Modern computational methods and their applications in materials science: Synergy of theory and experiment

Resume : We investigate the physical mechanisms responsible for structural and electrical changes in nm-thick amorphous (a)-SiO2 and a-HfO2 films in electronic devices using a multi-scale approach. The energetic parameters derived from a microscopic mechanism are used to predict the kinetics and macroscopic degradation parameters of structural degradation, such as the time-dependent dielectric breakdown (TDDB) statistics, and its voltage dependence. The structure and properties of symmetric TiN/SiO2/TiN and asymmetric Au/Ti/a-SiO1.95/Mo stacks described in [1] and HfO2 based stacks [2] are calculated using Density Functional Theory (DFT) and atomistic modelling. The bulk system (far from the interface) is approximated as stoichiometric polycrystalline HfO2 or amorphous (a)-SiO2 and HfO2, whereas the oxide/TiN interface is considered explicitly and constructed using DFT simulations assuming different degrees of hydroxylation of oxide surface [3]. Pairs of neutral O vacancies and charged O= interstitial ions are created as a result of electron injection from the cathode and localization of two electrons at structural precursor sites in disordered structures. The O= interstitial ions diffuse towards the anode in the electric field. Multi-scale modelling using rates of electron injection, defect creation and electron hopping through created defects is employed to describe the time evolution of the structure, leakage current and dielectric breakdown in oxide films [4]. The results explain quantitatively the kinetic of structural degradation and TDDB data reported in the literature for relatively thin (3–9 nm) a-SiO2 and a-HfO2 films. They demonstrate how the vacancy creation and field-driven movement of interstitial oxygen ions causes changes in oxide structure. [1] A. Mehonic, et al., Adv. Materials, 28(34), 7486-7493 (2016) [2] G. Bersuker et al. J. Appl. Phys. 110, 124518 (2011) [3] J. Cottom et al. ACS Appl. Mater. Interfaces 11, 36232 (2019) [4] A. Padovani et al. J. Appl. Phys. 121, 155101 (2017)

Resume : Chemical isovalent doping is an important tool in tuning mechanical, optical etc. properties of binary (e.g., II-VI or III-V) semiconductors. Typically, in A(x)B(1-x)C systems characterised by sufficiently broad miscibility of AC and BC parents ("C" being either cation or anion), the variation of properties with concentration would be continuous but not necessarily smooth. Examples of "irregularites" may, for example, involve an onset and evolution (depending on concentration) of "percolation doublets" in the vibration spectrum (see, e.g., [1,2]), as well as different response of these doublets to applied hydrostatic pressure [3,4]. Lattice vibrations, probed e.g. by Raman or infrared spectroscopy, are known to be sensitive to local environment (local order) around the vibrating atoms (or bonds). However, apart from cases of genuinely localized vibrations (due to, e.g., light impurities), the effect of environment may be of quite long range, involving the existence of certain structural patterns throughout the crystal, the connectivity of certain bonds, formation of chains, etc. This can be grasped as sensitivity of vibrations to structure at meso-scale [5]. This relation, which is, even in classical mechanical case, a manifestation of a problem of coupled vibrations over multiple masses and force constants, is virtually impossible to "decipher" directly. In practical terms, one usually chooses to confront the experiments with the results of first-principles lattice-dynamics calculations, performed either for intentionally designed structure models (e.g., single-impurity limit, interaction of impurities, onset of percolation, see e.g. [6]), or for "representative" supercells simulating a topologically disordered (under preservation of the underlying lattice type) pseudobinary alloy of a given concentration [1]. As the calculations are done at ab initio level (within the density functional theory), the optical and mechanical properties would follow ?included for the same price", enabling comparison with corresponding other experiments than vibrational spectroscopy. This latter, however, remains singled out by the richness of the information it provides. An overview will be given of problems (enigmatic types of behaviour of certain features in the vibration spectra on doping, or under hydrostatic pressure), addressed by Raman spectroscopy at the LCP-A2MC laboratory (group directed by Olivier Pagès) at the Université de Lorraine, resolved thanks to comparison with first-principles results, typically obtained with the use of the Siesta code [7]. Specific difficulties of vibration calculations on systems with hundreds of atoms will be discussed. -- References: -- [1] Mala N.Rao et al., Phys.Rev.B 89, 155201 (2014); [2] M.B. Shoker et al., J.Appl.Phys. 126, 105707 (2019); [3] Gopal K. Pradan et al., Phys.Rev.B 81, 115207 (2010); [4] M.B.Shoker et al., Sci.Rep. 10, 19803 (2020); [5] "Les phonons : un 'mésoscope' naturel pour l'étude du désordre d'alliage", PhD work by Allal Chafi at the Paul Verlaine University - Metz (2008), https://theses.fr/2008METZ034S; [6] A.V.Postnikov et al., Phys.Rev.B 71, 115206 (2005); [7] A. García, J.Chem.Phys. 152, 204108 (2020).

Resume : The band-gap engineering approach has been recognized as a powerful tool for tuning charge trapping properties of oxide compounds [1, 2]. The main idea of this approach is that cationic substitution in oxide crystal may change its band gap and, consequently, the energy levels of defects states can change their depth with respect to the band edges. The band-gap engineering effect has been experimentally evidenced for several classes of oxide compounds. However specific electronic-level mechanisms which govern this effect in a particular crystal still remain unknown. The present work reveals such mechanisms in the case of YAlO3 perovskite crystals in which Y cations are substituted with La. The DFT-based theoretical calculations with use of the Plane-Wave Pseudopotential method were carried out in order to determine the influence of La doping on the energy positions defect levels in the crystals bandgap of YAlO3. The geometry-optimized calculations were performed in the super-cell approach. The super-cells were constructed as 2x2x2 multiplication of the unit cell and comprised 160 atoms of YAlO3 crystal. Several kinds of point defects and defect combinations were modeled in the super-cells: natural vacancies and vacancy complexes, interstitial oxygen defects and combinations of such interstitials with natural vacancies, cationic antisites, iso- and aliovalent cationic substitutions, as well as several other combinations of such defects in Y0.75La0.25AlO3 mixed-cationic solid solution. Results obtained in the calculations were compared with corresponding experimental data on the optical absorption in the VUV-UV range, luminescence spectroscopy under synchrotron radiation excitation, thermally stimulated luminescence (TSL) in 300 - 500 °C temperature range which were carried out for the specially grown set of RAlO3 (R = Y, La, Gd, Yb, Lu) single crystals and solid solutions. The mechanism of the temperature shift of TSL glow peaks of (Y,Gd,La)AlO3:Mn4 microcrystalline phosphors was explained using the obtained computational results. The origin of traps, which form the TSL glow peaks of YAlO3 crystals above room temperature, is discussed. Acknowledgments The work was supported by the Polish National Science Centre (project no. 2018/31/B/ST8/00774), by the NATO SPS Project G5647, and by the National Research Foundation of Ukraine (grant 2020.01/0248). References [1] I.V. Vrubel, et al., Crystal Growth and Design, 17 (2017) 1863-1869 [2] M. Fasoli, et al. Physical Review B, 84 (2011) 081102(R)

Resume : Metal oxyfluorides represent a robust group of chemical compounds, surprisingly though, none of the ternary oxyfluorides contains a cation from group 11. Intending to find one, we focused on the silver derivative, the Ag2OF2 system, which may be considered as the 1:1 “adduct” of AgF2 and AgO. Both are semiconductors, but the first is a comproportionated one hosting immense antiferromagnetic exchange due to the presence of Ag(II) centres[1], while the latter is an example of disproportionation with diamagnetic centres Ag(I,III)[2]. In this work[3], possible crystal structures of the silver oxyfluoride were predicted using the evolutionary algorithm XtalOpt[4] in combination with DFT methods. We analysed the oxidation states of silver in the low-energy structures, possible magnetic interactions, and energetic stability with respect to the available substrates. Our findings suggest that the ground state corresponds to a mixture of 2 AgF and 1/2 O2. Still, silver oxyfluoride, if obtained, may form a metastable crystal with Ag(II) paramagnetic cations forming sheets with ligands. Detailed calculations show that such compound has narrowed bandgap and exhibits Ag-Ag superexchange via oxide ligands. However, the existence of a fully or partially disproportionated metallic compound cannot be ruled out. Finally, we outlined a prospect for the synthesis of polytypes of interest using diverse synthetic approaches, starting from the direct fluorination of Ag2O. References: [1] J. Gawraczyński, et al., Proc. Natl. Acad. Sci. 2019, 116, 1495–1500. [2] J. A. McMillan, J. Inorg. Nucl. Chem. 1960, 13, 28–31. [3] M. A. Domański, W. Grochala, J. Chem. Phys. 2021, 154, 204705. [4] D. C. Lonie, E. Zurek, Comput. Phys. Commun. 2011, 182, 372–387.

