Evidence of friction reduction in laterally graded materials

• Roberto Guarino,
• Gianluca Costagliola,
• Federico Bosia and
• Nicola Maria Pugno

Beilstein J. Nanotechnol. 2018, 9, 2443–2456, doi:10.3762/bjnano.9.229

• , Dassault Systèmes, France) and employing C3D8I elements, which are 8-node bricks with 8 points of integration and incompatible modes. The choice of this element type allows a good representation of the stress singularities at the edges (see Supporting Information File 5). A convergence study is carried out

Performance analysis of rigorous coupled-wave analysis and its integration in a coupled modeling approach for optical simulation of complete heterojunction silicon solar cells

• Ziga Lokar,
• Benjamin Lipovsek,
• Marko Topic and
• Janez Krc

Beilstein J. Nanotechnol. 2018, 9, 2315–2329, doi:10.3762/bjnano.9.216

• obtained previously [20]. However, we also show that the method can suffer in terms of accuracy for large (5 μm) textures for what is considered reasonable simulation time (about one day for the complete wavelength range of interest on a typical desktop PC). Additionally, RCWA may have convergence

• convergence towards a steady solution, 30 sublayers are sufficient for both angles of incidence, at least for wavelengths above 450 nm. The errors in JSC as a function of the number of sublayers (Figure 5e) indicate a lower |ΔJSC| for the case of normal incident light. 300 sublayers were used as the reference

• -vertical light incidence. The convergence of non-vertical incidence is again a bit worse than for the vertical incidence, although the differences are small from 500 nm onwards. The errors in JSC as a function of the number of sublayers show that the |JSC| error corresponding to case of normal incident

Intrinsic ultrasmall nanoscale silicon turns n-/p-type with SiO₂/Si₃N₄-coating

• Dirk König,
• Daniel Hiller,
• Noël Wilck,
• Birger Berghoff,
• Merlin Müller,
• Sangeeta Thakur,
• Giovanni Di Santo,
• Luca Petaccia,
• Joachim Mayer,
• Sean Smith and
• Joachim Knoch

Beilstein J. Nanotechnol. 2018, 9, 2255–2264, doi:10.3762/bjnano.9.210

• bonds of Si to O and N. The root mean square (RMS) and peak force convergence limits for all atoms were 3 × 10−4 Ha/a0 (Hartrees per Bohr radius) or 80 meV/nm and 4.5 × 10−4 Ha/a0 or 120 meV/nm, respectively. Tight convergence criteria were applied to the self-consistent field routine. Ultrafine

• Supporting Information File 1) due to the inter-NC distance of merely 1 nm, accounting for some ICT convergence from Si NCs to SiO2 or Si3N4. From Figure 2c we see that an ICT saturation is evident for ≥2 ML SiO2. This saturation is less apparent when Si3N4 is applied as the embedding matrix. We explain this

Numerical analysis of single-point spectroscopy curves used in photo-carrier dynamics measurements by Kelvin probe force microscopy under frequency-modulated excitation

• Pablo A. Fernández Garrillo,
• Benjamin Grévin and
• Łukasz Borowik

Beilstein J. Nanotechnol. 2018, 9, 1834–1843, doi:10.3762/bjnano.9.175

• red dashed line. The graphs depicting the results from simulations at 600 kHz and 3 MHz were zoomed-in so that the convergence process can be noticed. Simulated surface photovoltage spectroscopy curves of the F5BnPA region for different SPV built-up and decay input parameters. Experimental data was

Atomic-level characterization and cilostazol affinity of poly(lactic acid) nanoparticles conjugated with differentially charged hydrophilic molecules

• María Francisca Matus,
• Martín Ludueña,
• Cristian Vilos,
• Iván Palomo and
• Marcelo M. Mariscal

Beilstein J. Nanotechnol. 2018, 9, 1328–1338, doi:10.3762/bjnano.9.126

• calculations [38][39]. In this work, a modified version of the force field developed by Kim and van Duin, optimized for C/O/H/N/P systems [40], was used. The convergence criteria for energy minimization, rupture temperature limit and the optimal separation distance for PLA chains to build the PLA core were

• configuration was minimized using the Polak–Ribiere version of the conjugate gradient (CG) algorithm [41] with a convergence criteria of 1.0e−12 followed by an equilibration of 2 ns at 310 K using NVT ensemble (constant temperature and volume) and a timestep of 1 fs. A Nose–Hoover thermostat was used to control

Lyapunov estimation for high-speed demodulation in multifrequency atomic force microscopy

• David M. Harcombe,
• Michael G. Ruppert,
• Michael R. P. Ragazzon and
• Andrew J. Fleming

