There is significant interest in improving the performance of batteries to increase electrification of transportation and aviation. Recently, performance improvements have been in large part due to changes in the composition of the cathode material family, LiNixMnyCo(1−x−y)O2 (e.g., 111–622–811). Despite the importance of these materials and tremendous progress with density functional theory (DFT) calculations in understanding basic design principles, it is computationally prohibitively expensive to make this problem tractable. Specifically, predicting the open circuit voltage for any cathode material in this family requires evaluation of stability in a quaternary phase space. In this work, we develop machine-learning potentials using fingerprinting based on atom-centered symmetry functions, used with a neural network model, trained on DFT calculations with a prediction accuracy of 3.7 meV/atom and 0.13 eV/Å for energy and force, respectively. We perform hyperparameter optimization of the fingerprinting parameters using Bayesian optimization through the Dragonfly package. Using this ML calculator, we first test its performance in predicting thermodynamic properties within the Debye–Grüneisen model and find good agreement for most thermodynamic properties, including the Gibbs free energy and entropy. Then, we use this to calculate the Li-vacancy ordering as a function of Li composition to simulate the process of discharging/charging of the cathode using grand canonical Monte Carlo simulations. The predicted voltage profiles are in good agreement with the experimental ones and provide an approach to rapidly perform design optimization in this phase space. This study serves as a proof-point of machine-learned DFT surrogates to enable battery materials optimization.
REFERENCES
1.
S.
Sripad
and V.
Viswanathan
, “Performance metrics required of next-generation batteries to make a practical electric semi truck
,” ACS Energy Lett.
2
, 1669
–1673
(2017
).2.
A.
Bills
, S.
Sripad
, W. L.
Fredericks
, M.
Singh
, and V.
Viswanathan
, “Performance metrics required of next-generation batteries to electrify commercial aircraft
,” ACS Energy Lett.
5
, 663
–668
(2020
).3.
G. E.
Blomgren
, “The development and future of lithium ion batteries
,” J. Electrochem. Soc.
164
, A5019
–A5025
(2017
).4.
E. A.
Olivetti
, G.
Ceder
, G. G.
Gaustad
, and X.
Fu
, “Lithium-ion battery supply chain considerations: Analysis of potential bottlenecks in critical metals
,” Joule
1
, 229
–243
(2017
).5.
P.
Faguy
, “Next-generation lithium-ion batteries: Electrode architecture and cell materials research projects
,” Report No. BAT337, Department of Energy
, 2018
.6.
A.
Bhowmik
, I. E.
Castelli
, J. M.
Garcia-Lastra
, P. B.
Jørgensen
, O.
Winther
, and T.
Vegge
, “A perspective on inverse design of battery interphases using multi-scale modelling, experiments and generative deep learning
,” Energy Storage Mater.
21
, 446
(2019
).7.
G.
Houchins
and V.
Viswanathan
, “Towards ultra low cobalt cathodes: A high fidelity computational phase search of layered Li-Ni-Mn-Co oxides
,” J. Electrochem. Soc.
167
, 070506
(2020
).8.
H.
Sun
and K.
Zhao
, “Electronic structure and comparative properties of LiNixMnyCozO2 cathode materials
,” J. Phys. Chem. C
121
, 6002
–6010
(2017
).9.
C.
Liang
, F.
Kong
, R. C.
Longo
, S.
Kc
, J.-S.
Kim
, S.
Jeon
, S.
Choi
, and K.
Cho
, “Unraveling the origin of instability in Ni-rich LiNi1−2xCoxMnxO2 (NCM) cathode materials
,” J. Phys. Chem. C
120
, 6383
–6393
(2016
).10.
K.
Min
, K.
Kim
, C.
Jung
, S.-W.
Seo
, Y. Y.
Song
, H. S.
Lee
, J.
Shin
, and E.
Cho
, “A comparative study of structural changes in lithium nickel cobalt manganese oxide as a function of Ni content during delithiation process
,” J. Power Sources
315
, 111
–119
(2016
).11.
J.
Behler
, “Perspective: Machine learning potentials for atomistic simulations
,” J. Chem. Phys.
145
, 170901
(2016
).12.
T. T.
Nguyen
, E.
Székely
, G.
Imbalzano
, J.
Behler
, G.
Csányi
, M.
Ceriotti
, A. W.
Götz
, and F.
Paesani
, “Comparison of permutationally invariant polynomials, neural networks, and Gaussian approximation potentials in representing water interactions through many-body expansions
,” J. Chem. Phys.
148
, 241725
(2018
).13.
Y.
Zuo
, C.
Chen
, X.
Li
, Z.
Deng
, Y.
Chen
, J.
Behler
, G.
Csányi
, A. V.
