  Using a variational model based on non-linear elasticity we investigate
whether in a cubic-to-tetragonal phase transformation it is energetically
preferable to nucleate martensite within austenite. Under minimal growth
assumptions on the free energy density $W$ away from the wells, we derive
explicit upper bounds on $W^{qc}({\mathbb{I}})$, i.e. on the macroscopic free
energy density of a region that has been macroscopically deformed by the
identity map. The bounds only depend on material parameters, the temperature
difference and the growth of $W$ away from the wells. By comparing
$W^{qc}({\mathbb{I}})$ and $W({\mathbb{I}})$ we conclude that nucleation is
always energetically preferable and are able to provide quantitative upper
bounds for the gain in negative energy due to nucleation.
