Мартенситна фаза типу α″-Fe16N2 нестехіометричного складу: нинішній стан досліджень і мікроскопічний статистично-термодинамічний модель

Т. М. Радченко, О. С. Гаценко, В. В. Лізунов, В. А. Татаренко

Інститут металофізики ім. Г. В. Курдюмова НАН України, бульв. Академіка Вернадського, 36, 03142 Київ, Україна

Отримано 17.11.2020; остаточний варіант — 07.12.2020 Завантажити PDF logo PDF

Анотація
Оглянуто та проаналізовано літературні (експериментальні та теоретичні) дані стосовно тетрагонального мартенситу з леґувальними елементами втілення–заміщення та вакансіями. Особливу увагу приділено вивченню мартенситної фази типу α″-Fe16N2 з унікальними та перспективними магнетними властивостями як альтернативи рідкісноземельним інтерметалідам і пермендюру на світовому ринку виробництва постійних магнетів. Охоплено період від часу відкриття її до нинішнього стану досліджень. Розвинуто статистично-термодинамічний модель «гібридного» твердого розчину втілення–заміщення на основі кристалічної ОЦТ-ґратниці, де леґувальні неметалеві компоненти (домішкові атоми) можуть займати як міжвузля, так і вакантні вузли ОЦК(Т)-ґратниці металу. Враховано дискретну (атомарно-кристалічну) будову ґратниці, анізотропію пружности, а також «блокувальні» та деформаційні (у тому числі «розмірні) ефекти у міжатомових взаємодіях. Модель адаптовано до максимально впорядкованої за типом α″-Fe16N2 нестехіометричної фази мартенситу Fe–N з атомами Нітроґену в октаедричних міжвузлях і на вузлах ОЦТ-заліза вище його температури Кюрі. Наголошено на важливості адекватного набору (залежних від температури та концентрації) наявних (у літературі) мікроскопічних енергетичних параметрів взаємодій атомів і вакансій. З’ясовано особливості змінення, а саме, немонотонного зменшення, за підвищення температури відносної концентрації атомів N в октаедричних міжвузлях ОЦТ-Fe, а тому й (корельованого з цією концентрацією) ступеня його тетрагональности. У широкому діяпазоні змінення загального вмісту втілених атомів N продемонстровано співвідношення рівноважної концентрації залишкових вузлових вакансій із концентрацією термічно активованих вакансій бездомішкового ОЦК-Fe за фіксованої температури.

Ключові слова: фаза α″-Fe16N2, мартенсит Fe–N, твердий розчин втілення–заміщення, тетрагональність, вакансії, упорядкування атомів, нерідкісноземельні магнетні матеріяли, постійні магнети.

Citation: T. M. Radchenko, O. S. Gatsenko, V. V. Lizunov, and V. A. Tatarenko, Martensitic α″-Fe16N2-Type Phase of Non-Stoichiometric Composition: Current Status of Research and Microscopic Statistical-Thermodynamic Model, Progress in Physics of Metals, 21, No. 4: 580–618 (2020); doi: 10.15407/ufm.21.04.580


Цитована література (122)  
  1. J.-P. Wang, Environment-Friendly Bulk Fe16N2 Permanent Magnet: Review and Prospective, J. Magn. Magn. Mater., 497: 165962 (2020); https://doi.org/10.1016/j.jmmm.2019.165962
  2. J. Cui, M. Kramer, L. Zhou, F. Liu, A. Gabay, G. Hadjipanayis, B. Balasubramanian, and D. Sellmyer, Current Progress and Future Challenges in Rare-Earth-Free Permanent Magnets, Acta Mat., 158: 118 (2018); https://doi.org/10.1016/j.actamat.2018.07.049
  3. J.T. Dreyer, China’s Monopoly on Rare Earth Elements — and Why We Should Care (Philadelphia: Foreign Policy Research Institute: October 7, 2020); https://www.fpri.org/article/2020/10/chinas-monopoly-on-rare-earth-elements-and-why-we-should-care
  4. N.A. Mancheri, Chinese Monopoly in Rare Earth Elements: Supply–Demand and Industrial Applications, China Report, 48, No. 4: 449 (2013); https://doi.org/10.1177/0009445512466621
  5. L.H. Lewis and F. Jiménez-Villacorta, Perspectives on Permanent Magnetic Materials for Energy Conversion and Power Generation, Metall. Mater. Trans. A, 44: 2 (2013); https://doi.org/10.1007/s11661-012-1278-2
  6. M.J. Kramer, R.W. McCallum, I.A. Anderson, and S. Constantinides, Prospects for Non-Rare Earth Permanent Magnets for Traction Motors and Generators, JOM, 64: 752 (2012); https://doi.org/10.1007/s11837-012-0351-z
  7. O. Gutfleisch, M.A. Willard, E. Brück, C.H. Chen, S.G. Sankar, and J.P. Liu, Magnetic Materials and Devices for the 21st Century: Stronger, Lighter, and More Energy Efficient, Adv. Mater., 23, No. 7: 821 (2011); https://doi.org/10.1002/adma.201002180
  8. T.M. Radchenko, V.A. Tatarenko, and S.M. Bokoch, Diffusivities and Kinetics of Short-Range and Long-Range Orderings in Ni–Fe Permalloys, Metallofiz. Noveishie Tekhnol., 28, No. 12: 1699 (2006).