Resume : Raman spectroscopy is an indispensable tool for investigating properties of ceramic materials both in academic research as well as in industry. It provides rich information about chemical composition, local atomic structure, defects, symmetry, phases and phase transitions, strain state and many other properties that leave their fingerprints on the Raman spectra. Raman spectroscopy is a non-destructive technique allowing for fast data acquisition, thus making it suitable for an online, on-the-fly testing at the production site. Interpreting the measured spectra is facilitated by the existence of databases and theoretical methods, most notably, by symmetry analysis and ab-initio modeling. Theory and modeling of Raman spectra are rather well developed, however they primarily concentrate on the single-crystalline material form. Polycrystals, powders, or ceramics have received significantly less attention: They represent a collection of small single-crystalline grains that are oriented in all possible ways, which poses special challenges to their theoretical treatment. From a theoretical perspective, the Raman spectrum of this ensemble relies upon averaging the signals coming from each individual grain/crystallite. In the standard approach, this is accomplished by resorting to the so-called Placzek invariants. In our recent paper [1], we show the deficiencies of this method and introduce the new spherical averaging method that significantly improves the ability of theory to predict the Raman spectra of ceramic materials. We illustrate here the performance of the new method by calculating the spectra of polycrystalline BaTiO3, AlN, and LiNbO3 from first principles. The calculated spectra are not only able to predict peak positions and intensities with high accuracy, but also allow to obtain the asymmetric peak shape—characteristic for oblique phonons—in an unprecedented way. [1] Popov, M.N., Spitaler, J., Veerapandiyan, V.K. et al. Raman spectra of fine-grained materials from first principles. npj Comput Mater 6, 121 (2020)

Resume : Silver(II)/fluoride systems have been shown to be close electronic and magnetic analogues of copper(II)/oxide ones, the latter showing high temperature superconductivity. [1] Thus, it is possible to mimic cuprates? exceptional properties in fluoroargentates(II). In this work, ternary compounds of a general formula MAgF3 (M = K, Rb, Cs) have been studied. MAgF3 (M = K, Rb, Cs) compounds adopt distorted perovskite structure that is closely related to La2CuO4 ? parent compound of oxocuprate high-Tc superconductors. [2] It is known, that the type of interstitial atom (here: K-Cs) has a huge impact on the level of structural distortion and the vibrational spectra. Generally, the smaller the alkaline metal atom, the greater the distortion and the lower the symmetry. The relative cationic sizes affect geometry of Ag-F-Ag chains in which strong magnetic superexchange propagates. Superexchange constant calculated for those compounds proved to be impressively high (-113 meV for KAgF3; -144 meV for RbAgF3; 161 meV for CsAgF3). [4] Simultaneously, magnetic anisotropy is large, and these materials can be regarded as quasi 1D antiferromagnets. [3] Here, theoretical DFT calculations using GGA+U and HSE06 frameworks were conducted. Phonon band structure and phonon density of states were modelled using phonon direct method implemented in phonopy software. [5] Comparison of theoretical and experimental infrared and Raman spectra enabled vibrational mode assignment reaching very good correlation (R2>0.997) for all three compounds. Results helped to achieve deeper understanding of KAgF3 phase transition present at 230 K. Thermodynamically stable, orthorhombic low temperature polymorph of RbAgF3 was proposed. This work was supported by Polish National Science Center (NCN) within Maestro project (2017/26/A/ST5/00570) funding. M. Derzsi acknowledges the ERDF, R&I Operational Program (ITMS2014+: 313011W085), Scientific Grant Agency of the Slovak Republic grant (VG 1/0223/19) and the Slovak Research and Development Agency grant (APVV-18-0168). Z. Mazej acknowledges the Slovenian Research Agency for financial support within research program P1-0045 Inorganic Chemistry and Technology [1] J. Gawraczy?ski et al., PNAS 2019, 116, 5, 1495?1500. [2] R. H. Odenthal, R. Hoppe, Monatshefte für Chemie 1971, 102, 5, 1340?1350. [3] Z. Mazej et al., Cryst. Eng. Comm. 2009, 11, 8, 1702?1710. [4] D. Kurzyd?owski,W. Grochala, Angew. Chemie 2017, 56, 34, 10114?10117. [5] A. Togo and I. Tanaka, Scr. Mater. 2015, 108, 1?5.

Resume : Practical applications of a variety of functional materials depend crucially on their thermal properties, which are determined by the dynamics of atoms. The dynamics involves atomic vibrations as well as diffusion. Anharmonic lattice vibrations have very important role in leading to anomalous thermal properties. Diffusion pathways and time-scales are important in fast-ion conductors, which are useful as battery materials and fuel cells. We have used the techniques of lattice dynamics and molecular-dynamics simulations, and neutron scattering experiments, to investigate the dynamics and related material properties in a variety of solids. We shall show how negative thermal expansion in materials may arise due to anharmonic phonons [1], and identify the nature of these phonons. In fast-ion conductors, we have identified the features that facilitate the diffusion of lithium and sodium atoms, and the diffusion pathways in crystalline and amorphous structures [2]. Our recent studies on defected graphite [3] solves an outstanding problem of kinetics of defect annihilation on heating and release of large Wigner energy. Our work is of considerable importance to wider areas of graphitic materials including graphene and carbon nanotubes. [1] R. Mittal et al, Progress in Materials Science 92, 360 (2018); B. Singh et al, J. Phys. Chem. C 124, 7216-7228 (2020) [2] M. K. Gupta et al, Phys. Rev. B 103, 174109 (2021); Phys. Rev. Materials 4, 045802 (2020) [3] R. Mittal et al, Physical Review B 102, 064103 (2020)

Resume : The contamination of animal feed by mycotoxins fungi naturally occurs causing diseases and death in human and animals. The strict maximum mycotoxin levels regulations render crucial finding smart mycotoxin mitigation strategies. The most effective acknowledged approaches are forming bulky non-absorbable complexes with binding agents, reducing the bioavailability of mycotoxins. Among the detoxifiers, inorganic porous materials such as clays minerals are recognized effective especially for sequestering of Aflatoxin B1. Similarly, organic compounds such as activated charcoal have been demonstrated powerful adsorbent for several mycotoxins, including Deoxinivalenol (DON). However, the required doses for a significant detoxification leads to sequestrating of essential micronutrients such as vitamins or minerals. Biohybrid materials establish a weighted compromise between diverse mode of action of the singular components. On the other hand, the design of most promising formulation of biohybrid materials is challenge being it a complex multifunction of high-dimensional chemical space. The development of novel functional materials is costly and time-consuming especially in the contest of in vivo trials. The research involving living animals is guided by the principle of the “3Rs”, i.e. replacement, reduction and refinement when animals are used for scientific purposes to improve animal welfare and to minimize the environmental impact. Thus, the synergy of theory and experiment accelerates the screening of vast number of material formulations while incorporating the animal-derived models for detoxification testing. The computer-aided approach facilitates the design of effective materials and enable optimal design of in vivo experiments. In this contribution, we have built machine learning (ML) models that incorporate three distinctive factors underlying the detoxifier performance, i.e. the material formulation, the chemical structure of the targeted toxin and the process in which a mycotoxin-detoxifier (MDT) is applied. The models being trained using an extensive set of in vitro experiments are used as surrogates of real experiments for the exploration of promising MDTs. In this multidisciplinary study, we aimed to demonstrate three-fold applications of our approach (1) in the identification of high performing formulations for the regulated toxins, (2) in predicting detoxification of a wide set of yet-unregulated mycotoxins, and (3) in gaining insights into the in vitro detoxification mode of action through model feature importance analysis. Finally, biomarker detection-based in vivo validation of the material identified in (1) is demonstrated in a challenging DON detoxification trial in broiler chickens. Moreover, material modelling technique were implemented to gain inside on the detoxification mode of action.

Resume : Photoelectrocatalytic water splitting is a promising technique for sustainable fuel production, but its viability hinges on the availability of good photocatalysts. Bismuth vanadate, a transition-metal oxide semiconductor with a bandgap of ~2.4 eV, is a promising candidate for this purpose, though its performance is limited by slow hole transfer, high charge recombination rates, and low conductivity. An atomistic understanding of the origins of these issues is a key step towards solving them. Achieving this knowledge is nontrivial, however. Isolating the effects of e.g. a single dopant or defect is an incredible challenge experimentally, but computer modelling allows the study of any modifications on the level of individual atoms. We have performed first-principles calculations on native defects in bismuth vanadate, revealing their structural complexity and highlighting the importance of taking charge localization into account for this class of materials. Additionally, we show that oxygen vacancy-induced distortions in bismuth vanadate complicates phase identification of synthesized samples.

Resume : Global optimization methods have become widely available and popular for solving crystal structure from powder diffraction and have successfully been applied to the structures of organic, inorganic and organometallic materials. Many different stochastic global optimization methods have been explored, including simple Monte Carlo, genetic algorithms, evolutionary strategies, particle swarm and big bang?big crunch, but simulated annealing (SA) is the most widely used and has had the largest impact. Each method involves the generation of a random sequence of trial structures starting from an appropriate 3D model and moving it until a good match is found between the calculated and the observed pattern. The information about chemical knowledge of molecules is actively used to reduce the number of parameters to be varied: bond distances and angles are usually known and kept fixed while only the torsion angles are varied during the procedure. In addition, when the quantity of information available from a powder diffraction pattern is limited (due to, e.g., severe peak overlap, broad peaks, preferred orientation, presence of weak scatters) and/or the number of degrees of freedom is large, it may be necessary to add extra chemical information to the optimization process in order to obtain the correct solution. The use of restraints on bond distances and angles, the application of bond valence restraints, the use of anti-bumping restraints increase the probability to obtain only chemically plausible models. The simulated annealing approach is implemented in the EXPO2013[1] structure solution package. A parallel version of the algorithm is also available if you want to speed up your crystal structure solution using more than one processor and exploiting the whole available computing power. Running the procedure in parallel permits tackling structures with great complexity in a reasonable time. Structures with more than 15-20 degrees of freedom, several molecular fragments, presence of largely flexible atomic chains represent a complex problems for the crystal structure solution by SA: large number of moves per run, large number of runs are required to guarantee finding the global minimum and increasing the frequency of correct solutions. In addition, the use of dynamical occupancy correction in the case of non-molecular compounds or the introduction of constraints and restrains, requires the computation of geometrical parameters (distances and angles) between neighboring atoms including all symmetry equivalent positions. These expensive calculations could increase dramatically the computation time in case of a large number of atoms. Fortunately the calculation can be easily distributed between more CPU-cores by using the message passing parallelization paradigm. Examples of successful structure solutions are reported and advice for difficult cases will be provided. [1] A. Altomare, C. Cuocci, C. Giacovazzo, A. Moliterni, R. Rizzi, N. Corriero and A. Falcicchio, (2013). J. Appl. Cryst. 46, 1231-1235

