Abstract
Searching for superlubric heterostructures composed of transitional metal dichalcogenides monolayers is challenging due to the variety of constituent elements. In this study, a two-step machine learning approach based on domain features is employed to efficiently tackle this challenging task. Machine learning models are trained to predict complex domain features from structural features. Bayesian optimization is then used to search for superlubricants. Machine learning models are iteratively rechained based on a small number of high-accuracy calculations, saving computational time and ensuring accuracy. MoS2/WS2, MoS2/VS2, and NiS2/NbSSe heterostructures have been identified as superlubric heterostructures and confirmed through theoretical calculations. Under 1 ~ 5 N, the experimental friction coefficients at the interface of MoS2/WS2 are 12% ~ 36% lower compared to MoS2/MoSe2, which has previously been proven to exhibit superlubricity. These results validate the effectiveness of the two-step machine learning approach in searching for superlubric heterostructures in a significantly reduced time.
Similar content being viewed by others
Data availability
The structural information of some MX2 and MXY monolayers is obtained from the Materials Project (https://next-gen.materialsproject.org/materials) and 2Dmatpedia database (http://www.2dmatpedia.org/), which is detailed listed in Table S1 in the Supplementary information. The data generated and analyzed during the current study are not publicly available due to the project-specific restrictions but are available from the corresponding author on reasonable request.
Code availability
The code in this work is available upon request.
References
Hod, O. et al. Structural superlubricity and ultralow friction across the length scales. Nature 563, 485–492 (2018).
Müser, M. H. Structural lubricity: role of dimension and symmetry. Europhys. Lett. 66, 97–103 (2004).
Socoliuc, A. et al. Transition from stick-slip to continuous sliding in atomic friction: entering a new regime of ultralow friction. Phys. Rev. Lett. 92, 134301 (2004).
Sun, J. et al. Superlubricity enabled by pressure-induced friction collapse. J. Phys. Chem. Lett. 9, 2554–2559 (2018).
Tang, K. W. & Qi, W. H. Moiré pattern tuned electronic structures of van der Waals heterostructures. Adv. Funct. Mater. 30, 2002672 (2020).
Cui, Z. et al. High throughput theoretical prediction of the low friction at the interfaces of homo- and heterojunction composed of C3N. Appl. Surf. Sci. 612, 155718 (2023).
Dienwiebel, M. et al. Superlubricity of graphite. Phys. Rev. Lett. 92, 126101 (2004).
Filippov, A. E. et al. Torque and twist against superlubricity. Phys. Rev. Lett. 100, 046102 (2008).
Li, H. et al. Structural superlubricity in graphene/GaSe van der Waals heterostructure. Phys. Lett. A. 452, 128435 (2022).
Geim, A. K. & Grigorieva, I. V. Van der Waals heterostructures. Nature 499, 419–425 (2013).
Yuan, J., Yang, R. & Zhang, G. Structural superlubricity in 2D van der Waals heterojunctions. Nanotechnology 33, 102002 (2021).
Tian, J., Yin, X. & Li, J. Tribo-induced interfacial material transfer of an atomic force microscopy probe assisting superlubricity in a WS2/graphene heterojunction. ACS Appl. Mater. Interfaces 12, 4031–4040 (2019).
Song, Y. et al. Robust microscale superlubricity in graphite/hexagonal boron nitride layered heterojunctions. Nat. Mater. 17, 894–899 (2018).
Zhao, Y., Yang, L. & Liu, Y. Internal and external MoS2/GO heterostructure enhanced multi-point contact egg-box inspired SiOC for macroscopic ultra-low friction. Carbon 221, 118908 (2024).
Long, Y. et al. High-temperature superlubricity in MoS2/graphene van der Waals heterostructures. Nano. Lett. 24, 7572–7577 (2024).
Song, Y. et al. Structural superlubricity based on crystalline materials. Small 16, 1903018 (2020).
Mandelli, D. et al. Sliding friction of graphene/hexagonal–boron nitride heterojunctions: a route to robust superlubricity. Sci. Rep. 7, 10851 (2017).
Ge, X. Y. et al. Graphene superlubricity: a review. Friction 11, 1953–1973 (2023).
