  Materials that exhibit zero thermal expansion have numerous applications,
ranging from everyday ceramic hobs to telescope mirrors to devices in optics
and micromechanics. These materials include glass ceramics containing crystal
phases with negative thermal expansion in at least one crystallographic
direction, such as Ba1-xSrxZn2-2yMg2ySi2O7 solid solutions. However, the volume
increase associated with the martensitic phase transformation in these crystals
often hinders their use as zero thermal expansion materials at operating
temperatures near the transition temperature Tt. Here, an approach to rapidly
predict Tt of such materials as a function of chemical composition based on a
combination of density functional theory simulations and experiments has been
developed and applied to Ba1-xSrxZn2-2yMg2ySi2O7. Its central element is the
modeling of free energy as a function of temperature and chemical composition
using a composition-dependent Debye model augmented by an empirical correction,
which incorporates the effects of anharmonic lattice vibrations. This approach
provides Tt predictions with an estimated uncertainty of about 100 K, which is
similar to the accuracy of computationally much more demanding simulations of
polymorphous phase transitions. In addition, this approach allows
computationally efficient determination of the chemical compositions at which
the Ba1-xSrxZn2-2yMg2ySi2O7 phase with the desired thermal properties will be
formed during synthesis, facilitating the targeted design of zero thermal
expansion materials.
