journal article·2023-12-28Open access

Atomic cluster expansion for Pt–Rh catalysts: From ab initio to the simulation of nanoclusters in few steps

Yanyan Liang, Matous Mrovec, Yury Lysogorskiy, Miquel Vega-Paredes, Christina Scheu, Ralf Drautz

Journal of Materials Research· Volume 38· Issue 24

Abstract

Abstract Insight into structural and thermodynamic properties of nanoparticles is crucial for designing optimal catalysts with enhanced activity and stability. In this work, we present a semi-automated workflow for parameterizing the atomic cluster expansion (ACE) from ab initio data. The main steps of the workflow are the generation of training data from accurate electronic structure calculations, an efficient fitting procedure supported by active learning and uncertainty indication, and a thorough validation. We apply the workflow to the simulation of binary Pt–Rh nanoparticles that are important for catalytic applications. We demonstrate that the Pt–Rh ACE is able to reproduce accurately a broad range of fundamental properties of the elemental metals as well as their compounds while retaining an outstanding computational efficiency. This enables a direct comparison of atomistic simulations to high-resolution experiments. Graphical abstract
Source: crossref · Quality: baseline

Research context

OpenAlex topics: Machine Learning in Materials Science · Catalytic Processes in Materials Science · Electrocatalysts for Energy Conversion

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (59)

