In spite of their importance for understanding phonon transport phenomena in thin films and polycrystalline solids, the effects of boundary roughness scattering on phonon specularity and coherence are poorly understood because there is no general method for predicting their dependence on phonon momentum, frequency, branch and boundary morphology. Using the recently formulated atomistic S-matrix method, we develop a theory of boundary roughness scattering to determine the mode-resolved phonon coherence and specularity parameters from the scattering amplitudes. To illustrate the theory, we apply it to phonon scattering in realistic nonsymmetric graphene grain boundary (GB) models derived from atomic structure predictions. The method is validated by comparing its predictions with frequency-resolved results from lattice dynamics-based calculations. We prove that incoherent scattering is almost perfectly diffusive. We show that phonon scattering at the graphene GB is not diffuse although coherence and specularity are significantly reduced for long-wavelength flexural acoustic phonons. Our approach can be generalized to other atomistic boundary models.
It is widely assumed in the literature that the specularity parameters for phonon transmission (forward scattering) and reflection (backward scattering) at a boundary are identical, i.e., the statistical distributions of the transition probabilities between an incident phonon and the range of outgoing phonon modes are the same for both transmission and reflection. However, it is hypothesized by Li and McGaughey that separate specularity parameters are needed to describe the behavior of transmitted and reflected phonons in superlattices and polycrystalline materials correctly. We test this hypo…
Galerkin Methods for Boltzmann-Poisson transport with reflection conditions on rough boundaries
TU Wien - Institute for Analysis and Scientific Computing（维也纳工业大学分析与科学计算研究所）；The University of Texas at Austin - Institute for Computational Engineering and Sciences & Department of Mathematics（德克萨斯大学奥斯汀分校计算工程与科学学院及数学系）
Scattering of phonons at boundaries of a crystal (grains, surfaces, or solid/solid interfaces) is characterized by the phonon wavelength, the angle of incidence, and the interface roughness, as historically evaluated using a specularity parameter p formulated by Ziman [J. M. Ziman, Electrons and Phonons (Clarendon Press, Oxford, 1960)]. This parameter was initially defined to determine the probability of a phonon specularly reflecting or diffusely scattering from the rough surface of a material. The validity of Ziman's theory as extended to solid/solid interfaces has not been previously valida…
Graphene grain boundaries are known to affect phonon transport and thermal conductivity, suggesting that they may be used to engineer the phononic properties of graphene. Here, the effect of two buckled grain boundaries on long-wavelength flexural acoustic phonons has been investigated as a function of angle of incidence using molecular dynamics. The flexural acoustic mode has been chosen due to its importance to thermal transport. It is found that the transmission through the boundaries is strongly suppressed for incidence angles close to 35$^\circ$. Also, the grain boundaries are found to ac…
The strong interest in graphene has motivated the scalable production of high quality graphene and graphene devices. Since large-scale graphene films synthesized to date are typically polycrystalline, it is important to characterize and control grain boundaries, generally believed to degrade graphene quality. Here we study single-crystal graphene grains synthesized by ambient CVD on polycrystalline Cu, and show how individual boundaries between coalescing grains affect graphene's electronic properties. The graphene grains show no definite epitaxial relationship with the Cu substrate, and can c…
We study charge and spin transport along grain boundaries in single layer graphene in the presence of a quantizing magnetic field. Transport states in a grain boundary are produced by hybridization of Landau zero modes with interfacial states. In selected energy regimes quantum Hall edge states can be deflected either fully or partially into grain boundary states. The degree of edge state deflection is studied in the nonlocal conductance and in the shot noise. We also consider the possibility of grain boundaries as gate-switchable spin filters, a functionality enabled by counterpropagating tra…
The properties of polycrystalline materials are often dominated by the size of their grains and by the atomic structure of their grain boundaries. These effects should be especially pronounced in 2D materials, where even a line defect can divide and disrupt a crystal. These issues take on practical significance in graphene, a hexagonal two-dimensional crystal of carbon atoms; Single-atom-thick graphene sheets can now be produced by chemical vapor deposition on up to meter scales, making their polycrystallinity almost unavoidable. Theoretically, graphene grain boundaries are predicted to have d…
