Entropic stabilization of a structurally tolerant phase: The ionic phase of lithium alanate

Abstract In materials simulations, formation energies can provide valuable information about the stability of different crystal polymorphs. However, to obtain a complete picture, it is often essential to go beyond simple energetics and include free energies into the analysis as many crystal phases are stabilized by entropic contributions and phase transitions at finite temperatures are common. Traditionally, free energies of crystalline solids are computed through an analysis of the phonon band structure which is calculated within the harmonic approximation considering only the crystalline unit cell and its replication. But also methods that go beyond the harmonic approximation consider only one periodic structure to calculate free energies. We show that such an approach can overlook substantial configurational free energy contributions and does not allow us to reach a well defined thermodynamic limit. To overcome these problems, it is necessary to generate large periodic cells that can represent not only the perfect crystalline structure but also a very large number of defect structures. Only with a configurational density of states that is well converged with respect to the size of the cell, it is possible to obtain reliable estimates of phase transition temperatures. We illustrate this effect for lithium alanate where the configurational entropy contribution of the structurally tolerant ionic phase reduces the transition temperature to the polymeric phase by 150 K.