- Open Access
Atomic cluster expansion potentials for screw dislocations in BCC refractory metals
Phys. Rev. Materials 10, 103805 – Published 19 October, 2026
DOI: https://doi.org/10.1103/ppqn-x4c8
Abstract
Accurate atomistic modeling of screw dislocations in body-centered cubic (BCC) metals remains challenging because their plasticity is governed by complex dislocation glide behavior due to their compact threefold symmetric core structure and a strongly temperature-dependent flow stress induced by the large Peierls barrier. In the context of group 5 (V, Nb, and Ta) and group 6 (Mo and W) refractory metals (RMs), both classical interatomic potentials and some machine-learning potentials consistently fail to reproduce density functional theory (DFT) Peierls barriers and the glide plane. Here, we developed an array of atomic cluster expansion (ACE) potentials for these RMs by extending an existing DFT database. The developed ACE potentials significantly improve the description of screw dislocation properties, showing good agreement with the DFT references for Mo and W and substantial improvement for V, Nb, and Ta. The results show that transferability to screw dislocation behavior depends sensitively on both database composition and element-specific energetics and that achieving a single-humped Peierls barrier alone is not a sufficient validation metric for accurate prediction of dislocation glide. For Nb, Mo, and W, the developed ACE models also enable reliable calculation of kink-pair activation enthalpies, which are well described by both Kocks' law and a line-tension model.
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References (112)
- M. Ashby and J. Embury, The influence of dislocation density on the ductile-brittle transition in bcc metals, Scr. Metall. 19, 557 (1985).
- A. Johnson, The ductile-brittle transition in body-centred cubic transition metals, Philos. Mag. 7, 177 (1962).
- W. Han, Y. Lu, and Y. Zhang, Mechanism of ductile-to-brittle transition in body-centered-cubic metals: A brief review, Acta Metall. Sin. 59, 335 (2023).
- A. Argon, Strengthening Mechanisms in Crystal Plasticity (Oxford University Press, Oxford, 2007), Vol. 4.
- D. Caillard and J. L. Martin, Thermally Activated Mechanisms in Crystal Plasticity (Pergamon, Oxford, 2003).
- J. Christian, Some surprising features of the plastic deformation of body-centered cubic metals and alloys, Metall. Trans. A 14, 1237 (1983).
- M. Duesbery and G. Richardson, The dislocation core in crystalline materials, Crit. Rev. Solid State Mater. Sci. 17, 1 (1991).
- V. Vítek, R. C. Perrin, and D. K. Bowen, The core structure of (111) screw dislocations in bcc crystals, Philos. Mag. 21, 1049 (1970).
- K. Ito and V. Vitek, Atomistic study of non-Schmid effects in the plastic yielding of bcc metals, Philos. Mag. A 81, 1387 (2001).
- M. Wen and A. Ngan, Atomistic simulation of kink-pairs of screw dislocations in body-centred cubic iron, Acta Mater. 48, 4255 (2000).
- F. Maresca, D. Dragoni, G. Csányi, N. Marzari, and W. A. Curtin, Screw dislocation structure and mobility in body centered cubic Fe predicted by a Gaussian approximation potential, npj Comput. Mater. 4, 69 (2018).
- L. Dezerald, D. Rodney, E. Clouet, L. Ventelon, and F. Willaime, Plastic anisotropy and dislocation trajectory in bcc metals, Nat. Commun. 7, 11695 (2016).
- S. Starikov, Dislocation mobility function as a key to understanding plasticity of refractory metals and alloys, Comput. Mater. Sci. 246, 113411 (2025).
- L. Ventelon, F. Willaime, E. Clouet, and D. Rodney, Ab initio investigation of the Peierls potential of screw dislocations in bcc Fe and W, Acta Mater. 61, 3973 (2013).
- L. Dezerald, L. Ventelon, E. Clouet, C. Denoual, D. Rodney, and F. Willaime, Ab initio modeling of the two-dimensional energy landscape of screw dislocations in bcc transition metals, Phys. Rev. B 89, 024104 (2014).
