An-Pang Tsai, professor at Tohoku University, Sendai, Japan, passed away on May 25 2019 at the age of 60. He was a pioneer and a leader in the field of quasicrystals and complex intermetallic phases. With him the community has lost one of the brightest scientist in this field. This symposium is dedicated to his memory and illustrates the many different fields he has been contributing in crystallography, metallurgy, material science and solid-state physics and chemistry.
In this presentation we will highlight the many important contributions of the research conducted by An-Pang Tsai going from fundamental and basic research to their applications and the important impact it had on the scientific community. We can quote: the discovery of most of the thermodynamically stable quasicrystals including the stable binary quasicrystals named ‘Tsai-type’ quasicrystals, the physics allowing to understand which systems is favorable for quasicrystal growth, their atomic structure and physical properties, lattice dynamics, magnetism, mechanical properties. In view of applications he has been one of the first to promote the use of quasicrystals for light alloy reinforcement and more recently he developed a completely new field with new ideas for the development of new catalytic materials.
An-Pang Tsai also had a decisive impact in training the younger generation in the different labs he has ben leading. He always was enthusiast to explore new fields, proposing ambitious targets, but with the long-term perspective, without pressure and with the entire necessary scientific environment. He has coordinated researches in the field of quasicrystals and material sciences in Japan and abroad. In particular he started to organize annual meetings on quasicrystals in Japan in 1996, which continued for more than 20 years andhas organized or initiated number of international conferences.
From very early on in his career, An-Pang Tsai built up an impressive large number of collaborations all across the world, in Japan, Europe, USA, Canada, China and Taiwan. His generosity in sharing his discoveries, his constant curiosity and inspiring ideas have irrigated the quasicrystal community, promoting collaboration rather than competition, leading to major results in almost all aspects of quasicrystal researches and from experiments to theory. He always was available and ready to share his knowledge with senior scientists as well as with young students.
We have lost a great colleague and a good friend, and we will honour his memory by continuing his interdisciplinary research work, keeping his enthusiast and collaborative approach.
[1] de Boissieu M and Ishimasa T (2019) Acta Cryst. B 75 763.

The Al-Mn icosahedral quasicrystal discovered by Shechtman was a metastable phase [1]. Attempts at its structure solution immediately began after the discovery was declared. After the subsequent discovery of stable icosahedral quasicrystals, the study of their physical properties became more active in addition to the elucidation of their structures, but these quasicrystals were all formed in ternary systems [2]. Because chemical disorder of inherent in ternary icosahedral quasicrystals, it was difficult to achieve any structure solution which is comparable to what is obtained for ordinaryl crystal. Discovery of a stable binary icosahedral quasicrystal in a Cd-Yb alloy opened a route to the structure solution to at least for this particular type of quasicrystal [3]. This quasicrystal, now known as Tsai-type icosahedral quasicrystal, forms the largest group among known quasicrsytals and their approximant crystals forming systems. Although I was not directly involved in the discovery of this quasicrystal, I was present at the scene as a member of Tsai's group and took the first X-ray transmission Laue photographs (Fig. 1), which were appeared in the paper announcing the discovery [3]. In the beginning, the quality of Cd-Yb quasicrystal was not very good, but soon good quality was obtained, and higher-dimensional crystal structure analysis by means of single crystal X-ray diffraction became possible [4]. Here is the story of how we arrived at the structural solution of this particular icosahedral quasicrystal.

We had collaborated exciting themes in materials science together with Professor An Pang Tsai for 17 years (since 2002). Prof. Tsai began the investigation of catalytic materials in term of metallurgy at NIMS [1].

There are three important topics in the collaborative research with Professor Tsai. Firstly, we succeeded that novel catalytic materials were prepared by the leaching method of Al-Cu-Fe quasicrystalline (QC) [2]. The Al₆₃Cu₂₅Fe₁₂ QC is a promising precursor for Cu catalysts, whose constituent elements, compositions and quasi-periodic structure are in favor of processing high performance catalysts. Brittleness resulting from quasi-periodic structure enables one to obtain powder form for processing catalysts. Relatively low dissolution rate of Al due to quasi-periodic structure upon leaching with NaOH solution, generated homogeneous nanocomposite consisting of Fe₃O₄ and Cu and hence gave rise to high activity and thermal stability for steam reforming of methanol. Secondary, Prof. Tsai proposed a concept for a psudo-element material such as “PdZn = Cu” [3]. A clear correlation between electronic structure and CO₂ selectivity for steam reforming of methanol (SRM) was obtained with PdZn, PtZn, NiZn, and PdCd intermetallics on the basis of experiments and calculations. PdZn and PdCd also exhibited valence electronic densities of states and catalytic properties similar to that of Cu. Thirdly, a new concept of active sites for bulk-type metallic materials was proposed by Prof. Tsai, i.e., nano twin boundary [4]. According to the DFT calculation, surface density of the active six-coordinated atoms in nano porous gold (NPG) was comparable with that of supported gold nanoparticle catalysts. In addition, the energy profiles of reaction pathways for CO oxidation indicated that the six-coordinated sites created by twinning significantly contributed to the catalytic activity of NPG. I will overview of these topics in my presentation.