Charge transport across the interfaces in complex oxides attracts a lot of attention because it allows creating novel functionalities useful for device applications. In particular, it has been observed that movable domain walls in epitaxial BiFeO3 films possess enhanced conductivity that can be used for read out in ferroelectric-based memories. In this work, the relation between the polarization and conductivity in sol-gel BiFeO3 films with special emphasis on grain boundaries as natural interfaces in polycrystalline ferroelectrics is investigated. The grains exhibit self-organized domain stru…
Segregation to grain boundaries affects their cohesion, corrosion and embrittlement and plays a critical role in heterogeneous nucleation. In order to quantitatively study segregation and phase separation at grain boundaries, we derive a density-based phase-field model. In this model, we describe the grain boundary free energy based on available bulk thermodynamic data while an atomic grain boundary density is obtained using atomistic simulations. To benchmark the performance of the model, we study Mn grain boundary segregation in the Fe--Mn system. 3D simulation results are compared against a…
A space-charge model is applied to describe the equilibrium effects of segregation of double-donor oxygen vacancies to grain boundaries in dry and wet acceptor-doped samples of the perovskite oxide BaZrO3. The grain boundary core vacancy concentrations and electrostatic potential barriers resulting from different vacancy segregation energies are evaluated. Density-functional calculations on vacancy segregation to the mirror-symmetric Σ3 (112) [-110] tilt grain boundary are also presented. Our results indicate that oxygen vacancy segregation can be responsible for the low grain boundary proton …
We have investigated atomic and electronic structure of grain boundaries in monolayer MoS2, where relative angles between two different grains are 0 and 60 degree. The grain boundaries with specific relative angle have been formed with chemical vapor deposition growth on graphite and hexagonal boron nitride flakes; van der Waals interlayer interaction between MoS2 and the flakes restricts the relative angle. Through scanning tunneling microscopy and spectroscopy measurements, we have found that the perfectly stitched structure between two different grains of MoS2 was realized in the case of th…
Recent progress in large-area synthesis of monolayer molybdenum disulfide, a new two-dimensional direct-bandgap semiconductor, is paving the way for applications in atomically thin electronics. Little is known, however, about the microstructure of this material. Here we have refined chemical vapor deposition synthesis to grow highly crystalline islands of monolayer molybdenum disulfide up to 120 um in size with optical and electrical properties comparable or superior to exfoliated samples. Using transmission electron microscopy, we correlate lattice orientation, edge morphology, and crystallin…
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, b…
Faceted grain boundaries exhibit unusual segregation and migration tendencies. To gain a deeper understanding of how solute atoms interact with faceted interfacial structures during migration, this study probes the migration behavior of a faceted $Σ$11 boundary in Cu doped with Ag atoms. The solutes are found to segregate to the facet with more free volume and strongly reduce boundary velocity in one migration direction, but not the other, due to the presence of a directionally-dependent motion mechanism that can escape solute pinning and therefore speed up migration. Hence, a new mechanism of…
We investigate the scattering of long-wavelength flexural phonons against grain boundaries in graphene using molecular dynamics simulations. Three symmetric tilt grain boundaires are considered: one with a misorientation angle of $17.9^\circ$ displaying an out-of-plane buckling 1.5 nm high and 5 nm wide, one with a misorientation angle of $9.4^\circ$ and an out-of-plane buckling 0.6 nm high and 1.7 nm wide, and one with a misorientation angle of $32.2^\circ$ and no out-of-plane buckling. At the flat grain boundary, the phonon transmission exceeds 95 % for wavelengths above 1 nm. The buckled bo…
The objective of this research is to explore the formation/binding energetics and length scales associated with the interaction between He$_n$V clusters and grain boundaries in bcc $α$-Fe. In this work, we calculated formation/binding energies for 1-8 He atoms in a monovacancy at all potential grain boundary sites within 15 Å of the ten grain boundaries selected (122106 simulations total). The present results provide detailed information about the interaction energies and length scales of 1--8 He atoms with grain boundaries for the structures examined. A number of interesting new findings emer…
