publications

2024

1. Elastic shakedown and roughness evolution in repeated elastic–plastic contact

   Lucas Frérot, and Lars Pastewka

   Tribol. Lett. 72, 23 (2024)

   Abstractdoi PDF

   Surface roughness emerges naturally during mechanical removal of material, fracture, chemical deposition, plastic deformation, indentation, and other processes. Here, we use continuum simulations to show how roughness which is neither Gaussian nor self-affine emerges from repeated elastic–plastic contact of rough and rigid surfaces on a flat elastic–plastic substrate. Roughness profiles change with each contact cycle, but appear to approach a steady-state long before the substrate stops deforming plastically and has hence “shaken-down” elastically. We propose a simple dynamic collapse for the emerging power-spectral density, which shows that the multi-scale nature of the roughness is encoded in the first few indentations. In contrast to macroscopic roughness parameters, roughness at small scales and the skewness of the height distribution of the resulting roughness do not show a steady-state. However, the skewness vanishes asymptotically with contact cycle.

2. Sound waves, diffusive transport, and wall slip in nanoconfined compressible fluids

   Hannes Holey, Peter Gumbsch, and Lars Pastewka

   Phys. Rev. Fluids 9, 014203 (2024)

   Abstractdoi PDF

   Although continuum theories have been proven quite robust to describe confined fluid flow at molecular length scales, molecular dynamics (MD) simulations reveal mechanistic insights into the interfacial dissipation processes. Most MD simulations of confined fluids have used setups in which the lateral box size is not much larger than the gap height, thus breaking thin-film assumptions usually employed in continuum simulations. Here we explicitly probe the long-wavelength hydrodynamic correlations in confined simple fluids with MD and compare to gap-averaged continuum theories as typically applied in, e.g., lubrication. Relaxation times obtained from equilibrium fluctuations interpolate between the theoretical limits from bulk hydrodynamics and continuum formulations with increasing wavelength. We show how to exploit this characteristic transition to measure viscosity and slip length in confined systems simultaneously from equilibrium MD simulations. Moreover, the gap-averaged theory describes a geometry-induced dispersion relation that leads to overdamped sound relaxation at large wavelengths, which is confirmed by our MD simulations. Our results add to the understanding of transport processes under strong confinement and might be of technological relevance for the design of nanofluidic devices.

3. The bumpy road to friction control

   Viacheslav Slesarenko, and Lars Pastewka

   Science 383, 150–151 (2024)

   Abstractdoi PDF

   The frictional properties of material interfaces can be rationally designed.

4. Why soft contacts are stickier when breaking than when making them

   Antoine Sanner, Nityanshu Kumar, Ali Dhinojwala, Tevis D B Jacobs, and Lars Pastewka

   Sci. Adv. 10, eadl1277 (2024)

   Abstractdoi PDF

   Soft solids are sticky. They attract each other and spontaneously form a large area of contact. Their force of attraction is higher when separating than when forming contact, a phenomenon known as adhesion hysteresis. The common explanation for this hysteresis is viscoelastic energy dissipation or contact aging. Here, we use experiments and simulations to show that it emerges even for perfectly elastic solids. Pinning by surface roughness triggers the stick-slip motion of the contact line, dissipating energy. We derive a simple and general parameter-free equation that quantitatively describes contact formation in the presence of roughness. Our results highlight the crucial role of surface roughness and present a fundamental shift in our understanding of soft adhesion.

5. matscipy: materials science at the atomic scale with Python

   Petr Grigorev, Lucas Frérot, Fraser Birks, Adrien Gola, Jacek Golebiowski, Jan Grießer, Johannes L Hörmann, Andreas Klemenz, Gianpietro Moras, Wolfram G. Nöhring, Jonas A. Oldenstaedt, Punit Patel, Thomas Reichenbach, Thomas Rocke, Lakshmi Shenoy, Michael Walter, Simon Wengert, Lei Zhang, and James R. Kermode

   J. Open Source Softw. 9, 5668 (2024)

   Abstractdoi PDF

   Behaviour of materials is governed by physical phenomena that occur at an extreme range of length and time scales. Computational modelling requires multiscale approaches. Simulation techniques operating on the atomic scale serve as a foundation for such approaches, providing necessary parameters for upper-scale models. The physical models employed for atomic simulations can vary from electronic structure calculations to empirical force fields. However, construction, manipulation and analysis of atomic systems are independent of the given physical model but dependent on the specific application. matscipy implements such tools for applications in materials science, including fracture, plasticity, tribology and electrochemistry.

2023

1. An optimal preconditioned FFT-accelerated finite element solver for homogenization

   Martin Ladecký, Richard J. Leute, Ali Falsafi, Ivana Pultarová, Lars Pastewka, Till Junge, and Jan Zeman

   Appl. Math. Comput. 446, 127835 (2023)

   Abstractdoi PDF

   We generalize and provide a linear algebra-based perspective on a finite element (FE) homogenization scheme, pioneered by Schneider et al. (2017) and Leuschner and Fritzen (2018). The efficiency of the scheme is based on a preconditioned, well-scaled reformulation allowing for the use of the conjugate gradient or similar iterative solvers. The geometrically-optimal preconditioner—a discretized Green’s function of a periodic homogeneous reference problem—has a block-diagonal structure in the Fourier space which permits its efficient inversion using fast Fourier transform (FFT) techniques for generic regular meshes. This implies that the scheme scales as, like FFT, rendering it equivalent to spectral solvers in terms of computational efficiency. However, in contrast to classical spectral solvers, the proposed scheme works with FE shape functions with local supports and does not exhibit the Fourier ringing phenomenon. We show that the scheme achieves a number of iterations that are almost independent of spatial discretization. The scheme also scales mildly with phase contrast. We also discuss the equivalence between our displacement-based scheme and the recently proposed strain-based homogenization technique with finite-element projection.

2. Analytic elastic coefficients in molecular calculations: Finite strain, nonaffine displacements, and many-body interatomic potentials

   Jan Grießer, Lucas Frérot, Jonas A. Oldenstaedt, Martin H. Müser, and Lars Pastewka

   Phys. Rev. Mater. 7, 073603 (2023)

   Abstractdoi PDF

   Elastic moduli are among the most fundamental and important properties of solid materials, which is why they are routinely characterized in both experiments and simulations. While conceptually simple, the treatment of elastic coefficients is complicated by two factors not yet having been concurrently discussed: finite-strain and nonaffine, internal displacements. Here, we revisit the theory behind zero-temperature, finite-strain elastic moduli and extend it to explicitly consider nonaffine displacements. We further present analytical expressions for second-order derivatives of the potential energy for two-body and generic many-body interatomic potentials, such as cluster and empirical bond-order potentials. Specifically, we revisit the elastic constants of silicon, silicon carbide, and silicon dioxide under hydrostatic compression and dilatation. Based on existing and recent results, we outline the effect of multiaxial stress states as opposed to volumetric deformation on the limits of stability of their crystalline lattices.

3. Confinement-induced diffusive sound transport in nanoscale fluidic channels

   Hannes Holey, Peter Gumbsch, and Lars Pastewka

   Phys. Rev. Lett. 131, 084001 (2023)

   Abstractdoi PDF

   Molecular dynamics (MD) simulations have been widely used to study flow at molecular scales. Most of this work is devoted to study the departure from continuum fluid mechanics as the confining dimension decreases. Here, we present MD results under conditions where hydrodynamic descriptions typically apply, but focus on the influence of in-plane wavelengths. Probing the long wavelength limit in thermodynamic equilibrium, we observed anomalous relaxation of the density and longitudinal momentum fluctuations. The limiting behavior can be described by an effective continuum theory that describes a transition to overdamped sound relaxation for compressible fluids.

4. Entropic stress of grafted polymer chains in shear flow

   Jan Mees, Thomas C O’Connor, and Lars Pastewka

   J. Chem. Phys. 159 (2023)

   Abstractdoi PDF

   We analyze the shear response of grafted polymer chains in shear flow via coarse-grained molecular dynamics simulations with an explicit solvent. We find that the solvent flow penetrates into almost the whole brush for “mushroom”-type brushes but only a few bond distances for dense brushes. In all cases, the external stress on the wall equals the entropic stress associated with the distorted polymer conformations. We find that the external stress increases linearly with shear rate at low rates and sublinearly at high rates. The transition from linear to sublinear scaling occurs where chains react to flow by reorienting. Sublinear scaling with shear rate disappears if the shear rate is nondimensionalized with the effective relaxation time of chain subsegments located in the outer part of the brush that experiences flow.

5. Interatomic potentials: achievements and challenges

   Martin H. Müser, Sergey V. Sukhomlinov, and Lars Pastewka

   Adv. Phys. X 8, 2093129 (2023)

   Abstractdoi PDF

   Interatomic potentials approximate the potential energy of atoms as a function of their coordinates. Their main application is the effective simulation of many-atom systems. Here, we review empirical interatomic potentials designed to reproduce elastic properties, defect energies, bond breaking, bond formation, and even redox reactions. We discuss popular two-body potentials, embedded-atom models for metals, bond-order potentials for covalently bonded systems, polarizable potentials including charge-transfer approaches for ionic systems and quantum-Drude oscillator models mimicking higher-order and many-body dispersion. Particular emphasis is laid on the question what constraints ensue from the functional form of a potential, e.g., in what way Cauchy relations for elastic tensor elements can be violated and what this entails for the ratio of defect and cohesive energies, or why the ratio of boiling to melting temperature tends to be large for potentials describing metals but small for short-ranged pair potentials. The review is meant to be pedagogical rather than encyclopedic. This is why we highlight potentials with functional forms sufficiently simple to remain amenable to analytical treatments. Our main objective is to provide a stimulus for how existing approaches can be advanced or meaningfully combined to extent the scope of simulations based on empirical potentials.

6. Molecular mechanisms of self-mated hydrogel friction

   Jan Mees, Rok Simič, Thomas C. O’Connor, Nicholas D. Spencer, and Lars Pastewka

   Tribol. Lett. 71, 74 (2023)

   Abstractdoi PDF

   Self-mated hydrogel contacts show extremely small friction coefficients at low loads but a distinct velocity dependence. Here we combine mesoscopic simulations and experiments to test the polymer-relaxation hypothesis for this velocity dependence, where a velocity-dependent regime emerges when the perturbation of interfacial polymer chains occurs faster than their relaxation at high velocity. Our simulations reproduce the experimental findings, with speed-independent friction at low velocity, followed by a friction coefficient that rises with velocity to some power of order unity. We show that the velocity-dependent regime is characterized by reorientation and stretching of polymer chains in the direction of shear, leading to an entropic stress that can be quantitatively related to the shear response. The detailed exponent of the power law in the velocity dependent regime depends on how chains interact: We observe a power close to 1/2 for chains that can stretch, while pure reorientation leads to a power of unity. Our simulations quantitatively match experiments and show that the velocity dependence of hydrogel friction at low loads can be firmly traced back to the morphology of near-surface chains.

7. Molecular simulations of sliding on SDS surfactant films

   Johannes L Hörmann, Chenxu Liu, Yonggang Meng, and Lars Pastewka

   J. Chem. Phys. 158 (2023)

   Abstractdoi PDF

   We use molecular dynamics simulations to study the frictional response of monolayers of the anionic surfactant sodium dodecyl sulfate and hemicylindrical aggregates physisorbed on gold. Our simulations of a sliding spherical asperity reveal the following two friction regimes: at low loads, the films show Amonton’s friction with a friction force that rises linearly with normal load, and at high loads, the friction force is independent of the load as long as no direct solid-solid contact occurs. The transition between these two regimes happens when a single molecular layer is confined in the gap between the sliding bodies. The friction force at high loads on a monolayer rises monotonically with film density and drops slightly with the transition to hemicylindrical aggregates. This monotonous increase of friction force is compatible with a traditional plowing model of sliding friction. At low loads, the friction coefficient reaches a minimum at the intermediate surface concentrations. We attribute this behavior to a competition between adhesive forces, repulsion of the compressed film, and the onset of plowing.

8. Surface topography as a material parameter

   Tevis D. B. Jacobs, and Lars Pastewka

   MRS Bull. 47, 1205-1210 (2023)

   Abstractdoi PDF

   Materials science is about understanding the relationship between a material’s structure and its properties—in the sphere of mechanical behavior, this includes elastic modulus, yield strength, and other bulk properties. We show in this issue that, analogously, a material’s surface structure governs its surface properties—such as adhesion, friction, and surface stiffness. For bulk materials, microstructure is a critical component of structure; for surfaces, the structure is governed largely by surface topography. The articles in this issue cover the latest understanding of these structure–property connections for surfaces. This includes both the theoretical basis for how properties depend on topography, as well as the latest understanding of how surface topography emerges, how to measure and understand topography-dependent properties, and how to engineer surfaces to improve performance. The present article frames the importance of surface topography and its effect on properties; it also outlines some of the critical knowledge gaps that impede progress toward optimally performing surfaces.

9. Toward a continuum description of lubrication in highly pressurized nanometer-wide constrictions: The importance of accurate slip laws

   Andrea Codrignani, Stefan Peeters, Hannes Holey, Franziska Stief, Daniele Savio, Lars Pastewka, Gianpietro Moras, Kerstin Falk, and Michael Moseler

   Sci. Adv. 9, eadi2649 (2023)

   Abstractdoi PDF

   The Reynolds lubrication equation (RLE) is widely used to design sliding contacts in mechanical machinery. While providing an excellent description of hydrodynamic lubrication, friction in boundary lubrication regions is usually considered by empirical laws, because continuum theories are expected to fail for lubricant film heights h0 ≪ 10 nm, especially in highly loaded tribosystems with normal pressures pn ≫ 0.1 GPa. Here, the performance of RLEs is validated by molecular dynamics simulations of pressurized (with pn = 0.2 to 1 GPa) hexadecane in a gold converging-diverging channel with minimum gap heights h0 = 1.4 to 9.7 nm. For pn ≤0.4 GPa and h0 ≥5 nm, agreement with the RLE requires accurate constitutive laws for pressure-dependent density and viscosity. An additional nonlinear wall slip law relating wall slip velocities to local shear stresses extends the RLE’s validity to even the most severe loading condition pn = 1 GPa and h0 = 1.4 nm. Our results demonstrate an innovative route for continuum modeling of highly loaded tribological contacts under boundary lubrication.

10. Yielding under compression and the polyamorphic transition in silicon

    Jan Grießer, Gianpietro Moras, and Lars Pastewka

    Phys. Rev. Mater. 7, 055601 (2023)

    Abstractdoi PDF

    We investigate the behavior of amorphous silicon under hydrostatic compression using molecular simulations. During compression, amorphous silicon undergoes a discontinuous nonequilibrium transition from a low-density to a high-density structure at a pressure of around 13-16 GPa. Ensemble-averaged density and elastic constants change discontinuously across the transition. Densification of individual glassy samples occurs through a series of discrete plastic events, each of which is accompanied by a vanishing shear modulus. This is the signature of a series of elastic instabilities, similar to shear transformation zones observed during shear yielding of glasses. We compare the structure obtained during compression with a near-equilibrium form of amorphous silicon obtained by quenching a melt at constant pressure. This gives structures identical to nonequilibrium compression at low and high pressure, but the transition between them occurs gradually rather than discontinuously. Our observations indicate that the polyamorphic transition is of a nonequilibrium nature, and it has the characteristics of a yield transition that occurs under compression instead of shear.

2022

1. Contact.engineering—Create, analyze and publish digital surface twins from topography measurements across many scales

   Michael C Röttger, Antoine Sanner, Luke A Thimons, Till Junge, Abhijeet Gujrati, Joseph M Monti, Wolfram G Nöhring, Tevis D B Jacobs, and Lars Pastewka

   Surf. Topogr.: Metrol. Prop. 10, 035032 (2022)

   Abstractdoi PDF

   The optimization of surface finish to improve performance occurs largely through trial and error, despite significant advancements in the relevant science. There are three central challenges that account for this disconnect: (1) the challenge of integration of many different types of measurement for the same surface to capture the multi-scale nature of roughness; (2) the technical complexity of implementing spectral analysis methods, and of applying mechanical or numerical models to describe surface performance; (3) a lack of consistency between researchers and industries in how surfaces are measured, quantified, and communicated. Here we present a freely-available internet-based application which attempts to overcome all three challenges. First, the application enables the user to upload many different topography measurements taken from a single surface, including using different techniques, and then integrates all of them together to create a digital surface twin. Second, the application calculates many of the commonly used topography metrics, such as root-mean-square parameters, power spectral density (PSD), and autocorrelation function (ACF), as well as implementing analytical and numerical calculations, such as boundary element modeling (BEM) for elastic and plastic deformation. Third, the application serves as a repository for users to securely store surfaces, and if they choose, to share these with collaborators or even publish them (with a digital object identifier) for all to access. The primary goal of this application is to enable researchers and manufacturers to quickly and easily apply cutting-edge tools for the characterization and properties-modeling of real-world surfaces. An additional goal is to advance the use of open-science principles in surface engineering by providing a FAIR database where researchers can choose to publish surface measurements for all to use.

2. Crack-front model for adhesion of soft elastic spheres with chemical heterogeneity

   Antoine Sanner, and Lars Pastewka

   J. Mech. Phys. Solids 160, 104781 (2022)

   Abstractdoi PDF

   Adhesion hysteresis can be caused by elastic instabilities that are triggered by surface roughness or chemical heterogeneity. However, the role of these instabilities in adhesion hysteresis remains poorly understood because we lack theoretical and numerical models accounting for realistic roughness. Our work focuses on the adhesion of soft elastic spheres with low roughness or weak heterogeneity, where the indentation process can be described as a Griffith-like propagation of a nearly circular external crack. We discuss how to describe the contact of spheres with chemical heterogeneity that leads to fluctuations in the local work of adhesion. We introduce a variational first-order crack-perturbation model and validate our approach using boundary-element simulations. The crack-perturbation model faithfully predicts contact shapes and hysteretic force-penetration curves, provided that the contact perimeter remains close to a circle and the contact area is simply connected. Computationally, the crack-perturbation model is orders of magnitude more efficient than the corresponding boundary element formulation, allowing for realistic heterogeneity fields.

3. Dependence of adhesive friction on surface roughness and elastic modulus

   Daniel Maksuta, Siddhesh Dalvi, Abhijeet Gujrati, Lars Pastewka, Tevis D. B. Jacobs, and Ali Dhinojwala

   Soft Matter 18, 5843-5849 (2022)

   Abstractdoi PDF

   Friction is one of the leading causes of energy loss in moving parts, and understanding how roughness affects friction is of utmost importance. From creating surfaces with high friction to prevent slip and movement, to creating surfaces with low friction to minimize energy loss, roughness plays a key role. By measuring shear stresses of crosslinked elastomers on three rough surfaces of similar surface chemistry across nearly six decades of sliding velocity, we demonstrate the dominant role of adhesive frictional dissipation. Furthermore, while it was previously known that roughness-induced oscillations affected the viscoelastic dissipation, we show that these oscillations also control the molecular detachment process and the resulting adhesive dissipation. This contrasts with typical models of friction, where only the amount of contact area and the strength of interfacial bonding govern the adhesive dissipation. Finally, we show that all the data can be collapsed onto a universal curve when the shear stress is scaled by the square root of elastic modulus and the velocity is scaled by a critical velocity at which the system exhibits macroscopic buckling instabilities. Taken together, these results suggest a design principle broadly applicable to frictional systems ranging from tires to soft robotics.