Show source-provided references
1. T. Li, E.A. Marquis, P.A.J. Bagot, S.C. Tsang, G.D.W. Smith, Characterization of oxidation and reduction of a platinum-rhodium alloy by atom-probe tomography. Catal. Today 175(1), 552–557 (2011)10.1016/j.cattod.2011.03.046 ↗
2. D.D. Eley, W.O. Haag, B.C. Gates, H. Knoezinger, Advances in catalysis (Academic Press, New York, 1998)
3. K. Ravindra, L. Bencs, R. Van Grieken, Platinum group elements in the environment and their health risk. Sci. Total Environ. 318(1–3), 1–43 (2004)10.1016/S0048-9697(03)00372-3 ↗
4. N. Jung, D.Y. Chung, J. Ryu, S.J. Yoo, Y. Sung, Pt-based nanoarchitecture and catalyst design for fuel cell applications. Nano Today 9(4), 433–456 (2014)10.1016/j.nantod.2014.06.006 ↗
5. Z.A.C. Ramli, S.K. Kamarudin, Platinum-based catalysts on various carbon supports and conducting polymers for direct methanol fuel cell applications: a review. Nanoscale Res. Lett. 13, 1–25 (2018)10.1186/s11671-018-2799-4 ↗
6. Y. Sun, S. Polani, F. Luo, S. Ott, P. Strasser, F. Dionigi, Advancements in cathode catalyst and cathode layer design for proton exchange membrane fuel cells. Nat. Commun. 12(1), 5984 (2021)10.1038/s41467-021-25911-x ↗
7. R. Ghosh Chaudhuri, S. Paria, Core/shell nanoparticles: classes, properties, synthesis mechanisms, characterization, and applications. Chem. Rev. 112(4), 2373–2433 (2012)10.1021/cr100449n ↗
8. M.B. Gawande, A. Goswami, T. Asefa, H. Guo, A.V. Biradar, D. Peng, R. Zboril, R.S. Varma, Core-shell nanoparticles: synthesis and applications in catalysis and electrocatalysis. Chem. Soc. Rev. 44(21), 7540–7590 (2015)10.1039/C5CS00343A ↗
9. A. Garzón-Manjón, H. Meyer, D. Grochla, T. Löffler, W. Schuhmann, A. Ludwig, C. Scheu, Controlling the amorphous and crystalline state of multinary alloy nanoparticles in an ionic liquid. Nanomaterials 8(11), 903 (2018)10.3390/nano8110903 ↗
10. M. Vega-Paredes, R. Aymerich-Armengol, D. Arenas-Esteban, S. Martí-Sánchez, S. Bals, C. Scheu, A. Garzón Manjón, Electrochemical stability of rhodium-platinum core-shell nanoparticles: an identical location scanning transmission electron microscopy study. SSRN (2023). https://doi.org/10.2139/ssrn.447850310.2139/ssrn.4478503 ↗
11. D. Su, Advanced electron microscopy characterization of nanomaterials for catalysis. Green Energy Environ. 2(2), 70–83 (2017)10.1016/j.gee.2017.02.001 ↗
12. A. Garzón-Manjón, S. Zhang, B. Völker, M. Meischein, A. Ludwig, C. Scheu, Exploring stability of a nanoscale complex solid solution thin film by in situ heating transmission electron microscopy. MRS Bull. 47(4), 371–378 (2022)10.1557/s43577-021-00217-x ↗
13. P. Hohenberg, W. Kohn, Inhomogeneous electron gas. Phys. Rev. 136(3B), 864 (1964). https://doi.org/10.1103/PhysRev.136.B86410.1103/PhysRev.136.B864 ↗
14. W. Kohn, L.J. Sham, Self-consistent equations including exchange and correlation effects. Phys. Rev. 140(4A), 1133 (1965)10.1103/PhysRev.140.A1133 ↗
15. Y. Lysogorskiy, C.V.D. Oord, A. Bochkarev, S. Menon, M. Rinaldi, T. Hammerschmidt, M. Mrovec, A. Thompson, G. Csányi, C. Ortner, R. Drautz, Performant implementation of the atomic cluster expansion (pace) and application to copper and silicon. NPJ Comput. Mater. 7(1), 1–12 (2021). https://doi.org/10.1038/s41524-021-00559-910.1038/s41524-021-00559-9 ↗
16. Y. Lysogorskiy, A. Bochkarev, M. Mrovec, R. Drautz, Active learning strategies for atomic cluster expansion models. Phys. Rev. Mater. 7(4), 043801 (2023)10.1103/PhysRevMaterials.7.043801 ↗
17. M. Qamar, M. Mrovec, Y. Lysogorskiy, A. Bochkarev, R. Drautz, Atomic cluster expansion for quantum-accurate large-scale simulations of carbon. J. Chem. Theory Comput. (2023). https://doi.org/10.1021/acs.jctc.2c0114910.1021/acs.jctc.2c01149 ↗
18. R. Drautz, Atomic cluster expansion for accurate and transferable interatomic potentials. Phys. Rev. B 99(1), 014104 (2019)10.1103/PhysRevB.99.014104 ↗
19. R. Drautz, Atomic cluster expansion of scalar, vectorial, and tensorial properties including magnetism and charge transfer. Phys. Rev. B 102(2), 024104 (2020)10.1103/PhysRevB.102.024104 ↗