- C. R. Weinberger, G. J. Tucker, and S. M. Foiles, Peierls potential of screw dislocations in bcc transition metals: Predictions from density functional theory, Phys. Rev. B 87, 054114 (2013).
- P. Gordon, T. Neeraj, Y. Li, and J. Li, Screw dislocation mobility in bcc metals: The role of the compact core on double-kink nucleation, Modell. Simul. Mater. Sci. Eng. 18, 085008 (2010).
- D. Cereceda, A. Stukowski, M. Gilbert, S. Queyreau, L. Ventelon, M.-C. Marinica, J. Perlado, and J. Marian, Assessment of interatomic potentials for atomistic analysis of static and dynamic properties of screw dislocations in W, J. Phys.: Condens. Matter 25, 085702 (2013).
- L. M. Hale and C. Becker, Vacancy dissociation in body-centered cubic screw dislocation cores, Comput. Mater. Sci. 135, 1 (2017).
- S. Starikov, P. Grigorev, and P. A. Olsson, Angular-dependent interatomic potential for large-scale atomistic simulation of W–Mo–Nb ternary alloys, Comput. Mater. Sci. 233, 112734 (2024).
- R. Wang, X. Ma, L. Zhang, H. Wang, D. J. Srolovitz, T. Wen, and Z. Wu, Classical and machine learning interatomic potentials for bcc vanadium, Phys. Rev. Mater. 6, 113603 (2022).
- G. Ackland and R. Thetford, An improved -body semi-empirical model for body-centred cubic transition metals, Philos. Mag. A 56, 15 (1987).
- A. M. Goryaeva, J. Dérès, C. Lapointe, P. Grigorev, T. D. Swinburne, J. R. Kermode, L. Ventelon, J. Baima, and M.-C. Marinica, Efficient and transferable machine learning potentials for the simulation of crystal defects in bcc Fe and W, Phys. Rev. Mater. 5, 103803 (2021).
- L. Zhang, G. Csányi, E. van der Giessen, and F. Maresca, Efficiency, accuracy, and transferability of machine learning potentials: Application to dislocations and cracks in iron, Acta Mater. 270, 119788 (2024).
- S. Yin, Y. Zuo, A. Abu-Odeh, H. Zheng, X.-G. Li, J. Ding, S. P. Ong, M. Asta, and R. O. Ritchie, Atomistic simulations of dislocation mobility in refractory high-entropy alloys and the effect of chemical short-range order, Nat. Commun. 12, 4873 (2021).
- X.-G. Li, C. Chen, H. Zheng, Y. Zuo, and S. P. Ong, Complex strengthening mechanisms in the NbMoTaW multi-principal element alloy, npj Comput. Mater. 6, 70 (2020).
- J. Byggmästar, K. Nordlund, and F. Djurabekova, Gaussian approximation potentials for body-centered-cubic transition metals, Phys. Rev. Mater. 4, 093802 (2020).
- G. Nikoulis, J. Byggmästar, J. Kioseoglou, K. Nordlund, and F. Djurabekova, Machine-learning interatomic potential for W–Mo alloys, J. Phys.: Condens. Matter 33, 315403 (2021).
- H. Kwon, M. Shiga, H. Kimizuka, and T. Oda, Accurate description of hydrogen diffusivity in bcc metals using machine-learning moment tensor potentials and path-integral methods, Acta Mater. 247, 118739 (2023).
- K. Ito, T. Yokoi, K. Hyodo, and H. Mori, Machine learning interatomic potential with DFT accuracy for general grain boundaries in -Fe, npj Comput. Mater. 10, 255 (2024).
- J. Pan, H. Cheng, G. Yan, L. Zhang, W. Yu, and S. Shen, Atomic cluster expansion interatomic potential for defects and thermodynamics of Cu–W system, J. Appl. Phys. 136, 155108 (2024).
