The dependence of fractal dimension on measuring conditions of scanning probe microscopy

Zahn, W.; Zösch, Antje

doi:10.1007/s002160051466

Cited by 47 publications

(17 citation statements)

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“…The box-counting method [12,13] is directly derived from the definition of box-counting fractal dimension, as sketched in Figure 1. This count depends on the box size r, the boxcounting length N(r) and fractal dimension D according to Eq.…”

Section: Basic Theory Of the Box-counting Methods For The Determinatiomentioning

confidence: 99%

Fractal Analysis of TATB‐Based Explosive AFM Morphology at Different Conditions

Cheng

Liu

Guan

et al. 2007

Propellants Explo Pyrotec

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The morphology of in situ heated and stockpiled TATB-based explosive (TBE) was characterized by atomic force microscopy (AFM). The AFM images were analyzed by a fractal method and conventional methods. The result of the fractal analysis indicated that in the thermal process of TBE the binder chains were gradually activated with increasing temperature and resulted in a spread of binder and a decrease in the fractal dimension of the surface. The crystallinity of the binder increased with extending time above the glass transition temperature (T g ), which caused the surface structure dimension (D f ) to be more complicated.

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Section: Basic Theory Of the Box-counting Methods For The Determinatiomentioning

confidence: 99%

Fractal Analysis of TATB‐Based Explosive AFM Morphology at Different Conditions

Cheng

Liu

Guan

et al. 2007

Propellants Explo Pyrotec

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“…For each surface, the mean values of roughness descriptors with standard deviations over ten 1 × 1 mm scans from different samples are shown in Table 1. The scaled triangulation method (Dubuc et al 1989;De Santis et al 1997;Zahn and Zösch 1999) was used for the calculation of fractal dimension values. A power law relationship is found between the calculated surface area and the length resolution of digitized scan of all the surfaces, exhibiting self-affinity over a range of length scales (from 1 to 100 μm).…”

Section: Sample Preparation and Surface Characterizationmentioning

confidence: 99%

Stress-Dependent Electrical Contact Resistance at Fractal Rough Surfaces

et al. 2017

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The electrical contact resistance between contacting rough surfaces was studied under various compressive stresses. The samples considered here were isotropically roughened aluminium disks with upper and lower surfaces modified through polishing and sand blasting using different sized glass beads. Fractal geometry and roughness descriptors, including root mean square values of roughness and slope, were used to describe the topography of sample surfaces, based on the digitized profiles obtained from interferometry-based profilometry. The electrical contact resistances at the interfaces were obtained by applying a controlled current and measuring the resulting voltage, through the following scenarios: (1) over time for various applied testing currents, the resistance relaxation curves were measured at constant loads; (2) through voltage-current characteristics by means of a logarithmic sweeping current, the influence of the testing current on the electrical response of contacting rough surfaces was evaluated; and (3) for a given testing current, the electrical resistance through interfaces of different surface structures was measured under increasing compressive stresses. The experimental results show that the measured resistance depends closely on the measurement time, testing current, surface topology, and mechanical loading. At stresses from 0.03 to 1.18 MPa, the electrical resistance as a function of applied normal stress is found to follow a power law relation, the exponent of which is closely linked to the surface topology.

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“…Для расчета величин D f и D q известен круг методик [24,25], которые успешно применяются и дают результаты, описывающие трансформацию рельефа поверхности в зависимости: от внешних воздействий, от состояния материала; от процессов, проходящих в материале. Используя подобные методики, в определенной мере можно прогнозировать изменения в материале.…”

Section: экспериментальные и статистические методы исследования поверunclassified

Влияние изохронных отжигов на поверхностные характеристики лент металлического стекла Ni-=SUB=-50-=/SUB=-Ti-=SUB=-50-=/SUB=-

Бутенко¹,

Гиляров²,

Корсуков³

et al. 2020

Журнал Технической Физики

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In this paper we investigated the crystallization of NiTi metallic glass foils of equiatomic composition by XRD and AFM. The initial foil surface which was obtained by the melt spinning method contained only cristalline phases of impurities. Ten-minute annealing at 500°C leads to phase transition in the form of devitrification of Ni50Ti50 phase. The analisys of foil surface geometry included calculation of direct inhomogeneities characteristics, roughness and fractal dimension, as well as the parameters of multifractal fromalism. It was showen that after ten-minute heat treatment at 500°C all above mentioned characteristics have local extrema. In particular there is a minimum of the widths of the singularities spectra which indicates the monofractalization of the system.

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The dependence of fractal dimension on measuring conditions of scanning probe microscopy

Cited by 47 publications

References 0 publications

Fractal Analysis of TATB‐Based Explosive AFM Morphology at Different Conditions

Fractal Analysis of TATB‐Based Explosive AFM Morphology at Different Conditions

Stress-Dependent Electrical Contact Resistance at Fractal Rough Surfaces

Влияние изохронных отжигов на поверхностные характеристики лент металлического стекла Ni-=SUB=-50-=/SUB=-Ti-=SUB=-50-=/SUB=-

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