#### Prof. Dr. Dietrich E. Wolf

Theoretical Physics

University of Duisburg-Essen

##### Contact

- dietrich.wolf@uni-due.de
- +49 203 379 3327
- personal website

##### Hub

**Electrical charging overcomes the bouncing barrier in planet formation**

Steinpilz, T. and Joeris, K. and Jungmann, F. and Wolf, D. and Brendel, L. and Teiser, J. and Shinbrot, T. and Wurm, G.*Nature Physics*16 (2020)In protoplanetary disks, solid objects (so-called planetesimals) are formed from dust. Micrometre-sized dust grains grow into millimetre-sized aggregates. Once those aggregates have diameters exceeding a few centimetres, they become subject to concentration mechanisms such as the streaming instability, permitting the formation of self-gravitating clusters, which might eventually collapse into kilometre-sized planetesimals. However, for the streaming instability to set in, clumps spanning sizes from centimetres to decimetres are required in the centre of a protoplanetary disk. In the size range between millimetres and centimetres, aggregates bounce off each other rather than sticking together, and growth is stalled. Here we show in microgravity experiments that collisions between millimetre-sized grains lead to sufficient electrical charging for aggregation to bridge this gap between the bouncing barrier and the onset of the streaming instability. We computationally simulate aggregation and find that models agree with the experimental data only if electrical charging is present. We therefore propose that collisional charging may promote early growth in the size gap that current models of planetesimal formation cannot account for. © 2019, The Author(s), under exclusive licence to Springer Nature Limited.view abstract 10.1038/s41567-019-0728-9 **Element-specific displacements in defect-enriched TiO2: Indication of a flash sintering mechanism**

Jongmanns, M. and Wolf, D.E.*Journal of the American Ceramic Society*103 (2020)Flash sintering experiments of ceramics indicate the formation of a state far from equilibrium. It is hypothesized that this state is enriched by Frenkel defects. The possibility is investigated that such lattice defects are being generated by a proliferation of lattice vibrations that lie close to the Brillouin zone edge. We show by means of Molecular Dynamics simulations of rutile TiO2 that this mechanism generates Frenkel defects in concentrations far beyond equilibrium. These defects deform the whole lattice in a way that the mean-square displacements of the vibration amplitudes of the Ti and O atoms are specifically enhanced. This finding compares well to atomic displacement data of flash sintered rutile TiO2 reported recently. © 2019 The Authors. Journal of the American Ceramic Society published by Wiley Periodicals, Inc. on behalf of American Ceramic Society (ACERS)view abstract 10.1111/jace.16696 **Thermoelectrics versus thermophotovoltaics: Two approaches to convert heat fluxes into electricity**

Okanimba Tedah, I.A. and Maculewicz, F. and Wolf, D.E. and Schmechel, R.*Journal of Physics D: Applied Physics*52 (2019)Direct conversion of heat fluxes into electricity is usually done by thermoelectric generators (TEGs). For hot-side temperatures above 1000 K, thermal radiation carries a high energy density, comparable with the energy density extracted from TEGs and therefore a direct conversion of thermal radiation into electricity, named thermophotovoltaics (TPV), would also be an option. This paper compares both methods with respect to efficiency and extractable power density. The physical limits are estimated under simplified but realistic boundary conditions. For TPV the radiative detailed balance limit under black body radiation, which was calculated for different hot-side temperatures from 310 K to 3000 K for an optimized bandgap of the applied material was used. But, since very narrow bandgaps leading to strong non-radiative recombination mechanisms, the bandgap was limited to Eg ≥ 0.5 eV. The effect of suppressing sub-bandgap radiation as well as an enhanced radiation density in the nearfield (near-field TPV) were also included. The TEG efficiency and power density was calculated under thermal matching conditions with a heat transfer coefficient of Kcont = 250 W m-2 K-1 and an average device ZT̄ = 1. The results are compared with experimental data for TPV and TEGs from literature. It is shown, that up to 600 K hot-side temperature TEGs are superior to TPV, due to a significant higher power density. Above 1000 K TPV profits from higher efficiency by a similar power density. But above 2000 K TPV suffers from cell heating. The range 600 K to 1000 K is currently captured by high temperature thermoelectrics, but near-field TPV (NF-TPV) has good chances to compete with TEGs in this temperature range in the future. © 2019 IOP Publishing Ltd.view abstract 10.1088/1361-6463/ab1833 **Efficient p-n junction-based thermoelectric generator that can operate at extreme temperature conditions**

Chavez, R. and Angst, S. and Hall, J. and Maculewicz, F. and Stoetzel, J. and Wiggers, H. and Thanh Hung, L. and Van Nong, N. and Pryds, N. and Span, G. and Wolf, D.E. and Schmechel, R. and Schierning, G.*Journal of Physics D: Applied Physics*51 (2018)In many industrial processes, a large proportion of energy is lost in the form of heat. Thermoelectric generators can convert this waste heat into electricity by means of the Seebeck effect. However, the use of thermoelectric generators in practical applications on an industrial scale is limited in part because electrical, thermal, and mechanical bonding contacts between the semiconductor materials and the metal electrodes in current designs are not capable of withstanding thermal-mechanical stress and alloying of the metal-semiconductor interface when exposed to the high temperatures occurring in many real-world applications. Here we demonstrate a concept for thermoelectric generators that can address this issue by replacing the metallization and electrode bonding on the hot side of the device by a p-n junction between the two semiconductor materials, making the device robust against temperature induced failure. In our proof-of-principle demonstration, a p-n junction device made from nanocrystalline silicon is at least comparable in its efficiency and power output to conventional devices of the same material and fabrication process, but with the advantage of sustaining high hot side temperatures and oxidative atmosphere. © 2017 IOP Publishing Ltd.view abstract 10.1088/1361-6463/aa9b6a **Generation of Frenkel defects above the Debye temperature by proliferation of phonons near the Brillouin zone edge**

Jongmanns, M. and Raj, R. and Wolf, D.E.*New Journal of Physics*20 (2018)A novel, non-radiative mechanism is reported by which Frenkel pairs of vacancies and interstitials are generated in molar concentrations far above thermal equilibrium. This mechanism is demonstrated in molecular dynamics (MD) simulations of an aluminum single crystal with a free surface. They suggest that three conditions must be fulfilled: (i) lattice vibrations near the Brillouin zone edge are being excited, (ii) these vibrations proliferate at a sufficiently high rate, and (iii) the sample temperature is above the Debye temperature (but significantly below the melting point). The simulations employed an EAM potential for Al. We attempt to draw a confluence between our MD simulations and recent experiments on flash sintering of aluminum. The simulation results are also consistent with flash experiments on polycrystals and single crystals of zirconium and titanium oxides where the Debye temperature was discovered to be the lower limit for the onset of the flash. © 2018 The Author(s). Published by IOP Publishing Ltd on behalf of Deutsche Physikalische Gesellschaft.view abstract 10.1088/1367-2630/aadd5a **Nonequilibrium distribution functions in electron transport: Decoherence, energy redistribution and dissipation**

Stegmann, T. and Ujsághy, O. and Wolf, D.E.*New Journal of Physics*20 (2018)A new statistical model for the combined effects of decoherence, energy redistribution and dissipation on electron transport in large quantum systems is introduced. The essential idea is to consider the electron phase information to be lost only at randomly chosen regions with an average distance corresponding to the decoherence length. In these regions the electron's energy can be unchanged or redistributed within the electron system or dissipated to a heat bath. The different types of scattering and the decoherence leave distinct fingerprints in the energy distribution functions. They can be interpreted as a mixture of unthermalized and thermalized electrons. In the case of weak decoherence, the fraction of thermalized electrons show electrical and thermal contact resistances. In the regime of incoherent transport the proposed model is equivalent to a Boltzmann equation. The model is applied to experiments with carbon nanotubes. The excellent agreement of the model with the experimental data allows to determine the scattering lengths of the system. © 2018 The Author(s). Published by IOP Publishing Ltd on behalf of Deutsche Physikalische Gesellschaft.view abstract 10.1088/1367-2630/aab530 **Conditions for enhanced performance of segmented thermoelectrics under load**

Angst, S. and Wolf, D.E.*Journal of Physics D: Applied Physics*50 (2017)The Onsager-de Groot-Callen transport theory is used to investigate the performance of double segmented thermoelectrics as generators. We show that such an inhomogeneous device usually performs worse than predicted by the effective transport coefficients. This is caused by the difference of the open circuit Seebeck voltage and the Seebeck voltage under operating conditions. The electrical current and the related interface Peltier effect cause a self-organization of the temperature profile such that the temperature drop across the material with the higher absolute Seebeck coefficient is reduced. However, including Joule heating we derive conditions for the opposite effect resulting in an enhanced power. © 2017 IOP Publishing Ltd.view abstract 10.1088/1361-6463/aa7b0a **Dilute suspensions in annular shear flow under gravity: Simulation and experiment**

