A phenomenological model for structural phase transitions in incommensurate alkane/urea inclusion compounds

n-Alkane/urea inclusion compounds are crystalline materials in which n-alkane ‘guest’ molecules are located within parallel one-dimensional ‘host’ tunnels formed by a helical hydrogen-bonded arrangement of urea molecules. The periodic repeat distance of the guest molecules along the host tunnels is incommensurate with the periodic repeat distance of the host substructure. The structural properties of the high-temperature phase of these materials (phase I), which exist at ambient temperature, are described by a (3 + 1)-dimensional superspace. Recent publications have suggested that, in the prototypical incommensurate composite systems, n-nonadecane/urea and n-hexadecane/urea, two low-temperature phases II and ‘III’ exist and that one or both of these phases are described by a (3 + 2)-dimensional superspace. We present a phenomenological model based on symmetry considerations and developed in the frame of a pseudo-spin–phonon coupling mechanism, which accounts for the mechanisms responsible for the I ↔ II ↔ ‘III’ phase sequence. With reference to published experimental data, we demonstrate that, in all phases of these incommensurate materials, the structural properties are described by (3 + 1)-dimensional superspace groups. Around the temperature of the II ↔ ‘III’ transition, the macroscopic properties of the material are not actually associated with a phase transition, but instead represent a ‘crossover’ between two regimes involving different couplings between relevant order parameters

Polymorphic phase transformations of 3-chloro-trans-cinnamic acid and its solid solution with 3-bromo-trans-cinnamic acid

We have investigated the polymorphic phase transformations above ambient temperature for 3-chloro-trans-cinnamic acid (3-ClCA, C9H7ClO2) and a solid solution of 3-ClCA and 3-bromo-trans-cinnamic acid (3-BrCA, C9H7BrO2). At 413 K, the γ polymorph of 3-ClCA transforms to the β polymorph. Inter­estingly, the structure of the β polymorph of 3-ClCA obtained in this transformation is different from the structure of the β polymorph of 3-BrCA obtained in the corresponding polymorphic transformation from the γ polymorph of 3-BrCA, even though the γ polymorphs of 3-ClCA and 3-BrCA are isostructural. We also report a high-temperature phase transformation from a γ-type structure to a β-type structure for a solid solution of 3-ClCA and 3-BrCA (with a molar ratio close to 1:1). The γ polymorph of the solid solution is isostructural with the γ polymorphs of pure 3-ClCA and pure 3-BrCA, while the β-type structure produced in the phase transformation is structurally similar to the β polymorph of pure 3-BrCA

High-dimensional cluster analysis with the masked EM algorithm

This is an Open Access article published under a Creative Commons Attribution 3.0 Unported (CC BY 3.0) license https://creativecommons.org/licenses/by/3.0/Cluster analysis faces two problems in high dimensions: the "curse of dimensionality" that can lead to overfitting and poor generalization performance and the sheer time taken for conventional algorithms to process large amounts of high-dimensional data. We describe a solution to these problems, designed for the application of spike sorting for nextgeneration, high-channel-count neural probes. In this problem, only a small subset of features provides information about the cluster membership of any one data vector, but this informative feature subset is not the same for all data points, rendering classical feature selection ineffective.We introduce a "masked EM" algorithm that allows accurate and time-efficient clustering of up to millions of points in thousands of dimensions. We demonstrate its applicability to synthetic data and to real-world high-channel-count spike sorting data.Peer reviewe

Structural properties of methoxy derivatives of benzyl bromide, determined from powder X-ray diffraction data

Structure determination of 3,5-dimethoxybenzyl bromide and 3,4,5-trimethoxybenzyl bromide has been carried out from laboratory powder X-ray diffraction data using the direct-space Genetic Algorithm technique for structure solution followed by Rietveld refinement. These two compounds are of interest for their potential use as building blocks for the synthesis of dendritic materials. Although the two molecules differ only in the presence/absence of the methoxy group at the 4-position of the aromatic ring, the structural properties of the two materials are significantly differen

Determination of a complex crystal structure in the absence of single crystals : analysis of powder X-ray diffraction data, guided by solid-state NMR and periodic DFT calculations, reveals a new 2′-deoxyguanosine structural motif

