Disorder, structured diffuse scattering and the transmissionelectron microscope

Withers, Ray L.

doi:10.1524/zkri.2005.220.12.1027

Cited by 11 publications

(12 citation statements)

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“…51 These are precisely the methods which have informed much of our understanding of collective defect structures in conventional inorganic materials such as zeolites and transition-metal oxides. 52,53 We note that electron microscopy is the least translatable of these methods to the study of MOFs since so many systems are terminally sensitive to the electron beam. 54 Structured diffuse scattering characteristic of defect nanodomains was first observed in the Hf-containing analogue UiO-66(Hf ), prepared using high concentrations of formic acid modulator.…”

Section: Domain Structures In Mofsmentioning

confidence: 99%

Defects and disorder in metal organic frameworks

et al. 2016

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The wide-ranging properties of metal organic frameworks (MOFs) rely in many cases on the presence of defects within their structures and the disorder that is inevitably associated with such defects. In the present work we review several aspects of defects in MOFs, ranging from simple substitutional defects at metal cation or ligand positions, to correlated defects on a larger length scale and the extreme case of disorder associated with amorphous MOFs. We consider both porous and dense MOFs, and focus particularly on the way in which defects and disorder can be used to tune physical properties such as gas adsorption, catalysis, photoluminescence, and electronic and mechanical properties.

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Section: Domain Structures In Mofsmentioning

confidence: 99%

Defects and disorder in metal organic frameworks

et al. 2016

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“…133,135 It is thus natural to also investigate continuous diffraction spectra from a more mathematical perspective. Again, we briefly present illustrative examples, most of which have been analysed completely and rigorously by now.…”

Section: Systems With Continuous Diffractionmentioning

confidence: 99%

“…While diffraction is one measure of order, the existence of homometric structures of varying entropy 11,14 shows its limitations, as there are completely deterministic systems which cannot be distinguished from a randomly disordered system on the basis of pair correlations alone. Increasingly, the continuous or diffuse part of the diffraction is attracting attention, 40,133,135 not the least because improved experimental techniques make the diffuse part accessible. Improving our understanding of diffuse diffraction is desirable, in particular 1 INTRODUCTION in view of the implications on disorder.…”

Section: Introductionmentioning

confidence: 99%

Mathematical diffraction of aperiodic structures

Baake

Grimm

2012

Chem. Soc. Rev.

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Kinematic diffraction is well suited for a mathematical approach via measures, which has substantially been developed since the discovery of quasicrystals. The need for further insight emerged from the question of which distributions of matter, beyond perfect crystals, lead to pure point diffraction, hence to sharp Bragg peaks only. More recently, it has become apparent that one also has to study continuous diffraction in more detail, with a careful analysis of the different types of diffuse scattering involved. In this review, we summarise some key results, with particular emphasis on non-periodic structures. We choose an exposition on the basis of characteristic examples, while we refer to the existing literature for proofs and further details. IntroductionDiffraction techniques have dominated the structure analysis of solids for the last century, ever since von Laue and Bragg employed X-ray diffraction to determine the atomic structure of crystalline materials. Despite the availability of direct imaging techniques such as electron and atomic force microscopy, diffraction by X-rays, electrons and neutrons continues to be the method of choice to detect order in the atomic arrangements of a substance; see Cowley's book 35 and references therein for background.In its full generality, the diffraction of a beam of X-rays, electrons or neutrons from a macroscopic piece of solid is a complicated physical process. It is the presence of inelastic and multiple scattering, prevalent particularly in electron diffraction, which makes it essentially impossible to arrive at a complete mathematical description of the process. Here, we restrict to kinematic diffraction in the far-field or Fraunhofer limit. In this case, powerful tools of harmonic analysis are available to attack the direct problem of calculating the (kinematic) diffraction pattern of a given structure.In contrast, the inverse problem of determining a structure from its diffraction intensities is extremely involved. A diffraction pattern rarely determines a structure uniquely, as there can be homometric structures sharing the same autocorrelation (and hence the same diffraction). 9,54,57,103 We are far away from a complete understanding of the homometry classes of structures, in particular if the diffraction spectrum contains continuous components. At present, a picture is emerging, based on the analysis of explicit examples, which highlight how large the homometry classes may be.Originally, much of the effort concentrated on the pure point part of diffraction, also called the Bragg diffraction, for † Part of a themed issue on Quasicrystals in honour of the 2011 Nobel Prize in Chemistry winner, Professor Dan Shechtman.

