How to get maximum structure information from anisotropic displacement parameters obtained by three-dimensional electron diffraction: an experimental study on metal-organic frameworks

Three-dimensional electron diffraction (3D ED) has been used for ab initio structure determination of various types of nanocrystals, such as metal-organic frameworks (MOFs), zeolites, metal oxides and organic crystals. These crystals are often obtained as polycrystalline powders, which are too small for single-crystal X-ray diffraction (SCXRD). While it is now possible to obtain accurate atomic positions of nanocrystals by adopting kinematical refinement against 3D ED data, most new structures are refined with isotropic displacement parameters (U _eq), which limits the detection of possible structure disorders and atomic motions. Anisotropic displacement parameters (ADPs, U^ij ) obtained by anisotropic structure refinement, on the other hand, provide information about the average displacements of atoms from their mean positions in a crystal, which can provide insights with respect to displacive disorder and flexibility. Although ADPs have been obtained from some 3D ED studies of MOFs, they are seldom mentioned or discussed in detail. We report here a detailed study and interpretation of structure models refined anisotropically against 3D ED data. Three MOF samples with different structural complexity and symmetry, namely ZIF-EC1, MIL-140C and Ga(OH)(1,4-ndc) (1,4-ndcH₂ is naphthalene-1,4-dicarboxylic acid), were chosen for the studies. We compare the ADPs refined against individual data sets and how they are affected by different data-merging strategies. Based on our results and analysis, we propose strategies for obtaining accurate structure models with interpretable ADPs based on kinematical refinement against 3D ED data. The ADPs of the obtained structure models provide clear and unambiguous information about linker motions in the MOFs.

Chemical Diversity for Tailoring Negative Thermal Expansion

Negative thermal expansion (NTE), referring to the lattice contraction upon heating, has been an attractive topic of solid-state chemistry and functional materials. The response of a lattice to the temperature field is deeply rooted in its structural features and is inseparable from the physical properties. For the past 30 years, great efforts have been made to search for NTE compounds and control NTE performance. The demands of different applications give rise to the prominent development of new NTE systems covering multifarious chemical substances and many preparation routes. Even so, the intelligent design of NTE structures and efficient tailoring for lattice thermal expansion are still challenging. However, the diverse chemical routes to synthesize target compounds with featured structures provide a large number of strategies to achieve the desirable NTE behaviors with related properties. The chemical diversity is reflected in the wide regulating scale, flexible ways of introduction, and abundant structure-function insights. It inspires the rapid growth of new functional NTE compounds and understanding of the physical origins. In this review, we provide a systematic overview of the recent progress of chemical diversity in the tailoring of NTE. The efficient control of lattice and deep structural deciphering are carefully discussed. This comprehensive summary and perspective for chemical diversity are helpful to promote the creation of functional zero-thermal-expansion (ZTE) compounds and the practical utilization of NTE.

What Lies beneath a Metal-Organic Framework Crystal Structure? New Design Principles from Unexpected Behaviors

The rational design principles established for metal-organic frameworks (MOFs) allow clear structure-property relationships, fueling expansive growth for energy storage and conversion, catalysis, and beyond. However, these design principles are based on the assumption of compositional and structural rigidity, as measured crystallographically. Such idealization of MOF structures overlooks subtle chemical aspects that can lead to departures from structure-based chemical intuition. In this Perspective, we identify unexpected behavior of MOFs through literature examples. Based on this analysis, we conclude that departures from ideality are not uncommon. Whereas linker topology and metal coordination geometry are useful starting points for understanding MOF properties, we anticipate that deviations from the idealized crystal representation will be necessary to explain important and unexpected behaviors. Although this realization reinforces the notion that MOFs are highly complex materials, it should also stimulate a broader reexamination of the literature to identify corollaries to existing design rules and reveal new structure-property relationships.

Homo- and Heterosolvent Modifications of Hofmann-Type Flexible Two-Dimensional Layers for Colossal Interlayer Thermal Expansions

Two-dimensional Hofmann-type coordination polymers of type Mn(H₂O)₂[Pd(CN)₄]·xH₂O (1·xH₂O; x = 0, 1, and 4), Mn(H₂O)(MeOH)[Pd(CN)₄]·2MeOH (2·2MeOH), and Mn(MeOH)₂[Pd(CN)₄]·MeOH (3·MeOH) have been synthesized. The homosolvent-bound 1·4H₂O, 1·H₂O, and 3·MeOH polymers consist of undulating layer structures, whereas the structure of heterosolvent-bound 2·2MeOH consists of "Janus-like" flat layers in which water-bound and MeOH-bound-sides are present. 1·4H₂O and 1·H₂O exhibited anisotropic two-dimensional thermal expansions involving structural transformations of the undulating layers; one layer axis expands while the other contracts. 2·2MeOH exhibits anisotropic thermal expansion in which the flat layers shift sideways as the temperature is increased, with colossal interlayer expansion occurring (α_c = +200 MK^-1 over 140-180 K, α_c = +165 MK^-1 over 200-280 K). 3·MeOH also showed colossal interlayer expansion (α_c = +216 MK^-1) together with expansion of the undulating layers.

