How to measure energy dissipation in dynamic mode atomic force microscopy

When studying a mechanical system like an atomic force microscope (AFM) in dynamic mode it is intuitive and instructive to analyse the forces involved in tip–sample interaction. A different but complementary approach is based on analysing the energy that is dissipated when the tip periodically interacts with the sample surface. This method does not require solving the differential equation of motion for the oscillating cantilever, but is based entirely on the analysis of the energy flow in and out of the dynamic system. Therefore the problem of finding a realistic model to describe the tip–sample interaction in terms of non-linear force–distance dependencies and damping effects is omitted. Instead, it is possible to determine the energy dissipated by the tip–sample interaction directly by measuring such quantities as oscillation amplitude, frequency, phase shift and drive amplitude. The method proved to be important when interpreting phase data obtained in tapping mode, but is also applicable to a variety of scanning probe microscopes operating in different dynamic modes. Additional electronics were designed to allow a direct mapping of local energy dissipation while scanning a sample surface. By applying this technique to the cross-section of a polymer blend a material specific contrast was observed.     

Measuring vibration characteristics at large amplitude region of materials for high power ultrasonic vibration system

This study proposes a method of estimating the mechanical quality factor of materials for high-power ultrasonic vibration systems under large vibration amplitude conditions. The quality factors of several metals as well as some polymers are measured by this method. In this method, the quality factor is calculated as the ratio of the reactive energy stored in a specimen to the dissipated energy. The dissipated energy is estimated from the input/output mechanical energy to the specimen by measurement of the vibration intensity, while the reactive energy is measured as the kinetic energy of the vibration. Then, the quality factor for the specified part can be extracted using this method. In this report, quality factors for torsional vibration were measured at about 30 kHz as functions of the vibration strain.     

Mechanism of energy dissipation in a droplet cluster

It has been shown that thermocapillary processes on the surface of the drops in a drop cluster that appears above a locally heated liquid ensure additional energy transfer. Thus, the drop cluster is a typical dissipative structure. The energy dissipated by an individual drop of the cluster has been estimated.     

Influence of velocity in nanoscale friction processes

Force-microscopy images of boric acid crystals were obtained experimentally and simulated with the use of a two-dimensional mechanical model. An analysis of the stick and slip movement of the microscope tip shows that the energy-dissipation mechanism is strongly influenced by the non-linear dynamics of the sliding system. The contributions of stick and viscous forces on the energy dissipation (or friction forces) are studied as a function of the relative scanning velocity. At low relative velocities, the stick forces are shown to be responsible for the energy dissipation. This energy is velocity-dependent, due to the coupling between the two degrees of freedom of the sliding system. As the scanning velocity increases the stick forces are damped; the viscous force is then predominant in the energy-dissipation process. Received: 30 October 2001 / Accepted: 17 May 2002 / Published online: 22 November 2002 RID="*" ID="*"Corresponding author. Fax: +55-21/2295-9397, E-mail: prioli@vdg.fis.puc-rio.br     

Dynamical effects on the way to fusion of very heavy nuclei

The central collision of ⁴⁰Ar and ²⁰⁸Pb is studied considering the ellipsoidal deformations and isovector dipole mode of motion in the approaching phase. The collective energy dissipation is suggested to originate from the Fermi surface deformation which is treated as a kinematically independent mode of motion within the canonical Lagrange-Rayleigh dynamics. The possible extensions of the approach are discussed. The potential energy surface, calculated using the generalized (folded) surface potential, is studied. The saddle point in the potential energy surface lying at the border of strongly deformed compact configurations is located. The potential energy at this point is about 10MeV smaller than that of the ions touching each other in the spherical shape. The examination of trajectories followed by the system in its evolution shows that the inertia forces strongly hinder the motion of ions along the potential energy valley. The collective energy dissipated during the approach is found to be smaller than the difference in the potential energies at saddle point and at the touching configuration of unpolarized ions.     

Damage monitor and life prediction of carbon fiber-reinforced ceramic-matrix composites at room and elevated temperatures using hysteresis dissipated energy-based damage parameter

In this paper, the damage monitor and life prediction of carbon fiber-reinforced ceramic-matrix composites (C/SiC CMCs) have been investigated using the hysteresis dissipated energy-based damage parameter. The evolution of the interface shear stress, hysteresis dissipated energy, hysteresis dissipated energy-based damage parameter and the broken fibers fraction vs. cycle number, the fatigue life S?N curves of unidirectional, cross-ply and 2.5D C/SiC composites at room temperature and 800 °C in air atmosphere have been analyzed. For unidirectional C/SiC, the hysteresis dissipated energy and hysteresis dissipated energy-based damage parameter first increase and then decrease with cycle number, and the fatigue limit stress decreases from 88% tensile strength at room temperature to 20% of the tensile strength at 800 °C in air atmosphere; for cross-ply C/SiC, the hysteresis dissipated energy and hysteresis dissipated energy-based damage parameter decrease with increasing applied cycles, and the fatigue limit stress decreases from 85% tensile strength at room temperature to 22% tensile strength at 800 °C in air; and for 2.5D C/SiC, the hysteresis dissipated energy and hysteresis dissipated energy-based damage parameter increases with cycle number, and the fatigue limit stress decreases from 70% tensile strength at room temperature to 25% tensile strength at 800 °C in air.     