Resume : The Bilbao Crystallographic Server (www.cryst.ehu.es) is a free website with access to crystallographic data of space and point groups, magnetic space groups, subperiodic groups, their representations, and group-subgroup relations. A database on incommensurate modulated and composite structures, and a magnetic-structure database are also available. A wide range of complex solid-state physics and structure-chemistry aspects of materials studies are facilitated by the specialized software provided by the server. The server offers a set of structure-utility programs including basic tools for crystal-structure transformations or transformations compatible with a specific symmetry reduction. There are online tools for quantitative analysis of similarity of different structure models (helpful also for the recognition of identical or nearly-identical atomic arrangements of different compounds) or the analysis of crystal-structure relationships that are of great utility for the construction of family trees of homeotypic crystal structures. There are tools for systematic studies of phase-transition mechanisms including the evaluation of structural pseudosymmetry which could serve as a powerful method for the prediction of new ferroic materials. The presentation of the databases and programs offered by the Bilbao Crystallographic Server will be accompanied by case studies illustrating the capacity and efficiency of the online tools in material studies.

Resume : Designing of a new alloy for a specific application or improving upon a set of properties of a known alloy involves understanding of various correlations and interactions between various phenomena occurring at various time and length scales. Random experimentation for optimizing chemistry is financially prohibitive Manufacturing/processing plays a vital role in optimizing microscopic features such as grain size and volume fraction of various stable and metastable phases. Each of these phases can improve a desired property as well as adversely affect other targeted properties of an alloy. Thus, it is important to utilize information from available databases and develop data-driven models that can be used as a predictive tool. It is important to optimize composition of alloy and manufacturing protocols that will extremize targeted properties which are important. In this talk, a set of case studies will be discussed involving hard magnetic AlNiCo type alloys, soft magnetic FINEMET type alloys, Al-based alloys, Ni-base superalloys and Ti-based alloys for high temperature applications as well as for biomedical applications. This talk includes results from actual experiments, CALPHAD-based modeling, and application of several algorithms within the framework of Artificial Intelligence including supervised and unsupervised machine learning algorithms for developing metamodels, and evolutionary/genetic algorithms for multi-objective optimization.

Resume : Enzyme catalysts are an integral part of green chemistry strategies towards a more sustainable and resource-efficient chemical synthesis. However, the retrosynthesis of given targets with biocatalysed reactions remains a significant challenge: the substrate specificity, the potential to catalyse unreported substrates, and the specific stereo- and regioselectivity properties are domain-specific knowledge factors that hinders the adoption of biocatalysis in daily laboratory works. [1,2] Here, we use the molecular transformer architecture [3] to capture the latent knowledge about enzymatic activity from a large data set of publicly available enzymatic data, extending forward reaction and retrosynthetic pathway prediction to the domain of biocatalysis. We introduce a class token based on the EC classification scheme that allows to capture catalysis patterns among different enzymes belonging to same hierarchical families. The forward prediction model achieves a top-5 accuracy of 62.7%, while the single step retrosynthetic model shows a top-1 round-trip accuracy of 39.6%. The enzymatic data and the trained models are available through the RXN for Chemistry network (https://rxn.res.ibm.com and https://github.com/rxn4chemistry). [1] Katrin Hecht et al., Catalysts, 2020, 10(12), 1420 [2] Shuke Wu et al., Angewandte Chemie, 2021, 60(1), 88-119 [3] Philippe Schwaller et al., ACS Central Science, 2019, 5(9), 1572–1583

Resume : Doped reducible metal oxides have been investigated as possible materials for fuel cell electrodes in replacement of the more expensive and rare platinum. Of particular interest is noble metal doped ceria. In order to reduce the quantity of noble metal employed for the doping single atom catalysis (SAC) from dispersed atoms on the ceria surface has been considered. Here we assess the catalytic performance of Ag atoms on ceria surfaces by Density Functional Theory (DFT) calculations of the energies and pathways of H2 dissociation [1]. In all investigated models, the computed barrier of H2 dissociation is lowered by about 0.6 eV in comparison to that on metal-free CeO2. The results are used to interpret X-ray photoemission spectroscopy measurements of the changes of Ag oxidation state, concentration of Ce3+ ions, O vacancies, and hydroxyl groups on pristine and Ag-modified films during thermal reduction cycles in vacuum and under hydrogen exposure. The calculations show that the lower number of Ce3+ cations in the Ag doped samples can be explained in terms of a change of the oxidation state of the surface Ag, which is able to acquire some of the extra surface electrons created by the adsorbed hydrogen atoms and the oxygen vacancies that form under thermal treatment. The difference in the concentration of oxygen vacancies and hydroxyl groups between the pristine and doped samples at high annealing temperatures is explained in terms of the different activation barriers for H surface diffusion and reaction with the surface oxygen atoms to form water. Our results suggest a larger rate of water formation on the Ag-modified than on the pristine samples at high temperatures leading to a higher concentration of oxygen vacancies and a lower concentration of surface hydroxyl groups, in agreement with the experiment. [1] G. Righi, R. Magri, and A. Selloni, J. Phys. Chem. C, 123, 9875 (2019).

Resume : Covalent Organic Frameworks (COFs) are crystalline porous materials built from purely organic molecules linked by reversible bonds. The organic nature of these porous materials opens a broad chemical window for post-synthetic modifications. Imine-linked COFs exhibit an intrinsic Lewis basicity arising from the nature of their chemical bonds. This basic character makes nitrogen-rich COFs perfect scaffolds for anchoring catalytic active metal centres to their structure. Herein, we present the synthesis of a very active Pd-loaded imine COF for Suzuki-Miyaura couplings.[1] The material is prepared under two different synthetic scenarios: an early metalation of a highly defective material, and a more conventional post-synthetic metalation in a crystalline COF. By combining advanced synchrotron characterization including pair distribution function (PDF) analyses and X-ray absorption spectroscopy (XAS) and theoretical density functional theory (DFT) calculations, we can better understand the structural nature of the defects sites where catalytic palladium binds within the COF. Our results demonstrate that the presence of defects in an imine-linked COF affords to coordinative environments able to protect palladium nanoparticles from sintering, which is the most common deactivation mechanism of this catalytic material. 1- Romero-Muñiz et al. Angew. Chem. Int. Ed. 2020, 59,13013 –13020

Resume : The increasing demand for renewable energy has resulted in significant interest in energy storage devices like batteries and supercapacitors. Achieving better electrochemical efficiency for the storage devices plays a key role in their development. Spinel materials are commonly used as both the anode and the cathode of Li-ion-based storage devices. The compositional and structural versatility of spinels allows different engineering paths for device improvement. Here we show that straining a MnFe2O4 electrode will improve Li-ion diffusion. To show this we performed density functional theory and nudged elastic band calculations in different lattice strain values. The results show lower formation and activation energies for Li intercalation and diffusion in the 0.3% strained material. The lower energies in the strained material correspond to a three-fold increase in the diffusion coefficient compared to the unstrained material. We further show that increasing the strain to 0.5% would result in a five times increase in the diffusion coefficient. However, increasing the lattice parameter beyond this point results in a -1.8eV formation energy which suggests an undesired phase change. This work demonstrates the use of first-principle calculations as a means to suggest an engineering strategy.

Resume : Thanks to all the research efforts devoted to them, Perovskite Solar Cells (PSCs) have reached Power Conversion Efficiency (PCE) levels of current technology, silicon solar cells. Their adequate bandgap and very high charge carrier mobilities, together along with their very competitive cost make them the most promising materials to finally reach the long-time desired 3rd Generation of Solar Cells, with lower prices and higher efficiencies, whether alone or used in tandem configurations with other technologies like silicon. Nevertheless their stability is still far from being acceptable for commercialization, being between 5 and 10 times lower than silicon at best. All-inorganic perovskites like CsPbI3 are attracting high interest, trying to avoid more unstable organic cations, although in comparison to CH3NH3PbI3 (MAPI on behalf of their elements) they present only promising results yet, being necessary a profound study of their properties. In this work a review of the main structural, thermodynamical and mechanical properties of all-inorganic halide perovskites with general formula CsPb1-bSnb(I1-xBrx)3 is done, with the goal of elucidate the connection of those properties with the stability and its dependence upon the composition of the compounds. Our results will guide experimental groups in their growths. A DFT-based study has been performed, covering a wide range of chemical compositions, to analyze how the changes in composition affect those different properties and consequently the stability. A series of structural tolerance parameters, like the Goldschmidt factor, the Sun’s parameter and the intrinsic hardness have been revised. Also, thermodynamical stability in terms of formation enthalpies considering different competitor phases and compounds have been evaluated according to standard procedures. Finally, several mechanical properties defining response to different kind of stresses, as an important characteristic with a big impact on their absorptivity which relies on their crystallinity and stress state, have been obtained from the elastic constants following the stress-strain methodology. This way, a complete set of properties that properly describes the different facets of the intrinsic stability of these halide perovskites and their correlation is presented, providing a guide to improve stability through composition engineering. References: -Sanchez-Palencia P. Effect of the chemical composition on the structural, thermodynamical and mechanical properties of all inorganic halide perovskites., Inorganic Chemistry Frontiers, accepted. - Zhou Y, Zhao Y., Chemical stability and instability of inorganic halide perovskites., Energy Environ Sci. 2019;12(5):1495-1511. -Feng J., Mechanical properties of hybrid organic-inorganic CH3NH 3BX3 (B = Sn, Pb; X = Br, I) perovskites for solar cell absorbers., APL Mater. 2014;2(8). -Sun Q, Yin WJ., Thermodynamic Stability Trend of Cubic Perovskites., J Am Chem Soc. 2017;139(42):14905-14908.