Two years have passed since Professor A.P. Tsai passed away. Taking over Prof. A.P. Tsai’s spirits, now we are conducting research on novel metallic catalysis materials under the new system. We hope that those concepts of Prof. Tsai’s will lead to a principal for the development of metallic functional materials as well as metallic catalysts in the future.

[1] A.P. Tsai, M. Yoshimura, “Highly active quasicrystalline Al-Cu-Fe catalyst for steam reforming of methanol”, Applied Catalysis, A, 214 (2001) 237-241.; M. Yoshimura, A.P. Tsai, “Quasicrystal application on catalyst”, J. Alloys Compounds, 342 (2002) 451-454.

[2] For example T. Tanabe, S. Kameoka, M. Terauchi and A.P. Tsai, “Microstructure of leached Al-Cu-Fe quasicrystal with high catalytic performance for steam reforming of methanol”, Applied Catalysis, A, 384 (2010) 241-251.

[3] A.P. Tsai, S. Kameoka and Y. Ishii, “PdZn=Cu: Can an intermetallic compound replace an element ?”, J. Physical Soc. Jpn., 73 (2004) 3270-3273.

[4] M. Krajci, S. Kameoka and A.P. Tsai, “Twinning in fcc lattice creates low-coordinated catalytically active sites in porous gold”, J. Chem. Phys., 145 (2016) 084703.; ibid., 147 (2017) 044713.

The name of An-Pang Tsai is in first line connected with his pioneer work on quiasicrystalline and related crystalline materials, e.g. on the atomic structure of quasicrystals [1]. Less known are the studies of his group on chemical properties, in particular on catalytic materials. A mutual origin of the interest to this research field may be found in the search for possible application fields for quasicrystals and investigations on surface properties of quasicrystalline and approximant phases, i.e. oxidation behaviour [2] or etching reactions [3]. Logical continuation of these studies is the work of An Pang Tsai and his group on hydrogen absorption on intermetallic compounds [4,5] and high catalytic activity of amorphous intermetallic hydrides in hydrogenation of ethylene and CO₂ [6,7]. The subsequent studies were devoted to the influence of real structure of materials (Renee catalyst) or electronic factors on the catalytic activity [8,9]. Coming back to the possible applications of quasicrystals, the group of A. P. Tsai was working on activation of quasicrystalline surface and fabrication of a fine nanocomposite layer with high catalytic performance [10]. In the following years several new results were produced by A. P. Tsai and his co-workers on composite catalyst with mixed lamellar structures and dual catalytic functions, dominant factors of porous gold for CO oxidation, effects of Cu oxidation states on the catalysis of NO+CO and N₂O+CO reactions, preparation of dispersive Au nanoparticles on TiO₂ nanofibers from Al-Ti-Au intermetallic compound. The last product of the work of An Pang Tsai in the field of catalysis – although not finished by himself – was the special issue of Science and Technology of Advanced Materials giving an comprehensive overview of current research activities around the world [11].

[1] Takakura, H., Goméz, C. P., Yamamoto, A., de Boissieu, M., Tsai A. P. (2007). Nature Materials 6(1), 58. [2] Yamasaki, M., Tsai A. P. (2002). J. Alloys Compd. 342(1), 473. [3] Saito, K., Saito, Y., Sugawara, S., Shindo, R, Guo, J.-Q., Tsai, A. P. (2004) Phil. Mag. A, 84(10), 1011. [4] Endo, N., Kameoka, S., Tsai, A. P., Zou, L., Hirata, T., Nishimura, Ch. (2009). J. Alloys Compd. 485, 588. [5] Endo, N., Kameoka, S., Tsai, A. P., Zou, L., Hirata, T., Nishimura, Ch. (2010). J. Alloys Compd. 490, L24.

