Understanding 2D materials alloys using quantum chemistry simulations


2D materials have widespread applications that range from solid lubrication, nanostructured electronics to Li-and Na-ion batteries, credit to their unique structural and electronic properties. A review of published literature reveals that the majority of available theoretical and experimental studies tend to focus on the electronic and mechanical properties, while as phase behaviour of low dimensional materials which is equally important to inform synthesis strategies and understand service life, remains highly unexplored. To be specific, mesoscale experiments recently revealed that Ti-doped composite coatings possess better oxidation resistance compared to pristine MoS2 while preserving low friction coefficients. Previous research put forward an argument to rationalise good frictional behaviour in terms of vibrational properties. In their work, the low-frequency optical phonon modes taken to be associated with the perfect shear of two layers were extrapolated along the sliding path and taken as an indication of low energy barriers for sliding modes. Consequently, by assessing such descriptors across the transition-metal dichalcogenide (TMD) chemical space, the authors identified layered 2H-Ti1/4 Mo3/4S2, where a quarter of TM sites within the TM-S2 layers was seen to be occupied by Ti, as a candidate material with enhanced frictional properties compared with other analysed TMDs. However, despite the interest attracted by this compound, the exact structure and chemistry remain debatable.

In general, 2D materials have in recent times attracted considerable interest credit to their exotic electronic and mechanical properties; however, their phase behaviour is still vaguely understood. To address this, researchers from the University of Southampton: Andrea Silva (PhD candidate), Professor Tomas Polcar and Professor Denis Kramer investigated the phase behaviour of a compound that has captured the interest of the tribology community: i.e. (Mo:Ti) S2 alloys that have been identified as a promising material with enhanced tribological properties both by experiments and computational investigations. In particular, these (Mo:Ti) S2 binary alloys have shown good performance in solid lubrication applications. Their work is currently published in the research journal, Computational Materials Science.

In their approach, electronic structure calculations and statistical mechanics were used to predict a phase-separating behaviour for the system and trace its origin to the energetics of the d-band manifold due to crystal field splitting. The authors reported that their model, which was based on electronic-structure calculations and statistical mechanics was able to predict full phase separation in the system across hosts.

Remarkably, the solubility limits inferred from the MC simulations were in good agreement with the high-temperature synthesis of Ti-doped 2H-MoS2 as previously reported in preceding studies. More so, the phase behaviour of the system was understood in terms of a general electron-lattice coupling mechanism that the researchers argued could apply to other members of the TMD family and, if strong enough, lead to stable orderings and/or miscibility in other binary compounds.

In summary, the study presented a (Ti:Mo) S2 phase diagram resulting from considering TM substitutions within the native hosts of the pristine compounds. Interestingly, comparison between 3D bulk and 2D convex hulls revealed interlayer coupling and system dimensionality, at the origin of sought-after exotic electronic behaviour, were negligible regarding phase stability of the binary alloys. In a statement to Advances in Engineering, the authors explained that based on their observations, one could argue that their findings can be applied to most 2D materials in which phase stability is governed by the similar in-plane electron-lattice effect, while more subtle behaviour could arise in presence of magnetic or Coulombic interactions.

Understanding 2D materials alloys  using quantum chemistry simulations - Advances in Engineering

About the author

Denis Kramer holds the chair in Computational Materials Design at the Helmut-Schmidt-University Hamburg (Germany) and leads the New Energy Technologies research group at the University of Southampton (UK). He conducted his PhD at the Paul Scherrer Institut (CH) investigating two-phase flow phenomena in fuel cells. He received a post-doctoral fellowship from the German Academic Exchange Service in 2007, which enabled him to join the group of Gerbrand Ceder at the Massachusetts Institute of Technology (USA) to work on ab initio modelling of Li-Ion battery materials. In 2009, he relocated to the UK to work on core-shell electrocatalysts for fuel cell applications with Anthony Kucernak at Imperial College London. He became a faculty member at the University of Southampton in 2011, where stayed full-time until 2019. Currently, he splits his time between Southampton and Hamburg, where he builds a new chair to combine computational materials design with combinatorial synthesis and characterisation to develop technology-enabling materials for alternative energy technologies, especially fuel cells and batteries.

About the author

Andrea Silva graduated in 2017 at the University of Milan, Italy, in theoretical physics focusing on condensate matter and statistical physics. His thesis focused on a peculiar emerging phase of matter characterised by a vanishing static friction known as Aubry transition. In collaboration with an experimental group in Stuttgart, they observe this phenomena for the first time in a 2D colloidal system.

He was awarded a PhD in Engineering and Environment at the University of Southampton, UK, in 2021. The project was part of the consortium SOLUTION, funded under the EU Marie Skłodowska-Curie scheme. The SOLUTION project aimed to bridge theory and experiments in the field of solid lubrication, developing a deeper understanding of the material to benchmarking industrial solutions. Within this international project, he worked alongside a group in the Czech Technical University in Prague to design theoretical models to predict the phase behaviour and frictional properties of 2D materials, informing the synthesis effort of experimental groups.

Now he relocated to SISSA, Trieste, Italy, working as postdoc in the condensate matter theory group. His work focuses on theoretical descriptions of dissipation processes in nanoscale systems.


Andrea Silva, Tomas Polcar, Denis Kramer. Phase behaviour of (Ti:Mo) S2 binary alloys arising from electron-lattice coupling. Computational Materials Science: volume 186 (2021) 110044.

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