Petri Hirvonen

Thermal conductivity decomposition in two-dimensional materials: Application to graphene

Two-dimensional materials have unusual phonon spectra due to the presence of flexural (out-of-plane) modes. Although molecular dynamics simulations have been extensively used to study heat transport in such materials, conventional formalisms treat the phonon dynamics isotropically. Here, we decompose the microscopic heat current in atomistic simulations into in-plane and out-of-plane components, corresponding to in-plane and out-of-plane phonon dynamics, respectively. This decomposition allows for direct computation of the corresponding thermal conductivity components in two-dimensional materials. We apply this decomposition to study heat transport in suspended graphene, using both equilibrium and nonequilibrium molecular dynamics simulations. We show that the flexural component is responsible for about two-thirds of the total thermal conductivity in unstrained graphene, and the acoustic flexural component is responsible for the logarithmic divergence of the conductivity when a sufficiently large tensile strain is applied.

Multiscale modeling of polycrystalline graphene: A comparison of structure and defect energies of realistic samples from phase field crystal models

© 2016 American Physical Society. We extend the phase field crystal (PFC) framework to quantitative modeling of polycrystalline graphene. PFC modeling is a powerful multiscale method for finding the ground state configurations of large realistic samples that can be further used to study their mechanical, thermal, or electronic properties. By fitting to quantum-mechanical density functional theory (DFT) calculations, we show that the PFC approach is able to predict realistic formation energies and defect structures of grain boundaries. We provide an in-depth comparison of the formation energies between PFC, DFT, and molecular dynamics (MD) calculations. The DFT and MD calculations are initialized using atomic configurations extracted from PFC ground states. Finally, we use the PFC approach to explicitly construct large realistic polycrystalline samples and characterize their properties using MD relaxation to demonstrate their quality.

Bimodal grain-size scaling of thermal transport in polycrystalline graphene from large-scale molecular dynamics simulations

Grain boundaries in graphene are inherent in wafer-scale samples prepared by chemical vapor deposition. They can strongly influence the mechanical properties and electronic and heat transport in graphene. In this work, we employ extensive molecular dynamics simulations to study thermal transport in large suspended polycrystalline graphene samples. Samples of different controlled grain sizes are prepared by a recently developed efficient multiscale approach based on the phase field crystal model. In contrast to previous works, our results show that the scaling of the thermal conductivity with the grain size implies bimodal behavior with two effective Kapitza lengths. The scaling is dominated by the out-of-plane (flexural) phonons with a Kapitza length that is an order of magnitude larger than that of the in-plane phonons. We also show that, to get quantitative agreement with the most recent experiments, quantum corrections need to be applied to both the Kapitza conductance of grain boundaries and the thermal conductivity of pristine graphene, and the corresponding Kapitza lengths must be renormalized accordingly.

Interfacial mechanical testing of atomic layer deposited TiO2 and Al2O3 on a silicon substrate by the use of embedded SiO2 microspheres

In this paper the authors present a next generation measurement system for interfacial mechanical testing of especially atomic layer deposited (ALD) thin films. SiO2 microspheres were embedded in 100 and 300 nm thick ALD TiO2 and Al2O3, deposited at 110 °C, 200 °C and 300 °C on a silicon substrate. The embedded microspheres were detached using a fully programmable semi-automatic microrobotic assembly station employed to carry out the lateral pushing and detaching force F (μN) measurement. The area of interfacial fracture A (μm2) was measured using scanning electron microscopy and digital image analysis to calculate critical stress of interfacial fracture σ (MPa). Work W (J) and energy release rate G (J m−2) of interfacial fracture were also calculated from the measurement results. Interfacial fracture from the film-substrate interface occurred only for TiO2 deposited at 200 °C which had a crystalline structure with the biggest grain size, signifying that for all of the other samples, film adhesion was excellent, and significantly better than film cohesion. Quantitatively this means that thin film interfacial adhesion to the substrate was also higher than the values of the critical stresses and the measured energy release rates. Interfacial toughness seems to be related to film thickness and crystallinity in the case of TiO2, but with Al2O3 the interfacial toughness seems to increase with the deposition temperature. The method presented in this paper is generic, and can be applied for the evaluation of interfacial mechanical properties, such as adhesion, between any various film-substrate-sphere system of choice.

Kapitza thermal resistance across individual grain boundaries in graphene

We study heat transport across individual grain boundaries in suspended monolayer graphene using extensive classical molecular dynamics (MD) simulations. We construct bicrystalline graphene samples containing grain boundaries with symmetric tilt angles using the two-dimensional phase field crystal method and then relax the samples with MD. The corresponding Kapitza resistances are then computed using nonequilibrium MD simulations. We find that the Kapitza resistance depends strongly on the tilt angle and shows a clear correlation with the average density of defects in a given grain boundary, but is not strongly correlated with the grain boundary line tension. We also show that quantum effects are significant in quantitative determination of the Kapitza resistance by applying the mode-by-mode quantum correction to the classical MD data. The corrected data are in good agreement with quantum mechanical Landauer-Butticker calculations.

Energetics and structure of grain boundary triple junctions in graphene

Grain boundary triple junctions are a key structural element in polycrystalline materials. They are involved in the formation of microstructures and can influence the mechanical and electronic properties of materials. In this work we study the structure and energetics of triple junctions in graphene using a multiscale modelling approach based on combining the phase field crystal approach with classical molecular dynamics simulations and quantum-mechanical density functional theory calculations. We focus on the atomic structure and formation energy of the triple junctions as a function of the misorientation between the adjacent grains. We find that the triple junctions in graphene consist mostly of five-fold and seven-fold carbon rings. Most importantly, in addition to positive triple junction formation energies we also find a significant number of orientations for which the formation energy is negative.

Honeycomb and triangular domain wall networks in heteroepitaxial systems

A comprehensive study is presented for the influence of misfit strain, adhesion strength, and lattice symmetry on the complex Moiré patterns that form in ultrathin films of honeycomb symmetry adsorbed on compact triangular or honeycomb substrates. The method used is based on a complex Ginzburg-Landau model of the film that incorporates elastic strain energy and dislocations. The results indicate that different symmetries of the heteroepitaxial systems lead to distinct types of domain wall networks and phase transitions among various surface Moiré patterns and superstructures. More specifically, the results show a dramatic difference between the phase diagrams that emerge when a honeycomb film is adsorbed on substrates of honeycomb versus triangular symmetry. It is also shown that in the small deformation limit, the complex Ginzburg-Landau model reduces to a two-dimensional sine-Gordon free energy form. This free energy can be solved exactly for one dimensional patterns and reveals the role of domains walls and their crossings in determining the nature of the phase diagrams.

Heat transport in pristine and polycrystalline single-layer hexagonal boron nitride

We use a phase field crystal model to generate large-scale bicrystalline and polycrystalline single-layer hexagonal boron nitride (h-BN) samples and employ molecular dynamics (MD) simulations with the Tersoff many-body potential to study their heat transport properties. The Kapitza thermal resistance across individual h-BN grain boundaries is calculated using the inhomogeneous nonequilibrium MD method. The resistance displays strong dependence on the tilt angle, the line tension and the defect density of the grain boundaries. We also calculate the thermal conductivity of pristine h-BN and polycrystalline h-BN with different grain sizes using an efficient homogeneous nonequilibrium MD method. The in-plane and the out-of-plane (flexural) phonons exhibit different grain size scalings of the thermal conductivity in polycrystalline h-BN and the extracted Kapitza conductance is close to that of large-tilt-angle grain boundaries in bicrystals.