YOUNGWOOD, Pa. -- Background
Driving metal nanocrystals through nanotubes by electrical current is commonly observed for crystals that can easily slide within the tube. The mechanism by which the crystal moves is not well understood, although generally thought to be electromigration whereby flowing electrons transfer their momentum in collisions with the atoms.

However,

What happens when the nanotube has a constriction smaller than the crystal?

Obviously, the constriction blocks the crystal motion. But experiments [1,2] show the crystal somehow slips through the constriction. The thumbnail shows the crystal (a) before and (b) after moving in the constriction. Indeed, the claim is made that a solid metal nanocrystal can be made to slip through a very small constriction. See http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.1... (http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.110.185901)

Of course, if the crystal is heated beyond its melting point and becomes a liquid it could flow through the constriction. Or, if the crystal under high electromigration force may undergo plastic deformation, the crystal could be extruded through tthe constriction. However, temperatures are near ambient and the electromigration force relatively low to preclude extrusion, and therefore another mechanism is at play.

In this regard, the crystal is thought [1,2] to squeeze through the constriciton by the electromigration of surface atoms from the back to the front of the crystal, thereby avoiding plastic deformation of the crystal itself.

In support of electromigration, the crystal was simulated in kMC. kMC stands for kinetic Monte Carlo. The kMC simulation depends on the energy barrier between a pair of atoms. Atoms move if the energy available for the electromigration force over the pair separation distance exceeds the barrier height. Consistent with classical physics. both barriers and available energies depend on the thermal kT energy of the atoms. k stands for Boltzmann’s constant and T for absolute temperature. The results (Fig. 6 of [1]) give center of mass speed and electromigration force as a function of temperature.

Problem
Following classical physics, the kMC simulations depend on atom temperatures, but QM precludes temperatures in nanoscale crystals. QM stands for quantum mechanics. In fact, atoms in the nanocrystal have no heat capacity to conserve Joule heat from the current passing through the crystal, and therefore the temperature changes as required in kMC simulations do not occur.

QED Charging
In the alternative, crystal motion is proposed driven by charge created from EM radiation induced from the conservation of Joule heat by QED. EM stands for electromagnetic and QED for quantum electrodynamics. Conservation proceeds by the creation of non-thermal EM radiation at the TIR resonant frequency of the nanocrystal. TIR stands for total internal reflection. Lacking heat capacity by QM, QED conserves the Joule heat at the TIR frequency of the crystal by creating excitons (holon and electron pairs) that charge the crystal or upon recombination are emitted as EM radiation to the surroundings. See diverse QED applications at http://www.nanoqed.org, 2009 to 2014.

Discussion
QED induced EM radiation ionizes the iron atoms within the crystal at QM energies > 7.9 eV liberating electrons and leaving the crystal highly charged. In fact, the crystal undergoes a Coulomb explosion, although the atoms are contained within the nanotube. In effect, QED induces the Joule heat to charge the crystal to create a loosely bound state of atoms that allows the crystal to easily slip through the constriction. However, only a small fraction of the Joule heat is converted to a QED force as almost all the Joule heat is lost as EM radiation to the surroundings.

In the crystal, QM precludes conservation of Joule heat by an increase in temperature, and instead charge is created at the nanoscale that otherwise at the macroscale would increase the atom temperature. The amount of Joule heat necessary to create the charge necessary to just “loosen” the atoms may be estimated by equating the L-J potential having an attractive maximum energy ε at radius 21/6σ to the repulsive Coulomb potential. L-J stands for Lennard-Jones and ( σ, ε ) are L-J parameters for iron. See Paper “QED induced squeezing of nanocrystals” at Ibid, 2013.

Conclusions

1. The classical kMC analysis based on temperature is not applicable to derive the crystal motion because temperatures have no meaning at the nanoscale. Since QM denies the atoms the heat capacity to conserve Joule heat by an increase in temperature, QED conserves Joule heat by the creation of excitons that upon recombination produce EM radiation to ionize the atoms, Coulomb repulsion tends to overcome attraction between atoms and produce loosely bound atoms that slip through the constriction. Conversely, kMC can not convert Joule heat to excitons allowing recombination to charge the atoms and emit EM radiation.

2. The electromigration force is far too large to be consistent with the low center of mass velocities. In contrast, the QED induced force is far smaller because a very large fraction of the Joule heat is lost as EM radiation to the surroundings. Similarly, loosely connected QED charged atoms are likely to supersede the electromigration mechanism in limiting the life of nanoscale electrical interconnects.

References
[1] S. Coh, S. G. Louie, and M. L. Cohen, ”Theoretical study of solid iron nanocrystal movement inside a carbon nanotube,” Phys. Rev. B, 88, 045424 (2013)

[2] S. Coh, et al.,“Surface Atom Motion to Move Iron Nanocrystals through Constrictions in Carbon Nanotubes under the Action of an Electric Current,” PRL 110, 185901 (2013).


Contact
QED Radiations
852-5942-4802
thomas@nanoqed.org