4. Elastic property and fracture mechanics of lateral branch-branch junctions in cacti: A case study of Opuntia ficus-indica and Cylindropuntia bigelovii

   Max D. Mylo, Anna Hoppe, Lars Pastewka, Thomas Speck, and Olga Speck

   Front. Plant Sci. 13, 950860 (2022)

   Abstractdoi PDF

   Species with various reproductive modes accompanied by different mechanical properties of their (lateral) branch-branch junctions have evolved in the cactus subfamily Opuntioideae. Older branches of Opuntia ficus-indica with fracture-resistant junctions often bear flowers and fruits for sexual reproduction, whereas younger branches break off easily and provide offshoots for vegetative propagation. Cylindropuntia bigelovii plants are known for their vegetative reproduction via easily detachable branches that can establish themselves as offshoots. We characterized the elastic and fracture behaviors of these lateral junctions by tensile testing and analyzed local strains during loading. Additionally, we carried out finite element analyses to quantify the influence of five relevant tissue layers on joint elastic behavior. Our fracture analysis revealed various fracture modes: (i) most young samples of Opuntia ficus-indica failed directly at the junction and had smooth fracture surfaces, and relative fracture strain was on median 4% of the total strain; (ii) most older samples of Opuntia ficus-indica failed at the adjacent branch and exhibited rough fracture surfaces, and relative fracture strain was on median 47%; (iii) most samples of Cylindropuntia bigelovii abscised directly at the junction and exhibited cup and cone surfaces, and relative fracture strain was on median 28%. Various geometric and mechanical properties such as junction area, fracture energy, and tensile strength were analyzed with respect to significant differences between species and age of sample. Interestingly, the abscission of lateral branches naturally triggered by wind, passing animals, or vibration showed the following differences in maximum force: 153 N (older Opuntia ficus-indica), 51 N (young Opuntia ficus-indica), and 14 N (Cylindropuntia bigelovii).

5. Elimination of ringing artifacts by finite-element projection in FFT-based homogenization

   Richard J. Leute, Martin Ladecký, Ali Falsafi, Indre Jödicke, Ivana Pultarová, Jan Zeman, Till Junge, and Lars Pastewka

   J. Comp. Phys. 453, 110931 (2022)

   Abstractdoi PDF

   Micromechanical homogenization is often carried out with Fourier-accelerated methods that are prone to ringing artifacts. We here generalize the compatibility projection introduced by Vondřejc et al. (2014) [24] beyond the Fourier basis. In particular, we formulate the compatibility projection for linear finite elements while maintaining Fourier-acceleration and the fast convergence properties of the original method. We demonstrate that this eliminates ringing artifacts and yields an efficient computational homogenization scheme that is equivalent to canonical finite-element formulations on fully structured grids.

6. Fractal geometry of contacting patches in rough elastic contacts

   Joseph M. Monti, Lars Pastewka, and Mark O. Robbins

   J. Mech. Phys. Solids 160, 104797 (2022)

   Abstractdoi PDF

   Many naturally formed and processed surfaces are rough over a broad range of length scales. Surface roughness reduces the area of contact between solids, with ramifications for phenomena that depend on the geometry of the interface and the amount of direct contact, including friction and adhesion. In this work, we employ large-scale boundary-element simulations for nonadhesive, elastic solids to study the size dependence of contact patch mean pressure and geometry for patches formed between solids with self-affine fractal surface roughness across seven decades in patch area. Contact patches with diameters smaller than a crossover length scale of order the minimum wavelength of roughness are generally compact with simple geometries and bear pressures well described by Hertz theory. The patch pressure in contact patches larger than the crossover scale rises logarithmically before saturating at a finite value. Furthermore, the largest contact patches formed during our simulations are ramified and populated with regions out of contact, or bubbles, which reduce patch area and increase patch perimeter. As a result, we show that the mean contact diameter of the largest patches saturates, indicating that the patch contact area is proportional to the total patch perimeter. We quantify the effects of bubbles on patch area and perimeters as a function of Hurst exponent and contrast our findings with results of comparable bearing-area model calculations. The slow evolution of the mean patch pressure with patch size in our large-scale calculations explains the common observation that the global mean contact pressure depends on the structure of the roughness, the contact area, and even on system size.

7. Height-Averaged Navier–Stokes Solver for Hydrodynamic Lubrication

   Hannes Holey, Andrea Codrignani, Peter Gumbsch, and Lars Pastewka

   Tribol. Lett. 70, 36 (2022)

   Abstractdoi PDF

   Modelling hydrodynamic lubrication is crucial in the design of engineering components as well as for a fundamental understanding of friction mechanisms. The cornerstone of thin-film flow modelling is the Reynolds equation – a lower-dimensional representation of the Stokes equation. However, the derivation of the Reynolds equation is based on assumptions and fixed form constitutive relations, that may not generally be valid, especially when studying systems under extreme conditions. Furthermore, these explicit assumptions about the constitutive behaviour of the fluid prohibit applications in a multiscale scenario based on measured or atomistically simulated data. Here, we present a method that considers the full compressible Navier-Stokes equation in a height-averaged sense for arbitrary constitutive relations. We perform numerical tests by using a reformulation of the viscous stress tensor for laminar flow to validate the presented method comparing to results from conventional Reynolds solutions. The versatility of the method is shown by incorporating models for mass-conserving cavitation, wall slip and non-Newtonian fluids. This allows testing of new constitutive relations that not necessarily need to take a fixed form, and may be obtained from experimental or simulation data.

8. Magnetic-assisted soft abrasive flow machining studied with smoothed particle hydrodynamics

   Shoya Mohseni-Mofidi, Lars Pastewka, Matthias Teschner, and Claas Bierwisch

   Appl. Math. Model. 101, 38-54 (2022)

   Abstractdoi PDF

   In many microsystem applications, a nanometric surface quality is crucial to the performance of a device. Soft abrasive flow machining (SAFM) is capable of finishing surfaces at very fine scale with complex geometries since, unlike traditional flow machining processes, abrasive grains are carried by a very low viscosity fluid. Several empirical studies have been done to ensure final high quality surfaces by enhancing the performance of SAFM. However, the present study aims to propose a consistent numerical approach which can handle the fluid-structure interface problems as well as surface erosion to model SAFM and help to gain deeper understanding of the process. Moreover, the approach is employed to investigate the effect of an external magnetic field on the performance of the machining process. All phases, namely carrier fluid, abrasive grains and workpiece, and their interactions are fully resolved by using smoothed particle hydrodynamics. The abrasive grains are modeled by particles that are rigidly moved together. The approach is used to study the surface finishing of a Polymethyl Methacrylate-based microchannel under external magnetic fields. Results show that a magnetic field of suitable strength can considerably improve the material removal rate and hence enhance the performance of SAFM.

9. Nonequilibrium plastic roughening of metallic glasses yields self-affine topographies with strain-rate and temperature-dependent scaling exponents

   Wolfram G. Nöhring, Adam R. Hinkle, and Lars Pastewka

   Phys. Rev. Mater. 6, 075603 (2022)

   Abstractdoi PDF

   We study nonequilibrium roughening during compressive plastic flow of initially flat Cu₅₀Zr₅₀ metallic glass using large-scale molecular dynamics simulations. Roughness emerges at atomically flat interfaces beyond the yield point of the glass. A self-affine rough topography is imprinted at yield and is reinforced during subsequent deformation. The imprinted topographies have Hurst exponents that decrease with increasing strain rate and temperature. After yield, the root-mean-square roughness amplitude grows as the square root of the applied strain with a prefactor that also drops with increasing strain rate and temperature. Our calculations reveal the emergence of spatial power-law correlations from homogeneous samples during plastic flow with exponents that depend on the rate of deformation and the temperature. The results have implications for interpreting and engineering roughness profiles.

10. Scale-dependent roughness parameters for topography analysis

    Antoine Sanner, Wolfram G. Nöhring, Luke A. Thimons, Tevis D.B. Jacobs, and Lars Pastewka

    Appl. Surf. Sci. Adv. 7, 100190 (2022)

    Abstractdoi PDF

    The failure of roughness parameters to predict surface properties stems from their inherent scale-dependence; in other words, the measured value depends on how the parameter was measured. Here we take advantage of this scale-dependence to develop a new framework for characterizing rough surfaces: the Scale-Dependent Roughness Parameters (SDRP) analysis, which yields slope, curvature, and higher-order derivatives of surface topography at many scales, even for a single topography measurement. We demonstrate the relationship between SDRP and other common statistical methods for analyzing surfaces: the height-difference autocorrelation function (ACF), variable bandwidth methods (VBMs) and the power spectral density (PSD). We use computer-generated and measured topographies to demonstrate the benefits of SDRP analysis, including: novel metrics for characterizing surfaces across scales, and the detection of measurement artifacts. The SDRP is a generalized framework for scale-dependent analysis of surface topography that yields metrics that are intuitively understandable.

11. Surface lattice Green’s functions for high-entropy alloys

    Wolfram G Nöhring, Jan Grießer, Patrick Dondl, and Lars Pastewka

    Modelling Simul. Mater. Sci. Eng. 30, 015007 (2022)

    Abstractdoi PDF

    We study the surface elastic response of pure Ni, the random alloy FeNiCr and an average FeNiCr alloy in terms of the surface lattice Green’s function. We propose a scheme for computing per-site Green’s function and study their per-site variations. The average FeNiCr alloys accurately reproduces the mean Green’s function of the full random alloy. Variation around this mean is largest near the edge of the surface Brillouin-zone and decays as q −2 with wavevector q towards the Γ-point. We also present expressions for the continuum surface Green’s function of anisotropic solids of finite and infinite thickness and show that the atomistic Green’s function approaches continuum near the Γ-point. Our results are a first step towards efficient contact calculations and Peierls–Nabarro type models for dislocations in high-entropy alloys.

2021

1. Comprehensive topography characterization of polycrystalline diamond coatings

   Abhijeet Gujrati, Antoine Sanner, Subarna R. Khanal, Nicolaie Moldovan, Hongjun Zeng, Lars Pastewka, and Tevis D. B. Jacobs

   Surf. Topogr.: Metrol. Prop. 9, 014003 (2021)

   Abstractdoi PDF

   The surface topography of diamond coatings strongly affects surface properties such as adhesion, friction, wear, and biocompatibility. However, the understanding of multi-scale topography, and its effect on properties, has been hindered by conventional measurement methods, which capture only a single length scale. Here, four different polycrystalline diamond coatings are characterized using transmission electron microscopy to assess the roughness down to the sub-nanometer scale. Then these measurements are combined, using the power spectral density (PSD), with conventional methods (stylus profilometry and atomic force microscopy) to characterize all scales of topography. The results demonstrate the critical importance of measuring topography across all length scales, especially because their PSDs cross over one another, such that a surface that is rougher at a larger scale may be smoother at a smaller scale and vice versa. Furthermore, these measurements reveal the connection between multi-scale topography and grain size, with characteristic scaling behavior at and slightly below the mean grain size, and self-affine fractal-like roughness at other length scales. At small (subgrain) scales, unpolished surfaces exhibit a common form of residual roughness that is self-affine in nature but difficult to detect with conventional methods. This approach of capturing topography from the atomic- to the macro-scale is termed comprehensive topography characterization, and all of the topography data from these surfaces has been made available for further analysis by experimentalists and theoreticians. Scientifically, this investigation has identified four characteristic regions of topography scaling in polycrystalline diamond materials.

2. Distribution of Gaps and Adhesive Interaction Between Contacting Rough Surfaces

   Joseph M. Monti, Antoine Sanner, and Lars Pastewka

   Tribol. Lett. 69, 80 (2021)

   Abstractdoi PDF

   Understanding the distribution of interfacial separations between contacting rough surfaces is integral for providing quantitative estimates for adhesive forces between them. Assuming non-adhesive, frictionless contact of self-affine surfaces, we derive the distribution of separations between surfaces near the contact edge. The distribution exhibits a power-law divergence for small gaps, and we use numerical simulations with fine resolution to confirm the scaling. The characteristic length scale over which the power-law regime persists is given by the product of the rms surface slope and the mean diameter of contacting regions. We show that these results remain valid for weakly adhesive contacts and connect these observations to recent theories for adhesion between rough surfaces.

3. Green’s function method for dynamic contact calculations

   Joseph M. Monti, Lars Pastewka, and Mark O. Robbins

   Phys. Rev. E 103, 053305 (2021)

   Abstractdoi PDF

   Resolving atomic scale details while capturing long-range elastic deformation is the principal difficulty when solving contact mechanics problems with computer simulations. Fully atomistic simulations must consider large blocks of atoms to support long-wavelength deformation modes, meaning that most atoms are far removed from the region of interest. Building on earlier methods that used elastic surface Green’s functions to compute static substrate deformation, we present a numerically efficient dynamic Green’s function technique to treat realistic, time-evolving, elastic solids. Our method solves substrate dynamics in reciprocal space and utilizes precomputed Green’s functions that exactly reproduce elastic interactions without retaining the atomic degrees of freedom in the bulk. We invoke physical insights to determine the necessary number of explicit substrate layers required to capture the attenuation of subsurface waves as a function of surface wave vector. We observe that truncating substrate dynamics at depths that fall as a power of wave vector allows us to accurately model wave propagation without implementing arbitrary damping. The framework we have developed substantially accelerates molecular dynamics simulations of large elastic substrates. We apply the method to single asperity contact, impact, and sliding friction problems and present our preliminary findings.

4. Hard-material Adhesion: Which Scales of Roughness Matter?

   L. A. Thimons, A. Gujrati, A. Sanner, L. Pastewka, and T. D. B. Jacobs

   Exp. Mech. 61, 1109-1120 (2021)

   Abstractdoi PDF

   Surface topography strongly modifies adhesion of hard-material contacts, yet roughness of real surfaces typically exists over many length scales, and it is not clear which of these scales has the strongest effect. Objective: This investigation aims to determine which scales of topography have the strongest effect on macroscopic adhesion.

5. Molecular Simulations of Electrotunable Lubrication: Viscosity and Wall Slip in Aqueous Electrolytes

   Christian Seidl, Johannes L. Hörmann, and Lars Pastewka

   Tribol. Lett. 69, 22 (2021)

   Abstractdoi PDF

   We study the frictional response of water-lubricated gold electrodes subject to an electrostatic potential difference using molecular dynamics simulations. Contrary to previous studies on electrotunable lubrication that were carried out by fixing the charges, our simulations keep electrodes at fixed electrostatic potential using a variable charge method. For pure water and NaCl solutions, viscosity is independent of the polarization of the electrodes, but wall slip depends on the potential difference. Our findings are in agreement with previous analytical theories of how wall slip is affected by interatomic interactions. The simulations shed light on the role of electrode polarization for wall slip and illustrate a mechanism for controlling friction and nanoscale flow in simple aqueous lubricants.

6. Quantitative prediction of the fracture toughness of amorphous carbon from atomic-scale simulations

   S. Mostafa Khosrownejad, James R. Kermode, and Lars Pastewka

   Phys. Rev. Mater. 5, 023602 (2021)

   Abstractdoi PDF

   Fracture is the ultimate source of failure of amorphous carbon (a-C) films; however, it is challenging to measure fracture properties of a-C from nanoindentation tests, and results of reported experiments are not consistent. Here, we use atomic-scale simulations to make quantitative and mechanistic predictions of fracture of a-C. Systematic large-scale K-field controlled atomic-scale simulations of crack propagation are performed for a-C samples with densities of ρ=2.5, 3.0, and 3.5g/cm3 created by liquid quenches for a range of quench rates ˙Tq=10–1000K/ps. The simulations show that the crack propagates by nucleation, growth, and coalescence of voids. Distances of ≈1nm between nucleated voids result in a brittlelike fracture toughness. We use a crack growth criterion proposed by Drugan, Rice, and Sham [J. Mech. Phys. Solids 30, 447 (1982)] to estimate steady-state fracture toughness based on our short crack-length fracture simulations. Fracture toughness values of 2.4–6.0MPa√m for initiation and 3–10MPa√m for the steady-state crack growth are within the experimentally reported range. These findings demonstrate that atomic-scale simulations can provide quantitatively predictive results even for fracture of materials with a ductile crack propagation mechanism.

7. Solid-Phase Silicon Homoepitaxy via Shear-Induced Amorphization and Recrystallization

   Thomas Reichenbach, Gianpietro Moras, Lars Pastewka, and Michael Moseler

   Phys. Rev. Lett. 127, 126101 (2021)

   Abstractdoi PDF

   We study mechanically induced phase transitions at tribological interfaces between silicon crystals using reactive molecular dynamics. The simulations reveal that the interplay between shear-driven amorphization and recrystallization results in an amorphous shear interface with constant thickness. Different shear elastic responses of the two anisotropic crystals can lead to the migration of the amorphous interface normal to the sliding plane, causing the crystal with lowest elastic energy density to grow at the expense of the other one. This triboepitaxial growth can be achieved by crystal misorientation or exploiting elastic finite-size effects, enabling the direct deposition of homoepitaxial silicon nanofilms by a crystalline tip rubbing against a substrate.

2020

1. Constitutive relations for plasticity of amorphous carbon

   Richard Jana, Julian Lautz, S Mostafa Khosrownejad, W Beck Andrews, Michael Moseler, and Lars Pastewka

   J. Phys. Mater. 3, 035005 (2020)

   Abstractdoi PDF

   We deform representative volume elements of amorphous carbon obtained from melt-quenches in molecular dynamics calculations using bond-order and machine learning interatomic potentials. A Drucker-Prager law with a zero-pressure flow stress of 41.2 GPa and an internal friction coefficient of 0.39 describes the deviatoric stress during flow as a function of pressure. We identify the mean coordination number as the order parameter describing this flow surface. However, a description of the dynamical relaxation of the quenched samples towards steady-state flow requires an additional order parameter. We suggest an intrinsic strain of the samples and present equations for its evolution. Our results provide insights into rehybridization and pressure dependence of friction between coated surfaces as well as routes towards the description of amorphous carbon in macroscale models of deformation.

