Ferromagnetic resonance spectra of linear magnetosome chains

• Elizaveta M. Gubanova and
• Nikolai A. Usov

Beilstein J. Nanotechnol. 2024, 15, 157–167, doi:10.3762/bjnano.15.15

• superparamagnetic nanoparticles in ac magnetic field H1(t), it is convenient to rewrite Equation 7 in the form of the time-averaged integral where Δt is a certain time interval significantly exceeding the period of oscillations of the ac magnetic field, τ = 2π/ω. Using the small amplitude of the ac magnetic field

A distributed active patch antenna model of a Josephson oscillator

• Vladimir M. Krasnov

Beilstein J. Nanotechnol. 2023, 14, 151–164, doi:10.3762/bjnano.14.16

• oscillatory component induced by cavity modes and fluxons. This term generates the ac voltage, which we aim to determine: Small-amplitude, multimode analysis In the small-amplitude limit, ϕ ≪ 1, a perturbation approach can be used. A linear expansion of Equation 3 yields [16][29][31], Here, is the excess dc

• approximate analytic solution by expanding J0(x) ≃ 1 − x2/4 for small x. With such expansion, Equation 29 is reduced to a quadratic equation with the solution For overdamped JJs, α ≫ 1, it reduces to the small-amplitude result of Equation 25, |gn| = . For underdamped JJs, it qualitatively correctly predicts

Comparing the performance of single and multifrequency Kelvin probe force microscopy techniques in air and water

• Jason I. Kilpatrick,
• Emrullah Kargin and
• Brian J. Rodriguez

Beilstein J. Nanotechnol. 2022, 13, 922–943, doi:10.3762/bjnano.13.82

• cantilever. Under small amplitude conditions the tip can be positioned very close to the surface and as such there is an advantage in increasing the spatial resolution. The trade-off here is that the SNR will be small as the mechanical amplitude approaches the thermal noise limits of the cantilever. In

Two dynamic modes to streamline challenging atomic force microscopy measurements

• Alexei G. Temiryazev,
• Andrey V. Krayev and
• Marina P. Temiryazeva

Beilstein J. Nanotechnol. 2021, 12, 1226–1236, doi:10.3762/bjnano.12.90

• frequency curve is not observed; the frequency decreases monotonically as the probe approaches the sample. The reasons for this are discussed in [5]. The concept of large or small amplitude A0 is relative, say A0 = 20 nm may be too large for a sharp tip and too small for a blunt one. The main advantage of

Open-loop amplitude-modulation Kelvin probe force microscopy operated in single-pass PeakForce tapping mode

• Gheorghe Stan and
• Pradeep Namboodiri

Beilstein J. Nanotechnol. 2021, 12, 1115–1126, doi:10.3762/bjnano.12.83

• and small-amplitude ringing was low-pass filtered at 25 kHz, which is a few times larger than the bias frequency, such that the CPD calculations will not be affected by this filter, but below the first resonance frequency to remove the induced ringing. The filtered signal (red curve in Figure 2

Numerical analysis of vibration modes of a qPlus sensor with a long tip

• Kebei Chen,
• Zhenghui Liu,
• Yuchen Xie,
• Chunyu Zhang,
• Gengzhao Xu,
• Wentao Song and
• Ke Xu

Beilstein J. Nanotechnol. 2021, 12, 82–92, doi:10.3762/bjnano.12.7

• enough to allow for a stable small-amplitude operation [1]. The equivalent stiffness keq of the qPlus sensor is shown in Figure 8, which is calculated from the strain energy and the tip amplitude with an equivalent point-mass model [28]. We see in Figure 8c that for a 0.075 mm tip, there is an optimal

Dynamics of superparamagnetic nanoparticles in viscous liquids in rotating magnetic fields

• Nikolai A. Usov,
• Ruslan A. Rytov and
• Vasiliy A. Bautin

Beilstein J. Nanotechnol. 2019, 10, 2294–2303, doi:10.3762/bjnano.10.221

• , Figure 4 and Figure 5 show that for iron oxide nanoparticles very small SAR values should be observed if the particle diameter falls below 16 nm. In addition, RMFs of rather small amplitude have been used in these experiments. Using numerical simulations we determined the optimal particle diameters, as