  9. T.M. Radchenko and V.A. Tatarenko, Atomic-Ordering Kinetics and Diffusivities in Ni–Fe Permalloy, Defect Diffus. Forum, 273–276: 525 (2008); https://doi.org/10.4028/www.scientific.net/DDF.273-276.525
  10. V.A. Tatarenko and T.M. Radchenko, The Application of Radiation Diffuse Scattering to the Calculation of Phase Diagrams of F.C.C. Substitutional Alloys, Intermetallics, 11, Nos. 11–12: 1319 (2003); https://doi.org/10.1016/S0966-9795(03)00174-2
  11. S.M. Bokoch and V.A. Tatarenko, A Semi-Empirical Parameterization of Interatomic Interactions Based on the Statistical-Thermodynamic Analysis of the Data on Radiation Diffraction and Phase Equilibria in F.C.C.-Ni–Fe Alloys, Solid State Phenom., 138: 303 (2008); https://doi.org/10.4028/www.scientific.net/SSP.138.303
  12. V.A. Tatarenko, S.M. Bokoch, V.M. Nadutov, T.M. Radchenko, and Y.B. Park, Semi-Empirical Parameterization of Interatomic Interactions and Kinetics of the Atomic Ordering in Ni–Fe–C Permalloys and Elinvars, Defect Diffus. Forum, 280: 29 (2008); https://doi.org/10.4028/www.scientific.net/DDF.280-281.29
  13. Т.М. Radchenko and V.А. Tatarenko, Fe–Ni Alloys at High Pressures and Temperatures: Statistical Thermodynamics and Kinetics of the L12 or D019 Atomic Order, Usp. Fiz. Met., 9, No. 1: 1 (2008) (in Ukrainian); https://doi.org/10.15407/ufm.09.01.001
  14. V.A. Tatarenko, T.M. Radchenko, and V.M. Nadutov, Parameters of Interatomic Interaction in a Substitutional Alloy F.C.C. Ni–Fe According to Experimental Data about the Magnetic Characteristics and Equilibrium Values of Intensity of a Diffuse Scattering of Radiations, Metallofiz. Noveishie Tekhnol., 25, No. 10: 1303 (2003) (in Ukrainian).
  15. R.C. O’Handley, Modern Magnetic Materials: Principles and Applications (New York: Wiley: 2000).
  16. K.H. Jack, The Iron–Nitrogen System: the Preparation and the Crystal Structures of Nitrogen–Austenite (γ) and Nitrogen–Martensite (α′), Proc. R. Soc. London, Ser. A, 208: 200 (1951); https://doi.org/10.1098/rspa.1951.0154
  17. K.H. Jack, The Occurrence and the Crystal Structure of α″-Iron Nitride; a New Type of Interstitial Alloy Formed during the Tempering of Nitrogen–Martensite, Proc. Roy. Soc. London, Ser. A, 208: 216 (1951); https://doi.org/10.1098/rspa.1951.0155
  18. T.K. Kim and M. Takahashi, New Magnetic Material Having Ultrahigh Magnetic Moment, Appl. Phys. Lett., 20, No. 12: 492 (1972); https://doi.org/10.1063/1.1654030
  19. X. Hang, M. Matsuda, J.T. Held, K.A. Mkhoyan, and J.-P. Wang, Magnetic Structure of Fe16N2 Determined by Polarized Neutron Diffraction on Thin-Film Samples, Phys. Rev. B, 102, No. 10: 104402 (2020); https://doi.org/10.1103/PhysRevB.102.104402
  20. L. Feng, D. Zhanga, F. Wang, L. Dong, S. Chen, J. Liub, and X. Hui, A New Structure of the Environment-Friendly Material Fe16N2, Chem. Eng. Trans., 61: 1501 (2017); https://doi.org/10.3303/CET1761248
  21. Y. Sugita, H. Takahashi, M. Komuro, K. Mitsuoka, and A. Sakuma, Magnetic and Mössbauer Studies of Single‐Crystal Fe16N2 and Fe–N Martensite Films Epitaxially Grown by Molecular Beam Epitaxy, J. Appl. Phys., 76, No. 10: 6637 (1994); https://doi.org/10.1063/1.358157
  22. N. Ji, V. Lauter, X. Zhang, H. Ambaye, and J.-P. Wang, Strain Induced Giant Magnetism in Epitaxial Fe16N2 Thin Film, Appl. Phys. Lett., 102, No. 7: 072411 (2013); https://doi.org/10.1063/1.4792706