2. Optimization of surface textures in hydrodynamic lubrication through the adjoint method

   A. Codrignani, D. Savio, L. Pastewka, B. Frohnapfel, and R. Ostayen

   Tribol. Int. 148, 106352 (2020)

   Abstractdoi PDF

   In this work we assess the applicability of the adjoint optimization technique for determining optimal surface topographies of two surfaces in relative motion in presence of a thin lubricant films that can cavitate. Among the existing numerical tools for topology optimization in engineering problems, the adjoint method represents a promising and versatile technique, which can also be applied to the field of full film tribology. In particular, the design of surfaces with complex textures can thoroughly benefit from this method, as it allows dealing with a large number of degrees of freedom at low computational cost. We show that this optimization method can be successfully applied to cavitating lubricant flows such as in pin-on-disc tribometers, giving the possibility to extend the results also to other typical applications such as journal and slider bearings. It is shown that the adjoint method can optimize the whole gap height distribution point by point in a more efficient way than traditional optimization approaches and parametric studies. In particular, thanks to the sensitivity analysis the adjoint method is able to find the placement and depth profile of each texture element.

3. Pattern formation during deformation of metallic nanolaminates

   Adrien Gola, Ruth Schwaiger, Peter Gumbsch, and Lars Pastewka

   Phys. Rev. Mater. 4, 013603 (2020)

   Abstractdoi PDF

   We used nonequilibrium molecular dynamics simulations to study the shear deformation of metallic composites composed of alternating layers of Cu and Au. Our simulations reveal the formation of “vortices” or “swirls” if the bimaterial interfaces are atomically rough and if none of the {111} planes that accommodate slip in fcc materials are exactly parallel to this interface. We trace the formation of these patterns back to grain rotation, induced by hindering dislocations from crossing the bimaterial interface. The instability is accompanied by shear softening of the material. These calculations shed light on recent observations of pattern formation in plastic flow, mechanical mixing of materials, and the common formation of a tribomutation layer in tribologically loaded systems.

4. The emergence of small-scale self-affine surface roughness from deformation

   Adam R. Hinkle, Wolfram G. Nöhring, Richard Leute, Till Junge, and Lars Pastewka

   Sci. Adv. 6, eaax0847 (2020)

   Abstractdoi PDF

   Most natural and man-made surfaces appear to be rough on many length scales. There is presently no unifying theory of the origin of roughness or the self-affine nature of surface topography. One likely contributor to the formation of roughness is deformation, which underlies many processes that shape surfaces such as machining, fracture, and wear. Using molecular dynamics, we simulate the biaxial compression of single-crystal Au, the high-entropy alloy Ni36.67Co30Fe16.67Ti16.67, and amorphous Cu50Zr50 and show that even surfaces of homogeneous materials develop a self-affine structure. By characterizing subsurface deformation, we connect the self-affinity of the surface to the spatial correlation of deformation events occurring within the bulk and present scaling relations for the evolution of roughness with strain. These results open routes toward interpreting and engineering roughness profiles.

2019

1. Correlations of non-affine displacements in metallic glasses through the yield transition

   Richard Jana, and Lars Pastewka

   J. Phys. Mater. 2, 045006 (2019)

   Abstractdoi PDF

   We study correlations of non-affine displacements during simple shear deformation of Cu–Zr bulk metallic glasses in molecular dynamics calculations. In the elastic regime, our calculations show exponential correlation with a decay length that we interpret as the size of a shear transformation zone in the elastic regime. This correlation length becomes system-size dependent beyond the yield transition as our calculation develops a shear band, indicative of a diverging length scale. We discuss these observations in the context of a recent proposition of yield as a first-order phase transition.

2. Glass formation by severe plastic deformation of crystalline Cu|Zr nano-layers

   Suzhi Li, Lars Pastewka, and Peter Gumbsch

   Acta Mater. 165, 577-586 (2019)

   Abstractdoi PDF

   We use molecular dynamics simulation to study the formation of glasses during severe plastic deformation of crystalline Cu\textbarZr nano-layers in a simple shear geometry. The early stage of plasticity is governed by dislocation plasticity. Dislocation-interface interaction induces interface roughening and slow atomic-level intermixing around interfaces. A solid-state crystal-to-amorphous transition starts near the interfaces. At high strain, the interfaces are refined to merge, leading to the formation of an intermixed glassy zone that eventually spans our simulation cell. Dislocation emission is then suppressed and strain is fully accommodated by this glassy phase. We characterize the crystal-to-amorphous transition using local structural measures, such as the pair distribution function and Voronoi analysis. The onset of glass formation occurs at a critical shear strain that increases with layer thickness. Our simulations indicate that the parameter controlling this onset is the theoretical affine interface distance, i.e. the amorphization occurs at a critical value of around 3–4 nm that increases slightly with the increase of layer thickness. Our work provides insights on mechanically driven glass formation in multicomponent systems, as e.g. realized in ball-mills or high-pressure torsion experiments.

3. Linking energy loss in soft adhesion to surface roughness

   Siddhesh Dalvi, Abhijeet Gujrati, Subarna R. Khanal, Lars Pastewka, Ali Dhinojwala, and Tevis D. B. Jacobs

   Proc. Natl. Acad. Sci. U.S.A. 116, 25484-25490 (2019)

   Abstractdoi PDF

   A mechanistic understanding of adhesion in soft materials is critical in the fields of transportation (tires, gaskets, and seals), biomaterials, microcontact printing, and soft robotics. Measurements have long demonstrated that the apparent work of adhesion coming into contact is consistently lower than the intrinsic work of adhesion for the materials, and that there is adhesion hysteresis during separation, commonly explained by viscoelastic dissipation. Still lacking is a quantitative experimentally validated link between adhesion and measured topography. Here, we used in situ measurements of contact size to investigate the adhesion behavior of soft elastic polydimethylsiloxane hemispheres (modulus ranging from 0.7 to 10 MPa) on 4 different polycrystalline diamond substrates with topography characterized across 8 orders of magnitude, including down to the angstrom scale. The results show that the reduction in apparent work of adhesion is equal to the energy required to achieve conformal contact. Further, the energy loss during contact and removal is equal to the product of the intrinsic work of adhesion and the true contact area. These findings provide a simple mechanism to quantitatively link the widely observed adhesion hysteresis to roughness rather than viscoelastic dissipation.

4. Scratching Cu|Au Nanolaminates

   Adrien Gola, and Lars Pastewka

   Lubricants 7, 44 (2019)

   Abstractdoi PDF

   We used molecular dynamics simulations to study the scratching of Cu\textbarAu nanolaminates of 5 nm layer thickness with a nanoscale indenter of 15 nm radius at normal forces between 0.5 μ N and 2 μ N. Our simulations show that Au layers wear quickly while Cu layers are more resistant to wear. Plowing was accompanied by the roughening of the Cu\textbarAu heterointerface that lead to the folding of the nanolaminate structure at the edge of the wear track. Our explorative simulations hint at the complex deformation processes occurring in nanolaminates under tribological load.

5. Structural and elastic properties of amorphous carbon from simulated quenching at low rates

   Richard Jana, Daniele Savio, Volker L Deringer, and Lars Pastewka

   Model. Simul. Mater. Sci. Eng. 27, 085009 (2019)

   Abstractdoi PDF

   We generate representative structural models of amorphous carbon (a-C) from constant-volume quenching from the liquid with subsequent relaxation of internal stresses in molecular dynamics simulations using empirical and machine-learning interatomic potentials. By varying volume and quench rate we generate structures with a range of density and amorphous morphologies. We find that all a-C samples show a universal relationship between hybridization, bulk modulus and density despite having distinctly different cohesive energies. Differences in cohesive energy are traced back to slight changes in the distribution of bond-angles that will likely be linked to thermal stability of these structures.

6. Surface flaws control strain localization in the deformation of Cu|Au nanolaminate pillars

   Adrien Gola, Guang-Ping Zhang, Lars Pastewka, and Ruth Schwaiger

   MRS Comm. 9, 1067-1071 (2019)

   Abstractdoi PDF

   , The authors carried out matched experiments and molecular dynamics simulations of the compression of nanopillars prepared from Cu\textbarAu nanolaminates with up to 25 nm layer thickness. The stress–strain behaviors obtained from both techniques are in excellent agreement. Variation in the layer thickness reveals an increase in the strength with a decreasing layer thickness. Pillars fail through the formation of shear bands whose nucleation they trace back to the existence of surface flaws. This combined approach demonstrates the crucial role of contact geometry in controlling the deformation mode and suggests that modulus-matched nanolaminates should be able to suppress strain localization while maintaining controllable strength.

2018

1. Amorphous nickel nanophases inducing ferromagnetism in equiatomic Ni Ti alloy

   M.R. Chellali, S.H. Nandam, S. Li, M.H. Fawey, E. Moreno-Pineda, L. Velasco, T. Boll, L. Pastewka, R. Kruk, P. Gumbsch, and H. Hahn

   Acta Mater. 161, 47-53 (2018)

   Abstractdoi PDF

   Ni50Ti50 nm-sized amorphous particles are prepared using inert-gas condensation followed by in situ compaction. Elemental segregation of Ni and Ti is observed in the consolidated nanostructured material. Amorphous, nearly pure Nickel (96%) nanophases form within the amorphous Ni50Ti50 alloy. Combining atom probe tomography and scanning transmission electron microscopy with computer modelling, we explore the formation process of such amorphous nanophase structure. It is shown that the Ni rich amorphous phase in the consolidated nanostructured material is responsible for the ferromagnetic behavior of the sample whereas the rapidly quenched amorphous and crystalline samples with the same chemical composition (Ni50Ti50) were found to be paramagnetic. Due to the high cooling rate obtained using the inert gas condensation technique, an exceptional control over the crystallization processes is possible, promoting the formation of various amorphous phases, which are not obtained by standard rapid quenching techniques. Our findings demonstrate the potential of amorphous metallic nanostructures as advanced technological materials, and useful magnetic compounds.

2. Atomic-scale simulation of structure and mechanical properties of Cu1−xAgx|Ni multilayer systems

   Adrien Gola, Peter Gumbsch, and Lars Pastewka

   Acta Mater. 150, 236-247 (2018)

   Abstractdoi PDF

   We use a combination of atom-swap Monte-Carlo (MC) and molecular dynamics (MD) to study the structure and mechanical properties of Cu1−xAgx\textbarNi multilayers with 6 nm layer width for which the Ag-content is used to tune the lattice misfit. We find that the multilayers form a semi-coherent interface with a network of partial dislocations arranged in a regular triangular pattern. A combination of MC and MD was used to equilibrate Cu1−xAgx\textbarNi with x = 0%, 5% and 10%. Ag does not enter the Ni-layer but segregates and precipitates from the Cu layers. We find alloying of Cu and Ni at 600 K. All these findings are in good agreement with the experimental binary phase diagrams of the Cu-Ag, Ag-Ni and Cu-Ni systems. The resulting multilayer structures were then sheared parallel and perpendicular to the normal of the bilayer interface. Initial sliding takes place at the Cu\textbarNi interface within the misfit dislocation network, followed by emission of partial dislocations into the Cu layer. Flow stress increases with increasing Ag content. Additional calculations of biaxial tension that suppress sliding at the heterointerface show a similar trend. Strengthening can be attributed to Ag precipitates pinning the Cu\textbarNi heterointerface and to the formation of sessile stacking-fault tetrahedra from the misfit dislocation network whose density increases with the concentration of Ag in the Cu layer.

3. Characterization of small-scale surface topography using transmission electron microscopy

   Subarna R Khanal, Abhijeet Gujrati, Sai Bharadwaj Vishnubhotla, Pawel Nowakowski, Cecile S Bonifacio, Lars Pastewka, and Tevis D B Jacobs

   Surf. Topogr.: Metrol. Prop. 6, 045004 (2018)

   Abstractdoi PDF

   Multi-scale surface topography is critical to surface function, yet the very smallest scales of topography are not accessible with conventional measurement techniques. Here we demonstrate two separate approaches for measuring small-scale topography in a transmission electron microscope (TEM). The first technique harnesses ‘conventional’ methods for preparation of a TEM cross-section, and presents how these methods may be modified to ensure the preservation of the original surface. The second technique involves the deposition of the material of interest on a pre-fabricated substrate. Both techniques enable the observation and quantification of surface topography with Ångström-scale resolution. Then, using electron energy loss spectroscopy (EELS) to quantify the sample thickness, we demonstrate that there is no systematic effect of thickness on the statistical measurements of roughness. This result was verified using mathematical simulations of artificial surfaces with varying thickness. The proposed explanation is that increasing the side-view thickness of a randomly rough surface may change which specific features are sampled, but does not significantly alter the character (e.g. root-mean-square (RMS) values and power spectral density (PSD)) of the measured topography. Taken together, this work establishes a new approach to topography characterization, which fills in a critical gap in conventional approaches: i.e. the measurement of smallest-scale topography.

4. Chemical aging of large-scale randomly rough frictional contacts

   Zhuohan Li, Lars Pastewka, and Izabela Szlufarska

   Phys. Rev. E 98, 023001 (2018)

   Abstractdoi PDF

   It has been shown that contact aging due to chemical reactions in single asperity contacts can have a significant effect on friction. However, it is currently unknown how chemically induced contact aging of friction depends on roughness that is typically encountered in macroscopic rough contacts. Here we develop an approach that brings together a kinetic Monte Carlo model of chemical aging with a contact mechanics model of rough surfaces based on the boundary element method to determine the magnitude of chemical aging in silica-silica contacts with random roughness. Our multiscale model predicts that chemical aging for randomly rough contacts has a logarithmic dependence on time. It also shows that friction aging switches from a linear to a nonlinear dependence on the applied load as the load increase. We discover that surface roughness affects the aging behavior primarily by modifying the real contact area and the local contact pressure, whereas the effect of contact morphology is relatively small. Our results demonstrate how understanding of chemical aging can be translated from studies of single asperity contacts to macroscopic rough contacts.

5. Combining TEM, AFM, and Profilometry for Quantitative Topography Characterization Across All Scales

   Abhijeet Gujrati, Subarna R. Khanal, Lars Pastewka, and Tevis D. B. Jacobs

   ACS Appl. Mater. Interfaces 10, 29169-29178 (2018)

   Abstractdoi PDF

   Surface roughness affects the functional properties of surfaces, including adhesion, friction, hydrophobicity, biological response, and electrical and thermal transport properties. However, experimental investigations to quantify these links are often inconclusive, because surfaces are fractal-like and the values of measured roughness parameters depend on measurement size. Here we demonstrate the characterization of topography of an ultrananocrystalline diamond (UNCD) surface at the Ångström-scale using transmission electron microscopy (TEM), as well as its combination with conventional techniques to achieve a comprehensive surface description spanning eight orders of magnitude in size. We performed more than 100 individual measurements of the nanodiamond film using both TEM and conventional techniques (stylus profilometry and atomic force microscopy). While individual measurements of root-mean-square (RMS) height, RMS slope, and RMS curvature vary by orders of magnitude, we combine the various techniques using the power spectral density (PSD) and use this to compute scale-independent parameters. This analysis reveals that "smooth" UNCD surfaces have an RMS slope greater than one, even larger than the slope of the Austrian Alps when measured on the scale of a human step. This approach of comprehensive multi-scale roughness characterization, measured with Ångström-scale detail, will enable the systematic evaluation and optimization of other technologically relevant surfaces, as well as systematic testing of the many analytical and numerical models for the behavior of rough surfaces.

6. Computational Surface Chemistry of Tetrahedral Amorphous Carbon by Combining Machine Learning and Density Functional Theory

   Volker L. Deringer, Miguel A. Caro, Richard Jana, Anja Aarva, Stephen R. Elliott, Tomi Laurila, Gábor Csányi, and Lars Pastewka

   Chem. Mater. 30, 7438-7445 (2018)

   Abstractdoi PDF

   Tetrahedral amorphous carbon (ta-C) is widely used for coatings because of its superior mechanical properties and has been suggested as an electrode material for detecting biomolecules. Despite extensive research, however, the complex atomic-scale structures and chemical reactivity of ta-C surfaces are incompletely understood. Here, we combine machine learning, density functional tight binding, and density functional theory simulations to shed new light on this long-standing problem. We make atomistic models of ta-C surfaces, characterize them by local structural fingerprints, and provide a library of structures at different system sizes. We then move beyond the pure element and exemplify how chemical reactivity (hydrogenation and oxidation) can be modeled at the surfaces. Our work opens up new perspectives for modeling the surfaces and interfaces of amorphous solids, which will advance studies of ta-C and other functional materials.

7. Contact mechanics of graphene-covered metal surfaces

   Andreas Klemenz, Adrien Gola, Michael Moseler, and Lars Pastewka

   Appl. Phys. Lett. 112, 061601 (2018)

   Abstractdoi PDF

   We carry out molecular statics simulations of the indentation of bare and graphene-covered Pt (111) surfaces with smooth and rough indenters of radius 1.5 to 10?nm. Our simulations show that the plastic yield of bare surfaces strongly depends on atomic-scale indenter roughness such as terraces or amorphous disorder. Covering surfaces with graphene regularizes this response to the results obtained for ideally smooth indenters. Our results suggest that graphene monolayers and other 2D materials mitigate the effect of roughness, which could be exploited to improve the fidelity of experiments that probe the mechanical properties of interfaces.

8. DPD enables mesoscopic MRI simulation of slow flow

   Mueed Azhar, Suleman Shakil, Andreas Greiner, David Kauzlarić, and Jan G. Korvink

   Microfluid. Nanofluid. 22, 55 (2018)

   Abstractdoi PDF

   We present a novel method to simulate magnetic resonance imaging (MRI) for the assessment of slow flow at Reynolds number Re=0.02. We couple Bloch equations with dissipative particle dynamics (DPD) to study the effect of flow dynamics at the mesoscopic level on acquired MR images. The Bloch equations are used to propagate the evolution of the magnetization of particles while their trajectories are being computed simultaneously based on DPD interaction forces. The magnetic resonance assessment of fluid velocities is performed using a phase-contrast MRI technique, implemented by a spin echo single-sided bipolar gradient sequence. The computational cost for simulating the fluid flow is successfully reduced by an efficient implementation of a vectorized isochromat algorithm. We demonstrate successful simulation of laminar flow, flow with diffusion effects, and flow around an obstacle. The method can be used to simulate convective and diffusive flow MRI experiments at the mesoscopic level.

9. DPD of diffusion-weighted MRI

   M. Azhar, S. Shakil, A. Greiner, D. Kauzlarić, and J.G. Korvink

   Computers & fluids 172, 467-473 (2018)

   Abstractdoi PDF

   Diffusion weighted magnetic resonance imaging (DW-MRI) experiments can be simulated by coupling dissipative particle dynamics (DPD) with Bloch equations. DPD gives hydrodynamics with thermal fluctuations at a well-defined temperature by introducing momentum conserving particle interaction forces and a fluctuation dissipation theorem. The Bloch equations are a set of differential equations that describe the evolution of nuclear magnetization as a function of time. Here we successfully simulate DW-MRI by using the solution of Bloch equations for each DPD particle while computing its trajectories through DPD forces. To this end, a spin echo sequence combined with different diffusion-weighting gradients was implemented and tested for the diffusion of a fluid bound by different diffusion regimes. Fluid confinement was easily incorporated, which enabled investigating different diffusion regimes and the performance of different pulse sequences. The three different sequences applied were: spin echo single-sided bipolar gradient, spin echo two-sided bipolar gradient and spin echo uni-polar gradient; and the three imaged diffusion regimes of interest were: free diffusion, localization and motional narrowing.