Rotational Dynamics of Linkers in Metal⁻Organic Frameworks

Among the numerous fascinating properties of metal⁻organic frameworks (MOFs), their rotational dynamics is perhaps one of the most intriguing, with clear consequences for adsorption and separation of molecules, as well as for optical and mechanical properties. A closer look at the rotational mobility in MOF linkers reveals that it is not only a considerably widespread phenomenon, but also a fairly diverse one. Still, the impact of these dynamics is often understated. In this review, we address the various mechanisms of linker rotation reported in the growing collection of literature, followed by a highlight of the methods currently used in their study, and we conclude with the impacts that such dynamics have on existing and future applications.

Positive and Negative Two-Dimensional Thermal Expansion via Relaxation of Node Distortions

The ability to tune physical properties is attractive for the development of new materials for myriad applications. Understanding and controlling the structural dynamics in complicated network structures like coordination polymers (CPs) is particularly challenging. We report a series of two-dimensional CPs [Mn(salen)]₂[M(CN)₄]· xH₂O (M = Pt (1), PtI₂ (2), and MnN (3)) incorporating zigzag cyano-network layers that display composition-dependent anisotropic thermal expansion properties. Variable-temperature single-crystal X-ray structural analyses demonstrated that the thermal expansion behavior is caused by double structural distortions involving [Mn(salen)]⁺ units incorporated into the zigzag layers. Thermal relaxations produce structural transformations resulting in positive thermal expansion for 2·H₂O and negative thermal expansion for 3. In the case of 1·H₂O, the relaxation does not occur and zero thermal expansion results in the plane between 200 to 380 K. The present study proposes a new strategy based on structural distortions in coordination networks to control thermal responsivities of frameworks.

Zero in-Plane Thermal Expansion in Guest-Tunable 2D Coordination Polymers

Zero in-plane thermal expansion (TE) in a two-dimensional (2D) coordination polymer is demonstrated. The combination of components that expand and those that shrink into zigzag layers results in no net area change in the 2D materials with temperature. Single crystals of [Mn(salen)]₂[Mn(N)(CN)₄(guest)] (salen = N,N'-ethylenebis(salicylideneaminato), guest = MeOH and MeCN) were prepared, and variable-temperature single-crystal X-ray structural analyses demonstrated that these compounds exhibited both anisotropic positive and negative thermal expansion depending on the guest species. The TE behavior results from distortions of the octahedral coordination geometry of [Mn(salen)]⁺ units in the zigzag layers. When both guests MeOH and MeCN were incorporated into one material, [Mn(salen)]₂[Mn(N)(CN)₄(MeOH)_0.25(MeCN)_0.75], zero in-plane TE resulted in a range of temperature between 380 and 440 K.

Controlling Thermal Expansion: A Metal-Organic Frameworks Route

Controlling thermal expansion is an important, not yet resolved, and challenging problem in materials research. A conceptual design is introduced here, for the first time, for the use of metal-organic frameworks (MOFs) as platforms for controlling thermal expansion devices that can operate in the negative, zero, and positive expansion regimes. A detailed computer simulation study, based on molecular dynamics, is presented to support the targeted application. MOF-5 has been selected as model material, along with three molecules of similar size and known differences in terms of the nature of host-guest interactions. It has been shown that adsorbate molecules can control, in a colligative way, the thermal expansion of the solid, so that changing the adsorbate molecules induces the solid to display positive, zero, or negative thermal expansion. We analyze in depth the distortion mechanisms, beyond the ligand metal junction, to cover the ligand distortions, and the energetic and entropic effect on the thermo-structural behavior. We provide an unprecedented atomistic insight on the effect of adsorbates on the thermal expansion of MOFs as a basic tool toward controlling the thermal expansion.

Flexible MOFs under stress: pressure and temperature

In the recent past an enormous number of Metal–Organic Framework type compounds (MOFs) have been synthesized.