Resume : Synthetic garnets exhibit physical properties leading to opportunities of application for example as components of solid-state lasers [1], as optical high-pressure sensors [2, 3], and as substrates for epitaxial superconducting films [4]. Mechanical and elastic properties of garnets are of interest for Earth science, as minerals of garnet structure are components of the deep interior of the Earth [5]. Multicomponent garnets X(3)Y(2)Z(3)O(12), with divalent X, trivalent Y, and tetravalent Z cations exhibit properties such as high resistance for plastic flow even at high temperatures, and low thermal conductivity [6], and large Mohs hardness. In the present work, results of in-situ high-pressure X-ray diffraction and ab initio studies for Ca(3)Ga(2)Ge(3)O(12) garnet are presented. The in-situ X-ray diffraction experiments were carried out using the energy-dispersive method at a synchrotron beamline equipped with a large-anvil diffraction press. Analysis of the data collected for measured garnets, Ca(3)Ga(2)Ge(3)O(12) shows that the garnet structure is conserved in the studied pressure range. The lattice parameters of garnets were determined using the Le Bail method performed employing the Fullprof2k program. Based on obtained V(p) dependence, experimental Birch-Murnaghan equation of state was determined. Ab initio total-energy simulations were carried out within the framework of density functional theory (DFT) and The Vienna Ab-initio Simulation Package (VASP) [8] was used to perform calculations with the pseudopotential method and the projector augmented waves (PAW) scheme The set of plane waves was extended up to a kinetic energy cutoff of 520 eV, providing highly converged results. The exchange-correlation energy was obtained in the generalized gradient approximation (GGA) with the PBEsol prescription [9]. A dense Monkhorst−Pack grid o 4x4x4 of k-special points was used to perform Brillouin zone (BZ) integrations to ensure high convergence of 1-2 meV per atom in the total energy. Through the calculation of the forces on atoms and the stress tensor, the atomic positions and the unit cell parameters were fully optimized to obtain the relaxed structures at selected volumes. In the relaxed optimized configurations, the resulting forces on the atoms are less than 0.006 eV/Å, with deviations of the stress tensor from hydrostatic conditions (diagonal tensor) lower than 0.1 GPa. References [1] J. Lu, K. Ueda, H. Yagi, T. Yanagitani, Y. Akiyama, A.A. Kaminskii, J. Alloys Compds. 341, 220 (2002). [2] J. Liu, Y.K. Vohra, Appl. Phys. Lett. 64, 3386 (1994). [3] S. Kobyakov, A. Kaminska, A. Suchocki, D. Galanciak, M. Malinowski, Appl. Phys. Lett. 88, 234102 (2006). [4] P. Mukhopadhyay, Supercond. Sci. Technol. 7, 298 (1993). [5] S. Karato, Z. Wang, B. Liu, K. Fujino, Earth Planet. Sci. Lett. 130, 13 (1995). [6] N.P. Padture, P.G. Klemens, J. Am. Ceram. Soc. 80, 1018 (1996). [7] A. Durygin, V. Drozd, W. Paszkowicz, E. Werner-Malento, R. Buczko, A. Kaminska, S. Saxena, A. Suchocki, Appl. Phys. Lett. 95, 141902 (2009). [8] G. Kresse and J. Furthmüller, Computational materials science 6(1), 15 (1996). [9] J.P. Perdew, A. Ruzsinszky, G.I. Csonka, O.A. Vydrov, G.E. Scuseria, L.A. Constantin, X. Zhou, and K. Burke, Phys. Rev. Lett. 100(13), 136406 (2008).

Resume : One of the most unwanted processes in the area of joining in microelectronics is the formation of Intermetallic Compounds (IMCs)at the substrate/solder interface and their excessive growth due to the possibility of premature failure of electronic devices caused by cracking [1,2]. The IMCs formation is a diffusion-driven process, and suppressing this phenomenon may help overcome the problem by considering graphene-coated substrate to limit those harmful effects of IMCs presence. Investigated droplet represents one of the commonly used materials for the soldering process. In this work, we used experimentally as well as molecular dynamics methods for analyzing the structure, chemical composition and wettability of both copper surface and graphene-coated Cu surface with liquid Sn-Ag droplet. We discuss the impact of the graphene layer on wetting behavior, structure, as well as reactions that occurred at the Cu surface and Cu/Gn interface in contact with liquid Sn-Ag. Topological aspects were also included into consideration by performing Voronoi Analysis [3]. Microstructural investigation with chemical characterization was done using Scanning Electron Microscopy with Energy-dispersive X-Ray Spectrometer (SEM-EDS) and compared with molecular dynamics simulation results. For a better understanding of the observed phenomenon, we compared the present studies with our recent discoveries for graphene-coated Cu surface wetted with a liquid silver droplet [4]. Our studies show the formation of IMCs takes place at the interface of bare Cu – (Sn-Ag). Moreover, the presence of graphene helps in the suppression of the diffusion process at the interface as well as modifies the wetting behavior. References: 1. Luan, T.; Guo, W.; Yang, S.; Ma, Z.; He, J.; Yan, J. Effect of intermetallic compounds on mechanical properties of copper joints ultrasonic-soldered with Sn-Zn alloy. J. Mater. Process. Technol. 2017, 248, 123–129, doi:10.1016/j.jmatprotec.2017.04.019. 2. Xiong, M. Yue; Zhang, L. Interface reaction and intermetallic compound growth behavior of Sn-Ag-Cu lead-free solder joints on different substrates in electronic packaging. J. Mater. Sci. 2019, 54, 1741–1768, doi:10.1007/s10853-018-2907-y. 3. Żydek, A.; Wermiński, M.; Trybula, M.E. Description of grain boundary structure and topology in nanocrystalline aluminum using Voronoi analysis and order parameter. Comput. Mater. Sci. 2021, doi:10.1016/j.commatsci.2021.110660. 4. Drewienkiewicz, A.; Żydek, A.; Trybula, M.E.; Pstruś, J. Atomic Level Insight into Wetting and Structure of Ag Droplet on Graphene Coated Copper Substrate—Molecular Dynamics versus Experiment. Nanomaterials 2021, 11, 1465, doi:10.3390/nano11061465. Acknowledgments Financial support from the National Science Centre Poland, project No 018/29/B/ST8/02558. The authors are grateful for the computation time provided by PlGrid Infrastructure at Academic Computer Centre Cyfronet AGH.

Resume : Materials design, preparation, characterization and process of analysis of structura and physical properties are supported by analytical or numerical global search and optimization methods in multiparameters space. This variables of the space define the computational task. For many such tasks, analytical solutions cannot be found because of the character of the tsk, its complexity and/or a too large number of parameters to be optimized. Genetic algorithms forming a subfamily of methods based on evolutionary computation, are a useful tool inspired by biological principles of evolution, The genetic computations involve creation of search criteria and determination of ranges of variables and constraints, suitable for the given numerical task. These methods can be developed employing multiple and combined with other artificial-intelligence and classical approaches. In materials science and technology, the genetic algorithms have been successfully applied for materials design and for optimization of physicocheical properties. Their applications involve, in particlulaar the field of nanoscience, i.e. of 0D, 1D and 2D nanomaterials and nanodevices. In this presentation examples of such applications, known from literature, will be demonstrated.

Resume : Calcium orthovanadate (Ca3(VO4)2) is known to crystallize in R3c space group. The structure of natural and synthetic compounds of this family is complex (the hexagonal cell is large, a = 10. and c = 38) and constructed in a way allowing for various substitutions, with two columnar building units. Due to the complexity, there was a very little effort done from the theoretical point of view. First step for investigation of a material is its structural characterization. The crystal structure refinement of the synthesized sample was made by employing the Rietveld method using XRD data. The refinement procedure is based on the minimization of the weighted, squared differences between the observed and calculated intensities at every step in the diffraction pattern. The minimization was carried out using the reliability index parameters. Structural analysis of such complex structure may include advanced methods like employing the anomalous scattering effect (synchrotron) or combining various kinds of data (polycrystal data, single crystal data, X-ray and neutron data). As the structure includes five different cationic sites, where various substituents can be located, at low or high concentration (up to about 10%, but even much more in specific cases), the determination of structure requires refinement of the occupancies, separately at all these sites. This task meets difficulties arising as a function of the scattering factors of the contributing atoms. Recently, structural properties of whitlockite related material based on quantum chemical calculation were reported. By computational calculations, they were able to quantify the ability of whitlockite to hold substitutions and vacancies in preferential sites [1, 2]. In our study, we describe the computational issues of structure refinement, and investigate the structure properties of orthovandates whitlockite related material which is substituted with some transition metals (Co, Ni, Cu) by Rietveld refinement. As a result of structure refinement of various substitution model, the information about the host site for divalent substituent is obtained. Moreover, the stability of the occupation with varying temperature is analyzed. The results are in line with those previously reported for structurally related orthophosphate. 1. Jay, E. E. et al. Predicted energies and structures of β-Ca3(PO 4)2. J. Solid State Chem. 183, 2261–2267 (2010)., 2. Debroise, T. et al. One Step Further in the Elucidation of the Crystallographic Structure of Whitlockite. Cryst. Growth Des. 20, 2553–2561 (2020).