- F. Shuang, K. Liu, Y. Ji, W. Gao, L. Laurenti, and P. Dey, Modeling extensive defects in metals through classical potential-guided sampling and automated configuration reconstruction, npj Comput. Mater. 11, 118 (2025).
- S. Lyu, W. Li, Y. Xia, Y. Chen, and A. H. W. Ngan, Effects of chemical randomness on strength contributors and dislocation behaviors in a bcc multiprincipal element alloy, Phys. Rev. Mater. 7, 073602 (2023).
- M. Jiang, B. Xu, Y. Deng, S. Ma, J.-J. Kai, F. Gao, and H. Deng, Scaling reliable interatomic potentials to complex nuclear alloys via pretrained atomic models, npj Comput. Mater. 12, 82 (2026).
- Y. Luo, T. Wang, Z. Huang, Y. Su, S. Xu, P. K. Liaw, and X.-G. Li, Dislocation-induced ordering as a source of strengthening in refractory multi-principal element alloys, npj Comput. Mater. 12, 134 (2026).
- W. Wang, P. Kumar, D. H. Cook, F. Walsh, B. Zhang, P. P. Borges, D. Farkas, R. O. Ritchie, and M. Asta, Ductility mechanisms in complex concentrated refractory alloys from atomistic fracture simulations, npj Comput. Mater. 11, 330 (2025).
- J. Byggmästar, T. Lopes, Z. Fan, and T. Ala-Nissila, Nine-element machine-learned interatomic potentials for multiphase refractory alloys, arXiv:2603.04147.
- W. J. Szlachta, A. P. Bartók, and G. Csányi, Accuracy and transferability of Gaussian approximation potential models for tungsten, Phys. Rev. B 90, 104108 (2014).
- Y. Lysogorskiy, C. van der Oord, A. Bochkarev, S. Menon, M. Rinaldi, T. Hammerschmidt, M. Mrovec, A. Thompson, G. Csányi, C. Ortner, et al., Performant implementation of the atomic cluster expansion (PACE) and application to copper and silicon, npj Comput. Mater. 7, 97 (2021).
- G. Kresse and J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B 47, 558 (1993).
- G. Kresse and J. Hafner, Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium, Phys. Rev. B 49, 14251 (1994).
- G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
- 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).
- J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
- L. Zhang, G. Csányi, E. van der Giessen, and F. Maresca, Atomistic fracture in bcc iron revealed by active learning of Gaussian approximation potential, npj Comput. Mater. 9, 217 (2023).
- R. Wang, L. Zhu, S. Pattamatta, D. J. Srolovitz, and Z. Wu, The taming of the screw: Dislocation cores in bcc metals and alloys, Mater. Today 79, 36 (2024).
- Z. H. Aitken, V. Sorkin, Z. Gen Yu, S. Chen, T. Leong Tan, Z. Wu, and Y.-W. Zhang, Controlling screw dislocation core structure and Peierls barrier in bcc interatomic potentials, Int. J. Solids Struct. 303, 113004 (2024).
- G. Henkelman, B. P. Uberuaga, and H. Jónsson, A climbing image nudged elastic band method for finding saddle points and minimum energy paths, J. Chem. Phys. 113, 9901 (2000).
- R. Drautz, Atomic cluster expansion for accurate and transferable interatomic potentials, Phys. Rev. B 99, 014104 (2019).
- L. C. Erhard, J. Rohrer, K. Albe, and V. L. Deringer, Modelling atomic and nanoscale structure in the silicon–oxygen system through active machine learning, Nat. Commun. 15, 1927 (2024).
- A. Bochkarev, Y. Lysogorskiy, S. Menon, M. Qamar, M. Mrovec, and R. Drautz, Efficient parametrization of the atomic cluster expansion, Phys. Rev. Mater. 6, 013804 (2022).
- D. F. T. du Toit, Y. Zhou, and V. L. Deringer, Hyperparameter optimization for atomic cluster expansion potentials, J. Chem. Theory Comput. 20, 10103 (2024).