Schröer, K. and Kurzeja, P. and Schulz, S. and Brockmann, P. and Hussong, J. and Janas, P. and Wlokas, I. and Kempf, A. and Wolf, D.E.*EPJ Web of Conferences*140 (2017)A dilute suspension in annular shear flow under gravity was simulated using multi-particle collision dynamics (MPC) and compared to experimental data. The focus of the analysis is the local particle velocity and density distribution under the influence of the rotational and gravitational forces. The results are further supported by a deterministic approximation of a single-particle trajectory and OpenFOAM CFD estimations of the overcritical frequency range. Good qualitative agreement is observed for single-particle trajectories between the statistical mean of MPC simulations and the deterministic approximation. Wall contact and detachment however occur earlier in the MPC simulation, which can be explained by the inherent thermal noise of the method. The multi-particle system is investigated at the point of highest particle accumulation that is found at 2/3 of the particle revolution, starting from the top of the annular gap. The combination of shear flow and a slowly rotating volumetric force leads to strong local accumulation in this section that increases the particle volume fraction from overall 0.7% to 4.7% at the outer boundary. MPC simulations and experimental observations agree well in terms of particle distribution and a close to linear velocity profile in radial direction. © The Authors, published by EDP Sciences, 2017.view abstract 10.1051/epjconf/201714009034 **Mesostructural investigation of micron-sized glass particles during shear deformation - An experimental approach vs. DEM simulation**

Torbahn, L. and Weuster, A. and Handl, L. and Schmidt, V. and Kwade, A. and Wolf, D.E.*EPJ Web of Conferences*140 (2017)The interdependency of structure and mechanical features of a cohesive powder packing is on current scientific focus and far from being well understood. Although the Discrete Element Method provides a well applicable and widely used tool to model powder behavior, non-trivial contact mechanics of micron-sized particles demand a sophisticated contact model. Here, a direct comparison between experiment and simulation on a particle level offers a proper approach for model validation. However, the simulation of a full scale shear-tester experiment with micron-sized particles, and hence, validating this simulation remains a challenge. We address this task by down scaling the experimental setup: A fully functional micro shear-tester was developed and implemented into an X-ray tomography device in order to visualize the sample on a bulk and particle level within small bulk volumes of the order of a few micro liter under well-defined consolidation. Using spherical micron-sized particles (30 μm), shear tests with a particle number accessible for simulations can be performed. Moreover, particle level analysis allows for a direct comparison of experimental and numerical results, e.g., regarding structural evolution. In this talk, we focus on density inhomogeneity and shear induced heterogeneity during compaction and shear deformation. © The Authors, published by EDP Sciences, 2017.view abstract 10.1051/epjconf/201714003027 **Models of current sintering**

Angst, S. and Engelke, L. and Winterer, M. and Wolf, D.E.*EPJ Web of Conferences*140 (2017)Densification of (semi-)conducting particle agglomerates with the help of an electrical current is much faster and more energy efficient than traditional thermal sintering or powder compression. Therefore, this method becomes more and more common among experimentalists, engineers, and in industry. The mechanisms at work at the particle scale are highly complex because of the mutual feedback between current and pore structure. This paper extends previous modelling approaches in order to study mixtures of particles of two different materials. In addition to the delivery of Joule heat throughout the sample, especially in current bottlenecks, thermoelectric effects must be taken into account. They lead to segregation or spatial correlations in the particle arrangement. Various model extensions are possible and will be discussed. © The Authors, published by EDP Sciences, 2017.view abstract 10.1051/epjconf/201714013014 **Relaxation Times in Simple Shear and the Role of Walls**

Brendel, L. and Török, J. and Ries, A. and Wolf, D.E.*EPJ Web of Conferences*140 (2017)We study the relaxation time of granular media in simple shear by means of DEM simulations (the methods being Molecular Dynamics as well as Contact Dynamics) in two and three dimensions with rough and with smooth frictional walls. While the system with rough walls behaves according to its steady state constitutive laws, the systems with smooth walls show a much stronger increase of the relaxation time with driving strength than to be expected. Employing a dynamic non-local rheology model[1] allows for a stronger increase but not sufficiently so. © The Authors, published by EDP Sciences, 2017.view abstract 10.1051/epjconf/201714003088 **Sticking properties of ice grains**

Jongmanns, M. and Kumm, M. and Wurm, G. and Wolf, D.E. and Teiser, J.*EPJ Web of Conferences*140 (2017)We study the size dependence of pull-off forces of water ice in laboratory experiments and numerical simulations. To determine the pull-off force in our laboratory experiments, we use a liquid nitrogen cooled centrifuge. Depending on its rotation frequency, spherical ice grains detach due to the centrifugal force which is related to the adhesive properties. Numerical simulations are conducted by means of molecular dynamics simulations of hexagonal ice using a standard coarse-grained water potential. The pull-off force of a single contact between two spherical ice grains is measured due to strain controlled simulations. Both, the experimental study and the simulations reveal a dependence between the pull-off force and the (reduced) particle radii, which differ significantly from the linear dependence of common contact theories. © The Authors, published by EDP Sciences, 2017.view abstract 10.1051/epjconf/201714005007 **The cooperativity length in simple shear of dry granular media**

Ries, A. and Brendel, L. and Wolf, D.E.*Computational Particle Mechanics*4 (2017)The local flow rule and the cooperativity length are the crucial ingredients of non-local rheology of granular matter. Once they are known as functions of the stress ratio, one can predict steady-state flow in arbitrarily complex geometries. We show how these functions can most easily be extracted from simulated velocity profiles for three-dimensional simple shear. The critical behaviour at the yield threshold and its rounding by finite size effects are discussed. The simple shear is simulated with smooth frictional walls, which provide the spatial inhomogeneity necessary to determine the cooperativity length. They also allow for slip, so that the particle velocity at the wall adjusts itself according to the stress ratio and is sensitive to the bulk yield. © 2016, OWZ.view abstract 10.1007/s40571-016-0141-4 **Thermal resistance of twist boundaries in silicon nanowires by nonequilibrium molecular dynamics**

Bohrer, J.K. and Schröer, K. and Brendel, L. and Wolf, D.E.*AIP Advances*7 (2017)The thermal boundary resistance (Kapitza resistance) of (001) twist boundaries in silicon is investigated by nonequilibrium molecular dynamics simulations. In order to enable continuous adjustment of the mismatch angle, a cylindrical geometry with fixed atomic positions at the boundaries is devised. The influence of the boundary conditions on the Kapitza resistance is removed by means of a finite size analysis. Due to the diamond structure of silicon, twist boundaries with mismatch angles ϕ and 90°−ϕ are not equivalent, whereas those with ±ϕ or with 90°±ϕ are. The Kapitza resistance increases with mismatch angle up to 45°, where it reaches a plateau around 1.56±0.05Km2/GW. Between 80° and the 90°Σ1 grain boundary it drops by about 30%. Surprisingly, lattice coincidence at other angles (Σ5,Σ13,Σ27,Σ25) has no noticable effect on the Kapitza resistance. However, there is a clear correlation between the Kapitza resistance and the width of a non-crystalline layer at the twist boundaries. © 2017 Author(s).view abstract 10.1063/1.4979982 **Coupled molecular and cantilever dynamics model for frequency-modulated atomic force microscopy**

Klocke, M. and Wolf, D.E.*Beilstein Journal of Nanotechnology*7 (2016)A molecular dynamics model is presented, which adds harmonic potentials to the atomic interactions to mimic the elastic properties of an AFM cantilever. It gives new insight into the correlation between the experimentally monitored frequency shift and cantilever damping due to the interaction between tip atoms and scanned surface. Applying the model to ionic crystals with rock salt structure two damping mechanisms are investigated, which occur separately or simultaneously depending on the tip position. These mechanisms are adhesion hysteresis on the one hand and lateral excitations of the cantilever on the other. We find that the short range Lennard-Jones part of the atomic interaction alone is sufficient for changing the predominant mechanism. When the long range ionic interaction is switched off, the two damping mechanisms occur with a completely different pattern, which is explained by the energy landscape for the apex atom of the tip. In this case the adhesion hysteresis is always associated with a distinct lateral displacement of the tip. It is shown how this may lead to a systematic shift between the periodic patterns obtained from the frequency and from the damping signal, respectively. © 2016 Klocke and Wolf.view abstract 10.3762/bjnano.7.63 **Fractal substructure of a nanopowder generated by repeated fragmentation and sedimentation: the rôle of the dust**

Topic, N. and Wolf, D.E. and Pöschel, T.*Granular Matter*18 (2016)Packings of cohesive nanoparticles, that is nanopowders, may be obtained as the result of repeated fragmentation–reagglomeration cycles (Schwager et al. in Phys Rev Lett 100:218002, 2008) such that the resulting sediment reveals a fractal structure. The size distribution of the fragments after a fragmentation step is a superposition of a narrow distribution of large particles (chunks) whose size is determined by the cutting length and a power-law distribution for small particles, representing scale invariant dust. It was shown that the exponent of the power-law, (Formula presented.) , is in non-trivial relation to the fractal dimension, (Formula presented.) , via (Formula presented.). This poses the question for the structure of the sediment created by repeated fragmentation–reagglomeration cycles when the dust particles are excluded from the reagglomeration step. We found that even in this case, repeated fragmentation–reagglomeration cycles yield a sediment of fractal structure with slightly reduced fractal dimension while the dust exponent, (Formula presented.) , remains unchanged. © 2016, Springer-Verlag Berlin Heidelberg.view abstract 10.1007/s10035-015-0601-1 **Molecular dynamics simulations of thermal transport in isotopically modulated semiconductor nanostructures**

