Ядерна фізика та енергетика Nuclear Physics and Atomic Energy   ISSN: 1818-331X (Print), 2074-0565 (Online)   Publisher: Institute for Nuclear Research of the National Academy of Sciences of Ukraine   Languages: Ukrainian, English   Periodicity: 4 times per year   Open access peer reviewed journal

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A. Ya. Dzyublik^*, I. E. Anokhin, V. Yu. Spivak

Institute for Nuclear Research, National Academy of Sciences of Ukraine, Kyiv, Ukraine

^*Corresponding author. E-mail address: dzyublik@ukr.net

Abstract: The absorption cross-section of Mössbauer radiation in magnetic liquids is calculated, taking into consideration both translational and rotational Brownian motion of magnetic nanoparticles as well as stochastic reversals of their magnetization in the absence of an external magnetic field. The role of Brownian motion in ferrofluids is considered in the framework of the diffusion theory, while for the magnetorheological fluids with large nanoparticles, it is done with the aid of Langevin's approach. For stochastic rotation, we derived the equation analogous to Langevin's one and found the corresponding correlation function. In both cases, simple rotational correlation functions are obtained in the approximation of small rotations during the lifetime of the excited Mossbauer nuclei. Influence of the Néel's relaxations is considered in the framework of the Blume - Tjon model.

Keywords: Mössbauer effect, ferromagnetic nanoparticles, Brownian motion, Néel relaxations.

1. R.E. Rosensweig. Ferrohydrodynamics (Cambridge, London: Cambridge Univ. Press, 1985); republished (1997 New York: Dover. Publ. Inc., 1997). Google books

2. B.M. Berkovski, V. Bashtovoy. Magnetic Fluids and Applications Handbook (New York: Begell House Inc., 1996). https://doi.org/10.1615/978-1-56700-062-7.0

3. C. Scherer, A.M. Figueiredo Neto. Ferrofluids: properties and applications. Brazil. J. Phys. 35 (2005) 718. https://doi.org/10.1590/S0103-97332005000400018

4. D.H. Wang, W.H. Liao. Magnetorheological fluid dampers: A review of parametric modelling. Smart Mater. Struct. 20 (2011) 023001. https://doi.org/10.1088/0964-1726/20/2/023001

5. K. Ray, R. Moskowitz. Commercial applications of ferrofluids. J. Magn. Magn. Mater. 85 (1990) 233. https://doi.org/10.1016/0304-8853(90)90058-X

6. K. Ray, R. Moskowitz, R. Casciari. Advances in ferrofluid technology. J. Magn. Magn. Mater. 149 (1995) 174. https://doi.org/10.1016/0304-8853(95)00365-7

7. R. Pérez-Castillejos et al. The use of ferrofluids in micromechanics. Sens. Actuators A 84 (2000) 176. https://doi.org/10.1016/S0924-4247(99)00318-0

8. E.H. Kim et al. Synthesis of ferrofluid with magnetic nanoparticles by sonochemical method for MRI contrast agent. J. Magn. Magn. Mater. 289 (2005) 328. https://doi.org/10.1016/j.jmmm.2004.11.093

9. V.V. Mody, A. Singh, B. Wesley. Basics of magnetic nanoparticles for their application in the field of magnetic fluid hyperthermia. Eur. J. Nanomed. 5 (2013) 11. https://doi.org/10.1515/ejnm-2012-0008

10. K.M. Krishnan. Magnetic nanoparticles in medicine: progress, problems, and advances. IEEE Trans. Magn. 46 (2019) 2523. https://doi.org/10.1109/TMAG.2010.2046907

11. B. Gleich, J. Weizenecker. Tomographic imaging using the nonlinear response of magnetic particles. Nature 435 (2005) 1214. https://doi.org/10.1038/nature03808

12. R.M. Ferguson et al. Optimizing magnetite nanoparticles for mass sensitivity in magnetic particle imaging. Med. Phys. 38 (2011) 1619. https://doi.org/10.1118/1.3554646

13. R.J. Deissler, Y. Wu, M.A. Martens. Dependence of Brownian and Néel relaxation times on magnetic field strength. Med. Phys. 41 (2014) 012301. https://doi.org/10.1118/1.4837216

14. Y. Xiao, J. Du. Superparamagnetic nanoparticles for biomedical applications. J. Mater. Chem. B 8 (2020) 354. https://doi.org/10.1039/C9TB01955C

15. H.T.K. Duong et al. A guide to the design of magnetic particle imaging tracers for biomedical applications. Nanoscale 14 (2022) 3890. https://doi.org/10.1039/D2NR01897G

16. L. Néel. Théorie du trainage magnétique des ferromagnetiques en grains fins avec application aux terres cuites. Ann. Geophys. 5 (1949) 99. https://hal.science/hal-03070532

17. J. Landers et al. Simultaneous study of Brownian and Néel relaxation phenomena in ferrofluids by Mossbauer spectroscopy. Nano Lett. 16 (2016) 1150. https://doi.org/10.1021/acs.nanolett.5b04409

