Theoretical study of the frequency shift in bimodal FM-AFM by fractional calculus

• Elena T. Herruzo and
• Ricardo Garcia

Beilstein J. Nanotechnol. 2012, 3, 198–206, doi:10.3762/bjnano.3.22

• the force By defining a new variable u = A1cos(ωt − π/2), the frequency shift of the second mode (Equation 5) can be expressed as the convolution of the force gradient with the function , in the same way that the frequency shift of the first mode in conventional FM-AFM can be seen as the convolution

• mode and the half-integral of the force as deduced by Sader and Jarvis [27]. Δf1 can be seen as the convolution of the force with the function [24]: When the amplitude of the first mode is larger than the length scale of the interaction, the frequency shift of the first mode is related to the half

Current-induced forces in mesoscopic systems: A scattering-matrix approach

• Niels Bode,
• Silvia Viola Kusminskiy,
• Reinhold Egger and
• Felix von Oppen

Beilstein J. Nanotechnol. 2012, 3, 144–162, doi:10.3762/bjnano.3.15

• the Green’s function , the slow mechanical motion implies that varies slowly with the central time t = (t1 + t2)/2 and oscillates fast with the relative time τ = t1 − t2. The Wigner transform of a convolution C(t1,t2) = ∫ dt3A(t1,t3)B(t3,t2) is given by where we have dropped the higher-order

• Green’s functions (obtained in a straightforward manner by performing the convolution in Equation 31 explicitly and keeping terms up to ) we obtain Current conservation constrains both the frozen and full scattering matrices to be unitary. From the unitarity of the frozen S-matrix, S†S = 1, we obtain the

Direct-write polymer nanolithography in ultra-high vacuum

• Woo-Kyung Lee,
• Minchul Yang,
• Arnaldo R. Laracuente,
• William P. King,
• Lloyd J. Whitman and
• Paul E. Sheehan

Beilstein J. Nanotechnol. 2012, 3, 52–56, doi:10.3762/bjnano.3.6

• is a convolution of the topographic height and electronic properties of the polymer film, complicating the comparison. However, the polymer’s lying flat strongly suggests that alkyl side chains must interact more favorably with the silicon surface than with the oxide surface and so has a significant

STM visualisation of counterions and the effect of charges on self-assembled monolayers of macrocycles

• Tibor Kudernac,
• Natalia Shabelina,
• Wael Mamdouh,
• Sigurd Höger and
• Steven De Feyter

Beilstein J. Nanotechnol. 2011, 2, 674–680, doi:10.3762/bjnano.2.72

• nitrogen atoms. As STM contrast is a convolution of the physical height and the local density of states [28], the large iodides “sitting” on top of the macrocycle rim logically result in a strong STM signal. Additionally, higher polarisability of iodine, as compared to the other atoms present, can

Deconvolution of the density of states of tip and sample through constant-current tunneling spectroscopy

• Holger Pfeifer,
• Berndt Koslowski and
• Paul Ziemann

Beilstein J. Nanotechnol. 2011, 2, 607–617, doi:10.3762/bjnano.2.64

• –Kramers–Brillouin (WKB) description of tunneling processes. There, the experimentally determined tunneling current, I, is expressed as a convolution integral involving the sample and tip LDOS as well as the barrier behavior on equal footing. Thus, if there is just one I–V characteristic available for a

Investigation on structural, thermal, optical and sensing properties of meta-stable hexagonal MoO₃ nanocrystals of one dimensional structure

• Angamuthuraj Chithambararaj and
• Arumugam Chandra Bose

Beilstein J. Nanotechnol. 2011, 2, 585–592, doi:10.3762/bjnano.2.62

• to the bulk compound. The observed broadening is a convolution of the instrumental error, the reduced crystallite size and the existence of microstrain in the synthesized sample product. The overall contribution to the broadening is expressed as βhkl = βins + βsize + βstrain, where βins is the full

Distinguishing magnetic and electrostatic interactions by a Kelvin probe force microscopy–magnetic force microscopy combination