Frieling, R. and Eon, S. and Wolf, D. and Bracht, H.*Physica Status Solidi (A) Applications and Materials Science*213 (2016)In this paper, we investigate the effect of isotopic modulation on the thermal conductivity of semiconductor nanostructures. The isotope doping is of particular interest for the application of semiconductors as thermoelectric materials as it leaves the electronic properties practically unaffected while the phononic transport is retarded. This approach could increase the figure of merit of thermoelectric generators by decreasing the thermal conductivity of semiconductors. We use non-equilibrium molecular dynamics simulations to examine thermal transport in isotopically engineered semiconductors. The temperature profiles along the sample region deduced from the simulations allow the extraction of thermal conductivities. The reliability of the MD-predicted thermal conductivities is studied by analyzing the influence of the input parameters on the results. The first set of samples are isotopically modified silicon samples. The influence of temperature, isotopic composition, and ordering of isotopic defects on the thermal conductivity of silicon is studied. The second material system under investigation is silicon germanium alloys. The influence of isotopic modulation on the thermal conductivity of Si-Ge alloys is examined for varying chemical composition. The thermal conductivities predicted by MD are compared to results derived from the solution of the Boltzmann transport equation in the relaxation time approach. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.view abstract 10.1002/pssa.201532469 **Network theory for inhomogeneous thermoelectrics**

Angst, S. and Wolf, D.E.*New Journal of Physics*18 (2016)The Onsager-de Groot-Callen transport theory, implemented as a network model, is used to simulate the transient Harman method, which is widely used experimentally to determine all thermoelectric transport coefficients in a single measurement setup. It is shown that this method systematically overestimates the Seebeck coefficient for samples composed of two different materials. As a consequence, the figure of merit is also overestimated, if the thermal coupling of the measurement setup to the environment is weak. For a mixture of metal and semiconductor particles near metal percolation the figure of merit obtained by the Harman method is more than 100% too large. For a correct interpretation of the experimental data, information on composition and microstructure of the sample are indispensable. © 2016 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.view abstract 10.1088/1367-2630/18/4/043004 **Silicon-based nanocomposites for thermoelectric application**

Schierning, G. and Stoetzel, J. and Chavez, R. and Kessler, V. and Hall, J. and Schmechel, R. and Schneider, T. and Petermann, N. and Wiggers, H. and Angst, S. and Wolf, D.E. and Stoib, B. and Greppmair, A. and Stutzmann, M. and Brandt, M.S.*Physica Status Solidi (A) Applications and Materials Science*213 (2016)Here we present the realization of efficient and sustainable silicon-based thermoelectric materials from nanoparticles. We employ a gas phase synthesis for the nanoparticles which is capable of producing doped silicon (Si) nanoparticles, doped alloy nanoparticles of silicon and germanium (Ge), SixGe1-x, and doped composites of Si nanoparticles with embedded metal silicide precipitation phases. Hence, the so-called "nanoparticle in alloy" approach, theoretically proposed in the literature, forms a guideline for the material development. For bulk samples, a current-activated pressure-assisted densification process of the nanoparticles was optimized in order to obtain the desired microstructure. For thin films, a laser annealing process was developed. Thermoelectric transport properties were characterized on nanocrystalline bulk samples and laser-sintered-thin films. Devices were produced from nanocrystalline bulk silicon in the form of p-n junction thermoelectric generators, and their electrical output data were measured up to hot side temperatures of 750°C. In order to get a deeper insight into thermoelectric properties and structure forming processes, a 3D-Onsager network model was developed. This model was extended further to study the p-n junction thermoelectric generator and understand the fundamental working principle of this novel device architecture. Gas phase synthesis of composite nanoparticles; nanocrystalline bulk with optimized composite microstructure; laser-annealed thin film. The authors fabricated thermoelectric nanomaterials from doped silicon and silicon and germanium alloy nanoparticles, as well as composites of Si nanoparticles with embedded metal silicide nanoparticles. Processing was performed applying a current-activated pressure-assisted densification process for bulk samples and a laser annealing process for thin film samples. Devices were produced in the form of pn junction thermoelectric generators. A 3D-Onsager network model was used to understand the fundamental working principle of this novel device architecture. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.view abstract 10.1002/pssa.201532602 **Impurity-induced island pinning during electromigration**

Jongmanns, M. and Latz, A. and Wolf, D.E.*EPL*110 (2015)We study the electromigration-induced drift of monolayer Ag islands on Ag(111) which contain one Cu atom. For this purpose a three-dimensional self-learning kinetic Monte Carlo model was extended, and a realistic many-body potential was used. The only free parameters of the model are the effective valences of the Ag and Cu atoms. Due to the impurity, the island drift is significantly reduced, especially for small islands. This is traced back to sequential pinning and depinning events, which are analyzed in detail. Surprisingly, this phenomenon is qualitatively independent of the impurity's effective valence, as long as the impurity does not detach from the island edge. How strongly the drift velocity is reduced depends on the effective valence. Copyright © EPLA, 2015.view abstract 10.1209/0295-5075/110/16001 **Shear flow of cohesive powders with contact crystallization: experiment, model and calibration**

Weuster, A. and Strege, S. and Brendel, L. and Zetzener, H. and Wolf, D.E. and Kwade, A.*Granular Matter*17 (2015)This work presents an experimental and numerical investigation of the shear flow of a cohesive, caking powder. Utilizing potassium chloride (KCl) as a model material, the bulk’s flow behavior with respect to storage time is measured with a Schulze ring shear tester. Our results suggest that KCl cakes on a characteristic timescale (Formula Presented.), which is independent of the normal load. Based on a detailed product characterization, a generalized elastoplastic contact model for discrete element simulations combined with an approach of successive calibration is proposed. Mircoscopic parameters, which are not measured directly, are used as effective ones to fit the flow behavior of an idealized ensemble of particles to the experimental findings. Within this process, we investigate the influence of these microscopic parameters on macroscopic quantities as well as the bulk’s structure. Successful calibration confirms that the rheology of complex bulk materials, such as KCl, can be predicted efficiently with simplified numerical simulations. © 2015, Springer-Verlag Berlin Heidelberg.view abstract 10.1007/s10035-015-0555-3 **Structure of a three-dimensional nano-powder subjected to repeated fragmentation and sedimentation**

Topic, N. and Weuster, A. and Pöschel, T. and Wolf, D.E.*New Journal of Physics*17 (2015)We revisit the problem of the structure of a nano-powder subjected to repeated fragmentation and sedimentation, and extend the analysis to the more relevant three-dimensional (3D) case. One important question not addressed previously is how the fractal dimension and dust exponent depend on space dimension. We find that the qualitative behavior of the nano-powder in three dimensions is similar to that in two dimensions. But the fractal dimension changes from 1.6 ± 0.1 in two dimensions to 2.1 ± 0.1 in three dimensions. The scaling relation between the fractal dimension and the dust exponent characterizing the fragment size distribution is the same as in two dimensions. The universality of these exponents is addressed by comparing the results with a much simpler lattice model. Although the different settling kinetics of the fragments leads to different anisotropies, the fractal properties are not affected. © 2015 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.view abstract 10.1088/1367-2630/17/1/013024 **Analysis of a decision model in the context of equilibrium pricing and order book pricing**

Wagner, D.C. and Schmitt, T.A. and Schäfer, R. and Guhr, T. and Wolf, D.E.*Physica A: Statistical Mechanics and its Applications*415 (2014)An agent-based model for financial markets has to incorporate two aspects: decision making and price formation. We introduce a simple decision model and consider its implications in two different pricing schemes. First, we study its parameter dependence within a supply-demand balance setting. We find realistic behavior in a wide parameter range. Second, we embed our decision model in an order book setting. Here, we observe interesting features which are not present in the equilibrium pricing scheme. In particular, we find a nontrivial behavior of the order book volumes which reminds of a trend switching phenomenon. Thus, the decision making model alone does not realistically represent the trading and the stylized facts. The order book mechanism is crucial.© 2014 Elsevier B.V. All rights reserved.view abstract 10.1016/j.physa.2014.08.013 **Anisotropy of electromigration-induced void and island drift**

Latz, A. and Sindermann, S.P. and Brendel, L. and Dumpich, G. and Meyer zu Heringdorf, F.-J. and Wolf, D.E.*Journal of Physics Condensed Matter*26 (2014)By means of our novel self-learning kinetic Monte Carlo model (Latz et al 2012 J. Phys.: Condens. Matter 24 485005) we study the electromigration-induced drift of monolayer voids and islands on unpassivated surfaces of single crystalline Ag(111) and Ag(001) films at the atomic scale. Regarding the drift velocity, we find a non-monotonic size dependence for small voids. The drift direction is aligned with the electromigration force only along high symmetry directions, while halfway between, the angle enclosed by them is maximal. The magnitude of these directional deviations strongly depends on the system parameter, which are investigated in detail. The simulation results are in accordance with void motion observed in experiments performed on Ag(111). © 2014 IOP Publishing Ltd.view abstract 10.1088/0953-8984/26/5/055005 **Anisotropy of force distributions in sheared soft-particle systems**

