Electronic-Structure Origin of Cation Disorder in Transition-Metal Oxides

Cation disorder is an important design criterion for technologically relevant transition-metal (TM) oxides, such as radiation-tolerant ceramics and Li-ion battery electrodes. In this Letter, we use a combination of first-principles calculations, normal mode analysis, and band-structure arguments to pinpoint a specific electronic-structure effect that influences the stability of disordered phases. We find that the electronic configuration of a TM ion determines to what extent the structural energy is affected by site distortions. This mechanism explains the stability of disordered phases with large ionic radius differences and provides a concrete guideline for the discovery of novel disordered compositions.

Figure 1

(a) TM site distortion in the ${\text{LiTMO}}_2$ ground state structures (layered $\alpha -{\mathrm{NaFeO}}_2$ structure and $\gamma -{\mathrm{LiFeO}}_2$ structure) and in the SQS of all first and second-row TMs except Mn and Tc. The distortions are decomposed into contributions from different normal mode symmetry groups. The first normal mode (${\nu }_1$) corresponds to an isotropic scaling and is not considered. ${\nu }_2$ is the Jahn-Teller distortion, ${\nu }_3$ corresponds to bending distortions, ${\nu }_4$ to twisting, and ${\nu }_5$ describes the displacement of the TM from the center of the site. (b) Schematic of the normal modes of an octahedral TM site grouped by symmetry (rotations and translations are not shown).

Figure 2

Change of the electronic states (top) and the band energy (bottom) upon distortion of an octahedral TM site in the direction of (a) the Jahn–Teller mode (${\nu }_2$) and (b) the TM-displacement mode (${\nu }_5$). The band energies for four electronic configurations are shown: $d^0$ (blue circles), $d^4$ high spin (hs, red squares), $d^6$ low spin (ls, green line), and $d^8$ (gray dashed line). The energies shown in panel (a) are based on the conventional Jahn–Teller mode (compression or elongation in $z$ direction) which is a linear combination of the normal coordinates of type ${\nu }_2$ shown in Fig. 1. The energy and distortion scales are equal for both normal modes. The labels in the top panels indicate the TM $d$ orbitals that contribute most for distortions along the Cartesian $z$ direction.

Figure 3

(a) Number of ${\mathrm{LiNi}}_{0.5}{\mathrm{Ti}}_{0.5}{\mathrm{O}}_2$ and ${\mathrm{LiNi}}_{0.5}{\mathrm{Mn}}_{0.5}{\mathrm{O}}_2$ configurations within a $100\mathrm{meV}/\mathrm{cation}$ from the ground state out of 469 distinct configurations with up to four formula units. (b) Energy per cation and TM site distortion of the 50 most stable (b) ${\mathrm{LiNi}}_{0.5}{\mathrm{Ti}}_{0.5}{\mathrm{O}}_2$ and (c) ${\mathrm{LiNi}}_{0.5}{\mathrm{Mn}}_{0.5}{\mathrm{O}}_2$ configurations. Only TM-displacement (${\nu }_5$) distortions are considered.