Beilstein J. Nanotechnol. 2018, 9, 490–498, doi:10.3762/bjnano.9.47

• particular frequency is recovered by Filter description The Lyapunov filter [28] is implemented as a linear observer as shown in Figure 2. A key property of the filter is exponential convergence of the estimated states [29], with the tunable loop gain constant γ governing the speed of convergence. The filter

• -phase pair of . A key requirement to ensure exponential convergence of to x, is to guarantee that c is persistently excited [29]. Convergence is shown for the single-frequency filter in [28], and can easily be extended for the multifrequency case. Furthermore, exponential convergence of means that

Adsorption of iron tetraphenylporphyrin on (111) surfaces of coinage metals: a density functional theory study

• Hao Tang,
• Nathalie Tarrat,
• Véronique Langlais and
• Yongfeng Wang

Beilstein J. Nanotechnol. 2017, 8, 2484–2491, doi:10.3762/bjnano.8.248

• to 1 eV (as in [11]). The convergence condition of the self-consistent electronic loops was set to 10−6 eV, while the atomic positions were relaxed until the forces reached a value lower than 0.01 eV/Å. The atoms of the two bottom layers of the metal slab were kept fixed at their bulk positions and

Robust procedure for creating and characterizing the atomic structure of scanning tunneling microscope tips

• Sumit Tewari,
• Koen M. Bastiaans,
• Milan P. Allan and
• Jan M. van Ruitenbeek

Beilstein J. Nanotechnol. 2017, 8, 2389–2395, doi:10.3762/bjnano.8.238

• analysis of the results of this procedure we define a parameter that could capture the convergence of the tip structure to this symmetric state. This same parameter should also serve to verify whether tips such as those in Figure 3 and Figure 4 converged to the same state. For comparing the constant-height

• normalized to the maximum current level which for the above figures are 38 and 24 nA, respectively Ratio of major to minor axis of the elliptical fit showing the convergence of the tip apex structure to a circularly symmetric shape. Three independent runs are shown by blue, green and red symbols. The two

Numerical investigation of the tribological performance of micro-dimple textured surfaces under hydrodynamic lubrication

• Kangmei Li,
• Dalei Jing,
• Jun Hu,
• Xiaohong Ding and
• Zhenqiang Yao

Beilstein J. Nanotechnol. 2017, 8, 2324–2338, doi:10.3762/bjnano.8.232

• accuracy of calculation and the rate of convergence, the meshing operation follows several criteria: (1) the use of structured grids, as far as possible; (2) the ratio of the length of the longest element edge to the length of the shortest element edge should be controlled below 5:1; (3) the skewness

Modelling focused electron beam induced deposition beyond Langmuir adsorption

• Dédalo Sanz-Hernández and
• Amalio Fernández-Pacheco

Beilstein J. Nanotechnol. 2017, 8, 2151–2161, doi:10.3762/bjnano.8.214

• saturated monolayers, appearance of multilayers, or the convergence from the multilayer model to the Langmuir model, can be understood in terms of the characteristic time scales of the system. These results are synthesized in a set of dimensionless FEBID frequency maps for Langmuir, and homogeneous and

Magnetic properties of optimized cobalt nanospheres grown by focused electron beam induced deposition (FEBID) on cantilever tips

• Soraya Sangiao,
• César Magén,
• Darius Mofakhami,
• Grégoire de Loubens and
• José María De Teresa

Beilstein J. Nanotechnol. 2017, 8, 2106–2115, doi:10.3762/bjnano.8.210

• a probe-corrected FEI Titan 60-300 equipped with a high brightness field emission gun (X-FEG), a CEOS corrector for the condenser system and a Gatan Tridiem 866 ERS image filter/spectrometer. The EELS acquisition was performed with a convergence angle of 25 mrad, a collection semi-angle of around 60

Structural model of silicene-like nanoribbons on a Pb-reconstructed Si(111) surface

• Agnieszka Stępniak-Dybala and
• Mariusz Krawiec

Beilstein J. Nanotechnol. 2017, 8, 1836–1843, doi:10.3762/bjnano.8.185

• cutoff for all calculations was set to 340 eV, and the Brillouin zone was sampled by a 5 × 2 × 1 Monkhorst–Pack k-points grid [51], 640 eV and 9 × 3 × 1 grid in convergence tests, which resulted in changes of the surface energies of less than 0.1 meV/Å2. The spin–orbit interaction has not been included

α-Silicene as oxidation-resistant ultra-thin coating material

• Ali Kandemir,
• Fadil Iyikanat,
• Cihan Bacaksiz and
• Hasan Sahin

Beilstein J. Nanotechnol. 2017, 8, 1808–1814, doi:10.3762/bjnano.8.182

• of at 500 eV. A 3 × 3 × 1 k-point mesh was used for the structural relaxation. The criterion of convergence of energy was chosen as 10−5 eV between two ionic steps, and the maximum force allowed on each atom is 0.1 meV/Å. At least 13 Å of vacuum were applied along z-direction to hinder interactions

