Research

2D Non-van der Waals Materials

2D materials are traditionally associated with the sheets forming bulk layered compounds bonded by weak van der Waals (vdW) forces. The recent surprising experimental exfoliation of atomically thin 2D sheets from non-vdW bonded oxides opens up a new perspective for this diverse class of nanostructures. Non-vdW 2D materials thus form an emerging category of low dimensional compounds possessing a wide range of novel properties enabling unique functionalities in particular due to their surface termination by cations.

We have recently been the first to apply data-driven research principles to this novel materials class to outline several dozens of new candidates [1,2,3]. We employed the AFLOW software and database – one of the largest materials repositories world wide with over 3.5 million entries. Several compounds were identified exhibiting ultra low exfoliation energies ultimately as small as that of graphene. This can be traced back to both strong structural relaxations of the 2D sheet as well as a low oxidation state of the surface cations. All systems were characterized according to their structural, electronic, and magnetic properties. Several compounds showcase the emergence of surface states, potential topological features as well as versatile surface spin polarizations making them an attractive platform for fundamental and applied nanoscience [1,3].

We also showed that the magnetic state of these nanoscale systems can be selectively controlled via surface passivation [4]. Hydrogenation of the surface dangling bonds gives rise to a switching of the magnetic states, modification of the local spin symmetries of several candidates, and even facilitates to initiate ferromagnetism for representatives that are diamagnetic in the pristine case. Our current work focuses on outlining general principles determining the exfoliability of non-vdW compounds and on the dedicated functionalization of the systems.

[1] R. Friedrich, M. Ghorbani-Asl, S. Curtarolo, and A. V. Krasheninnikov, Data-Driven Quest for Two-Dimensional Non-van der Waals Materials, Nano Letters 22, 989 (2022). doi.org/10.1021/acs.nanolett.1c03841

[2] A. P. Balan, A. B. Puthirath, S. Roy, G. Costin, E. F. Oliveira, M. A. S. R. Saadi, V. Sreepal, R. Friedrich, P. Serles, A. Biswas, S. A. Iyengar, N. Chakingal, S. Bhattacharyya, S. K. Saju, S. C. Pardo, L. M. Sassi, T. Filleter, A. Krasheninnikov, D. S. Galvao, R. Vajtai, R. R. Nair, and P. M. Ajayan, Non-van der Waals quasi-2D materials; Recent Advances in Synthesis, Emergent Properties, and Applications, Materials Today 58, 164 (2022). doi.org/10.1016/j.mattod.2022.07.007

[3] T. Barnowsky, A. V. Krasheninnikov, and R. Friedrich, A New Group of Two-Dimensional Non-van der Waals Materials with Ultra Low Exfoliation Energies, Advanced Electronic Materials 9, 2201112 (2023). doi.org/10.1002/aelm.202201112

[4] T. Barnowsky, S. Curtarolo, A. V. Krasheninnikov, T. Heine, and R. Friedrich, Magnetic State Control of Non-van der Waals 2D Materials by Hydrogenation, Nano Letters 24, 3874 (2024). doi.org/10.1021/acs.nanolett.3c04777

High-entropy ceramics

High-entropy materials are an emerging class of compounds where the maximization of (configurational) entropy rather than the minimization of enthalpy is the key design principle. In addition to high-entropy alloys, in recent years, high-entropy ceramics have attracted particular attention wich consist of an ordered anion sublattice out of carbon, nitrogen, oxygen or boron and a chemically disordered cation sublattice containing several - typically five or more - different transition metal species. Due to the disorder, these materials exhibit a range of appealing mechanical, thermal, electronic, and catalytic properties.

The computational design of these random systems must first be made feasible by taking into account a proper ensemble of ordered structures representing the disordered state. This can be achieved by the so called partial occupation scheme. Moreover, it has to address the challenging task of balancing both entropic as well as enthalpic contributions for the synthesizability of these compounds. While the previously introduced entropy forming ability descriptor (EFA) is capable of predicting the high-entropy single-phase formation of a range of high-entropy carbides, it shows shortcomings for other high-entropy ceramics classes. We recently contributed to the solution of this issue by the formulation of the disordered enthalpy-entropy descriptor (DEED) which successfully enabled the prediction of synthesicability of a wide rage of high-entropy carbides, carbo-nitrides, and borides [1]. Successful experimental verification of the predictions is provided for 17 novel compositions. The ongoing research focuses on expanding the predictions as well as to study the properties of the discovered materials in detail.

