Impact of O-Si-O bond angle fluctuations on the Si-O bond-breakage rate

摘要

We extend the McPherson model for the silicon-oxygen bond-breakage in a manner to capture the impact of the O-Si-O angle fluctuations (typical for amorphous SiO_2) on the breakage rate. In the McPherson model the transition of the Si ion from the 4-fold coordinated position to the 3-fold coordination is considered as rupture of the Si-O bond. We have studied the potential barrier (separating these saddle points) transformation induced by the O-Si-O bond angle variations and found that the secondary minimum occurs at a critical angle of about 107.75°. Since the Si ion "finds" the way corresponding to the highest breakage probability we used the two-dimensional downhill simplex method in order to find the direction of this maximal rate. It was shown that if the O-Si-O angle deviates from its nominal value 109.48° (typical for α-quartz) corresponding to the regular SiO_4 tetrahedron the symmetry aggravates and the secondary minimum is rotated. Calculated dependencies of the breakage rate on the electric field demonstrate the linear slope in the log-lin scale thus reflecting the linear reduction of the activation energy for the bond-breakage vs. field. The family of distribution functions for breakage rate calculated with a fixed step of field shows that the curves do not change their form and are shifted in parallel with the field. This tendency supports the thermo-chemical model for the bond-breakage also in the case of strongly fluctuating O-Si-O angles. As a consequence, dependencies of the mean value of the rate, its standard deviation and the nominal rate (calculated for the angle of 109.48°) have the same slope on a log-lin scale. The wide spread of the breakage rate is reflected by the high value of its standard deviation.