[6] Endo, N., Kameoka, S., Tsai, A. P., Hirata, T., Nishimura, Ch. (2011). Mat. Trans. 52, 1794.

[7] Endo, N., Ito, Sh., Tomishige, K., Kameoka, S., Tsai, A. P., Hirata, T., Nishimura, Ch. (2011). Catalysis Today, 164, 293.

[8] Nozawa, K., Endo, N., Kameoka, S., Tsai, A. P., Ishii, Y. (2011). J. Phys. Soc. Jpn. 80, 064801.

[9] Murao, R., Sugiyama, K., Kameoka, S., Tsai, A. P. (2012). Key Eng. Mat. 508, 304.

[10] Kameoka, S., Tanabe, T., Satoh, F., Terauchi, M., Tsai A. P. (2014). Sci. Techn. Adv. Mat. 15, 1878.

[11] Special issue IMc (2019). Sci. Techn. Adv. Mat. 20

We will present several interesting structures of thin films grown on Tsai-type quasicrystal, icosahedral (i)-Ag-In-Yb, studied by various experimental techniques including scanning tunnelling microscopy (STM). The results include three dimensional quasicrystalline films of single elements [1] and molecular films [2] (Figure 1).

The i-Ag-In-Yb quasicrystal is built by rhombic triacontahedral (RTH) clusters and its surface is formed at the bulk atomic planes that bisect the RTH clusters [3]. When Pb is deposited on the fivefold i-Ag-In-Yb surface, the Pb atoms adsorb at the sites that were originally occupied by the cluster atoms and thus produce quasicrystalline film in three-dimension [1]. This observation is evidenced in other systems as well, namely Pb on the threefold and twofold i-Ag-In-Yb surfaces [4, 5] and In, Sb and Bi on the fivefold i-Ag-In-Yb surface [6].

We also found that Pentacene molecules deposited on the fivefold i-Ag-In-Yb surface adsorb at tenfold-symmetric sites of Yb atoms around surface-bisected RTH clusters, yielding quasicrystalline order [2]. The selective adsorption of Pentacene on Yb sites is also observed on the threefold and twofold surfaces of the same sample.

The phenomena of adsorption on selective sites is also found on Al-based quasicrystals. C₆₀ molecules preferably adsorb on Fe or Mn when deposited on surfaces of i-Al-Pd-Mn and i-Al-Cu-Fe [2, 7], yielding quasicrystalline order of C₆₀. The compatibility between the characteristic lengths of the substrate and the size of adsorbates has led to the growth of unprecedented epitaxial structures

His ideas about AuSi

https://www2.mrc-lmb.cam.ac.uk/groups/murshudov/content/emda/emda.html

http://www.xray.cz/mstruct

http://crm2.univ-lorraine.fr/lab/en/software/mopro/

https://team.inria.fr/nano-d/software/

Ample

Martin Karlsen, Berrak Ozer, Peter Strickland, Simon Westrip, Nicola Ascroft, Brian McMahon, Dave Holden, Song Sang Koh and Simon J. L. Billinge

https://simbad.readthedocs.io/en/latest/

The recent surpassing of 1 million structures in the Cambridge Structural Database [1] offered a moment for celebration and an opportunity to reflect. Achieving this significant milestone is a testament to the exemplary initiatives and engagement emanating from the crystallographic community over many decades. The development of semantic representation formats [2], the cultivation of joined-up publishing workflows, and the broad adoption of standards all pre-empted the principles, guidelines and practices that have come to dominate the discourse around research data preservation and reuse today [3]. We cannot however rest on our laurels. The curation activities of organisations such as the Cambridge Crystallographic Data Centre remain of critical importance and must continue to evolve. We must ensure that our data resources remain relevant and can be readily utilised by the data-driven approaches being applied to the complex scientific problems of today.

This presentation will offer reflections on the successes of the crystallographic community that have been critical in ensuring the outputs of the past can conform to the expectations and demands of the future. It will highlight how these have enabled a wealth of structural chemistry knowledge to be applied across industry and academia to innovate and educate [4]. Additionally, it will look at the challenges and opportunities presented by an evolving research publication landscape, new experimental and computational methods, and the desire for greater reproducibility and richer reuse of structural chemistry data.

[1] Groom C. R., Bruno I. J., Lightfoot M. P. & Ward S. C. (2016). Acta Crystallogr. Sect. B Struct. Sci. Cryst. Eng. Mater. 72(2), 171.

