2D materials; Molybdenum disulfide; Holey substrate; van der Waals interaction; Kirchhoff–Love shell; Isogeometric analysis
Résumé :
[en] This work develops, discretizes, and validates a continuum model of a molybdenum disulfide (MoS2) monolayer interacting with a periodic holey silicon nitride (Si3N4) substrate via van der Waals (vdW) forces. The MoS2 layer is modeled as a geometrically nonlinear Kirchhoff–Love shell, and vdW forces are modeled by a Lennard-Jones (LJ) potential, simplified using approximations for a smooth substrate topography. Both the shell model and LJ interactions include novel extensions informed by close comparison with fully-atomistic calculations. The material parameters of the shell model are calibrated by comparing small-strain tensile and bending tests with atomistic simulations. This model is efficiently discretized using isogeometric analysis (IGA) for the shell structure and a pseudo-time continuation method for energy minimization. The IGA shell model is validated against fully-atomistic calculations for several benchmark problems with different substrate geometries. Agreement with atomistic results depends on geometric nonlinearity in some cases, but a simple isotropic St.Venant–Kirchhoff model is found to be sufficient to represent material behavior. We find that the IGA discretization of the continuum model has a much lower computational cost than atomistic simulations, and expect that it will enable efficient design space exploration in strain engineering applications. This is demonstrated by studying the dependence of strain and curvature in MoS2 over a holey substrate as a function of the hole spacing on scales inaccessible to atomistic calculations. The results show an unexpected qualitative change in the deformation pattern below a critical hole separation.
Disciplines :
Ingénierie, informatique & technologie: Multidisciplinaire, généralités & autres
Auteur, co-auteur :
Choi, Moon-Ki ✱
Pasetto, Marco ✱
SHEN, Zhaoxiang ✱; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Engineering (DoE)
Tadmor, Ellad B.
Kamensky, David
✱ Ces auteurs ont contribué de façon équivalente à la publication.
Co-auteurs externes :
yes
Langue du document :
Anglais
Titre :
Atomistically-informed continuum modeling and isogeometric analysis of 2D materials over holey substrates
Alnæs, M., Logg, A., Oelgaard, K., Rognes, M., Wells, G., Unified form language: A domain-specific language for weak formulations of partial differential equations. ACM Trans. Math. Software 40:2 (2014), 9:1–9:37.
Amestoy, P.R., Buttari, A., L'Excellent, J.Y., Mary, T., Performance and Scalability of the Block Low-Rank Multifrontal Factorization on Multicore Architectures. ACM Trans. Math. Software 45 (2019), 2:1–2:26.
Amestoy, P.R., Duff, I.S., Koster, J., L'Excellent, J.Y., A fully asynchronous multifrontal solver using distributed dynamic scheduling. SIAM J. Matrix Anal. Appl. 23:1 (2001), 15–41.
Arroyo, M., Belytschko, T., Continuum mechanics modeling and simulation of carbon nanotubes. Meccanica 40:4 (2005), 455–469.
Barretta, R., Marotti de Sciarra, F., Variational nonlocal gradient elasticity for nano-beams. Internat. J. Engrg. Sci. 143 (2019), 73–91.
Brenner, D.W., Shenderova, O.A., Harrison, J.A., Stuart, S.J., Ni, B., Sinnott, S.B., A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. J. Phys.: Condens. Matter 14:4 (2002), 783–802.
Castellanos-Gomez, A., Roldán, R., Cappelluti, E., Buscema, M., Guinea, F., van der Zant, H.S.J., Steele, G.A., Local strain engineering in atomically thin MoS2. Nano Lett. 13:11 (2013), 5361–5366.
Cottrell, J.A., Hughes, T.J.R., Bazilevs, Y., Isogeometric Analysis: Toward Integration of CAD and FEA. 2009, Wiley.
Ding, C., Tamma, K.K., Lian, H., Ding, Y., Dodwell, T.J., Bordas, S.P.A., Uncertainty quantification of spatially uncorrelated loads with a reduced-order stochastic isogeometric method. Comput. Mech. 67 (2021), 1255–1271.
Dwyer, J.R., Harb, M., Through a window, brightly: a review of selected nanofabricated thin-film platforms for spectroscopy, imaging, and detection. Appl. Spectrosc. 71:9 (2017), 2051–2075.
Ge, D., Lu, L., Zhang, J., Zhang, L., Ding, J., Reece, P.J., Electrochemical fabrication of silicon-based micro-nano-hybrid porous arrays for hybrid-lattice photonic crystal. ECS J. Solid State Sci. Technol., 6(12), 2017, P893.
