The temperature which is used for characterization of the structure of a glass-forming melt. The notion of fictive temperature Tf was formulated by Tool (1946) and, since then, has been used broadly to describe properties of glass-forming substances inside and below the glass transition region. Tool defined the fictive temperature of a substance in a non-equilibrium state as the actual temperature of the same substance in the equilibrium (liquid) state whose structure is similar to that of the non-equilibrium substance. This definition can be illustrated by the following figure which shows a method to determine Tf for any substance using the value of a property of this substance, when temperature dependencies of this property for glassy (αg) and liquid (αl) states are known.
It follows from the definition above that, for the glassy state, Tf does not depend on temperature, and, for the liquid state, Tf is always equal to the actual temperature of a substance. For rate cooling Tf below the glass transition region is equal to Tg, obtained at the same cooling rate.
It should be noted that in most cases the structure of a glass is not similar to the structure of the same substance in a liquid state at any temperature. Thus for any Tf of glass, there could be an infinite number of different structures of glasses which would have the same property value but behave differently during subsequent heating or long isothermal holds. Quite often Tf determined for different properties of the same glass are not equal to each other. Nevertheless, the fictive temperature is a very convenient characteristic of glass and is widely used in literature on glass properties.