Boberski, J. and Reza Shaebani, M. and Wolf, D.E.*EPL*108 (2014)In this numerical study, measurements of the contact forces inside a periodic twodimensional sheared system of soft frictional particles are reported. The distribution P(fn) of normalized normal forces fn = Fn/Fn exhibits a gradual broadening with the increase of the pure shear deformation γ, leading to a slower decay for large forces. The process, however, slows down and P(fn) approaches an invariant shape at high γ. By introducing the joint probability distribution P(fn, ?) in sheared configurations, it is shown that for a fixed direction ?, the force distribution decays faster than exponentially even in a sheared system. The overall broadening can be attributed to the averaging over different directions in the presence of shear-induced stress anisotropy. The distribution of normalized tangential forces almost preserves its shape for arbitrary applied strain. © EPLA, 2014.view abstract 10.1209/0295-5075/108/44002 **Approach to structural anisotropy in compacted cohesive powder**

Strege, S. and Weuster, A. and Zetzener, H. and Brendel, L. and Kwade, A. and Wolf, D.E.*Granular Matter*16 (2014)We investigate the mesoscopic regime between microscopic particle properties and macroscopic bulk behavior and present a complementary approach of physical experiments and discrete element method simulations to explore the development of the microstructure of cohesive powders during compaction. On the experimental side, a precise micro shear tester (μ ST) for very small powder samples has been developed and integrated into a high resolution X-ray microtomography (XMT) system. The combination of μ ST and XMT provides the unique possibility to access the 3D microstructure and the particle network inside manipulated powder samples experimentally. In simulations we explore the structural changes resulting from compaction: a Hertzian contact model is utilized for compaction of an isotropic initial configuration created by a geometrical algorithm. As a first result of this approach we present the analysis of the compaction of slightly cohesive SiO2 particles with special regard to bulk density, heterogeneity, compaction law and structural anisotropy. © 2013 Springer-Verlag Berlin Heidelberg.view abstract 10.1007/s10035-013-0454-4 **Decoherence-induced conductivity in the one-dimensional Anderson model**

Stegmann, T. and Ujsághy, O. and Wolf, D.E.*AIP Conference Proceedings*1610 (2014)We study the effect of decoherence on the electron transport in the one-dimensional Anderson model by means of a statistical model [1, 2, 3, 4, 5]. In this model decoherence bonds are randomly distributed within the system, at which the electron phase is randomized completely. Afterwards, the transport quantity of interest (e.g. resistance or conductance) is ensemble averaged over the decoherence configurations. Averaging the resistance of the sample, the calculation can be performed analytically. In the thermodynamic limit, we find a decoherence-driven transition from the quantum-coherent localized regime to the Ohmic regime at a critical decoherence density, which is determined by the second-order generalized Lyapunov exponent (GLE) [4]. © 2014 AIP Publishing LLC.view abstract 10.1063/1.4893515 **Dissipation signals due to lateral tip oscillations in FM-AFM**

Klocke, M. and Wolf, D.E.*Beilstein Journal of Nanotechnology*5 (2014)We study the coupling of lateral and normal tip oscillations and its effect on the imaging process of frequency-modulated dynamic atomic force microscopy. The coupling is induced by the interaction between tip and surface. Energy is transferred from the normal to the lateral excitation, which can be detected as damping of the cantilever oscillation. However, energy can be transferred back into the normal oscillation, if not dissipated by the usually uncontrolled mechanical damping of the lateral excitation. For certain cantilevers, this dissipation mechanism can lead to dissipation rates larger than 0.01 eV per period. The mechanism produces an atomic contrast for ionic crystals with two maxima per unit cell in a line scan. © 2014 Klocke and Wolf.view abstract 10.3762/bjnano.5.213 **High temperature thermoelectric device concept using large area PN junctions**

Chavez, R. and Angst, S. and Hall, J. and Stoetzel, J. and Kessler, V. and Bitzer, L. and Maculewicz, F. and Benson, N. and Wiggers, H. and Wolf, D. and Schierning, G. and Schmechel, R.*Journal of Electronic Materials*43 (2014)A new high temperature thermoelectric device concept using large area nanostructured silicon p-type and n-type (PN) junctions is presented. In contrast to conventional thermoelectric generators, where the n-type and p-type semiconductors are connected electrically in series and thermally in parallel, we experimentally demonstrate a device concept in which a large area PN junction made from highly doped densified silicon nanoparticles is subject to a temperature gradient parallel to the PN interface. In the proposed device concept, the electrical contacts are made at the cold side eliminating the hot side substrate and difficulties that go along with high temperature electrical contacts. This concept allows temperature gradients greater than 300 K to be experimentally applied with hot side temperatures larger than 800 K. Electronic properties of the PN junctions and power output characterizations are presented. A fundamental working principle is discussed using a particle network model with temperature and electric fields as variables, and which considers electrical conductivity and thermal conductivity according to Fourier's law, as well as Peltier and Seebeck effects. © 2014 TMS.view abstract 10.1007/s11664-014-3073-x **Lattice degradation by moving voids during reversible electromigration**

Sindermann, S.P. and Latz, A. and Spoddig, D. and Schoeppner, C. and Wolf, D.E. and Dumpich, G. and Meyer zu Heringdorf, F.-J.*Journal of Applied Physics*116 (2014)Electromigration driven void motion is studied in Ag wires with an initially well-defined single crystal lattice by in situ scanning electron microscopy. Voids are moving in opposite direction to the electron flow. When the electron current is reversed, voids exactly retrace their previous motion path with an increased drift velocity: The microstructure of the Ag wire "remembers" the motion path of the initial voids. To investigate the nature of this memory effect, we analyzed the crystal lattice with electron backscatter diffraction after passing of a void. The results show a permanent lattice degradation caused by the moving void. The implication of this finding for the reversibility of EM will be discussed. © 2014 AIP Publishing LLC.view abstract 10.1063/1.4889816 **Localization under the effect of randomly distributed decoherence**

Stegmann, T. and Ujsághy, O. and Wolf, D.E.*European Physical Journal B*87 (2014)Electron transport through disordered quasi one-dimensional quantum systems is studied. Decoherence is taken into account by a spatial distribution of virtual reservoirs, which represent local interactions of the conduction electrons with their environment. We show that the decoherence distribution has observable effects on the transport. If the decoherence reservoirs are distributed randomly without spatial correlations, a minimal degree of decoherence is necessary to obtain Ohmic conduction. Below this threshold the system is localized and thus, a decoherence driven metal-insulator transition is found. In contrast, for homogenously distributed decoherence, any finite degree of decoherence is sufficient to destroy localization. Thus, the presence or absence of localization in a disordered one-dimensional system may give important insight about how the electron phase is randomized. © 2014 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.view abstract 10.1140/epjb/e2014-40997-3 **Phonon coherence in isotopic silicon superlattices**

Frieling, R. and Radek, M. and Eon, S. and Bracht, H. and Wolf, D.E.*Applied Physics Letters*105 (2014)Recent experimental and theoretical investigations have confirmed that a reduction in thermal conductivity of silicon is achieved by isotopic silicon superlattices. In the present study, non-equilibrium molecular dynamics simulations are performed to identify the isotope doping and isotope layer ordering with minimum thermal conductivity. Furthermore, the impact of isotopic intermixing at the superlattice interfaces on phonon transport is investigated. Our results reveal that the coherence of phonons in isotopic Si superlattices is prevented if interfacial mixing of isotopes is considered. © 2014 AIP Publishing LLC.view abstract 10.1063/1.4897002 **Recent advances in the simulation of particle-laden flows**

Harting, J. and Frijters, S. and Ramaioli, M. and Robinson, M. and Wolf, D.E. and Luding, S.*European Physical Journal: Special Topics*223 (2014)A substantial number of algorithms exists for the simulation of moving particles suspended in fluids. However, finding the best method to address a particular physical problem is often highly nontrivial and depends on the properties of the particles and the involved fluid(s) together. In this report, we provide a short overview on a number of existing simulation methods and provide two state of the art examples in more detail. In both cases, the particles are described using a Discrete Element Method (DEM). The DEM solver is usually coupled to a fluid-solver, which can be classified as grid-based or mesh-free (one example for each is given). Fluid solvers feature different resolutions relative to the particle size and separation. First, a multicomponent lattice Boltzmann algorithm (mesh-based and with rather fine resolution) is presented to study the behavior of particle stabilized fluid interfaces and second, a Smoothed Particle Hydrodynamics implementation (mesh-free, meso-scale resolution, similar to the particle size) is introduced to highlight a new player in the field, which is expected to be particularly suited for flows including free surfaces. © EDP Sciences, Springer-Verlag 2014.view abstract 10.1140/epjst/e2014-02262-3 **Thermal conductivity of isotopically controlled silicon nanostructures**

