Redox freezing temperature and Bartenev equation in a 25Na2O-15B2O3-60SiO2 glass doped with chromium and manganese

In a melt with the base mol% composition 25Na₂O-15B₂O₃-60SiO₂, doped with chromium and manganese, a redox reaction takes place during cooling the melt. This reaction was studied using high temperature UV-vis spectroscopy. Above 600 °C, the reaction is in equilibrium and shifted during cooling to the Cr³⁺ and Mn³⁺ species. At temperatures between 500 and 600 °C, the kinetics of the redox reaction is decisive and the cooling rate plays an important part. At temperatures < 500 °C, the reaction is frozen in. The smaller the cooling rate, the smaller is the Cr⁶⁺ concentration and the lower is the fictive redox temperature.The kinetics of the reaction was described by a differential equation assuming Arrhenian behaviour. The equation was numerically solved and fictive temperatures were calculated. These temperatures depended on cooling rate similar to Bartenev equation. Activation energies calculated hereof were around 38 kJ?mol⁻¹ larger than those inserted into the kinetic equation. The experimentally determined activation energy is 565 kJ?mol⁻¹, a value much larger than the activation energies of diffusion of the polyvalent elements. The rate determining step in the case of the Cr³⁺/Cr⁶⁺/Mn²⁺/Mn³⁺ system is the electron transfer reaction, because a notable structural rearrangement is necessary during the course of the electron transfer reaction (Cr³⁺ and Cr⁶⁺ occur in octahedral and tetrahedral coordination, respectively). The latter leads to a large inner reorganisation energy and to an activation energy similar to that of the viscous flow. In the case of the redox reaction between copper and arsenic, the activation energy is much smaller (210 kJ?mol⁻¹), because here the coordination numbers do not change during the course of the redox reaction.