Formation and Migration Enthalpy from Elemental and Cooperative Diffusion in Lead Silicate Supercooled Liquid and Glass

Abstract

Diffusivity, conductivity, and viscosity data of the PbO⋅SiO₂ were collected in the liquid, supercooled liquid, and glassy states. The difference in the dependence of diffusivity, viscous flow, and ionic conductivity on temperature below and above the glass transition temperature (T_g) is interpreted as a discontinuity in the charge carrier’s mobility mechanisms, including new proposals for ionic diffusivity. Charge carrier displacement occurs by an activated mechanism below T_g and through a cooperative mechanism above this temperature. Fitting diffusivity and conductivity data with the proposed model allows one to determine the enthalpies of charge carrier formation and migration separately. In particular, we present experimental results of lead and silicon diffusion species (D_Pb and D_Si) at deep and low undercoolings in PbSiO₃—considering 16 orders of magnitude and comparing the effective diffusivity for viscous flow, D_η, and its activation energy. A decoupling temperature T_d between the cationic diffusivity and the diffusivity calculated from viscosity, i.e., D_η < (D_Si ≈ D_Pb) was noted. In fact, a noticeable change in the lead self-diffusion coefficients around T_d = 1.19T_g also contributed to this analysis. Thus, above T_d, silicon and lead control the transport mechanism involved in viscous flow, while below this temperature some simpler structures must control the transport process. Such results suggest that viscous flow requires a cooperative motion of some “structural units” rather than just jumps of one or a few isolated atoms, as it occurs in conductivity below T_d. Also, cooperatively rearranging regions or the size of the structural units are quite similar for both processes above T_d.