Bracht, H. and Eon, S. and Frieling, R. and Plech, A. and Issenmann, D. and Wolf, D. and Lundsgaard Hansen, J. and Nylandsted Larsen, A. and Ager Iii, J.W. and Haller, E.E.*New Journal of Physics*16 (2014)Nanostructured semiconductors open the opportunity to independently tailor electric and thermal conductivity by manipulation of the phonon transport. Nanostructuring of materials is a highly promising strategy for engineering thermoelectric devices with improved efficiency. The concept of reducing the thermal conductivity without degrading the electrical conductivity is most ideally realized by controlled isotope doping. This work reports on experimental and theoretical investigations on the thermal conductivity of isotopically modulated silicon nanostructures. State-of-the-art pump-and-probe experiments are conducted to determine the thermal conductivity of the different nanostructures of isotopically enriched silicon layers epitaxially grown on natural silicon substrates. Concomitant molecular dynamics calculations are performed to study the impact of the silicon isotope mass, isotope interfaces, and of the isotope layer ordering and thickness on the thermal conductivity. Engineering the isotope distribution is a striking concept to reduce the thermal conductivity of silicon without affecting its electronic properties. This approach, using isotopically engineered silicon, might pave the way for future commercial thermoelectric devices. © 2014 IOP Publishing and Deutsche Physikalische Gesellschaft.view abstract 10.1088/1367-2630/16/1/015021 **A parallel version of the contact dynamics method**

Shojaaee, Z. and Shaebani, M.R. and Brendel, L. and Török, J. and Wolf, D.E.*AIP Conference Proceedings*1542 (2013)We present a fully parallel version of the contact dynamics simulation method. The algorithm works for an arbitrary number of processors while dynamically balancing the load using a hierarchical domain decomposition method. We notably achieve 100% efficiency for large enough systems. Each processor calculates independently the contact forces belonging to its domain via an iterative scheme, while data exchange between domains happens only after each iteration step. The partially parallel update at the domain boundaries leads to additional iterations. However, this effect vanishes with increasing number of particles allowing for an effective parallelization. © 2013 AIP Publishing LLC.view abstract 10.1063/1.4811893 **Anisotropic elasticity in sheared packings of frictional disks**

Shaebani, M.R. and Boberski, J. and Wolf, D.E.*Traffic and Granular Flow 2011*(2013)We study the effect of unilaterality of the interparticle interactions on the elastic response of granular materials. The anisotropy of the contact network is related to the opening of contacts during quasi-static shear deformations.As a result, local incremental constitutive relations describing the evolution of stress in terms of shear and volumetric strains are proposed, and it is shown that the macroscopic elastic behavior of anisotropic granular assemblies under biaxial deformations can be described by three independent elastic moduli: bulk, shear, and anisotropy modulus. We show that the bulk and shear moduli are independent of the imposed shear deformation if scaled by the contact density, and the magnitude of the anisotropy modulus is proportional to the ratio between shear and volumetric strain. The theoretical predictions are qualitatively in agreement with MD simulation results far from the jamming transition © Springer-Verlag Berlin Heidelberg 2013.view abstract 10.1007/978-3-642-39669-4__33 **Characteristics of Casimir-like forces in fluidized granular media**

Shaebani, M.R. and Sarabadani, J. and Wolf, D.E.*AIP Conference Proceedings*1542 (2013)Fluctuations of the hydrodynamic fields in a driven granular fluid induce effective long-range forces between the immersed intruder particles. By means of numerical simulations and analytical calculations we verify that the Casimir-like force between two immobile intruders is attractive when the volume fraction of the granular fluid is sufficiently high. However, a crossover from attraction to repulsion occurs as the density decreases. The distance between the intruders, and the restitution coefficient are the other control parameters of the transition. We investigate the nonadditive property of the interactions, and clarify the impact of dimensionality and particle shape. © 2013 AIP Publishing LLC.view abstract 10.1063/1.4812052 **Coexistence and transition between shear zones in slow granular flows**

Moosavi, R. and Shaebani, M.R. and Maleki, M. and Török, J. and Wolf, D.E. and Losert, W.*Physical Review Letters*111 (2013)We report experiments on slow granular flows in a split-bottom Couette cell that show novel strain localization features. Nontrivial flow profiles have been observed which are shown to be the consequence of simultaneous formation of shear zones in the bulk and at the boundaries. The fluctuating band model based on a minimization principle can be fitted to the experiments over a large variation of morphology and filling height with one single fit parameter, the relative friction coefficient μrel between wall and bulk. The possibility of multiple shear zone formation is controlled by μrel. Moreover, we observe that the symmetry of an initial state, with coexisting shear zones at both side walls, breaks spontaneously below a threshold value of the shear velocity. A dynamical transition between two asymmetric flow states happens over a characteristic time scale which depends on the shear strength. © 2013 American Physical Society.view abstract 10.1103/PhysRevLett.111.148301 **Effect of size polydispersity on micromechanical properties of static granular materials**

Shaebani, M.R. and Madadi, M. and Luding, S. and Wolf, D.E.*AIP Conference Proceedings*1542 (2013)We analytically investigate the influence of particle size polydispersity on the micromechanical properties of granular packings. In order to approximate the macroscopic quantities in terms of the microscale details, we develop a meanfield approach. It is shown that the trace of the fabric and stress tensors, and the elements of the stiffness tensor can be expressed in terms of dimensionless correction factors (which depend only on the moments of the size distribution), besides the average packing properties such as packing fraction, mean coordination number, and mean normal force. The results of numerical simulations confirm the validity of our analytical predictions, as long as the size distribution is not too wide. © 2013 AIP Publishing LLC.view abstract 10.1063/1.4812071 **Erratum: A three-dimensional self-learning kinetic Monte Carlo model: Application to Ag(111) (Journal of Physics Condensed Matter (2012) 24 (485005))**

Latz, A. and Brendel, L. and Wolf, D.E.*Journal of Physics Condensed Matter*25 (2013)view abstract 10.1088/0953-8984/25/5/059501 **Evolution of the contact distribution in sheared 2D granular packings**

Boberski, J. and Shaebani, M.R. and Wolf, D.E.*AIP Conference Proceedings*1542 (2013)We study the elastic response and the fabric evolution of sheared granular materials by looking at the underlying dynamics at the level of individual contacts. Unilateral interparticle interactions lead to opening and closing of contacts during quasi-static shear deformations, which anisotropically modify the fabric and affect the elastic response of the material. Additionally, the presence of non-affine motions leads to softening of the response. We numerically investigate the evolution of the contact orientation distribution of a two dimensional packing, during isotropic compression and bi-axial shear deformation processes. In the isotropic compression case, the normal overlap distribution can be well fitted by a Gaussian, and broadens with a width which linearly grows with the volumetric strain. This is in contrast to the (volume conserving) pure shear case, where the width remains approximately unaffected by the shear strain. © 2013 AIP Publishing LLC.view abstract 10.1063/1.4811983 **Evolution of the force distributions in jammed packings of soft particles**

Boberski, J. and Shaebani, M.R. and Wolf, D.E.*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*88 (2013)The evolution of the force distributions during the isotropic compression of two-dimensional packings of soft frictional particles is investigated numerically. Regardless of the applied deformation, the normal contact force distribution P(fn) can be fitted by the product of a power law, and a stretched exponential, while the tangential force distribution P(ft) is fitted well by a Gaussian. With increasing strain, the asymptotic behavior at large forces does not change, but both P(fn) and P(ft) exhibit a broadening, even though, when scaled with the average forces, their widths decrease. Furthermore, the distribution of friction mobilization P(η) is a decreasing function of η=|ft|/(μfn), except for an increased probability of fully mobilized contacts (η=1). The excess coordination number of the packings increases with the applied strain, indicating that the more a packing is compressed the more stable it becomes. © 2013 American Physical Society.view abstract 10.1103/PhysRevE.88.064201 **Lattice dependent motion of voids during electromigration**

Sindermann, S.P. and Latz, A. and Dumpich, G. and Wolf, D.E. and Meyer zu Heringdorf, F.-J.*Journal of Applied Physics*113 (2013)The influence of the crystal lattice configuration to electromigration processes, e.g., void formation and propagation, is investigated in suitable test structures. They are fabricated out of self-assembled, bi-crystalline Ag islands, grown epitaxially on a clean Si(111) surface. The μm-wide and approximately 100 nm thick Ag islands are a composition of a Ag(001) and a Ag(111) part. By focused ion beam milling, they are structured into wires with a single grain boundary, the orientation of which can be chosen arbitrarily. In-situ scanning electron microscopy (SEM) allows to capture an image sequence during electrical stressing and monitors the development of voids and hillocks in time. To visualize the position and motion of voids, we calculate void maps using a threshold algorithm. Most of the information from the SEM image sequence is compressed into one single image. Our present electromigration studies are based on in-situ SEM investigations for three different lattice configurations: Ag(001) (with electron current flow in [110] direction), Ag(111) (with electron current flow in [112] direction), and additionally 90°rotated Ag(111) (with electron current flow in [110] direction). Our experimental results show that not only the formation and shape but also the motion direction of voids strongly depends on the crystal orientation. © 2013 American Institute of Physics.view abstract 10.1063/1.4798367 **Local elastic fields in granular solids**

