First-Order Localized-Electron⇆Collective-Electron Transition in LaCoO3

Abstract

Precision x-ray measurements of the motions of the atoms in LaCo${\mathrm{O}}_3$ every 50°C from room temperature to 1000°C indicate that the crystal space group is $R\overline{3}c$ below 375°C and $R\overline{3}$ above 375°C. In the symmetry $R\overline{3}$ there are two distinguishable octahedral cobalt positions, ${\mathrm{Co}}_{\mathrm{I}}$ having larger crystalline fields than ${\mathrm{Co}}_{\mathrm{II}}$. Since high- and low-spin cobalt ions are simultaneously present, this indicates preferential long-range ordering of low-spin cobalt at ${\mathrm{Co}}_{\mathrm{I}}$ sites, and of high-spin cobalt at ${\mathrm{Co}}_{\mathrm{II}}$ sites for $T>\mathrm{}375\mathrm{}$°C. Calorimetric data show a first-order transition at $T_t=937\mathrm{}$°C and a higher order transition in the temperature interval $125<T<\mathrm{}375\mathrm{}$°C, which is also manifest in a large Debye-Waller factor in this interval and in a plateau in the curve of reciprocal susceptibility versus temperature. At about 650°C there is some evidence, from differential thermal-analysis data, of another higher order transition. The electrical conductivity increases with increasing temperature below 650°C, but much more rapidly in the interval $125<T<\mathrm{}650\mathrm{}$°C than below 125°C. It is nearly temperature-independent in the interval $650<T<\mathrm{}937\mathrm{}$°C and is continuous through the first-order transition. However, above 937°C the resistivity increases with temperature as in a metal. The space group remains $R\overline{3}$ and the pseudocubic cell edge is continuous through the first-order phase change, but the rhombohedral angle drops abruptly from 60.4° to 60° and the ${\mathrm{La}}^{3+}$ ions are shifted discontinously along the $c$ axis toward a ${\mathrm{Co}}_{\mathrm{I}}$ ion. Similar ${\mathrm{La}}^{3+}$-ion displacements occur in the temperature interval $400<T<\mathrm{}650\mathrm{}$°C. The Debye-Waller factor decreases by an order of magnitude on going to the high-temperature phase. It is pointed out that crystal-field and band theory should describe two different thermodynamic states of electrons: localized and collective. The data are interpreted to indicate (1) that the first-order phase change at $T_t=937\mathrm{}$°C is a localized-electron $\leftrightarrows$ collective-electron phase change for electrons in orbitals of $e_g$ symmetry, higher temperatures introducing a Fermi surface and partial disproportionation between high- and low-spin cations at ${\mathrm{Co}}_{\mathrm{II}}$ and ${\mathrm{Co}}_{\mathrm{I}}$ positions; (2) that the number of charge carriers is constant through the transition, because the number of localized charge carriers is saturated below $T_t$ and just above $T_t$ the bandwidth of the collective-electron states is $\Delta \epsilon <k{T}_t$; (3) that the mobilities of the charge carriers are also continuous through the transition, the activation energy for a localized-electron hop becoming $\ll \mathrm{kT}$ at $T\le 937$°C; (4) that the higher-order transition in the interval $125<T<\mathrm{}375\mathrm{}$°C represents a region of short-range order, the ordered phase occurring at higher temperatures where the populations of high- and low-spin cobalt ions approach one another; and (5) that exciton transfer is an important mechanism in LaCo${\mathrm{O}}_3$.