  23. J. Liu, G. Guo, X. Zhang, F. Zhang, B. Ma, and J.-P. Wang, Synthesis of α″-Fe16N2 Foils with an Ultralow Temperature Coefficient of Coercivity for Rare-Earth-Free Magnets, Acta Mat., 184: 143 (2020); https://doi.org/10.1016/j.actamat.2019.11.052
  24. N. Ji, X. Liu, and J.-P. Wang, Theory of Giant Saturation Magnetization in α″-Fe16N2: Role of Partial Localization in Ferromagnetism of 3d Transition Metals, New J. Phys., 12: 063032 (2010); https://doi.org/10.1088/1367-2630/12/6/063032
  25. J.-P. Wang, N. Ji, X. Liu, Y. Xu, C. Sanchez-Hanke, Y. Wu, F.M.F. de Groot, L.F. Allard, and E. Lara-Curzio, Fabrication of Fe16N2 Films by Sputtering Process and Experimental Investigation of Origin of Giant Saturation Magnetization in Fe16N2, IEEE Trans. Magn., 48, No. 5: 1710 (2012); https://doi.org/10.1109/TMAG.2011.2170156
  26. S. Bhattacharjee and S.-C. Lee, First-Principles Study of the Complex Magnetism in Fe16N2, Sci. Rep., 9: 8381 (2019); https://doi.org/10.1038/s41598-019-44799-8
  27. K.H. Jack, The Synthesis, Structure, and Characterization of α″-Fe16N2, J. Appl. Phys., 76: 6620 (1994); https://doi.org/10.1063/1.358482
  28. K.H. Jack, The Synthesis and Characterization of Bulk α″-Fe16N2, J. Alloys Compd., 222, Nos. 1, 2: 160 (1995); https://doi.org/10.1016/0925-8388(94)04901-7
  29. H.A. Wriedt, N.A. Gokcen, and R.H. Nafziger, The Fe–N (Iron–Nitrogen) System, Bull. Alloy Phase Diagrams, 8, 355 (1987); https://doi.org/10.1007/BF02869273
  30. E.H.D.M. van Voorthuysen, D.O. Boerma, and N.C. Chechenin, Low-Temperature Extension of the Lehrer Diagram and the Iron–Nitrogen Phase Diagram, Metall. Mater. Trans. A, 33: 2593 (2002); https://doi.org/10.1007/s11661-002-0380-2
  31. M. Naito, K. Uehara, R. Takeda, Y. Taniyasu, and H. Yamamoto, Growth of Iron Nitride Thin Films by Molecular Beam Epitaxy, J. Crystal Growth, 415: 36 (2015); https://doi.org/10.1016/j.jcrysgro.2014.12.022
  32. S. Grachev, D.M. Borsa, S. Vongtragool, and D.O Boerma, The Growth of Epitaxial Iron Nitrides by Gas Flow Assisted MBE, Surf. Sci., 482–485, Pt. 2: 802 (2001); https://doi.org/10.1016/S0039-6028(00)01084-0
  33. T. Weber, L. de Wit, F.W. Saris, and P. Schaaf, Search for Giant Magnetic Moments in Ion-Beam-Synthesized α″-Fe16N2, Thin Solid Films, 279, Nos. 1–2: 216 (1996); https://doi.org/10.1016/0040-6090(95)08176-3
  34. E. Leroy, C.D. Mariadassou, H. Bernas, O. Kaitasov, and R. Krishnan, The Road to Fe16N2 Formation in N+ Implanted 57Fe Enriched Films, Appl. Phys. Let., 67, No. 4: 560 (1995); https://doi.org/10.1063/1.115169
  35. K. Nakajima and S. Okamoto, Nitrogen-Implantation-Induced Transformation of Iron to Crystalline Fe16N2 in Epitaxial Iron Films, Appl. Phys. Lett., 54, No. 25: 2536 (1989); https://doi.org/10.1063/1.101543
  36. S. Okamoto, O. Kitakami, and Y. Shimada, α″-Fe16N2 Phase Epitaxially Grown by Sputter Beam Method, J. Appl. Phys., 79, No. 4: 5250 (1996); https://doi.org/10.1063/1.361301
  37. Z.-Y. Yao, H. Jiang, Z.-K. Liu, D.-D. Huang, F.-G. Qin, S.-C. Zhu, and Y.-X. Sun, J. Magn. Magn. Mater., 177–181, Pt. 2: 1291 (1998); https://doi.org/10.1016/S0304-8853(97)01020-2