Boberski, J. and Brendel, L. and Wolf, D.E.*AIP Conference Proceedings*1542 (2013)The modeling of the elastic properties of disordered or granular solids requires a theory of elasticity that takes non-affine deformations into account. Using a linearized force law, the non-affine elastic deformations are calculated. Based on the microscopically exact expressions for the local strain and stress fields, a way to calculate maps of the local linear elastic constants for fictional granular packings is presented. The elastic constants are found to be scale and system size independent withing an appropriate parameter range. Deviations from classical elasticity due to the micropolar nature of granular materials is studied. © 2013 AIP Publishing LLC.view abstract 10.1063/1.4811960 **Long-range interactions in randomly driven granular fluids**

Shaebani, M.R. and Sarabadani, J. and Wolf, D.E.*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*88 (2013)We study the long-range spatial correlations in the nonequilibrium steady state of a randomly driven granular fluid with the emphasis on obtaining the explicit form of the static structure factors. The presence of immobile particles immersed in such a fluidized bed of fine particles leads to the confinement of the fluctuation spectrum of the hydrodynamic fields, which results in effective long-range interactions between the intruders. The analytical predictions are in agreement with the results of discrete element method simulations. By changing the shape and orientation of the intruders, we address how the effective force is affected by small changes in the boundary conditions. © 2013 American Physical Society.view abstract 10.1103/PhysRevE.88.022202 **Magnetotransport along a boundary: From coherent electron focusing to edge channel transport**

Stegmann, T. and Wolf, D.E. and Lorke, A.*New Journal of Physics*15 (2013)We study theoretically how electrons, coherently injected at one point on the boundary of a two-dimensional electron system, are focused by a perpendicular magnetic field B onto another point on the boundary. Using the non-equilibrium Green's function approach, we calculate the generalized four-point Hall resistance Rxy as a function of B. In weak fields, Rxy shows the characteristic equidistant peaks observed in the experiment and explained by classical cyclotron motion along the boundary. In strong fields, Rxy shows a single extended plateau reflecting the quantum Hall effect. In intermediate fields, we find superimposed upon the lower Hall plateaus anomalous oscillations, which are neither periodic in 1/B (quantum Hall effect) nor in B (classical cyclotron motion). The oscillations are explained by the interference between the occupied edge channels, which causes beatings in Rxy. In the case of two occupied edge channels, these beatings constitute a new commensurability between the magnetic flux enclosed within the edge channels and the flux quantum. Introducing decoherence and a partially specular boundary shows that this new effect is quite robust. © IOP Publishing and Deutsche Physikalische Gesellschaft.view abstract 10.1088/1367-2630/15/11/113047 **Multiple shear banding in granular materials**

Moosavi, R. and Shaebani, M.R. and Maleki, M. and Török, J. and Wolf, D.E.*Traffic and Granular Flow 2011*(2013)We present numerical and experimental evidences for multiple shear band formation in sheared granular materials. A modified Couette cell with a split bottom near the outer cylinder is made rough by gluing glass beads on all boundaries. The cell is filled with the same beads and sheared by slowly rotating the inner cylinder and the attached bottomdisk. A wide shear band is mostly observed at the free surface of the material. However, depending on the filling height and grain size, simultaneous shear bands may form near the confining walls and in the middle of the system. By minimizing the rate of energy dissipation, we numerically find similar velocity profiles for intermediate filling heights and relatively large grain sizes. © Springer-Verlag Berlin Heidelberg 2013.view abstract 10.1007/978-3-642-39669-4__32 **Self-learning kinetic Monte Carlo model for arbitrary surface orientations**

Latz, A. and Brendel, L. and Wolf, D.E.*Materials Research Society Symposium Proceedings*1559 (2013)While the self-learning kinetic Monte Carlo (SLKMC) method enables the calculation of transition rates from a realistic potential, implementations of it were usually limited to one specific surface orientation. An example is the fcc (111) surface in Latz et al. 2012, J. Phys.: Condens. Matter 24, 485005. This work provides an extension by means of detecting the local orientation, and thus allows for the accurate simulation of arbitrarily shaped surfaces. We applied the model to the diffusion of Ag monolayer islands and voids on a Ag(111) and Ag(001) surface, as well as the relaxation of a three-dimensional spherical particle. © 2013 Materials Research Society.view abstract 10.1557/opl.2013.691 **Simulation of current-activated pressure-assisted densification**

Angst, S. and Schierning, G. and Wolf, D.E.*AIP Conference Proceedings*1542 (2013)Cohe sive particles usually form very porous agglomerates. They support loads up to a consolidation pressure, which increases with decreasing particle size. Compaction of nano-powders can therefore be very costly and time consuming. If the particles are electrically conducting, which is the case e.g. for novel nano-structured thermoelectric materials, the technique of current-activated pressure-assisted densification (CAPAD) turns out to have many advantages. Electrical power deposited locally as Joule heat lowers the consolidation pressure such that higher densities without much coarsening are obtained. We present a new model combining particle dynamics, calculated by molecular dynamic methods, with a network model including thermoelectric properties. © 2013 AIP Publishing LLC.view abstract 10.1063/1.4812001 **Simulation of sheared, caking powder**

Weuster, A. and Brendel, L. and Wolf, D.E.*AIP Conference Proceedings*1542 (2013)We introduce a visco-elastic contact model for DEM simulations, which takes caking into account and investigate the impacts of this time dependent inter particle cohesion force on the bulk behavior under biaxial deformation. Starting from the assumption that the cohesion force between two particles develops on a characteristic timescale tc, we show, that two regimes can be identified. If tc is small compared to the shear rate ̇γ, full cohesion is reached within the typical contact duration. The cohesion strength remains homogeneous throughout the sample. However, if tc ≫ ̇γ crystallization bridges at fluctuating contacts never fully recover. Heterogeneous cohesion forces and granules are the consequence. © 2013 AIP Publishing LLC.view abstract 10.1063/1.4811981 **A three-dimensional self-learning kinetic Monte Carlo model: Application to Ag(111)**

Latz, A. and Brendel, L. and Wolf, D.E.*Journal of Physics Condensed Matter*24 (2012)The reliability of kinetic Monte Carlo (KMC) simulations depends on accurate transition rates. The self-learning KMC method (Trushin etal 2005 Phys.Rev.B 72 115401) combines the accuracy of rates calculated from a realistic potential with the efficiency of a rate catalog, using a pattern recognition scheme. This work expands the original two-dimensional method to three dimensions. The concomitant huge increase in the number of rate calculations on the fly needed can be avoided by setting up an initial database, containing exact activation energies calculated for processes gathered from a simpler KMC model. To provide two representative examples, the model is applied to the diffusion of Ag monolayer islands on Ag(111), and the homoepitaxial growth of Ag on Ag(111) at low temperatures. © 2012 IOP Publishing Ltd.view abstract 10.1088/0953-8984/24/48/485005 **An adaptive hierarchical domain decomposition method for parallel contact dynamics simulations of granular materials**

Shojaaee, Z. and Reza Shaebani, M. and Brendel, L. and Török, J. and Wolf, D.E.*Journal of Computational Physics*231 (2012)A fully parallel version of the contact dynamics (CD) method is presented in this paper. For large enough systems, 100% efficiency has been demonstrated for up to 256 processors using a hierarchical domain decomposition with dynamic load balancing. The iterative scheme to calculate the contact forces is left domain-wise sequential, with data exchange after each iteration step, which ensures its stability. The number of additional iterations required for convergence by the partially parallel updates at the domain boundaries becomes negligible with increasing number of particles, which allows for an effective parallelization. Compared to the sequential implementation, we found no influence of the parallelization on simulation results. © 2011 Elsevier Inc.view abstract 10.1016/j.jcp.2011.09.024 **Decoherence-induced conductivity in the discrete one-dimensional Anderson model: A novel approach to even-order generalized Lyapunov exponents**

Zilly, M. and Ujsághy, O. and Woelki, M. and Wolf, D.E.*Physical Review B - Condensed Matter and Materials Physics*85 (2012)A recently proposed statistical model for the effects of decoherence on electron transport manifests a decoherence-driven transition from quantum-coherent localized to Ohmic behavior when applied to the one-dimensional Anderson model. Here we derive the resistivity in the Ohmic case and show that the transition to localized behavior occurs when the coherence length surpasses a value which only depends on the second-order generalized Lyapunov exponent ξ -1. We determine the exact value of ξ -1 of an infinite system for arbitrary uncorrelated disorder and electron energy. Likewise all higher even-order generalized Lyapunov exponents can be calculated, as exemplified for fourth order. An approximation for the localization length (inverse standard Lyapunov exponent) is presented, by assuming a log-normal limiting distribution for the dimensionless conductance T. This approximation works well in the limit of weak disorder, with the exception of the band edges and the band center. © 2012 American Physical Society.view abstract 10.1103/PhysRevB.85.075110 **Electrical transport in semiconductor nanoparticle arrays: Conductivity, sensing and modeling**

