文摘
The proton-conducting network in lanthanum orthophosphate, LaPO4, has been theoretically clarified from first principles in the present study. It consists of as many as 20 kinds of migration paths with potential barriers below 1 eV, which are classified into three groups, i.e., rotations and intra- and intertetrahedral hoppings. As the results of the kinetic Monte Carlo simulations using the network of the migration paths, the calculated proton diffusion coefficients have anisotropy reflecting the monoclinic crystal structure, particularly large anisotropy in the ca-plane. It results from the dominant proton migration in the directions of [011], [011虆], [111], and [11虆1], whose potential barriers are 0.7 eV. The calculated activation energies of the diffusion coefficients in the fastest, the slowest, and the b-axis (unique axis) directions are 0.68, 0.76, and 0.70 eV (= 66, 73, and 68 kJ/mol), respectively, in the temperature range from 500 to 1500 K. These values are lower than the experimentally reported activation energies by conductivity measurements in the range of 0.8鈥?.0 eV. The major origin of the discrepancy is association effects between protons and dopants. The calculated association energy between protons and strontium dopants is 0.31 eV (30 kJ/mol), which makes the slope of the conductivity curves steeper by 0.21鈥?.11 eV in the temperature range of 773鈥?073 K.