We present quantum-based simulations of single grain boundary reflectivity of electrons in metals, Cu and Ag. We examine twin and non-twin grain boundaries using non-equilibrium Green's function and first principles methods. We also investigate the mechanism of reflectivity in grain boundaries by modeling atomic vacancies, disorder, and orientation and find that the change in grain orientation and disorder in the boundary itself both contribute significantly to reflectivity. We find that grain boundary reflectivity may vary widely depending on the grain boundary structure consistent with exper…
We investigate the influence of grain boundaries (GBs), line defects (LDs), and chirality on thermal transport in graphene using non-equilibrium Green's functions. At room temperature the ballistic thermal conductance is ~4.2 GW/m^2/K, and single GBs or LDs yield transmission from 50-80% of this value. LDs with carbon atom octagon defects have lower thermal transmission than GBs with pentagon and heptagon defects. We apply our findings to study the thermal conductivity of polycrystalline graphene for practical applications, and find that the type and size of GBs play an important role when gra…
Despite the structures and properties of tilt grain boundaries of graphite surface and graphene have been extensively studied, their effect on the structures and electronic spectra of graphene layers has not been fully addressed. Here we study effects of one-dimensional tilt grain boundaries on structures and electronic spectra of graphene multilayers by scanning tunneling microscopy and spectroscopy. A tilt grain boundary of a top graphene sheet in graphene multilayers leads to a twist between consecutive layers and generates superstructures (Moiré patterns) on one side of the boundary. Our r…
A new dislocation structure-square-octagon pair (4|8) is discovered in two-dimensional boron nitride (h-BN), via first-principles calculations. It has lower energy than corresponding pentagon-heptagon pairs (5|7), which contain unfavorable homo-elemental bonds. Based on the structures of dislocations, grain boundaries (GB) in BN are investigated. Depending on the tilt angle of grains, GB can be either polar (B-rich or N-rich), constituted by 5|7s, or un-polar, composed of 4|8s. The polar GBs carry net charges, positive at B-rich and negative at N-rich ones. In contrast to GBs in graphene which…
We reveal that phononic thermal transport in graphene is not immune to grain boundaries (GBs) aligned along the direction of the temperature gradient. Non-equilibrium molecular dynamics simulations uncover a large reduction in the phononic thermal conductivity ($κ_p$) along linear ultra-narrow GBs comprising periodically-repeating pentagon-heptagon dislocations. Green's function calculations and spectral energy density analysis indicate that $κ_p$ is the complex manifestation of the periodic strain field, which behaves as a reflective diffraction grating with both diffuse and specular phonon r…
Topological defects in graphene, dislocations and grain boundaries, are still not well understood despites the considerable number of experimental observations. We introduce a general approach for constructing dislocations in graphene characterized by arbitrary Burgers vectors as well as grain boundaries, covering the whole range of possible misorientation angles. By using ab initio calculations we investigate thermodynamic and electronic properties of these topological defects, finding energetically favorable symmetric large-angle grain boundaries, strong tendency towards out-of-plane deforma…
It is well known that the twinning is an important mode of plastic deformation in nanocrystalline materials. As a result, it is expected that the twin can interact with different grain boundaries (GBs) during the plastic deformation. Understanding these twin-GB interactions is crucial for our understanding of mechanical behavior of materials. In this work, the twin interaction with different $Σ$11 symmetric and asymmetric tilt GBs has been investigated in BCC Fe using molecular dynamics (MD) simulations. The results indicate that twin nucleate from the crack or GB and, its interaction with $Σ$…
In the paper we predict a distinctive change of magnetic properties and considerable increase of the Curie temperature caused by the strain fields of grain boundaries in ferromagnetic films. It is shown that a sheet of spontaneous magnetization may arise along a grain boundary at temperatures greater than the bulk Curie temperature. The temperature dependence and space distribution of magnetization in a ferromagnetic film with grain boundaries are calculated. We found that $45^\circ$ grain boundaries can produce long-range strain fields that results in the width of the magnetic sheet along the…