Leven, I. et al. Robust superlubricity in Graphene/h-BN heterojunctions. J. Phys. Chem. Lett. 4, 115–120 (2012).
Acikgoz, O. & Baykara, M. Z. Speed dependence of friction on single-layer and bulk MoS2 measured by atomic force microscopy. Appl. Phys. Lett. 116, 071603 (2020).
Li, P. et al. Lattice distortion optimized hybridization and superlubricity of MoS2/MoSe2 heterointerfaces via Moiré patterns. Appl. Surf. Sci. 613, 155760 (2023).
Li, H. et al. Superlubricity between MoS2 monolayers. Adv. Mater. 29, 1701474 (2017).
Xu, P. et al. A first-principles study on the superlubricity of two-dimensional graphene/ZrS2 heterostructure. Tribol. Int. 174, 107727 (2022).
Büch, H. et al. Superlubricity of epitaxial monolayer WS2 on graphene. Nano. Res. 11, 5946–5956 (2018).
Wang, L. F. et al. Superlubricity of two-dimensional fluorographene/MoS2 heterostructure: a first-principles study. Nanotechnology 25, 385701 (2014).
Vazirisereshk, M. R. et al. Friction anisotropy of MoS2: effect of tip–sample contact quality. J. Phys. Chem. Lett. 11, 6900–6906 (2020).
Ru, G. L. et al. Interlayer friction and superlubricity in bilayer graphene and MoS2/MoSe2 van der Waals heterostructures. Tribol. Int. 151, 106483 (2020).
Zhang, W. L. et al. Soluble, exfoliated two-dimensional nanosheets as excellent aqueous lubricants. ACS Appl. Mater. Inter. 8, 32440–32449 (2016).
Zhao, Y. et al. 3D-printed topological MoS2/MoSe2 heterostructures for macroscale superlubricity. ACS Appl. Mater. Inter. 13, 34984–34995 (2021).
Gao, X. et al. Constructing WS2/MoS2 nano-scale multilayer film and understanding its positive response to space environment. Surf. Coat. Tech. 353, 8–17 (2018).
Vazirisereshk, M. R. et al. Origin of nanoscale friction contrast between supported graphene, MoS2, and a Graphene/MoS2 heterostructure. Nano. Lett. 19, 5496–5505 (2019).
Komanduri, R. & Chandrasekaran, N. Molecular dynamics simulation of atomic-scale friction. Phys. Rev. B. 61, 14007 (2000).
Jordan, M. I. & Mitchell, T. M. Machine learning: trends, perspectives, and prospects. Science 349, 255–260 (2015).
Zou, C. X., Li, J. S. & Wang, W. Y. Integrating data mining and machine learning to discover high-strength ductile titanium alloys. Acta Mater. 202, 211–221 (2021).
Liu, Z. G., Zhao, X. P. & Wang, H. Y. A first-principles and machine learning combined method to investigate the interfacial friction between corrugated graphene. Model. Simul. Mater. Sc. 29, 035011 (2021).
Zhao, X. et al. Machine learning method to predict the interlayer sliding energy barrier of polarized MoS2 layers. Comput. Mater. Sci. 220, 112062 (2023).
Niu, Y. et al. Calculation and prediction of sliding energy barriers by first-principles combined with machine learning. Ceram. Int. 49, 24752–24761 (2023).
Jeong, H. et al. First-principles design of an ultralow frictional interface of a black phosphorus and graphene heterostructure with oxide functionalization and high-pressure conditions. Appl. Surf. Sci. 608, 155092 (2023).
Wang, C. Q. et al. Friction properties of black phosphorus: a first-principles study. Nanotechnology 34, 275703 (2023).
Gao, E. et al. Computational prediction of superlubric layered heterojunctions. ACS Appl. Mater. Interfaces 13, 33600–33608 (2021).
Jain, A. et al. Commentary: The Materials Project: a materials genome approach to accelerating materials innovation. APL Mater. 1, 011002 (2013).
Zhou, J. et al. 2DMatPedia, an open computational database of two-dimensional materials from top-down and bottom-up approaches. Sci. Data. 6, 86 (2019).
Pedregosa, F., Varoquaux, G. & Gramfort, A. Scikit-learn: machine learning in Python. J. Mach. Learn. Res. 12, 2825–2830 (2011).