Ge, D., Zhang, Y., Chen, H., Zhen, G., Wang, M., Jiao, J., Zhang, L., Zhu, S., Effect of patterned silicon nitride substrate on Raman scattering and stress of graphene. Mater. Des., 198, 2021, 109338.
Ghaffari, R., Duong, T.X., Sauer, R.A., A new shell formulation for graphene structures based on existing ab-initio data. Int. J. Solids Struct. 135 (2018), 37–60.
Ghaffari, R., Sauer, R.A., Modal analysis of graphene-based structures for large deformations, contact and material nonlinearities. J. Sound Vib. 423 (2018), 161–179.
Ghaffari, R., Sauer, R.A., A new efficient hyperelastic finite element model for graphene and its application to carbon nanotubes and nanocones. Finite Elem. Anal. Des. 146 (2018), 42–61.
Ghobadi, N., A comparative study of the mechanical properties of multilayer MoS2 and graphene/MoS2 heterostructure: effects of temperature, number of layers and stacking order. Curr. Appl. Phys. 17:11 (2017), 1483–1493.
Guénolé, J., Nöhring, W.G., Vaid, A., Houllé, F., Xie, Z., Prakash, A., Bitzek, E., Assessment and optimization of the fast inertial relaxation engine (FIRE) for energy minimization in atomistic simulations and its implementation in LAMMPS. Comput. Mater. Sci., 175, 2020, 109584.
Halgren, T.A., The representation of van der Waals (vdw) interactions in molecular mechanics force fields: potential form, combination rules, and vdw parameters. J. Am. Chem. Soc. 114:20 (1992), 7827–7843.
Heinz, H., Lin, T.-J., Mishra, R.K., Emami, F.S., Thermodynamically consistent force fields for the assembly of inorganic, organic, and biological nanostructures: the INTERFACE force field. Langmuir 29:6 (2013), 1754–1765.
Herrema, A.J., Kiendl, J., Hsu, M.-C., A framework for isogeometric-analysis-based optimization of wind turbine blade structures. Wind Energy 22:2 (2019), 153–170.
Homolya, M., Mitchell, L., Luporini, F., Ham, D., TSFC: A structure-preserving form compiler. SIAM J. Sci. Comput. 40:3 (2018), C401–C428.
Jiang, J.-W., Parametrization of Stillinger–Weber potential based on valence force field model: application to single-layer MoS2 and black phosphorus. Nanotechnology, 26(31), 2015, 315706.
Johari, P., Shenoy, V.B., Tuning the electronic properties of semiconducting transition metal dichalcogenides by applying mechanical strains. ACS Nano 6:6 (2012), 5449–5456 PMID: 22591011.
Kamensky, D., Open-source immersogeometric analysis of fluid–structure interaction using FEniCS and tIGAr. Comput. Math. Appl. 81 (2021), 634–648 Development and Application of Open-source Software for Problems with Numerical PDEs.
Kamensky, D., Bazilevs, Y., tIGAr: Automating isogeometric analysis with FEniCS. Comput. Methods Appl. Mech. Engrg. 344 (2019), 477–498.
Kiendl, J., Isogeometric Analysis and Shape Optimal Design of Shell Structures. (Ph.D. thesis), 2011, Lehrstuhl für Statik, Technische Universität München.
Kiendl, J., Hsu, M.-C., Wu, M.C.H., Reali, A., Isogeometric Kirchhoff—Love shell formulations for general hyperelastic materials. Comput. Methods Appl. Mech. Engrg. 291 (2015), 280–303.
Kirby, R.C., Logg, A., A compiler for variational forms. ACM Trans. Math. Software 32:3 (2006), 417–444.
Lennard-Jones, J.E., On the determination of molecular fields. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 106 (1924), 463–477.
Li, M., Huang, H., Tu, L., Wang, W., Li, P., Lu, Y., Abnormal nonlocal scale effect on static bending of single-layer MoS2. Nanotechnology, 28(21), 2017, 215706.
Liang, T., Phillpot, S.R., Sinnott, S.B., Parametrization of a reactive many-body potential for Mo–S systems. Phys. Rev. B, 79, 2009, 245110.
Logg, A., Wells, G.N., DOLFIN: Automated finite element computing. ACM Trans. Math. Software 37:2 (2010), 20:1–20:28.
Logg, A., Wells, G., Mardal, K.-A., Automated Solution of Differential Equations By the Finite Element Method. the FEniCS Book. 2012, Springer.