Derivatives of guanine exhibit diverse supramolecular chemistry, with a variety of distinct hydrogen-bonding motifs reported in the solid state, including ribbons and quartets, which resemble the G-quadruplex found in nucleic acids with sequences rich in guanine. Reflecting this diversity, the solid-state structural properties of 3′,5′-bis-O-decanoyl-2′-deoxyguanosine, reported in this paper, reveal a hydrogen-bonded guanine ribbon motif that has not been observed previously for 2′-deoxyguanosine derivatives. In this case, structure determination was carried out directly from powder XRD data, representing one of the most challenging organic molecular structures (a 90-atom molecule) that has been solved to date by this technique. While specific challenges were encountered in the structure determination process, a successful outcome was achieved by augmenting the powder XRD analysis with information derived from solid-state NMR data and with dispersion-corrected periodic DFT calculations for structure optimization. The synergy of experimental and computational methodologies demonstrated in the present work is likely to be an essential feature of strategies to further expand the application of powder XRD as a technique for structure determination of organic molecular materials of even greater complexity in the future

Ab-initio random structure searching of organic molecular solids : assessment and validation against experimental data

This paper explores the capability of using the DFT-D ab-initio random structure searching (AIRSS) method to generate crystal structures of organic molecular materials, focusing on a system (m-aminobenzoic acid; m-ABA) that is known from experimental studies to exhibit abundant polymorphism. Within the structural constraints selected for the AIRSS calculations (specifically, centrosymmetric structures with Z = 4 for zwitterionic m-ABA molecules), the method is shown to successfully generate the two known polymorphs of m-ABA (form III and form IV) that have these structural features. We highlight various issues that are encountered in comparing crystal structures generated by AIRSS to experimental powder X-ray diffraction (XRD) data and solid-state magic-angle spinning (MAS) NMR data, demonstrating successful fitting for some of the lowest energy structures from the AIRSS calculations against experimental low-temperature powder XRD data for known polymorphs of m-ABA, and showing that comparison of computed and experimental solid-state NMR parameters allows different hydrogen-bonding motifs to be discriminated

NMR crystallography as a vital tool in assisting crystal structure determination from powder XRD data

Powder X-ray diffraction (XRD) and solid-state NMR spectroscopy are complementary techniques for investigating the structural properties of solids, and there are considerable opportunities and advantages to applying these techniques synergistically together in determining the structural properties of crystalline solids. This article provides an overview of the potential to exploit structural information derived from solid-state NMR data to assist and enhance the process of crystal structure determination from powder XRD data, focusing in particular on the structure determination of organic molecular materials

Circumventing a challenging aspect of crystal structure determination from powder diffraction data

Schmidt and co-workers [Acta Cryst. (2022), B78, 195–213], report a strategy for structure determination from powder XRD data in which unit-cell determination and structure solution are combined within a single process, rather than handling them as sequential stages on the structure determination pathway. This strategy offers the prospect to achieve successful structure determination in cases for which conventional approaches for indexing powder XRD data prove to be challenging

Object Relations in the Museum: A Psychosocial Perspective

This article theorises museum engagement from a psychosocial perspective. With the aid of selected concepts from object relations theory, it explains how the museum visitor can establish a personal relation to museum objects, making use of them as an ‘aesthetic third’ to symbolise experience. Since such objects are at the same time cultural resources, interacting with them helps the individual to feel part of a shared culture. The article elaborates an example drawn from a research project that aimed to make museum collections available to people with physical and mental health problems. It draws on the work of the British psychoanalysts Donald Winnicott and Wilfred Bion to explain the salience of the concepts of object use, potential space, containment and reverie within a museum context. It also refers to the work of the contemporary psychoanalyst Christopher Bollas on how objects can become evocative for individuals both by virtue of their intrinsic qualities and by the way they are used to express personal idiom

The Casimir force and the quantum theory of lossy optical cavities

We present a new derivation of the Casimir force between two parallel plane mirrors at zero temperature. The two mirrors and the cavity they enclose are treated as quantum optical networks. They are in general lossy and characterized by frequency dependent reflection amplitudes. The additional fluctuations accompanying losses are deduced from expressions of the optical theorem. A general proof is given for the theorem relating the spectral density inside the cavity to the reflection amplitudes seen by the inner fields. This density determines the vacuum radiation pressure and, therefore, the Casimir force. The force is obtained as an integral over the real frequencies, including the contribution of evanescent waves besides that of ordinary waves, and, then, as an integral over imaginary frequencies. The demonstration relies only on general properties obeyed by real mirrors which also enforce general constraints for the variation of the Casimir force.Comment: 18 pages, 6 figures, minor amendment