10. Embedded atom method potential for studying mechanical properties of binary Cu–Au alloys

    Adrien Gola, and Lars Pastewka

    Model. Simul. Mater. Sci. Eng. 26, 055006 (2018)

    Abstractdoi PDF

    We present an embedded atom method (EAM) potential for the binary Cu–Au system. The unary phases are described by two well-tested unary EAM potentials for Cu and Au. We fitted the interaction between Cu and Au to experimental properties of the binary intermetallic phases Cu3Au, CuAu and CuAu3. Particular attention has been paid to reproducing stacking fault energies in order to obtain a potential suitable for studying deformation in this binary system. The resulting energies, lattice constant, elastic properties and melting points are in good agreement with available experimental data. We use nested sampling to show that our potential reproduces the phase boundaries between intermetallic phases and the disordered face-centered cubic solid solution. We benchmark our potential against four popular Cu–Au EAM parameterizations and densityfunctional theory calculations.

11. Molecular probes reveal deviations from Amontons’ law in multi-asperity frictional contacts

    B. Weber, T. Suhina, T. Junge, L. Pastewka, A. M. Brouwer, and D. Bonn

    Nat. Comm. 9, 888 (2018)

    Abstractdoi PDF

    Amontons’ law defines the friction coefficient as the ratio between friction force and normal force, and assumes that both these forces depend linearly on the real contact area between the two sliding surfaces. However, experimental testing of frictional contact models has proven difficult, because few in situ experiments are able to resolve this real contact area. Here, we present a contact detection method with molecular-level sensitivity. We find that while the friction force is proportional to the real contact area, the real contact area does not increase linearly with normal force. Contact simulations show that this is due to both elastic interactions between asperities on the surface and contact plasticity of the asperities. We reproduce the contact area and fine details of the measured contact geometry by including plastic hardening into the simulations. These new insights will pave the way for a quantitative microscopic understanding of contact mechanics and tribology.

12. Numerical Simulations and Validation of Contact Mechanics in a Granodiorite Fracture

    Tobias Kling, Daniel Vogler, Lars Pastewka, Florian Amann, and Philipp Blum

    Rock Mech. Rock Eng. 51, 2805-2824 (2018)

    Abstractdoi PDF

    Numerous rock engineering applications require a reliable estimation of fracture permeabilities to predict fluid flow and transport processes. Since measurements of fracture properties at great depth are extremely elaborate, representative fracture geometries typically are obtained from outcrops or core drillings. Thus, physically valid numerical approaches are required to compute the actual fracture geometries under in situ stress conditions. Hence, the objective of this study is the validation of a fast Fourier transform (FFT)-based numerical approach for a circular granodiorite fracture considering stress-dependent normal closure. The numerical approach employs both purely elastic and elastic–plastic contact deformation models, which are based on high-resolution fracture scans and representative mechanical properties, which were measured in laboratory experiments. The numerical approaches are validated by comparing the simulated results with uniaxial laboratory tests. The normal stresses applied in the axial direction of the cylindrical specimen vary between 0.25 and 10 MPa. The simulations indicate the best performance for the elastic–plastic model, which fits well with experimentally derived normal closure data (root-mean-squared error = 9 µm). The validity of the elastic–plastic model is emphasized by a more realistic reproduction of aperture distributions, local stresses and contact areas along the fracture. Although there are differences in simulated closure for the elastic and elastic–plastic models, only slight differences in the resulting aperture distributions are observed. In contrast to alternative interpenetration models or analytical models such as the Barton–Bandis models and the “exponential repulsion model”, the numerical simulations reproduce heterogeneous local closure as well as low-contact areas (\textless 2%) even at high normal stresses (10 MPa), which coincides with findings of former experimental studies. Additionally, a relative hardness value of 0.14 for granitic rocks, which defines the general resistance to non-elastic deformation of the contacts, is introduced and successfully applied for the elastic–plastic model.

13. Shear melting of silicon and diamond and the disappearance of the polyamorphic transition under shear

    Gianpietro Moras, Andreas Klemenz, Thomas Reichenbach, Adrien Gola, Hiroshi Uetsuka, Michael Moseler, and Lars Pastewka

    Phys. Rev. Mater. 2, 083601 (2018)

    Abstractdoi PDF

    Molecular dynamics simulations of diamond-cubic silicon and carbon under combined shear and compression show the formation of an amorphous solid with liquidlike structure at room temperature. Consistent with the opposite density changes of the two crystals upon melting, the amorphous material is denser than the crystal in silicon and less dense than the crystal in carbon. As a result, its rate of formation is enhanced by pressure in silicon but suppressed in carbon. These results are particularly unexpected for silicon, whose amorphous structure is supposed to be liquidlike only when hydrostatically compressed above the polyamorphic transition pressure (∼14 GPa). Below this pressure, amorphous silicon is expected to have a low-density structure with density close to that of the diamond-cubic crystal. Our simulations show that this polyamorphic transition disappears under shear and high-density, liquidlike amorphous silicon with metallic ductility forms even at low pressure. These results are potentially transferable to other diamond-cubic crystals, like germanium and ice I_h, and provide insights into nonequilibrium materials transformations that govern friction and wear in tribological systems.

14. The origin of surface microstructure evolution in sliding friction

    Christian Greiner, Zhilong Liu, Reinhard Schneider, Lars Pastewka, and Peter Gumbsch

    Scr. Mater. 153, 63-67 (2018)

    Abstractdoi PDF

    Abstract A typical tribologically induced microstructure displays a discontinuity parallel to the surface separating the near-surface layer from the bulk. Despite its ubiquitous observation, the origin of this layer underneath the surface remains elusive. Here, we show that already after the first loading pass a localized dislocation structure is found at a depth of 100–150 nm. This structure is linked to the inhomogeneous stress field under the moving indenter, where dislocations are trapped when the stress drops below the material’s yield stress. Control of the initial tribological loading could therefore be exploited to design surfaces and materials with superior tribological properties.

2017

1. Meeting the Contact-Mechanics Challenge

   Martin H. Müser, Wolf B. Dapp, Romain Bugnicourt, Philippe Sainsot, Nicolas Lesaffre, Ton A. Lubrecht, Bo N. J. Persson, Kathryn Harris, Alexander Bennett, Kyle Schulze, Sean Rohde, Peter Ifju, W. Gregory Sawyer, Thomas Angelini, Hossein Ashtari Esfahani, Mahmoud Kadkhodaei, Saleh Akbarzadeh, Jiunn-Jong Wu, Georg Vorlaufer, András Vernes, Soheil Solhjoo, Antonis I. Vakis, Robert L. Jackson, Yang Xu, Jeffrey Streator, Amir Rostami, Daniele Dini, Simon Medina, Giuseppe Carbone, Francesco Bottiglione, Luciano Afferrante, Joseph Monti, Lars Pastewka, Mark O. Robbins, and James A. Greenwood

   Tribol. Lett. 65, 118 (2017)

   Abstractdoi PDF

   This paper summarizes the submissions to a recently announced contact-mechanics modeling challenge. The task was to solve a typical, albeit mathematically fully defined problem on the adhesion between nominally flat surfaces. The surface topography of the rough, rigid substrate, the elastic properties of the indenter, as well as the short-range adhesion between indenter and substrate, were specified so that diverse quantities of interest, e.g., the distribution of interfacial stresses at a given load or the mean gap as a function of load, could be computed and compared to a reference solution. Many different solution strategies were pursued, ranging from traditional asperity-based models via Persson theory and brute-force computational approaches, to real-laboratory experiments and all-atom molecular dynamics simulations of a model, in which the original assignment was scaled down to the atomistic scale. While each submission contained satisfying answers for at least a subset of the posed questions, efficiency, versatility, and accuracy differed between methods, the more precise methods being, in general, computationally more complex. The aim of this paper is to provide both theorists and experimentalists with benchmarks to decide which method is the most appropriate for a particular application and to gauge the errors associated with each one.

2. Quantitative characterization of surface topography using spectral analysis

   Tevis D B Jacobs, Till Junge, and Lars Pastewka

   Surf. Topogr.: Metrol. Prop. 5, 013001 (2017)

   Abstractdoi PDF

   Roughness determines many functional properties of surfaces, such as adhesion, friction, and (thermal and electrical) contact conductance. Recent analytical models and simulations enable quantitative prediction of these properties from knowledge of the power spectral density (PSD) of the surface topography. The utility of the PSD is that it contains statistical information that is unbiased by the particular scan size and pixel resolution chosen by the researcher. In this article, we first review the mathematical definition of the PSD, including the one- and two-dimensional cases, and common variations of each. We then discuss strategies for reconstructing an accurate PSD of a surface using topography measurements at different size scales. Finally, we discuss detection and mitigating artifacts at the smallest scales, and how to compute upper/lower bounds on functional properties obtained from models. We accompany our discussion with virtual measurements on computer-generated surfaces. This discussion summarizes how to analyze topography measurements to reconstruct a reliable PSD. Analytical models demonstrate the potential for tuning functional properties by rationally tailoring surface topography - however, this potential can only be achieved through the accurate, quantitative reconstruction of the power spectral density of real-world surfaces.

3. Scale- and load-dependent friction in commensurate sphere-on-flat contacts

   Tristan A. Sharp, Lars Pastewka, Vincent L. Lignères, and Mark O. Robbins

   Phys. Rev. B 96, 155436 (2017)

   Abstractdoi PDF

   Contact of a spherical tip with a flat elastic substrate is simulated with a Green’s-function method that includes atomic structure at the interface while capturing elastic deformation in a semi-infinite substrate. The tip and substrate have identical crystal structures with nearest-neighbor spacing $d$ and are aligned in registry. Purely repulsive interactions between surface atoms lead to a local shear strength that is the local pressure times a constant local friction coefficient $\alpha$. The total friction between tip and substrate is calculated as a function of contact radius $a$ and sphere radius $R$, with $a$ up to ${10}^{3}d$ and $R$ up to $4\times {10}^{4}d$. Three regimes are identified depending on the ratio of $a$ to the core width of edge dislocations in the center of the contact. This ratio is proportional to $\alpha a^2/Rd$. In small contacts, all atoms move coherently and the total friction coefficient $\mu =\alpha$. When the contact radius exceeds the core width, a dislocation nucleates at the edge of the contact and rapidly advances to the center where it annihilates. The friction coefficient falls as $\mu \sim \alpha {(\alpha a^2/Rd)}^{-2/3}$. An array of dislocations forms in very large contacts and the friction is determined by the Peierls stress for dislocation motion. The Peierls stress rises with pressure, and $\mu$ rises with increasing load.

4. The atomic simulation environment—a Python library for working with atoms

   Ask Hjorth Larsen, Jens Jørgen Mortensen, Jakob Blomqvist, Ivano E Castelli, Rune Christensen, Marcin Dułak, Jesper Friis, Michael N Groves, Bjørk Hammer, Cory Hargus, Eric D Hermes, Paul C Jennings, Peter Bjerre Jensen, James Kermode, John R Kitchin, Esben Leonhard Kolsbjerg, Joseph Kubal, Kristen Kaasbjerg, Steen Lysgaard, Jón Bergmann Maronsson, Tristan Maxson, Thomas Olsen, Lars Pastewka, Andrew Peterson, Carsten Rostgaard, Jakob Schiøtz, Ole Schütt, Mikkel Strange, Kristian S Thygesen, Tejs Vegge, Lasse Vilhelmsen, Michael Walter, Zhenhua Zeng, and Karsten W Jacobsen

   J. Phys. Condens. Matter 29, 273002 (2017)

   Abstractdoi PDF

   The atomic simulation environment (ASE) is a software package written in the Python programming language with the aim of setting up, steering, and analyzing atomistic simulations. In ASE, tasks are fully scripted in Python. The powerful syntax of Python combined with the NumPy array library make it possible to perform very complex simulation tasks. For example, a sequence of calculations may be performed with the use of a simple ’for-loop’ construction. Calculations of energy, forces, stresses and other quantities are performed through interfaces to many external electronic structure codes or force fields using a uniform interface. On top of this calculator interface, ASE provides modules for performing many standard simulation tasks such as structure optimization, molecular dynamics, handling of constraints and performing nudged elastic band calculations.

2016

1. Activation and mechanochemical breaking of C–C bonds initiate wear of diamond (110) surfaces in contact with silica

   Anke Peguiron, Gianpietro Moras, Michael Walter, Hiroshi Uetsuka, Lars Pastewka, and Michael Moseler

   Carbon 98, 474-483 (2016)

   Abstractdoi PDF

   Diamond surfaces wear when sliding against silica – a much softer material. Although this plays a major role in chemical mechanical planarization of diamond or machining of rocks, the underlying microscopic mechanisms are hardly understood. Here, the stability of diamond (110) surfaces in sliding contact with amorphous silica and with amorphous silicon (a mechanically similar reference system) is studied by quantum-chemical simulations. Interfacial C–Si bonds with amorphous silicon are too weak to harm diamond (110) surfaces. Conversely, strong C–O and C–Si bonds form between silica and diamond. However, this alone is insufficient to challenge interfacial diamond-like C–C bonds during sliding. Analysis of local forces and electronic structure shows that bonding to silica can chemically activate C–C bonds between terminating carbon zigzag chains and bulk diamond when the zigzag chains stay aromatic. Mechanochemical breaking of these weak bonds and subsequent lifting of C–C–C zigzag units mark the onset of wear on diamond (110) surfaces. This is in contrast to the silicon case, where the higher interfacial bond density renders the diamond surface non-aromatic and diamond-like.

2. Boundary lubrication of heterogeneous surfaces and the onset of cavitation in frictional contacts

   Daniele Savio, Lars Pastewka, and Peter Gumbsch

   Sci. Adv. 2, e1501585 (2016)

   Abstractdoi

   Surfaces can be slippery or sticky depending on surface chemistry and roughness. We demonstrate in atomistic simulations that regular and random slip patterns on a surface lead to pressure excursions within a lubricated contact that increase quadratically with decreasing contact separation. This is captured well by a simple hydrodynamic model including wall slip. We predict with this model that pressure changes for larger length scales and realistic frictional conditions can easily reach cavitation thresholds and significantly change the load-bearing capacity of a contact. Cavitation may therefore be the norm, not the exception, under boundary lubrication conditions.

3. Contact area of rough spheres: Large scale simulations and simple scaling laws

   Lars Pastewka, and Mark O. Robbins

   Appl. Phys. Lett. 108, 221601 (2016)

   Abstractdoi PDF

   We use molecular simulations to study the nonadhesive and adhesive atomic-scale contact of rough spheres with radii ranging from nanometers to micrometers over more than ten orders of magnitude in applied normal load. At the lowest loads, the interfacial mechanics is governed by the contact mechanics of the first asperity that touches. The dependence of contact area on normal force becomes linear at intermediate loads and crosses over to Hertzian at the largest loads. By combining theories for the limiting cases of nominally flat rough surfaces and smooth spheres, we provide parameter-free analytical expressions for contact area over the whole range of loads. Our results establish a range of validity for common approximations that neglect curvature or roughness in modeling objects on scales from atomic force microscope tips to ball bearings.

4. Dissipative particle dynamics of diffusion-NMR requires high Schmidt-numbers

   Mueed Azhar, Andreas Greiner, Jan G. Korvink, and David Kauzlarić

   J. Chem. Phys. 144, 244101 (2016)

   Abstractdoi PDF

   We present an efficient mesoscale model to simulate the diffusion measurement with nuclear magnetic resonance (NMR). On the level of mesoscopic thermal motion of fluid particles, we couple the Bloch equations with dissipative particle dynamics (DPD). Thereby we establish a physically consistent scaling relation between the diffusion constant measured for DPD-particles and the diffusion constant of a real fluid. The latter is based on a splitting into a centre-of-mass contribution represented by DPD, and an internal contribution which is not resolved in the DPD-level of description. As a consequence, simulating the centre-of-mass contribution with DPD requires high Schmidt numbers. After a verification for fundamental pulse sequences, we apply the NMR-DPD method to NMR diffusion measurements of anisotropic fluids, and of fluids restricted by walls of microfluidic channels. For the latter, the free diffusion and the localisation regime are considered.

5. Elasticity limits structural superlubricity in large contacts

   Tristan A. Sharp, Lars Pastewka, and Mark O. Robbins

   Phys. Rev. B 93, 121402 (2016)

   Abstractdoi PDF

   Geometrically imposed force cancellations lead to ultralow friction between rigid incommensurate crystalline asperities. Elastic deformations may avert this cancellation but are difficult to treat analytically in finite and three-dimensional systems. We use atomic-scale simulations to show that elasticity affects the friction only after the contact radius $a$ exceeds a characteristic length set by the core width of interfacial dislocations $b_{\text{core}}$. As $a$ increases past $b_{\text{core}}$, the frictional stress for both incommensurate and commensurate surfaces decreases to a constant value. This plateau corresponds to a Peierls stress that drops exponentially with increasing $b_{\text{core}}$ but remains finite.

6. Molecular Dynamic Simulation of Collision-Induced Third-Body Formation in Hydrogen-Free Diamond-Like Carbon Asperities

   Julian Lautz, Lars Pastewka, Peter Gumbsch, and Michael Moseler

   Tribol. Lett. 63, 26 (2016)

   Abstractdoi PDF

   The collision of two cylindrical hydrogen-free diamond-like carbon (DLC) asperities with approximately 60 % sp³ hybridization has been studied using classical molecular dynamics. The severity of the collision can be controlled by the impact parameter b that measures the width of the projected overlap of the two cylinders. For a cylinder radius of R = 23 nm, three collisions with b = 0.5 nm, b = 1 nm and b = 2.0 nm are compared. While for the two small b a single shear band between the collision partners and a strongly localized sp²/sp¹ hybridised third-body zone between the asperities is observed, the b = 2 nm collision is accompanied by pronounced plastic deformation in both asperities that destabilize the metastable sp³-rich phase leading to a drastic increase in the amount of rehybridized tribomaterial. In addition, pronounced roughening of the cylinder surfaces, asymmetric material transfer and the generation of wear debris are found in this case. For the b = 0.5 and 1 nm collision, the evolution of third-body volume can be quantitatively described by a simple geometric overlap model that assumes a sliding-induced phase transformation localized between both asperities. For b = 2 nm, this model underestimates the third-body volume by more than 150 % indicating that plasticity has to be taken into account in simple geometric models of severe DLC/DLC asperity collisions.