Fabrication of phase masks from amorphous carbon thin films for electron-beam shaping

• Lukas Grünewald,
• Dagmar Gerthsen and
• Simon Hettler

Beilstein J. Nanotechnol. 2019, 10, 1290–1302, doi:10.3762/bjnano.10.128

• prepared by FIB milling. Bright-field TEM imaging (Figure 4c) reveals the desired sinusoidal thickness profile. However, a large offset thickness (t0 = 67 nm) and a comparably small amplitude thickness (ta = 36 nm) are visible. This observation is unexpected because a few more repetitions lead to the

An iridescent film of porous anodic aluminum oxide with alternatingly electrodeposited Cu and SiO₂ nanoparticles

• Menglei Chang,
• Huawen Hu,
• Haiyan Quan,
• Hongyang Wei,
• Zhangyi Xiong,
• Jiacong Lu,
• Pin Luo,
• Yaoheng Liang,
• Jianzhen Ou and
• Dongchu Chen

Beilstein J. Nanotechnol. 2019, 10, 735–745, doi:10.3762/bjnano.10.73

• sealing the pores with hot water was to close the pores in the anodic oxide film and hence to avoid impurities entering the film. Electrochemical properties Electrochemical impedance testing was carried out by applying a small-amplitude AC voltage to the system and measuring the ratio of the signal

Investigation of CVD graphene as-grown on Cu foil using simultaneous scanning tunneling/atomic force microscopy

• Majid Fazeli Jadidi,
• Umut Kamber,
• Oğuzhan Gürlü and
• H. Özgür Özer

Beilstein J. Nanotechnol. 2018, 9, 2953–2959, doi:10.3762/bjnano.9.274

• an inequivalent electronic structure in HOPG or multilayer graphene due to the presence of a carbon atom or a hollow site underneath. In this work, we report small-amplitude, simultaneous STM/AFM imaging using a metallic (tungsten) tip, of the graphene surface as-grown by chemical vapor deposition

• array with maxima located in between the two carbon atoms was acquired in STM topography. Keywords: atomic force microscopy; CVD graphene; scanning tunneling microscopy; simultaneous operation; small amplitude; Introduction Graphene has been widely studied because of its potential use in future

• insight on relative contrast mechanisms in STM and AFM, on a graphene surface. In the past, we used this small-amplitude STM/AFM technique in order to investigate surfaces such as Si(100) [28], Cu(100) [29], Si(111) [30], and more recently Si(111) again, with an improved force resolution [31

Effective sensor properties and sensitivity considerations of a dynamic co-resonantly coupled cantilever sensor

• Julia Körner

Beilstein J. Nanotechnol. 2018, 9, 2546–2560, doi:10.3762/bjnano.9.237

• Equation 11 as well as the amplitudes of the resonance peaks. In case of negative eigenfrequency deviation, i.e., f2 < f1, the lower left branch corresponds to the left resonance peak a which has a small amplitude and whose resonance frequency is changing because it corresponds to the nanocantilever. The

Material discrimination and mixture ratio estimation in nanocomposites via harmonic atomic force microscopy

• Weijie Zhang,
• Yuhang Chen,
• Xicheng Xia and
• Jiaru Chu

Beilstein J. Nanotechnol. 2017, 8, 2771–2780, doi:10.3762/bjnano.8.276

• it is rather difficult to distinguish the two materials owing to the small amplitude difference. When the drive frequency is larger than the FR frequency, the harmonic amplitudes on PS and LDPE are 3.49 ± 0.05 nm and 2.11 ± 0.09 nm, respectively, see Figure 3c. The amplitude magnitude and the

Velocity dependence of sliding friction on a crystalline surface

• Christian Apostoli,
• Giovanni Giusti,
• Jacopo Ciccoianni,
• Gabriele Riva,
• Rosario Capozza,
• Rosalie Laure Woulaché,
• Andrea Vanossi,
• Emanuele Panizon and
• Nicola Manini