Shapeev
, A. P.
Thompson
, M. A.
Wood
et al., “Performance and cost assessment of machine learning interatomic potentials
,” J. Phys. Chem. A
124
, 731
–745
(2020
).14.
Y.
Shao
, M.
Hellström
, P. D.
Mitev
, L.
Knijff
, and C.
Zhang
, “PiNN: A python library for building atomic neural networks of molecules and materials
,” J. Chem. Inf. Model.
60
, 1184
(2020
).15.
M.
Ceriotti
, “Unsupervised machine learning in atomistic simulations, between predictions and understanding
,” J. Chem. Phys.
150
, 150901
(2019
).16.
N.
Artrith
, A.
Urban
, and G.
Ceder
, “Efficient and accurate machine-learning interpolation of atomic energies in compositions with many species
,” Phys. Rev. B
96
, 014112
(2017
).17.
C.
Delmas
, C.
Fouassier
, and P.
Hagenmuller
, “Structural classification and properties of the layered oxides
,” Physica B+C
99
, 81
–85
(1980
).18.
H.
Arai
, S.
Okada
, H.
Ohtsuka
, M.
Ichimura
, and J.
Yamaki
, “Characterization and cathode performance of Li1−xNi1+xO2 prepared with the excess lithium method
,” Solid State Ionics
80
, 261
–269
(1995
).19.
J. E.
Enkovaara
, C.
Rostgaard
, J. J.
Mortensen
, J.
Chen
, M.
Dułak
, L.
Ferrighi
, J.
Gavnholt
, C.
Glinsvad
, V.
Haikola
, and H.
Hansen
, “Electronic structure calculations with GPAW: A real-space implementation of the projector augmented-wave method
,” J. Phys.: Condens. Matter
22
, 253202
(2010
).20.
J.
Wellendorff
, K. T.
Lundgaard
, A.
Møgelhøj
, V.
Petzold
, D. D.
Landis
, J. K.
Nørskov
, T.
Bligaard
, and K. W.
Jacobsen
, “Density functionals for surface science: Exchange-correlation model development with Bayesian error estimation
,” Phys. Rev. B
85
, 235149
(2012
).21.
J.
Behler
and M.
Parrinello
, “Generalized neural-network representation of high-dimensional potential-energy surfaces
,” Phys. Rev. Lett.
98
, 146401
(2007
).22.
J.
Behler
, “Atom-centered symmetry functions for constructing high-dimensional neural network potentials
,” J. Chem. Phys.
134
, 074106
(2011
).23.
A.
Khorshidi
and A. A.
Peterson
, “Amp: A modular approach to machine learning in atomistic simulations
,” Comput. Phys. Commun.
207
, 310
–324
(2016
).24.
K.
Kandasamy
, K. R.
Vysyaraju
, W.
Neiswanger
, B.
Paria
, C. R.
Collins
, J.
Schneider
, B.
Poczos
, and E. P.
Xing
, “Tuning hyperparameters without grad students: Scalable and robust Bayesian optimisation with dragonfly
,” J. Mach. Learn. Res.
21
(81
), 1
–27
(2020
).25.
P.
Auer
, “Using confidence bounds for exploitation-exploration trade-offs
,” J. Mach. Learn. Res.
3
, 397
–422
(2002
).26.
N.
Srinivas
, A.
Krause
, S.
Kakade
, and M.
Seeger
, “Gaussian process optimization in the bandit setting: No regret and experimental design
,” in Proceedings of the 27th International Conference on International Conference on Machine Learning
(Omnipress
, 2010
), pp. 1015
–1022
.27.
W. R.
Thompson
, “On the likelihood that one unknown probability exceeds another in view of the evidence of two samples
,” Biometrika
25
, 285
–294
(1933
).28.
D. R.
Jones
, M.
Schonlau
, and W. J.
Welch
, “Efficient global optimization of expensive black-box functions
,” J. Global Optim.
13
, 455
–492
(1998
).29.
C.
Qin
, D.
Klabjan
, and D.
Russo
, “Improving the expected improvement algorithm
,” in Advances in Neural Information Processing Systems
(Curran Associates, Inc.
, 2017
), pp. 5381
–5391
.30.
H.
Suwa
, J. S.
Smith
, N.
Lubbers
, C. D.
Batista
, G.-W.
Chern
, and K.
Barros
, “Machine learning for molecular dynamics with strongly correlated electrons
,” Phys. Rev. B
99
, 161107
(2019
).31.
X.-G.
Lu
, M.
Selleby
, and B.
Sundman
, “Calculations of thermophysical properties of cubic carbides and nitrides using the Debye–Grüneisen model
,” Acta Mater.
55
, 1215
–1226
(2007
).32.
V. L.
Moruzzi
, J. F.