- E. V. Podryabinkin and A. V. Shapeev, Active learning of linearly parametrized interatomic potentials, Comput. Mater. Sci. 140, 171 (2017).
- Y. Lysogorskiy, A. Bochkarev, M. Mrovec, and R. Drautz, Active learning strategies for atomic cluster expansion models, Phys. Rev. Mater. 7, 043801 (2023).
- A. Stukowski, Visualization and analysis of atomistic simulation data with OVITO—The open visualization tool, Modell. Simul. Mater. Sci. Eng. 18, 015012 (2010).
- J. Li, C.-Z. Wang, J.-P. Chang, W. Cai, V. V. Bulatov, K.-M. Ho, and S. Yip, Core energy and Peierls stress of a screw dislocation in bcc molybdenum: A periodic-cell tight-binding study, Phys. Rev. B 70, 104113 (2004).
- A. Stroh, Dislocations and cracks in anisotropic elasticity, Philos. Mag. 3, 625 (1958).
- W. Cai, V. V. Bulatov, J. Chang, J. Li, and S. Yip, Periodic image effects in dislocation modelling, Philos. Mag. 83, 539 (2003).
- : Atomistic Manipulation Toolkit, https://www.ctcms.nist.gov/potentials/atomman/.
- A. H. Larsen et al., The atomic simulation environment—A Python library for working with atoms, J. Phys.: Condens. Matter 29, 273002 (2017).
- P. Grigorev, L. Frérot, F. Birks, A. Gola, J. Golebiowski, J. Grießer, J. L. Hörmann, A. Klemenz, G. Moras, W. G. Nöhring, et al., : Materials science at the atomic scale with Python, J. Open Source Software 9, 5668 (2024).
- 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, et al., —A flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales, Comput. Phys. Commun. 271, 108171 (2022).
- E. Bitzek, P. Koskinen, F. Gähler, M. Moseler, and P. Gumbsch, Structural relaxation made simple, Phys. Rev. Lett. 97, 170201 (2006).
- P.-W. Ma and S. L. Dudarev, Effect of stress on vacancy formation and migration in body-centered-cubic metals, Phys. Rev. Mater. 3, 063601 (2019).
- CRC Handbook of Chemistry and Physics, edited by W. M. Haynes, D. R. Lide, and T. J. Bruno (CRC Press, Boca Raton, 2017).
- D. Bolef, Elastic constants of single crystals of the bcc transition elements V, Nb, and Ta, J. Appl. Phys. 32, 100 (1961).
- D. I. Bolef and J. De Klerk, Elastic constants of single-crystal mo and w between 77° and 500° K, J. Appl. Phys. 33, 2311 (1962).
- K. J. Carroll, Elastic constants of niobium from 4.2 to 300 K, J. Appl. Phys. 36, 3689 (1965).
- D. I. Bolef and J. de Klerk, Anomalies in the elastic constants and thermal expansion of chromium single crystals, Phys. Rev. 129, 1063 (1963).
- C. Kittel and P. McEuen, Introduction to Solid State Physics, 8th ed. (Wiley, Hoboken, NJ, 2005).
- Atomic Defects in Metals/Atomare Fehlstellen in Metallen, edited by H. Ullmaier (Springer, Berlin, 1991).
- X.-C. Zhang, S. Cao, L.-J. Zhang, R. Yang, and Q.-M. Hu, Unstable stacking fault energy and Peierls stress for evaluating slip system competition in body-centered cubic metals, J. Mater. Res. Technol. 22, 3413 (2023).
- K. Liu, Z. Wei, W. Gao, P. Dey, M. H. Sluiter, and F. Shuang, Heterogeneous ensemble enables a universal uncertainty metric for atomistic foundation models, npj Comput. Mater. 12, 34 (2026).
- P. A. Olsson, Semi-empirical atomistic study of point defect properties in bcc transition metals, Comput. Mater. Sci. 47, 135 (2009).