Resume : The key requriments for the design of an efficient photocatalyst are (1) good visible light absorption, (2) favorable position of the edges of the valence and conduction bands, (3) charge carriers separation upon excitation, (4) high carriers mobility, (5) chemical stability [1]. Composite materials in which the units are in intimate contact thanks to the formation of a junction region can in principle successfully address all these aspects. For instance, when the band edges are positioned according to a type-II alignement, than the photogenerated electrons and holes migrate towards different components of the heterojunction, hindering recombination and enhancing the efficiency of the redox processes; the combination of a low band gap semiconductor with a water resistant thin oxide film can lead to a visible-light active and chemically stable photocatalyist; etc. A representative example of a composite photocatalyst is the mixed-phase anatase-rutile P25 powder, the gold standard to test photocatalytic efficiency of new materials. The possibility to engineer and design new interfaces between different semiconductors opens in principle a variety of possibile solutions to the problem. This is based on the choice of the surface terminations that are interfaced, the nature of the chemical bonds, the occurrence of a charge transfer at the interface, the possibility to growth nanofilms exploiting quantum confinment effects, etc. Using adavanced electronic structure methods we will discuss the underlying phisical principles and we will show how it is possible to conceive new material interfaces and explore their performances using first principles approaches [2-13]. Beside the classical thermodynamic aspects related to the band positions in the components of the heterojunction, also the electron mobility and charge carrier efficiency will be discussed, addressing in this way the important kinetic aspects of a photocatalytic process. [1] H .Wang, et al. Chem. Soc. Reviews, 43, 5234 (2014). [2] E. Cerrato, C. Gionco, M. C. Paganini, E. Giamello, E. Albanese, G. Pacchioni, ACS App. Ener. Mater., 1, 4247 (2018). [3] G. Di Liberto, S. Tosoni, G. Pacchioni, J. Phys. Chem. Lett. 10, 2372 (2019). [4] G. Di Liberto, S. Tosoni, G. Pacchioni, J. of Physics: Conden. Matter, 31, 434001 (2019). [5] G. Di Liberto, S. Tosoni, G. Pacchioni, PCCP - PhysChemChemPhy, 21, 21497 (2019). [6] G. Di Liberto, S. Tosoni, G. Pacchioni, ChemCatChem, 12, 2097 (2020). [7] G. Di Liberto, S. Tosoni, F. Illas, G. Pacchioni, J. of Chem. Phys., 152, 184704 (2020). [8] L. A. Cipriano, G. Di Liberto, S. Tosoni, G. Pacchioni, Nanoscale, 12, 17494 (2020). [9] G. Di Liberto, S. Tosoni, G. Pacchioni, J. of Physics: Conden. Matter, 33, 075001 (2021). [10] G. Di Liberto, O. Fatale, G. Pacchioni, PCCP – PhysChemChemPhys, 23, 3031 (2021). [11] G. Di Liberto, S. Tosoni, G. Pacchioni, Adv. Funct. Mater., 31, 2009472 (2021). [12] G. Di Liberto, S. Tosoni, G. Pacchioni, Catal. Sci. & Technol. in press (2021). [13] L. A. Cipriano G. Di Liberto, S. Tosoni, G. Pacchioni, J. Phys. Chem. C in press (2021).

Resume : Development of nitride based optoelectronic devices is supported by extensive computational efforts in several areas: simulations of molecular processes at semiconductor surfaces; incorporation of atoms into the solid phase, electric transport in the device structures, strain and spontaneous polarization and related electric fields in optically active structures, light emission and other recombination types. These subject require different analysis tools which will be discussed. Molecular processes require use of ab initio simulations in density functional theory (DFT) formulation. These basic techniques were recently supplemented by new aspects: electric field at surfaces and charge transfer contribution to adsorption energy. The subject was supplemented by incorporation of enthalpy and entropy contributions that allow to obtain pressure/temperature dependence of the surface state. Incorporation of atoms, including dopants was also investigated by ab initio methods. The calculations incorporating above mentioned field and charge effects provide deep insight into the semiconductor doping in the growth stage. That allows to determine the doping problems, especially acute in AlN-rich wide bandgap devices. The use of polarization doping allows to alleviate the doping problems these AlN-rich device structures. Spontaneous and strain induced piezoelectric polarization leads to electric fields in the polar multiquantum wells (MQWs) that drastically reduces radiative recombination efficiency via Quantum Confined Stark Effect (QCSE) by electron-hole separation. The direct ab initio simulations allow to obtain the wavefunction overlap and consequently the radiative transition rates. This is supplemented by drift-diffusion approach allowing to obtain the electric fields and the carrier transport in the whole optoelectronic devices. The approach is supplemented by the various recombination types that are directly simulated by advanced ab initio approaches, including GW formulation allowing to capture essential features of exciton recombination in the optoelectronic devices active structures.

Resume : The spin coating process is the method to make a thin film having a uniform thickness. In the semiconductor industry, the spin coating is mostly conducted for the photo-resist coating to be used as masking film during the photolithography process. It proceeds as a wafer is placed on the rotating chuck and then the photo-resist is deposited on the center area of the wafer and the photo-resist spreads out to the edge side of the wafer and forms a thin film. It is important to understand the impact of each control factor on the thickness and uniformity of the photo-resist to achieve predictable and reproducible photo-resist thickness. In this paper, we investigated the thickness variation phenomenon with respect to the viscosity of the photo-resist on each wafer position using computational fluid dynamics simulation. In addition, we conducted experiments on the real wafers reflecting the simulation results and evaluating the optimum condition to reduce the thickness variation.

Resume : Graphene (Gr) has aroused great interest among the scientific community thanks to its fascinating properties and promising applications in many technological fields. Nevertheless, over the last years, the frontline of research has moved from the study of basic properties of pure graphene layers to chemical modified forms, i.e. doped graphene, and its interaction with other systems, such as nanoparticles, or surfaces (like Gr/metal interfaces), turning graphene into a reactive material suitable for novel applications such as gas- storage and sensing. In this work, our experimental colleagues developed a novel scalable growth method to produce high-quality nitrogen-doped graphene (N-Gr) on Ni(111), and the produced N-Gr layers were thoroughly characterized at the atomic level by Scanning Tunneling Microscopy and X-ray Photoelectron Spectroscopy in combination with our Density Functional Theory (DFT) simulations in order to identify and fully characterize the N dopants (S. Fiori, D. Perilli, et al., Carbon, 2021, 171, 704-710). We found how nitrogen does not just have a huge impact on the structural and electronic properties of graphene, but also on its chemical properties, like molecule permeation. The molecule permeation of graphene is important for electrochemistry-based applications, as well as in other applications like gas-sensing and gas-trapping. In this work we considered the intercalation of CO molecules. Based on the synergic contribution of DFT calculations and experiments, we unraveled the mechanism of CO intercalation at the Gr/Ni interface, which is highly facilitated by the presence of N-dopants (D. Perilli, S. Fiori, et al., The Journal of Physical Chemistry Letters, 2020, 11 (20), 8887-8892), Similar mechanisms are likely to apply to other cases of molecular intercalation at the Gr/M interface, where the process has been observed but not yet explained. A clear solution to this puzzle is a crucial step towards engineering the Gr/M interface in order to design and realize systems with tailored properties. The presence of intercalated CO molecules significantly affects the electronic properties of graphene: we observe an electron transfer from the Gr layer to CO. This originates a sizeable p-doping effect, with a shift of the Fermi level roughly proportional to the coverage, as large as 0.86 eV for 0.57 ML of intercalated CO (S. Del Puppo, V. Carnevali, D. Perilli, et al., Carbon, 2021, 176, 253-261). Such a high sensitivity of the Gr doped state to the presence of intercalated CO molecules opens the way to the design of new sensors based on the Graphene/Ni(111) interface to easily detect and quantify the presence of this harmful gas.