18. P.P. Craig, N. Sutin. Mossbauer effect in liquids: influence of diffusion broadening. Phys. Rev. Lett. 11 (1963) 460. https://doi.org/10.1103/PhysRevLett.11.460

19. D.St.P. Bunbury et al. Study of diffusion in glycerol by the Mossbauer effect of Fe57. Phys. Lett. 6 (1963) 34. https://doi.org/10.1016/0031-9163(63)90210-5

20. T. Bonchev et al. A study of Brownian motion by means of the Mossbauer effect. Sov. Phys. JETP 23 (1966) 42. http://jetp.ras.ru/cgi-bin/r/index/e/23/1/p42?a=list

21. K.P. Singh, J.G. Mullen. Mössbauer study of Brownian motion in liquids: colloidal cobaltous hydroxy stannate in glycerol, ethanol-glycerol, and aqueous-glycerol solutions. Phys. Rev. A 6 (1972) 2354. https://doi.org/10.1103/PhysRevA.6.2354

22. V.N. Dubinin. Influence of viscosity of colloidal solutions on the magnitude of resonance absorption of γ-quanta. Ukr. J. Phys. 13 (1968) 1547. (Rus)

23. S.L. Kordyuk et al. Mössbauer effect in a disperse system. Sov. Phys. JETP 25 (1967) 400. http://jetp.ras.ru/cgi-bin/r/index/e/25/2/p400?a=list

24. V.G. Bhide et al. Effect of Brownian motion on the Mössbauer line shape. Phys. Rev. B 3 (1971) 673. https://doi.org/10.1103/PhysRevB.3.673

25. K.S. Singwi, A. Sjölander. Resonance absorption of nuclear gamma rays and the dynamics of atomic motions. Phys. Rev. 120 (1960) 1093. https://doi.org/10.1103/PhysRev.120.1093

26. A.V. Zatovski. Contribution to the theory of the Mössbauer effect on Brownian particles. Sov. Phys. JETP 32 (1971) 274. http://jetp.ras.ru/cgi-bin/r/index/e/32/2/p274?a=list

27. O.Ya. Dzyublik. On the theory of the Mössbauer effect on Brownian particles. Ukr. J. Phys. 18 (1973) 1454. (Ukr)

28. A.Ya. Dzyublik. Mossbauer effect in ellipsoidal Brownian particles. Sov. Phys. JETP 40 (1975) 763. http://jetp.ras.ru/cgi-bin/r/index/e/40/4/p763?a=list

29. A.M. Afanas'ev, P.V. Hendriksen, S. Morup. Influence of rotational diffusion of the Mössbauer spectrum of ultrafine particles in a supercooled liquid. Hyperf. Inter. 88 (1994) 35. https://doi.org/10.1007/BF02068700

30. A.Ya. Dziublik. Theory of the Mössbauer effect on magnetic Brownian particles. Ukr. J. Phys. 23 (1978) 881.

31. J. Landers et al. In-field orientation and dynamics of ferrofluids studied by Mossbauer spectroscopy. ACS Appl. Mater. Interfaces 11 (2018) 3160. https://doi.org/10.1021/acsami.8b16356

32. M.A. Chuev et al. Separation of contributions of the magnetic relaxation and diffusion of nanoparticles in ferrofluids by analyzing the hyperfine structure of Mossbauer spectra. JETP Lett. 108 (2018) 59. https://doi.org/10.1134/S0021364018130064

33. R. Gabbasov et al. Study of Brownian motion of magnetic nanoparticles in viscous media by Mössbauer spectroscopy. J. Magn. Magn. Mater. 475 (2019) 146. https://doi.org/10.1016/j.jmmm.2018.11.044

34. V.M. Cherepanov et al. Study of the Brownian broadening in the Mössbauer spectra of magnetic nanoparticles in colloids with different viscosities. Crystal. Rep. 65 (2020) 398. https://doi.org/10.1134/S1063774520030074

35. M. Blume, J.A. Tjon. Mössbauer spectra in a fluctuating environment. Phys. Rev. 165 (1968) 446. https://doi.org/10.1103/PhysRev.165.446

36. A. Einstein. Zur Theorie der Brownschen Bewegung. Ann. Phys. 19 (1906) 371. https://doi.org/10.1002/andp.19063240208

37. M.A. Leontovich. Introduction to Thermodynamics. Statistical Physics (Moskva: Vysshaya Shkola, 1983). (Rus)

38. S. Chandrasekhar. Stochastic problems in physics and astronomy. Rev. Mod. Phys. 15 (1943) 1. https://doi.org/10.1103/RevModPhys.15.1

39. L.D. Landau, E.M. Lifshitz. Mechanics. 3d edition (Oxford: Elsevier Ltd, 1976). Google books

40. G. Kirchhoff. Vorlesungen über Mechanik (Leipzig: B.G. Teubner, 1897). Google books