20. G. Dusson, M. Bachmayr, G. Csanyi, R. Drautz, S. Etter, C. van der Oord, C. Ortner, Atomic cluster expansion: completeness, efficiency and stability. J. Comput. Phys. 454, 110946 (2022)10.1016/j.jcp.2022.110946 ↗
21. A. Bochkarev, Y. Lysogorskiy, S. Menon, M. Qamar, M. Mrovec, R. Drautz, Efficient parametrization of the atomic cluster expansion. Phys. Rev. Mater. 6, 013804 (2022). https://doi.org/10.1103/PhysRevMaterials.6.01380410.1103/PhysRevMaterials.6.013804 ↗
22. A. Bochkarev, Y. Lysogorskiy, C. Ortner, G. Csányi, R. Drautz, Multilayer atomic cluster expansion for semilocal interactions. Phys. Rev. Res. 4(4), 042019 (2022)10.1103/PhysRevResearch.4.L042019 ↗
23. G. Kresse, J. Hafner, Ab initio molecular dynamics for liquid metals. Phys. Rev. B 47, 558–561 (1993). https://doi.org/10.1103/PhysRevB.47.55810.1103/PhysRevB.47.558 ↗
24. G. Kresse, J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6(1), 15–50 (1996)10.1016/0927-0256(96)00008-0 ↗
25. G. Kresse, J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54(16), 11169 (1996)10.1103/PhysRevB.54.11169 ↗
26. J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996)10.1103/PhysRevLett.77.3865 ↗
27. B. Grabowski, T. Hickel, J. Neugebauer, Ab initio study of the thermodynamic properties of nonmagnetic elementary fcc metals: exchange-correlation-related error bars and chemical trends. Phys. Rev. B 76, 024309 (2007). https://doi.org/10.1103/PhysRevB.76.02430910.1103/PhysRevB.76.024309 ↗
28. T.R. Mattsson, A.E. Mattsson, Calculating the vacancy formation energy in metals: Pt, Pd, and Mo. Phys. Rev. B 66, 214110 (2002). https://doi.org/10.1103/PhysRevB.66.21411010.1103/PhysRevB.66.214110 ↗
29. R. Tran, Z. Xu, B. Radhakrishnan, D. Winston, W. Sun, K.A. Persson, S.P. Ong, Surface energies of elemental crystals. Sci. Data 3(1), 1–13 (2016)10.1038/sdata.2016.80 ↗
30. R. Tran, X. Li, J.H. Montoya, D. Winston, K.A. Persson, S.P. Ong, Anisotropic work function of elemental crystals. Surf. Sci. 687, 48–55 (2019)10.1016/j.susc.2019.05.002 ↗
31. H. Zheng, X. Li, R. Tran, C. Chen, M. Horton, D. Winston, K.A. Persson, S.P. Ong, Grain boundary properties of elemental metals. Acta Mater. 186, 40–49 (2020)10.1016/j.actamat.2019.12.030 ↗
32. Y. Waseda, K. Hirata, M. Ohtani, High-temperature thermal expansion of platinum, tantalum, molybdenum, and tungsten measured by x-ray diffraction. High Temp.—High Press. 7(2), 221–226 (1975)
33. M. Nuding, M. Ellner, Influence of the isotypical A9, A10 and B11 solvents on the partial atomic volume of tin. J. Alloys Compd. 252(1–2), 184–191 (1997)10.1016/S0925-8388(96)02733-8 ↗
34. G. Simmons, Single crystal elastic constants and calculated aggregate properties. J. Grad. Res. Center 34(1), 1 (1965)
35. A.S. Darling, The elastic and plastic properties of the platinum metals. Platin. Metal Rev. 10(1), 14–19 (1966)10.1595/003214066X1011419 ↗
36. A. Buch, Pure metals properties, a scientific-technical handbook (ASM International, Metals Park, 1999)
37. R.W. Cahn, P. Haasen, Physical metallurgy, vol. 1 (Elsevier, New York, 1996)
38. F.R. De Boer, W. Mattens, R. Boom, A.R. Miedema, A.K. Niessen, Cohesion in metals. Transition metal alloys, vol. 1 (North Holland, Netherlands, 1988)
39. T. Angsten, T. Mayeshiba, H. Wu, D. Morgan, Elemental vacancy diffusion database from high-throughput first-principles calculations for fcc and hcp structures. New J. Phys. 16(1), 015018 (2014)10.1088/1367-2630/16/1/015018 ↗
40. R.W. Balluffi, Vacancy defect mobilities and binding energies obtained from annealing studies. J. Nucl. Mater. 69, 240–263 (1978). https://doi.org/10.1016/0022-3115(78)90247-710.1016/0022-3115(78)90247-7 ↗
41. T.M. Project, Materials data on Pt by materials project (2020). https://doi.org/10.17188/1189002
42. T.M. Project, Materials data on Rh by materials project (2020). https://doi.org/10.17188/128792010.17188/1287920 ↗
43. W.R. Tyson, W.A. Miller, Surface free energies of solid metals: estimation from liquid surface tension measurements. Surf. Sci. 62(1), 267–276 (1977). https://doi.org/10.1016/0039-6028(77)90442-310.1016/0039-6028(77)90442-3 ↗
