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- Larsson, Ragnar, 1960, et al.
(författare)
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Atomistic continuum modeling of graphene membranes
- 2011
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Ingår i: Computational Materials Science. - : Elsevier BV. - 0927-0256. ; 50:5, s. 1744-1753
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Tidskriftsartikel (refereegranskat)abstract
- The paper deals with the modeling of thin, monolayer graphene membranes, which have significant electrical and physical properties used for nano- or micro-devices, such as resonators and nanotransistors. The membrane is considered as a homogenized graphene monolayer on the macroscopic scale, and a continuum–atomistic multiscale approach is exploited, focusing the Tersoff–Brenner (TB) potential for the interaction between the carbonic bonds. The associated Representative atomistic Unit Lattice (RUL) is thereby considered as a micro-scale quasi-continuum placed in context of computational homogenization. In this development, the Cauchy–Born rule (CBN) is extended by the atomic fluctuation to allow for relaxation in the RUL. The paper discusses the handling of the TB-potential, both in the context of macro–micro homogenization, and in the context of numerical implementation perspectives. In particular, explicit expressions of the homogenized membrane forces and stiffness are expressed in terms of the first and second gradient of the potential, with due consideration to the involved “non-local” pairwise interaction in the model. In addition, the detailed resulting macroscopic non-linear and linearized finite element response is formulated in terms of the relaxed lattice level atomistic response. Numerical results are provided for the lattice response in terms of the apparent anisotropic behavior induced by the graphene atomic structure. An assessment of the convergence of RULs with respect to different deformation states of the lattice membrane is also carried out. Finally, a validation of an experiment of a circular graphene membrane, using atomic force microscopy (AFM) measurements, is provided based on standard TB-parameters available in the literature.
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| 2. |
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| 3. |
- Samadikhah, Kaveh, 1982, et al.
(författare)
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Continuum - Molecular Modeling of Graphene Lattice
- 2010
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Ingår i: Proc. IV European Conference on Computational Mechanics.
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Konferensbidrag (refereegranskat)abstract
- In the present contribution we address the modeling of graphene membranes - the thinnest membrane structure man ever has produced. Due to the covalent bond configuration of the Carbon, the nano-membranes are predicted to have promising electrical as well as mechanical properties;resonators, force/mass sensors and nanoswitches are some examples of the future graphene's applications.A hierarchy of modeling approaches are investigated in order to assess the proper scale bridging strategy with respect to graphene membrane structures. Accurate models, such as Ab-Initio (AI) and Density Function Theory (DFT), are exploited and compared to a first order homogenized, higher scale Molecular Dynamics (MD) approach for a set of planar unit lattices. The lower scale AI, DFT and MD-models are conveniently used to model the behavior of small to medium size lattices,whereas the extension to large scale lattices and membrane structures becomes overly computationally demanding.
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| 4. |
- Samadikhah, Kaveh, 1982, et al.
(författare)
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Continuum-molecular modelling of graphene
- 2012
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Ingår i: Computational materials science. - : Elsevier BV. - 0927-0256 .- 1879-0801. ; 53:1, s. 37-43
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Tidskriftsartikel (refereegranskat)abstract
- membranes using a hierarchical modeling strategy to bridge the scales required to describe and understand the material. Quantum Mechanical (QM) and optimized Molecular Mechanical (MM) models are used to describe details on the nanoscale, while a multiscale continuum mechanical method is used to model the graphene response at the device or micrometer scale. The complete method is obtained on the basis of the Cauchy Born Rule (CBR), where the continuum model is coupled to the atomic field via the CBR and a local discrete fluctuation field. The MM method, often used to model carbon structures, involves the Tersoff--Brenner (TB) potential; however, when applying this potential to graphene with standard parameters one obtains material stress behavior much weaker than experiments. On the other hand, the more fundamental Hartree Fock and Density Functional Theory (DFT) methods are computationally too expensive and very limited in terms of their applicability to model the geometric scale at the device level. In this contribution a simple calibration of some of the TB parameters is proposed in order to reproduce the results obtained from QM calculations. Subsequently, the fine-tuned TB--potential is used for the multiscale modeling of a nano indentation sample, where experimental data are available. Effects of the mechanical response due the calibration are demonstrated.
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| 5. |
- Samadikhah, Kaveh, 1982, et al.
(författare)
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General elasticity theory for graphene membranes based on molecular dynamics
- 2007
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Ingår i: Materials Research Society Symposium Proceedings. - 0272-9172. - 9781605608266 ; 1057, s. 109-114
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Konferensbidrag (refereegranskat)abstract
- We have studied the mechanical properties of suspended graphene membranes using molecular dynamics (MD) and generalized continuum elasticity theory (GE) in order to develop and assess a continuum description for graphene. The MD simulations are based on a valence force field model which is used to determine the deformation and the elastic energy of the membrane (EMD) as a function of external forces. For the continuum description, we use the expression Econt = Estretching + Ebending for the elastic energy functional. The elastic parameters (tensile rigidity and Poisson ratio) entering Econt are determined by requiring that E cont = EMD for a set of deformations. Comparisons with the MD results show excellent agreement. We find that the elastic energy of a supported graphene sheets is typically dominated by the nonlinear stretching terms whereas a linear description is valid only for very small deflections. This implies that in some applications, i.e. NEMS, a linear description is of limited applicability.
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| 6. |
- Samadikhah, Kaveh, 1982
(författare)
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Modelling of a single layer graphene membrane
- 2010
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The present contribution deals with the modeling of thin graphene membranes. Such membranes have a significant electrical and physical properties used for nano or microdevices like resonators and Atomic Force/mass Measurements (AFM) [1]. The membrane is considered as a homogenized graphene monolayer on the macroscopic structural scale. In this development the stress response on the scale of the actual atomistic microstructure is resolved based on the CBN rule for the inter-atomic kinematics. Explicit expressionsfor the homogenized membrane forces are derived, assuming atomistic pairwise interactionbetween the atoms at zero degrees Kelvin, as well as the resulting effective membrane stiffness.The resulting static behavior, using the proposed modeling approach, of a graphene monolayer sheet is presented and compared with an experimental AFM. Subsequently, a proposed potential based on Tersoff Brenner formulation is used for the multiscale modeling, where the standard parameters generally shows a too week stiffness response of TB based method. Consequently, in order to ameliorate the result, a fine tuning of the TB-parameters is proposed by comparing lattice responses of different quantum mechanicalsimulations is considered.
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