Abstract
Three machine-learned potentials (SNAP, NNP, ACE) were created from the same training set of DFT energies and forces for a total of 1024 structures. DFT calculations were performed with the PBE functional and the Grimme D3 corrections. DFT energies can be reproduced within a few meV by the potentials. The potentials are evaluated how they predict structures, thermal expansion coefficients, and ionic conductivities of α- and β-eucryptite. Structures and thermal expansion coefficients are in good agreement with experimental values. All potentials reproduce the negative thermal expansion coefficient along the c axis of β-eucryptite, although only ACE calculates a negative thermal expansion coefficient for the volume. Ionic conductivities can be predicted only qualitatively correct. Molecular dynamics simulations performed with some of the potentials at higher temperatures can result in unphysical structures.
Graphical abstract
Similar content being viewed by others
Data availability
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.
Code availability
The software used for this work is available from Materials Design Inc. (http://www.materialsdesign.com).
References
J.-R. Hill, C. M. Freeman, and L. Subramanian, in Reviews in Computational Chemistry, edited by K. B. Lipkowitz and D. B. Boyd (Wiley-VCH, John Wiley and Sons, Inc., New York, 2000), pp. 141–216.
A.P. Thompson, L.P. Swiler, C.R. Trott, S.M. Foiles, G.J. Tucker, J. Comput. Phys. 285, 316 (2015)
M.A. Wood, A.P. Thompson, J. Chem. Phys. 148, 241721 (2018)
M.A. Cusentino, M.A. Wood, A.P. Thompson, J. Phys. Chem. A 124, 5456 (2020)
A. Singraber, T. Morawietz, J. Behler, C. Dellago, J. Chem. Theory Comput. 15, 3075 (2019)
A. Singraber, J. Behler, C. Dellago, J. Chem. Theory Comput. 15, 1827 (2019)
R. Drautz, Phys. Rev. B 99, 014104 (2019)
H. Böhm, Phys. Status Solidi A 30, 531 (1975)
U.V. Alpen, H. Schulz, G.H. Talat, H. Böhm, Solid State Commun. 23, 911 (1977)
W. Nagel, H. Böhm, Solid State Commun. 42, 625 (1982)
R.T. Johnson, B. Morosin, M.L. Knotek, R.M. Biefeld, Phys. Lett. A 54, 403 (1975)
F. Shin-ichi, S. Satoshi, S. Kaduhiro, T. Hitoshi, Solid State Ion. 167, 325 (2004)
R. Sheil, Y.-C. Perng, J. Mars, J. Cho, B. Dunn, M.F. Toney, J.P. Chang, A.C.S. Appl, Mater. Interfaces 12, 56935 (2020)
B. Singh, M.K. Gupta, R. Mittal, M. Zbiri, S. Rols, S.J. Patwe, S.N. Achary, H. Schober, A.K. Tyagi, S.L. Chaplot, Phys. Chem. Chem. Phys. 19, 15512 (2017)
B. Singh, M.K. Gupta, R. Mittal, S.L. Chaplot, J. Mater. Chem. A 6, 5052 (2018)
Y. Niu, W. Li, L. Liu, M.V.M. Nitou, J. Nie, Z. Mei, F. Cao, W. Lv, Appl. Phys. Lett. 121, 243904 (2022)
A.I. Lichtenstein, R.O. Jones, H. Xu, P.J. Heaney, Phys. Rev. B 58, 6219 (1998)
R. Sprengard, K. Binder, M. Brändle, U. Fotheringham, J. Sauer, W. Pannhorst, J. Non-Cryst, Solids 274, 264 (2000)
B. Narayanan, A.C.T. van Duin, B.B. Kappes, I.E. Reimanis, C.V. Ciobanu, Modelling Simul. Mater. Sci. Eng. 20, 015002 (2011)
J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)
J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 78, 1396 (1997)
P.E. Blöchl, Phys. Rev. B 50, 17953 (1994)
S. Grimme, J. Comp. Chem. 25, 1463 (2004)
G. Kresse, J. Hafner, Phys. Rev. B 47, 558 (1993)
