Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Entropy-dominated stacking fault nucleation in compressed Cu thin films

Jacques G. Amar*

Danny Perez

Akemi McHan

  • *Contact author: jacques.amar@utoledo.edu
  • Contact author: danny_perez@lanl.gov
  • Contact author: amchan@niu.edu

Phys. Rev. Materials 10, 023603 – Published 23 February, 2026

DOI: https://doi.org/10.1103/qt4n-2qf8

Abstract

We study stacking fault (SF) formation in compressed Cu thin films using harmonic transition state theory (HTST), harmonic variational transition state theory (HVTST), and molecular dynamics (MD). Motivated by prior simulations showing extremely large transition rates, we quantify the temperature, strain, and size dependence of SF nucleation free-energy barriers. Due to a very large change in vibrational entropy along the SF nucleation pathway, HTST predicts prefactors up to 1046/sec, around 34 orders of magnitude higher than so-called standard prefactors. HTST rates are, however, significantly higher than direct MD observations. HVTST reconciles these two approaches by predicting the occurrence of strong non-Arrhenius behavior at high temperatures due to the displacement of the optimal dividing surface for the reaction. Our results demonstrate that entropic effects can dominate defect formation in strained metallic films, leading to strongly anomalous kinetics and underscoring the necessity of a variational treatment for obtaining quantitatively reliable nucleation rates.

Physics Subject Headings (PhySH)

Article Text

References (28)

  1. B. Müller, L. Nedelmann, B. Fischer, A. Fricke, and K. Kern, Strain relief in metal heteroepitaxy on face‐centered‐cubic(100): Cu/Ni(100), J. Vac. Sci. Technol. A 14, 1878 (1996).
  2. B. Müller, B. Fischer, L. Nedelmann, A. Fricke, and K. Kern, Strain relief at metal interfaces with square symmetry, Phys. Rev. Lett. 76, 2358 (1996).
  3. V. Fournée, J. Ledieu, T. Cai, and P. A. Thiel, Influence of strain in Ag on Al(111) and Al on Ag(100) thin film growth, Phys. Rev. B 67, 155401 (2003).
  4. I. Khatri, E. H. Sabbar, Y. Shim, and J. G. Amar, Mechanism of stacking fault formation in metal (100) heteroepitaxial growth, Phys. Rev. Mater. 4, 113403 (2020).
  5. S. Ryu, K. Kang, and W. Cai, Entropic effect on the rate of dislocation nucleation, Proc. Natl. Acad. Sci. USA 108, 5174 (2011).
  6. S. Bagchi and D. Perez, Anomalous entropy-driven kinetics of dislocation nucleation, Nat. Commun. 16, 912 (2025).
  7. B. P. Uberuaga, R. G. Hoagland, A. F. Voter, and S. M. Valone, Direct transformation of vacancy voids to stacking fault tetrahedra, Phys. Rev. Lett. 99, 135501 (2007).
  8. D. Perez, S.-N. Luo, A. F. Voter, and T. C. Germann, Entropic stabilization of nanoscale voids in materials under tension, Phys. Rev. Lett. 110, 206001 (2013).
  9. M. Nahavandian, S. Sarkar, S. Bagchi, D. Perez, and E. Martinez, From anti-Arrhenius to Arrhenius behavior in a dislocation-obstacle bypass: Atomistic simulations and theoretical investigation, Comput. Mater. Sci. 239, 112954 (2024).
  10. D. H. Warner and W. Curtin, Origins and implications of temperature-dependent activation energy barriers for dislocation nucleation in face-centered cubic metals, Acta Mater. 57, 4267 (2009).
  11. W. K. Kim and E. B. Tadmor, Entropically stabilized dislocations, Phys. Rev. Lett. 112, 105501 (2014).
  12. L. D. Nguyen, K. L. Baker, and D. H. Warner, Atomistic predictions of dislocation nucleation with transition state theory, Phys. Rev. B 84, 024118 (2011).
  13. S. Ogata, Free-energy-based atomistic study of nucleation kinetics and thermodynamics of defects in metals; plastic strain carrier “plaston”, in The Plaston Concept: Plastic Deformation in Structural Materials (Springer Nature Singapore, Singapore, 2022), pp. 37–56.
  14. R. Namakian, D. Moldovan, and T. D. Swinburne, Temperature dependent stacking fault free energy profiles and partial dislocation separation in fcc Cu, Comput. Mater. Sci. 218, 111971 (2023).
  15. X. Zhang, B. Grabowski, F. Körmann, A. V. Ruban, Y. Gong, R. C. Reed, T. Hickel, and J. Neugebauer, Temperature dependence of the stacking-fault Gibbs energy for Al, Cu, and Ni, Phys. Rev. B 98, 224106 (2018).
  16. K. V. Werner, M. Naeem, F. Niessen, L. Zhu, M. Villa, X.-L. Wang, and M. A. Somers, Experimental and computational assessment of the temperature dependency of the stacking fault energy in face-centered cubic high-entropy alloys, Acta Mater. 278, 120271 (2024).
  17. 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, and 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).
  18. A. Stukowski, Visualization and analysis of atomistic simulation data with OVITO–the Open Visualization Tool, Modell. Simul. Mater. Sci. Eng. 18, 015012 (2010).
  19. Y. Mishin, M. J. Mehl, D. A. Papaconstantopoulos, A. F. Voter, and J. D. Kress, Structural stability and lattice defects in copper: Ab initio, tight-binding, and embedded-atom calculations, Phys. Rev. B 63, 224106 (2001).
  20. M. P. Allen and D. J. Tildesley, in Computer Simulations of Liquids (Oxford, New York, 1987) p. 263.
  21. G. Henkelman, B. P. Uberuaga, and H. A. Jónsson, A climbing image nudged elastic band method for finding saddle points and minimum energy paths, J. Chem. Phys. 113, 9901 (2000).
  22. G. H. Vineyard, Frequency factors and isotope effects in solid state rate processes, J. Phys. Chem. Solids 3, 121 (1957).
  23. D. G. Truhlar and B. C. Garrett, Variational transition-state theory, Acc. Chem. Res. 13, 440 (1980).
  24. T. D. Swinburne and M.-C. Marinica, Unsupervised calculation of free energy barriers in large crystalline systems, Phys. Rev. Lett. 120, 135503 (2018).
  25. C. Huang, A. F. Voter, and D. Perez, Scalable kernel polynomial method for calculating transition rates, Phys. Rev. B 87, 214106 (2013).
  26. S. Saroukhani and D. Warner, Investigating dislocation motion through a field of solutes with atomistic simulations and reaction rate theory, Acta Mater. 128, 77 (2017).
  27. A. Yelon, B. Movaghar, and H. Branz, Origin and consequences of the compensation (Meyer-Neldel) law, Phys. Rev. B 46, 12244 (1992).
  28. A. Yelon, B. Movaghar, and R. S. Crandall, Multi-excitation entropy: Its role in thermodynamics and kinetics, Rep. Prog. Phys. 69, 1145 (2006).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation