Understanding mechanisms of thermal expansion in complex oxide thin-films from first principles: Role of high-order phonon-strain anharmonicity

The thermal properties of materials are critically important to various technologies and increasingly the target design efforts. However, it is only relatively recent advances in first-principles computational techniques that have enabled researchers explore microscopic mechanisms properties, such as expansion. We use Gr\"{u}neisen theory expansion combination with density functional calculations quasiharmonic approximation uncover PbTiO$_3$ thin-films terms elastic vibrational contributions free energy. Surprisingly, we find although structural parameters evolve temperature if they dominated by linear elasticity, strongly anharmonic, large changes constants both misfit strain temperature. show a fortuitous near-cancellation between different types anharmonicity gives rise this behavior. Our results illustrate importance high-order phonon-strain determining temperature-dependent thin-films, highlight complex manner which expansion, intertwined.