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.

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.

Millimeter-wave stealth radio for special operations forces

For Special Operations Forces, an important attribute of any future radio will be the ability to conceal transmissions from the enemy while transmitting large amounts of data for situational awareness and communications. These requirements will mean that military wireless systems designers will need to consider operating frequencies in the mm-wave bands: The high data rates that are achievable at these frequencies and the propagation characteristics at this wavelength will provide many benefits for the implementation of 'stealth radio'. This article discusses some of the recent advances in RF front-end technology, alongside physical layer transmission schemes that could be employed for millimeter-wave soldier-mounted radio. The operation of a hypothetical millimeter-wave soldier-to-soldier communications system that makes use of smart antenna technology is also described.

Nonconservative generalized current-induced forces

A recent result for the curl of forces on ions under steady-state current in atomic wires with noninteracting electrons is extended to generalized forces on classical degrees of freedom in the presence of mean-field electron-electron screening. Current is described within a generic multiterminal picture, forces within the Ehrenfest approximation, and screening within an adiabatic, but not necessarily spatially local, mean-field picture.

Nonconservative current-induced forces: A physical interpretation

We give a physical interpretation of the recently demonstrated non-conservative nature of interatomic forces in current-carrying nanostructures. We start from the analytical expression for the curl of these forces, and evaluate it for a point defect in a current-carrying system. We obtain a general definition of the capacity of electrical current flow to exert a non-conservative force, and thus do net work around closed paths, by a formal non-invasive test procedure. Second, we show that the gain in atomic kinetic energy in time, generated by non-conservative current-induced forces, is equivalent to the uncompensated stimulated emission of directional phonons. This connection with electron-phonon interactions quantifies explicitly the intuitive notion that non-conservative forces work by angular momentum transfer.

A comparison of the strengths of gastropod shells with forces generated by potential crab predators

Carcinus manenas, Liocarcinus puber and Cancer pagurs are thought to be three likely crab predators of the gastropod Calliostoma Zizyphinum. In order to compare the strenghts of predators and their prey, the whole shell and aperture lip strengh of white and pink Calliostoma morphotypes and the maximum forces exerted by the chelipeds of three crab species were measured. Although white shells were thicker than pink shells, Calliostoma colour morphotyes did not differ significantly in either the force required to break the shell lip or the whole shell. Both Liocarcinus puber and Carcinus maenas have dimorphic chelipeds and their “crusher” chelipeds deliver almost double the forces generated by the‘cutter’chelipeds. In constrast, Cancer pagurus has monomorphic chelipeds both delivering similar forces. When compared with Calliostoma shell strenght, the forces generated by the‘crusher’chelipeds of most L. puber tested were, in general, sufficient to break the shell lip of Calliostoma shells, whereas forces generated by the‘cutter’chelipeds of only the larger individuals were sufficient to break the shell lip. In C. manenas, forces generated by both the‘cutter’and‘crusher’chelipeds often exceeded the minimum recorded force required to break the shell lip and the‘crusher’cheliped reached the minimum force required to break whole Calliostoma shells. Both chelipeds of all C. pagurus tested generated forces in excess of the minimum required to break the shell lip, and the proportion of individuals capable of generating the minimum force required to break the whole shell increased with the size of the size of the crab. Carcinus maenas and Cancer pagurus were capable of breaking both the shell lips and the whole shells of a wider range of shell sizes than L. puber.

Animal group forces resulting from predator avoidance and competition minimization

A new model to explain animal spacing, based on a trade-off between foraging efficiency and predation risk, is derived from biological principles. The model is able to explain not only the general tendency for animal groups to form, but some of the attributes of real groups. These include the independence of mean animal spacing from group population, the observed variation of animal spacing with resource availability and also with the probability of predation, and the decline in group stability with group size. The appearance of "neutral zones" within which animals are not motivated to adjust their relative positions is also explained. The model assumes that animals try to minimize a cost potential combining the loss of intake rate due to foraging interference and the risk from exposure to predators. The cost potential describes a hypothetical field giving rise to apparent attractive and repulsive forces between animals. Biologically based functions are given for the decline in interference cost and increase in the cost of predation risk with increasing animal separation. Predation risk is calculated from the probabilities of predator attack and predator detection as they vary with distance. Using example functions for these probabilities and foraging interference, we calculate the minimum cost potential for regular lattice arrangements of animals before generalizing to finite-sized groups and random arrangements of animals, showing optimal geometries in each case and describing how potentials vary with animal spacing. (C) 1999 Academic Press.</p>