- S. Han, L. A. Zepeda-Ruiz, G. J. Ackland, R. Car, and D. J. Srolovitz, Interatomic potential for vanadium suitable for radiation damage simulations, J. Appl. Phys. 93, 3328 (2003).
- M. R. Fellinger, H. Park, and J. W. Wilkins, Force-matched embedded-atom method potential for niobium, Phys. Rev. B 81, 144119 (2010).
- Z. Fan, É. Maras, M. Cottura, M.-C. Marinica, and E. Clouet, Structure and coherency of bcc Nb precipitates in hcp Zr matrix from atomistic simulations, Phys. Rev. Mater. 8, 113601 (2024).
- G. P. P. Pun, K. A. Darling, L. J. Kecskes, and Y. Mishin, Angular-dependent interatomic potential for the Cu–Ta system and its application to structural stability of nano-crystalline alloys, Acta Mater. 100, 377 (2015).
- R. Ravelo, T. C. Germann, O. Guerrero, Q. An, and B. L. Holian, Shock-induced plasticity in tantalum single crystals: Interatomic potentials and large-scale molecular-dynamics simulations, Phys. Rev. B 88, 134101 (2013).
- X. W. Zhou, R. A. Johnson, and H. N. G. Wadley, Misfit-energy-increasing dislocations in vapor-deposited CoFe/NiFe multilayers, Phys. Rev. B 69, 144113 (2004).
- Y. Chen, X. Liao, N. Gao, W. Hu, F. Gao, and H. Deng, Interatomic potentials of W–V and W–Mo binary systems for point defects studies, J. Nucl. Mater. 531, 152020 (2020).
- H. Park, M. R. Fellinger, T. J. Lenosky, W. W. Tipton, D. R. Trinkle, S. P. Rudin, C. Woodward, J. W. Wilkins, and R. G. Hennig, Ab initio based empirical potential used to study the mechanical properties of molybdenum, Phys. Rev. B 85, 214121 (2012).
- M.-C. Marinica, L. Ventelon, M. R. Gilbert, L. Proville, S. L. Dudarev, J. Marian, G. Bencteux, and F. Willaime, Interatomic potentials for modelling radiation defects and dislocations in tungsten, J. Phys.: Condens. Matter 25, 395502 (2013).
- D. R. Mason, D. Nguyen-Manh, and C. S. Becquart, An empirical potential for simulating vacancy clusters in tungsten, J. Phys.: Condens. Matter 29, 505501 (2017).
- R. C. Ehemann, J. W. Nicklas, H. Park, and J. W. Wilkins, Ab initio based empirical potential applied to tungsten at high pressure, Phys. Rev. B 95, 184101 (2017).
- N. Chaari, E. Clouet, and D. Rodney, First-principles study of secondary slip in zirconium, Phys. Rev. Lett. 112, 075504 (2014).
- B. Bienvenu, L. Dezerald, D. Rodney, and E. Clouet, Ab initio informed yield criterion across body-centered cubic transition metals, Acta Mater. 236, 118098 (2022).
- S. Starikov and D. Smirnova, Optimized interatomic potential for atomistic simulation of Zr-Nb alloy, Comput. Mater. Sci. 197, 110581 (2021).
- C. Woodward and S. I. Rao, Flexible ab initio boundary conditions: Simulating isolated dislocations in bcc Mo and Ta, Phys. Rev. Lett. 88, 216402 (2002).
- L. Dezerald, L. Proville, L. Ventelon, F. Willaime, and D. Rodney, First-principles prediction of kink-pair activation enthalpy on screw dislocations in bcc transition metals: V, Nb, Ta, Mo, W, and Fe, Phys. Rev. B 91, 094105 (2015).
- N. Zotov and B. Grabowski, Molecular dynamics simulations of screw dislocation mobility in bcc Nb, Modell. Simul. Mater. Sci. Eng. 29, 085007 (2021).
- G. H. Vineyard, Frequency factors and isotope effects in solid state rate processes, J. Phys. Chem. Solids 3, 121 (1957).
