Author: JFR Archilla (pdf slides 950 Kb, poster,   proceedings' abstract and pdf copy)
With J Cuevas and FR Romero.

Abstract:
     Some silicates experience reconstructive transformations, which implies the breaking of the bond between silicon and oxygen, a particularly strong one. Therefore, high activation energies and a very slow reaction speed are expected. However, recent experiments in some layered silicates as mica muscovite have been performed at temperatures 600 C below the lowest experimental results previously reported [J. Mater. Chem. 13 (2003) 1835]. The reaction time at 300 C to obtain a 36% of the muscovite transformed is a few days instead of years.
      We suggest an explanation based in the existence of anharmonic, localized vibrations, called breathers in the cation layer [J. Phys. Chem. B 110 (2006) 24112]. We consider transversal vibrations for which the harmonic frequency is known. Far infrared spectra allows the determination of the on-site potential, which is highly nonlinear. We construct a Hamiltonian model and perform numerical simulations. In this system we can obtain numerically exact breather and their corresponding frequencies and energies. The latter can be as large as several hundreds KJ/mol, i.e., larger than the activation energy.
      To obtain the breather statistics, first, we deliver to the system a given energy with random positions and velocities, after some time of evolution the system is thermalized, but it is difficult to distinguish breathers from the subjacent sea of phonons. Second, by adding some dissipative term at the borders, the system is cooled, the phonons disappear but the breathers are left in place. Third, we calculate the breather energies and obtain the mean number of breathers and their energy distribution.
      Breathers have a different statistics that of the phonons as they tend to overpopulate higher energies [Chaos 13 (2003) 637]. However, the distribution of breathers can not be fitted with the theory developed in the previous reference. Detailed observations of the numerical results show that there are many differen types of breathers, as breathers with different symmetries and multibreathers. We consequently modify the theory and obtain a reasonable good fitting with the numerical distribution.
      The number of breathers is much smaller than the number of phonons, but only the excitations with energy above the activation energy, which is estimated to be 100-200 KJ/mol will have influence on the reaction rate. The increase of the reaction rate with breathers will be roughly equal to the ratio between the number of breathers and the number of phonons above the activation energy. We estimate it in about 10⁴-10⁵, in other words, as the three days experimental time leads to about 30% of the transformation performed, the time without breathers to obtain the same result, would be 10⁴-10⁵ times larger and, thus, completely unobservable. Therefore we can consider that breathers are good candidates as an explanation to low temperature reconstructive transformations.

The 5th International Workshop on Complex Systems, Sendai, Japan, September 25-28, 2007.
Presented by JFR Archilla