7. Offset-corrected Δ-Kohn-Sham scheme for semiempirical prediction of absolute x-ray photoelectron energies in molecules and solids

   Michael Walter, Michael Moseler, and Lars Pastewka

   Phys. Rev. B 94, 041112 (2016)

   Abstractdoi PDF

   Absolute binding energies of core electrons in molecules and bulk materials can be efficiently calculated by spin paired density-function theory employing a Δ-Kohn-Sham (ΔKS) scheme corrected by offsets that are highly transferable. These offsets depend on core level and atomic species and can be determined by comparing ΔKS energies to experimental molecular x-ray photoelectron spectra. We demonstrate the correct prediction of absolute and relative binding energies on a wide range of molecules, metals, and insulators.

8. Reibung unter Zugzwang

   Lars Pastewka

   Phys. J. 15, 16–17 (2016)

2015

1. Energy filtering transmission electron microscopy and atomistic simulations of tribo-induced hybridization change of nanocrystalline diamond coating

   M.I. De Barros Bouchet, C. Matta, B. Vacher, Th. Le-Mogne, J.M. Martin, J. Lautz, T. Ma, L. Pastewka, J. Otschik, P. Gumbsch, and M. Moseler

   Carbon 87, 317-329 (2015)

   Abstractdoi PDF

   The tribofilm formed on nanocrystalline diamond coating during ultralow friction in presence of water and glycerol lubrication has been studied experimentally by energy filtering transmission electron microscopy (EF-TEM) and electron energy loss spectroscopy (EELS) on focus ion beam (FIB) cross sections. Surprisingly, even under mild tribological conditions, a tribo-induced hybridization change (sp³ towards sp²) can be clearly detected at the top of the coating resulting in the formation of a 40 nm thick amorphous sp² rich carbon layer with embedded diamond nanoparticles less than 5 nm diameter. Classical molecular dynamics simulations of diamond single crystal asperity collisions can explain this finding. Tribochemical amorphization of the contact zone between the colliding diamond grains followed by fracture events at the asperity shoulders produces ultra-nanodiamonds that remain attached to the amorphous carbon phase. An additional atomistic sliding simulation of two ultra-nanocrystalline diamond coatings yields an amorphous sp² rich carbon layer that grows at a rate that is comparable to corresponding layers on the softest diamond single crystal surfaces.

2. Low Speed Crack Propagation via Kink Formation and Advance on the Silicon (110) Cleavage Plane

   James R. Kermode, Anna Gleizer, Guy Kovel, Lars Pastewka, Gábor Csányi, Dov Sherman, and Alessandro De Vita

   Phys. Rev. Lett. 115, 135501 (2015)

   Abstractdoi PDF

   We present density functional theory based atomistic calculations predicting that slow fracturing of silicon is possible at any chosen crack propagation speed under suitable temperature and load conditions. We also present experiments demonstrating fracture propagation on the Si(110) cleavage plane in the ∼100 m/s speed range, consistent with our predictions. These results suggest that many other brittle crystals could be broken arbitrarily slowly in controlled experiments.

2014

1. A hydro-kinetic scheme for the dynamics of hydrogen bonds in water-like fluids

   Nasrollah Moradi, Andreas Greiner, Simone Melchionna, Francesco Rao, and Sauro Succi

   Phys. Chem. Chem. Phys. 16, 15510 (2014)

   Abstractdoi PDF

   A hydro-kinetic scheme for water-like fluids, based on a lattice version of the Boltzmann equation, is presented and applied to the popular TIP3P model of liquid water. By proceeding in much larger steps than molecular dynamics, the scheme proves to be very effective in attaining global minima of classical pair potentials with directional and radial interactions, as confirmed by further simulations using the three-dimensional Ben-Naim water potential. The scheme is shown to reproduce the propensity of water to form nearly four hydrogen bonds per molecule, as well as their statistical distribution in the presence of thermal fluctuations, at a linear cost of computational time with the system size.

2. Atomic Scale Mechanisms of Friction Reduction and Wear Protection by Graphene

   Andreas Klemenz, Lars Pastewka, S. G. Balakrishna, Arnaud Caron, Roland Bennewitz, and Michael Moseler

   Nano Lett. 14, 7145-7152 (2014)

   Abstractdoi PDF

   We study nanoindentation and scratching of graphene-covered Pt(111) surfaces in computer simulations and experiments. We find elastic response at low load, plastic deformation of Pt below the graphene at intermediate load, and eventual rupture of the graphene at high load. Friction remains low in the first two regimes, but jumps to values also found for bare Pt(111) surfaces upon graphene rupture. While graphene substantially enhances the load carrying capacity of the Pt substrate, the substrate’s intrinsic hardness and friction are recovered upon graphene rupture.

3. Contact between rough surfaces and a criterion for macroscopic adhesion

   Lars Pastewka, and Mark O. Robbins

   Proc. Natl. Acad. Sci. U.S.A. 111, 3298-3303 (2014)

   Abstractdoi PDF

   At the molecular scale, there are strong attractive interactions between surfaces, yet few macroscopic surfaces are sticky. Extensive simulations of contact by adhesive surfaces with roughness on nanometer to micrometer scales are used to determine how roughness reduces the area where atoms contact and thus weakens adhesion. The material properties, adhesive strength, and roughness parameters are varied by orders of magnitude. In all cases, the area of atomic contact is initially proportional to the load. The prefactor rises linearly with adhesive strength for weak attractions. Above a threshold adhesive strength, the prefactor changes sign, the surfaces become sticky, and a finite force is required to separate them. A parameter-free analytic theory is presented that describes changes in these numerical results over up to five orders of magnitude in load. It relates the threshold adhesive strength to roughness and material properties, explaining why most macroscopic surfaces do not stick. The numerical results are qualitatively and quantitatively inconsistent with classical theories based on the Greenwood-Williamson approach that neglect the range of adhesion and do not include asperity interactions.

4. Lattice Boltzmann modeling of water-like fluids

   Sauro Succi, Nasrollah Moradi, Andreas Greiner, and Simone Melchionna

   Front. Physics 2, 00022 (2014)

   Abstractdoi

   We review recent advances on the mesoscopic modeling of water-like fluids, based on the lattice Boltzmann (LB) methodology. The main idea is to enrich the basic LB (hydro)-dynamics with angular degrees of freedom responding to suitable directional potentials between water-like molecules. The model is shown to reproduce some microscopic features of liquid water, such as an average number of hydrogen bonds per molecules (HBs) between 3 and 4, as well as a qualitatively correct statistics of the hydrogen bond angle as a function of the temperature. Future developments, based on the coupling the present water-like LB model with the dynamics of suspended bodies, such as biopolymers, may open new angles of attack to the simulation of complex biofluidic problems, such as protein folding and aggregation, and the motion of large biomolecules in complex cellular environments.

5. SYMPLER: SYMbolic ParticLE simulatoR with grid-computing interface

   David Kauzlarić, Marek Dynowski, Lars Pastewka, Andreas Greiner, and Jan G. Korvink

   Comput. Phys. Commun. 185, 1085-1099 (2014)

   Abstractdoi PDF

   We present the main design concepts of the object-oriented particle dynamics code SYMPLER. With this freely available software, simulations can be performed ranging from microscopic classical molecular dynamics up to the Lagrangian particle-based discretisation of macroscopic continuum mechanics equations. We show how the runtime definition of arbitrary degrees of freedom and of arbitrary equations of motion allows for modular and symbolic computation with high flexibility. Arbitrary symbolic expressions for inter-particle forces can be defined as well as fluxes of arbitrarily many additional scalar, vectorial or tensorial degrees of freedom. The integration in a high performance grid computing environment makes huge geographically distributed computational resources accessible to the software by an easy-to-use interface.

6. Surface passivation and boundary lubrication of self-mated tetrahedral amorphous carbon asperities under extreme tribological conditions

   Pedro A. Romero, Lars Pastewka, Julian Von Lautz, and Michael Moseler

   Friction 2, 193-208 (2014)

   Abstractdoi PDF

   Tetrahedral amorphous carbon coatings have the potential to significantly reduce friction and wear between sliding components. Here, we provide atomistic insights into the evolution of the sliding interface between naked and hydrogen-passivated ta-C sliding partners under dry and lubricated conditions. Using reactive classical atomistic simulations we show that sliding induces a sp³ to sp² rehybridization and that the shear resistance is reduced by hydrogen-passivation and hexadecane-lubrication—despite our finding that nanoscale hexadecane layers are not always able to separate and protect ta-C counter surfaces during sliding. As asperities deform, carbon atoms within the hexadecane lubricant bind to the ta-C sliding partners resulting in degradation of the hexadecane molecules and in increased material intermixing at the sliding interface. Hydrogen atoms from the passivation layer and from the hexadecane chains continue to be mixed within a sp² rich sliding interface eventually generating a tribo-layer that resembles an a-C:H type of material. Upon separation of the sliding partners, the tribo-couple splits within the newly formed sp² rich a-C:H mixed layer with significant material transfer across the sliding partners. This leaves behind a-C:H coated ta-C surfaces with dangling C bonds, linear C chains and hydrocarbon fragments.

7. Wear, Plasticity, and Rehybridization in Tetrahedral Amorphous Carbon

   Tim Kunze, Matthias Posselt, Sibylle Gemming, Gotthard Seifert, Andrew R. Konicek, Robert W. Carpick, Lars Pastewka, and Michael Moseler

   Tribol. Lett. 53, 119-126 (2014)

   Abstractdoi PDF

   Wear in self-mated tetrahedral amorphous carbon (ta-C) films is studied by molecular dynamics and near-edge X-ray absorption fine structure spectroscopy. Both theory and experiment demonstrate the formation of a soft amorphous carbon (a-C) layer with increased sp² content, which grows faster than an a-C tribolayer found on self-mated diamond sliding under similar conditions. The faster sp³→sp² transition in ta-C is explained by easy breaking of prestressed bonds in a finite, nanoscale ta-C region, whereas diamond amorphization occurs at an atomically sharp interface. A detailed analysis of the underlying rehybridization mechanism reveals that the sp³→sp² transition is triggered by plasticity in the adjacent a-C. Rehybridization therefore occurs in a region that has not yet experienced plastic yield. The resulting soft a-C tribolayer is interpreted as a precursor to the experimentally observed wear.

2013

1. Adaptive molecular decomposition: Large-scale quantum chemistry for liquids

   Tommi T. Järvi, Leonhard Mayrhofer, Jussi Polvi, Kai Nordlund, Lars Pastewka, and Michael Moseler

   J. Chem. Phys. 138, 104108 (2013)

   Abstractdoi PDF

   We present a linear-scaling method based on self-consistent charge non-orthogonal tight-binding. Linear scaling is achieved using a many-body expansion, which is adjusted dynamically to the instantaneous molecular configuration of a liquid. The method is capable of simulating liquids over large length and time scales, and also handles reactions correctly. Benchmarking on typical carbonate electrolytes used in Li-ion batteries displays excellent agreement with results from full tight-binding calculations. The decomposition slightly breaks the Hellmann-Feynman theorem, which is demonstrated by application to water. However, an additional correction also enables dynamical simulation in this case.

2. Comment on “Friction Between a Viscoelastic Body and a Rigid Surface with Random Self-Affine Roughness”

   Iakov A Lyashenko, Lars Pastewka, and Bo Nils Johan Persson

   Phys. Rev. Lett. 111, 189401 (2013)

   Abstractdoi PDF

   A Comment on the Letter by Q. Li, M. Popov, A. Dimaki, A.E. Filippov, S. Kürschner, and V.L. Popov, Phys. Rev. Lett. 111, 034301 (2013). The authors of the Letter offer a Reply.

3. Experimental and Numerical Atomistic Investigation of the Third Body Formation Process in Dry Tungsten/Tungsten-Carbide Tribo Couples

   Pantcho Stoyanov, Pedro A. Romero, Tommi T. Järvi, Lars Pastewka, Matthias Scherge, Priska Stemmer, Alfons Fischer, Martin Dienwiebel, and Michael Moseler

   Tribol. Lett. 50, 67-80 (2013)

   Abstractdoi PDF

   The third body in tungsten/tungsten-carbide sliding systems is studied using a combination of experiments and atomistic simulations. Ex situ X-ray photoelectron spectroscopy and focused ion beam analysis of the structural and chemical changes near the surfaces reveals that sliding of tungsten against tungsten-carbide results in plastic deformation of the W surface, leading to grain refinement, and the formation of a mechanically mixed amorphous layer on the WC counter body. Molecular dynamics simulations of W/WC sliding couples exhibit the formation of a nanoscale amorphous W/WC interface. The infrequent occurrence of atomic jamming events in the interface resulted in the emission of dislocations into the W bulk and the generation of amorphous shear bands in the WC counter body in agreement with the different third bodies observed in W and WC after the experiments.

4. Finite-size scaling in the interfacial stiffness of rough elastic contacts

   Lars Pastewka, Nikolay Prodanov, Boris Lorenz, Martin H. Müser, Mark O. Robbins, and Bo N. J. Persson

   Phys. Rev. E 87, 062809 (2013)

   Abstractdoi PDF

   The total elastic stiffness of two contacting bodies with a microscopically rough interface has an interfacial contribution K that is entirely attributable to surface roughness. A quantitative understanding of K is important because it can dominate the total mechanical response and because it is proportional to the interfacial contributions to electrical and thermal conductivity in continuum theory. Numerical simulations of the dependence of K on the applied squeezing pressure p are presented for nominally flat elastic solids with a range of surface roughnesses. Over a wide range of p, K rises linearly with p. Sublinear power-law scaling is observed at small p, but the simulations reveal that this is a finite-size effect. We derive accurate, analytical expressions for the exponents and prefactors of this low-pressure scaling of K by extending the contact mechanics theory of Persson to systems of finite size. In agreement with our simulations, these expressions show that the onset of the low-pressure scaling regime moves to lower pressure as the system size increases.

5. Lattice Boltzmann implementation of the three-dimensional Ben-Naim potential for water-like fluids

   Nasrollah Moradi, Andreas Greiner, Francesco Rao, and Sauro Succi

   J. Chem. Phys. 138, 124105 (2013)

   Abstractdoi PDF

   We develop a three-dimensional lattice Boltzmann (LB) model accounting for directional interactions between water-like molecules, based on the so-called Ben-Naim (BN) potential [A. Ben-Naim, Molecular Theory of Water and Aqueous Solutions: Part I: Understanding Water (World Scientific Publishing Company, 2010); A. Ben-Naim, “Statistical mechanics of ‘waterlike’ particles in two dimensions. I. Physical model and application of the Percus-Yevick equation,” J. Chem. Phys. 54, 3682 (1971)]10.1063/1.1675414. The water-like molecules are represented by rigid tetrahedra, with two donors and two acceptors at the corners and interacting with neighboring tetrahedra, sitting on the nodes of a regular lattice. The tetrahedra are free to rotate about their centers under the drive of the torque arising from the interparticle potential. The orientations of the water molecules are evolved in time via an overdamped Langevin dynamics for the torque, which is solved by means of a quaternion technique. The resulting advection-diffusion-reaction equation for the quaternion components is solved by a LB method, acting as a dynamic minimizer for the global energy of the fluid. By adding thermal fluctuations to the torque equation, the model is shown to reproduce some microscopic features of real water, such as an average number of hydrogen bonds per molecules (HBs) between 3 and 4, in a qualitative agreement with microscopic water models. Albeit slower than a standard LB solver for ordinary fluids, the present scheme opens up potentially far-reaching scenarios for multiscale applications based on a coarse-grained representation of the water solvent.

6. Li+ adsorption at prismatic graphite surfaces enhances interlayer cohesion

   Lars Pastewka, Sami Malola, Michael Moseler, and Pekka Koskinen

   J. Power Sources 239, 321-325 (2013)

   Abstractdoi PDF

   We use density functional calculations to determine the binding sites and binding energies of Li⁺ at graphene edges and prismatic graphite surfaces. Binding is favorable at bare and carbonyl terminated surfaces, but not favorable at hydrogen terminated surfaces. These findings have implications for the exfoliation of graphitic anodes in lithium-ion batteries that happens if solute and solvent co-intercalate. First, specific adsorption facilitates desolvation of Li⁺. Second, chemisorption lowers the surface energy by about 1 J m⁻² prismatic surface area, and gives graphite additional stability against exfoliation. The results offer an explanation for experiments that consistently show exfoliation for hydrogenated graphite, but show no exfoliation for oxygenated graphite.

7. Lithium Chalcogenidotetrelates: LiChT—Synthesis and Characterization of New Li⁺ Ion Conducting Li/Sn/Se Compounds

   Thomas Kaib, Philipp Bron, Sima Haddadpour, Leonhard Mayrhofer, Lars Pastewka, Tommi T. Järvi, Michael Moseler, Bernhard Roling, and Stefanie Dehnen

   Chem. Mater. 25, 2961-2969 (2013)

   Abstractdoi PDF

   Five new lithium chalcogenidotetrelates, so-called “LiChT” phases, with the elemental combination Li/Sn/Se, Li₄[SnSe₄] (1), ¹_∞Li₂[SnSe₃] (2), and the respective solvates Li₄[SnSe₄]·13H₂O (3), Li₄[Sn₂Se₆]·14H₂O (4), and Li₄[SnSe₄]·16MeOH (5) were generated in single-crystalline form. We present and discuss syntheses, crystal structures, spectroscopic and thermal behavior, as well as Li+ ion conducting properties of the phases that represent uncommon Li⁺ ion conducting materials with a maximum conductivity found for 1 (σ_20°C = 2 × 10^–5 S·cm^–1, σ_100°C = 9 × 10^–4 S·cm^–1). The latter was elucidated via impedance spectroscopy and further studied by electronic structure calculations, revealing vacancy migration as the dominant Li⁺ transport mechanism. Thus, studies on a selenido-LISICON family were found to be a very interesting starting point for an extension of the LISICON-related solid state lithium ion conductors (SSLIC).

8. Markovian equations of motion for non-Markovian coarse-graining and properties for graphene blobs

   D Kauzlarić, J T Meier, P Español, A Greiner, and S Succi

   New J. Phys. 15, 125015 (2013)

   Abstractdoi PDF

   We obtain Markovian equations of motion for a many body system of interacting coarse-grained (CG) variables and additional fluxes. The investigated CG variables belong to the special family of linear combinations of atomistic degrees of freedom. The system of Markovian equations of motion approximates Mori’s exact non-Markovian generalized Langevin equation and is easy to solve by computer simulation. All parameters of the equations can be obtained from equilibrium molecular dynamics simulations of the investigated microscopic system. These parameters are either equal to the famous static covariances from Mori’s continued fraction or they represent generalized constant friction matrices. We propose two different ways to compute these friction matrices based on Mori’s continued fraction. Finally, some of the parameters are computed numerically for the special case of centre of mass variables in the graphene lattice and it is found that the CG variables interact with their additional fluxes in a spatially very local way.

