions contrast with related polymorphs obtained at high temperature (850 degrees C). KxZrSe3 synthesised at low temperatures crystallises in orthorhombic Cmc21, while the polymorph obtained at high temperatures crystallises in Immm. The two structures prepared under drastically different conditions differ by relative shifting of ZrSe3 layers. In contrast, CsxZrSe3 shows the Immm polymorph at low temperature and the Cmc2(1) polymorph at high temperatures, while a single RbxZrSe(3) polymorph in Immm is formed at both temperatures. Intercalation of Ca from liquid ammonia facilitates the co-intercalation of the solvent because of the strong solvation of Ca2+. This compound has severe faulting due to the flexibility in the relative shifts of adjacent ZrSe3 layers.

Sr2NiO2Cu2Se2, comprising alternating [Sr2NiO2]2+ and [Cu2Se2]2- layers, is reported. Powder neutron diffraction shows that the Ni2+ ions, which are in a highly elongated NiO4Se2 environment with D4h symmetry, adopt a high-spin configuration and carry localized magnetic moments which order antiferromagnetically below ∼160 K in a √2a × √2a × 2c expansion of the nuclear cell with an ordered moment of 1.31(2) μB per Ni2+ ion. The adoption of the high-spin configuration for this d8 cation in a pseudo-square-planar ligand field is supported by consideration of the experimental bond lengths and the results of density functional theory (DFT) calculations. This is in contrast to the sulfide analogue Sr2NiO2Cu2S2, which, according to both experiment and DFT calculations, has a much more elongated ligand field, more consistent with the low-spin configuration commonly found for square-planar Ni2+, and accordingly, there is no evidence for magnetic moment on the Ni2+ ions. Examination of the solid solution Sr2NiO2Cu2(Se1-x S x )2 shows direct evidence from the evolution of the crystal structure and the magnetic ordering for the transition from high-spin selenide-rich compounds to low-spin sulfide-rich compounds as a function of composition. Compression of Sr2NiO2Cu2Se2 up to 7.2 GPa does not show any structural signature of a change in the spin state. Consideration of the experimental and computed Ni2+ coordination environments and their subtle changes as a function of temperature, in addition to transitions evident in the transport properties and magnetic susceptibilities in the end members, Sr2NiO2Cu2Se2 and Sr2NiO2Cu2S2, suggest that simple high-spin and low-spin models for Ni2+ may not be entirely appropriate and point to further complexities in these compounds.

We report the synthesis, crystal structure, thermal response, and electrochemical behaviour of the Prussian blue analogue (PBA) K2Cu[Fe(CN)6]. From a structural perspective, this is the most complex PBA yet characterised: its triclinic crystal structure results from an interplay of cooperative Jahn–Teller order, octahedral tilts, and a collective `slide' distortion involving K-ion displacements. These different distortions give rise to two crystallographically-distinct K-ion channels with different mobilities. Variable-temperature X-ray powder diffraction measurements show that K-ion slides are the lowest-energy distortion mechanism at play, as they are the only distortion to be switched off with increasing temperature. Electrochemically, the material operates as a K-ion cathode with a high operating voltage, and an improved initial capacity relative to higher-vacancy PBA alternatives. On charging, K+ ions are selectively removed from a single K-ion channel type and the slide distortions are again switched on and off accordingly. We discuss the functional importance of various aspects of structural complexity in this system, placing our discussion in the context of other related PBAs.

We report the synthesis, crystal structure, thermal response, and electrochemical behavior of the Prussian blue analogue (PBA) K2Cu[Fe(CN)6]. From a structural perspective, this is the most complex PBA yet characterized: its triclinic crystal structure results from an interplay of cooperative Jahn-Teller order, octahedral tilts, and a collective "slide" distortion involving K-ion displacements. These different distortions give rise to two crystallographically distinct K-ion channels with different mobilities. Variable-temperature X-ray powder diffraction measurements show that K-ion slides are the lowest-energy distortion mechanism at play, as they are the only distortion to be switched off with increasing temperature. Electrochemically, the material operates as a K-ion cathode with a high operating voltage and an improved initial capacity relative to higher-vacancy PBA alternatives. On charging, K+ ions are selectively removed from a single K-ion channel type, and the slide distortions are again switched on and off accordingly. We discuss the functional importance of various aspects of structural complexity in this system, placing our discussion in the context of other related PBAs.

In the dense metal-organic framework Na[Mn(HCOO)_{3}], Mn^{2+} ions (S=5/2) occupy the nodes of a "trillium" net. We show that the system is strongly magnetically frustrated: the Néel transition is suppressed well below the characteristic magnetic interaction strength; short-range magnetic order persists far above the Néel temperature; and the magnetic susceptibility exhibits a pseudo-plateau at 1/3-saturation magnetization. A simple model of nearest-neighbor Heisenberg antiferromagnetic and dipolar interactions accounts quantitatively for all observations, including an unusual 2-k magnetic ground state. We show that the relative strength of dipolar interactions is crucial to selecting this particular ground state. Geometric frustration within the classical spin liquid regime gives rise to a large magnetocaloric response at low applied fields that is degraded in powder samples as a consequence of the anisotropy of dipolar interactions.

The development of sustainable and efficient cryogenic cooling materials is currently the subject of extensive research, with the aim of relieving the dependence o fcurrent low-temperature cooling methods on expensive and nonrenewable liquid helium. One potential method to achieve this is the use of materials demonstrating the magnetocaloric effect, where the cycling of an applied magneticfield leads to a net coolingeffect due to changes in magnetic entropy upon application and removal of an externalmagneticfield. This study details the synthesis and characterization of aLn3(adipate)4.5(DMF)2series (where Ln = Gd-Er) of metal-organic framework (MOF)materials incorporating aflexible adipate ligand and their associated magnetocaloric andthermal expansion properties. The magnetocaloric performance of theGd3(adipate)4.5(DMF)2material was found to exhibit the highest magnetic entropy changesof the series, with a peak entropy change of 36.4 J kg-1K-1for a 5-0 Tfield change at atemperature of 2 K, which is suited for ultra-low-temperature cooling applications. Thermal expansion properties were also investigated within these materials, demonstrating modest negative and large positive thermal expansion identified along the different crystallographic axes within the MOF structures over a 100-300 K temperature range that demonstrated the novel mechanical properties of these adipate framework structures.