Resume : Computational methods provide a more extensive horizon and convenient means for analyzing the behavior and properties of materials. Although atomic scale calculation can give the properties of materials, by which it is difficult to stimulate the macroscale experiments. Comparatively, the finite element method (FEM) is used to assist the experiments for further reflecting the relationship between material structure and properties. Specifically, FEM builds general models from the discrete experiments and extends them to continuous process, which can liberate the repeated experiments. An alternative application for FEM is to exert influence on the general models for predicting the property evolution, which can provide guidance for experimenters. Eutectic materials have been widely used in structural materials, semiconductor, optical devices and many other fields. The unique properties of eutectic materials have been extensively investigated. Among these properties, the stress field and strain field in the eutectic structure have additional effects on many other properties (i.e., diffusion, electroconductivity). Because of the existence of multiphase structure, the load transfer and its distribution between multiphases are one of the most basic characteristics deserved to be studied. The load transfer effect has been widely investigated especially in structural materials. Besides, temperature also has a significant effect on the load transfer and its distribution. The experiments on eutectic alloys show that the hard phase can effectively share the stress on the soft matrix, and the load transfer effect of the hard phase increases with the increase of temperature. However, this phenomenon at different temperatures demonstrated by experiments are discrete. Based on the experiments, the eutectic structure model is established by FEM to simulate the effect of the continuous process of temperature change on the load transfer. Meanwhile, the load distribution with the change of temperature can be illustrated as well. Therefore, discrete experimental process is integrated into a continuous process by computational methods. The large volume fraction of interfaces inside eutectic structure is the source of many specific properties. Based on the eutectic structure model, the interface can be adjusted by FEM to predict the impact of interface property variation on the overall performance, then the reliability of the simulation can be verified by comparing with the experimental results. Hence, the influence on load transfer and its distribution has been investigated by introducing transition structure around the eutectic phase interface by FEM. It has shown that the existence of rigid transition structure is helpful for improving the load transfer effect of hard phase. Furthermore, it is suggested that the initial stress field caused by the transition structure can also affect the load transfer effect of hard phase. During the experiments afterwards, the precipitate layer with higher elastic modulus is induced at the interface of eutectic phase, and the layer also reduces the initial tensile strain at the interface. The test results prove that the existence of the precipitate layer improves the load transfer effect of the eutectic phase. Above all, the calculation on the influence of temperature and interface on load transfer in eutectic structure has shown its applications in completing discrete experimental processes or assistance in experimental design.

Resume : The use of Scanning Probe Microscope (SPM) images to visualize the surfaces of materials plays an important role on their characterization. However, they suffer from an inherent trading off between image resolution (pixel size) and measurement (scanning) range which implies that SPM images can display only a limited range of the scales of material surfaces. This limitation becomes critical in the metrology of hierarchical multiscale surfaces since they develop structures at multiple scales that cannot be captured in a single SPM image. To solve this problem and foster the metrology of hierarchical surfaces, we develop a computational method to hybridize SPM images of different magnifications in order to generate full-scale surfaces overcoming the scale limitation of SPM metrology. The so-called Fourier Stitching Method (FSM) is based on the Fourier transforms of SPM images and their stitching in frequency space to get the full-scale Fourier transform which finally is stochastically inversed to obtain the full-scale surface. The latter has the resolution and the measurement range of the high and low magnification images respectively spanning a wide range of scales. The method is first validated in 1D and 2D synthesized rough surfaces with a wide variety of characteristics (Gaussian and non-Gaussian, fractal or periodic-like) and then is applied in real experimental surfaces of polymers and metals which have been treated to obtain multiscale hierarchical structures.

Resume : A lot of progress has been made in recent years in the development of machine learning (ML) potentials for atomistic simulations [1]. Neural network potentials (NNPs), which have been introduced more than two decades ago [2], are an important class of ML potentials. While the first generation of NNPs has been restricted to small molecules with only a few degrees of freedom, the second generation extended the applicability of ML potentials to high-dimensional systems containing thousands of atoms by constructing the total energy as a sum of environment-dependent atomic energies [3]. Long-range electrostatic interactions can be included in third-generation NNPs employing environment-dependent charges [4], but only recently limitations of this locality approximation could be overcome by the introduction of fourth-generation NNPs [5], which are able to describe non-local charge transfer using a global charge equilibration step. In this talk an overview about the evolution of high-dimensional neural network potentials will be given along with typical applications in large-scale atomistic simulations. [1] J. Behler, J. Chem. Phys. 145 (2016) 170901. [2] T. B. Blank, S. D. Brown, A. W. Calhoun, D. J. Doren, J. Chem. Phys. 103 (1995) 4129. [3] J. Behler, M. Parrinello, Phys. Rev. Lett. 98 (2007) 146401. [4] N. Artrith, T. Morawietz, J. Behler, Phys. Rev. B 83 (2011) 153101. [5] T. W. Ko, J. A. Finkler, S. Goedecker, J. Behler, Nature Comm. 12 (2021) 398.

Resume : Energy functionals which depend explicitly on each individual orbital density, rather than the total charge density, appear naturally when applying self-interaction corrections to density-functional theory. Rather than a limitation, we argue that this is a powerful feature, and show how it is possible to interpret the orbital-dependency of densities and potentials as an effective frequency dependency. Here we focus on the case of Koopmans-compliant functionals, and discuss their application to study extended systems. Such a frame is naturally amenable to describe electronic spectroscopies [1], and is free from e.g. the constraint of having derivative discontinuities in the exact formulation. Excellent agreement is achieved for ionization potentials and affinities, fundamental gaps, and deeper orbital levels (photoemission) for both molecules and solids [2-5]. We believe that a functional theory for the spectral density is therefore emerging, able to address at the same time total energies and spectral properties. [1] A. Ferretti, I. Dabo, M. Cococcioni, N. Marzari, Phys. Rev. B 89, 195134 (2014). [2] N.-L. Nguyen, G. Borghi, A. Ferretti, I. Dabo, N. Marzari, Phys. Rev. Lett. 114, 166405 (2015). [3] N. Colonna, A. Ferretti, N.-L. Nguyen, N. Marzari, J. Chem. Theory Comput. 14, 2549 (2018). [4] N.-L. Nguyen, N. Colonna, A. Ferretti, N. Marzari, Phys. Rev. X 8, 021051 (2018). [5] N. Colonna, N.-L. Nguyen, A. Ferretti, N. Marzari, J. Chem. Theory Comput. 15, 1905 (2019).

Resume : An implementation of density functional embedding theory, within the frozen density embedding formalism [1], for molecules and periodic systems in the TURBOMOLE program package [2] using Gaussian basis functions is presented. The subsystem of interest may be described by density functional theory (DFT) or wave function theory (WFT) methods, while the environment density is determined using DFT. Employing an embedding potential based either on non-additive kinetic energy density functional or a level-shift projection operator [3], DFT-in-DFT or WFT-in-DFT is performed. While the embedding potential may be updated during the embedding procedure for DFT-in-DFT calculations, the WFT-in-DFT utilize a fixed embedding potential. The Coulomb contribution to the Kohn-Sham matrices of the subsystems as well as to the embedding potential is efficiently calculated using a combination of density fitting and continuous fast multipole methods [4]. The exchange-correlation and the non-additive kinetic energy potentials are evaluated using the linear scaling hierarchical integration scheme [5]. Furthermore, the embedding scheme is coupled with a recent and highly efficient real time-time dependent DFT implementation [6] that allows for the study of the non-linear optical response of the embedded subsystem. [1] T. Wesolowski, A. Warshel, J. Phys. Chem. 97, 8050 (1993). [2] TURBOMOLE 7.1, a development of the University of Karlsruhe and Forschungszentrum Karlsruhe GmbH, 1989-2007, TURBOMOLE GmbH, since 2007; available from http://www.turbomole.com. [3] F. Manby, M. Stella, J. Goodpaster, T. Miller, J. Chem. Theory Comput. 8, 2564 (2012). [4] R. Łazarski, A. M. Burow, M. Sierka, J. Chem. Theory Comput. 11, 3029 (2015). [5] A. Burow, M. Sierka, J. Chem. Theory Comput. 7, 3097 (2011). [6] C. Müller, M. Sharma, M. Sierka, J Comput Chem. 41, 2573 (2020).

Resume : Electrochemical characterisation of materials and interfaces requires detailed knowledge of their stoichiometric composition and local geometry. Despite the enormous progress in recent years, however, there is no experimental technique yet that can provide direct, simultaneous time and spatial resolution of quantitative stoichiometry changes during electrochemical cycling. This limitation hinders atomistic interpretation of experiments and prevents the development of improved electrochemical solutions. Within accuracy compromises and intrinsic modelling approximations, quantitative insights can be derived, in principle, using quantum mechanical simulations based on Density Functional Theory (DFT). Nevertheless, whereas modelled structures can be optimised by DFT energy screening, stoichiometric changes are not immediately accessible, as no DFT-based method can currently provide a complete and highly accurate “first principles digital twin” of the electrochemical system under scrutiny. To overcome this stalemate, a novel strategy based on combined DFT-experiment resolution of stoichiometric changes during electrochemical processes has recently been proposed in the literature [1]. This scheme makes use of Electrochemical Quartz Crystal Microbalance (EQCM) experiments to simultaneously measure changes of mass and charge of electroactive materials. In the general case of more than two species involved in a redox process, the system of equations for the EQCM mass and charge conservation becomes mathematically undetermined, with more unknown stoichiometric coefficients than the two available equations. This leads to a set of infinite possible EQCM-compatible stoichiometric solutions and, thence, uncertainty on the stoichiometry of the material upon electrochemical cycling. The proposed method conveniently selects stoichiometric compositions among the infinite set of solutions and generate atomistic models from them. These models are subsequently optimised using DFT simulations. Analysis of the computed results allows identifying energetically and thermodynamically favoured stoichiometries and structures. This procedure offers an alternative route to investigate complex electrochemical processes at the nanoscale level from experimental aided, first principles simulations, without the need of extra ad-hoc, uncontrolled approximations [2]. Even though this new strategy is general and applicable to any electrode material that can be electrochemically grown or deposited on an EQCM-electrode, the complexity of building models from EQCM data is substantial, resulting in several tedious and time-consuming steps. To overcome such barriers, here we present ALC_EQCM, a new software suite capable to automate the approach. We illustrate the workflow for the case of Ni(OH)2 to investigate the electrochemical ageing of the material [1]. We also present applications to the research of electrodeposition processes. We believe that closer interaction between EQCM and DFT experts is essential for the development of the method and extension of its reach. We hope the present contribution stimulates useful discussion towards the uptake of the ALC_EQCM software by the community, adding to the already available tool-kit for fundamental research in electrochemistry. [1] T-H. Wu, I. Scivetti, et al. ACS Appl. Energy Mater. 2020, 3, 4, 3347–3357. [2] S. I. Cordoba‐Torres et al. J. Electrochem. Soc. 1991, 138, 1548-1553.