9. Molecular Dynamics Simulations of Nanoparticle Interactions with a Planar Wall: Does Shape Matter?

   Andreas Fuchs, David Kauzlarić, Andreas Greiner, Sauro Succi, and Jan. G. Korvink

   Commun. Comput. Phys. 13, 900-915 (2013)

   Abstractdoi

   We investigate the hydrodynamic interactions of spherical colloidal nano particles and nano tetrahedra near a planar wall by means of molecular dynamics (MD) simulations of rigid particles within an all-atom solvent. For both spherical and nano-tetrahedral particles, we find that the parallel and perpendicular components of the local diffusion coefficient and viscosity, show good agreement with hydrodynamic theory of Faxén and Brenner. This provides further evidence that low perturbations from sphericality of a nanoparticle’s shape has little influence on its local diffusive behaviour, and that for this particular case, the continuum theory fluid dynamics is valid even down to molecular scales.

10. On the Validity of the Method of Reduction of Dimensionality: Area of Contact, Average Interfacial Separation and Contact Stiffness

    I. A. Lyashenko, Lars Pastewka, and Bo N. J. Persson

    Tribol. Lett. 52, 223-229 (2013)

    Abstractdoi PDF

    It has recently been suggested that many contact mechanics problems between solids can be accurately studied by mapping the problem on an effective one-dimensional (1D) elastic foundation model. Using this 1D mapping, we calculate the contact area and the average interfacial separation between elastic solids with nominally flat but randomly rough surfaces. We show, by comparison to exact numerical results, that the 1D mapping method fails even qualitatively. We also calculate the normal interfacial stiffness K and compare it with the result of an analytic study. We attribute the failure of the elastic foundation model to the incorrect treatment of the long-range elastic coupling between the asperity contact regions.

11. SPH based optimization of electrowetting-driven digital microfluidics with advanced actuation patterns

    Dennis Weiß, Andreas Greiner, Jan Lienemann, and Jan G. Korvink

    Int. J. Mod. Phys. C 24, 1340012 (2013)

    Abstractdoi PDF

    Fast and thorough mixing is a crucial operation of digital microfluidic devices, where discrete and small fluid portions are moved and processed. In this paper, we want to analyze and to optimize the mixing process by substituting conventional motion and superposing oscillatory and translational modes. An accurate multiphase smoothed particle hydrodynamics (SPH) discretization for incompressible flow is instantiated. Different harmonic excitation patterns for the solid–liquid surface energy are applied and their influence on droplet mode shapes, formation of eddies and the Shannon entropy of droplet fluid components are measured. We tailor enhanced actuation patterns which improve mixing grade and reduce mixing time.

12. Screened empirical bond-order potentials for Si-C

    Lars Pastewka, Andreas Klemenz, Peter Gumbsch, and Michael Moseler

    Phys. Rev. B 87, 205410 (2013)

    Abstractdoi PDF

    Typical empirical bond-order potentials are short ranged and give ductile instead of brittle behavior for materials such as crystalline silicon or diamond. Screening functions can be used to increase the range of these potentials. We outline a general procedure to combine screening functions with bond-order potentials that does not require refitting any of the potential’s properties. We use this approach to modify J. Tersoff’s [Phys. Rev. B 39, 5566 (1989)], P. Erhart and K. Albe’s [Phys. Rev. B 71, 35211 (2005)], and T. Kumagai et al.’s [Comput. Mater. Sci. 39, 457 (2007)] Si, C, and Si-C potentials. The resulting potential formulations correctly reproduce brittle materials’ response and give an improved description of amorphous phases.

2012

1. Bond order potentials for fracture, wear, and plasticity

   Lars Pastewka, Matous Mrovec, Michael Moseler, and Peter Gumbsch

   MRS Bull. 37, 493-503 (2012)

   Abstractdoi

   Coulson’s bond order is a chemically intuitive quantity that measures the difference in the occupation of bonding and anti-bonding orbitals. Both empirical and rigorously derived bond order expressions have evolved in the course of time and proven very useful for atomistic modeling of materials. The latest generation of empirical formulations has recently been augmented by screening-function approaches. Using friction and wear of diamond and diamond-like carbon as examples, we demonstrate that such a screened bond order scheme allows for a faithful description of dynamical bond-breaking processes in materials far from equilibrium. The rigorous bond order expansions are obtained by systematic coarse-graining of the tight binding approximation and form a bridge between the electronic structure and the atomistic modeling hierarchies. They have enabled bottom-up derivations of bond order potentials for covalently bonded semiconductors, transition metals, and multicomponent intermetallics. The recently developed magnetic bond order potential gives a correct description of both directional covalent bonds and magnetic interactions in iron and is able to correctly predict the stability of bulk Fe polymorphs as well as the intricate properties of dislocation cores. The bond order schemes hence represent a family of reliable and powerful models that can be applied in large-scale simulations of complex processes involving fracture, wear, and plasticity.

2. Insight into the micro scale dynamics of a micro fluidic wetting-based conveying system by particle based simulation

   Jan Lienemann, Dennis Weiß, Andreas Greiner, David Kauzlaric, Oliver Grünert, and Jan G. Korvink

   Microsyst. Technol. 18, 523-530 (2012)

   Abstractdoi PDF

   We simulate a microfluidic conveying system using the many-body dissipative particle dynamics method (MDPD). The conveying system can transport micro parts to a specified spot on a surface by letting them float inside or on top of a droplet, which is pumped by changing the wetting behaviour of the substrate, e.g., with electrowetting on dielectrics. Subsequent evaporation removes the fluid; the micro part remains on its final position, where a second substrate can pick it up. In this way, the wetting control can be separate from the final device substrate. The MDPD method represents a fluid by particles, which are interpreted as a coarse graining of the fluid’s molecules. The choice of interaction forces allows for free surfaces. To introduce a contact angle model, non-moving particles beyond the substrate interact with the fluid particles by MDPD forces such that the required contact angle emerges. The micro part is simulated by particles with spring-type interaction forces.

3. Markovian dissipative coarse grained molecular dynamics for a simple 2D graphene model

   David Kauzlarić, Pep Español, Andreas Greiner, and Sauro Succi

   J. Chem. Phys. 137, 234103 (2012)

   Abstractdoi PDF

   Based upon a finite-element “coarse-grained molecular dynamics” (CGMD) procedure, as applied to a simple atomistic 2D model of graphene, we formulate a new coarse-grained model for graphene mechanics explicitly accounting for dissipative effects. It is shown that, within the Mori-projection operator formalism, the reversible part of the dynamics is equivalent to the finite temperature CGMD-equations of motion, and that dissipative contributions to CGMD can also be included within the Mori formalism. The CGMD nodal momenta in the present graphene model display clear non-Markovian behavior, a property that can be ascribed to the fact that the CGMD-weighting function suppresses high-frequency modes more effectively than, e.g., a simple center of mass (COM) based CG procedure. The present coarse-grained graphene model is also shown to reproduce the short time behavior of the momentum correlation functions more accurately than COM-variables and it is less dissipative than COM-CG. Finally, we find that, while the intermediate time scale represented directly by the CGMD variables shows a clear non-Markovian dynamics, the macroscopic dynamics of normal modes can be approximated by a Markovian dissipation, with friction coefficients scaling like the square of the wave vector. This opens the way to the development of a CGMD model capable of describing the correct long time behavior of such macroscopic normal modes.

4. Seamless elastic boundaries for atomistic calculations

   Lars Pastewka, Tristan A. Sharp, and Mark O. Robbins

   Phys. Rev. B 86, 075459 (2012)

   Abstractdoi PDF

   Modeling interfacial phenomena often requires both a detailed atomistic description of surface interactions and accurate calculations of long-range deformations in the substrate. The latter can be efficiently obtained using an elastic Green’s function if substrate deformations are small. We present a general formulation for rapidly computing the Green’s function for a planar surface given the interatomic interactions, and then coupling the Green’s function to explicit atoms. The approach is fast, avoids ghost forces, and is not limited to nearest-neighbor interactions. The full system comprising explicit interfacial atoms and an elastic substrate is described by a single Hamiltonian and interactions in the substrate are treated exactly up to harmonic order. This concurrent multiscale coupling provides simple, seamless elastic boundary conditions for atomistic simulations where near-surface deformations occur, such as nanoindentation, contact, friction, or fracture. Applications to surface relaxation and contact are used to test and illustrate the approach.

2011

1. A Low-Cost Electromagnetic Generator for Vibration Energy Harvesting

   Emmanuel Bouendeu, Andreas Greiner, Patrick J. Smith, and Jan G. Korvink

   IEEE Sensors J. 11, 107-113 (2011)

   Abstractdoi PDF

   This paper reports on a low-cost high-performance generator, which is based on a hybrid approach that uses polymethyl methalcrylate and electrodeposited foil to convert mechanical vibration into electrical power based on Faraday’s law of magnetic induction. The generator is equipped with four wire-wound micro-coils that can be used separately or connected together depending on the voltage and electrical power requirement of the application. The fabricated generator which has a harvester effectiveness of 55.5% was able to supply a 500-Ω load with 422 μW of electrical power. Investigations have revealed that the utilization factor of the mechanical resonator can be used as an indicator of the lifetime of the generator with respect to fatigue analysis. The reported generator weighs only 12.7 g and is a good candidate for applications where lightweight generators are important.

2. A non-local extension of the Phillips model for shear induced particle migration

   D. Kauzlarić, A. Greiner, and J. G. Korvink

   Microsyst. Technol. 17, 265-272 (2011)

   Abstractdoi PDF

   We present a simple and natural extension of Phillips’ model (Phillips in Phys Fluids A 4(1):30–40, 1992) for shear induced particle migration in concentrated suspensions. It is based on considering an effective deformation rate as it is experienced by a solid particle of finite size. In this way the solid fraction does not converge anymore to the maximum packing in the centre of Poiseuille-like flows where the deformation rate vanishes, and the steady state concentration profile becomes dependent on the particle diameter a. In addition, the migration rate in the extended model scales with aⁿ, where 2 < n < 3 in contrast to the strict a 2-scaling of the original Phillips-model.

3. Anisotropic mechanical amorphization drives wear in diamond

   Lars Pastewka, Stefan Moser, Peter Gumbsch, and Michael Moseler

   Nat. Mater. 10, 34-38 (2011)

   Abstractdoi PDF

   Diamond is the hardest material on Earth1. Nevertheless, polishing diamond is possible with a process that has remained unaltered for centuries and is still used for jewellery and coatings: the diamond is pressed against a rotating disc with embedded diamond grit2. When polishing polycrystalline diamond, surface topographies become non-uniform because wear rates depend on crystal orientations3. This anisotropy is not fully understood4 and impedes diamond’s widespread use in applications that require planar polycrystalline films, ranging from cutting tools5 to confinement fusion6. Here, we use molecular dynamics to show that polished diamond undergoes an sp3–sp2 order–disorder transition resulting in an amorphous adlayer with a growth rate that strongly depends on surface orientation and sliding direction, in excellent correlation with experimental wear rates7. This anisotropy originates in mechanically steered dissociation of individual crystal bonds8. Similarly to other planarization processes9, the diamond surface is chemically activated by mechanical means. Final removal of the amorphous interlayer proceeds either mechanically or through etching by ambient oxygen.

4. Bottom-up coarse-graining of a simple graphene model: The blob picture

   David Kauzlarić, Julia T. Meier, Pep Español, Sauro Succi, Andreas Greiner, and Jan G. Korvink

   J. Chem. Phys. 134, 064106 (2011)

   Abstractdoi PDF

   The coarse-graining of a simple all-atom 2D microscopic model of graphene, in terms of “blobs” described by center of mass variables, is presented. The equations of motion of the coarse-grained variables take the form of dissipative particle dynamics (DPD). The coarse-grained conservative forces and the friction of the DPD model are obtained via a bottom-up procedure from molecular dynamics (MD) simulations. The separation of timescales for blobs of 24 and 96 carbon atoms is sufficiently pronounced for the Markovian assumption, inherent to the DPD model, to provide satisfactory results. In particular, the MD velocity autocorrelation function of the blobs is well reproduced by the DPD model, provided that the effect of friction and noise is taken into account. However, DPD cross-correlations between neighbor blobs show appreciable discrepancies with respect to the MD results. Possible extensions to mend these discrepancies are briefly outlined.

5. Charge-transfer model for carbonaceous electrodes in polar environments

   Lars Pastewka, Tommi T. Järvi, Leonhard Mayrhofer, and Michael Moseler

   Phys. Rev. B 83, 165418 (2011)

   Abstractdoi PDF

   A realistic treatment of metallic and semimetallic systems in polar environments requires an explicit treatment of charges induced into the metallic surface. In classical electrostatics, a metallic surface is properly described if the electric field perpendicular to the surface vanishes. For nanoscale materials, however, charge screening is imperfect because the nanoscale object’s surface density of states is finite. Here, we demonstrate that from quantum considerations a classical mean-field charge-transfer model can be extracted, which is demonstrated for graphene and metallic single-wall carbon nanotubes. The model is easily parametrized and gives an approximate description of the binding of point charges on these structures. Potential applications include the modeling of charged or fully biased nanoscale systems in a polar environment, which we demonstrate by simulating a water droplet in a biased graphene nanocapacitor at a fraction of the computational cost of a fully quantum-mechanical treatment.

6. Constrained simulations of flow in haemodynamic devices: towards a computational assistance of magnetic resonance imaging measurements

   Iva Cenova, David Kauzlarić, Andreas Greiner, and Jan G. Korvink

   Phil. Trans. R. Soc. A. 369, 2494-2501 (2011)

   Abstractdoi PDF

   Cardiovascular diseases, mostly related to atherosclerosis, are the major cause of death in industrial countries. It is observed that blood flow dynamics play an important role in the aetiology of atherosclerosis. Especially, the blood velocity distribution is an important indicator for predisposition regions. Today magnetic resonance imaging (MRI) delivers, in addition to the morphology of the cardiovascular system, blood flow patterns. However, the spatial resolution of the data is slightly less than 1 mm and owing to severe restrictions in magnetic field gradient switching frequencies and intensities, this limit will be very hard to overcome. In this paper, constrained fluid dynamics is applied within the smoothed particle hydrodynamics formalism to enhance the MRI flow data. On the one hand, constraints based on the known volumetric flow rate are applied. They prove the plausibility of the order of magnitude of the measurements. On the other hand, the higher resolution of the simulation allows one to determine in detail the flow field between the coarse data points and thus to improve their spatial resolution.

7. Design Synthesis of Electromagnetic Vibration-Driven Energy Generators Using a Variational Formulation

   Emmanuel Bouendeu, Andreas Greiner, Patrick J. Smith, and Jan G. Korvink

   J. Microelectromech. Syst. 20, 466-475 (2011)

   Abstractdoi PDF

   This paper reports upon the design of electromagnetic vibration-driven energy generators using a variational formulation to derive the equation of motion of such generators, thereby gaining insight into the device physics. Using this approach, the characteristics of the generator are analytically studied, a newly developed optimization theory of the generator is derived, and a guide for the sizing process is described. A fabricated prototype of an electromagnetic vibration harvester is presented. For the fabrication of the prototype, printed circuit board materials and PMMA have been used to lower the cost and to achieve lightweight device. Analytical and experimental results are presented and compared. The fabricated harvester weighs 7 g, delivers 315 μW at optimum excitation parameters at room temperature, and has a mechanical damping ratio of 0.0186. Experimental and analytical results show good agreement with the newly developed optimization theory. An analytical expression of the optimum load resistance is also developed and validated with experimental results, which show the frequency dependence of the optimum load resistance. It is also demonstrated that the optimization process needs two iterations if the mechanical damping ratio is unknown at the start of development and that the coil parameters represent the degree of freedom of the designer.

8. Design of high stroke electrostatic micropumps: a charge control approach with ring electrodes

   Emanuele Bertarelli, Alberto Corigliano, Andreas Greiner, and Jan G. Korvink

   Microsyst. Technol. 17, 165-173 (2011)

   Abstractdoi PDF

   A novel design strategy to avoid pull-in occurrence in electrostatic micro electro mechanical systems is proposed. It combines charge control with ring electrodes, on a circular geometry. This idea is introduced here for the design of efficient and reliable high stroke electrostatic diaphragm micropumps, while it has a broad potential applicability. A minimal lumped one degree-of-freedom model is derived and used to introduce and demonstrate the proposed approach for a circular plate geometry. Finite element models are subsequently adopted for a more detailed device modelling. As expected, charge control exhibits a stabilizing effect with respect to voltage drive, but not sufficient to achieve a full-range stability for the considered geometry. When the electrode area is properly defined, stability range can be extended up to gap closure in the central part of the membrane. In this configuration, the increase in voltage required for full-range device drive would be relevant, while in charge control the penalty is considerably lower. Finally, loading conditions and geometrical parameters for an optimized actuation are suggested.

9. Formation and Oxidation of Linear Carbon Chains and Their Role in the Wear of Carbon Materials

   Gianpietro Moras, Lars Pastewka, Peter Gumbsch, and Michael Moseler

   Tribol. Lett. 44, 355-365 (2011)

   Abstractdoi PDF

   The atomic-scale processes taking place during the sliding of diamond and diamond-like carbon surfaces are investigated using classical molecular dynamics simulations. During the initial sliding stage, diamond surfaces undergo an amorphization process, while an sp³ to sp² conversion takes place in tetrahedral amorphous carbon (ta-C) and amorphous hydrocarbon (a-C:H) surface layers. Upon separation of the sliding samples, the interface fails. A rather smooth failure occurs for a-C:H, where the hydrogen atoms present in the bulk passivate the chemically active carbon dangling bonds. Conversely, sp-hybridized carbon chains are observed to form on diamond and ta-C surfaces. These carbynoid structures are known to undergo a fast degradation process when in contact with oxygen. Using quantum-accurate density functional theory simulations, we present a possible mechanism for the oxygen-induced degradation of the carbon chains, leading to oxidative wear of the sp phase on diamond and ta-C surfaces upon exposure to air. Oxygen molecules chemisorb on C–C bonds of the chains, triggering the cleavage of the chains through concerted O–O and C–C bond-breaking reactions. A similar reaction caused by adsorption of water molecules on the carbon chains is ruled out on energetic grounds. Further O₂ adsorption causes the progressive shortening of the resulting, O-terminated, chain fragments through the same O–O and C–C bond breaking mechanism accompanied by the formation of CO₂ molecules.

