On the statistical theory of the shape of multiple quantum nmr spectra in solids

Capa

Citar

Texto integral

Acesso aberto Acesso aberto
Acesso é fechado Acesso está concedido
Acesso é fechado Somente assinantes

Resumo

The statistical model developed in this work allows us to calculate the shape of the multiple quantum (MQ) NMR spectra (the dependence of the amplitudes of the corresponding multiple quantum coherences on their orders) by decomposing the desired time-correlation functions (TCF) over the infinite set of orthogonal operators and by using some well-known facts from the physics of traditional model systems. The resulting expression contains series with terms depending on the gradually growing up with the time number of spins in clusters of correlated spins. The influence of the possible degradation of these clusters on the shape of the spectra is taken into account. Analytical and numerical calculations were performed for various parameter values included in the final expressions. The developed theory adequately describes the results of numerical calculations of the MQ spectra performed by us and experiments: the transformation of the Gaussian profile into an exponential one, the asymptotics (wings) of the spectrum depending on the coherence order M, the dependence of the relaxation rate of the MQ spectrum on M, as well as the narrowing and stabilization of the MQ spectrum under the influence of perturbation.

Texto integral

Acesso é fechado

Sobre autores

V. Zobov

Kirensky Institute of Physics, Federal Research Center KSC SB RAS

Autor responsável pela correspondência
Email: rsa@iph.krasn.ru
Rússia, Krasnoyarsk

A. Lundin

Semenov Federal Research Center for Chemical Physics, Russian Academy of Sciences