Janak
, and K.
Schwarz
, “Calculated thermal properties of metals
,” Phys. Rev. B
37
, 790
–799
(1988
).33.
J.-P.
Poirier
and A.
Tarantola
, “A logarithmic equation of state
,” Phys. Earth Planet. Inter.
109
, 1
–8
(1998
).34.
P.-W.
Guan
, G.
Houchins
, and V.
Viswanathan
, “Uncertainty quantification of DFT-predicted finite temperature thermodynamic properties within the Debye model
,” J. Chem. Phys.
151
, 244702
(2019
).35.
A. B.
Alchagirov
, J. P.
Perdew
, J. C.
Boettger
, R. C.
Albers
, and C.
Fiolhais
, “Energy and pressure versus volume: Equations of state motivated by the stabilized Jellium model
,” Phys. Rev. B
63
, 224115
(2001
).36.
D.
Frenkel
, “Free-energy computations and first-order phase transitions
,” in Molecular-Dynamics Simulation of Statistical-Mechanical Systems
, edited by G.
Ciccotti
and W. G.
Hoover
(Elsevier
, Amsterdam
, 1985
), p. 151
.37.
A.
Boutin
, B.
Tavitian
, A. H.
Fuchs
et al., “Grand canonical Monte Carlo simulations of adsorption of mixtures of xylene molecules in faujasite zeolites
,” Faraday Discuss.
106
, 307
–323
(1997
).38.
A. V.
Bondi
, “van der Waals volumes and radii
,” J. Phys. Chem.
68
, 441
–451
(1964
).39.
R.
Christensen
, H. A.
Hansen
, and T.
Vegge
, “Identifying systematic DFT errors in catalytic reactions
,” Catal. Sci. Technol.
5
, 4946
–4949
(2015
).40.
M. W.
Chase
, Jr., NIST-JANAF Thermochemical Tables
, Journal of Physical and Chemical Reference Data Monographs Vol. 9 (AIP
, 1998
).41.
Y.-M.
Choi
, S.-I.
Pyun
, J.-S.
Bae
, and S.-I.
Moon
, “Effects of lithium content on the electrochemical lithium intercalation reaction into LiNiO2 and LiCoO2 electrodes
,” J. Power Sources
56
, 25
–30
(1995
).42.
T.
Ohzuku
, A.
Ueda
, and M.
Nagayama
, “Electrochemistry and structural chemistry of LiNiO2 (R3m) for 4 volt secondary lithium cells
,” J. Electrochem. Soc.
140
, 1862
(1993
).43.
S.
Laubach
, S.
Laubach
, P. C.
Schmidt
, D.
Ensling
, S.
Schmid
, W.
Jaegermann
, A.
Thißen
, K.
Nikolowski
, and H.
Ehrenberg
, “Changes in the crystal and electronic structure of LiCoO2 and LiNiO2 upon Li intercalation and de-intercalation
,” Phys. Chem. Chem. Phys.
11
, 3278
–3289
(2009
).44.
J.
Tarascon
, G.
Vaughan
, Y.
Chabre
, L.
Seguin
, M.
Anne
, P.
Strobel
, and G.
Amatucci
, “In situ structural and electrochemical study of Ni1-xCoxO2 metastable oxides prepared by soft chemistry
,” J. Solid State Chem.
147
, 410
–420
(1999
).45.
J.
Hummelshøj
, J.
Blomqvist
, S.
Datta
, T.
Vegge
, J.
Rossmeisl
, K.
Thygesen
, A.
Luntz
, K.
Jacobsen
, and J.
Nørskov
, “Communications: Elementary oxygen electrode reactions in the aprotic Li-air battery
,” J. Chem. Phys.
132
, 071101
(2010
).46.
H.
Xia
, S. Y.
Meng
, L.
Lu
, and G.
Ceder
, “Electrochemical behavior and Li diffusion study of LiCoO2 thin film electrodes prepared by PLD
,” available at http://hdl.handle.net/1721.1/3582 (last accessed May 2020).47.
H.
Li
, N.
Zhang
, J.
Li
, and J.
Dahn
, “Updating the structure and electrochemistry of LixNiO2 for 0 ≤ x ≤ 1
,” J. Electrochem. Soc.
165
, A2985
(2018
).48.
F.
Schipper
, E. M.
Erickson
, C.
Erk
, J.-Y.
Shin
, F. F.
Chesneau
, and D.
Aurbach
, “Review—Recent advances and remaining challenges for lithium ion battery cathodes I. Nickel-rich, LiNixCoyMnzO2
,” J. Electrochem. Soc.
164
, A6220
–A6228
(2017
).© 2020 Author(s).
2020
Author(s)
You do not currently have access to this content.
