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Connecting lattice compatibility conditions to transformation energy barriers in shape memory materials

Owen Rettenmaier, Srikanth Patala, and Christopher A. Schuh

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Phys. Rev. Materials 10, 073601 – Published 6 July, 2026

DOI: https://doi.org/10.1103/z3n5-52gc

Abstract

Thermal hysteresis is a critical design parameter for shape memory materials, particularly for shape memory ceramics, where high hysteresis may be associated with catastrophic cracking upon transformation. A direct framework for predicting hysteresis from the atomistic level does not exist, so proxies such as the interfacial compatibility condition, λ2, are used for the computational design of shape memory materials. In this paper, we introduce a framework that directly links interfacial compatibility to the energy barriers encountered during the phase transformation. We derive these barriers using adjusted Nudged Elastic Band calculations for two prototypical shape memory systems: zirconia-ceria and NiTi. Although our method does not explicitly simulate the martensite-austenite interface, we demonstrate that the structural pathway followed during the transformation samples the same atomistic structures as that interface. Furthermore, we show that the different correlations observed between the two material classes are fundamentally linked to differences in their shear moduli. These results help explain why our results reveal a strong correlation between interfacial compatibility and the transformation energy barriers: the atomic distortions required to effect the transformation are present whether at interfaces or not, and are accommodated elastically. This approach establishes a computationally efficient, quantum-accurate, method for determining energy barriers directly linked to thermal hysteresis, facilitating the design of resilient shape memory materials.

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References (41)