Email: ya-andylun2012@yandex.ru
Rússia, Moscow

Bibliografia

  1. N. Bloembergen, E. M. Purcell, and R. V. Pound, Phys. Rev. 73, 679 (1948). https://doi.org/10.1103/PhysRev.73.679
  2. V.O. Zavel’skii and A. A. Lundin, Russ. J. Phys. Chem. B 10, 379 (2016). https://doi.org/10.1134/S1990793116030118
  3. A.A. Lundin and V. E. Zobov, J. Exp. Theor. Phys., 127, 305 (2018) https://doi.org/10.1134/S1063776118080216
  4. A.A. Lundin, V.E. Zobov, Russian Journal of Physical Chemistry B, 15, 839 (2021). https://doi.org/10.1134/S1990793121050079
  5. A. Abragam, The Principles of Nuclear Magnetism (Clarendon, Oxford, 1961), Chs. 4,6,10.
  6. R. Ernst, G. Bodenhausen, and A. Wokaun, Principles of NMR in One and TwoDimensions (Clarendon, Oxford, 1987).
  7. B. Blumich, Essential NMR for Scientists and Engineers (Springer, Berlin, Heidelberg, 2005).
  8. P.-K. Wang, J.-P. Ansermet, S. L. Rudaz, Z. Wang, S. Shore, Ch. P. Slichter, and J.M. Sinfelt, Science 234, 35 (1986). https://doi.org/10.1126/science.234.4772.35
  9. J. Baum and A. Pines, J. Am. Chem. Soc. 108, 7447 (1986).
  10. S.I. Doronin, A.V. Fedorova, E.B. Fel’dman, and A.I. Zenchuk, J. Chem. Phys. 131,104109 (2009). https://doi.org/10.1063/1.3231692
  11. J. Baum, M. Munovitz, A.N. Garroway, A. Pines, J. Chem. Phys. 83, 2015 (1985). https://doi.org/10.1063/1.449344
  12. Advances in Chemical Physics / Eds. I. Prigogine, S.A. Rice (Wiley&Sons, 1987). Vol. 66. P. 1. https://doi.org/10.1002/97804701429.29.ch1
  13. R. Balesku, Equilibrium and Nonequilibrium Statistical Mechanics (Wiley, New York, 1978), Vol. 2.
  14. J. Preskill, Lecture Notes for Physics, Vol. 229: Quantum Information and Computation (California Inst. Technol., (1998)).
  15. V.E.Zobov and A.A. Lundin, J. Exp. Theor. Phys.,131, 273 (2020). https://doi.org/10.1134/S1063776120060096
  16. A.I. Larkin, Y.N. Ovchinnikov, JETP, 28, 1200, (1969).
  17. F.D. Domínguez, M.C. Rodríguez, R. Kaiser, D. Suter, and G.A. Álvarez, Phys. Rev.A, 104, 012402, (2021). https://doi.org/10.1103/PhysRevA.104.012402
  18. S.H. Shenker, D. Stanford, J. High Energy Phys., 3, 067 (2014). https://doi.org/10.1007/JHEP03(2014)067
  19. D.E. Parker, X. Cao, A. Avdoshkin, T. Scaffidi, E. Altman, Phys.Rev.X, 9, 041017 (2019). https://doi.org/10.1103/PhysRevX.9.041017
  20. Q. Wang, F. Perez-Bernal, Phys.Rev.A, 100, 062113 (2019). https://doi.org/10.1103/PhysRevA.100.062113
  21. Y. Gu, A. Kitaev, P. Zhang, J. High Energy Phys., 2022, 133 (2022). https://doi.org/10.1007/JHEP03(2022)133
  22. C. Gross and I. Bloch, Science 357, 995 (2017). https://doi.org/10.1126/science.aal3837
  23. R. Blatt and C.F. Roos, Nature Phys. 8, 277 (2012). https://doi.org/10.1038/nphys2252
  24. A.K. Khitrin, Chem. Phys. Lett. 274, 217 (1997) https://doi.org/10.1016/S0009-2614(97)00661-1
  25. V.E. Zobov and A.A. Lundin, J. Exp. Theor. Phys., 103, 904 (2006). https://doi.org/10.1134/S1063776106120089
  26. V.E. Zobov and A.A. Lundin, JETP Lett. 105, 51 (2017) https://doi.org/0.7868/S0370274X17080082
  27. M. Gattner, Ph. Hauke, and A.M. Rey, Phys. Rev. Lett. 120, 040402 (2018). https://doi.org/10.1103/PhysRevLett.120.040402
  28. S.I. Doronin, E.B. Fel’dman, and I.D. Lazarev, Phys. Rev. А 100, 022330 (2019). https://doi.org/ doi: 10.1103/Phys.Rev.A.100.022330
  29. S.I.Doronin, E.B. Fel’dman, and I. D. Lazarev, Phys.Lett.A 406, 127458 (2021). https://doi.org/10.1016/j.physleta.2021.127458
  30. K. X. Wei, P. Peng, O. Shtanko, I. Marvian, S. Lloyd, C. Ramanathan, and P. Cappellaro, Phys. Rev. Lett. 123, 090605 (2019). https://doi.org/10.1103/PhysRevLett.123.090605
  31. P.W. Anderson, P.R. Weiss, Rev. Mod. Phys., 25, 269 (1953). https://doi.org/10.1103/RevModPhys.25.269
  32. J.R. Klauder, P.W. Anderson, Phys.Rev.,125, 912 (1962). https://doi.org/10.1103/PhysRev.125.912
  33. S. Lacelle, S. Hwang and B. Gerstein, J. Chem. Phys., 99, 8407 (1993). https://doi.org/10.1063/1.465616
  34. R.H. Schneder, H. Schmiedel, Phys. Lett. A, 30, 298 (1969). https://doi.org/10.1016/0375-9601(69)91005-6
  35. W.K. Rhim, A. Pines, J.S. Waugh, Phys. Rev. B, 3, 684 (1971). https://doi.org/10.1103/PhysRevB.3.684
  36. A.A. Lundin and V.E. Zobov, J. Exp. Theor. Phys. 120, 762 (2015). https://doi.org/10.1134/S1063776115040093
  37. F. Lado, J.D. Memory, G.W. Parker, Phys.Rev.B, 4, 1406 (1971). https://doi.org/10.1103/PhysRevB.4.1406
  38. M.H. Lee, Phys.Rev.Lett., 52, 1579 (1984). https://doi.org/10.1103/PhysRevLett.52.1579
  39. M.H. Lee, J. Hong, Phys.Rev.B, 32, 7734 (1985). https://doi.org/10.1103/PhysRevB.32.7734
  40. J.M. Liu, G. Müller, Phys.Rev.A, 42, 5854 (1990). https://doi.org/10.1103/PhysRevA.42.5854
  41. M.H. Lee, I.M. Kim, W.P. Cummings, R. Dekeyser, J. Phys.: Condens. Matter, 7, 3187 (1995). https://doi.org/10.1088/0953-8984/7/16/013
  42. V.L. Bodneva, A.A. Lundin, and A.V. Milyutin, Theor. Math. Phys. 106 (3), 370, (1996). https://doi.org/10.1007/BF02071482
  43. M. Böhm, H. Leschke, M. Henneke, et al., Phys. Rev. B, 49, 5854 (1994).
  44. V.A. Il’in and G.D. Kim, Linear Algebra and Analytic Geometry (Mosk. Gos. Univ., Moscow, (2008)), Chap. 13 [in Russian].
  45. A.A. Lundin, V.E. Zobov, Appl. Magn. Res. 47, 701 (2016). https://doi.org/10.1007/s00723-016-0770-z
  46. V.E. Zobov, A.A. Lundin, Appl. Magn. Res. 52, 879 (2021). https://doi.org/10.1007/s00723-021-01342-1
  47. H.G. Krojanski, D. Suter, Phys. Rev. Lett., 97, 150503 (2006). https://doi.org/10.1103/PhysRevLett.97.150503
  48. H.G. Krojanski, D. Suter, Phys.Rev.A.,74, 062319 (2006). https://doi.org/10.1103/PhysRevA.74.062319
  49. G. Cho, P. Cappelaro, D. G. Cory, and C. Ramanathan, Phys. Rev. B 74, 224434, (2006). https://doi.org/10.1103/PhysRevB.74.224434
  50. V.E. Zobov, A.A. Lundin, Russ., J. Phys. Chem., B 2, 676 (2008).
  51. A.P., Prudnikov, U.A. Briachkov, O.I.Marichev, Integraly i ryadi (Moskva, Nauka (1981)), Section 2.3.16(2) [in Russian].
  52. V.E. Zobov, A.A. Lundin, J. Exp. Theor. Phys.,135, 752 (2022). https://doi.org/10.1134/S1063776122110139
  53. G.A. Alvarez, R. Kaiser, D. Suter, Ann. Phys. (Berlin) 525, 833 (2013). https://doi.org/10.1002/andp.201300096
  54. H.G. Krojanski and D. Suter, Phys. Rev. Lett. 93, 090501 (2004). https://doi.org/10.1103/PhysRevLett.93.090501
  55. V.E. Zobov and A.A. Lundin, J. Exp. Theor. Phys., 112, 451 (2011). https://doi.org/10.1134/S1063776111020129
  56. G.A. Álvarez, D. Suter,Phys.Rev.Lett., 104, 230403 (2010). https://doi.org/10.1103/PhysRevLett.104.230403
  57. V.E. Zobov and A.A. Lundin, J. Exp. Theor. Phys. 113, 1006 (2011). https://doi.org/10.1134/S1063776111140111
  58. G.A. Álvarez, D. Suter, R. Kaiser, Science, 349, 846 (2015). https://doi.org/10.1126/science.1261160
  59. G.A. Alvarez, D. Suter, Phys.Rev.A 84, 012320 (2011) https://doi.org/10.1103/PhysRevA.84.012320
  60. V.E. Zobov and A.A. Lundin, JETP Letters, 117, 932 (2023) https://doi.org/10.1134/S0021364023601525
  61. M.V. Phedoryuk, Asimptotika: Integraly i ryadi. (Moskva, Nauka (1987)) Chapter II, §1 [in Russian].
  62. S.Y. Umanskii et al., Russ. J. Phys. Chem. B, 17, 346 (2023) https://doi.org/10.1134/S199079312302032X
  63. V.E. Kirillov, V.E. Yurkov, M.S. Korobov et al. // Russ. J. Phys. Chem. B. 2023. V. 17. № 6. P.
  64. E.V. Morozov, A.V. Ilyichov, V.M. Buznik // Russ. J. Phys. Chem. B. 2023. V. 17. № 6. P. 1361.