G. Kresse, J. Hafner, Phys. Rev. B 49, 14251 (1994)
G. Kresse, J. Furthmüller, Comput. Mat. Sci. 6, 15 (1996)
G. Kresse, J. Furthmüller, Phys. Rev. B 54, 11169 (1996)
Materials Design Inc., MedeA 3.7 (Materials Exploration and Design Analysis, 2023). www.materialsdesign.com
P.E. Blöchl, O. Jepsen, O.K. Andersen, Phys. Rev. B 49, 16223 (1994)
P. Daniels, C.A. Fyfe, Am. Mineral. 86, 279 (2001)
H. Schulz, J. Am. Ceram. Soc. 57, 313 (1974)
A. Rohskopf, C. Sievers, N. Lubbers, M.A. Cusentino, J. Goff, J. Janssen, M. McCarthy, D.M.O. de Zapiain, S. Nikolov, K. Sargsyan, D. Sema, E. Sikorski, L. Williams, A.P. Thompson, M.A. Wood, J. Open Source Softw. 8, 5118 (2023)
A. Singraber, M. P. Bircher, S. Reeve, D. W. H. Swenson, J. Lauret, P. David, CompPhysVienna/n2p2: Version 2.1.4 (2021). https://doi.org/10.5281/zenodo.4750573
A. Bochkarev, Y. Lysogorskiy, S. Menon, M. Qamar, M. Mrovec, R. Drautz, Phys. Rev. Mater. 6, 013804 (2022)
J. Behler, M. Parrinello, Phys. Rev. Lett. 98, 146401 (2007)
G. Imbalzano, A. Anelli, D. Giofré, S. Klees, J. Behler, M. Ceriotti, J. Chem. Phys. 148, 241730 (2018)
M. Gastegger, L. Schwiedrzik, M. Bittermann, F. Berzsenyi, P. Marquetand, J. Chem. Phys. 148, 241709 (2018)
J.P. Perdew, A. Ruzsinszky, G.I. Csonka, O.A. Vydrov, G.E. Scuseria, L.A. Constantin, X. Zhou, K. Burke, Phys. Rev. Lett. 100, 136406 (2008)
S. Plimpton, J. Comput. Phys. 117, 1 (1995)
A.P. Thompson, H.M. Aktulga, R. Berger, D.S. Bolintineanu, W.M. Brown, P.S. Crozier, P.J. in ’t Veld, A. Kohlmeyer, S.G. Moore, T.D. Nguyen, R. Shan, M.J. Stevens, J. Tranchida, C. Trott, S.J. Plimpton, Comput. Phys. Commun. 271, 108171 (2022)
Y. Zuo, C. Chen, X. Li, Z. Deng, Y. Chen, J. Behler, G. Csányi, A.V. Shapeev, A.P. Thompson, M.A. Wood, S.P. Ong, J. Phys. Chem. A 124, 731 (2020)
J. Birkenstock, Strukturen und Phasen des β-Eukryptits sowie die Sammlung von Beugungsdaten mit axialen q-Scans, PhD Thesis (Johannes Gutenberg-Universität Mainz, 2002)
P. Kubisiak, A. Eilmes, J. Phys. Chem. B 124, 9680 (2020)
Y. Chen, S. Manna, C.V. Ciobanu, I.E. Reimanis, J. Am. Ceram. Soc. 101, 347 (2018)
Z. Deng, C. Chen, X.-G. Li, S.P. Ong, Npj Comput. Mater. 5, 1 (2019)
Schott AG, Intern. Commun. (2023)
J. Zhang, A. Celestian, J.B. Parise, H. Xu, P.J. Heaney, Am. Mineral. 87, 566 (2002)
Funding
Not applicable.
Author information
Authors and Affiliations
Contributions
All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by J-RH. The first draft of the manuscript was written by J-RH and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
Corresponding author
Ethics declarations
Conflict of interest
Jörg-Rüdiger Hill is an employee and shareholder of Materials Design Inc. which distributes the MedeA software environment used for this work.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary Information
Below is the link to the electronic supplementary material.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Hill, JR., Mannstadt, W. Machine-learned potentials for eucryptite: A systematic comparison. Journal of Materials Research 38, 5188–5197 (2023). https://doi.org/10.1557/s43578-023-01183-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1557/s43578-023-01183-7