Condition of Glass Transition in the Fluctuation Free Volume
Theory and the Lindemann Criterion for Melting

D. S. Sanditov and S. Sh. Sangadiev

Buryat State University, ul. Smolina 24a, Ulan-Ude, Buryat Republic, 670000 Russia

Abstract—The fluctuation free volume V_f in liquids and glasses is primarily determined by certain limiting
root-mean-square (rms) deviations of kinetic units from the equilibrium positions ~ . The condition
of glass transition in liquids implies that the volume fraction of fluctuation free volume f_g in liquids takes some
constant value at the glass transition temperature T_g, that is, f_g = const. In the physical meaning,
this condition is analogous to the well-known Lindemann criterion for melting /a² const at T = T_m, where
a is the characteristic interatomic distance. With regard to this aspect, the nature of fluctuation free volumes in
vitreous systems is discussed. The values of f_g are calculated for potassium borate and sodium germanate
glasses. It is found that the condition of glass transition f_g const 0.025 is fulfilled only to a first approxima-
tion. A quite regular dependence of f_g on the nature of glass-forming systems is revealed. In potassium borate
glasses, an increase in the K₂O content from 0 to 34 mol % causes the fraction of fluctuation free volume to
decrease from 0.034 to 0.026.

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