[1] S. Divilov, H. Eckert, D. Hicks, C. Oses, C. Toher, R. Friedrich, M. Esters, M. J. Mehl, A. C. Zettel, Y. Lederer, E. Zurek, J.-P. Maria, D. W. Brenner, X. Campilongo, S. Filipovic, W. G. Fahrenholtz, C. J. Ryan, C. M. DeSalle, R. J. Crealese, D. E. Wolfe, A. Calzolari, and S. Curtarolo, Disordered enthalpy-entropy descriptor for high-entropy ceramics discovery, Nature 625, 66 (2024). doi.org/10.1038/s41586-023-06786-y

Thermodynamic stability - method development

Thermodynamics is the key to materials discovery and design since synthesizability can be ensured for thermodynamically stable systems. While there have been significant successes in calculating finite temperature effects from first principles, the computational modeling of formation enthalpies — rigorously quantifying the thermodynamic stability as the enthalpy difference between the material and its elemental references — still poses a fundamental challenge. In particular for ionic materials such as oxides, standard (semi-)local and even currently available more advanced ab initio approaches yield only inaccurate predictions with errors of several hundred meV/atom which inhibits materials design.

We have recently introduced the coordination corrected enthalpies (CCE) method yielding highly accurate room temperature formation enthalpies with mean absolute errors down to 27 meV/atom, i.e., on par with the room temperature energy scale [1]. It is based on an intuitive parametrization of density functional errors with respect to the bonding topology and the cation oxidation states of the compound. In addition to the high quantitative accuracy, CCE is also capable of correcting the relative energetics of different polymorphs at fixed composition — a qualitative advantage versus earlier schemes.

The method has also been implemented into the AFLOW software for computational materials design as the AFLOW-CCE module [2,3,4]: a tool where users can input a structure file and receive the CCE corrections and formation enthalpies. As the method is based on cation coordination numbers and oxidation states, the software also includes the functionality to retrieve this information for a given structure. The implementation features a command line tool, a web interface, and a Python environment [2,3,4]. Within the further development, CCE is generalized to all other anion classes requiring corrections [5]. The method will hence be leveraged to correctly asses the energetics and to realize the predictive design of novel bulk, nanoscale as well as high-entropy phases.

[1] R. Friedrich, D. Usanmaz, C. Oses, A. Supka, M. Fornari, M. Buongiorno Nardelli, C. Toher, and S. Curtarolo, Coordination corrected ab initio formation enthalpies, Nature Partner Journal Computational Materials 5, 59 (2019). doi.org/10.1038/s41524-019-0192-1

[2] R. Friedrich, M. Esters, C. Oses, S. Ki, M. J. Brenner, D. Hicks, M. J. Mehl, C. Toher, and S. Curtarolo, Automated coordination corrected enthalpies with AFLOW-CCE, Physical Review Materials 5, 043803 (2021). doi.org/10.1103/PhysRevMaterials.5.043803

[3] M. Esters, C. Oses, S. Divilov, H. Eckert, R. Friedrich, D. Hicks, M. J. Mehl, F. Rose, A. Smolyanyuk, A. Calzolari, X. Campilongo, C. Toher, and S. Curtarolo,
aflow.org: a web ecosystem of databases, software and tools, Computational Materials Science 216, 111808 (2023). doi.org/10.1016/j.commatsci.2022.111808

[4] C. Oses, M. Esters, D. Hicks, S. Divilov, H. Eckert, R. Friedrich, M. J. Mehl, A. Smolyanyuk, X. Campilongo, A. van de Walle, J Schroers, A.G. Kusne, I. Takeuchi, E. Zurek, M. Buongiorno Nardelli, M. Fornari, Y. Lederer, O. Levy, C. Toher, and S. Curtarolo, aflow++: a C++ framework for autonomous materials design, Computational Materials Science 217, 111889 (2023). doi.org/10.1016/j.commatsci.2022.111889

[5] R. Friedrich and S. Curtarolo, AFLOW-CCE for the thermodynamics of ionic materials, The Journal of Chemical Physics 160, 042501 (2024). doi.org/10.1063/5.0184917