• Miriam Jaafar,
• Oscar Iglesias-Freire,
• Luis Serrano-Ramón,
• Manuel Ricardo Ibarra,
• Jose Maria de Teresa and
• Agustina Asenjo

Beilstein J. Nanotechnol. 2011, 2, 552–560, doi:10.3762/bjnano.2.59

• (i.e., with the main feedback switched off). The frequency shift results from a convolution between the tip–sample force gradient and a weight function. For low oscillation amplitudes, the frequency shift of the cantilever, at a retrace distance large enough to avoid van der Waals interactions, is

The role of the cantilever in Kelvin probe force microscopy measurements

• George Elias,
• Thilo Glatzel,
• Ernst Meyer,
• Alex Schwarzman,
• Amir Boag and
• Yossi Rosenwaks

Beilstein J. Nanotechnol. 2011, 2, 252–260, doi:10.3762/bjnano.2.29

• calculated and found to be relatively small. Keywords: boundary elements method; cantilever; convolution; Kelvin probe force microscopy; point spread function; Introduction The effect of the measuring probe in electrostatic force based microscopies, such as Kelvin probe force microscopy (KPFM) [1], is very

Extended X-ray absorption fine structure of bimetallic nanoparticles

• Carolin Antoniak

Beilstein J. Nanotechnol. 2011, 2, 237–251, doi:10.3762/bjnano.2.28

• coefficients of the original data multiplied by a window function, i.e., the k dependent EXAFS data are transformed in several intervals of k. However, this leads to a high resolution in k only, at the expense of good resolution in r, and vice versa, since cutting the signal corresponds to a convolution

• between the original data and the cutting window. Convolution in k is identical to multiplication in r, and since the FT of a sharp cut contains all possible values of r, the FT of the EXAFS data will be smeared out. This shows that cutting the signal into several parts is the right way to obtain

Manipulation of gold colloidal nanoparticles with atomic force microscopy in dynamic mode: influence of particle–substrate chemistry and morphology, and of operating conditions

• Samer Darwich,
• Karine Mougin,
• Akshata Rao,
• Enrico Gnecco,
• Shrisudersan Jayaraman and
• Hamidou Haidara

Beilstein J. Nanotechnol. 2011, 2, 85–98, doi:10.3762/bjnano.2.10

• organization of the particles. The shape of the particles is well defined, and the structure of some aggregates can be recognized, due to the absence of convolution effects that usually arise from the water layer which may cover the particles under ambient conditions. This image thus shows that the transfer

Structure, morphology, and magnetic properties of Fe nanoparticles deposited onto single-crystalline surfaces

• Armin Kleibert,
• Wolfgang Rosellen,
• Mathias Getzlaff and
• Joachim Bansmann

Beilstein J. Nanotechnol. 2011, 2, 47–56, doi:10.3762/bjnano.2.6

• convolution effects in the STM which become important when the particle size is comparable or larger than the tip diameter [63]. The tip convolution in general also superimposes details of the particle shape as, e.g., surface facets. Numerical deconvolution of the STM images has been shown to provide a tool

Defects in oxide surfaces studied by atomic force and scanning tunneling microscopy

• Thomas König,
• Georg H. Simon,
• Lars Heinke,
• Leonid Lichtenstein and
• Markus Heyde

Beilstein J. Nanotechnol. 2011, 2, 1–14, doi:10.3762/bjnano.2.1

• is a convolution of the actual contact potential difference with the tip geometry [48]. The depressions in the contact potential at the APDBs have approximately a full width at half minimum of 3 nm (see Figure 12b). The lateral extension of the APDBs is approximately 1.5 nm and the oxide unit cell is

• expanded by an additional row of oxygen atoms by 0.3 nm at that position [41]. Assuming the change of the contact potential to be approximately located in this range (between 0.3 and 1.5 nm), the recorded contact potential is broadened by a factor of 2 to 10 due to the convolution with the tip geometry