When crystals undergo phase transitions involving group-subgroup relationships, distinct regions of the low-symmetry child structure can possess distinct directions of the order parameter, which are related to one another via broken parent symmetries. The crystallographic community typically refer to these regions as domains. An interfacial boundary where two or more domains meet constitute a topological defect. Because such defects can either strategically or inadvertently influence material properties, it is important to understand what types of topological domain-interface defects (TBIDs) can arise in a given material. We will demonstrate that TBIDs can be algebraically characterized and classified using basic tools from group theory.

When doing structural refinements of total scattering data from highly crystalline compounds, one starts by choosing an atomic model and then imposing constraints that dictate how the atoms are allowed to move. These constraints are typically based on space group symmetry. The resulting structure representation is useful and accurate for a large range of compounds, however, it has its limitations for materials with a significant amount of disorder. It is particularly necessary to accurately describe this disorder when fitting total scattering data in the real space as pair distribution functions. To represent such disordered, but still significantly crystalline compounds, one would ideally want to fit the data with a ‘big-box’ model containing anything from a hundred to a few thousand atoms. Unfortunately, this can lead to a large number of variables to refine and an overfitting of the data with meaningless results. Alternatively, it is possible to construct models where multiple atoms are constrained to move in a collective fashion, controlled by a small number of variables [1,2].

Here we present one such approach, relying on our a priori knowledge of the structure at hand. For oxides with perovskite structure, ABO₃, we know that they tend to distort in ways that keep the BO₆ octahedra intact. The resulting distortions can therefore often be described by one of 23 unique tilting patterns of the rigid octahedra, identified by Glazer in the '70s [3]. Fitting a model of any of the tilting patterns to scattering data requires refinement of no more than four variables at once – one lattice parameter and a maximum of three tilt amplitudes. We have implemented this approach into diffpy-CMI, a flexible tool for fitting pair distribution function data. Using the method, we analyse a series of scattering data from well-known perovskites and determine their degree and type of structural tilting disorder.

[1] Sartbaeva, A. ‘Quadrupolar Ordering in LaMnO₃ Revealed from Scattering Data and Geometric Modeling’. Phys. Rev. Lett. 99, no. 15 (2007): 155503.

[2] Senn, M. S. et al. ‘Emergence of Long-Range Order in BaTiO₃ from Local Symmetry-Breaking Distortions’. Phys. Rev. Lett. 116, no. 20 (2016): 207602.

[3] Glazer, A. M. ‘The Classification of Tilted Octahedra in Perovskites’. Acta Cryst. B 28, no. 11 (1972): 3384–92.

Introduction: In the past decades, the solubility of the pharmaceuticals in human body has been become lower. To solve this problem, the cocrystal have been considerate. By forming a new crystal structure with an additive which is called as coformer (CF), the dissolution property of the active pharmaceutical ingredient (API) can be modified. But by now, the screening of the cocrystal is mostly carried by experiments. Even there are some approaches attempt to screening the API and CF pair for cocrystal formation by machine learning, but most of them use semi-empirical descriptor or atomic-based molecular structure descriptor to make the chemistry understandable to the computer. However, this make it is very hard to get a machine learning model which can be generalized to the cases which is not learned before. So, in this research, 3D convolution neural network (3D-CNN) is employed with 3D charge distribution calculated by Universal ForceField (UFF) and Gasteiger partial charge method (GPC) to achieve a general model. Also, the performance of new build model is compared with the atomic-based methodology used before such as Graph Convolutional Network (GCN), neural network with extensive connectivity fingerprint (ECFP-NN).

Method & Result: The experimental datasets from the literature is used for this research. UFF and GPC are applied to get the initial position and charge of the API and CF, then charge is mapped to a new 3D coordinate system which set the longest edge of the Oriented Bounding Box (OBB) of the molecular as the x-axis, the middle edge as y-axis, the shortest one as z-axis, and the centre of the OBB as the (0,0,0). Finally, the new mapped charge of APIs and CFs is transformed to 3D arrays for inputs to 3D-CNN. The hyperparameter of 3D-CNN is determined by training datasets with Bayesian-optimization with 5-flod cross-validation. 3D-CNN shows a training accuracy 80% and accuracy 71% with the test datasets that contain none of the molecular in training datasets, while the ECFP-NN and GCN only give test accuracy lower than 65%. Because the 3D charge information is directly link to the cocrystal formation between API and CF.

Water in confined geometries or near surfaces exhibits radically different properties depending on its environment. The physics of the new states of water is often discussed in terms of the distortion of its tetrahedral local symmetry and/or in terms of the frustration of its hydrogen-bond network. At the extreme opposite of these views is the investigation of the physical properties of the molecules when they are isolated from each other. This is experimentally challenging and related studies are scarce [1,2,3].

By combined use of wide-angle X-ray scattering, inelastic neutron scattering, density functional theory (DFT) and DFT molecular dynamics (MD) simulations, we investigated the structure, dynamics and stability of the water wetting-layer in single-walled aluminogermanate imogolite nanotubes [4]: an archetypal system for synthetically controllable and monodisperse nanochannels. We demonstrate that the water wetting-layer is strongly bound and solid-like up to 300 K under atmospheric pressure. Atomic-scale characterisation of the wetting-layer reveals organisation of the H₂O molecules in a curved triangular sublattice stabilised by the formation of three H-bonds to the nanotube's inner surface, with covalent interactions sufficiently strong to promote energetically favourable decoupling of the H₂O molecules in the adlayer. The dynamics of the water molecules is markedly different from that of bulk water. It is dictated by its interactions with the nanotube and conversely, this structural water impacts the dynamics of the nanotube. The peculiar dynamics of hydroxyl groups in dry imogolite nanotubes will also be discussed based on MD simulations and on elastic neutron scattering measurements.

