Tomlinson model

Tomlinson model

Loss Mechanisms in Piezoelectrics

Published in Kenji Uchino, High-Power Piezoelectrics and Loss Mechanisms, 2020

We introduce the “Prandtl–Tomlinson Model” here which explains plastic deformations in a crystal from the dry friction mechanism viewpoint on atomic scales.54,55 This model is a hybrid type between the Coulomb (friction), solid and viscous damping, introduced in Chapter 3. Let us consider the simplest 1D model of a mass m in a periodic potential with the wave number k under an external force F with a viscous damping (proportional to velocity) factor ξ, as illustrated in Figure 9.48a. Using the coordinate u of the mass, and the period force amplitude N, we obtain the following dynamic equation: mu¨=F−ξu˙−Nsin(ku)

On the asymptotic expressions of critical energy barrier in Prandtl-Tomlinson model

View Article

Journal Information

Published in International Journal of Smart and Nano Materials, 2019

Rong-Guang Xu, Yuan Xiang, Qi Rao, Yongsheng Leng

The Prandtl-Tomlinson (PT) model [8,9] (usually only referred to as the Tomlinson model) is the most widely used and successful minimalistic model to describe atomistic scale friction, which can be experimentally investigated by dragging an AFM tip along a crystalline surface. It is shown schematically in Figure 1. The motion of the AFM tip can be described by a thermally activated hopping process on a periodic potential. Within the framework of the PT model, the tip is represented by a point mass pulled by a harmonic spring of effective elastic constant over a sinusoidal corrugation potential which describes the interactions between the tip and substrate. The time-dependent interaction between the AFM tip and substrate can be expressed by the PT potential

Explore chapters and articles related to this topic

Loss Mechanisms in Piezoelectrics

On the asymptotic expressions of critical energy barrier in Prandtl-Tomlinson model