Hartner, S. and Schwesig, D. and Plümel, I. and Wolf, D.E. and Lorke, A. and Wiggers, H.*NanoScience and Technology*79 (2012)Electrical properties of nanoparticle ensembles are dominated by interparticle transport processes, mainly due to particle-particle and particle-contact interactions. Thismakes their electrical properties dependent on the network properties such as porosity and particle size and is a main prerequisite for solid- state gas sensors, as the surrounding gas atmosphere influences the depletion layer surrounding each particle. Different kinds of nanoparticle arrays such as pressed pellets, printed layer, and thin films prepared by molecular beam-assisted deposition are characterized with respect to their electrical transport properties. Experimental results are shown for the electrical and sensing properties of several metal oxide nanoparticle ensembles and the influence of porosity is investigated during compaction of nanoparticle powders exposed to an external force. A model describing these properties is developed and it is shown that for a given material only porosity, geometry, and particle size influence the overall electrical properties. The model developed for the description of current transport in particulate matter can also be utilized to describe current-assisted sintering. © Springer-Verlag Berlin Heidelberg 2012.view abstract 10.1007/978-3-642-28546-2_10 **Influence of polydispersity on micromechanics of granular materials**

Shaebani, M.R. and Madadi, M. and Luding, S. and Wolf, D.E.*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*85 (2012)We study the effect of polydispersity on the macroscopic physical properties of granular packings in two and three dimensions. A mean-field approach is developed to approximate the macroscale quantities as functions of the microscopic ones. We show that the trace of the fabric and stress tensors are proportional to the mean packing properties (e.g., packing fraction, average coordination number, and average normal force) and dimensionless correction factors, which depend only on the moments of the particle-size distribution. Similar results are obtained for the elements of the stiffness tensor of isotropic packings in the linear affine response regime. Our theoretical predictions are in good agreement with the simulation results. © 2012 American Physical Society.view abstract 10.1103/PhysRevE.85.011301 **Laser-sintered thin films of doped SiGe nanoparticles**

Stoib, B. and Langmann, T. and Matich, S. and Antesberger, T. and Stein, N. and Angst, S. and Petermann, N. and Schmechel, R. and Schierning, G. and Wolf, D.E. and Wiggers, H. and Stutzmann, M. and Brandt, M.S.*Applied Physics Letters*100 (2012)We present a study of the morphology and the thermoelectric properties of short-pulse laser-sintered (LS) nanoparticle (NP) thin films, consisting of SiGe alloy NPs or composites of Si and Ge NPs. Laser-sintering of spin-coated NP films in vacuum results in a macroporous percolating network with a typical thickness of 300 nm. The Seebeck coefficient for LS samples is the same as for bulk samples prepared by current-assisted sintering and is typical for degenerate doping. The electrical conductivity of LS films is influenced by two-dimensional percolation effects and rises with increasing temperature, approximately following a power-law. © 2012 American Institute of Physics.view abstract 10.1063/1.4726041 **Magnetic vortices induced by a moving tip**

Magiera, M.P. and Hucht, A. and Hinrichsen, H. and Dahmen, S.R. and Wolf, D.E.*EPL*100 (2012)A two-dimensional easy-plane ferromagnetic substrate, interacting with a dipolar tip which is magnetised perpendicular with respect to the easy plane is studied numerically by solving the Landau-Lifshitz Gilbert equation. Due to the symmetry of the dipolar field of the tip, in addition to the collinear structure a magnetic vortex structure becomes stable. It is robust against excitations caused by the motion of the tip. We show that for high excitations the system may perform a transition between the two states. The influence of domain walls, which may also induce this transition, is examined. © Copyright EPLA, 2012.view abstract 10.1209/0295-5075/100/27004 **Nanopowder sintering**

Wolf, D.E. and Brendel, L. and Fendrich, M. and Zinetullin, R.*NanoScience and Technology*79 (2012)We define nanopowder sintering as the conversion of a loose agglomerate of nanoparticles into a nanostructured solid. This means that grain boundaries between the particles must survive the sintering process to a large extent. The key issue here is structural self organization; external control is limited to macroscopic parameters like temperature and pressure, while the desired structure on the particle scale should then form by itself. This chapter reviews, how the early, intermediate, and late stages of sintering are influenced by the presence of grain boundaries, with a special focus on particle sizes in the nanometer range. A new, efficient computer simulation model is presented and its applicability to Ni- and to ITO-particles is briefly discussed. © Springer-Verlag Berlin Heidelberg 2012.view abstract 10.1007/978-3-642-28546-2_7 **Nonadditivity of fluctuation-induced forces in fluidized granular media**

Shaebani, M.R. and Sarabadani, J. and Wolf, D.E.*Physical Review Letters*108 (2012)We investigate the effective long-range interactions between intruder particles immersed in a randomly driven granular fluid. The effective Casimir-like force between two intruders, induced by the fluctuations of the hydrodynamic fields, can change its sign when varying the control parameters: the volume fraction, the distance between the intruders, and the restitution coefficient. More interestingly, by inserting more intruders, we verify that the fluctuation-induced interaction is not pairwise additive. The simulation results are qualitatively consistent with the theoretical predictions based on mode coupling calculations. These results shed new light on the underlying mechanisms of collective behaviors in fluidized granular media. © 2012 American Physical Society.view abstract 10.1103/PhysRevLett.108.198001 **Shear flow of dense granular materials near smooth walls. I. Shear localization and constitutive laws in the boundary region**

Shojaaee, Z. and Roux, J.-N. and Chevoir, F. and Wolf, D.E.*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*86 (2012)We report on a numerical study of the shear flow of a simple two-dimensional model of a granular material under controlled normal stress between two parallel smooth frictional walls moving with opposite velocities ±V. Discrete simulations, which are carried out with the contact dynamics method in dense assemblies of disks, reveal that, unlike rough walls made of strands of particles, smooth ones can lead to shear strain localization in the boundary layer. Specifically, we observe, for decreasing V, first a fluidlike regime (A), in which the whole granular layer is sheared, with a homogeneous strain rate except near the walls, then (B) a symmetric velocity profile with a solid block in the middle and strain localized near the walls, and finally (C) a state with broken symmetry in which the shear rate is confined to one boundary layer, while the bulk of the material moves together with the opposite wall. Both transitions are independent of system size and occur for specific values of V. Transient times are discussed. We show that the first transition, between regimes A and B, can be deduced from constitutive laws identified for the bulk material and the boundary layer, while the second one could be associated with an instability in the behavior of the boundary layer. The boundary zone constitutive law, however, is observed to depend on the state of the bulk material nearby. © 2012 American Physical Society.view abstract 10.1103/PhysRevE.86.011301 **Shear flow of dense granular materials near smooth walls. II. Block formation and suppression of slip by rolling friction**

Shojaaee, Z. and Brendel, L. and Török, J. and Wolf, D.E.*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*86 (2012)The role of rotational degrees of freedom and of microscopic contact properties at smooth walls in two dimensional planar shear has been investigated by contact dynamics simulations of round hard frictional particles. Our default system setup consists of smooth frictional walls, giving rise to slip. We show that there exists a critical microscopic friction coefficient at the walls, above which they are able to shear the granular medium. We observe distinctive features at this critical point, which to our knowledge have not been reported before. Activating rolling friction at smooth walls reduces slip, leading to similar shear behavior as for rough walls (with particles glued on their surface). Our simulations with rough walls are in agreement with previous results, provided the roughness is strong enough. In the limit of small roughness amplitude, however, the distinctive features of shearing with smooth walls are confirmed. © 2012 American Physical Society.view abstract 10.1103/PhysRevE.86.011302 **Simulation of electromigration effects on voids in monocrystalline Ag**

Latz, A. and Wolf, D.E.*Materials Research Society Symposium Proceedings*1428 (2012)Understanding electromigration effects in monocrystalline metal becomes of increasing interest with decreasing width and thickness of interconnects. Using a three-dimensional, atomistic model based on the Kinetic Monte Carlo method, we investigate voids in monocrystalline silver. Subject to electromigration, voids begin to drift. We show that the drift velocity not only depends on the void size, but also on the electromigration force direction, with respect to the crystallographic orientation. © 2012 Materials Research Society.view abstract 10.1557/opl.2012.1099 **Simulation of electromigration effects on voids in monocrystalline Ag films**

Latz, A. and Sindermann, S. and Brendel, L. and Dumpich, G. and Meyer zu Heringdorf, F.-J. and Wolf, D.E.*Physical Review B - Condensed Matter and Materials Physics*85 (2012)We developed a three-dimensional, atomistic model based on the kinetic Monte Carlo method to investigate how voids penetrating a monocrystalline silver film are affected by electromigration. The simulations show a clear dependency between the nonequilibrium shape of the voids and the crystallographic orientation of the film. The simulation results are in accordance with experimental results on bicrystalline silver wires. © 2012 American Physical Society.view abstract 10.1103/PhysRevB.85.035449 **Statistical model for the effects of phase and momentum randomization on electron transport**