The above results point the way to a systematic study of the effects of different water loadings and water-soluble reactants in complex oxide-based nanoreactors starting from, but not limited to, the imogolite family.

[1] C. Beduz et al., PNAS 109, 12894 (2012)

[2] A.I. Kolesnikov et al., Phys. Rev. Lett. 116, 167802 (2016)

[3] T.R. Prisk et al., Phys. Rev. Lett. 120, 196001 (2018)

[4] G. Monet et al., Nanoscale Adv. 2, 1869 (2020)

The aim of the presented work is the theoretical investigation of the dynamical effects in the integrated coherent and diffuse X-ray scattering intensity from imperfect crystals in Bragg diffraction geometry. We considered the sensitivity of the crystal reflectivity integrated with various ways to the characteristics of Coulomb-type defects.

A hydrogen atom is assigned to an arbitrary general position of the space group of a centrosymmetric cubic crystal. The phases of the structure factors are obtained. These phases are associated with the |F_obs|. The result of atoms and centrosymmetric cubic space groups is that an approximate structure of the crystal is contained or embedded in the many peaks of the calculated electron densities. The purpose of this article is to establish this basic result. For applications of this property to crystal structure determination, we have some remarks:

(i) Atomic numbers and atomic scattering factors of atoms in the crystals are not employed. Hence, the electron densities reveal non-hydrogen atoms, as well as hydrogen atoms. The electron densities of the peaks do not follow the trend of the atomic numbers.

(ii) After the structures of crystals, including disordered crystals, are determined, we can compare the atomic coordinates with the peaks in the calculated electron densities, to see if there are large discrepancies, in particular, hydrogen atoms. If needed, we may apply to crystals in the literature.

(iii) Unlike Patterson peaks, the peaks in the calculated electron densities are distinct and sharp for hydrogen atoms, light atoms or heavy atoms.

(iv) Like deconvolution of Patterson peaks, we may have devices to identify the approximate structure in the calculated electron densities. Environment about each atom may be considered.

(v) If a partial structure is obtained, we may be able to locate the remaining atoms, for example hydrogen atoms, from the peaks in the calculated electron densities. The partial structure is extended. This applies to locating atoms along a polypeptide chain.

(vi) In the calculated electron densities, we may obtain peaks in special positions with coordinates fixed by symmetry. Hence we obtain a partial structure which can then be extended, as in (v).

(vii) Crystal structure may be determined by the means of a systematic and routine method [1].

(viii) This article leads to two fundamental and important questions in X-ray crystallography: What is the result of using atomic numbers and centrosymmetric cubic space groups? What is the result of using atomic scattering factors and centrosymmetric cubic space groups? If we can obtain an answer to one of these questions, the peaks in the calculated electron densities may then be classified into species of atoms. This is very useful for determination of the approximate structure.

[1] Yuen, P. S. Determination of structure of CoS₂ by the means of a simple new method; a solution to the phase problem for centrosymmetric cubic crystals. (Unpublished).

Keywords: IUCr2020; abstracts; general position; equal phases; approximate structure;

Determination of structure of CoS₂ by the means of a simple new method;

a solution to the phase problem for centrosymmetric cubic crystals

P. S. Yuen

237 Des Voeux Road West, 5th Floor, HONG KONG

puisumyuen@netvigator.com

The result of atoms and centrosymmetric cubic space groups is that an approximate structure of the crystal is contained or embedded in the many peaks of the calculated electron densities [1]. The number of peaks is finite. In this article, we use a systemic and routine method to identify peaks of this approximate structure for CoS₂. All peaks along the diagonal of the unit cell are located. There are four Co and eight S atoms in a unit cell. The four Co atoms must be in (4a) or (4b) positions. The eight S atoms must be in (8c) positions. We use all sixteen combinations of the peaks, subjected to these constraints. For each combination, we use refinement by the minimization of the R factor. Two structures of CoS₂ are determined. About this simple new method, we have some remarks:

(i) The method is a simple deterministic method. Chemical knowledge and environment about each atom is not used. Isomorphic replacements are not employed. Only diffraction intensities are employed. This is purely a method in X-ray crystallography. Non-crystallographers may apply this method or the procedures in [1] to solve simple crystal structures.

(ii) All or most hydrogen atoms, light atoms and heavy atoms are located.

(iii) If we have more than one computer, these computers may be used in parallel for the combinations.

(iv) If there is more than one structure which satisfies the experimental diffraction intensities, all these structures may be determined by this method.

(v) In principle, this method can be applied to determine the structure of a very large protein. Structures of all centrosymmetric cubic crystals can be determined. In practice, we will use the procedures in [1].

(vi) We may regard this method as a solution to the phase problem for centrosymmetric cubic crystals.

(vii) If we try to apply this method to a complicated structure, the number of the combinations will be very large. If we include knowledge of environment about each atom, we can significantly reduce the number of combinations.

(viii) The procedures in [1] and the simple new method in this article represent some basic and new knowledge in X-ray crystallography. Much more work can be done. Crystallographers with expertise in the Patterson function or direct methods may combine these with this simple new method.

(ix) If we can obtain an answer to one of two questions in [1], the peaks in the calculated electron densities may follow the trend of atomic numbers. This greatly reduces the number of combinations.

[1] Yuen, P. S. Result of using atoms and centrosymmetric cubic space groups. (Unpublished).

Keywords: IUCr2020; abstracts; approximate structure; constraints; combinations;