Lutsko, J.F., Generalized expressions for the calculation of elastic constants by computer simulation. J. Appl. Phys. 65:8 (1989), 2991–2997.
Mokhalingam, A., Ghaffari, R., Sauer, R.A., Gupta, S.S., Comparing quantum, molecular and continuum models for graphene at large deformations. Carbon 159 (2020), 478–494.
Momeni, K., Ji, Y., Wang, Y., Paul, S., Neshani, S., Yilmaz, D.E., Shin, Y.K., Zhang, D., Jiang, J.-W., Park, H.S., Sinnott, S., van Duin, A., Crespi, V., Chen, L.-Q., Multiscale computational understanding and growth of 2D materials: a review. Npj Comput. Mater., 6(1), 2020, 22.
Mortazavi, B., Ostadhossein, A., Rabczuk, T., van Duin, A.C.T., Mechanical response of all-MoS2 single-layer heterostructures: a ReaxFF investigation. Phys. Chem. Chem. Phys. 18:34 (2016), 23695–23701.
Mounet, N., Gibertini, M., Schwaller, P., Campi, D., Merkys, A., Marrazzo, A., Sohier, T., Castelli, I.E., Cepellotti, A., Pizzi, G., Marzari, N., Two-dimensional materials from high-throughput computational exfoliation of experimentally known compounds. Nature Nanotechnol. 23 (2018), 246–252.
Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Zhang, Y., Dubonos, S.V., Grigorieva, I.V., Firsov, A.A., Electric field effect in atomically thin carbon films. Science 306:5696 (2004), 666–669.
Peelaers, H., Van de Walle, C.G., Effects of strain on band structure and effective masses in MoS2. Phys. Rev. B, 86, 2012, 241401.
Piegl, L., Tiller, W., The NURBS Book (Monographs in Visual Communication). second ed., 1997, Springer-Verlag, New York.
Plimpton, S., Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117:1 (1995), 1–19.
Schillinger, D., Ruthala, P.K., Nguyen, L.H., Lagrange extraction and projection for NURBS basis functions: A direct link between isogeometric and standard nodal finite element formulations. Internat. J. Numer. Methods Engrg. 108:6 (2016), 515–534 nme.5216.
Shirazian, F., Ghaffari, R., Hu, M., Sauer, R.A., Hyperelastic material modeling of graphene based on density functional calculations. PAMM, 18(1), 2018, e201800419.
Shokrieh, M.M., Zibaei, I., Determination of the appropriate gradient elasticity theory for bending analysis of nano-beams by considering boundary conditions effect. Latin Am. J. Solids Struct. 12:12 (2015), 2208–2230.
Tadmor, E.B., Miller, R.E., Elliott, R.S., Continuum Mechanics and Thermodynamics: From Fundamental Principles To Governing Equations. 2012, Cambridge University Press.
Tambo, N., Liao, Y., Zhou, C., Ashley, E.M., Takahashi, K., Nealey, P.F., Naito, Y., Shiomi, J., Ultimate suppression of thermal transport in amorphous silicon nitride by phononic nanostructure. Sci. Adv., 6(39), 2020, eabc0075.
Vuong, A.V., Giannelli, C., Jüttler, B., Simeon, B., A hierarchical approach to adaptive local refinement in isogeometric analysis. Comput. Methods Appl. Mech. Engrg. 200:49 (2011), 3554–3567.
Wang, Q.H., Kalantar-Zadeh, K., Kis, A., Coleman, J.N., Strano, M.S., Electronics and optoelectronics of two-dimensional transition metal dichalcogenides. Nature Nanotechnol. 7:11 (2012), 699–712.
Xiong, S.Y., Cao, G., Bending response of single layer MoS2. Nanotechnology, 27, 2016, 10:105701.
Zhang, K., Tadmor, E.B., Energy and moiré patterns in 2D bilayers in translation and rotation: A study using an efficient discrete–continuum interlayer potential. Extreme Mech. Lett. 14 (2017), 16–22.
Zhang, K., Tadmor, E.B., Structural and electron diffraction scaling of twisted graphene bilayers. J. Mech. Phys. Solids 112 (2018), 225–238.
Zhao, H., Liu, X., Fletcher, A.H., Xiang, R., Hwang, J.T., Kamensky, D., An open-source framework for coupling non-matching isogeometric shells with application to aerospace structures. Comput. Math. Appl. 111 (2022), 109–123.
Zibouche, N., Kuc, A., Heine, T., From layers to nanotubes: Transition metal disulfides TMS2. Eur. Phys. J. B, 85, 2012, 49.