Beilstein J. Nanotechnol. 2017, 8, 2186–2199, doi:10.3762/bjnano.8.218

• larger and larger transfer of momentum from the slider to the chain. Of course the observed small-amplitude oscillations of vCM are almost entirely the result of the oscillations induced in the few chain atoms directly interacting with the slider, with the vast majority of far-away atoms remaining

Stick–slip boundary friction mode as a second-order phase transition with an inhomogeneous distribution of elastic stress in the contact area

• Iakov A. Lyashenko,
• Vadym N. Borysiuk and
• Valentin L. Popov

Beilstein J. Nanotechnol. 2017, 8, 1889–1896, doi:10.3762/bjnano.8.189

• properties of the system, ξ(t) represents random processes in the heat fluctuation of a small amplitude which cannot significantly affect the system behavior. Nevertheless, it is necessary to take them into account due to the peculiarities of the further numerical calculations [23]. In explicit form

Dynamic of cold-atom tips in anharmonic potentials

• Tobias Menold,
• Peter Federsel,
• Carola Rogulj,
• Hendrik Hölscher,
• József Fortágh and
• Andreas Günther

Beilstein J. Nanotechnol. 2016, 7, 1543–1555, doi:10.3762/bjnano.7.148

• oscillation frequency and amplitude, as it shows less noise. This stems from the fact that the autocorrelation function is based on a histogram of N2 particle pair distances (see methods section), whereas the detector signal is based on the N detection events. In addition, frequency components with small

• amplitude are strongly suppressed in the correlation analysis. This can be seen when using a generalized form of the detector signal from Equation 16 with the coefficients Kj depending on the specific oscillation parameters and outcoupling position. The normalized autocorrelation function then reads with

Generalized Hertz model for bimodal nanomechanical mapping

• Aleksander Labuda,
• Marta Kocuń,
• Waiman Meinhold,
• Deron Walters and
• Roger Proksch

Beilstein J. Nanotechnol. 2016, 7, 970–982, doi:10.3762/bjnano.7.89

• modes). Parameters associated with both resonances can be measured and used to extract quantitative nanomechanical information about the sample surface. Driving the first eigenmode at a large amplitude and a higher eigenmode at a small amplitude simultaneously provides four independent observables that

• -amplitude dynamic AFM, where the interaction amplitude A1 greatly exceeds δmax. Meanwhile, the second (or higher) eigenmode is deliberately driven at a small amplitude A2, such that the interaction stiffness it experiences is roughly constant throughout one of the higher eigenmode oscillation cycles

• AFM, both eigenmodes behave like independent SHO’s because the first mode is driven in the large-amplitude limit and the second is driven in the small-amplitude limit. An empirical verification of this independence will be performed and discussed later. In principle, both Δk1 and Δk2 can be measured

Nanoscale effects in the characterization of viscoelastic materials with atomic force microscopy: coupling of a quasi-three-dimensional standard linear solid model with in-plane surface interactions

• Santiago D. Solares

Beilstein J. Nanotechnol. 2016, 7, 554–571, doi:10.3762/bjnano.7.49

• -mode using a single oscillation frequency in the small-amplitude regime. However, even in these most ideal situations, there still exist challenges associated with the shape of the tip, which does not necessarily impart uniform compressive strain, but may cause both compressive and shear strains with

Charge and heat transport in soft nanosystems in the presence of time-dependent perturbations

• Alberto Nocera,
• Carmine Antonio Perroni,
• Vincenzo Marigliano Ramaglia and
• Vittorio Cataudella

Beilstein J. Nanotechnol. 2016, 7, 439–464, doi:10.3762/bjnano.7.39

Nonconservative current-driven dynamics: beyond the nanoscale

• Brian Cunningham,
• Tchavdar N. Todorov and
• Daniel Dundas

Beilstein J. Nanotechnol. 2015, 6, 2140–2147, doi:10.3762/bjnano.6.219

• . Longitudinal atomic displacements in a wire with 200 dynamical atoms as a function of position (horizontal axis) and time (vertical axis), for an applied bias of 0.2 V, starting from the zero-bias relaxed geometry. The simulation employs the small-amplitude adiabatic steady-state description of Equation 6. The

