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

Calculations of helium separation via uniform pores of stanene-based membranes

• Guoping Gao,
• Yan Jiao,
• Yalong Jiao,
• Fengxian Ma,
• Liangzhi Kou and
• Aijun Du

Beilstein J. Nanotechnol. 2015, 6, 2470–2476, doi:10.3762/bjnano.6.256

• cut-off energy for plane waves was set at 500 eV, and the convergence criteria for residual force and energy on each atom during structure relaxation were set to 0.005 eV/Å and 10−5 eV, respectively. The vacuum space was more than 20 Å, which was enough to avoid the interaction between periodic images

Ultrastructural changes in methicillin-resistant Staphylococcus aureus induced by positively charged silver nanoparticles

• Dulce G. Romero-Urbina,
• Humberto H. Lara,
• J. Jesús Velázquez-Salazar,
• M. Josefina Arellano-Jiménez,
• Eduardo Larios,
• Anand Srinivasan,
• Jose L. Lopez-Ribot and
• Miguel José Yacamán

Beilstein J. Nanotechnol. 2015, 6, 2396–2405, doi:10.3762/bjnano.6.246

• emission transmission electron microscope operated at 200 kV. HAADF-STEM bacterial cell images were obtained using Cs-corrected JEOL JEM-ARM-200F microscope in both bright-field (BF) and dark-field (DF) modes. The microscope was operated at 200 kV using a convergence angle of 26 mrad and collection semi

Surface engineering of nanoporous substrate for solid oxide fuel cells with atomic layer-deposited electrolyte

• Sanghoon Ji,
• Waqas Hassan Tanveer,
• Wonjong Yu,
• Sungmin Kang,
• Gu Young Cho,
• Sung Han Kim,
• Jihwan An and
• Suk Won Cha

Beilstein J. Nanotechnol. 2015, 6, 1805–1810, doi:10.3762/bjnano.6.184

• Sanghoon Ji Waqas Hassan Tanveer Wonjong Yu Sungmin Kang Gu Young Cho Sung Han Kim Jihwan An Suk Won Cha Graduate School of Convergence Science and Technology, Seoul National University, Iui-dong, Yeongtong-gu, Suwon 443-270, South Korea Department of Mechanical Engineering, Seoul National

Simple and efficient way of speeding up transmission calculations with k-point sampling

• Jesper Toft Falkenberg and
• Mads Brandbyge

Beilstein J. Nanotechnol. 2015, 6, 1603–1608, doi:10.3762/bjnano.6.164

• wavefunctions, which tend to be elaborate. In this paper we present a simple and efficient post-processing interpolation scheme which can significantly speed up the convergence with respect to k-points. We illustrate the method by applying it to various graphene-based nano-structures which are prone to bad

• convergence due to its vanishing density of states at the Fermi level. In the remaining parts of the paper we first explain the workings of the interpolation scheme in section Results and Discussion, while we investigate various test cases in section Example cases, and finally discuss limitations to the

• resolution. Often the rough behavior of the transmission is already seen with a limited number of k-points but the convergence of the average is slow since the functions are changing abruptly with energy, e.g., around a band onset or a resonance. The position of the abrupt feature will typically shift in a

Can molecular projected density of states (PDOS) be systematically used in electronic conductance analysis?

• Tonatiuh Rangel,
• Gian-Marco Rignanese and
• Valerio Olevano

Beilstein J. Nanotechnol. 2015, 6, 1247–1259, doi:10.3762/bjnano.6.128

• not affect the conductance profile provided that convergence is reached. What actually changes is rather the PDOS, and hence, the interpretation of the conductance in these terms. Computational details Our calculations are carried out within the DFT-Landauer framework. The exchange-correlation energy

• is approximated using the PBE functional [43]. We use ABINIT [44] for ground state calculations and WanT [45][46] to construct Wannier functions and for conductance calculations. All the results presented here are obtained by well-converged calculations, using the same convergence parameters as in

• several sets of WFs. The one presenting the minimum spread (the most localized) does not necessarily correspond to the real physical situation, and this cannot be known a priori. The calculated conductance does not depend on the chosen basis set, provided the basis is complete and at convergence. On the

Tunable magnetism on the lateral mesoscale by post-processing of Co/Pt heterostructures

