Fig. 9

Evolution with temperature of the in- (a_//, orange and red triangles) and out-of-plane (c_⊥, blue triangles) lattice parameters of Pb(Zr_0.2Ti_0.8)O₃ thin film deposited on SrTiO₃ (b, black diamonds), compared with the one of tetragonal bulk Pb(Zr_0.2Ti_0.8)O₃ (empty circles: c (black) and a (purple)). Misfit dislocations are present at the interface as a_// ≠ b, relaxing partially the deposition strain (ε^deposition) at the deposition temperature (T_d). This strain is transfered through the Poisson’s coefficient to c_⊥. It adds to the ferroelastic strain as the film is already ferroelectric. When cooled through T ^bulk_C , a spontaneous strain (ε^spont) appears, both for the a and c lattice parameters. Under T ^bulk_C , the pseudocubic bulk lattice parameter (a₀) becomes different from the bulk lattice parameters and keeps a linear evolution represented by a full line. The second full line underneath starts from the extrapolated value a_//(T_d) and diverges from the doted line that stands for the thermal evolution of the effective substrate b*(T). This divergence represents the thermal strain (ε^Δth) that develops into the film. The misfit strain is the sum of these three strains and is calculated by the relative difference between a_// and a₀