  38. D.C. Sun, E.Y. Jiang, M.B. Tian, C. Lin, and X.X. Zhang, Epitaxial Single crystal Fe16N2 Films Grown by Facing Targets Sputtering, J. Appl. Phys., 79, No. 4: 5440 (1996); https://doi.org/10.1063/1.361843
  39. N. Ji, M.S. Osofsky, V. Lauter, L.F. Allard, X. Li, K.L. Jensen, H. Ambaye, E. Lara-Curzio, and J.-P. Wang, Perpendicular Magnetic Anisotropy and High Spin-Polarization Ratio in Epitaxial Fe–N Thin Films, Phys. Rev. B, 84, No. 24: 245310 (2011); https://doi.org/10.1103/PhysRevB.84.245310
  40. X. Zhang, K. Nomura, and J.-P. Wang, New Insight on the Mössbauer Spectra for Fe16N2 Thin Films with High Saturation Magnetization, Jap. J. Appl. Phys., 58, No. 12: 120907 (2019); https://doi.org/10.7567/1347-4065/ab5273
  41. M.A. Brewer, C.J. Echer, K.M. Krishnan, T. Kobayashi, and A. Nakanishi, Magnetic and Physical Microstructure of Fe16N2 Films Grown Epitaxially on Si(001), J. Appl. Phys., 81, No. 8: 4128 (1997); https://doi.org/10.1063/1.365102
  42. H. Takahashi, H. Shoji, and M. Takahashi, Structure and Magnetic Moment of Fe16N2 Sputtered Film, J. Magn. Magn. Mater., 174, Nos. 1–2: 57 (1997); https://doi.org/10.1016/S0304-8853(97)00213-8
  43. M. Takahashi, H. Shoji, H. Takahashi, H. Nashi, and T. Wakiyama, Magnetic Moment of α″-Fe16N2 Films, J. Appl. Phys., 76, No. 10: 6642 (1994); https://doi.org/10.1063/1.358431
  44. Y.F. Jiang, J.M. Liu, P.K. Suri, G. Kennedy, N.N. Thadhani, D.J. Flannigan, and J.P. Wang, Preparation of an α″-Fe16N2 Magnet via a Ball Milling and Shock Compaction Approach, Adv. Eng. Mat., 18, No. 6: 1009 (2015); https://doi.org/10.1002/adem.201500455
  45. Y. Jiang, V. Dabade, L.F. Allard, E.L.-C., R. James, and J.-P. Wang, Synthesis of α″-Fe16N2 Compound Anisotropic Magnet by the Strained-Wire Method, Phys. Rev. Applied, 6, No. 2: 024013 (2016); https://doi.org/10.1103/PhysRevApplied.6.024013
  46. H. Shinno and K. Saito, Effects of Film Thickness on Formation Processes of Fe16N2 in Nitrogen Ion-Implanted Fe Films, Surf. Coat. Technol., 103–104: 129 (1998); https://doi.org/10.1016/S0257-8972(98)00388-0
  47. J.M.D. Coey, K. O’Donnell, Q. Qinian, E. Touchais, and K.H. Jack, The Magnetization of Alpha″Fe16N2, J. Phys.: Condens. Matter, 6, No. 4: L23 (1994); https://doi.org/10.1088/0953-8984/6/4/001
  48. J.M.D. Coey, The Magnetization of Bulk α′Fe16N2, J. Appl. Phys., 76, No. 10: 6632 (1994); https://doi.org/10.1063/1.358156
  49. M.Q. Huang, W.E. Wallace, S. Simizu, and S.G.Sankar, Magnetism of α′-FeN Alloys and α″-(Fe16N2) Fe Nitrides, J. Magn. Magn. Mater., 135, No. 2: 226 (1994); https://doi.org/10.1016/0304-8853(94)90350-6
  50. X. Bao and R.M. Metzger, Synthesis and Properties of α″-Fe16N2 in Magnetic Particles, J. Appl. Phys., 75, No. 10: 5870 (1994); https://doi.org/10.1063/1.356988
  51. H. Takahashi, M. Komuro, M. Hiratani, and M. Igarashi, Anomalous Hall Resistivities of Single-Crystal Fe16N2 and Fe–N Martensite Films Epitaxially Grown by Molecular Beam Epitaxy, J. Appl. Phys., 84, No. 3: 1493 (1998); https://doi.org/10.1063/1.368253
  52. H. Tanaka, S. Nagakura, Y. Nakamura, and Y. Hirotsu, Electron Crystallography Study of Tempered Iron–Nitrogen Martensite and Structure Refinement of Precipitated α″-Fe16N2, Acta Mat., 45, No. 4: 1401 (1997); https://doi.org/10.1016/S1359-6454(96)00270-4