The magnetotransport properties of antidot lattices containing artificially designed grain boundaries have been measured. We find that the grain boundaries broaden the commensurability resonances and displace them anisotropically. These phenomena are unexpectedly weak but differ characteristically from isotropic, Gaussian disorder in the antidot positions. The observations are interpreted in terms of semiclassical trajectories which tend to localize along the grain boundaries within certain magnetic field intervals. Furthermore, our results indicate how the transport through superlattices gene…
Perturbations of the two dimensional carbon lattice of graphene, such as grain boundaries, have significant influence on the charge transport and mechanical properties of this material. Scanning tunneling microscopy measurements presented here show that localized states near the Dirac point dominate the local density of states of grain boundaries in graphene grown by chemical vapor deposition. Such low energy states are not reproduced by theoretical models which treat the grain boundaries as periodic dislocation-cores composed of pentagonal-heptagonal carbon rings. Using ab initio calculations…
In light of the race towards macroscale superlubricity of graphitic contacts, the effect of grain boundaries on their frictional properties becomes of central importance. Here, we elucidate the unique frictional mechanisms characterizing topological defects along typical grain boundaries that can vary from being nearly flat to highly corrugated, depending on the boundary misfit angle. We find that frictional energy dissipation over grain boundaries can originate from variations of compressibility along the surface, heat produced during defect (un)buckling events, and elastic energy storage in …
Grain boundaries in epitaxial graphene on the SiC(000$\bar{1}$) substrate are studied using scanning tunneling microscopy and spectroscopy. All investigated small-angle grain boundaries show pronounced out-of-plane buckling induced by the strain fields of constituent dislocations. The ensemble of observations allows to determine the critical misorientation angle of buckling transition $θ_c = 19 \pm~2^\circ$. Periodic structures are found among the flat large-angle grain boundaries. In particular, the observed $θ= 33\pm2^\circ$ highly ordered grain boundary is assigned to the previously propose…
We study how low-energy charge carriers scatter off periodic and linear graphene grain boundaries oriented along the zigzag direction with a periodicity three times greater than that of pristine graphene. These defects map the two Dirac points into the same position, and thus allow for intervalley scattering to occur. Starting from graphene's first-neighbor tight-binding model we show how can we compute the boundary condition seen by graphene's massless Dirac fermions at such grain boundaries. We illustrate this procedure for the 3-periodic pentagon-only grain boundary, and then work out the l…
Graphene, a two-dimensional honeycomb lattice of carbon atoms, is of great interest in (opto)electronics and plasmonics and can be obtained by means of diverse fabrication techniques, among which chemical vapor deposition (CVD) is one of the most promising for technological applications. The electronic and mechanical properties of CVD-grown graphene depend in large part on the characteristics of the grain boundaries. However, the physical properties of these grain boundaries remain challenging to characterize directly and conveniently. Here, we show that it is possible to visualize and investi…
We have investigated by means of first principles calculations the structural and electronic properties of hydrogenated graphene structures with distinct grain boundary defects. Our total energy results reveal that the adsorption of a single H is more stable at grain boundary defect. The electronic structure of the grains boundaries upon hydrogen adsorption have been examined. Further total energy calculations indicate that the adsorption of two H on two neighbor carbons, forming a basic unit of graphane, is more stable at the defect region. Therefore, we expect that these extended defects wou…
We report on the formation process of skyrmion lattice (SkL) domain boundaries in FeGe using Lorentz transmission electron microscopy and small-angle electron diffraction. We observed that grain boundaries and edges play an important role in the formation of SkL domain boundaries; The SkL domain boundary is stabilized at the intersection of two grains. A micromagnetic simulation using the Landau-Lifshitz-Gilbert equation revealed that the SkL domains separated by a boundary represent the lowest energy configuration. Conversely, in a wide area, SkL domain boundaries were not formed and SkL doma…
Ab initio calculations indicate that while the electronic states introduced by grain boundaries in graphene are only partially confined to the defect core, a domain boundary introduces states near the Fermi level that are very strongly confined to the core of the defect, and that display a ferromagnetic ground state. The domain boundary is fully immersed within the graphene matrix, hence this magnetic state is protected from reconstruction effects that have hampered experimental detection in the case of ribbon edge states. Furthermore, our calculations suggest that charge transfer between one-…
