Current-induced forces: a simple derivation

We revisit the problem of forces on atoms under current in nanoscale conductors. We derive and discuss the five principal kinds of force under steady-state conditions from a simple standpoint that—with the help of background literature—should be accessible to physics undergraduates. The discussion aims at combining methodology with an emphasis on the underlying physics through examples. We discuss and compare two forces present only under current—the non-conservative electron wind force and a Lorentz-like velocity-dependent force. It is shown that in metallic nanowires both display significant features at the wire surface, making it a candidate for the nucleation of current-driven structural transformations and failure. Finally we discuss the problem of force noise and the limitations of Ehrenfest dynamics

Charge exchange emission from solar wind helium ions

Charge exchange X-ray and far-ultraviolet (FUV) aurorae can provide detailed insight into the interaction between solar system plasmas. Using the two complementary experimental techniques of photon emission spectroscopy and translation energy spectroscopy, we have studied state-selective charge exchange in collisions between fully ionized helium and target gasses characteristic of cometary and planetary atmospheres (H2O, CO2, CO, and CH4). The experiments were performed at velocities typical for the solar wind (200-1500 km s(-1)). Data sets are produced that can be used for modeling the interaction of solar wind alpha particles with cometary and planetary atmospheres. These data sets are used to demonstrate the diagnostic potential of helium line emission. Existing Extreme Ultraviolet Explorer (EUVE) observations of comets Hyakutake and Hale-Bopp are analyzed in terms of solar wind and coma characteristics. The case of Hale-Bopp illustrates well the dependence of the helium line emission to the collision velocity. For Hale-Bopp, our model requires low velocities in the interaction zone. We interpret this as the effect of severe post-bow shock cooling in this extraordinary large comet.

A Maxwell relation for current-induced forces

A Maxwell relation is presented involving current-induced forces. It provides a new physical picture of the origin of current-induced forces and in the small-voltage limit it enables the identification of a simple thermodynamic potential which drives electromigration. The question of whether current-induced forces are conservative or non-conservative is discussed briefly in the light of these insights.

Are current-induced forces conservative?

The expression for the force on an ion in the presence of current can be derived from first principles without any assumption about its conservative character. However, energy functionals have been constructed that indicate that this force can be written as the derivative of a potential. On the other hand, there exist specific arguments that strongly suggest the contrary. We propose physical mechanisms that invalidate such arguments and demonstrate their existence with first-principles calculations. While our results do not constitute a formal resolution to the fundamental question of whether current-induced forces are conservative, they represent a substantial step forward in this direction.

Reply to comment on 'Counterbalancing forces in electromigration'

Reply to comment by K-H W Chu.

Counterbalancing forces in electromigration

In electromigration (EM) experiments on metallic wires, a flux of atoms can lead to motion of the centre of mass (COM) of the wire. Hence, it may be tempting to assume that the flow of current produces a net force on the wire as a whole. We point out, on the basis of known momentum-balance arguments, that the net force on a metallic wire due to a passing steady-state current is zero. This is possible, because in addition to EM driving forces, acting on scattering centres, there are counterbalancing forces, acting on the rest of the system. Drift of the COM in EM experiments occurs inevitably because the substrate keeps the crystal lattice of the wire fixed, while allowing diffusion of defects in the bulk of the wire. This drift is not evidence for a net force on the wire.

Electromigration of vacancies in copper

The total current-induced force on atoms in a Cu wire containing a vacancy are calculated using the self consistent one-electron density matrix in the presence of an electric current, without separation into electron-wind and direct forces. By integrating the total current-induced force, the change in vacancy migration energy due to the current is calculated. We use the change in migration energy with current to infer an effective electromigration driving force F-e. Finally, we calculate the proportionality constant rho* between F-e and the current density in the wire.

Current-induced forces in atomic-scale conductors

We present a self-consistent tight-binding formalism to calculate the forces on individual atoms due to the flow of electrical current in atomic-scale conductors. Simultaneously with the forces, the method yields the local current density and the local potential in the presence of current flow, allowing a direct comparison between these quantities. The method is applicable to structures of arbitrary atomic geometry and can be used to model current-induced mechanical effects in realistic nanoscale junctions and wires. The formalism is implemented within a simple Is tight-binding model and is applied to two model structures; atomic chains and a nanoscale wire containing a vacancy.

Many ways to say 'no', different ways to say 'yes': Applying Q-Methodology to understand public acceptance of wind farm proposals

This paper explores the nature of public acceptance of wind farms by investigating the discourses of support and objection to a proposed offshore scheme. It reviews research into opposition to wind farms, noting previous criticisms that this has tended to provide descriptive rather than explanatory insights and as a result, has not effectively informed the policy debate. One explanation is that much of this research has been conceived within an unreflective positivist research frame, which is inadequate in dealing with the subjectivity and value-basis of public acceptance of wind farm development. The paper then takes a case study of an offshore wind farm proposal in Northern Ireland and applies Q-Methodology to identify the dominant discourse of support and objection. It is argued that this provides new insights into the nature of wind farm conflicts, points to a number or recommendations for policy functions of an example of how this methodology can act as a potential bridge between positivist and post-positivist approaches to policy analysis.