Anderson, O. L. A simplified method for calculating the Debye temperature from elastic constants. J. Phys. Chem. Solids 24, 909–917 (1963).
Willhelm, D. et al. Predicting van der Waals heterostructures by a combined machine learning and density functional theory approach. ACS Appl Mater. Inter. 14, 25907–25919 (2022).
Shi, W. & Wang, Z. Mechanical and electronic properties of Janus monolayer transition metal dichalcogenides. J. Phys. Condens. Matter 30, 215301 (2018).
Xu, Y. et al. A novel ultra-low friction heterostructure: aluminum substrate-honeycomb borophene/graphene heterojunction. Comput. Mater. Sci. 205, 111236 (2022).
Yuan, R. H. et al. Accelerated discovery of large electrostrains in BaTiO3-based piezoelectrics using active learning. Adv. Mater. 30, 1702884 (2018).
Yang, C. et al. A machine learning-based alloy design system to facilitate the rational design of high entropy alloys with enhanced hardness. Acta Mater. 222, 117431 (2022).
Zhang, H. et al. Machine learning assisted composition effective design for precipitation strengthened copper alloys. Acta Mater. 215, 117118 (2021).
Ataca, C., Şahin, H. & Ciraci, S. Stable, single-layer MX2 transition-metal oxides and dichalcogenides in a honeycomb-like structure. J. Phys. Chem. C. 116, 8983–8999 (2012).
Mao, Y. Q. et al. The electronic, mechanical properties and in-plane negative Poisson’s ratio in novel pentagonal NiX2 (X = S, Se, Te) monolayers with strong anisotropy: a first-principles prediction. Comput. Mater. Sci. 216, 111873 (2023).
Kahraman, Z., Yagmurcukardes, M. & Sahin, H. Functionalization of single-layer TaS2 and formation of ultrathin Janus structures. J. Mater. Res. 35, 1397–1406 (2020).
Zhang, Y. et al. Atomic-scale superlubricity in Ti2CO2@MoS2 layered heterojunctions interface: a first principles calculation study. ACS Omega 6, 9013–9019 (2021).
Lundberg, S. M. et al. From local explanations to global understanding with explainable AI for trees. Nat. Mach. Intell. 2, 56–67 (2020).
Guo, Y. F., Qiu, J. P. & Guo, W. L. Reduction of interfacial friction in commensurate graphene/h-BN heterostructures by surface functionalization. Nanoscale 8, 575–580 (2016).
Wen, M. J. et al. Dihedral-angle-corrected registry-dependent interlayer potential for multilayer graphene structures. Phys. Rev. B. 98, 235404 (2018).
Reguzzoni, M. et al. Potential energy surface for graphene on graphene: ab initio derivation, analytical description, and microscopic interpretation. Phys. Rev. B. 86, 245434 (2012).
Berman, A., Drummond, C. & Israelachvili, J. Amontons’ law at the molecular level. Tribol. Lett. 4, 95–101 (1998).
Liu, P. & Zhang, Y. W. A theoretical analysis of frictional and defect characteristics of graphene probed by a capped single-walled carbon nanotube. Carbon 49, 3687–3697 (2011).
Sun, S. et al. Molecular dynamics study of the robust superlubricity in penta-graphene van der Waals layered structures. Tribol. Int. 177, 107988 (2023).
Plenge, P. et al. The antidepressant drug vilazodone is an allosteric inhibitor of the serotonin transporter. Nat. Commun. 12, 5063 (2021).
Idrissi, H. et al. Atomic-scale viscoplasticity mechanisms revealed in high ductility metallic glass films. Sci. Rep. 9, 13426 (2019).
Kresse, G. & Furthmuller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B. 54, 11169 (1996).
Kohn, W. & Sham, L. J. Self-consistent equations including exchange and correlation effects. Phy. Rev. 140, A1133–A1138 (1965).
Perdew, J. P., Burke, K. & Wang, Y. Generalized gradient approximation for the exchange-correlation hole of a many-electron system. Phys. Rev. B. 54, 16533–16539 (1996).
Blochl, P. E. Projector augmented-wave method. Phys. Rev. B Condens Matter 50, 17953–17979 (1994).
