The thermal stability of amorphous ionic solids is usually attributed to kinetic considerations related to mass transport. However, there are a number of amorphous ionic solids, which have recently been described, whose unusual resistance to nucleation and subsequent crystallization cannot be explained by mass transport limitations. Examples have been found in a large variety of fields, spanning the range from thin solid films to biomineralization. This poses a question regarding a possible common mechanism for the stabilization of amorphous ionic solids. Here we present a model which explains the formation and thermal stability of quasi-amorphous thin films of BaTiO3, one of the amorphous systems recently described which exhibit unusual thermal stability. On the basis of the experimental evidence presented we suggest that nucleation of the crystalline phase can occur only if the amorphous phase undergoes volume expansion upon heating and transforms into an intermediate low density amorphous phase. If volume expansion is unobstructed by external mechanical constraints, nucleation proceeds freely. However, thin films are clamped by a substrate; therefore, volume expansion is restricted and the low-density intermediate phase is not formed. As a result, under certain conditions, nucleation may be completely suppressed and the phase which appears is quasi-amorphous. A quasi-amorphous film is under compressive stress and as long as the mechanical constraints are in place it remains stable at the temperatures that normally lead to crystallization of amorphous BaTiO3. Quasi-amorphous thin films of BaTiO3 exhibit pyroelectricity, the origin of which is also explained by the proposed model.