10. Parameter preserving model order reduction for MEMS applications

    U. Baur, P. Benner, A. Greiner, J.G. Korvink, J. Lienemann, and C. Moosmann

    Math. Comput. Model. Dyn. Syst. 17, 297-317 (2011)

    Abstractdoi PDF

    Model order reduction techniques are known to work reliably for finite element-type simulations of micro-electro-mechanical systems devices. These techniques can tremendously shorten computational times for transient and harmonic analyses. However, standard model reduction techniques cannot be applied if the equation system incorporates time-varying matrices or parameters that are to be preserved for the reduced model. However, design cycles often involve parameter modification, which should remain possible also in the reduced model. In this article we demonstrate a novel parameterization method to numerically construct highly accurate parametric ordinary differential equation systems based on a small number of systems with different parameter settings. This method is demonstrated to parameterize the geometry of a model of a micro-gyroscope, where the relative error introduced by the parameterization lies in the region of . We also present recent developments on semi-automatic order reduction methods that can preserve scalar parameters or functions during the reduction process. The first approach is based on a multivariate Padé-type expansion. The second approach is a coupling of the balanced truncation method for model order reduction of (deterministic) linear, time-invariant systems with interpolation. The approach is quite flexible in allowing the use of numerous interpolation techniques like polynomial, Hermite, rational, sinc and spline interpolation. As technical examples we investigate a micro anemometer as well as the gyroscope. Speed-up factors of 20–80 could be achieved, while retaining up to six parameters and keeping typical relative errors below 1%.

11. Progressive Shortening of sp-Hybridized Carbon Chains through Oxygen-Induced Cleavage

    Gianpietro Moras, Lars Pastewka, Michael Walter, Johann Schnagl, Peter Gumbsch, and Michael Moseler

    J. Phys. Chem. C 115, 24653-24661 (2011)

    Abstractdoi PDF

    Linear sp-hybridized carbon chains have recently been proposed as one-dimensional nanostructures for electronic applications and as intermediate products in many nanoscale processes. However, their synthesis and observation are affected by their degradation upon oxygen exposure. Carbon chains consisting of alternating single and triple bonds (polyynic) are reported to be more stable than those consisting of double bonds (cumulenic), but the details of the degradation mechanism are still unknown. We use density functional theory to show that adsorption of O2 on carbon chains anchored to carbon substrates can cause their cleavage through the collective scission of O–O and C–C bonds, yielding separate CO-terminated chains. Further O2 attack progressively shortens them, causing CO2 formation. While the shortening process has general validity, the cleavage step of the reaction is exothermic for cumulenic chains only. Perturbations of the ideal structure, such as bending of the chains or modifications to the structure of their termination, affect the oxidation mechanism and can make the cleavage reaction exothermic for polyynic chains as well. These results contribute to the interpretation of the available experimental results and reveal atomic-scale details of the oxidation process, thus allowing predictions on the chemistry of nanostructured carbon surfaces and suggesting possible new directions for the study of the chemical stability of carbynoid structures.

12. Revised periodic boundary conditions: Fundamentals, electrostatics, and the tight-binding approximation

    Oleg O. Kit, Lars Pastewka, and Pekka Koskinen

    Phys. Rev. B 84, 155431 (2011)

    Abstractdoi PDF

    Many nanostructures today are low-dimensional and flimsy, and therefore get easily distorted. Distortion-induced symmetry breaking makes conventional, translation-periodic simulations invalid, which has triggered developments for new methods. Revised periodic boundary conditions (RPBC) is a simple method that enables simulations of complex material distortions, either classically or quantum mechanically. The mathematical details of this easy-to-implement approach, however, have not been discussed before. Therefore, in this paper, we summarize the underlying theory, present the practical details of RPBC, especially related to a nonorthogonal tight-binding formulation, discuss selected features, electrostatics in particular, and suggest some examples of usage. We hope this article can give more insight into RPBC, and it will help and inspire new software implementations capable of exploring the physics and chemistry of distorted nanomaterials.

13. Simulation of micro powder injection moulding: Powder segregation and yield stress effects during form filling

    Andreas Greiner, David Kauzlarić, Jan G. Korvink, Richard Heldele, Michael Schulz, Volker Piotter, Thomas Hanemann, Oxana Weber, and Jürgen Haußelt

    J. Eur. Ceram. Soc. 31, 2525-2534 (2011)

    Abstractdoi PDF

    We report on our development of a computational tool for the simulation of micro powder injection moulding (micro-PIM) based on a description of the fluid flow by the smoothed particle hydrodynamics (SPH) method. The feedstocks used in micro-PIM expose rather complicated rheological features. Insertion of appropriate material models is discussed, as, e.g., the yield stress behaviour. Insight is gained into the moulding process through simulation of the injection into a bending specimen with an obstacle in the flow as an example. The effect of shear induced migration is shown to be reproduced and compared to the segregation phenomena arising in experimental findings.

14. Smoothed particle hydrodynamics simulation of shear-induced powder migration in injection moulding

    David Kauzlarić, Lars Pastewka, Hagen Meyer, Richard Heldele, Michael Schulz, Oxana Weber, Volker Piotter, Jürgen Hausselt, Andreas Greiner, and Jan G. Korvink

    Phil. Trans. R. Soc. A 369, 2320-2328 (2011)

    Abstractdoi PDF

    We present the application of the smoothed particle hydrodynamics (SPH) discretization scheme to Phillips’ model for shear-induced particle migration in concentrated suspensions. This model provides an evolution equation for the scalar mean volume fraction of idealized spherical solid particles of equal diameter which is discretized by the SPH formalism. In order to obtain a discrete evolution equation with exact conservation properties we treat in fact the occupied volume of the solid particles as the degree of freedom for the fluid particles. We present simulation results in two- and three-dimensional channel flow. The two-dimensional results serve as a verification by a comparison to analytic solutions. The three-dimensional results are used for a comparison with experimental measurements obtained from computer tomography of injection moulded ceramic microparts. We observe the best agreement of measurements with snapshots of the transient simulation for a ratio D(c)/D(η)=0.1 of the two model parameters.

15. Smoothed particle hydrodynamics-based numerical investigation on sessile, oscillating droplets

    Dennis Weiß, Jan Lienemann, Andreas Greiner, David Kauzlarić, and Jan G. Korvink

    Phil. Trans. R. Soc. A. 369, 2565-2573 (2011)

    Abstractdoi PDF

    Forced oscillations in sessile droplets can be exploited in electrowetting mixing of fluid fractions. The necessary complex flows and large shape deformations require a numerical investigation of fluid dynamics in the transient regime. We provide a means to characterize oscillations qualitatively and quantitatively with the goal to examine and to classify flow patterns occurring inside. A superposition of different harmonic excitation patterns gives the possibility to control the convective flow. In this investigation, we apply a generic and accurate multi-phase smoothed particle hydrodynamics model to a two-dimensional three-phase flow and consider an oscillating droplet sitting on a substrate and immersed in a fluidic phase. These vibrations are investigated in two ways: the analysis of a step response due to an abrupt change of the contact angle is applied to identify the resonance frequencies. Secondly, the time evolution of the shape of the droplet in terms of harmonic functions is determined. Their amplitudes are examined in the time and frequency domain. This gives the possibility to relate resonance frequencies to mode shapes and to detect a coupling between them. Our approach is successfully applied to different numerical case studies.

16. Three Routes to the Friction Matrix and Their Application to the Coarse-Graining of Atomic Lattices

    David Kauzlarić, Pep Español, Andreas Greiner, and Sauro Succi

    Macromol. Theory Simul. 20, 526-540 (2011)

    Abstractdoi PDF

    The calculation of the friction matrix in the coarse-grained (CG) description of an atomistic system is a crucial issue, in order to properly account for the dissipative effects inherent to any reduced representation of the atomistic dynamics. Within the Mori-Zwanzig projection operator approach to CG, there are several possibilities for the definition of the friction matrix, depending on the projector that is being used. In this paper, the connection of two of these projectors (Mori’s and Zwanzig’s) is discussed and the corresponding merits and limitations are analysed. Moreover, three different ways of computing the friction matrix in the Mori’s framework are presented, along with a discussion of their mutual connections. By the example of CG centre of mass blob variables in the graphene lattice, it is shown that, even though the three approaches are equivalent from a theoretical viewpoint, they may differ considerably in terms of practical implementation for computer simulation purposes. In the given example, which is representative for atomic lattices, it turns out that a linear regression of the velocity–velocity correlation function, inspired by the Einstein–Helfand approach, is the least error-prone against disturbances from optical modes.

2010

1. Atomistic Insights into the Running-in, Lubrication, and Failure of Hydrogenated Diamond-Like Carbon Coatings

   Lars Pastewka, Stefan Moser, and Michael Moseler

   Tribol. Lett. 39, 49-61 (2010)

   Abstractdoi PDF

   The tribological performance of hydrogenated diamond-like carbon (DLC) coatings is studied by molecular dynamics simulations employing a screened reactive bond-order potential that has been adjusted to reliably describe bond-breaking under shear. Two types of DLC films are grown by CH2 deposition on an amorphous substrate with 45 and 60 eV impact energy resulting in 45 and 30% H content as well as 50 and 30% sp3 hybridization of the final films, respectively. By combining two equivalent realizations for both impact energies, a hydrogen-depleted and a hydrogen-rich tribo-contact is formed and studied for a realistic sliding speed of 20 m s−1 and loads of 1 and 5 GPa. While the hydrogen-rich system shows a pronounced drop of the friction coefficient for both loads, the hydrogen-depleted system exhibits such kind of running-in for 1 GPa, only. Chemical passivation of the DLC/DLC interface explains this running-in behavior. Fluctuations in the friction coefficient occurring at the higher load can be traced back to a cold welding of the DLC/DLC tribo-surfaces, leading to the formation of a transfer film (transferred from one DLC partner to the other) and the establishment of a new tribo-interface with a low friction coefficient. The presence of a hexadecane lubricant leads to low friction coefficients without any running-in for low loads. At 10 GPa load, the lubricant starts to degenerate resulting in enhanced friction.

2. Molecular dynamics simulation of gold solid film lubrication

   Lars Pastewka, Joël Peguiron, Peter Gumbsch, and Michael Moseler

   Int. J. Mater. Res. 101, 981-988 (2010)

   Abstractdoi PDF

   The lubrication mechanisms in ultrathin solid gold films confined between two rough nickel surfaces have been investigated employing classical molecular dynamics with a second moment tight-binding potential. Three types of nickel surfaces are considered: Ni(111), Ni(001) single- and an Ni(001) - (111) bicrystal. In all three systems, gold layers that have been quenched from the melt organise in (111) layers parallel to the nickel interfaces. The relative sliding of the two single crystal nickel tribopartners requires a shear stress of around 170 MPa - a value that is almost one order of magnitude lower than the ideal plastic shear stress of single crystal bulk gold. This reduced stress can be explained by a misfit dislocation mechanism in a single plane close to the Ni/Au interface. In the case of the Ni(001) - (111) bicrystal, the nickel grain boundaries induce grain boundaries in the quenched gold film which vanish during sliding. During subsequent sliding the nickel grain boundaries act as nucleation centres for dislocation loops leading to an increased shear stress of 490 MPa. The same is observed for an embedded hydrocarbon impurity. Also here dislocation loops are emitted on (111) planes that are tilted with respect to the sliding plane.

2009

1. A factorized central moment lattice Boltzmann method

   M. Geier, A. Greiner, and J. G. Korvink

   Eur. Phys. J. Spec. Top. 171, 55-61 (2009)

   Abstractdoi PDF

   We determine appropriate attractors for higher than third-order central moments for the relaxation process in three-dimensional lattice Boltzmann methods. It was previously assumed that the appropriate attractors for the relaxation of these moments were their equilibria values as derived from a Maxwell-Boltzmann distribution. However, when the attractor for fourth-order central moments is derived that way, the solution of three-dimensional lattice Boltzmann differs significantly from the analytical solution of the Navier-Stokes equation for simple test cases like Poiseuille flow. We show that the Navier-Stokes solution is recovered when we chose products of low order central moments as the attractors of the higher order central moments.

2. Bubble functions for the lattice Boltzmann method and their application to grid refinement

   M. Geier, A. Greiner, and J. G. Korvink

   Eur. Phys. J. Spec. Top. 171, 173-179 (2009)

   Abstractdoi PDF

   We present a new methodology of velocity field interpolation for the lattice Boltzmann method. The local information on spatial velocity gradients stored in the nodal momentum distribution function is exploited. We achieve quadratic interpolation order between neighboring nodes. Second-order bubble functions are derived from which the off-grid velocity field can be computed. A simple grid-refinement technique based on the bubble functions is introduced.

3. Surface amorphization, sputter rate, and intrinsic stresses of silicon during low energy Ga+ focused-ion beam milling

   Lars Pastewka, Roland Salzer, Andreas Graff, Frank Altmann, and Michael Moseler

   Nucl. Instrum. Meth. B 267, 3072-3075 (2009)

   Abstractdoi PDF

   Transmission electron microscopy (TEM) is a standard technique to characterize microelectronic device structures. As structures shrink to the nanoscale, surface damage produced by focused ion beam (FIB) sample preparation destroying the region of interest and degrading the resolution of TEM images becomes increasingly a problem. The thickness of the damaged layer at the sidewalls of a prepared cross section is around 20–30 nm for silicon at typical beam energies of 30 keV. In order to reduce these artifacts to a minimum low beam energies have been proposed for FIB polishing. We use a combination of molecular dynamics simulations and experiments to assess the influence of the focused ion beam on the surface structure of silicon for beam energies ranging from 1–5 keV and a grazing angle of 10° typically used in low voltage FIB polishing. Under these conditions, the thickness of the amorphous layer depends linearly on the beam energy. Intrinsic surface stresses introduced by FIB are always tensile and of a magnitude of around 1 GPa.

4. Understanding the microscopic processes that govern the charge-induced deformation of carbon nanotubes

   Lars Pastewka, Pekka Koskinen, Christian Elsässer, and Michael Moseler

   Phys. Rev. B 80, 155428 (2009)

   Abstractdoi PDF

   While carbon nanotubes have technological potential as actuators, the underlying actuation mechanisms remain poorly understood. We calculate charge-induced stresses and strains for electrochemical actuation of carbon nanotubes with different chiralities and defects, using density-functional theory and various tight-binding models. For a given deformation mode the concept of bonding and antibonding orbitals can be redefined depending on the sign of a differential band-structure stress. We use this theoretical framework to analyze orbital contributions to the actuation. These show charge asymmetric behavior which is due to next-nearest-neighbor hopping while Coulombic contributions account for approximately charge-symmetric isotropic deformations. In the typical case of a (10,10) tube strains around 0.1% with 1 nN force along the tube axis are obtained. Defects and functional groups have negligible influence on the actuation. In multiwall tubes we find charge inversion on the inner tubes due to Friedel-type oscillations which could lead to a slight magnification of charge-induced strains. Finally, we consider photoactuation of nanotubes and predict that transitions between van-Hove singularities can be expected to expand the tubes.

2008

1. A dissipative particle dynamics model of carbon nanotubes

   Orly Liba, David Kauzlarić, Zeév R. Abrams, Yael Hanein, Andreas Greiner, and Jan G. Korvink

   Mol. Sim. 34, 737-748 (2008)

   Abstractdoi PDF

   A mesoscale dissipative particle dynamics model of single wall carbon nanotubes (CNTs) is designed and demonstrated. The coarse-grained model is produced by grouping together carbon atoms and by bonding the new lumped particles through pair and triplet forces. The mechanical properties of the simulated tube are determined by the bonding forces, which are derived by virtual experiments. Through the introduction of van der Waals interactions, tube–tube interactions were studied. Owing to the reduced number of particles, this model allows the simulation of relatively large systems. The applicability of the presented scheme to model CNT based mechanical devices is discussed.

2. Describing bond-breaking processes by reactive potentials: Importance of an environment-dependent interaction range

   Lars Pastewka, Pablo Pou, Rubén Pérez, Peter Gumbsch, and Michael Moseler

   Phys. Rev. B 78, 161402 (2008)

   Abstractdoi PDF

   First nearest-neighbor models are routinely used for atomistic modeling of covalent materials. Neighbors are usually determined by looking for atoms within a fixed interaction range. While these models provide a faithful description of material properties near equilibrium, the limited interaction range introduces problems in heterogeneous environments and when bond-breaking processes are of concern. We demonstrate in this Rapid Communication that the reliability of reactive bond-order potentials is substantially improved by using an environment-dependent first nearest-neighbor definition.

3. Integrated process simulation of primary shaping: multi scale approaches

   D. Kauzlarić, J. Lienemann, L. Pastewka, A. Greiner, and J. G. Korvink

   Microsyst. Technol. 14, 1789-1796 (2008)

   Abstractdoi PDF

   Abstract{&}nbsp;{&}nbsp;We investigate simulation approaches for the modelling of the primary shaping processes micro powder injection moulding and micro casting. We could reproduce the segregation during micro powder injection moulding (MicroPIM) with a simulation using particle methods. The phase field method allows for accurate prediction of the dynamics of solidification of a melt, whereby model order reduction is used to limit the computational effort. The results give valuable advice for the process conduct and the dimensioning of the micro parts.

4. Investigation of the Dynamic Behavior of Bridged Nanotube Resonators by Dissipative Particle Dynamics Simulation

   Orly Liba, Yael Hanein, David Kauzlaric, Andreas Greiner, and Jan G. Korvink

   Int. J. Mult. Comp. Eng. 6, 549-562 (2008)

   Abstractdoi PDF

   Carbon nanotube (CNT)-based bridged resonators are investigated using a mesoscale dissipative particle dynamics model. Owing to their nanometer size, low mass, and ultrahigh resonance frequency, CNT-based resonators have the potential to become excellent tension, strain, or mass sensors. In this report, the resonance frequency of tubes of different lengths and in different states of tension is extracted from the numerical results and shown to fit with continuum elastic theory. Since in many cases, CNTs are produced slacked rather than taut, the effect of slackness on the resonance frequencies is presented and shown to reduce the sensitivity of the resonator considerably. According to our simulations, temperature has a major effect on the resonance frequencies and should be considered when analyzing bridged resonators. The investigation includes measurements of the vibration amplitude at different temperature, tube length, and strain. The intrinsic quality factor of carbon nanotube resonators is also discussed. Finally, the simulations presented here show that the dissipative particle dynamics model is suited to describe CNT devices such as resonator-based sensors.

5. Model Order Reduction for Circuit Level Simulation of RF MEMS Frequency Selective Devices

   L. Del Tin, A. Greiner, and J. G. Korvink

   Sen. Lett. 6, 1-8 (2008)

   Abstractdoi

   The development of complex radio frequency circuits with integrated micromechanical devices requires the availability of tools for predictive design, optimization and verification of the complete system. In this paper, a methodology towards this goal is proposed. It enables the extraction of non-linear low order models of vibrating micromechanical devices suitable for use in a standard circuit level simulator. The reduction of the complexity of the model is achieved by using moment matching model order reduction, together with an approximated lumped description of the electrostatic forces. In this way, both high simulation accuracy and low computational complexity are obtained.