  53. Y. Sugita, H. Takahashi, M. Komuro, and M. Igarashi, Magnetic and Electrical Properties of Single‐Phase, Single‐Crystal Fe16N2 Films Epitaxially Grown by Molecular Beam Epitaxy, J. Appl. Phys., 79, No. 8: 5576 (1996); https://doi.org/10.1063/1.362246
  54. E. Kita, K. Shibata, Y. Sasaki, M. Kishimoto, and H. Yanagihara, Magnetic Anisotropy in Spherical Fe16N2 Core–Shell Nanoparticles Determined by Torque Measurements, AIP Advances, 7, No. 5: 056212 (2017); https://doi.org/10.1063/1.4974276
  55. S. Kikkawa, A. Yamada, Y. Masubuchi, and T. Takeda, Fine Fe16N2 Powder Prepared by Low-Temperature Nitridation, Mater. Res. Bull., 43, No. 12: 3352 (2008); https://doi.org/10.1016/j.materresbull.2008.02.008
  56. T. Ogawa, Y. Ogata, R. Gallage, N. Kobayashi, N. Hayashi, Y. Kusano, S. Yamamoto, K. Kohara, M. Doi, and M. Takano, Challenge to the Synthesis of α″-Fe16N2 Compound Nanoparticle with High Saturation Magnetization for Rare Earth Free New Permanent Magnetic Material, Appl. Phys. Express, 6, No. 7: 073007 (2013); https://doi.org/10.7567/APEX.6.073007
  57. T. Kojima, S. Kameoka, M. Mizuguchi, K. Takanashi, and A.-P. Tsai, FeNi and Fe16N2 Magnets Prepared Using Leaching, Mater. Trans., 60, No. 6: 1066 (2019); https://doi.org/10.2320/matertrans.M2019019
  58. J. Liu, G. Guo, F. Zhang, Y. Wu, B. Ma, and J.-P. Wang, Synthesis of α″-Fe16N2 Ribbons with a Porous Structure, Nanoscale Adv., 1, No. 4: 1337 (2019); https://doi.org/10.1039/C9NA00008A
  59. Y. Sugita, K. Mitsuoka, M. Komuro, H. Hoshiya, Y. Kozono, and M. Hanazono, Giant Magnetic Moment and Other Magnetic Properties of Epitaxially Grown Fe16N2 Single-Crystal Films, J. Appl. Phys., 70, No. 10: 5977 (1991); https://doi.org/10.1063/1.350067
  60. H. Jiang, K. Tao, and H. Li, J. Phys.: Condens. Matter., 6, No. 18: L279 (1994); https://doi.org/10.1088/0953-8984/6/18/004
  61. I. Fall and J.-M.R. Genin, Mössbauer Spectroscopy Study of the Aging and Tempering of High Nitrogen Quenched Fe–N Alloys: Kinetics of Formation of Fe16N2 Nitride by Interstitial Ordering in Martensite, Metall. Mater. Trans. A, 27: 2160 (1996); https://doi.org/10.1007/BF02651871
  62. X. Zhang, M. Yang, Y. Jiang, L.F. Allard, and J.-P. Wang, Thermal Stability of Partially Ordered Fe16N2 Film on Non-Magnetic Ag under Layer, J. Appl. Phys., 115, No. 17, 17A767 (2014); https://doi.org/10.1063/1.4869065
  63. Y. Shinpei, R. Gallage, Y. Ogata, Y. Kusano, N. Kobayashi, T. Ogawa, N. Hayashi, K. Kohara, M. Takahashi, and M. Takano, Quantitative Understanding of Thermal Stability of α″-Fe16N2, Chem. Commun., 49, No. 70: 7708 (2013); https://doi.org/10.1039/C3CC43590C
  64. M.H. Han, W.J. Kim, E.K. Lee, H. Kim, S. Lebègue, and J.J Kozak, Theoretical Study of the Microscopic Origin of Magnetocrystalline Anisotropy in Fe16N2 and Its Alloys: Comparison with the Other L10 Alloys, J. Phys.: Condens. Matter., 32, No. 3: 035801 (2020); https://doi.org/10.1088/1361-648X/ab422c
  65. N.J. Szymanski, V. Adhikari, M.A. Willard, P. Sarin, D. Gall, and S.V. Khare, Prediction of Improved Magnetization and Stability in Fe16N2 through Alloying, J. Appl. Phys., 126, No. 9: 093903 (2019); https://doi.org/10.1063/1.5109571
  66. M. Kopcewicz, J. Jagielski, G. Gawlik, and A. Grabias, Role of Alloying Elements in the Stability of Nitrides in Nitrogen-Implanted α-Fe, J. Appl. Phys., 78, No. 2: 1312 (1995); https://doi.org/10.1063/1.360373