The reason why the half-integer quantum Hall effect (QHE) is suppressed in graphene grown by chemical vapor deposition (CVD) is unclear. We propose that it might be connected to extended defects in the material and present results for the quantum Hall effect in graphene with [0001] tilt grain boundaries connecting opposite sides of Hall bar devices. Such grain boundaries contain 5-7 ring complexes that host defect states that hybridize to form bands with varying degree of metallicity depending on grain boundary defect density. In a magnetic field, edge states on opposite sides of the Hall bar …
We use numerical simulations to predict peculiar magnetotransport fingerprints in polycrystalline graphene, driven by the presence of grain boundaries of varying size and orientation. The formation of Landau levels is shown to be restricted by the polycrystalline morphology, requiring the magnetic length to be smaller than the average grain radius. The nature of localization is also found to be unusual, with strongly localized states at the center of Landau levels (including the usually highly robust zero-energy state) and extended electronic states lying between Landau levels. These extended …
Electronic states confined to zero angle grain boundaries in single layer graphene are analyzed using topological band theoretic arguments. We identify a hidden chiral symmetry which supports symmetry protected zero modes in projected bulk gaps. These branches occupy a finite fraction of the interface-projected Brillouin zone and terminate at bulk gap closures, manifesting topological transitions in the occupied manifolds of the bulk systems that are joined at an interface. These features are studied by numerical calculations on a tight binding lattice and by analysis of the geometric phases o…
The thermal boundary resistance (Kapitza resistance) of (001) twist grain boundaries in silicon nanowires depends on the mismatch angle. This dependence is systematically investigated by means of nonequilibrium molecular dynamics simulations. Grain boundary systems with and without coincidence site lattice are compared. The Kapitza resistance increases with twist angle up to 40°. For larger angles, it varies only little around 1.56 $\pm$ 0.05 K m^2/GW, except for a drop by 30% near the 90° Σ 1 grain boundary. Finite size effects due to the fixed outer boundary conditions of the nanowire are ne…
We present analytical relations for the dark recombination current of a $pn^+$ junction with positively charged columnar grain boundaries in the high defect density regime. We consider two defect state configurations relevant for positively charged grain boundaries: a single donor state and a continuum of both acceptors and donors. Compared to a continuum of acceptor+donor states, or to the previously studied single acceptor+donor state, the grain boundary recombination of a single donor state is suppressed by orders of magnitude. We show numerically that superposition holds near the open-circ…
We study mesoscopic transport in the Q1D wires and rings made of a 2D conductor of width W and length L >> W. Our aim is to compare an impurity-free conductor with grain boundaries with a grain-free conductor with impurity disorder. A single grain boundary is modeled as a set of the 2D-$δ$-function-like barriers positioned equidistantly on a straight line and disorder is emulated by a large number of such straight lines, intersecting the conductor with random orientation in random positions. The impurity disorder is modeled by the 2D $δ$-barriers with the randomly chosen positions and signs. T…
Electronic, transport, and spin properties of grain boundaries (GBs) are investigated in electrostatically doped graphene at finite electron densities within the Hartree and Hubbard approximations. We demonstrate that depending on the character of the GBs, the states residing on them can have a metallic character with a zero group velocity or can be fully populated losing the ability to carry a current. These states show qualitatively different features in charge accumulation and spin polarization. We also demonstrate that the semiclassical Thomas-Fermi approach provides a satisfactory approxi…
During the fabrication process of large scale silicene through common chemical vapor deposition (CVD) technique, polycrystalline films are quite likely to be produced, and the existence of Kapitza thermal resistance along grain boundaries could result in substantial changes of their thermal properties. In the present study, the thermal transport along polycrystalline silicene was evaluated by performing a multiscale method. Non-equilibrium molecular dynamics simulations (NEMD) was carried out to assess the interfacial thermal resistance of various constructed grain boundaries in silicene as we…