- J. E. Dorn and S. Rajnak, Nucleation of kink pairs and the Peierls' mechanism of plastic deformation, LBNL Report No. UCRL-10833 (Lawrence Berkeley National Laboratory, 1963).
- A. Seeger and U. Holzwarth, Slip planes and kink properties of screw dislocations in high-purity niobium, Philos. Mag. 86, 3861 (2006).
- L. Hollang, M. Hommel, and A. Seeger, The flow stress of ultra-high-purity molybdenum single crystals, Phys. Stat. Sol. (A) 160, 329 (1997).
- D. Brunner, Comparison of flow-stress measurements on high-purity tungsten single crystals with the kink-pair theory, Mater. Trans., JIM 41, 152 (2000).
- L. Yang and J. Moriarty, Kink-pair mechanisms for /2 screw dislocation motion in bcc tantalum, Mater. Sci. Eng. A 319-321, 124 (2001).
- N. Zotov and B. Grabowski, Entropy of kink pair formation on screw dislocations: An accelerated molecular dynamics study, Modell. Simul. Mater. Sci. Eng. 30, 065004 (2022).
- L. Proville, D. Rodney, and M.-C. Marinica, Quantum effect on thermally activated glide of dislocations, Nat. Mater. 11, 845 (2012).
- V. Vitek, M. Mrovec, and J. Bassani, Influence of non-glide stresses on plastic flow: From atomistic to continuum modeling, Mater. Sci. Eng. A 365, 31 (2004).
- R. Gröger, A. Bailey, and V. Vitek, Multiscale modeling of plastic deformation of molybdenum and tungsten: I. Atomistic studies of the core structure and glide of screw dislocations at 0 K, Acta Mater. 56, 5401 (2008).
- U. Kocks, A. Argon, and M. Ashby, Models for macroscopic slip, Prog. Mater. Sci. 19, 171 (1975).
- G. Po, Y. Cui, D. Rivera, D. Cereceda, T. D. Swinburne, J. Marian, and N. Ghoniem, A phenomenological dislocation mobility law for bcc metals, Acta Mater. 119, 123 (2016).
- D. Rodney and L. Proville, Stress-dependent Peierls potential: Influence on kink-pair activation, Phys. Rev. B 79, 094108 (2009).
- A. Allera, T. D. Swinburne, A. M. Goryaeva, B. Bienvenu, F. Ribeiro, M. Perez, M.-C. Marinica, and D. Rodney, Activation entropy of dislocation glide in body-centered cubic metals from atomistic simulations, Nat. Commun. 16, 8367 (2025).
- P. Gordon, T. Neeraj, and M. Mendelev, Screw dislocation mobility in bcc metals: A refined potential description for -Fe, Philos. Mag. 91, 3931 (2011).
- G. Dusson, M. Bachmayr, G. Csányi, R. Drautz, S. Etter, C. van der Oord, and C. Ortner, Atomic cluster expansion: Completeness, efficiency and stability, J. Comput. Phys. 454, 110946 (2022).
- T. Leveau, L. Ventelon, M.-C. Marinica, and E. Clouet, Segregation of hydrogen on screw dislocations in tungsten and its impact on dislocation mobility, Acta Mater. 306, 121869 (2026).
- J. Byggmästar, K. Nordlund, and F. Djurabekova, Modeling refractory high-entropy alloys with efficient machine-learned interatomic potentials: Defects and segregation, Phys. Rev. B 104, 104101 (2021).
- J. Byggmästar, K. Nordlund, and F. Djurabekova, Simple machine-learned interatomic potentials for complex alloys, Phys. Rev. Mater. 6, 083801 (2022).
- L. Zhang, ACE-BCC-TMs: ACE potentials for bcc transition metals, https://github.com/leiapple/ACE-BCC-TMs.
- I. M Sobol', Distribution of points in a cube and approximate evaluation of integrals, USSR Comput. Math. Math. Phys. 7, 86 (1967).