Hydration-dependent anomalous thermal expansion behaviour in a coordination polymer

A polar coordination polymer has been synthesised that exhibits anomalous anisotropic thermal expansion. The guest water molecules of the as-synthesised complex can be removed on activation without loss of crystal singularity to yield the fully dehydrated form that shows considerably different thermal expansion behaviour compared to its hydrated analogue.

Crystallographic studies of gas sorption in metal-organic frameworks

Metal-organic frameworks (MOFs) are a class of porous crystalline materials of modular design. One of the primary applications of these materials is in the adsorption and separation of gases, with potential benefits to the energy, transport and medical sectors. In situ crystallography of MOFs under gas atmospheres has enabled the behaviour of the frameworks under gas loading to be investigated and has established the precise location of adsorbed gas molecules in a significant number of MOFs. This article reviews progress in such crystallographic studies, which has taken place over the past decade, but has its origins in earlier studies of zeolites, clathrates etc. The review considers studies by single-crystal or powder diffraction using either X-rays or neutrons. Features of MOFs that strongly affect gas sorption behaviour are discussed in the context of in situ crystallographic studies, specifically framework flexibility, and the presence of (organic) functional groups and unsaturated (open) metal sites within pores that can form specific interactions with gas molecules.

Structure and thermal expansion of the tungsten bronze Pb2KNb5O15

Negative thermal expansion and abnormal spontaneous polarization direction along b axis in tetragonal tungsten bronze Pb₂KNb₅O₁₅ are presented. A Pb–O covalency, octahedrons cooperative rotation mechanism is proposed.

A hybrid with uniaxial negative thermal expansion behaviour: the synergistic role of organic and inorganic components

Through the study on a new Mn₂(api)Sb₂S₅compound, we propose a strategy for designing a novel hybrid with uniaxial NTE behaviour based on the synergistic role of organic and inorganic components.

Multifunctional MOFs through CO2fixation: a metamagnetic kagome lattice with uniaxial zero thermal expansion and reversible guest sorption

The properties of atmospheric CO₂fixation, metamagnetism, reversible guest adsorption and zero thermal expansion have been combined in a single robust MOF, [Cu₃(bpac)₃(CO₃)₂](ClO₄)₂·H₂O (1·H₂O).

Phase transitions, prominent dielectric anomalies, and negative thermal expansion in three high thermally stable ammonium magnesium-formate frameworks

We present three Mg-formate frameworks, incorporating three different ammoniums: [NH4][Mg(HCOO)3] (1), [CH3CH2NH3][Mg(HCOO)3] (2) and [NH3(CH2)4NH3][Mg2(HCOO)6] (3). They display structural phase transitions accompanied by prominent dielectric anomalies and anisotropic and negative thermal expansion. The temperature-dependent structures, covering the whole temperature region in which the phase transitions occur, reveal detailed structural changes, and structure-property relationships are established. Compound 1 is a chiral Mg-formate framework with the NH4(+) cations located in the channels. Above 255 K, the NH4(+) cation vibrates quickly between two positions of shallow energy minima. Below 255 K, the cations undergo two steps of freezing of their vibrations, caused by the different inner profiles of the channels, producing non-compensated antipolarization. These lead to significant negative thermal expansion and a relaxor-like dielectric response. In perovskite 2, the orthorhombic phase below 374 K possesses ordered CH3CH2NH3(+) cations in the cubic cavities of the Mg-formate framework. Above 374 K, the structure becomes trigonal, with trigonally disordered cations, and above 426 K, another phase transition occurs and the cation changes to a two-fold disordered state. The two transitions are accompanied by prominent dielectric anomalies and negative and positive thermal expansion, contributing to the large regulation of the framework coupled the order-disorder transition of CH3CH2NH3(+). For niccolite 3, the gradually enhanced flipping movement of the middle ethylene of [NH3(CH2)4NH3](2+) in the elongated framework cavity finally leads to the phase transition with a critical temperature of 412 K, and the trigonally disordered cations and relevant framework change, providing the basis for the very strong dielectric dispersion, high dielectric constant (comparable to inorganic oxides), and large negative thermal expansion. The spontaneous polarizations for the low-temperature polar phases are 1.15, 3.43 and 1.51 μC cm(-2) for 1, 2 and 3, respectively, as estimated by the shifts of the cations related to the anionic frameworks. Thermal and variable-temperature powder X-ray diffraction studies confirm the phase transitions, and the materials are all found to be thermally stable up to 470 K.