Nano-contact microscopy of supracrystals

• Adam Sweetman,
• Nicolas Goubet,
• Ioannis Lekkas,
• Marie Paule Pileni and
• Philip Moriarty

Beilstein J. Nanotechnol. 2015, 6, 1229–1236, doi:10.3762/bjnano.6.126

• small amplitude (of order 0.1−0.3 nm, see below) normal to the surface. The use of constant height imaging (using a similar protocol to that described previously [30][33]) allows us to probe the tip–sample interaction on the repulsive branch of the frequency shift curve, which is typically not available

Optimization of phase contrast in bimodal amplitude modulation AFM

• Mehrnoosh Damircheli,
• Amir F. Payam and
• Ricardo Garcia

Beilstein J. Nanotechnol. 2015, 6, 1072–1081, doi:10.3762/bjnano.6.108

• bimodal excitation. The phase contrast │Δ│=│ (gold) − (PS)│ also shows a maximum with respect to A1/A01. The behavior is very similar to the one observed for conservative interactions (Figure 2c) except for A02 ≥ 1 nm where the maximum is displaced to very small amplitude ratios. This is due to the cross

Stiffness of sphere–plate contacts at MHz frequencies: dependence on normal load, oscillation amplitude, and ambient medium

• Jana Vlachová,
• Rebekka König and
• Diethelm Johannsmann

Beilstein J. Nanotechnol. 2015, 6, 845–856, doi:10.3762/bjnano.6.87

• contacts: linear and nonlinear regime We first consider the viscoelastic contact. According to the small-load approximation, the complex frequency shift at small amplitude is given as [35][36] Δf and ΔΓ are the shifts of the frequency and the half-bandwidth at half-height, respectively. The parameter Γ is

Accurate, explicit formulae for higher harmonic force spectroscopy by frequency modulation-AFM

• Kfir Kuchuk and
• Uri Sivan

Beilstein J. Nanotechnol. 2015, 6, 149–156, doi:10.3762/bjnano.6.14

• resonance frequency. In frequency modulation-AFM (FM-AFM), the force is usually reconstructed from the resonance frequency shift, which in the small amplitude regime is proportional to the derivative of the force with respect to tip–surface distance. Similarly, it has been recognized that higher harmonics

• differentiating n times with respect to z one finds which is similar to the small amplitude approximation derived from Equation 2 As expected, higher harmonics are proportional to higher derivatives, while the frequency shift used in first harmonic force spectroscopy is proportional to the first derivative. This

• and Figure 2 demonstrate the accuracy of our formulae. Figure 1a,b confirms, in the small amplitude regime, the increased sensitivity to short range interaction of force reconstruction using higher harmonics compared with the Sader–Jarvis formula. As the oscillation amplitude grows smaller compared

Probing viscoelastic surfaces with bimodal tapping-mode atomic force microscopy: Underlying physics and observables for a standard linear solid model

• Santiago D. Solares

Beilstein J. Nanotechnol. 2014, 5, 1649–1663, doi:10.3762/bjnano.5.176

• by using contact resonance techniques [4][5][6][7][8], whereby classical properties are approximated by using contact models under small-amplitude oscillatory deformations. Such characterization is much more challenging to carry out by using intermittent-contact techniques due to the non-linear

• the sample storage and loss moduli. Similarly, in contact resonance methods [4][5][6][7][8] the user generally measures the cantilever frequency response to small amplitude excitations, from which an effective resonance frequency and quality factor can be computed and post-processed to also give the

Resonance of graphene nanoribbons doped with nitrogen and boron: a molecular dynamics study

• Ye Wei,
• Haifei Zhan,
• Kang Xia,
• Wendong Zhang,
• Shengbo Sang and
• Yuantong Gu

Beilstein J. Nanotechnol. 2014, 5, 717–725, doi:10.3762/bjnano.5.84

• shows that the GNR is vibrating along both lateral and length directions (see the insets in Figure 11a). It is evident that the vibration behavior is dominated by the vertical vibration, as indicated by the extremely small amplitude of the translational vibration comparing with that of the vertical