2005, October Marc Hayoun

1
Derivation and validation of model potentials for
Li2O from DF TMarc HayounLaboratoire des
Solides IrradiésCEA/DSM, Ecole Polytechnique,
CNRS UMR 7642Palaiseau, France
Madeleine Meyer, Juan García Rodeja (post-doc)
2
Outline

• 1. Motivations
• 2. Ab initio results
• 3. Fitting potentials for Li2O
• 4. Validation of the potentials
• 5. Conclusions

3
Motivations

• Modelling oxides
• ab initio
• phenomenological potentials
• fitting potentials from ab initio data,
  parameters and fitting quantities criteria ?
• Simulation of generical properties at the atomic
  scale
• Step towards more "technological" oxides

1. Motivations
4
Lithium oxide why ?

• Simple oxide, purely ionic
• Reliability of ab initio calculations
• Experimental results available
• Superionic conductor at T gt Tc
• superionic phase at high temperature
• high electric conductivity
• fast diffusion of Li

1. Motivations
5
Cationic Frenkel defect
Oxygen Lithium Intestitial lithium Cationic
vacancy
antifluorite structure
1. Motivations
6
Overview of the approach
Molecular Dynamics
Interatomic potential
Atomic trajectories
Fitting
Analysis
ValidationLattice Parameter Heat
Capacity Thermal vibrations Diffusion
coefficientetc.
Ab initio data
Diffusion mechanism
1. Motivations
7
Ab initio results

• Ground state properties
• Total energy obtained by DFT-LDA
• Computation of the lattice parameter at T 0 K
• Computation of the elastic constants at T 0 K
• Computation of the ionic charges from the
  electronic density

2. Ab initio results
8
Electronic iso-density surfaces
2. Ab initio results
9
Integration of the e- density (8 e-)
Nominal charges of O2- and Li ions for the
phenomenological interatomic potential
2. Ab initio results
10
Fitting potentials for Li2O
Interatomic potential
Molecular Dynamics
Atomic trajectories
Fitting
Analysis
ValidationLattice Parameter Heat
Capacity Thermal vibrations Diffusion
coefficientetc.
Ab initio data
Diffusion mechanism
3. Fitting potentials for Li2O
11
Fitting method

• from ab initio data
• Short-range contributions to the energy and
  pressure differences between different
  configurations
• ? sampling of the interatomic distances
• Fitting criteria ?
• Influence of the potential parameters ?
• Influence of the fitting quantities ?
• Potential adapted to high T simulations
• computation time
• ionic
• generic behaviour of Li2O
• Rigid-ion model

3. Fitting potentials for Li2O
12
Rigid-ion model

• Adapted at high temperature
• Energy is mainly coulombic
• Fitting of the short-range terms
• 10 of the total energy ? difficult
• Maximum of 12 parameters

3. Fitting potentials for Li2O
13
Fitting configurations
3. Fitting potentials for Li2O
14
Fitting configurations
3. Fitting potentials for Li2O
15
Fitting configurations
3. Fitting potentials for Li2O
16
Fitting configurations
3. Fitting potentials for Li2O
17
Sampling the distances
3. Fitting potentials for Li2O
18
Five empirical potentials
3. Fitting potentials for Li2O
19
Validation of the potentials
Molecular Dynamics
Interatomic potential
Atomic trajectories
Fitting
Analysis
ValidationLattice Parameter Heat
Capacity Thermal vibrations Diffusion
coefficientetc.
Ab initio data
Diffusion mechanism
4. Validation of the potentials
20
Lattice parameter a(T)

• Underestimate of a(T)
• P3, P6, P8A slope // to experimental data
• P8B, P11 different slope
• ?? P3, P6, P8A

4. Validation of the potentials
21
Heat capacity Cv(T)

• Phase transition
• Tc position of the peak
• P8B, P11peak more pronounced
• P3, P6, P8A same Tc
• Compatible with the experimental values
• ?? P3, P6, P8A

4. Validation of the potentials
22
Thermal vibrations ltu2gt

• order of magnitude in agreement with the
  experimental values
• ?? P3, P6, P8A

4. Validation of the potentials
23
Diffusion coefficient D

• P3, P6, P8A similar behaviour in agreement with
  experiment
• P11, P8Bwrong behaviour
• ?? P3, P6, P8A

4. Validation of the potentials
24
Arrhenius plots of D

• Oishi (tracer) ?HDLi2.50.3 eV
• Conductivity ?HDLi1.75 à 2 eV
• P6, P8A ?HDLi??.3 eV
• ?? P6, P8A

4. Validation of the potentials
25
Conclusions

• Analysis of the validation of the potentials
• All potentials phase transition CV(T),
  diffusion of Li
• Discrimination with af(T), Log(DLi)f(T)
• Influence of the choice of the fitting data
• Forces unadapted
• ?E and ?P of ? configurations efficient
• ?P important role
• The best results are obtained when
• the number of parameters is restricted
• attractive terms (O-O, Li-Li) repulsive term
  Li-O
• ? qualitative quantitative analysis / defects
  and atomic diffusion

Rodeja, Meyer, Hayoun, Modelling Simul. Mater.
Sci. Eng. 9, 81 (2001)
5. Conclusions