Ab Initio Computation for Materials Characterization Elements of ICME Workshop, UIUC, July 2014 Maria Chan Center for Nanoscale Materials & CEES Energy Frontier Research Ctr Argonne 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 Characterization stimulus material signal ??? machinery

Materials Characterization stimulus material = unknown arrangement of atoms + electronic/ magnetic state ??? machinery signal

Materials Characterization stimulus material signal ??? machinery photons (visible, x-ray, infrared) electrons, voltage, magnetic field, etc synchrotrons, microscopes, spectrometers, etc

Materials Characterization stimulus 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 Skeptical experimental collaborator Confident experimental collaborator

Case studies: Li-ion & Li-O 2 batteries porous air electrode electrolyte Lithium anode Li+ Oxygen Li-ion battery Li + cathode electrolyte anode Li-O 2 (“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 voltage Electrochemical characterization = electron beam Electron microscopy

X- RAY D IFFRACTION (XRD) 2d sin  = n Image credit: Wikipedia

Li-air (Li-O 2 ) battery porous air electrode electrolyte Lithium anode Li+ Oxygen 2Li+O 2  Li 2 O 2 or 2Li+½O 2  Li 2 O or? How do electrocatalysts affect Li-O 2 reaction?

MnO 2 : put Li/Li+O into tunnels?  MnO 2 Mn O 2x2 1x1 ramsdellite-MnO 2 2x1 Li DFT Calculations PBE+U ~200 structures

Li 2 O & Li 2 O 2 ~ 3V Li 0.5 MnO V LiMnO V Energetics (& experience) suggest Li insertion into tunnels likely  increasing voltage  OLiMn

Li 2 O & Li 2 O 2 ~ 3V  increasing voltage  Li Li 2 O. MnO 2  3.3V 0.125Li 2 O. MnO V  Li x O y insertion into tunnels also plausible Li 2 O 2 unit  3.1 V Li 0.5 MnO V LiMnO V OLiMn Trahey et al, Adv Energy Mat 2013, Ch. 5 in “The Li-air Battery” Ed. Imanishi 2014 Predictions: Li x O y 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 MnO 2 a b c In-situ lattice parameters (a=b, c) change during cycling

DFT also captures volume changes hydrated MnO 2 (H 2 O) MnO 2 (Li 2 O) MnO 2 Li 0. 5 MnO 2 Li (Li 2 O) MnO 2 XRD: Johnson et al, J Power Sources 1997 (compared to pure  MnO 2 ) but not individual lattice parameter changes, i.e. a/c ratio

In-situ XRD data+DFT model consistent with Li+O co-insertion b c d e f Amount of Li 2 O in tunnel Amount of Li in tunnel

But precise ratio not obtained b c d e f Amount of Li 2 O in tunnel Amount of Li in tunnel ? 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 D IFFRACTION (XRD) & N ON - RESONANT I NELASTIC X- RAY S CATTERING (NIXS) Image credit: Tim Fister

A tale of two structures: Li 2 O 2  H (eV/O 2 ) FéherFöppl PBE HSE Experimental-6.57(9), O-O distance 1.28Å 1.55Å Formation energies from density functional theory calculations Chan et al, J. Phys. Chem. Lett., 2, 2483 (2011) Which one is the actual structure of Li 2 O 2 ? 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 initio Bethe- Salpeter Equation) 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

P AIR D ISTRIBUTION F UNCTION (PDF) & E LECTROCHEMISTRY 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) x in Li x Si V vs Li/Li + …. which don’t form at room temperature (data is at 415  C) Li x Si: complex crystalline phases

Li ? Si

relax 1 by 1 lowest energy Si Li DFT simulation of Li insertion Si Surface Li 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 function Ex-situ measurements (at APS) Baris Key et al JACS 2011

(111) (110) Goldman, Long, Gewirth, Nuzzo Adv. 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 crystalline Si amorphous Li x Si 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!

E LECTROCHEMISTRY AND S URFACE S TRESS MEASUREMENTS

Au Li What Li/Au surface processes occur before lithiation? Au: model electrode model system: gold surface

Initiation of Li ~ 1 V LiClO 4 PC 1. onset ~ 1V ionic liquid

Large voltage range for Li deposition LiClO 4 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

LiClO 4 PC Stress 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 eV  other terms <0.05 eV

Alternative surface alloy model 1 heating overlayer model to 500K 0.98 V subsurface Li Au adatoms

Alternative surface alloy model 2 overlayer + subsurface Li 0.87 V small 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-EE ). Center for Nanoscale Materials, supported by the U. S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under contract No. DE-AC02-06CH 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- 06CH 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