Dependence of the Fictive Temperature of Glass on Cooling Rate

TLDR

Ritland’s equation linking cooling rate and fictive temperature for glasses without memory is extended to glasses with memory that exhibit a spectrum of relaxation times. Assuming a temperature‑independent relaxation‑time spectrum, the limiting fictive temperature T′f is related to the cooling rate q by d ln|q|/d(1/T′f)=−Δh*/R, where Δh* is the activation enthalpy for the structural‑relaxation times. Differential‑scanning‑calorimetry measurements of T′f versus q for B₂O₃, 0.4Ca(NO₃)₂–0.6KNO₃, and borosilicate crown glasses show that Δh* equals the shear‑viscosity activation enthalpy, and that T′f values from volume and enthalpy data for the crown glass coincide.

Abstract

An equation derived by Ritland relating the cooling rate and fictive temperature for glasses without memory is extended to those with memory, i.e. those which exhibit a spectrum of relaxation times. Provided that the spectrum of relaxation times is temperature‐independent, the limiting fictive temperature, T′ f , obtained when a glass is cooled through the transition region, is shown to be related to the cooling rate, q , by d In | q |/ d (1/ T'f )=‐Δ h ★/ R where R is the ideal gas constant and Δ h ★ the activation enthalpy for the relaxation times controlling the structural relaxation. Values of T′ f vs q obtained from enthalpy measurements by differential scanning calorimetry are presented for B 2 O 3 , 0.4Ca(NO 3 ) 2 —0.6KNO 3 , and borosilicate crown glasses; Δ h ★ is equal, within experimental error, to the activation enthalpy for shear viscosity. Values of T′ f from volume and enthalpy measurements obtained at the same cooling rate for the borosilicate crown glass are equal.