Ab initio calculations of proton migration properties in Gd-doped BaCeO 3

Transcription

1 Ab initio calculations of proton migration properties in Gd-doped BaCeO 3 Jessica Hermet 1,2, François Bottin 1, Grégory Geneste 1, Guilhem Dezanneau 2 1 CEA, DAM, DIF, F Arpajon, France 2 Laboratoire SPMS, CNRS-UMR8580, ECP, Grande Voie des Vignes, Châtenay-Malabry Cedex, France SSPC 16 SEPTEMBER 2012

2 OUTLINE Structure of BaCeO 3 Ab initio calculations of barriers Parameters Results - stable positions, - energy barriers KMC Simulations Parameters and assumptions Results - mechanisms frequencies, - location of defects, - diffusion coefficients Conclusion SSPC 16 SEPTEMBER 2012 PAGE 2

3 STRUCTURE OF BACEO 3 Structure: distorted perovskite (Pnma) Orthorhombic structure up to 550 K (low symmetry) 2 tilts (a - b + a - ) BaCeO 3 : good protonic conductivity Especially when doped with a trivalent element Creation of oxygen vacancy Hydration: Gd V o dry Gd + H 2 O hydrated Gd H + H + Gd Gd:BaCeO3 = Electrolyte for Protonic Ceramic Fuel Cell SSPC 16 SEPTEMBER 2012 PAGE 3

4 AB INITIO CALCULATIONS Parameters Abinit Code (plane-waves) PAW method GGA-PBE exchange correlation Spin-polarized (because of Gd) Highly parallelized 80 atoms supercell Calculations One geometry optimization per configuration - (1 proton, 1 dopant) - (1 oxygen vacancy, two dopants) Energy barrier between two configurations using the string method - (to find Minimum Energy Path) SSPC 16 SEPTEMBER 2012 PAGE 4

5 Relative energy (ev) AB INITIO CALCULATIONS Energetics Hydration enthalpy = ev (per H 2 0 molecule) Stable positions for the proton 16 differents positions are found - 8 close to the dopant Gd - 8 far from the dopant Gd Ce1 Ce2 Ce a 1b 1c 1d 2a 2b 2c 2d Positions of the proton Hermet,J. ; Bottin, F.; Dezanneau, G.; Geneste, G. Physical Review B, 2012, 85, SSPC 16 SEPTEMBER 2012 PAGE 5

6 AB INITIO CALCULATIONS Proton diffusion mechanisms Energy barrier calculations (=84 values) 3 kinds: Reorientation Intra-octahedra hopping Inter-octahedra hopping Mechanism Intra hopping Inter hopping Reorientation E moy (ev) 0.38 σ= σ= σ=0.16 SSPC 16 SEPTEMBER 2012 PAGE 6

7 KMC SIMULATIONS Kinetic Monte Carlo (KMC) Method to simulate the time evolution of a system where processes can occur with a known rate Conditions and assumptions: Parameters: Simulation box = 8*8*8 cubic cell (2560 atoms) steps per simulation (= from 20 ns up to 1 µs) Temperature from 300K up to 1500K (no longer Pnma structure experimentally) Doping rate between 1/64 (1.5%) and 1/4 (25%) Assumptions: Oxygen vacancies and Gadolinium dopants are fixed (initially randomly distributed) No long-range electrostatic interactions One oxygen can only welcome one proton - choice based on : i/ proton repulsion, ii/ 2 protons on the same oxygen is not a stable configuration - NB: simulations with the possibility of 4 protons per oxygen lead to similar results Main Goal : activation energy and protonic conductivity how dopant affects conduction PAGE 7 SSPC 16 SEPTEMBER 2012

8 KMC SIMULATIONS Relative frequencies of the different mechanisms Temperature dependence Doping rate dependence δ=6.25% T=900K Reo Intra Inter 300K 600K 900K 1200K 1500K Reo Intra Inter 1.56% 3.13% 6.25% 12.50% SSPC 16 SEPTEMBER 2012 PAGE 8