[2] Hall S. R. & McMahon B. (2016). Data Sci. J. 15(3), 1.

[3] Wilkinson M. D., Dumontier M., Aalbersberg IjJ., et al. (2016). Sci Data. 3(1), 1.

[4] Taylor R., Wood P. A. (2019) Chem Rev. 119(16), 9427.

The Research Collaboratory for Structural Bioinformatics Protein Data Bank (RCSB PDB), the US data center for the global PDB archive and a founding member of the Worldwide Protein Data Bank partnership, serves tens of thousands of data depositors in the Americas and Oceania and makes 3D macromolecular structure data available at no charge and without restrictions to millions of RCSB.org users around the world, including > 800 000 educators, students and members of the curious public using PDB101.RCSB.org. PDB data depositors include structural biologists using macromolecular crystallography, nuclear magnetic resonance spectroscopy, 3D electron microscopy and micro-electron diffraction. PDB data consumers accessing our web portals include researchers, educators, and students studying fundamental biology, biomedicine, biotechnology, bioengineering, and energy sciences. During the past two years, the research-focused RCSB PDB web portal (RCSB.org) has undergone a complete redesign, enabling improved searching with full Boolean operator logic and more facile access to PDB data integrated with > 40 external biodata resources. New features and resources will be described in detail using examples that showcase recently released structures of SARS-CoV-2 proteins and host cell proteins relevant to understanding and addressing the COVID-19 global pandemic.

The Inorganic Crystal Structure Database (ICSD) has been collecting published crystal structures for more than 40 years. In addition, the database offers the structures in curated and extended form. In the process of adding a structure to the database, a series of tests are run to verify data integrity and correctness. Furthermore, the data is enriched with additional or missing information, which can help to detect possible discrepancies. Some of the procedures used will be explained here, and examples will be given to show how careful evaluation of crystallographic parameters and the addition of missing parameters improves the quality of the crystal structure entry.

The Powder Diffraction File™ (PDF®) is a comprehensive materials database containing data for inorganic materials including minerals (natural and synthetic), metals and alloys, and high-tech ceramics, as well as organic materials such as pharmaceuticals, excipients and polymers. Databases, including the PDF, that provide structural details can be used for a range of materials characterization analyses, including (but not limited to) phase identification, quantitative analysis, and structure modelling for Rietveld refinement and whole-pattern fitting. As a result, structural databases are one of the key tools used in the crystallographic community [1]. Though these databases do tend to have some common applications, they often differ in content, format, and functionality. ICDD’s PDF databases primary purpose is to serve as a quality reference tool for the powder diffraction community.

Historically, the PDF has contained entries constructed as d-spacing and intensity (d-I) reduced diffraction pattern representations for phase identification. These condensed entries reduced storage space requirements, and increased search speed capabilities. With the advancement of computer hardware and software, and the transition of the PDF to a relational database format, storage space and speed capabilities have become less limiting [2]. Over time the PDF has grown exponentially, and has evolved to where it is now common practice to construct entries of full digital patterns. In addition to being a powerful characterization database used for the analysis of single and multi-phase X-ray diffraction data, the ICDD has systematically been adding raw data digital pattern references for crystalline and non-crystalline materials since 2008; with an emphasis on excipients and polymers [3]. The addition of full digital patterns has enabled the analysis and identification of disordered and amorphous materials using a combination of the raw data pattern and d-I lists, or whole pattern similarity searching. The evolution of raw data archiving in the Powder Diffraction File will be discussed in this presentation, with emphasis on the benefits and increased capabilities for characterization of materials in both research and industrial applications including pharmaceutical, forensic, and energy sectors.

[1] Kuzel, R. and Danis, S. (2007). Mater. Struct. Chem., Biol., Phys. Technol. 14, pp.89–96.

[2] Gates-Rector, S., & Blanton, T. (2019). Powder Diffraction, 34(4), pp. 352-360.

[3] Fawcett, T., Gates-Rector, S., Gindhart, A., Rost, M., Kabekkodu, S., Blanton, J., & Blanton, T. (2019). Powder Diffraction, 34(2), pp. 164-183.