44. C. Steiner, B. Schönfeld, M.J. Portmann, M. Kompatscher, G. Kostorz, A. Mazuelas, T. Metzger, J. Kohlbrecher, B. Demé, Local order in Pt-47at. Rh measured with x-ray and neutron scattering. Phys. Rev. B 71, 104204 (2005). https://doi.org/10.1103/PhysRevB.71.10420410.1103/PhysRevB.71.104204 ↗
45. P.E.A. Turchi, V. Drchal, J. Kudrnovský, Stability and ordering properties of fcc alloys based on Rh, Ir, Pd, and Pt. Phys. Rev. B 74, 064202 (2006). https://doi.org/10.1103/PhysRevB.74.06420210.1103/PhysRevB.74.064202 ↗
46. S. Curtarolo, D. Morgan, G. Ceder, Accuracy of ab initio methods in predicting the crystal structures of metals: a review of 80 binary alloys. Calphad 29(3), 163–211 (2005)10.1016/j.calphad.2005.01.002 ↗
47. Z.W. Lu, S.H. Wei, A. Zunger, Long-range order in binary late-transition-metal alloys. Phys. Rev. Lett. 66(13), 1753 (1991)10.1103/PhysRevLett.66.1753 ↗
48. Z.W. Lu, B.M. Klein, A. Zunger, Ordering tendencies in Pd-Pt, Rh-Pt, and Ag-Au alloys. J. Phase Equilib. 16, 36–45 (1995)10.1007/BF02646247 ↗
49. J. Pohl, K. Albe, Phase equilibria and ordering in solid Pt-Rh calculated by means of a refined bond-order simulation mixing model. Acta Mater. 57(14), 4140–4147 (2009). https://doi.org/10.1016/j.actamat.2009.05.02510.1016/j.actamat.2009.05.025 ↗
50. G.L.W. Hart, S. Curtarolo, T.B. Massalski, O. Levy, Comprehensive search for new phases and compounds in binary alloy systems based on platinum-group metals, using a computational first-principles approach. Phys. Rev. X 3, 041035 (2013). https://doi.org/10.1103/PhysRevX.3.04103510.1103/PhysRevX.3.041035 ↗
51. E. Raub, Metals and alloys of the platinum group. J. Less-Common Met. 1(1), 3–18 (1959)10.1016/0022-5088(59)90014-1 ↗
52. P.E. Blöchl, Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994). https://doi.org/10.1103/PhysRevB.50.1795310.1103/PhysRevB.50.17953 ↗
53. 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, LAMMPS—a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. Comput. Phys. Commun. 271, 108171 (2022). https://doi.org/10.1016/j.cpc.2021.10817110.1016/j.cpc.2021.108171 ↗
54. B. Sadigh, P. Erhart, A. Stukowski, A. Caro, E. Martinez, L. Zepeda-Ruiz, Scalable parallel Monte Carlo algorithm for atomistic simulations of precipitation in alloys. Phys. Rev. B 85, 184203 (2012). https://doi.org/10.1103/PhysRevB.85.18420310.1103/PhysRevB.85.184203 ↗
55. A.H. Larsen, J.J. Mortensen, J. Blomqvist, I.E. Castelli, R. Christensen, M. Dułak, J. Friis, M.N. Groves, B. Hammer, C. Hargus, E.D. Hermes, P.C. Jennings, P.B. Jensen, J. Kermode, J.R. Kitchin, E.L. Kolsbjerg, J. Kubal, K. Kaasbjerg, S. Lysgaard, J.B. Maronsson, T. Maxson, T. Olsen, L. Pastewka, A. Peterson, C. Rostgaard, J. Schiøtz, O. Schütt, M. Strange, K.S. Thygesen, T. Vegge, L. Vilhelmsen, M. Walter, Z. Zeng, K.W. Jacobsen, The atomic simulation environment-a python library for working with atoms. J. Condens. Matter. Phys. 29(27), 273002 (2017)10.1088/1361-648X/aa680e ↗
56. W.K. Hastings, Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57(1), 94–109 (1970)10.1093/biomet/57.1.97 ↗
57. A. Stukowski, Visualization and analysis of atomistic simulation data with ovito-the open visualization tool. Model. Simul. Mater. Sci. Eng. 18(1), 015012 (2009). https://doi.org/10.1016/j.cattod.2011.03.04610.1016/j.cattod.2011.03.046 ↗
58. V. Berova, A.G. Manjón, M. Vega-Paredes, T. Schwarz, N.A. Rivas, K. Hengge, T. Jurzinsky, C. Scheu, Influence of the shell thickness on the degradation of Ru@Pt core-shell catalysts in PEM fuel cells. J. Power Sources 554, 232327 (2023)10.1016/j.jpowsour.2022.232327 ↗
59. A.G. Manjón, M. Vega-Paredes, V. Berova, T. Gänsler, T. Schwarz, N.A.R. Rivas, K. Hengge, T. Jurzinsky, C. Scheu, Insights into the performance and degradation of Ru@Pt core-shell catalysts for fuel cells by advanced (scanning) transmission electron microscopy. Nanoscale 14(48), 18060–18069 (2022)10.1039/D2NR04869H ↗