9 KMC SIMULATIONS Location of protonic defects Close or far from the dopant Assuming a fully-hydrated system (no oxygen vacancy) Number of possible protonic sites : 8*8*8*3*4 = 6144 Number of protons between 8 (δ=1.5625%) and 128 (δ=25%) Occupation of close sites (to be compared with the percentage of close sites) Average on ten million KMC steps (minus equilibration time depending on T) Doping rate= (Percentage of close sites) % (3.13%) 3.125% (6.25%) 6.25% (12.37%) 12.5% (23.31%) 25% (43.62%) 300K 50% [16.0] 57% [9.1] 69% [5.5] 79% [3.4] 91% [2.1] 600K 17% [5.4] 28% [4.5] 43% [3.5] 60% [2.6] 78% [1.8] 900K 9% [2.9] 18% [2.9] 31% [2.5] 48% [2.1] 69% [1.6] 1200K 7% [2.2] 14% [2.2] 26% [2.1] 42% [1.8] 63% [1.4] 1500K 7% [2.2] 12% [1.9] 23% [1.9] 38% [1.6] 60% [1.4] SSPC 16 SEPTEMBER 2012 PAGE 9

10 KMC SIMULATIONS Location of protonic defects Initially randomly distributed Relaxation time to get the equilibrated distribution - Long at low temperature ( steps) - Short at high temperature ( 1000 steps) At T=300K, δ=6.25% Initial After steps After steps After steps Close proton Far proton Dopant SSPC 16 SEPTEMBER 2012 PAGE 10

11 Diffusion coefficient (m2/s) KMC SIMULATIONS Diffusion coefficients ν=ν 0 exp[-δe/k B T] <r²>=6dt D=D 0 exp[-e a /k B T] Previous calculation with ν 0 =10 13 Hz 6.25% : E a = 0.37 ev 12.5% : E a = 0.36 ev 25% : E a = 0.34 ev 3E-08 3E % 12.50% 20.00% 25.00% Previous study 0% : E a = 0.49 ev a 10% : E a = 0.45 ev b Calculations with ν 0 =k B T/h 6.25% : E a = 0.45 ev 12.5% : E a = 0.44 ev 20% : E a = 0.43 ev 25% : E a = 0.42 ev 3E-10 3E /T a Münch, W.; Kreuer, K.-D.; Seifert, G. & Maier, J. Solid State Ionics, 2000, , b Kreuer, K.; Schönherr, E. & Maier, J. Solid State Ionics, 1994, 70-71, Part 1, SSPC 16 SEPTEMBER 2012 PAGE 11

12 CONCLUSION AND PROSPECTS Conclusion Proton diffusion is more efficient with inter-octahedral transfer (due to tilted structure) Proportion inter/intra-octahedral hopping decreases with doping rate Proportion hopping/reorientation increases with temperature Protonic defects are preferentially located near a dopant But not completely trapped (or all of them will be near a dopant) And activation energy slightly decreases with doping rate, suggesting an easier diffusion as we put more dopant in the material. On-going work Implementation of Ewald summation in KMC code To take into account electrostatic interaction more accurately Path Integral Molecular Dynamics (PIMD) To take into account the quantum nature of proton SSPC 16 SEPTEMBER 2012 PAGE 12

13 STRING METHOD Path before iteration 1) Move images according to atomic forces 2) Re-parametrization Path after iteration

14 AB INITIO CALCULATIONS Conditions Uncharged supercell More realistic representation of the material No need to apply corrections [1 proton for 1 dopant] or [1 vacancy for 2 dopants] Limits of our study Only one proton in a supercell ( no effect of two protons) NB: tests with two proton facing each other, or on the same oxygen lead to unstable configurations. Only one dopant configurations where two or more dopants are neighbors are not taken into account No oxygen vacancy around SSPC 16 SEPTEMBER 2012 PAGE 14