  67. R. Gupta R, A. Tayal, S.M. Amir, M. Gupta, A. Gupta, M. Horisberger, and J. Stahn, Formation of Iron Nitride Thin Films with Al and Ti Additives, J. Appl. Phys. 111, No. 10: 103520 (2012); https://doi.org/10.1063/1.4718579
  68. H.Y. Wang and E.Y. Jiang, Enhancement of the thermal stability of Fe16N2 by Ti Addition, J. Phys.: Condens. Matter, 9, No. 13: 2739 (1997); https://doi.org/10.1088/0953-8984/9/13/011
  69. L. Ke, K.D. Belashchenko, M. van Schilfgaarde, T. Kotani, and V.P. Antropov, Effects of Alloying and Strain on the Magnetic Properties of Fe16N2, Phys. Rev. B, 88, No. 2: 024404 (2013); https://doi.org/10.1103/PhysRevB.88.024404
  70. Y. Jiang, B. Himmetoglu, M. Cococcioni, and J.-P. Wang, DFT Calculation and Experimental Investigation of Mn Doping Effect in Fe16N2, AIP Adv., 6, No. 5: 056007 (2016); https://doi.org/10.1063/1.4943059
  71. M. Takahashi, H. Takahashi, H. Nashi, H. Shoji, and T. Wakiyama, M. Kuwabara, Structure and Magnetic Moment of α″-Fe16N2 Compound Films: Effect of Co and H on Phase Formation, J. Appl. Phys., 79, No. 8: 5564 (1996); https://doi.org/10.1063/1.362244
  72. Y. Sun, Y.-X. Yao, M.C. Nguyen, C.Z. Wang, K.M. Ho, and V. Antropov, Spatial decomposition of magnetic anisotropy in magnets: Application to doped Fe16N2, Phys. Rev. B, 102, No. 3: 134429 (2020); https://doi.org/10.1103/PhysRevB.102.134429
  73. I. Khan, S. Park, and J. Hong, Magnetic Properties of Fe16–x(Ta/W)xN2 Ternary Alloy: First Principles and Atomistic Simulations, J. Phys.: Condens. Matter, 32, No. 2: 025801 (2019); https://doi.org/10.1088/1361-648X/ab3ffa
  74. N. Ishiwata, C. Wakabayashi, and H. Urai, Soft Magnetism of High-Nitrogen-Concentration FeTaN Film, J. Appl. Phys., 69, No. 8: 5616 (1991); https://doi.org/10.1063/1.347940
  75. K. Nakanishi, O. Shimizu, and S. Yoshida, Magnetic Properties of Fe–X–N (X = Zr, Hf, Nb, Ta) Films, IEEE Translation J. Magn. Jap., 7, No. 2: 128 (1992); https://doi.org/10.1109/TJMJ.1992.4565344
  76. K. Nago, H. Sakakima, and K. Ihara, Microstructures and Magnetic Properties of Fe–(Ta,Nb,Zr)–N Alloy Films, IEEE Translation J. Magn. Jap., 7, No. 2: 119 (1992); https://doi.org/10.1109/TJMJ.1992.4565343
  77. M. Widenmeyer, L. Shlyk, A. Senyshyn, R. Mönig, and R. Niewa, Structural and Magnetic Characterization of Single-Phase Sponge-Like Bulk α″-Fe16N2, Z. Anorg. Allg. Chem., 641, No. 2: 348 (2015); https://doi.org/10.1002/zaac.201500013
  78. J.M.D. Coey and P.A.I. Smith, Magnetic Nitrides, J. Magn. Magn. Mater., 200: 404 (1999); https://doi.org/10.1016/S0304-8853(99)00429-1
  79. S. Bhattacharyya, Iron Nitride Family at Reduced Dimensions: A Review of Their Synthesis Protocols and Structural and Magnetic Properties, J. Phys. Chem. C, 119, No. 4: 1601 (2015); https://doi.org/10.1021/jp510606z
  80. V.M. Nadutov, V.A. Tatarenko, and K.L. Tsinman, Statistical-Thermodynamic Analysis of Disorder–Order Structural Phase Transformations in F.C.C.-Fe–N Alloy, Metallofizika, 14, No. 11: 42 (1992) (in Russian).
  81. A.V. Ruban, Self-Trapping of Carbon Atoms in α-Fe during the Martensitic Transformation: A Qualitative Picture from ab initio Calculations, Phys. Rev. B, 90, No. 14: 144106 (2014); https://doi.org/10.1103/PhysRevB.90.144106