Protein Data Bank Japan (PDBj) accepts and processes regional 3D structure data of biological macromolecules since 2000. We celebrated our 20th anniversary of our regional Data-in activities last year. Our Data-out service has a much longer history, dating back to before the establishment of PDBj. The first protein structure from Asia was determined at the Institute for Protein Research (IPR) in 1971 at 4 Å [1] and a subsequent structure at 2.3 Å solved in 1973 [2] was deposited to the PDB in 1975 as the 21st entry in PDB. Based on these early contributions to the crystallographic community, IPR founded the Crystallographic Research Centre and installed several 4-circule diffractometers, and developed the Imaging Plate detectors of R-axis series later [3] together with Rigaku. In addition to above activities, IPR was assigned as the National Affiliated Centre of Cambridge Crystallographic Data Centre from 1978 and keep serving until now (http://www.protein.osaka-u.ac.jp/CSD/, Fig.1). Distribution of the PDB data from IPR started in 1979 as a regional data centre, initially by magnetic tape and later by CD-ROM, until the installation of an official mirror site of Brookhaven PDB in 1998. Since 2001, we have provided our newly developed online Data-out services freely and publicly through our own web site (https://pdbj.org; Fig.2), which includes our molecular graphics viewer, Molmil; a molecular surface database for functional sites, eF-site; and a database of protein dynamics calculated via normal mode analysis, Promode Elastic [4], and we have served since 2003 as a founding member of the worldwide PDB (https://wwpdb.org). During the COVID-19 pandemic, we have provided a COVID-19 featured page in three Asian languages (Japanese, Chinese and Korean) and have started a new service archiving raw X-ray image data directly related to deposited PDB entries (XRDa, https://xrda.pdbj.org; Fig.3) [5]. Since we already have BMRBj (formerly PDBj-BMRB) and EMPIAR-PDBj on-site, XRDa completes the regional experimental raw data archives of the related PDB, BMRB and EMDB entries from the three major experimental methods; Macromolecular Crystallography, NMR spectroscopy and 3D Electron Microscopy.

[1] Ashida, T., Ueki, T., Tsukihara, T., Sugihara, A., Takano, T. & Kakudo, M. (1971) J. Biochem. 70, 913–924. [2] Ashida, T., Tanaka, N., Yamane, T., Tsukihara, T. & Kakudo, M. (1973) J. Biochem., 73, 463–465.

[3] Sato, M., Katsube, Y. & Hayashi, K. (1993) J. Appl. Cryst., 26, 733-735.

[4] Kinjo, A.R., Bekker, G.-J., Wako, H., Endo, S., Tsuchiya, Y., Sato, H., Nishi, H., Kinoshita, K., Suzuki, H., Kawabata, T., Yokochi, M., Iwata, T., Kobayashi, N., Fujiwara, T., Kurisu, G. & Nakamura, H. (2018) Protein Sci., 27, 95-102.

[5] Bekker, G.-J. & Kurisu, G. in preparation

The in-surface crystallography of the family of three-periodic minimal surfaces (TPMS) consisting of the Primitive, Diamond, and Gyroid surfaces has been explored in detail in recent decades [1, 2]. We begin by reviewing the underlying group theory and geometry as well as the relationship between the TPMS and their universal covering space, hyperbolic two-space, the fundamentals of which are shown in Figure 1(a).

We describe how these methods can be used to tailor the topology and geometry of three-periodic nets realised as embeddings commensurate with the symmetries of these surfaces [3-5] as shown in Figure 1(b). Using these ideas, we demonstrate how a number of nets with pre-specified topological properties are readily produced in this manner and assess their relevance for further study in the context of reticular chemistry and soft matter materials science.

Finally, we present preliminary results on visualisation methods for understanding how these patterns and nets are realised in simulations of liquid crystals in bulk [6] and confined polymer systems. Using an array of methods from computational geometry, we visualise these simulations in hyperbolic two-space to facilitate easy comparisons and further analysis as shown in Figure 1(c).

The authors thank Anders Dahl, Myfanwy Evans, Olaf-Delgado Friedrichs, Benedikt Kolbe, Stuart Ramsden, Vanessa Robins, Gerd Schröder-Turk, and Monique Teillaud for discussions and feedback on these topics and results.

