Ab Initio Computation for Materials Characterization

Elements of ICME Workshop, UIUC, July 2014

Maria ChanCenter for Nanoscale Materials &CEES Energy Frontier Research CtrArgonne National Laboratory

Collaborators• Lynn Trahey, Zhenzhen Yang,

Mali Balasubramanian, Mike Thackeray, Tim Fister, Argonne National Lab

• Jeff Greeley, Purdue University• Eric Shirley, NIST• Chris Wolverton, Northwestern University• Chris Buurma, Tadas Paulauskas, Robert Klie, University

of Illinois at Chicago• Hadi Tavassol, Maria Caterello, Andy Gewirth, David

Cahill, UIUC

Materials Characterizationstimulus

material signal

???machinery

Materials Characterizationstimulusmaterial =

unknownarrangement

of atoms

+ electronic/magnetic

state

???machinery

signal

Materials Characterizationstimulus

material signal

???machinery

photons (visible, x-ray, infrared) electrons, voltage, magnetic field, etc

synchrotrons, microscopes, spectrometers, etc

Materials Characterizationstimulus

material

signal: absorption, scattering, diffraction,

image, current, etc???

machinery

Ab initio materials modeling

{Properties}(e.g. energy, voltage,band structure etc)

DFT, QMC, etc

Life goal of a computational materials scientist

Skepticalexperimental collaborator

Confidentexperimental collaborator

Case studies: Li-ion & Li-O2 batteries

porous air electrode

electrolyteLithiumanode

Li+

Oxygen

Li-ion battery

Li+

cathodeelectrolyteanode

Li-O2 (“Li-Air”) battery

Some x-ray characterization techniques• x-ray diffraction– crystal structures, lattice parameters

• pair-distribution function– local coordination up to ~10Å

• x-ray absorption/inelastic scattering– local electronic environment

= X-rays

Other modes of characterization

= current or voltageElectrochemical characterization

= electron beamElectron microscopy

X-RAY DIFFRACTION (XRD) 2d sin = n

Image credit: Wikipedia

Li-air (Li-O2) battery

porous air electrode

electrolyteLithiumanode

Li+

Oxygen

2Li+O2Li2O2 or2Li+½O2Li2O or?

How do electrocatalysts affect Li-O2 reaction?

MnO2: put Li/Li+O into tunnels?

MnO2

MnO2x2

1x1

ramsdellite-MnO2

2x1

Li DFT CalculationsPBE+U~200 structures

Li2O & Li2O2~ 3V

Li0.5MnO2

3.2-3.5 VLiMnO2

2.5-2.7 V

Energetics (& experience) suggest Li insertion into tunnels likely

increasing voltage

OLiMn

Li2O & Li2O2~ 3V

increasing voltage

Li0.5.0.25Li2O.

MnO2

3.3V

0.125Li2O.MnO2

2.9 V

LixOy insertion into tunnels also plausible

Li2O2 unit3.1 V Li0.5MnO2

3.2-3.5 VLiMnO2

2.5-2.7 V

OLiMn

Trahey et al, Adv Energy Mat 2013, Ch. 5 in “The Li-air Battery” Ed. Imanishi 2014

Predictions: LixOy go into tunnel, O removal kinetically limited

Does this actually happen?Synchrotron XRD shows lattice parameter changes, but crystal structure mostly remains

Ref: Yang, Trahey, Chan, et al, in preparation

In-situ XRD changes during cycling

Lattice parameter changes

MnO2

a b

c

In-situ lattice parameters (a=b, c) change during cycling

DFT also captures volume changes

hydr

ated

MnO

2

(H2O

) 0.12

5MnO

2

(Li 2O) 0.125

MnO 2

Li 0. 5MnO 2

Li 0. 25(Li 2

O) 0.125MnO 2

XRD: Johnson et al, J Power Sources 1997

(com

pare

d to

pur

e

MnO

2 )

but not individual lattice parameter changes, i.e. a/c ratio

0 20 402

3

4

Time (hr)Vo

ltage

(V) a

In-situ XRD data+DFT model consistent with Li+O co-insertion

bc d

e f

Amount of Li2O in tunnel Amou

nt o

f Li i

n tu

nnel

0 20 402

3

4

Time (hr)Vo

ltage

(V) a

But precise ratio not obtained

bc d

e f

Amount of Li2O in tunnel Amou

nt o

f Li i

n tu

nnel

?

Need another technique e.g. x-ray absorption

Moral of the story• XRD is good for observing structural changes

during a process for a mostly crystalline material

• DFT calculations give approximate volume changes, but not perfectly accurate

• Other techniques that measure electronic structures may be needed

X-RAY DIFFRACTION (XRD) & NON-RESONANT INELASTIC X-RAY SCATTERING (NIXS)

Image credit: Tim Fister

A tale of two structures: Li2O2

H (eV/O2) Féher FöpplPBE -5.69 -6.24HSE06 -5.90 -6.52

Experimental -6.57(9), -6.557

O-O distance 1.28Å 1.55Å

Formation energies fromdensity functional theory calculations

Chan et al, J. Phys. Chem. Lett., 2, 2483 (2011)

Which one is the actual structure of Li2O2? DFT predicts Föppl – verification?