Resume : Advancements in computational and experimental methods allow for enhanced characterization of materials for energy applications. A key to the successful research is application of reliable and feasible computational approach. Here we present our investigation of Li x FePO 4 orthophosphates and fluorite- and pyrochlore-type zirconate materials which are applied as functional materials in energy storage devices [1]. In particular, we discuss atomistic modeling of thermodynamic properties such as formation enthalpies, stability, and solubility limits, that enable characterization of: (1) miscibility gap in Li x FePO 4 and (2) stabilization of zirconia upon doping with Yttrium. In additions, we show an accurate framework for derivation of the ionic conductivity in the yttria-stabilized zirconia. With these examples we highligh the improvements that have to be made to thestandard computational methods, to enhance their predictive capabilities. References: [1] Kowalski, He & Cheong, Frontiers in Energy Research, 9, 653542 (2021).

Resume : The family of IV-VI topological crystalline insulator (TCI) materials feature band inversions located at four nonequivalent L points in the Brillouin zone. The resulting nontrivial topology of their electronic band states is protected by mirror plane symmetry. Due to the bulk-edge correspondence topologically protected electronic states appear at the surfaces of the crystal and at one dimensional edges of TCI nanostructures. They are described by Dirac cones dispersion. During the talk I will show haw the tight binding and Green function recursive methods allow for study of various properties of the edge states. Mainly: their localization, the influence of a surface roughness on the Dirac cones splitting [1] and the topology of one dimensional states at the surface steps [2]. I would like to discuss also various higher order topologies of electronic bands which appear in the low dimensional heterostructures of TCIs. In thin films the mutual interaction of the surface and interface states can lead to Rashba splitting [3] but also to new topological properties of the structures [4]. Nanowires can host topologically protected hinge and core states. In the cases when it is possible I will confront our results with experimental findings. [1] C. M. Polley, R. Buczko, A. Forsman, P. Dziawa, A. Szczerbakow, R. Rechciński, B. J. Kowalski, T. Story, M. Trzyna, M. Bianchi, A. Grubišić Čabo, P. Hofmann, O. Tjernberg, and T. Balasubramanian, ACS Nano 12, 617-626 (2018). [2] R. Rechciński and R. Buczko, Phys. Rev. B 98, 245302 (2018). [3] R. Rechciński, M. Galicka, M. Simma, V.V. Volobuev, O. Caha, J. Sánchez-Barriga, P. S. Mandal, E. Golias, A. Varykhalov, O. Rader, G. Bauer, P. Kacman, R. Buczko, and G. Springholz, Advanced Funct. Matt. 2008885 (2021), [4] S. Safaei, M. Galicka, P. Kacman and R. Buczko, New J. Phys. 17, 063041 (2015)

Resume : The efficient and accurate calculation of how ionic quantum and thermal fluctuations impact the free energy of a crystal, its atomic structure, and phonon spectrum is one of the main challenges of solid state physics, especially when strong anharmonicity invalidates any perturbative approach. To tackle this problem, we present the implementation on a modular Python code of the stochastic self-consistent harmonic approximation method. This technique rigorously describes the full thermodyamics of crystals accounting for nuclear quantum and thermal anharmonic fluctuations. The approach requires the evaluation of the Born-Oppenheimer energy, as well as its derivatives with respect to ionic positions (forces) and cell parameters (stress tensor) in supercells, which can be provided, for instance, by first principles density-functional-theory codes. The method performs crystal geometry relaxation on the quantum free energy landscape, optimizing the free energy with respect to all degrees of freedom of the crystal structure. It can be used to determine the phase diagram of any crystal at finite temperature. It enables the calculation of phase boundaries for both first-order and second-order phase transitions from the Hessian of the free energy. Finally, the code can also compute the anharmonic phonon spectra, including the phonon linewidths, as well as phonon spectral functions.

Resume : One of the great challenges of condensed-matter physics is the description, understanding, and prediction of the effects of the Coulomb interaction on materials properties. In electronic spectra, the Coulomb interaction causes a renormalization of excitation energies and a transfer of spectral weight. Most importantly, it can lead to qualitatively new structures, such as satellites in photoemission or double-plasmon resonances in energy-loss spectra. Being a genuine signature of dynamical correlation, they are absent in a non-interacting picture but can be understood in terms of the coupling between different elementary excitations. In this framework, a key physical ingredient is the dynamical screening of the Coulomb interaction, containing charge excitations such as plasmons and excitons. It can be accurately calculated within time-dependent density-functional theory (including double plasmons [1]) or by solving the Bethe-Salpeter equation. Its microscopic picture can be obtained from the mixed dynamic structure factor that is measured by coherent inelastic X-ray scattering spectroscopy [2]. Building upon a detailed knowledge of dynamical screening, the cumulant expansion of the Green's function can efficiently explain plasmon and exciton satellites in the photoemission spectra of several materials, ranging from simple metals to correlated transition-metal oxides [3]. Finally, the combined effect of many-body interactions and experimental conditions can lead to novel signatures in the measured spectra [4], underlining the need to bridge the gap between theory and experiments. [1] M. Panholzer et al. Phys. Rev. Lett. 120, 166402 (2018). [2] I. Reshetnyak et al., Phys. Rev. Research 1, 032010(R) (2019). [3] See e.g. J. S. Zhou et al. Phys. Rev. B 97, 035137 (2018). [4] J. S. Zhou et al. PNAS 117 28602 (2020).

Resume : Abstract: Cuprous oxide has been conceived as a potential alternative to traditional organic hole-transport layers in hybrid halide perovskite-based solar cells. Device simulations predict record efficiencies using this semiconductor, but experimental results do not yet show this trend. More detailed knowledge about the Cu2O/perovskite interface is mandatory to improve the photoconversion efficiency. Using density functional theory calculations, we study here the interfaces of CH3NH3PbI3 with Cu2O to assess their influence on device performance. Several atomistic models of these interfaces are provided for the first time, considering different compositions of the interface atomic planes. The interface electronic properties are discussed on the basis of the optimal theoretical situation, but in connection with the experimental realizations and device simulations. It is shown that the formation of vacancies in the Cu2O terminating planes is essential to eliminate dangling bonds and trap states. The four interface models that fulfill this condition present a band alignment favorable for photovoltaic conversion. Energy of adhesion and charge transfer across the interfaces are also studied. The termination of CH3NH3PbI3 in PbI2 atomic planes seems optimal to maximize the photoconversion efficiency.

Resume : Computational techniques are well placed to investigate tissues and processes in the body that are difficult to access experimentally. This talk will show how computer simulations have predicted the structures and properties of biocompatible phosphate glasses and created models for collagen to identify age-related damage to soft tissue in human tendons.

Resume : Nowadays Nano Particles (NPs) play a fundamental role in both fundamental and applied research, due to peculiar effects related to nano confinement. Due to their reduced dimensions, precise atomistic information on NPs are difficult to achieve at the experimental level and, in this perspective, computational tools based on molecular modeling, in synergy with experimental advanced characterization techniques, can provide important information on several aspects such as: nucleation and growth mechanisms, stoichiometry, structural arrangements driven by kinetic/thermodynamic factors, chemical ordering. The precise control of all these features in the synthetic preparation of NPs are of crucial importance, due to the close relations between them and the responsive properties of these systems when subjected to an external perturbation. In this presentation an overview of the latest computational algorithms, employing both un-reactive and reactive (ReaxFF) force-fields, developed in our group will be presented, aiming at the investigation of: a) the growth modes of metal-oxide NPs of 1st row transition metals [1-2]; b) the chemical-ordering patterns which can be found in alloyed (transition-metal) NPs (nano-alloys) [3]. More specifically, regarding point a), it will be shown how the computational procedure has to be specifically tailored when simulating two completely different reactive environments: the growth of zinc oxide NPs in a high-T gas-phase plasma reactor [1] or the formation of iron oxide NPs in a solution environment from the decomposition of organo-metallic precursors in low-T conditions [2]. References: 1. G. Barcaro, S. Monti, L. Sementa, V. Carravetta, JCTC, 2019, 15, 2010 2. G. Barcaro and S. Monti, Nanoscale, 2020, 12, 3103 3. G. Barcaro, L. Sementa, A. Fortunelli, PCCP 2014, 16, 24256

Resume : Despite ZnO's key technological importance, its crystallization characteristics are currently relatively poorly understood. This is due to the overwhelming computational effort required for dedicated simulations, which precludes direct use of DFT-based methods and requires fine interatomic potentials, capable of correctly accounting for the structural diversity of ZnO. With the goal to tackle ZnO crystallization in an homogeneous liquid phase we have built and validated a robust Machine Learning Interatomic Potential (MLIP) suitable for large-scale simulations (nanosecond-long molecular dynamics of several hundreds of atoms). The potential is based on physically motivated mathematical formulation and a constrained Lasso-Lars method is used for identification and adjustment of its relevant parameters. The training database is composed of DFT-GGA results on a variety of ordered crystalline structures, but also includes disordered and amorphous configurations, such as those obtained in high-temperature molecular dynamics simulations. With the new MLIP, we have performed molecular dynamics simulations on the freezing of bulk ZnO liquid with particular emphasis on the singular role of cooling rate and applied pressure. Using a data-driven structural characterization approach to identify alternative ZnO polymorphs, we were able to access the birth of the initial zinc oxide crystal in the surrounding liquid and to track its behavior during subsequent growth.