  82. E. Bain, The Nature of Martensite, Trans. AIME, 70, 25 (1924).
  83. G.V. Kurdjumov and G. Sachs, Über den Mechanismus der Stahlhärtung, Z. Phys., 64: 325 (1930) (in German); https://doi.org/10.1007/BF01397346
  84. Y. Jiang, X. Zhang, A. Al Mehedi, M. Yang, and J.-P. Wang, A Method to Evaluate α″-Fe16N2 Volume Ratio in FeN Bulk Material by XPS, Matter. Res. Express, 2, No. 11: 116103 (2015); https://doi.org/10.1088/2053-1591/2/11/116103
  85. J. Li, W. Yuan, X. Peng, Y. Yang, J. Xu, X. Wang, B. Hong, H. Jin, D. Jin, and H. Ge, AIP Advances, 6, No. 12: 125104 (2016); https://doi.org/10.1063/1.4967950
  86. N. Ji, L.F. Allard, E. Lara-Curzio, and J.-P. Wang, N site Ordering Effect on Partially Ordered Fe16N2, Appl. Phys. Lett., 98, No. 9: 092506 (2011); https://doi.org/10.1063/1.3560051
  87. Y. Hayashi and T. Sugeno, Nature of Boron in α-Iron, Acta Metall., 18, No. 6: 693 (1970); https://doi.org/10.1016/0001-6160(70)90099-4
  88. R.B. McLellan, Chemical Metallurgy of Iron and Steel (London: Iron and Steel Institute: 1973), p. 337.
  89. V.N. Bugaev and V.A. Tatarenko, Interaction and Arrangement of Atoms in Interstitial Solid Solutions Based on Close-Packed Metals (Kiev: Naukova Dumka: 1989) (in Russian).
  90. V.G. Gavriljuk, V.M. Nadutov, and K. Ullakko, Low Temperature Ageing of Fe–N Martensite, Scr. Met. Mater., 25, No. 4: 905 (1991); https://doi.org/10.1016/0956-716X(91)90246-W
  91. V.A. Tatarenko and K.L. Tsinman, Temperature- and Concentration-Dependent Tetragonality of a ‘Hybrid’ Binary Solution in Which Non-Metal Atoms Can Occupy Both Interstices and Sites of the B.C.T. Metal Lattice with Vacancies, Metallofiz. Noveishie Tekhnol., 18, No. 10: 32 (1996) (in Russian).
  92. A.G. Khachaturyan, Theory of Structural Transformations in Solids (Mineola, New York: Dover Publications, Inc.: 2008).
  93. V.A. Starenchenko, O.D. Pantyukhova, S.V. Starenchenko, and S.N. Kolupaeva, Mechanisms of Deformation-Induced Destruction of Long-Range Order Related to the Generation of Antiphase Boundaries and Point Defects in Alloys with the L12 Superstructure, Phys. Met. Metallogr., 91, No. 1: 85 (2001).
  94. R.B. McLellan, The Thermodynamics of Hybrid Binary Interstitial–Substitutional Solid Solutions, J. Phys. Chem. Solids, 50, No. 1: 49 (1989); https://doi.org/10.1016/0022-3697(89)90472-1
  95. A. Udyansky, J. von Pezold, A. Dick, and J. Neugebauer, Orientational Ordering of Interstitial Atoms and Martensite Formation in Dilute Fe-Based Solid Solutions, Phys. Rev. B, 83, No. 18: 184112 (2011); https://doi.org/10.1103/PhysRevB.83.184112
  96. A.G. Khachaturyan and G.A. Shatalov, Phase Transformation Associated with Radiation Defects, Fiz. Tverdogo Tela, 12, No. 10: 2969 (1970) (in Russian).
  97. M.A. Krivoglaz, X-Ray and Neutron Diffraction in Nonideal Crystals (Eds. (Berlin–Heidelberg: Springer: 1996); https://doi.org/10.1007/978-3-642-74291-0
  98. V.A. Tatarenko and C.L. Tsinman, Strain-Induced and ‘Blocking’ Effects in Statistical Thermodynamics of ‘Orientationally’ Ordered Interstitial Solid Solutions, Physics of Real Crystals (Ed. V.G. Baryakhtar) (Kiev: Naukova Dumka: 1992), p. 244 (in Russian).
  99. V.M. Nadutov, V.A. Tatarenko, C.L. Tsynman, and K. Ullakko, Interatomic Interaction and Atomic Ordering in Fe–N Martensite, Metallofiz. Noveishie Tekhnol., 16, No. 8: 34 (1994).
  100. V.B. Molodkin, V.A. Tatarenko, and C.L. Tsinman, Influence of the Temperature Dependence of Static Displacements of Metal Ions on Diffraction Effects in an Ordered Nonstoichiometric Interstitial Phase Based on a B.C.C. Metal, Metallofizika, 15, No. 9: 26 (1993) (in Russian).
  101. L.A. Girifalco, Statistical Physics of Materials (New York: John Wiley and Sons: 1973).
  102. I.M. Melnyk, T.M. Radchenko, and V.A. Tatarenko, Semi-Empirical Parameterization of Interatomic Interactions, Which is Based on Statistical-Thermodynamic Analysis of Data on Phase Equilibriums in B.C.C.-Fe–Co Alloy. I. Primary Ordering, Metallofiz. Noveishie Tekhnol., 32, No. 9: 1191 (2010) (in Ukrainian).