6. The running-in of amorphous hydrocarbon tribocoatings: a comparison between experiment and molecular dynamics simulations

   L. Pastewka, S. Moser, M. Moseler, B. Blug, S. Meier, T. Hollstein, and P. Gumbsch

   Int. J. Mater. Res. 99, 1136-1143 (2008)

   Abstractdoi PDF

   Amorphous hydrocarbon (a-C:H) films have enormous potential as low friction, wear resistant coatings. Here, we present a plasma assisted chemical vapour deposition process for a-C:H that exhibits growth rates of 100 nm min^–1 and higher. The tribological performance of the resulting a-C:H films has been studied experimentally by reciprocating sliding of an a-C:H-coated Si₃N₄ ball on an a-C:H-coated 100Cr6 steel substrate and by subsequent micro Raman spectroscopy of the wear track. Running-in of the coatings is observed and characterised by a rapid decrease in the friction coefficient accompanied by a significant increase in sp² hybridisation in the wear track. In order to gain a deeper understanding of the underlying running-in mechanisms, the sliding of two a-C:H films under a load of 5 GPa has been studied by classical molecular dynamics employing a range-corrected Brenner bond-order potential. The simulations reproduce the experimental trends and explain the running-in by a combination of smoothing and chemical passivation of both tribosurfaces. Consequently, both mechanisms should be controlled in order to produce tribological coatings for applications with optimum energy-efficiency.

2007

1. Properties of the cascaded lattice Boltzmann automaton

   Martin Geier, Andreas Greiner, and Jan G. Korvink

   Int. J. Mod. Phys. C 18, 455-462 (2007)

   Abstractdoi PDF

   The theory of the lattice Boltzmann automaton is based on a moment transform which is not Galilean invariant. It is explained how the central moments transform, used in the cascaded lattice Boltzmann method, overcomes this problem by choosing the center of mass coordinate system as the frame of reference. Galilean invariance is restored and the form of the kinetic theory is unaffected. Conservation laws are not compromised by the high order polyinomials in the equilibrium distribution arising from the central moment transform. Two sources of instabilities in lattice Boltzmann simulations are discussed: negative numerical viscosity due to insufficient Galilean invariance and aliasing. The cascaded lattice Boltzmann automaton overcomes both problems. It is discussed why aliasing is unavoidable in lattice Boltzmann methods that rely on a single relaxation time. An appendix lists the complete scattering operator of the D2Q9 cascaded lattice Boltzmann automaton.

2006

1. A Bottom-up approach to Grid-Computing at a University: the Black-Forest-Grid Initiative

   R. Backofen, H.-G. Borrmann, W. Deck, A. Dedner, L. De Raedt, K. Desch, M. Diesmann, M. Geier, A. Greiner, W. R. Hess, J. Honerkamp, St. Jankowski, I. Krossing, A. W. Liehr, A. Karwath, R. Klöfkorn, R. Pesché, T. Potjans, M. C. Röttger, L. Schmidt-Thieme, G. Schneider, B. Voß, B. Wiebelt, P. Wienemann, and V.-H. Winterer

   PIK - Praxis der Informationsverarbeitung und Kommunikation 29, 81-87 (2006)

   Abstractdoi PDF

   Recent years have seen a rapid increase in the need for highperformance computing. These demands come from disciplines such as particle physics traditionally relying on High Performance Computing (HPC) but lately also from the various branches of life science that have matured into quantitative disciplines. The classical infrastructure of university computer centres results to be unsuited to cope with the new requirements for a multitude of reasons. Here we discuss the causes of this failure and present a solution developed at the University of Freiburg in a collaborative effort of several faculties. We demonstrate that using state of the art grid computing technology the problem can now be addressed in a bottom-up approach. The organizational, technical, and financial components of our framework, the Black Forest Grid Initiative (BFG) are described and results of its implementation are presented. In the process, a number of new questions have emerged which the next phase of our project needs to address.

2. Cascaded digital lattice Boltzmann automata for high Reynolds number flow

   Martin Geier, Andreas Greiner, and Jan G. Korvink

   Phys. Rev. E 73, 066705 (2006)

   Abstractdoi PDF

   Lattice Boltzmann methods are of limited applicability for direct numerical simulation of turbulent flow due to instabilities in the zero viscosity limit. We observe that this is caused by an insufficient degree of Galilean invariance of the relaxation-type Lattice Boltzmann collision operator. The cascaded digital lattice Boltzmann automata described here, provides a method with which to achieve stable collision operators down to the limit of zero viscosity.

3. Modeling, Simulation, and Optimization of Electrowetting

   J. Lienemann, A. Greiner, and J.G. Korvink

   IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 25, 234-247 (2006)

   Abstractdoi PDF

   Electrowetting is an elegant method to realize the motion, dispensing, splitting, and mixing of single droplets in a microfluidic system without the need for any mechanical—and fault-prone—components. By only applying an electric voltage, the interfacial energy of the fluid–solid interface is altered and the contact line of the droplet is changed. However, since the droplet shape is usually heavily distorted, it is difficult to estimate the droplet shape during the process. Further, it is often necessary to know if a process, e.g., droplet splitting on a given geometry, is possible at all, and what can be done to increase the system’s reliability. It is thus important to use computer simulations to gain an understanding about the behavior of a droplet for a given electrode geometry and voltage curve. Special care must be exercised when considering surface-tension effects. We present computer simulations done with the Surface Evolver program and a template library combined with a graphical user interface (GUI) that facilitates standard tasks in the simulation of electrowetting arrays.

4. Read-out concepts for multiplexed bead-based fluorescence immunoassays on centrifugal microfluidic platforms

   L. Riegger, M. Grumann, T. Nann, J. Riegler, O. Ehlert, W. Bessler, K. Mittenbuehler, G. Urban, L. Pastewka, T. Brenner, R. Zengerle, and J. Ducrée

   Sens. Actuat. A-Phys. 126, 455-462 (2006)

   Abstractdoi PDF

   We present novel concepts to process and read out multiplexed, bead-based fluorescence immunoassays. At the start of the read-out process, a statistically arranged monolayer of color-encoded beads is aggregated in a detection chamber. Each bead is first identified by incorporated color tags which are either dyes or luminescing quantum dots (QDs). Subsequently, the reaction-specific fluorescence signal is quantified. The read-out process is accelerated by an in-house-developed image-processing algorithm. The optical read-out device consists of standard components, e.g. a color CCD-camera as detection unit, an LED as light source, optical filters, and a drive to spin the polymer disk. The liquid handling along the complete assay protocol is realized on a centrifugal lab-on-a-disk platform. We successfully demonstrate the performance of this device by the implementation of a hepatitis A and a tetanus assay. (C) 2005 Elsevier B.V. All rights reserved.

5. Thermostat with a local heat-bath coupling for exact energy conservation in dissipative particle dynamics

   Lars Pastewka, David Kauzlarić, Andreas Greiner, and Jan G. Korvink

   Phys. Rev. E 73, 037701 (2006)

   Abstractdoi PDF

   We present a Markov process which models particle hydrodynamics with conservation of the first three momenta. This is achieved by extending the [Peters, Europhys. Lett. 66, 311 (2004)] and [Lowe, Europhys. Lett. 47, 145 (1999)] method to incorporate energy conservation. The equivalence of the energy conserving Peters method and dissipative particle dynamics with energy conservation (DPDE) in the limit of a vanishing time step is shown. Simple numerical experiments clearly demonstrate the applicability of the methods. This overcomes current limitations of DPDE in the study of complex fluids in the (N,V,E) ensemble.

2004

1. Avoiding spurious velocity overshoots in hydrodynamic simulations of deep submicron devices by a physical modelling of heat transport

   L Varani, C Palermo, J C Vaissiere, A Greiner, and L Reggiani

   Semicond. Sci. Technol. 19, S142-S144 (2004)

   Abstractdoi

   We show that spurious peaks in velocity profiles emerging from hydrodynamic simulators of submicron n⁺nn⁺ Si structures are washed out by using a field-dependent thermal conductivity calculated within a correlation function formalism.

2. Capacitance, induced charges, and bound states of biased carbon nanotube systems

   Pawel Pomorski, Lars Pastewka, Christopher Roland, Hong Guo, and Jian Wang

   Phys. Rev. B 69, 115418 (2004)

   Abstractdoi PDF

   Although it has long been known that the classical notions of capacitance need modification at the nanoscale, in order to account for important quantum effects, very few first-principles investigations of these properties exist for any real material systems. Here we present the results of a large-scale ab initio investigation of the capacitance properties of carbon nanotube systems. The simulations are based on a recently developed real-space nonequilibrium Green’s-function approach, with special attention being paid to the treatment of the bound states present in the system. In addition, use has been made of a symmetry decomposition scheme for the charge density. This is needed both to speed up the calculations and in order to study the origins of the induced charges. Specific systems investigated include two and three nested nanotube shells, the insertion of a capped nanotube into another, a connected (12,0)/(6,6) nanotube junction, and the properties of a nanotube acting as a probe over a flat aluminum surface. First-principles estimates of the capacitance matrix coefficients for all these systems are provided, along with a discussion of the quantum corrections. For the case of the nanotube junction, the numerical value of the capacitance is sufficiently high, as to be useful for future device applications.

2003

1. Modeling, Simulation, and Experimentation of a Promising New Packaging Technology: Parallel Fluidic Self-Assembly of Microdevices

   J. Lienemann, A. Greiner, J. G. Korvink, X. Xiong, Y. Hanein, and K. F. Böhringer

   Sensors Update 13, 3-43 (2003)

   Abstractdoi

   The parallel fluidic self-assembly of microdevices is a new technology that promises to speed up the production of complex microsystems made up of many separate parts. The technology brings many advantages. First, it enables a mix of chipmaking technologies for each of the component parts, with each technology selected for its particular technical or financial benefits. Second, it eliminates the need for pick-and-place assembly that would unnecessarily slow down any manual assembly technique. Third, it enables massively parallel assembly, almost independent of the number of parts involved, and thereby mimics the elegant parallelism inherent in microchip circuit manufacture. In this chapter we explore this new technology with the ultimate goal of discovering the practical limits for its practical use in manufacturing real microsystems. The driving force of the assembly process is interface surface tension, and our approach is to find the simplest models that correctly describe the attachment, orientation, and bonding of parts to a suitably prepared substrate. We follow both an analytical and a numerical approach in describing the surface tension effects, the latter mainly to gain geometrical generality, and we couple modeling and simulation with suitable laboratory experiments. The ultimate goal of this work is to find practical design rules with which to select bond site geometries and the properties of participating liquids, and to find practical tolerances for all required geometrical and rheological parameters. This chapter extensively documents all results found to date, and carefully cites other work in this area.

2001

1. Numerical Offset Optimization of Magnetic Field Sensor Microsystems (Numerische Offsetverminderung in Magnetfeld-Mikrosensoren)

   J.G. Korvink, A. Greiner, and J. Lienemann

   tm - Technisches Messen 68, 298 (2001)

   Abstractdoi PDF

   This paper rewievs the modeling of magnetic field sensor microsystems with respect to the origins of offsets. We cover the modeling of silicon-based semiconductor Hall sensors in an inhomogeneous magnetic field, including 3D transport effects. In particular we discuss the automatic geometric optimization of sensor devices. The optimization strategy achieves offset reduction with simultaneous maximazation of device sensitivity. The topology optimization method changes the conductivity of a Hall plate locally, converging to an optimum conduction geometry. After showing representative results, we discuss currently available commercial and experimental software tools and their capabilities.

2000

1. Carrier kinetics from the diffusive to the ballistic regime: linear response near thermodynamic equilibrium

   Andreas Greiner, Lino Reggiani, Tilmann Kuhn, and Luca Varani

   Semicond. Sci. Technol. 15, 1071-1081 (2000)

   Abstractdoi

   We present a general formalism for the calculation of correlation functions (CFs) for transport processes through ultra-small structures based on a Wigner function representation. Linear response coefficients are obtained from the CFs at thermal equilibrium. The formalism is applied to a finite conductor in three, two and one dimensions, where we study the transition from diffusive to ballistic regimes for non-degenerate and degenerate conditions. Analytical expressions are given for the limiting cases. Electrical and thermal conductances are expressed in terms of characteristic time- and lengthscales, which are the scattering time and the mean free path in the diffusive regime as well as the transit time and device length in the ballistic regime. For a 1D, degenerate, ballistic system of fermions we find for the electrical conductance the fundamental unit G = 2e²/h, for the differential thermoelectric power a = 0 and for the thermal conductance the fundamental unit K = p²k_B²T/(3h), which has been found to hold for the ballistic case of bosons with zero chemical potential as well. We provide the frequency dependence of the kinetic coefficients associated with different timescales belonging to the microscopic system.

1999

1. Transport coefficients for carriers with fractional exclusion statistics: the correlation function approach

   A Greiner

   Physica B 272, 75-77 (1999)

   Abstractdoi PDF

   We report explicit expressions for the Onsager–Kelvin kinetic coefficients of quasi-particles obeying fractional exclusion statistics. By using the correlation function approach the kinetic coefficients from the ballistic to the diffusive transport regime are obtained.

1998

1. Carrier Thermal Conductivity: Analysis and Application to Submicron-Device Simulation

   A. Greiner, L. Varani, L. Reggiani, M. C. Vecchi, T. Kuhn, and P. Golinelli

   VLSI Design 8, 59-64 (1998)

   Abstractdoi PDF

   Within a correlation-function (CF) formalism, the kinetic coefficientsof charge carriers in semiconductors are studied under different conditions. For the case of linear response in equilibrium, thetransitions from the non-degenerate to the degenerate regimes as wellas from ballistic to diffusive conditions are discussed within ananalytical model. Generalizing the method to high-field transport innondegenerate semiconductors, the CFs are determined by Monte Carlo (MC) calculations for bulk silicon from which the appropriate thermalconductivity has been obtained and included into the hydrodynamic code HEIELDS. For an n⁺nn⁺ submicron structure the temperatureand velocity profiles of the carriers have been calculated with HFIELDS.

2. Comment on “Quantized Thermal Conductance of Dielectric Quantum Wires”

   A. Greiner, L. Reggiani, and T. Kuhn

   Phys. Rev. Lett. 81, 5037-5037 (1998)

   Abstractdoi PDF

   A Comment on the Letter by Luis G. C. Rego, and George Kirczenow, Phys. Rev. Lett. 81, 232 (1998). The authors of the Letter offer a Reply.

3. Modelling surface-scattering effects in the solution of the Boltzmann transport equation based on the spherical-harmonics expansion

   Andreas Greiner, Maria Cristina Vecchi, and Massimo Rudan

   Semicond. Sci. Technol. 13, 1080-1089 (1998)

   Abstractdoi

   In a spherical-harmonics expansion formulation of the semi-classical Boltzmann transport equation the influence of surface scattering mechanisms on device characteristics has been investigated. The main feature of this work is to account for global as well as for local scattering mechanisms. The models associated with the surface scattering mechanisms have been applied to the simulation of MOS devices and they proved able to reproduce the mobility degradation of semi-empirical mobility models and experimental data. Moreover, the experimentally detected universal mobility behaviour of inversion layers is quantitatively reproduced by our model.

1997

1. Dynamical Onsager Coefficients in One-Dimensional Ballistic Transport

   A. Greiner, L. Varani, L. Reggiani, and T. Kuhn

   phys. stat. sol. (b) 204, 343-345 (1997)

   Abstractdoi

   Within a correlation-function (CF) formalism we present a theoretical analysis of the Kelvin-Onsager coefficients (KOC) relating generalized fluxes to the applied external forces for a carrier system in a one-dimensional ballistic structure. We consider a two terminal device with length l terminated by ideal contacts and investigate the transition from equilibrium to non-equilibrium conditions. The basis of the kinetic description are the transport equations for the Wigner function and the associated variance. The correlation functions of extensive variables (e.g. carrier number and energy) and the respective currents correspond to moments of the Wigner correlation function and the Fourier transform of the current correlation functions yield the dynamical Kelvin-Onsager coefficients.

2. Thermal Conductivity and Lorenz Number for One-Dimensional Ballistic Transport

   Andreas Greiner, Lino Reggiani, Tilmann Kuhn, and Luca Varani

   Phys. Rev. Lett. 78, 1114-1117 (1997)

   Abstractdoi PDF

   We study the thermal conductivity and Lorenz number of charge carriers for one-dimensional ballistic transport within the correlation function formalism. The carrier transit time between two ideal contacts is found to substitute for the collision time in the definition of a ballistic thermal conductivity. A universal thermal conductance K=2π²k_B²T/3h is naturally obtained for the degenerate case. Dispersion curves for the thermal conductivity and the Lorenz number associated with different time scales belonging to the microscopic system are given for the first time.

1996

1. A universal thermal conductance of charge carriers

   A. Greiner, L. Reggiani, T. Kuhn, and L. Varani

   Il Nuovo Cimento D 18, 1471-1473 (1996)

   Abstractdoi PDF

   A universal thermal conductance of charge carriers K=2π²k_B²T/3h is rigorously derived within a correlation-function formalism. Similar to the case of the universal electrical conductance G=2e²/h this result pertains to one-dimensional, ballistic, and degenerate conditions for non-interacting particles.

2. Correlation Function Approach to Thermal Conductivity and Lorenz Number of Charge Carriers

   Andreas Greiner, Lino Reggiani, and P. Golinelli

   Lith. J. Phys. 36, 542 - 549 (1996)

1994

1. The role of vertical transport and capture of electrons and holes for the transient optical response in quantum-well heterostructures

   H. Hillmer, T. Kuhn, A. Greiner, S. Hansmann, and H. Burkhard

   Opt. Quant. Electron. 26, S691-S703 (1994)

   Abstractdoi PDF

   The transient optical response of quantum wells (QWs) after optical and electrical carrier injection into the barrier layers is studied experimentally and theoretically. We have varied the transport geometry in GaAs/AlGaAs and InGaAs/InAlGaAs heterostructures and emphasize the basic principles for a theoretical treatment of electron and hole capture into QWs for a proper description of vertical carrier transport in the barriers of QW heterostructures. Comparing our experimental data with the results of theoretical model calculations, we determine the capture, reflection and transmission probabilities, the ambipolar diffusivities and the ambipolar mobilities in the barriers of GaAs/AlGaAs, as a model system. The temporal evolution of the electron and the hole capture current densities at the QWs are studied in detail for a wide variation of the injected carrier densities. Amplitude modulation experiments are performed for InGaAs/InAlGaAs QW laser devices providing increasing 3 dB frequencies for decreasing confinement layer thickness, indicating the influence of carrier transport in the barriers.

1992

1. Phenomenological field theories for layered materials: Equations of motion and continuity conditions

   A. Greiner, and G. Mahler

   Phys. Rev. B 46, 7132-7143 (1992)

   Abstractdoi PDF

   In many cases synthetic structures are specified on length scales large compared to the interatomic distances. On such scales local phenomenological field theories are being used that dispose of the atomic structure but allow one to make extensive use of higher-level bulk properties. We derive equations of motion including higher-order spatial derivatives, which can be adopted to various effective continua like Schrödinger fields for electrons in solids, electromagnetic fields in dielectrics, and acoustic or optical displacement fields. For these generalized fields we solve the long-standing problem of how to derive a complete set of continuity conditions at a plane interface. In the same way continuity conditions for interacting fields (e.g., polaritons) are obtained.