Rationalising point defect substitution in Li-ion cathodes through atomistic statistical thermodynamics approaches

Transcription

1 Rationalising point defect substitution in Li-ion cathodes through atomistic statistical thermodynamics approaches Bath Materials Conference Michael Mercer, S. Schlueter, D. Kramer, H.E. Hoster

2 Li-ion battery Spinel Bcc metal E cell = ΔG nf = (µ cathode µ anode ) nf = µ cathode nf Li 1+y Mn 2-y O 4 cathode Li foil anode Separator or LiMn 2 O 4 ) Li metal Image: borrowed from Ran Liu s group homepage, Penn State

3 E cell / mv dq/dv (arb. units) ΔS (J mol 1 K 1 ) Context Battery aging and quality validation: needs non-destructive analysis techniques. Voltage and dq/dv profiles: mixture of enthalpy and entropy information: E cell vs. Li/Li Cathode Li fraction, x Cathode Li fraction, x E cell = ΔG nf Entropy profiling: entropy from Li/vacancy configurations. = Time / h TΔS ΔH nf E cell x T = 1 ΔS x nf Li content, x Voltage

4 Effect of aging on dq/dv and entropy profiles * Shift ** Shift Amplitude change ΔS change Evolution of peak heights and positions during cycling. Peak position shift: Li rebalancing between anode and cathode. Peak magnitude change: point defect formation? Need atomistic understanding of origins of the changes. *L. Zhang et al., Energies 10 (2017) 1147 **P. J. Osswald et al., Electrochim. Acta 177 (2015) 270

5 1 Disorder 0.5 Li fraction in cathode, x 0 Test case: Li x Mn 2 O 4 (Monte Carlo simulations) ΔS (J mol 1 K 1 ) LiMn 2 O 4 structure Voltage profile Voltage vs. Li/Li Entropy Li content, profile x 4 Order Disorder Low cost, commercially relevant material with high symmetry. Requires defect substitution to improve cycling stability Li content, x Well defined order/disorder transition: good test system for model validation. M.P. Mercer et al., Electrochim. Acta 241 (2017)

6 Defects pin Li to lattice Li + tetrahedron Mn 3+ /Mn 4+ octahedron Defect (oxidation state 3+) Pinned Li Unpinned Li

7 dx/dv (V -1 ) ΔS (J mol 1 K 1 ) Monte Carlo: effect of defects on profiles Defect Experimental percentage Suppression of ordered phase: decrease in dq/dv and entropy peak amplitudes. Profiles tend towards a single solid solution. Discrepancy with high defect fraction: better energy parameters needed.

8 Motivation: mean field approach Developed faster method based on a mean field (Bragg-Williams) approximation, for parameter validation*. Statistical mechanics approach over two sublattices: Bragg-Williams approximation: all configs of N 1 particles on sublattice 1 and N 2 on sublattice 2 have equal energies. Can then determine the partition function over O(N) degenerate energy levels, giving fast output even on conventional PC. *See also: E.Leiva et al., J. Electrochem. Soc. 164 (2017) A6154 (applied to graphite)

9 Mean field approach: pairwise interactions between neighbours Previous work, e.g.* J 2 (next nearest neighbours) Hamiltonian J 1 (nearest neighbours) Our modification J 2 J 2 + δ E 0 = point term n 1,n 2 = sublattice occupancies Experimental Sim, δ = 0 Sim, δ 0 J 1 J 2 - δ δ term: represents more complex effects arising from triplets and higher clusters not normally possible to describe in Bragg-Williams. *Gao et al., Phys. Rev B 54 (1996) 3878

10 Comparison of model with experiment Model 1: Optimal parameters energy parameters fitted for all compositions. Pinned Li + params Model 2: Best fit parameters for LiMn 2 O 4 assumed to be valid for all compositions. Pinned Li only

11 Conclusions Defects disturb ordered state: Smaller entropy change and dq/dv peaks. Voltage shifts. Simulations provide insight to understand the reasons why: Mean field simulations allow high throughput experimental/model comparisons. Pinned Li explanation gives qualitatively correct behaviour; interaction parameters must also change to explain trends. Must account for changes in parameters during intercalation too. V x T p,x = 1 nf rs x y = 0% y = 15%

12 Outlook Comparison of mean field approximation with Monte Carlo simulations, using effective cluster interactions from DFT. Additional validation of entropy method using in-situ XANES (STFC Proof of Concept). Development of mean field approximation to examine the profiles of LMO/graphite full cells, with systematically varied LMO compositions (RSC Mobility).

