Phase Diagrams and Diffusion in Multicomponent Oxides from FirstPrinciples

1
Phase Diagrams and Diffusion in Multi-component
Oxides from First-Principles
Anton Van der Ven working in Prof. Ceders
group Department of Materials Science and
Engineering
2
Oxide Phase Diagrams
Yttria Stabilized ZrO2

• Optimization of materials properties often done
  by doping
• Phase diagram maps stable phases versus
  temperature and concentration

C. Pascual, P. Duran, J Am Cer Soc 66 1 (1983)
23-27
V. Stubican, et. al. J Am Cer Soc 61 1-2 17-21
(1978).
3
(No Transcript)
4
Phase Stability as Function of Temperature and
Composition
Requires free energy instead of energy
5
Thermodynamics of Multi-component Solids
ES energy of microstate S
6
Microscopic Excitations
7
Configurational Disorder
Cu-Au Cu and Au on fcc lattice
LiCoO2 Li and vacancies
CaO-MgO cations in octahedral sites
8
Configurational Variables

• Binary system alloy (A, B atoms)
• Assign occupation variables to each position in
  crystal

if atom A occupies site i
if atom B occupies site i
Total of 2N configurations
9
Coarse Graining to a lattice model
phase space
Each box a configuration
often we set
10
Polynomials of occupation variables form a basis
in configuration space
11
Cluster Expansion
Configurational energy E(s) (or free energy F(s))
can be expanded in terms of polynomials of
occupation variables
Vijk Effective Cluster Interactions (ECI)
12
Determination of ECI
Calculate energies of 30-100 configurations usin
g accurate first principles method (LDA,GGA)
Fit the ECI such that the cluster expansion
reproduces the energies calculated from first
principles (with least squares or linear
programming)
13
First-principles energies of a few ordered
configurations
Fit cluster expansion
Monte Carlo simulations
Thermodynamic properties
14
Intercalation Oxide as Cathode in Rechargeable
Lithium Battery
15
LixCoO2
16
First principles energies (LDA)of different
lithium-vacancy configurations
17
Cluster expansion for O3 host
18
Calculated LixCoO2 phase diagram
19
Calculated lattice parameter
20
Calculated phase diagram
Experimental phase diagram
Reimers, Dahn, J.Electrochem. Soc,
(1992) Amatucci et al, J. Electrochem. Soc.
(1996) Z. Chen, et al, J. Electrochem. Soc
(2002) Y. Shoa-Horn, (2003).
21
Calculated lattice parameter
Experimental lattice parameter
22
Calculated LixNiO2 phase diagram
23
Interstitial diffusion in systems with
configurational disorder
Kubo-Green relations
Thermodynamic factor
Self diffusion coefficient
24
Transition state theory
25
Migration barrier as a function of configuration
Local cluster expansion

Conventional cluster expansion

Kinetic Monte Carlo simulations
A. Van der Ven et al, PRB 64, 184307 (2001)
26
Migration mechanism in LixCoO2
Lithium
Cobalt
Oxygen
Divacancy hop Mechanism (DVH)
Single vacancy hop mechanism (SVH)
27
Lithium
Cobalt
Oxygen
Divacancy hop
Single vacancy hop
28
Many types of hop possibilities in the lithium
plane
29
Migration barriers depend configuration and
concentration
Single-vacancy mechanism
Divacancy mechanism
30
Barrier dependence on concentration
Co3 Co4 as lithium is
removed increased electrostatic repulsion
for Li in the activated state
31
Local Cluster expansion for divacancy migration
barrier
32
Calculated diffusion coefficient
Diffusion coefficient at 300 K
Thermodynamic factor Q
33
Strong concentration dependenceof diffusion
coefficient
Diffusion Coefficient
Average activation barrier
34
Divacancy cartwheel motion
35
Conclusions

• Inclusion of configurational degrees of freedom
  are essential in first principles studies of
  thermodynamic properties of alloys and
  multi-component oxides
• The cluster expansion is a powerful tool to model
  the configurational energy of alloys
  multi-component oxides and inclusion of
  vibrational and electronic degrees of freedom can
  be done naturally through coarse graining
• The cluster expansion can also be extended to
  study diffusion in multi-component systems.
• A study of diffusion in LixCoO2 has shown that
  local environment and concentration have a large
  influence on the diffusion coefficient