Resume : Polymers are an integral part of our everyday life and modern technology. Polymer informatics efforts are underway more vigorously than ever before to efficiently and effectively develop, design, and discover new polymers that meet specific application needs. So far, these data-driven efforts have focused largely on single-property predictors and homopolymers. Here, we present a multi-property predictor for homopolymer and copolymers using multi-task deep neural networks. The effectiveness of our multi-task approach is because inherent property correlations present in the dataset are exploited implicitly. Advanced polymer fingerprinting and deep-learning schemes that incorporate multi-task and meta learning are proposed to solve the emerging problems of our approach. Trained on a large experimental data set of thermal and mechanical properties, we showcase how our models can be used to optimize polyhydroxyalkanoates (biodegradable polymer family) for packaging applications. Our developed models are accurate, fast, flexible, and scalable to other polymer properties when suitable data become available. Production-ready models are deployed at https://polymergenome.org/.

Resume : Microstructural characteristics and corrosion behavior of the single-phase and binary- phase Mg-xSc (wt.%, x=5, and 15) were investigated. Both single and binary phases Mg-Sc alloys displayed typical peritectic microstructure, where Sc-depleted areas were surrounded by Sc-rich zones. The MgSc phases were prone to precipitate in Mg-rich zones of Mg-15Sc, which was beneficial to the enhancement of yield strength. To analyze the corrosion behavior, experimental and first-principles studies were conducted. The single-phase Mg-5Sc alloy show the lowest weight loss rate with 0.6 mg/cm2/day, which was one order of magnitude smaller than that of binary-phase Mg- 15Sc alloy. The potential difference, the cathode H2 evolution kinetics, and the surface layer containing Sc2O3 were believed to be the main reasons for the difference of corrosion behavior of single-phase and binary-phase Mg-Sc alloys.

Resume : For more than 120 years, experiments on a range of systems have shown an unexpected correlation between diffusion pre-exponential factors and energy barriers. This compensation effect, or the Meyer-Neldel rule, implies a universal linear relation between the activation energy and the entropy. While a number of phenomenological explanations have been proposed, these could not be directly tested against experimental data. Building on extensive catalogues of activated events generated with the activation-relaxation technique (ART nouveau) in a number of disordered systems, we lift this restriction and demonstrate how the deformation of the energy landscape affects the vibrational density of state that dominates the entropic contributions. Showing that the harmonic approximation captures the essential part of the compensation effect, we find that the deformation associated with diffusion both softens low and stiffens high frequency phonons. Softening generally dominates as barrier increase, creating a compensation effect. This correlation, however, is held only on average and huge fluctuations in prefactors are observed on an event by event basis. These can affect the evolution of materials and cannot be neglected without being assessed. Part of the work is done in collaboration with Alecsandre Sauvé-Lacoursière (U. Montréal), Gilles Adjanor and Christophe Domain (EDF, France)

Resume : Over the past decade a revolution has taken place in how we do large scale molecular dynamics. While previously first principles accuracy was solely the purview of explicit electronic structure methods such as density functional theory, the new approaches have allowed the extension of highly accurate, first principles simulations to the atomic scale, where electrons are not treated explicitly any more, and therefore hundreds of thousands of atoms can be simulated. These quantum mechanically accurate force fields and interatomic potentials are fitted to electronic structure data and at first used techniques inspired by those used in machine learning and artificial intelligence research: neural networks, kernel regression, etc. It is a quickly moving field, and - having learned key lessons about representation, symmetry and regularisation - there appears to be some semblance of convergence between the diverse methods, which now also include polynomial expansions carried to high dimension.

Resume : Over the years a tremendous amount of data on materials have been gathered whether by academic experimentalists building up databases, or during manufacturing process investigations. The shear amount of data makes the use of it intractable by humans at a global scale and is hence limited to very specific uses by specialists. We present a data-driven approach for formulations of novel materials via autoencoders-based models. Using deep-learning techniques, we are trying to find important correlations and patterns in the underlaying data and by doing so, improve existing products and design new ones, using the groundwork laid by Kingma and Bombarelli. Starting from data that can consists of various inputs like compositions, processes or even aging conditions, and as outputs, product properties. We encoded the input into three latent representations utilizing encoder-decoder neural-network structures. From these trained latent space vector, the property can be predicted by a separate feed-forward neural network. Alternatively, one can optimize any given property with a given target value, by searching the latent space using a Gaussian process, to retrieve the corresponding compositions and processes. The scheme has been successfully applied to various material case studies in the past: ranging from polymers and epoxy resin to different alloys and it is general enough to be applied to much broader types of industrial problems. As an example of the broad potential use of such an algorithm, we present an application to the phase prediction of ceramic materials. We used commercially available databases consisting of binary and ternary diagrams to train an AI system able to predict properties such as the phases resulting from the mixture of compounds at any given temperatures and pressures conditions.

Resume : Electron holography is a TEM method, which can be used to determine phase shift of electron wave. The phase shift restored from a hologram consists of two components, which originate from electric and magnetic fields. These two components can be separated and quantified if at least two holograms are obtained for different configurations of magnetic field of a sample. One common way for this to be accomplished is to acquire hologram of a sample facing up, invert the sample, and acquire another hologram of the sample facing down. Inverting the sample upside-down doesn't affect the phase shift component related to electric field, but changes the sign of magnetic field's contribution. Hence, the difference of phase shifts restored from such holograms gives only the magnetic component of the total phase shift. Another possibility involves the use of objective lens in order to apply external magnetic field to a sample in-situ. The value and direction of external magnetic field can be altered by switching the current flowing through the winding of objective lens. Assuming that electric field does not change during this operation, the difference of magnetization between two states can be calculated. The reconstruction of a single hologram is a straightforward and simple process. However the procedure of determining magnetic field of a sample becomes complicated if there is a number of holograms acquired in various experimental configurations. For instance, holograms acquired for different sample orientations have to be aligned together, i.e. one of them must be flipped, rotated and shifted with respect to the other, if electric and magnetic phase shifts are to be separated. On a similar basis, if there is a sample drift and several holograms are acquired in order to average them together, then they also have to be aligned beforehand. Changing the current of the objective lens, in order to apply external magnetic field to a sample, affects the imaging conditions and causes rotation, rescaling and distortion of the observed image. Due to these difficulties and in order to accelerate and simplify the process of hologram reconstruction, hologram alignment and calculation of magnetic field, PyHoLo software has been developed, making the whole procedure semi-automatic. PyHoLo is a standalone program written in Python language, which allows to read electron holograms, restore phase shifts, align holograms, apply calculations to phase images and visualize results, e.g. maps of magnetic field. The overview of electron holography experiment, as well as PyHoLo software and its workflow will be presented. Results obtained for thin foil of magnetic FeCuSiB sample will be shown and discussed. Acknowledgments This research was co-financed by the Polish National Science Center (Grant No. UMO-2013/11/B/ST3/04244).

Resume : AgF2 attracts attention because of its similarities to precursors of high-temperature superconductors - cuprate compounds[1]. Despite the presence of strongly puckered (rather than flat) [AgF2] layers, this compound is characterized by large intra-sheet superexchange constant (J2D) which is as high as 70% of the values characteristic for oxocuprates. However, all previous attempts to dope this compound, or metalize it using elevated pressure, have failed[2]. Theoretical analysis shows that polaron formation (charge localization) is likely for bulk AgF2 due to narrow band width[1], but could be avoided if the layers are flattened[3]. Encouraged by the latest theoretical study of the possibility of stabilization of flat AgF2 monolayer on a proper substrate (heteroepitaxy)[4] and e-doping[5], we theoretically investigated the possibility of h-doping of the flat AgF2 monolayer. Within the Density Functional Theory (with Coulomb exchange, DFT+U) framework, we show two possible ways of h-doping: 1) gradual top-fluorination of flat AgF2 monolayer and 2) bonding strong oxidizer - PtF6. Top-fluorination was conducted in three stages: 25%, 50%, and 100% on three different substrates (various lattice constants). This approach allowed for puckering [4] or ferrodistortive bonding pattern within the AgFx layer. Fluorination turns out to be energy-preferred for two substrates: RbMgF3 and LiF. Based on the entropy of F2 gas, we estimate the values of temperatures below which each step of fluorination of AgF2 is facile. We show that across the entire range of fluorination, an undistorted antiferromagnetic AgFx layer is energy-preferred with Ag (II) and high-spin state of Ag(III), if additional F atoms are attached. The high value of spin for apical F atoms may indicate that these chemical species are similar to F* radicals. The band gap decreases inversely to the degree of fluorination. Use of the strong oxidizer, PtF6, also preserves the antiferromagnetic ordering of the AgF2 layer. Noticeable changes in the value of local magnetic moments are present only for Ag atoms strictly bonded to PtF6. Projected dx2-y2 and dz2 states of Ag atoms reveal partial depopulation of valence states (mainly dz2). [1] J. Gawraczyński, et al., PROC NAT ACAD SCI USA 116(5): 1495, (2019) [2] A. Grzelak, et al., DALTON TRANS 46(43): 14742-14745, (2017) [3] S. Bandaru, et al., PHYS REV MATER (2021) [4] A. Grzelak, et al., PHYS REV MATER 4(8): 084405 2020 [5] A. Grzelak, et al., ANGEW CHEM INT ED ENGL, (2021)