13 Thanks for your attention! Defects disturb ordered state: Smaller entropy change and dq/dv peaks. Voltage shifts. Simulations provide insight to understand the reasons why: Mean field simulations allow high throughput experimental/model comparisons. Pinned Li explanation gives qualitatively correct behaviour; interaction parameters must also change to explain trends. Must account for changes in parameters during intercalation too. V x T p,x = 1 nf rs x y = 0% y = 15%

14 Li-ion battery Spinel Bcc metal E cell = ΔG nf = (µ cathode µ anode ) nf = µ cathode nf Li 1+y Mn 2-y O 4 cathode Li foil anode Separator or LiMn 2 O 4 ) Li metal Image: borrowed from Ran Liu s group homepage, Penn State

15 E cell / mv dq/dv (arb. units) ΔS (J mol 1 K 1 ) Context Battery aging and quality validation: needs non-destructive analysis techniques. Voltage and dq/dv profiles: mixture of enthalpy and enthalpy information: E cell vs. Li/Li Cathode Li fraction, x Cathode Li fraction, x E cell = ΔG nf Entropy profiling: entropy from Li/vacancy configurations. = Time / h TΔS ΔH nf E cell x T x 1 x 2 0 = 1 ΔS x nf E cell vs. Li/Li Voltage

16 Effect of aging on dq/dv and entropy profiles * Shift ** Shift Amplitude change ΔS change Evolution of peak heights and positions during cycling. Peak position shift: Li rebalancing between anode and cathode. Peak magnitude change: point defect formation? Need atomistic understanding of origins of the changes. *L. Zhang et al., Energies 10 (2017) 1147 **P. J. Osswald et al., Electrochim. Acta 177 (2015) 270

17 1 Disorder 0.5 Li fraction in cathode, x 0 Test case: Li x Mn 2 O 4 (Monte Carlo simulations) ΔS (J mol 1 K 1 ) LiMn 2 O 4 structure Voltage profile Voltage vs. Li/Li Entropy Li content, profile x 4 Order Disorder Low cost, commercially relevant material with high symmetry. Requires defect substitution to improve cycling stability Li content, x Well defined order/disorder transition: good test system for model validation. M.P. Mercer et al., Electrochim. Acta 241 (2017)

18 Defects pin Li to lattice Li + tetrahedron Mn 3+ /Mn 4+ octahedron Defect (oxidation state 3+) Pinned Li Unpinned Li

19 dx/dv (V -1 ) ΔS (J mol 1 K 1 ) Monte Carlo: effect of defects on profiles Defect percentage Suppression of ordered phase: decrease in dq/dv and entropy peak amplitudes. Profiles tend towards a single solid solution. Discrepancy with high defect fraction: better energy parameters needed.

20 Motivation: mean field approach Developed faster method based on a mean field (Bragg-Williams) approximation, for parameter validation*. Statistical mechanics approach over two sublattices: Bragg-Williams approximation: all configs of N 1 particles on sublattice 1 and N 2 on sublattice 2 have equal energies. Can then determine the partition function over O(N) degenerate energy levels, giving fast output even on conventional PC. *See also: E.Leiva et al., J. Electrochem. Soc. 164 (2017) A6154 (applied to graphite)

21 Mean field approach: pairwise interactions between neighbours Previous work, e.g.* J 2 (next nearest neighbours) Hamiltonian J 1 (nearest neighbours) Our modification J 2 J 2 + δ Experimental Sim, δ = 0 Sim, δ 0 J 1 J 2 - δ δ term: represents more complex effects arising from triplets and higher clusters not normally possible to describe in Bragg-Williams. *Kim and Pyun, Electrochim. Acta 46 (2001) 987

22 Effect of changing interaction parameters: mean field model (nearest neighbour parameter J 1 ) Nearest neighbour interaction parameter is in mev. No order/disorder transition below a certain threshold. Eventually: two separate solid solutions. Response of next nearest neighbour parameter J 2 is similar but opposite.

23 Effect of changing interaction parameters: mean field model (energy separation, delta) Experimental Change in one parameter: allows difference in peak height and width from complex atomistic models to be achieved. Parameters: E 0 = 4.1 ev J 1 = 30 mev (repulsive) J 2 = mev (attractive)

24 Comparison of model with experiment Model 1: Optimal parameters chosen for all compositions. Model 2: Best fit parameters for LiMn 2 O 4 assumed to be valid for all compositions.

25 Conclusions Defects disturb ordered state: Smaller entropy change and dq/dv peaks. Voltage shifts. Simulations provide insight to understand the reasons why: Mean field simulations allow high throughput experimental/model comparisons. Pinned Li explanation gives qualitatively correct behaviour; interaction parameters must also change to explain trends. Must account for changes in parameters during intercalation too. V x T p,x = 1 nf rs x y = 0% y = 15% m.mercer1@lancaster.ac.uk

26 Outlook Comparison of mean field approximation with Monte Carlo simulations, using effective cluster interactions from DFT. Additional validation of entropy method using in-situ XANES (STFC Proof of Concept). Development of mean field approximation to examine the profiles of LMO/graphite full cells, with systematically varied LMO compositions (RSC Mobility).

27 Thanks for your attention! Defects disturb ordered state: Smaller entropy change and dq/dv peaks. Voltage shifts. Simulations provide insight to understand the reasons why: Mean field simulations allow high throughput experimental/model comparisons. Pinned Li explanation gives qualitatively correct behaviour; interaction parameters must also change to explain trends. Must account for changes in parameters during intercalation too. V x T p,x = 1 nf rs x y = 0% y = 15%