[1] Sadoc, J.-F. & Charvolin, J. (1989). Acta Crystallogr. A 45, 10-20.
[2] Robins, V., Ramsden, S., & Hyde, S. T. (2004). Eur. Phys. J. B 39(3), 365-375.
[3] Pedersen, M. C. & Hyde, S. T. (2018). Proc. Natl. Acad. Sci. U. S. A. 115(27), 6905-6910.
[4] Pedersen, M. C., Delgado-Friedrichs, O., & Hyde, S. T. (2018). Acta Crystallogr. A 74(3), 223-232.
[5] Hyde, S. T. & Pedersen, M. C. (2021). Proc. Roy. Soc. A 477, 20200372.
[6] Kirkensgaard, J. J. K., Evans, M. E., de Campo, L., & Hyde, S. T. (2014). Proc. Natl. Acad. Sci. U. S. A. 111(4), 1271-1276.

We introduce flat-branched semisimplicial (FBS) complexes as a universal language to describe aperiodic structures of finite local complexity. An FBS-complex naturally represents the set of local atomic arrangements occurring in the structure. It includes both metric and combinatorial data; the flexibility of the latter allows for incorporation of structural constraints on a longer range. An FBS-complex can embody "local rules" of any kind, whether or not they impose a perfect long-range order. We propose an algorithm for exploration of local rules in terms of an FBS-complex directly from the phased diffraction data. The FBS complex describing a structure entirely determines the density of atomic species, and yields experimentally verifiable constraints on their contribution to the structure factors.

The study of chromatic symmetries to describe physical properties of crystals and mapping of individual orientations in twins has extended the field of mathematical crystallography. This paper discusses chromatic, partially chromatic or achromatic properties of symmetries or partial operations of a coordinated coloring of a symmetrical pattern, which has a potential to describe a crystalline structure. Here, we consider a symmetrical pattern P consisting of disjoint congruent copies of a symmetrical motif M.

A coordinated coloring of P is a coloring that is perfect and transitive under the global symmetry group G of P, satisfying the condition that the coloring of M is also perfect and transitive under its symmetry group K (a local symmetry group). This means that G and K consists of elements that effect a permutation of the colors of the coloring of P and M respectively. If the coloring of P or M has two (respectively more than two) colors, then G or K is called a dichromatic (respectively polychromatic) symmetry group.

A global symmetry, a local symmetry, or a partial operation (an isometry of the plane that sends one motif to another, which may not be a global or local symmetry of P) of a coordinated coloring of P can be classified as either achromatic if it fixes all the colors; chromatic if it moves all the colors, and partially chromatic if it exchanges some colors, and fixes the rest.

As an example, consider the coordinated 4 – coloring of P given in the given figure. Each region in every motif is assigned a color from the set S={blue,yellow,red,green}. Every element of G=<2 0,0;m_[10];m_[01];z(1,0)>≅p2mm (a polychromatic symmetry group) permutes the colors in the 4 – coloring of P. We also note that in this coloring, every element of K=<4⁺ 0,0;m_[10]>≅4mm permutes the colors assigned to the triangles in the motif M. The dichromatic group of M is 4'mm': we have the 90^o rotation and two reflections that change colors, while two reflections fix colors. The dichromatic group of each of the other motifs is also 4'mm'.

The local chromatic symmetries of M exchanging blue and red are 4'⁺,4',m'_[11], and m'_{[11 ̅ ]}. On the other hand, the local achromatic symmetries of M fixing the colors blue and red are 2,m_[10] , and m_[01] . The global symmetries in P can be characterized as: z⁽⁴⁾ (1,0) (chromatic) sending blue to yellow, yellow to red, red to green, and green to blue; 2^(2,2) 0,0, and m^(2,2)_[01] (partially chromatic) exchanging yellow and green, and fixing red and blue; and m_[10] (achromatic) fixing all the colors. The 4-coloring of the frieze pattern is described by the group [p⁽⁴⁾ 2^(2,2) m^(2,2) m]⁽⁴⁾. The chromatic partial operations that map M to zM are also shown in the figure. Sending blue to yellow as well as red to green are z⁽²⁾ (1,0),2⁽²⁾ 1/2,0 ,m⁽²⁾_[01] 1/2,0 , and g⁽²⁾_[01] (1,0). Sending blue to green and red to yellow are 4⁽²⁾⁺ 1/2,1/2, 4^(2)- 1/2,(1/2) ̅, g⁽²⁾_[11](1/2,1/2) 1/2,0 and g⁽²⁾_{[11 ̅ ]}(1/2,1/2) 1/2,0.

In this talk, examples of coordinated colorings of Frieze and Plane Crystallographic patterns will be presented.