Laser processing of thin-film multilayer structures: comparison between a 3D thermal model and experimental results

• Babak B. Naghshine and
• Amirkianoosh Kiani

Beilstein J. Nanotechnol. 2017, 8, 1749–1759, doi:10.3762/bjnano.8.176

• phase change algorithms are called and the last sub-step is repeated until convergence. Phase change and ablation algorithms Phase change and ablation algorithms were only applied in the last sub-step and at all the points where Tn+1/3 or Tn+2/3 were higher than the boiling point, they were reduced to

• cell became smaller (Δz was reduced by Ablative energy × Δt/(ρLv)) and the laser energy was decreased by the ablative energy. The last sub-step was repeated until convergence (Ablative energy = 0). Figure 10 shows the phase change flowchart for evaporation. Similar algorithms are considered for melting

Adsorption and diffusion characteristics of lithium on hydrogenated α- and β-silicene

• Fadil Iyikanat,
• Ali Kandemir,
• Cihan Bacaksiz and
• Hasan Sahin

Beilstein J. Nanotechnol. 2017, 8, 1742–1748, doi:10.3762/bjnano.8.175

• -layer Ag(111) surface. Lattice constants and total energies were computed using the conjugate-gradient algorithm. The total energy difference between the sequential steps in the iterations was taken to be 10−5 eV for the convergence criterion. The total force in the unit cell was reduced to a value of

A review of demodulation techniques for amplitude-modulation atomic force microscopy

• Michael G. Ruppert,
• David M. Harcombe,
• Michael R. P. Ragazzon,
• S. O. Reza Moheimani and
• Andrew J. Fleming

Beilstein J. Nanotechnol. 2017, 8, 1407–1426, doi:10.3762/bjnano.8.142

• merit is important to determine both the speed of convergence and the amount of noise suppression in the estimate. This relationship is clearly identified by plotting the total integrated noise of the amplitude estimate against the tracking bandwidth for a known input noise density. Lastly, the

• ]. Characteristic and fundamental to its working principle is the existence of a linear system model that describes the dynamics to be estimated and the presence of feedback generated from the Kalman gain, which dictates the rate of convergence. This structure is schematically shown in Figure 5. A linear time

• law via a Lyapunov stability proof to show boundedness of the error, hence the name. An additional persistency of excitation property [64] guarantees exponential convergence of the parameters. The estimator can be written in the compact form [45][46] where γ is the constant gain parameter for tuning

3D continuum phonon model for group-IV 2D materials

• Morten Willatzen,
• Lok C. Lew Yan Voon,
• Appala Naidu Gandi and
• Udo Schwingenschlögl

Beilstein J. Nanotechnol. 2017, 8, 1345–1356, doi:10.3762/bjnano.8.136

• ) based codes. One of the earliest applications to group-IV elemental 2D materials was for the important prediction of the stability of silicene and germanene [1]. These are complex calculations and prone to qualitative errors due to the various approximations such as convergence criteria and use of

Two-dimensional silicon and carbon monochalcogenides with the structure of phosphorene

• Dario Rocca,
• Ali Abboud,
• Ganapathy Vaitheeswaran and
• Sébastien Lebègue

Beilstein J. Nanotechnol. 2017, 8, 1338–1344, doi:10.3762/bjnano.8.135

• threshold of at least 10−4 Ry/Bohr the phonon curves have been computed by using density functional perturbation theory [32]. The kinetic-energy cut-off convergence has been carefully tested for each system and a 12 × 12 × 1 k-point grid was used (supposing that the z direction is perpendicular to the two

Calculating free energies of organic molecules on insulating substrates

• Julian Gaberle,
• David Z. Gao and
• Alexander L. Shluger

Beilstein J. Nanotechnol. 2017, 8, 667–674, doi:10.3762/bjnano.8.71

• can be obtained for small systems, the larger the configurational space the more challenging the calculations become and convergence is not guaranteed [32][42]. In particular, when the free-energy landscape varies by several kT along the reaction coordinate, MD is often insufficient for sampling the

• high-energy states. The challenge of achieving convergence can be addressed by running constrained MD, where the system evolves along a defined reaction coordinate in order to improve the sampling of high-energy, low- probability states [31]. In this paper we investigated the free energy of of 1,3,5

• these quantities on simulation time is investigated in order to check for convergence. The results show that subtle features in the free-energy landscape can be resolved with very long trajectories even if the calculations are not fully converged. Furthermore, entropic contributions to free energy can

Computing the T-matrix of a scattering object with multiple plane wave illuminations

• Martin Fruhnert,
• Ivan Fernandez-Corbaton,
• Vassilios Yannopapas and
• Carsten Rockstuhl