Elastic characterization of closed cell foams from impedance tube absorption tests

A method is presented to determine the bulk elastic properties of isotropic elastic closed-cell foams from impedance tube sound absorption tests. For such foams, a resonant sound absorption is generally observed, where acoustic energy is transformed into mechanical vibration, which in turn is dissipated into heat due to structural damping. This article shows how the bulk Young's modulus, Poisson's ratio, and damping loss factor can be deduced from the resonant absorption. Also, an optimal damping loss factor yielding 100% of absorption at the first resonance is defined from the developed theory. The method is introduced for a sliding edge condition which is an ideal condition. Then, the method is extended to a bonded edge condition which is more easily achievable and additionally enables the identification of the Poisson's ratio. The method is experimentally tested on expanding closed-cell foams to find their elastic properties in both cases. Using the found properties, sound absorption predictions using an equivalent solid model with and without surface absorption are compared to measurements. Good correlations are obtained when considering surface absorption.     

超椭圆柱面梯度线圈设计

超椭圆柱设计表面能够减小线圈与目标的距离,提高空间利用率,扩大成像区域的有效范围.提出利用流函数法及柱面的可展性在超椭圆柱面上设计核磁共振成像系统中的梯度线圈.根据Biot-Savart定律建立磁场强度与流函数的表达式,采用最小二乘法和Tikhonov正则化方法构造了双目标设计函数.利用柱面的可展性提高了基于分片离散流函数计算电磁场的数值精度,通过L-曲线方法实现了正则参数的合理选取.通过引入适当的流函数边界约束条件,把梯度线圈的优化问题转化为适定线性方程组的直接求解问题.通过数值算例验证了超椭圆柱面展开求解方法的正确性.优化结果显示,在满足线性度误差小于5%的设计约束下,该方法在设计超椭圆柱面线圈驱动电流分布的同时有效控制了梯度线圈的能耗.     

热传导中的变分原理

采用力学中建立最小势能原理和最小余能原理的加权余量法,分别得到了热传导中势能型与余能型的变分原理。通过对势能型变分原理的分析发现,对于可逆的导热过程,“力”(热流)在“位移”(温度)上做的“功”完全转换为物体的“势能”,即热量传递势容。而在不可逆的稳态导热过程中,这个势能完全被耗散掉了,成为传递势容耗散。对于非稳态导热过程,则类似于粘弹性物体,热流在温度位移上做的“功”一部分转换为物体的传递势容,而另外一部分成为传递势容的耗散。     

A mathematical model of Panin’s prefracture zones and stability of subcritical cracks

Basic concept underlying Griffith’s theory of fracture of solids was that, similar to liquids, solids possess surface energy and, in order to propagate a crack by increasing its surface area, the corresponding surface energy must be compensated through the externally added or internally released energy. This assumption works well for brittle solids, but is not sufficient for quasi-brittle and ductile solids. Some new forms of energy components must be incorporated into the energy balance equation, from which the input of energy needed to propagate the crack and subsequently the stress at the onset of fracture can be determined. The additional energy that significantly dominates over the surface energy is the irreversible energy dissipated by the way of the plastic strains that precede the leading edge of a moving crack. For stationary cracks the additional terms within the energy balance equation were introduced by Irwin and Orowan. An extension of these concepts is found in the experimental work of V. Panin, who has shown that the irreversible deformation is primarily confined to the prefracture zones associated with a stationary or a slowly growing crack. The present study is based on the structured cohesive crack model equipped with the “unit step growth” or “fracture quantum”. This model is capable to encompass all the essential issues such as stability of subcritical cracks, quantization of the fracture process and fractal geometry of crack surfaces, and incorporate them into one consistent theoretical representation.     

Time-dependent density-functional molecular-dynamics study of the isotope effect in chemicurrents

The energy dissipation into electron-hole pairs has been simulated ab initio within time-dependent density-functional theory for spin-unpolarized hydrogen atoms interacting with the Al on-top site at the Al(1 1 1) surface. The electron-hole pair excitation spectra are characterized by an approximately exponentially decaying tail of the electron energy distribution. It is shown that both the energy dissipated into electron-hole pairs and the excitation spectra, and hence the chemicurrent yield, show an isotope dependence identical to what expected from the linear friction ansatz and the forced oscillator model.     

Evidence of subsurface oxygen vacancy ordering on reduced CeO2(111)

Surface and subsurface oxygen vacancies on the slightly reduced CeO(2)(111) surface have been studied by atomic resolution dynamic force microscopy at 80 K. Both types of defect are clearly identified by the comparison of the observed topographic features with the corresponding structures predicted from recent first-principles calculations. By combining two simultaneously acquired signals (the topography and the energy dissipated from the cantilever oscillation), we are able to unambiguously locate subsurface oxygen vacancies buried at the third surface atomic layer. We report evidence of local ordering of these subsurface defects that suggests the existence of a delicate balance between subtle interactions among adjacent subsurface oxygen vacancy structures.     