• Oleksandr V. Dobrovolskiy,
• Maksym Kompaniiets,
• Roland Sachser,
• Fabrizio Porrati,
• Christian Gspan,
• Harald Plank and
• Michael Huth

Beilstein J. Nanotechnol. 2015, 6, 1082–1090, doi:10.3762/bjnano.6.109

• the step size was 0.8 nm. Nano-diffraction and simulations A convergence angle of 1.0 mrad was used to generate electron nanodiffraction patterns in the STEM mode. These diffraction patterns were recorded energy-filtered on a 16-bit CCD. To collect the nanodiffraction images over the complete layer

Multiscale modeling of lithium ion batteries: thermal aspects

• Arnulf Latz and
• Jochen Zausch

Beilstein J. Nanotechnol. 2015, 6, 987–1007, doi:10.3762/bjnano.6.102

• ]. This method does not constitute an analytical proof that the averaged solution of the microscopic equations does converge in a strict mathematical sense towards the solution of the averaged set of equations. Here, further analytical work or numerical convergence studies will be necessary. If a quantity

• explicit forward Euler discretization based on the same time step and is thus fast to solve. However, due to the time-step limitations for explicit schemes the step size here can automatically decrease based on the given parameters to ensure stable convergence. Despite the fact that on the microscale the

Statistics of work and orthogonality catastrophe in discrete level systems: an application to fullerene molecules and ultra-cold trapped Fermi gases

• Antonello Sindona,
• Michele Pisarra,
• Mario Gravina,
• Cristian Vacacela Gomez,
• Pierfrancesco Riccardi,
• Giovanni Falcone and
• Francesco Plastina

Beilstein J. Nanotechnol. 2015, 6, 755–766, doi:10.3762/bjnano.6.78

• clusters are explicitly taken into account except for the one removed from the reference atom. Convergence for C60 and leads to optimized ground state wave functions made of single Slater determinants of 179 pairs of occupied molecular orbitals (MOs), which are linear combinations of 1135 contracted

Nanometer-resolved mechanical properties around GaN crystal surface steps

• Jörg Buchwald,
• Marina Sarmanova,
• Bernd Rauschenbach and
• Stefan G. Mayr

Beilstein J. Nanotechnol. 2014, 5, 2164–2170, doi:10.3762/bjnano.5.225

• are nearly constant for all step heights except for the closest atom which feels the stress significantly. This behavior reflects the better convergence properties of 1/y2 (Equation 6). From an experimental point of view, it is hardly possible to evaluate the microscopical expressions (Equation 7) for

• presented by Vlassak and Nix [20], who connected the indentation modulus to the Barnett–Lothe tensors for anisotropic materials [21]. For the one-atom indentation, (Figure 3), M behaves similarly to stress fluctuations with better convergence below the step and a similar decrease in the elastic constants on

UHV deposition and characterization of a mononuclear iron(III) β-diketonate complex on Au(111)

• Irene Cimatti,
• Silviya Ninova,
• Valeria Lanzilotto,
• Luigi Malavolti,
• Luca Rigamonti,
• Brunetto Cortigiani,
• Matteo Mannini,
• Elena Magnano,
• Federica Bondino,
• Federico Totti,
• Andrea Cornia and
• Roberta Sessoli

Beilstein J. Nanotechnol. 2014, 5, 2139–2148, doi:10.3762/bjnano.5.223

• together with GTH double-ζ polarized molecularly optimized basis sets for all atomic species. The energy cut-off applied to the plane wave basis sets was set to 400 Ry. Geometry optimizations were performed with the PBEsol functional [49]. In all cases, the convergence criteria were fixed at 1 × 10−6

Quasi-1D physics in metal-organic frameworks: MIL-47(V) from first principles

• Danny E. P. Vanpoucke,
• Jan W. Jaeken,
• Stijn De Baerdemacker,
• Kurt Lejaeghere and
• Veronique Van Speybroeck

Beilstein J. Nanotechnol. 2014, 5, 1738–1748, doi:10.3762/bjnano.5.184

• positions and cell shape. The convergence criterion is set to a difference in energy of less than 1.0 × 10−7 eV between subsequent ionic steps. After full relaxation, the forces on the ions are then found to be below 1.2 meV/Å. The density of states (DOS) was obtained by using a denser k-point grid of 3 × 3