  1. G. Eggeler, E. Hornbogen, A. Yawny, A. Heckmann, and M. Wagner, Structural and functional fatigue of NiTi shape memory alloys, Mater. Sci. Eng. A 378, 24 (2004).
  2. S. Kajiwara and T. Kikuchi, Dislocation structures produced by reverse martensitic transformation in a Cu-Zn alloy, Acta Metall. 30, 589 (1982).
  3. E. Hornbogen, Review thermo-mechanical fatigue of shape memory alloys, J. Mater. Sci. 39, 385 (2004).
  4. D. Farache, S. Mishra, S. Tripathi, and A. Strachan, Role of dislocations on martensitic transformation temperatures and microstructure: A molecular dynamics study, J. Appl. Phys. 136, 035106 (2024).
  5. E. L. Pang, C. A. McCandler, and C. A. Schuh, Reduced cracking in polycrystalline ZrO2−CeO2 shape-memory ceramics by meeting the cofactor conditions, Acta Mater. 177, 230 (2019).
  6. E. L. Pang, Towards crack-resistant polycrystalline zirconia shape-memory ceramics with low hysteresis, Ph.D. thesis, Massachusetts Institute of Technology, 2021.
  7. J. Cui, Y. S. Chu, O. O. Famodu, Y. Furuya, J. Hattrick-Simpers, R. D. James, A. Ludwig, S. Thienhaus, M. Wuttig, Z. Zhang, et al., Combinatorial search of thermoelastic shape-memory alloys with extremely small hysteresis width, Nat. Mater. 5, 286 (2006).
  8. R. Freitas, M. Asta, and M. De Koning, Nonequilibrium free-energy calculation of solids using LAMMPS, Comput. Mater. Sci. 112, 333 (2016).
  9. Z. Wu and J. W. Lawson, Theoretical investigation of phase transitions in the shape memory alloy NiTi, Phys. Rev. B 106, L140102 (2022).
  10. O. T. Rettenmaier, J. J. Gabriel, and S. Patala, Modeling martensitic transformation temperatures in Zirconia-Ceria solid solutions using machine learning interatomic potentials, Modell. Simul. Mater. Sci. Eng. 32, 085023 (2024).
  11. C. Verdi, F. Karsai, P. Liu, R. Jinnouchi, and G. Kresse, Thermal transport and phase transitions of zirconia by on-the-fly machine-learned interatomic potentials, npj Comput. Mater. 7, 156 (2021).
  12. Y. Zou, S. Xiang, and C. Dai, Investigation on the efficiency and accuracy of methods for calculating melting temperature by molecular dynamics simulation, Comput. Mater. Sci. 171, 109156 (2020).
  13. E. L. Pang, G. B. Olson, and C. A. Schuh, Low-hysteresis shape-memory ceramics designed by multimode modelling, Nature (London) 610, 491 (2022).
  14. X. Yang, L. Ma, and J. Shang, Martensitic transformation of Ti50 (Ni50−x Cux) and Ni50 (Ti50−x Zrx) shape-memory alloys, Sci. Rep. 9, 3221 (2019).
  15. J. Lee, Y. Ikeda, and I. Tanaka, First-principles screening of structural properties of intermetallic compounds on martensitic transformation, npj Comput. Mater. 3, 52 (2017).
  16. Z. Zhang, R. D. James, and S. Müller, Energy barriers and hysteresis in martensitic phase transformations, Acta Mater. 57, 4332 (2009).
  17. N. A. Zarkevich and D. D. Johnson, Shape-memory transformations of NiTi: Minimum-energy pathways between austenite, martensites, and kinetically limited intermediate states, Phys. Rev. Lett. 113, 265701 (2014).
  18. D. Sheppard, P. Xiao, W. Chemelewski, D. D. Johnson, and G. Henkelman, A generalized solid-state nudged elastic band method, J. Chem. Phys. 136, 074103 (2012).
  19. N. A. Zarkevich and D. D. Johnson, Between harmonic crystal and glass: Solids with dimpled potential-energy surfaces having multiple local energy minima, Crystals 12, 84 (2022).
  20. J. B. Haskins, A. E. Thompson, and J. W. Lawson, Ab initio simulations of phase stability and martensitic transitions in NiTi, Phys. Rev. B 94, 214110 (2016).
  21. A. Ghasemi, P. Xiao, and W. Gao, Nudged elastic band method for solid-solid transition under finite deformation, J. Chem. Phys. 151, 054110 (2019).
  22. 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, et al., The atomic simulation environment—A Python library for working with atoms, J. Phys.: Condens. Matter 29, 273002 (2017).
  23. J.-Y. Zhang, G. Huynh, T. Albaret, F.-Z. Dai, and D. Rodney, Transformation-induced plasticity in CeO2−ZrO2 ceramics: Atomic-scale insights using a deep neural network potential, Acta Mater. 285, 120661 (2025).
  24. H. Peng, Z.-H. Yang, J. Sun, and J. P. Perdew, SCAN+ rVV10: A promising van der Waals density functional, Phys. Rev. X 6, 041005 (2016).
  25. H. Tang, Y. Zhang, Q.-J. Li, H. Xu, Y. Wang, Y. Wang, and J. Li, High accuracy neural network interatomic potential for NiTi shape memory alloy, Acta Mater. 238, 118217 (2022).
  26. F. Therrien, P. Graf, and V. Stevanović, Matching crystal structures atom-to-atom, J. Chem. Phys. 152, 074106 (2020).
  27. A. Stukowski, Visualization and analysis of atomistic simulation data with OVITO–the open visualization tool, Modell. Simul. Mater. Sci. Eng. 18, 015012 (2010).
  28. J. Frenzel, E. P. George, A. Dlouhy, C. Somsen, M.-X. Wagner, and G. Eggeler, Influence of Ni on martensitic phase transformations in NiTi shape memory alloys, Acta Mater. 58, 3444 (2010).
  29. G. Li, T. Yu, N. Zhang, and M. Chen, The effect of Ni content on phase transformation behavior of NiTi alloys: An atomistic modeling study, Comput. Mater. Sci. 215, 111804 (2022).
  30. N. A. Zarkevich and D. D. Johnson, Stable atomic structure of NiTi austenite, Phys. Rev. B 90, 060102(R) (2014).
  31. E. L. Pang, G. B. Olson, and C. A. Schuh, The mechanism of thermal transformation hysteresis in ZrO2−CeO2 shape-memory ceramics, Acta Mater. 213, 116972 (2021).
  32. A. Jain, S. P. Ong, G. Hautier, W. Chen, W. D. Richards, S. Dacek, S. Cholia, D. Gunter, D. Skinner, G. Ceder, and K. A. Persson, The Materials Project: A materials genome approach to accelerating materials innovation, APL Mater. 1, 011002 (2013).
  33. M. de Jong, W. Chen, T. Angsten, A. Jain, R. Notestine, A. Gamst, M. Sluiter, C. K. Ande, S. van der Zwaag, J. J. Plata, C. Toher, S. Curtarolo, G. Ceder, K. A. Persson, and M. Asta, Charting the complete elastic properties of inorganic crystalline compounds, Sci. Data 2, 150009 (2015).
  34. H. Ren, B. Zhu, J. Zhu, Y. Hao, B. Yu, and Y. Li, The structural phase transition and elastic properties of zirconia under high pressure from first-principles calculations, Solid State Sci. 13, 938 (2011).
  35. H. Kandil, J. Greiner, and J. Smith, Single-crystal elastic constants of yttria-stabilized zirconia in the range 20° to 700° C, J. Am. Ceram. Soc. 67, 341 (1984).
  36. M.-X. Wagner and W. Windl, Lattice stability, elastic constants and macroscopic moduli of NiTi martensites from first principles, Acta Mater. 56, 6232 (2008).
  37. J. Wang and H. Sehitoglu, Martensite modulus dilemma in monoclinic NiTi-theory and experiments, Int. J. Plast. 61, 17 (2014).
  38. G. Kresse and J. Furthmüller, Efficiency of ab initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci. 6, 15 (1996).
  39. S. De, A. P. Bartók, G. Csányi, and M. Ceriotti, Comparing molecules and solids across structural and alchemical space, Phys. Chem. Chem. Phys. 18, 13754 (2016).
  40. F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay, Scikit-learn: Machine learning in Python, J. Mach. Learn. Res. 12, 2825 (2011).
  41. O. Rettenmaier, S. Patala, and C. A. Schuh, Data supporting “Connecting lattice compatibility conditions to transformation energy barriers in shape memory materials”, Zenodo, 2026, doi: 10.5281/zenodo.19410558.

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Phys. Rev. Materials 10, 073601– Published 6 July, 2026
  • Received 4 April 2026
  • Accepted 9 June 2026
Article part of CHORUS
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