Superspace-group symmetry is essential to the unambiguous description of modulated structures, and a correct understanding of their physical properties. An exhaustive enumeration of superspace groups in up to 3+3 dimensions were announced in 2014. We now announce an exhaustive enumeration of magnetic superspace groups in up to 3+3 dimensions (over 250,000 groups). With these tables in hand, we have developed an algorithm and tool that detects the superspace-group (magnetic or non-magnetic) of an arbitrary modulated structure, given the amplitudes and phases of its modulations in P1 symmetry, and identifies it in the exhaustive symmetry-group table. This capability has been integrated into both the FINSYM and ISOCIF packages of the ISOTROPY software suite, and has been integrated with JANA 2000. The ISODISTORT package, which use group-representations to generate incommensurate structure models based on a given parent structure, now automatically identifies the unique magnetic superspace-group of each magnetically modulated child structure. Anyone can access these data sources and tools online to generate, symmetrize, transform, or otherwise explore magnetic or non-magnetic modulated structure models.

We present a classification of magnetic point groups which give an answer to the question: Which magnetic groups can describe a given magnetic mode?
There are 32 categories of magnetic point groups which describe 64 unique different magnetic modes: 16 with a ferromagnetic component and 48 without. This classification focused on magnetic modes is helpful for finding the magnetic space group which can describe the magnetic symmetry of the material.

The classification selects the magnetic space groups and the magnetic site-symmetry point groups which are compatible with a number of magnetic phenomena e.g. collinear antiferromagnetism and ferromagnetism, spin roerientation, antiferromagnetism with weak ferromagnetism. The use of our classification is demonstrated on a number of well-studied materials, e.g. alpha-Fe2O3, rare earth orthoferrites, RFeO3. It is particularly useful for materials with weak ferromagnetism. Examples of use for neutron powder diffraction studies are discussed in the context of the paper by Shirane (1958).

This presentation based on the paper (ib5097) recently accepted to Acta Cryst A.

https://www.olexsys.org/

https://www.olexsys.org/

https://journals.iucr.org/j/issues/2021/03/00/in5046/

Open slot

https://pdfitc.org/

https://www.diffpy.org/products/diffpycmi/index.html

https://www.cryst.ehu.es/

https://github.com/scipion-ed

http://www.conplot.org/

https://topospro.com/

https://topcryst.com/

https://github.com/tproffen/DiffuseCode

AUSPEX

http://users.uoi.gr/nkourkou/winpssp/

http://www.crystal.chem.uu.nl/distr/eval/

https://github.com/YellProgram/Yell

Structure prediction, and the theoretical computation of reliable superconducting transition temperatures, have undoubtedly played a major role in the discovery of novel high temperature superconductivity in dense hydrides.[1] While the field has delivered room temperature superconductivity,[2] the technological relevance will be limited while the phenomenon is restricted to extremely high pressures. Furthermore, the number of experimental research groups that can study the properties of these compounds at megabar pressures is limited, restricting the potential scientific impact. Rightly, the field is focusing on identifying compounds that superconduct at high temperatures, but much lower pressures. But there are considerable obstacles to progress. The number of theoretical candidates far exceed those experimentally confirmed, suggesting more attention should be paid to predicting synthesisability. It is becoming clear that metastability favours high temperature superconductivity, but how should we choose from the multitude of metastable candidates? Experimentally determined structures are frequently not found to be dynamically stable in static calculations, but full dynamics is computationally expensive, and difficult to account for in high throughput searches. At the same time, it is not clear how to compute superconducting transition temperatures in highly dynamic systems. So far, most attention has been paid to perfect crystals. Doping and deviation from perfect stoichiometry, and well as defects (both point, and extended, such as grain boundaries and interfaces) are likely to be important to the detailed properties of these materials. Finally, as we turn to exploring a broader range of compounds, in the ternaries and beyond, structure prediction becomes more challenging, not least in terms of the management of the quantities of data generated, and the computation of large numbers of superconducting transition temperatures. I will show some recent results which go some way to addressing this.

[1] Pickard, Chris J., Ion Errea, and Mikhail I. Eremets. "Superconducting hydrides under pressure." Annual Review of Condensed Matter Physics 11 (2020): 57-76.

[2] Snider, Elliot, Nathan Dasenbrock-Gammon, Raymond McBride, Mathew Debessai, Hiranya Vindana, Kevin Vencatasamy, Keith V. Lawler, Ashkan Salamat, and Ranga P. Dias. "Room-temperature superconductivity in a carbonaceous sulfur hydride." Nature 586, no. 7829 (2020): 373-377.