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“…The intensity of this diffuse scattering is temperature-dependent (see SI), indicating that its origin is dynamic rather than either static or compositional. 28 The scattering is also transverse polarised in that the intensity of the observed diffuse streaking is strongest along directions of reciprocal space perpendicular to the streaking itself; this is a second indication that its origin is displacive. 28,30 In general terms the scattering takes the form of diffuse planes, running across the hkl * ± h + l, h + l, 2l * regions of reciprocal space.…”

mentioning

confidence: 99%

“…28 The scattering is also transverse polarised in that the intensity of the observed diffuse streaking is strongest along directions of reciprocal space perpendicular to the streaking itself; this is a second indication that its origin is displacive. 28,30 In general terms the scattering takes the form of diffuse planes, running across the hkl * ± h + l, h + l, 2l * regions of reciprocal space. It also obeys the extinction conditions h+k +l = 2n, allowing us to infer that the atoms responsible are separated by 1 2 111 vectors in real-space: 28 i.e., the Cd.…”

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confidence: 99%

Charge-ice dynamics in the negative thermal expansion material Cd(CN)2

et al. 2012

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We use variable-temperature (150-300 K) single-crystal X-ray diffraction to re-examine the interplay between structure and dynamics in the ambient phase of the isotropic negative thermal expansion (NTE) material Cd(CN)2. We find strong experimental evidence for the existence of low-energy vibrational modes that involve off-centering of Cd 2+ ions. These modes have the effect of increasing network packing density-suggesting a mechanism for NTE that is different to the generally-accepted picture of correlated Cd(C/N)4 rotation modes. Strong local correlations in the displacement directions of neighbouring cadmium centres are evident in the existence of highly-structured diffuse scattering in the experimental X-ray diffraction patterns. Monte Carlo simulations suggest these patterns might be interpreted in terms of a basic set of 'ice-rules' that establish a mapping between the dynamics of Cd(CN)2 and proton ordering in cubic ice VII.PACS numbers: 65.40. De, 64.60.Cn, Of the few materials known to exhibit the rare property of isotropic negative thermal expansion (NTE; volume contraction on heating), cubic Cd(CN) 2 shows the strongest such effect.1-3 Its volume coefficient of thermal expansion α = d ln V /dT = −61.2(12) MK −1 is substantially more negative than the thermal expansion coefficients of typical engineering materials are positive (α 30 MK −1 ). 4 The origin of NTE in this material has never been identified conclusively, despite the related material Zn(CN) 2 (which also shows NTE, but at a reduced level) having been the focus of a significant number of experimental and computational studies. 1,5-9Both compounds share the anticuprite structure in which tetrahedral Zn or Cd centres are connected via linear M-C-N-M linkages [ Fig. 1(a)].10,11 Density functional theory (DFT) calculations suggest that the phonon relations are similar in the two materials, with the more pronounced NTE effect of Cd(CN) 2 a result of an enhanced pressure sensitivity of the low-energy mode frequencies. 7The atomic displacements associated with these crucial low-frequency modes are generally assumed to involve concerted rotations of M(C/N) 4 coordination tetrahedra, which result in transverse displacements of the C and N atoms away from the M. . .M axes.1,5,7-9,12 Thermal population of these modes would give rise to larger transverse displacements-hence reducing both the M. . .M separation and the unit cell dimensions.Yet there are reasons to suspect that the dynamical behaviour in Cd(CN) 2 and Zn(CN) 2 might differ more strongly than is presently appreciated. It is known, for example, that Cd(CN) 2 exhibits a structural phase transition at 150 K that is not observed in Zn(CN) 2 at temperatures down to 20 K (albeit that the precise nature of this transition has not yet been reported). 1This means that the P n3m anticuprite structure used in DFT calculations 7 does not actually reflect the thermodynamic ground state at 0 K. And whereas tetrahedral geometry is the most common coordination motif for Zn 2+ ions in cyanide complexes, 13,...

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Disorder, structured diffuse scattering and the transmissionelectron microscope

Cited by 11 publications

References 53 publications

Defects and disorder in metal organic frameworks

Defects and disorder in metal organic frameworks

Mathematical diffraction of aperiodic structures

Charge-ice dynamics in the negative thermal expansion material Cd(CN)2

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