Monkhorst, H. J. & Pack, J. D. Special points for Brillouin-zone integrations. Phys. Rev. B. 13, 5188–5192 (1976).
Grimme, S. et al. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 132, 154104 (2010).
Restuccia, P. et al. Ideal adhesive and shear strengths of solid interfaces: a high throughput ab initio approach. Comput. Mater. Sci. 154, 517–529 (2018).
Zhong, W. & Tománek, D. First-principles theory of atomic-scale friction. Phys. Rev. Lett. 64, 3054–3057 (1990).
Losi, G., Restuccia, P. & Righi, M. C. Superlubricity in phosphorene identified by means of ab initio calculations. 2D Mater. 7, 025033 (2020).
Jiang, J.-W. & Zhou, Y.-P. Parameterization of Stillinger-Weber Potential for Two- Dimensional Atomic Crystals. in Handbook of Stillinger-Weber Potential Parameters for Two-Dimensional Atomic Crystals (IntechOpen, 2017).
Ruan, X. P. et al. Robust superlubricity and moiré lattice’s size dependence on friction between graphdiyne layers. ACS Appl. Mater. Inter. 13, 40901–40908 (2021).
Ru, G. L. et al. Superlubricity in bilayer isomeric tellurene and graphene/tellurene van der Waals heterostructures. Tribol. Int. 159, 106974 (2021).
Guo, W. L. et al. Coupled defect-size effects on interlayer friction in multiwalled carbon nanotubes. Phys. Rev. B. 72, 075409 (2005).
Wei, B. Y. et al. A molecular dynamics study on the tribological behavior of molybdenum disulfide with grain boundary defects during scratching processes. Friction 9, 1198–1212 (2020).
He, J. et al. Synergistic lubrication effect of Al2O3 and MoS2 nanoparticles confined between iron surfaces: a molecular dynamics study. J. Mater. Sci. 56, 9227–9241 (2021).
Rappi, A. K., Casewit, C. J. & Colwell, K. S. UFF, a full periodic table force field for molecular mechanics and molecular dynamics simulations. J. Am. Chem. Soc. 114, 10024–10039 (1992).
Mardiyah, R. U. et al. Energy cohesive calculation for some pure metals using the Lennard-Jones potential in lammps molecular dynamics. J. Phys. Conf. Ser. 1491, 012020 (2020).
Grimme, S. Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J. Comput. Chem. 27, 1787–1799 (2006).
Chen, L. et al. Nanomanufacturing of silicon surface with a single atomic layer precision via mechanochemical reactions. Nat. Commun. 9, 1542 (2018).
Susarla, S. et al. Deformation mechanisms of vertically stacked WS(2) /MoS(2) heterostructures: the role of interfaces. Acs. Nano. 12, 4036–4044 (2018).
Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117, 1–19 (1995).
Acknowledgements
This work was supported by the financial support from the Natural Science Basic Research Program of Shaanxi (Program No. 2025JC-YBQN-781), Natural Science Fund of Shaanxi Province for the key project (2021JZ-07), the Fundamental Research Funds of the Central Universities (G2025KY06202), and the Research Fund of the State Key Laboratory of Solidification Processing (NPU) (2023-TZ-01), Leading Talents in Scientific and Technological Innovation Program of Shaanxi Province.
Author information
Authors and Affiliations
Contributions
L.C. conceptualized and found the project. Y.J.H. and H.Y.Z. was responsible for the construction of the database. R.Y.L. and H.M. prepared the construction of the 3D-printed point-contact structures and was responsible for the friction test. J.Q.S. performed the MD simulations. Z.L. was responsible for the development, training, and analysis of the machine learning method. F.Z. and W.M.L. supervised the research. X.L.F. conceived the project and interpreted the findings. All authors have read and approved the manuscript.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary information
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
About this article
Cite this article
Chen, L., Huang, Y., Zhang, H. et al. Domain features-informed two-step machine learning: accelerating the search for superlubric heterostructures. npj Comput Mater (2026). https://doi.org/10.1038/s41524-026-01996-0
Received:
Accepted:
Published:
DOI: https://doi.org/10.1038/s41524-026-01996-0
