Role of Ga ³⁺ and Cu ²⁺ in the high interstitial oxide-ion diffusivity of Pr ₂NiO ₄-based oxides: Design concept of interstitial ion conductors through the higher-valence d ¹⁰ dopant and Jahn-Teller effect

We have investigated the crystal structure, nuclear- and electron-density distributions, electronic structure, and oxygen permeation rate of three K ₂NiF ₄-type oxides of Pr ₂(Ni _0.75Cu _0.25) _0.95Ga _0.05O _4+δ, Pr ₂Ni _0.75Cu _0.25O _4+δ, and Sr ₂Ti _0.9Co _0.1O _4-ε, in order to study the role of d ¹⁰ Ga ³⁺, Jahn-Teller Cu ²⁺, and interstitial oxygen O3 in the high oxygen diffusivity of Pr ₂(Ni _0.75Cu _0.25) _0.95Ga _0.05O _4+δ. The composition Pr ₂(Ni _0.75Cu _0.25) _0.95Ga _0.05O _4+δ has a larger amount of interstitial oxygen O3 atoms (δ = 0.31 at room temperature (RT)) compared with Pr ₂Ni _0.75Cu _0.25O _4+δ (δ = 0.19 at RT) and the oxygen deficient Sr ₂Ti _0.9Co _0.1O _4-ε (ε = 0.02 at RT). The interstitial O3 atom is stabilized by (1) the substitution of (Ni,Cu) ²⁺ by higher valence Ga ³⁺, (2) static atomic displacements of the apical O2 oxygen, and (3) local relaxation near d ¹⁰ Ga ³⁺. Nuclear-density distributions of Pr ₂(Ni _0.75Cu _0.25) _0.95Ga _0.05O _4+δ and Pr ₂Ni _0.75Cu _0.25O _4+δ at high temperatures have visualized the -O2-O3-O2- diffusional pathway of oxide ions, which indicates an interstitialcy diffusion mechanism. Doping of the Jahn-Teller Cu ²⁺ in Pr ₂NiO _4+δ stabilizes the high-temperature disordered tetragonal I4/mmm phase and makes the apical O2 atoms more mobile. The apical O2 is more mobile compared to the equatorial O1, because the longer covalent (Ni,Cu,Ga)-O2 bond is weaker than the shorter (Ni,Cu,Ga)-(equatorial O1) one, as evidenced by the experimental and theoretical electron-density analysis. The interstitial O3 is more mobile due to the lower coordination number (CN = 4) compared with the lattice O1 and O2 atoms (CN = 6). It was found that the minimum nuclear density on the O2-O3 pathway ρ _N(T) is a useful microscopic parameter for the oxygen diffusivity. The ρ _N(T) is regarded as the oxygen probability density at the bottleneck for diffusion. The oxygen permeation rate ρ _P(T) increases with an increase of ρ _N(T). The activation energy for oxygen diffusion estimated by the plots of log (the normalized oxygen permeation rate ρ _P(T)/δ) against T ^-1 (reciprocal of absolute temperature) is relatively independent of temperature as well as the formation energy of oxygen atoms at the bottleneck from the plots of log(ρ _N(T)/δ) against T ^-1. These results indicate that the amount of interstitial oxygen δ is proportional to the carrier concentration for the oxide-ion diffusion. Doping of higher-valence Ga ³⁺ at (Ni,Cu) ²⁺ site in Pr ₂Ni _0.75Cu _0.25O _4+δ does not change largely the activation energy for the oxygen permeation and formation energy of oxygen atoms at the bottleneck but increases the amount of excess interstitial oxygen (carrier concentration), which yields the high oxygen permeation rate of 262 μ mol min ^-1 cm ^-2 in Pr ₂(Ni _0.75Cu _0.25) _0.95Ga _0.05O _4.13 at 900 °C. The present work demonstrates the design concept of interstitial ion conductors through the higher-valence d ¹⁰ dopant and Jahn-Teller effect.