Competition between electron and phonon excitations in the scattering of nitrogen atoms and molecules off tungsten and silver metal surfaces

We investigate the role played by electron-hole pair and phonon excitations in the interaction of reactive gas molecules and atoms with metal surfaces. We present a theoretical framework that allows us to evaluate within a full-dimensional dynamics the combined contribution of both excitation mechanisms while the gas particle-surface interaction is described by an ab initio potential energy surface. The model is applied to study energy dissipation in the scattering of N(2) on W(110) and N on Ag(111). Our results show that phonon excitation is the dominant energy loss channel, whereas electron-hole pair excitations represent a minor contribution. We substantiate that, even when the energy dissipated is quantitatively significant, important aspects of the scattering dynamics are well captured by the adiabatic approximation.     

Energy dissipation of a friction damper

In this paper the energy dissipated through friction is analysed for a type of friction dampers used to reduce squeal noise from railway wheels. A one degree-of-freedom system is analytically studied. First the existence and stability of a periodic solution are demonstrated and then the energy dissipated per cycle is determined as a function of the system parameters. In this way the influence of the mass, natural frequency and internal damping of the friction damper on the energy dissipation is established. It is shown that increasing the mass and reducing the natural frequency and internal damping of the friction damper maximizes the dissipated energy.     

Theory of multifrequency atomic force microscopy

We develop a theory that explains the origin of the high force sensitivity observed in multifrequency force microscopy experiments. The ability of the microscope to extract complementary information on the surface properties is increased by the simultaneous excitation of several flexural cantilever modes. The force sensitivity in multifrequency operation is about 0.2 pN. The analytical model identifies the virial and the energy dissipated by the tip-surface forces as the parameters responsible for the material contrast. The agreement obtained among the theory, experiments and numerical simulations validates the model.     

Analysis of energy dissipation in an elastic moving string with a viscous damper at one end

In this paper transverse vibration of an axially moving viscoelastic string with a viscous damper at one end is investigated analytically. The string is assumed to be travelling with constant velocity and the length of string is constant or time varying. The linear and nonlinear mathematical models are derived using the Lagrangian function and implemented using a finite element method. The method considers a time varying state space function applied to the linear model, the Newmark-Beta method is used to solve the response for the nonlinear problem numerically. The case of energy dissipated by a viscoelastic damper at one end of the string for different axial string velocities is considered. When a disturbance arrives at the boundary an exact value for the damper which provides maximum energy dissipation is investigated. Finally, numerical simulations are presented to establish the feasibility of the method.     

Approximation of Composition and Temperature Dependent Heat Conductivity and Optimization of Thermoelectric Energy Conversion in Silicon–Germanium Alloys

We analyze the efficiency as thermoelectric energy converter of a silicon–germanium alloy with composition and temperature dependent heat conductivity. The dependency on composition is determined by a non-linear regression method (NLRM), while the dependency on temperature is approximated by a first-order expansion in the neighborhood of three reference temperatures. The differences with respect to the case of thermal conductivity depending on composition only are pointed out. The efficiency of the system is analyzed under the assumption that the optimal energy conversion corresponds to the minimum rate of energy dissipated. The values of composition and temperature which minimize such a rate are calculated as well.     

Nonlinear vibration control and energy harvesting of a beam using a nonlinear energy sink and a piezoelectric device

This paper presents an optimal design for a system comprising a nonlinear energy sink (NES) and a piezoelectric-based vibration energy harvester attached to a free–free beam under shock excitation. The energy harvester is used for scavenging vibration energy dissipated by the NES. Grounded and ungrounded configurations are examined and the systems parameters are optimized globally to both maximize the dissipated energy by the NES and increase the harvested energy by piezoelectric element. A satisfactory amount of energy has been harvested as electric power in both configurations. The realization of nonlinear vibration control through one-way irreversible nonlinear energy pumping and optimizing the system parameters result in acquiring up to 78 percent dissipation of the grounded system energy.     

Dissipation Energy in Tapping-Mode Atomic Force Microscopes Caused by Liquid Bridge

The dissipation of energy during the process of contact and separation between a tip and a sample is very important for understanding the phase images in the tapping mode of atomic force microscopes(AFMs). In this study, a method is presented to measure the dissipated energy between a tip and a sample. The experimental results are found to be in good agreement with the theoretical model, which indicates that the method is reliable.Also, this study confirms that liquid bridges are mainly produced by extrusion modes in the tapping mode of AFMs.     

Energy approach to the description of magnetoelastic damping in ferromagnets

Using the Green's function method for a system of 90° domain walls (DW) for the equilibrium and Poisson equations in which the surface density of the magnetic pole energy is accounted for, we have found an expression for the displacement of a DW in the quasistatic approximation and its flexure which is represented in the form of three terms, and also its interaction force with point and linear defects. Thus we have used the equations which describe the condition for dislodgement of the DW from defects to find relations which describe the number of irreversible jumps of the wall, the energy dissipated per jump, and the magnetoelastic loss with a uniform distribution of defects over the DW.