The remarkable high-temperature superconducting behavior of H₃S (T_C=200 K, [1]) and LaH₁₀ (T_C=250 K [2]) at about 150 GPa catalyzed the search for superconductivity in compressed ternary hydrides. The highest critical temperature of 288 K at 275 GPa has been found recently in the C-S–H system [3]. High-temperature superconductivity in these compounds is due to the formation of metallic hydrogen sublattice, which is obtained by pulsed laser heating of various elements with hydrogen at extremely high pressures achieved during compression on diamond anvils. In this report we will present new results of studies of high-pressure chemistry, magnetic and superconducting properties of YH₆, UH₇, ThH₁₀, CeH_9-10, PrH₉, NdH₉, EuH₉ and BaH₁₂ binary and (La,Y)H₁₀ ternary polyhydrides discovered in the last 2 years by collaboration of IC RAS, LPI, Skoltech and Jilin University (China). Perspectives of design of light and magnetic sensors (SQIUDs) based on superhydrides synthesized in miniature diamond anvil cells will be discussed.

References:
[1] Drozdov A P, Eremets M I, Troyan I A, Ksenofontov V and Shylin S I, 2015, Nature, 525, 73–76.
[2] Drozdov A P, Kong P P, Minkov V S, Besedin S P, Kuzovnikov M A,Mozaffari S, Balicas L, Balakirev F F, Graf D E, Prakapenka V B,Greenberg E, Knyazev D A, Tkacz M and Eremets M I, 2019, Nature 569, 528–531.
[3] Snider E, Dasenbrock-Gammon N, McBride R, Debessai M, Vindana H, Vencatasamy K, Lawler K, Salamat A et al., 2020, Nature, 586, 373–377.

Artem R. Oganov

Skolkovo Institute of Science and Technology, 3 Nobel St., 121205 Moscow, Russia

Chemical behavior of the elements can be rationalized and anticipated based on a few properties, such as electronegativity, radius (atomic, ionic, van der Waals radii), polarizability, valence state. Among these, electronegativity plays perhaps the most important role – chemical reactivity of the elements, bond energies, directions and heats of reactions, and many properties of molecules and solids are related to electronegativities of the elements. The oldest and the most widely used is Pauling’s scale of electronegativity, developed in 1932 (see [1]) and based on bond energies. However, later it was found (e.g., [2]) that Pauling’s formula, relating bond energies with electronegativity differences, is very inaccurate for significantly ionic bonds. We have proposed [3] another formula, which works well for bonds with any degree of ionicity, and obtained a new thermochemical scale of electronegativities for all elements. New electronegativities better follow chemical intuition than traditional Pauling’s values (e.g. charge transfer in transition metal borides and hydrides is described qualitatively better, and so are oxyacids).
We have also studied another important concept – Mendeleev numbers, introduced in 1984 by Pettifor [4]. Pettifor showed that chemical behavior of the elements can be approximately characterized by just one number, which he called the Mendeleev number; he assigned these numbers to all elements, but the physical meaning of these remained unclear. We have shown [5] that Mendeleev number can be obtained by principal components analysis (PCA) or even a simple linear correlation applied to the set of points “atomic radius – electronegativity – polarizability” of all elements. This dimensionality reduction gives a single variable giving mathematically the best one-parameter description of the chemistry of the elements – the Mendeleev number. We have shown [5] that thus defined Mendeleev numbers perform better than those proposed by Pettifor [4]. Accurate representations of the chemical space require all key properties of the atoms to be explicitly used, but reduced-dimensionality representations (such as representation by Mendeleev numbers) allow easier visualization of big data.

This work is funded by Russian Science Foundation (grant 19-72-30043).

[1] Pauling, L. The Nature of the Chemical Bond 3rd edn (Cornell University Press, 1960).
[2] Matcha, R. L. (1983). Theory of the chemical bond. 6. Accurate relationship between bond energies and electronegativity differences. J. Am. Chem. Soc. 105, 4859–4862.
[3] Tantardini C., Oganov A.R. (2021). Thermochemical electronegativities of the elements. Nature Communications 12, 2087.
[4] Pettifor D.G. (1984). A chemical scale for crystal structure maps. Solid State Commun. 51, 31-34.
[5] Allahyari Z., Oganov A.R. (2020). Nonempirical definition of Mendeleev numbers: organizing the chemical space. J. Phys. Chem. C124, 23867-23878.