Thermomechanical stabilization of electron small polarons in SrTiO3 assessed by the quasiharmonic approximation

Abstract

We predict a predominance diagram for electron defects in the temperature-hydrostatic stress space for SrTiO 3 by combining density functional theory and the quasiharmonic approximation. We discovered two regimes where small polarons dominate: under tensile stress at lower temperature due to a larger relaxation volume of the defect , and under compressive stress at higher temperature due to a smaller and larger formation entropy. This provides a means to modulate the electronic conductivity via controlling the underlying charge carrier. Furthermore, the results challenge the common association between larger and charge localization by demonstrating that at high temperature the free electron can induce larger compared to the small polaron. This finding is attributed to the ability of the free electron to generate greater vibrational entropy upon finite isothermal expansion. DOI: 10.1103/PhysRevB.95.161110 An electron can move freely in a periodic crystal unless the lattice is polarizable, in which case the electron can begin to exhibit localization by deforming surrounding ions to form a so-called large polaron. Assisted by lattice vibrations, electron localization can become enhanced to be self-trapped on a single ion. The latter is termed a small polaron or a self-trapped electron. While large polarons traverse crystals in a rapid bandlike fashion, small polarons tend to hop slowly from one ion to the next [1]. Holstein predicted that in a given polarizable crystal, a transition from large to small polaron behavior occurs as the temperature increases above half the Debye temperature D [2]. Understanding and controlling the extent of electron localization in the family of metal oxides underpins their performance in various applications. For example, delocalization is desired for increasing the electronic conductivity of oxides that function for water splitting and CO 2 reduction [3]. On the other hand, the ease of creating oxygen vacancies in reducible metal oxides is generally correlated with localizing electrons on neighboring host cations; that is, reducing them [4][5][6]. Temperature and stress are readily available thermodynamic forces to tune the degree of localization of electronic defects. In this Rapid Communication, we reveal how the localization of electron polarons in the metal oxide SrTiO 3 is controlled by these forces, primarily via changes in relaxation volume of electronic defects with temperature and pressure.Strontium titanate (SrTiO 3 ) is an archetype of the versatile perovskite oxides family. The electronic defects (electrons and holes) of bulk SrTiO 3 give rise to desirable properties not possessed by the underlying perfect crystal such as superconductivity [7] [16] by suggesting that in the dilute limit (i.e., less than 1% defect per unit cell) large polarons prevail, and at higher doping concentrations small polarons prevail. Density functional theory (DFT) calculations at temperature 0 K consistently predict the predominance of free electrons over small polarons [15,16], where it is ...

Conductivity of iron‐doped strontium titanate in the quenched and degraded states

“…Both the Arrhenius and polaron models fit the temperature‐dependent conductivity equally well and the activation energy found here is similar to predicted migration barriers of polarons in oxygen deficient SrTiO 3‐x predicted from density functional theory . Additionally, if the measured conductivity and activation energy are due to Ti 3+ polarons, then based on first principles work they are likely associated with point defects, in addition to (by definition) the lattice deformation.…”

Survey of acceptor dopants in SrTiO3: Factors limiting room temperature hole concentration

“…To be consistent with the notation used in computational studies on oxides and semiconductors, and with the defect notation employed here, small polarons will be represented by n X and p X for bulk electron and hole polarons localized on atom X, respectively. In SrTiO 3 , first‐principle calculations indicate bulk small hole polarons centered around an O atom () are stable, but bulk small electron polarons on Ti ( or Ti 3+ ) are not favorable in most conditions . Defect stabilized small electron polarons on Ti (Ti 3+ complexes) were found to be stable in proximity to oxygen vacancies, but it is impractical with current computational capabilities to find local minima in the configuration space associated with every charged defect considered in this work.…”

“…Recent computational work has probed some properties of SrTiO 3 doped with K and Na, nonmetal elements like N, and transition metals like Fe, Mn, and Ni, but the results are not connected to a thermodynamic model of the defect chemistry. The role of small electron or hole polarons has also been investigated computationally . In discussing polarons, it is necessary to distinguish between bulk and defect stabilized polarons or, in the language used in conventional ceramics literature for small electron polarons, Ti 3+ , and Ti 3+ complexes.…”

“…The role of small electron or hole polarons has also been investigated computationally. 31,[38][39][40] In discussing polarons, it is necessary to distinguish between bulk and defect stabilized polarons or, in the language used in conventional ceramics literature for small electron polarons, Ti 3+ , and Ti 3+ complexes. To be consistent with the notation used in computational studies on oxides and semiconductors, and with the defect notation employed here, small polarons will be represented by n X and p X for bulk electron and hole polarons localized on atom X, respectively.…”

Electro-chemo-mechanical effects of lithium incorporation in zirconium oxide

“…In Ref. [44] it was suggested that this is a viable way to obtain the relaxation volume of charged defects in DFT supercells where the ambiguity of defining pressure in charged cells [45] is removed by fitting to an equation of state. We also note that the fractional volume change does not depend significantly on cell size, which is discussed in detail in SM, Sec.…”