Stegmann, T. and Zilly, M. and Ujśaghy, O. and Wolf, D.E.*European Physical Journal B*85 (2012)A simple statistical model for the effects of dephasing on electron transport in one-dimensional quantum systems is introduced, which allows to adjust the degree of phase and momentum randomization independently. Hence, the model is able to describe the transport in an intermediate regime between classical and quantum transport. The model is based on B̈uttiker's approach using fictitious reservoirs for the dephasing effects. However, in contrast to other models, at the fictitious reservoirs complete phase randomization is assumed, which effectively divides the system into smaller coherent subsystems, and an ensemble average over randomly distributed dephasing reservoirs is calculated. This approach reduces not only the computation time but allows also to gain new insight into system properties. In this way, after deriving an efficient formula for the disorder-averaged resistance of a tight-binding chain, it is shown that the dephasing-driven transition from localized-exponential to ohmic-linear behavior is not affected by the degree of momentum randomizing dephasing. © Springer-Verlag 2012.view abstract 10.1140/epjb/e2012-30348-y **Strongly anisotropic nonequilibrium phase transition in Ising models with friction**

Angst, S. and Hucht, A. and Wolf, D.E.*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*85 (2012)The nonequilibrium phase transition in driven two-dimensional Ising models with two different geometries is investigated using Monte Carlo methods as well as analytical calculations. The models show dissipation through fluctuation induced friction near the critical point. We first consider high driving velocities and demonstrate that both systems are in the same universality class and undergo a strongly anisotropic nonequilibrium phase transition, with anisotropy exponent θ=3. Within a field theoretical ansatz the simulation results are confirmed. The crossover from Ising to mean field behavior in dependency of system size and driving velocity is analyzed using crossover scaling. It turns out that for all finite velocities the phase transition becomes strongly anisotropic in the thermodynamic limit. © 2012 American Physical Society.view abstract 10.1103/PhysRevE.85.051120 **The effect of Peltier heat during current activated densification**

Becker, A. and Angst, S. and Schmitz, A. and Engenhorst, M. and Stoetzel, J. and Gautam, D. and Wiggers, H. and Wolf, D.E. and Schierning, G. and Schmechel, R.*Applied Physics Letters*101 (2012)It is shown that current-activated pressure-assisted densification (CAPAD) is sensitive to the Peltier effect. Under CAPAD, the Peltier effect leads to a significant redistribution of heat within the sample during the densification. The densification of highly p-doped silicon nanoparticles during CAPAD and the properties of the obtained samples are investigated experimentally and by computer simulation. Both, simulation and experiments, indicate clearly a higher temperature on the cathode side and a decreasing temperature from the center to the outer shell. Furthermore, computer simulations provide additional insights into the temperature profile which explain the anisotropic properties of the measured sample. © 2012 American Institute of Physics.view abstract 10.1063/1.4731272 **Thermoreflectance imaging of percolation effects and dynamic resistance in indium tin oxide nanoparticle layers**

Chavez, R. and Angst, S. and Maize, K. and Gondorf, A. and Schierning, G. and Wolf, D.E. and Lorke, A. and Shakouri, A.*Journal of Applied Physics*112 (2012)Thin films of indium tin oxide nanoparticles are studied using charge-coupled device thoermoreflectance. High resolution sub-micron thermal images confirm that percolation in current conduction induces strongly inhomogeneous heat loads on the thin film. We experimentally show that the inhomogeneous current densities induce thousands of micro-hotspots that can be 20 hotter than the average Joule heating in the thin film layer and show comparable behavior in a resistor network. In addition to the percolation induced micro-hotspots, we report major hotspots, with non-Joule behavior, whose temperature response is greater than I 2. We demonstrate that a temperature dependent resistor can account for an effective exponent larger than 2. Finally, it is shown that while ambient molecules modify the thin film conductivity by at least 20, current conduction and percolation effects remain largely unchanged, but such chemical reactions can be nonetheless detected with thermoreflectance. © 2012 American Institute of Physics.view abstract 10.1063/1.4757960 **Unilateral interactions in granular packings: A model for the anisotropy modulus**

Shaebani, M.R. and Boberski, J. and Wolf, D.E.*Granular Matter*14 (2012)Unilateral interparticle interactions have an effect on the elastic response of granular materials due to the opening and closing of contacts during quasi-static shear deformations. A simplified model is presented, for which constitutive relations can be derived. For biaxial deformations the elastic behavior in this model involves three independent elastic moduli: bulk, shear, and anisotropy modulus. The bulk and the shear modulus, when scaled by the contact density, are independent of the deformation. However, the magnitude of the anisotropy modulus is proportional to the ratio between shear and volumetric strain. Sufficiently far from the jamming transition, when corrections due to non-affine motion become weak, the theoretical predictions are qualitatively in agreement with simulation results. © Springer-Verlag 2012.view abstract 10.1007/s10035-012-0329-0 **From nanoparticles to nanocrystalline bulk: Percolation effects in field assisted sintering of silicon nanoparticles**

Schwesig, D. and Schierning, G. and Theissmann, R. and Stein, N. and Petermann, N. and Wiggers, H. and Schmechel, R. and Wolf, D.E.*Nanotechnology*22 (2011)Nanocrystalline bulk materials are desirable for many applications as they combine mechanical strength and specific electronic transport properties. Our bottom-up approach starts with tailored nanoparticles. Compaction and thermal treatment are crucial, but usually the final stage sintering is accompanied by rapid grain growth which spoils nanocrystallinity. For electrically conducting nanoparticles, field activated sintering techniques overcome this problem. Small grain sizes have been maintained in spite of consolidation. Nevertheless, the underlying principles, which are of high practical importance, have not been fully elucidated yet. In this combined experimental and theoretical work, we show how the developing microstructure during sintering correlates with the percolation paths of the current through the powder using highly doped silicon nanoparticles as a model system. It is possible to achieve a nanocrystalline bulk material and a homogeneous microstructure. For this, not only the generation of current paths due to compaction, but also the disintegration due to Joule heating is required. The observed density fluctuations on the micrometer scale are attributed to the heat profile of the simulated powder networks. © 2011 IOP Publishing Ltd.view abstract 10.1088/0957-4484/22/13/135601 **Magnetic friction: From Stokes to Coulomb behavior**

Magiera, M.P. and Angst, S. and Hucht, A. and Wolf, D.E.*Physical Review B - Condensed Matter and Materials Physics*84 (2011)We demonstrate that in a ferromagnetic substrate which is continuously driven out of equilibrium by a field moving with constant velocity v, at least two types of friction may occur when v goes to zero. The substrate may feel a friction force proportional to v (Stokes friction) if the field changes on a time scale which is larger than the intrinsic relaxation time. On the other hand, the friction force may become independent of v in the opposite case (Coulomb friction). These observations are analogous to, e.g., solid friction. The effect is demonstrated in both the Ising (one spin dimension) and the Heisenberg (three spin dimensions) models, irrespective of which kind of dynamics (Metropolis spin-flip dynamics or Landau-Lifshitz-Gilbert precessional dynamics) is used. For both models the limiting case of Coulomb friction can be treated analytically. Furthermore we present an empiric expression reflecting the correct Stokes behavior and therefore yielding the correct crossover velocity and dissipation. © 2011 American Physical Society.view abstract 10.1103/PhysRevB.84.212301 **Minimal dissipation theory and shear bands in biaxial tests**

Stegmann, T. and Török, J. and Brendel, L. and Wolf, D.E.*Granular Matter*13 (2011)True biaxial tests of granular materials are investigated by applying the principle of minimal dissipation and comparing to two dimensional contact dynamics simulations. It is shown that the macroscopic steady state manifested by constant stress ratio and constant volume is the result of the ever changing microscopic structure which minimizes the dissipation rate. The shear band angle in the varying shear band structures is found to be constant. We also show that introducing friction on the walls reduces the degeneracy of the optimal shear band structures to one for a wide range of parameters which gives a non-constant stress ratio curve with varying aspect ratio that can be calculated. © 2011 Springer-Verlag.view abstract 10.1007/s10035-011-0280-5 **Spin waves cause non-linear friction**

Magiera, M.P. and Brendel, L. and Wolf, D.E. and Nowak, U.*EPL*95 (2011)Energy dissipation is studied for a hard magnetic tip that scans a soft magnetic substrate. The dynamics of the atomic moments are simulated by solving the Landau-Lifshitz-Gilbert (LLG) equation numerically. The local energy currents are analysed for the case of a Heisenberg spin chain taken as substrate. This leads to an explanation for the velocity dependence of the friction force: The non-linear contribution for high velocities can be attributed to a spin wave front pushed by the tip along the substrate. Copyright © 2011 EPLA.view abstract 10.1209/0295-5075/95/17010 **Conductance of DNA molecules: Effects of decoherence and bonding**

Zilly, M. and Ujsághy, O. and Wolf, D.E.*Physical Review B - Condensed Matter and Materials Physics*82 (2010)The influence of decoherence and bonding on the linear conductance of single double-stranded DNA molecules is examined by fitting a phenomenological statistical model developed recently to experimental results. The DNA molecule itself is described by a tight-binding ladder model with parameters obtained from published ab initio calculations. The good agreement with the experiments on sequence and length dependence gives a hint on the nature of conduction in DNA and at the same time provides a crucial test of the model. © 2010 The American Physical Society.view abstract 10.1103/PhysRevB.82.125125

#### dynamic force microscopy

#### epitaxial growth

#### sintering