Beilstein J. Nanotechnol. 2017, 8, 614–626, doi:10.3762/bjnano.8.66

• vectors of the surface of an imaginary sphere. They are distributed with the same nearest neighbor distance, as is shown in Figure 1. The polarization of the electric field is then chosen randomly for each wave. To check the convergence of our method we increase the number of illuminations used to

• calculation with a finer mesh. Dimer We now consider a slightly more complex object to further investigate the convergence of our method. The dimer, i.e., two coupled spheres, is a suitable example, because we can calculate the T-matrix semi-analytically as a reference. We get the T-matrix of the single

• illuminations, depicted with their wave vectors in green. Convergence of the T-matrix calculation with the increase of the number of plane wave illuminations. The minimum number of illuminations to solve for all the unknown entries of the T-matrix for the multipole order N = 2 is 16. The error is shown for two

Association of aescin with β- and γ-cyclodextrins studied by DFT calculations and spectroscopic methods

• Ana I. Ramos,
• Pedro D. Vaz,
• Susana S. Braga and
• Artur M. S. Silva

Beilstein J. Nanotechnol. 2017, 8, 348–357, doi:10.3762/bjnano.8.37

• calculations by creating different complex geometries that could represent the real complex. The geometries were optimised at the M06-2X/6-31g(d) level with tight convergence criteria, including dispersion energy corrections (D3) and in the presence of a solvation model to simulate the presence of water. It

• correlation as developed by Truhlar and Zhao [34]. Pople’s 6-31G(d) basis set was used on all atoms. All geometries were optimised without any geometry constraints at the M06-2X/6-31G(d) level of theory as mentioned above. The optimisation approach also included the use of tight convergence criteria. To

Monolayer graphene/SiC Schottky barrier diodes with improved barrier height uniformity as a sensing platform for the detection of heavy metals

• Ivan Shtepliuk,
• Jens Eriksson,
• Volodymyr Khranovskyy,
• Tihomir Iakimov,
• Anita Lloyd Spetz and
• Rositsa Yakimova

Beilstein J. Nanotechnol. 2016, 7, 1800–1814, doi:10.3762/bjnano.7.173

• the Becke3LYP level of density functional theory with a 6-31G basis set on carbon and a basis set of Stuttgart-Dresden SDD effective core potentials [53] on Cd, Hg and Pb atoms. DFT calculations of small graphene clusters and geometry optimization are performed using the default convergence criteria

Photocurrent generation in carbon nanotube/cubic-phase HfO₂ nanoparticle hybrid nanocomposites

• Protima Rauwel,
• Augustinas Galeckas,
• Martin Salumaa,
• Frédérique Ducroquet and
• Erwan Rauwel

Beilstein J. Nanotechnol. 2016, 7, 1075–1085, doi:10.3762/bjnano.7.101

• 80 kV. For the EELS data acquisition, the convergence and collection angles were set to 14.6 mrad and 24 mrad, respectively, for a camera length of 4 cm, a condenser aperture of 50 µm and a spectrometer slit of 3 mm. For these values, the energy resolution measured as the full width at half maximum

The hydraulic mechanism in the hind wing veins of Cybister japonicus Sharp (order: Coleoptera)

• Jiyu Sun,
• Wei Wu,
• Mingze Ling,
• Bharat Bhushan and
• Jin Tong

Beilstein J. Nanotechnol. 2016, 7, 904–913, doi:10.3762/bjnano.7.82

• pressure measurement (Figure 5) was connected to the sensor and had missing elytra. Simulation The hexahedral mesh is orthogonal and gridded [28]. Thus, it will speed up convergence and improve the calculation accuracy. In Figure 1E, the total grid number shown in the graph is 135,000. At the same time

Free vibration of functionally graded carbon-nanotube-reinforced composite plates with cutout

• Mostafa Mirzaei and
• Yaser Kiani

Beilstein J. Nanotechnol. 2016, 7, 511–523, doi:10.3762/bjnano.7.45

• accuracy of the presented solution method, convergence and comparison studies are carried out. Next, parametric studies are provided to explore the effects of carbon nanotube characteristics on the frequencies of the perforated plate. The following convention is established for boundary conditions herein

• , whereas G23 is taken equal to 1.2G12 [28]. Convergence and comparison studies Convergence and comparison studies are presented in this section. First, the convergence study allows for the necessary shape functions to be obtained with the series expansion of the Ritz method, with results shown in Table 2

• ][30][31][32][33][34]. Convergence study on the first three frequency parameters of SSSS isotropic homogeneous square plates with a/h = 100, ν = 0.3 and two cutout ratios. First four frequency parameters for square CCCC isotropic homogeneous plates with ν = 0.3, a/h = 100 and various square cutout