  103. M.A. Krivoglaz, Diffuse Scattering of X-Rays and Neutrons by Fluctuations (Berlin–Heidelberg: Springer: 1996).
  104. B.N. Brockhouse, H.E. Abou-Helal, and E.D. Hellman, Lattice Vibrations in Iron at 296 K, Solid State Commun., 5, No. 4: 211 (1967); https://doi.org/10.1016/0038-1098(67)90258-X
  105. R. Kohlhaas, Ph. Dünner, and N. Schmitz-Pranghe, Uber die Temperaturabhangigkeit der Gitterparameter von Eisen, Kobalt und Nickel im Bereich Hoher Temperaturen, Z. Angew. Phys., 23, No. 4: 245 (1967) (in German).
  106. J.A. Rayne and B.S. Chandrasekhar, Elastic Constants of Iron from 4.2 to 300 K, Phys. Rev., 122, No. 6: 1714 (1961); https://doi.org/10.1103/PhysRev.122.1714
  107. D.J. Dever, Temperature Dependence of the Elastic Constants in α-Iron Single Crystals: Relationship to Spin Order and Diffusion Anomalies, J. Appl. Phys., 43, No. 8: 3293 (1972); https://doi.org/10.1063/1.1661710
  108. L. Cheng, A. Boöttger, Th.H. de Keijser, and E.J. Mittemeijer, Lattice Parameters of Iron–Carbon and Iron–Nitrogen Martensites and Austenites, Scr. Met. Mater., 24, No. 3: 509 (1990); https://doi.org/10.1016/0956-716X(90)90192-J
  109. G.M. Stoica, A.D. Stoica, M.K. Miller, and D. Ma, Temperature-Dependent Elastic Anisotropy and Mesoscale Deformation in a Nanostructured Ferritic Alloy, Nature Commun., 5: 1 (2014); https://doi.org/10.1038/ncomms6178
  110. Z.S. Basinski, W. Hume-Rothery, and A.L. Sutton, The Lattice Expansion of Iron, Proc. R. Soc. Lond. A, 229: 459 (1955); https://doi.org/10.1098/rspa.1955.0102
  111. W.G. Wolfer, Fundamental Properties of Defects in Metals, Comprehensive Nuclear Materials (Eds. R.J.M. Konings, T.R. Allen, R.E. Stoller, and Sh. Yamanaka) (Amsterdam–Kidlington–Oxford–Waltham: Elsevier Science: 2012), p. 1; https://doi.org/10.1016/B978-0-08-056033-5.00001-X
  112. T.-S. Kuan, A. Warshel, and O. Schnepp, Intermolecular Potentials for N2 Molecules and the Lattice Vibrations of Solid α-N2, J. Chem. Phys., 52, No. 6: 3012 (1970); https://doi.org/10.1063/1.1673432
  113. W.A. Harrison, Pseudopotentials in the Theory of Metals (New York: W.A. Benjamin Inc.: 1966).
  114. W.A. Harrison, Solid State Theory (New York: Dover Publ. Inc.: 1979).
  115. M.S. Blanter and A.G. Khachaturyan, Stress-Induced Interaction of Pairs of Point Defects in BCC Solutions, Met. Trans. A, 9, No. 6: 753 (1978); https://doi.org/10.1007/BF02649784
  116. E.S. Machlin, Pair Potential Model of Intermetallic Phases—I, Acta Met., 22, No. 1: 95 (1974); https://doi.org/10.1016/0001-6160(74)90129-1
  117. L. Brewer, Prediction of High Temperature Metallic Phase Diagrams, High-Strength Materials (Ed. V.F. Zackay) (New York: John Wiley and Sons: 1965), Ch. 2, p. 12.
  118. L. Brewer, The Cohesive Energies of the Elements (Rep. LBL-3720, Revised May 4, 1977) (Berkeley, CA, USA: Lawrence Berkeley Laboratory: 1977); https://escholarship.org/uc/item/08p2578m
  119. V.G. Weizer and L.A. Girifalco, Vacancy–Vacancy Interaction in Copper, Phys. Rev., 120, No. 3: 837 (1960); https://doi.org/10.1103/PhysRev.120.837
  120. R. Yamamoto and M.J. Doyama, The Interactions between Vacancies and Impurities in Metals by the Pseudopotential Method, J. Phys. F: Met. Phys., 3, No. 8: 1524 (1973); https://doi.org/10.1088/0305-4608/3/8/007
  121. A.A. Smirnov, Theory of Vacancies in Metals and Alloys and Its Applications to Substitutional Alloys (Kiev: Naukova Dumka: 1993) (in Russian).
  122. V.N. Bugaev, V.A. Tatarenko, and C.L. Tsinman, A Content of Site Vacancies in Binary Interstitial Alloys Based on F.C.C. Iron, Metallofiz. Noveishie Tekhnol., 17, No. 2: 32 (1995) (in Russian).