Methylammonium lead iodide ($\mathrm{MAPb}{\mathrm{I}}_3$) is a material of intense topical interest because of its potential applications in highly efficient solar cells, and its phase transitions and dynamical features have fundamental effects on its optoelectronic properties. We present a detailed strain analysis of the cubic-tetragonal-orthorhombic structural transitions in $\mathrm{MAPb}{\mathrm{I}}_3$ using Landau free energy expansions and group theory combined with experimental spontaneous strains and heat capacity data. We find that the cubic-tetragonal transition exhibits the nearly tricritical characteristic with a modest entropy change. In contrast, the tetragonal-orthorhombic transition is strongly first-order, with a much larger entropy change which is a feature of an order-disorder transition associated with the freezing of the $\mathrm{M}{\mathrm{A}}^{+}$ cations. We also observe a pronounced anomaly in the shear strain $e_4$ in the orthorhombic structure near 85 K, indicating a pseudo-Jahn-Teller distortion owing to the formation of Pb $6s^2$ lone-pair states, correlating with electron polaron formation. These findings clarify the interplay of lattice distortion and molecular dynamics in $\mathrm{MAPb}{\mathrm{I}}_3$. By revealing the fundamental strain-mediated mechanisms of these transitions, our work provides insights for strain engineering of hybrid perovskite devices, with implications for their stability and optoelectronic performance.

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• Entropy
• Landau theory
• Order parameters
• Phase transitions
• Strain