Both proposed from XRD in 1950’s

X-ray diffraction patterns

Errors (“Residuals”) × 3

Synchrotron vs “lab” XRD

Cu K

calculated

(ab initioBethe-SalpeterEquation)

NIXS better distinguishes between two

measured

Moral of the story• XRD refinement is not always

perfect!• DFT formation energies are strong

indicators of relative phase stability, but independent verification is a bonus

• Synchrotron XRD give additional information over lab XRD

• NIXS is sensitive to local structures

PAIR DISTRIBUTION FUNCTION (PDF) & ELECTROCHEMISTRY

Image credit: Billinge, Z. Kristallogr. 219 (2004) 117

X-ray Powder Diffraction

Structure function

Pair distribution function

Lithiating cr-Si – atomistic picture?

Carbon, transition metal oxides: Li goes into empty sites

Si

Li

?

carbon

Wen and Huggins, J. Solid State Chem 37, 271 (1981)

0 1 2 3 4 5x in LixSi

00.

1

0.2

0

.3

0.

4V

vs L

i/Li+

…. which don’t form at room temperature(data is at 415C)

LixSi: complex crystalline phases

Li ?

Si

relax1 by 1

lowest energy

SiLiDFT simulation of Li insertion

Si

SurfaceLi

Li sites

repeat

Evolution of atomic configurations as amount of Li increases

increasing Li content

Corroboration with PDF from APS Computed Si-Si

radial distribution functionEx-situ measurements

(at APS)

Baris Key et al JACS 2011

(111)

(110)

Goldman, Long, Gewirth, NuzzoAdv. Func. Mater. 2011

Compare surface orientations:DFT simulation results

(100) (111) (110)

Different orientations: similar expansion at full lithiation

Anisotropy in lithiation voltages V(110) > V(111)

insertion through (110) is more thermodynamically favorable

voltage anisotropic expansion?

How does voltage difference lead to anisotropic expansion?

time

Solution to diffusion equation

Note: Li enters side surfaces >> top surface isotropic diffusion coefficient

crys

talli

ne S

i

amor

phou

s Li xS

i

10 m

Chan, Wolverton & Greeley, JACS 2012

Orientation-dependent voltage subsequently validated by experiment

Pharr et al Nano Lett. 2012, 12, 5039

Moral of the story• PDF is suitable for

amorphous/disordered materials and can be used for qualitative verification of DFT simulations

• Prediction of a yet-unmeasured quantity is paramount for verification of any new modeling approach!

ELECTROCHEMISTRY AND SURFACE STRESS MEASUREMENTS

2t 0g   g – g6(1 )Yt C

Au

Li

What Li/Au surface processes occur before lithiation?

Au: model electrode

model system: gold surface

Initiation of Li deposition @ ~ 1 V

LiClO4 PC

1. onset ~ 1V

ionic liquid

Large voltage range for Li deposition

LiClO4 PC

2. broad reductive feature

ionic liquid

Overlayer (upd) models

1.1V

obtained from genetic algorithm using DFT

Li

Au

Voltage curve from overlayer model

Multilayers

Li

Au

Considered 1-5 Li layers

LiClO4 PCStress during deposition

3. stress: compressive & magnitude increases with more Li

Stress from Li overlayers stress is compressive magnitude increases

with amount of Li magnitude comparable

to experiment

Surface alloy: substitutional models

Simple cluster expansion describes energetics well: each surface/subsurface Li

lowers energy by 1.2/1.5 eV Li-Li nearest neighbor raises

energy by 0.13-0.17 eV other terms <0.05 eV

Alternative surface alloy model 1heating overlayer model to 500K0.98 V

subsurface Li

Au adatoms

Alternative surface alloy model 2overlayer + subsurface Li 0.87 Vsmall compressive stress

surface alloy models may explain stripping peak

Tavassol, Chan, Catarello, Greeley, Cahill, Greeley, Gewirth, J Electrochem Soc 2013

Moral of the story

• Observing multiple properties (current and stress in this case) under the same stimulus gives tighter constraints on explanation

• DFT allows reasonable predictions of surface stress

… and a lot more!• Vibrational spectroscopy (Raman, FTIR)• Nuclear resonance (NMR)• Other x-ray: absorption, fluorescence,

photoelectron, etc• Neutrons (~x-rays in some ways)

Keys to linking ab initio modeling with characterization

1. Figuring out how to get an atomistic model – global minimization e.g genetic algorithm, disorder sampling, cluster expansion, step-by-step simulations, experimental images

Keys to linking ab initio modeling with characterization

2. Calibrating the accuracy of predicted quantities

Keys to linking ab initio modeling with characterization

3. Enjoy it!

Funding: Center for Electrical Energy Storage (CEES): Tailored Interfaces, DOE Energy Frontier Research Center at Argonne National Laboratory, Northwestern University, and University of Illinois at Urbana Champaign, funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences. US Department of Energy Sunshot Program (DOE-EE00005659). Center for Nanoscale Materials, supported by the U. S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under contract No. DE-AC02-06CH11357. The authors also acknowledge grants of computer time from the Fusion cluster in the Laboratory Computing Resource Center at Argonne National Laboratory.

This talk has been created by UChicago Argonne, LLC, Operator of Argonne National Laboratory ("Argonne"). Argonne, a U.S. Department of Energy Office of Science laboratory, is operated under Contract No. DE-AC02-06CH11357. The U.S. Government retains for itself, and others acting on its behalf, a paid-up, nonexclusive, irrevocable worldwide license in said article to reproduce, prepare derivative works, distribute copies to the public, and perform publicly and display publicly, by or on behalf of the Government.

Acknowledgements