Arquivos suplementares

Arquivos suplementares
Ação
1. JATS XML
Baixar
2. Fig. 1. Comparison of the experimental MC spectrum [53] (filled circles) at p = 0 and T = 11τ0 (τ0 = 57.6 ps) with the results of theoretical calculations: calculation using the formula GM (T) = (1 + 2^2 M2/K) exp (-2^2 M2/K)/42K at K— = 428 (1), 550 (2) and 700 (3); curve 4 – calculation using the Gauss formula GM (T) = exp(-M 2/K)/4PK at K = 428. Only the right halves of the spectra are shown.

Baixar (25KB)
Metadados
3. Fig. 2. Comparison of four experimental MC spectra at p = 0 and different durations of preparatory periods [53]: T = 5 (filled circles), 8 (squares), 11 (triangles) and 14τ0 (open circles), where τ0 = 57.6 ps, with theoretical MC spectra calculated using the formula GM (T) = (1 + 2—2 M2/ K) exp (-2^2 M2/ K)/LK, respectively, at: K— = 50 (1), 150 (2),

Baixar (31KB)
Metadados
4. Fig. 3. Multiquantum spectra (logarithmic values ​​of the right halves) for T = 5 (squares) and 8 (crosses), calculated at C = 0.001 and A = 0 both by formula (36) (solid lines) and by numerical integration of expression (21) taking into account formula (27). The dashed line is the calculation by the simplified formula (36), obtained after removing θ(′1) in expressions (36) and (34).

Baixar (28KB)
Metadados
5. Fig. 4. Multiquantum spectra (logarithmic values ​​of the right halves) for T = 8, calculated at C = 0.0001 both by formula (36) (solid lines) and by numerical integration of expression (21) taking into account formula (27): α = 1 (squares) and α = 0 (crosses). In both cases, integration over K was carried out from M to 1,000,000.

Baixar (23KB)
Metadados
6. Fig. 5. Emitted at the disturbance parameter p = 0.108 and two different preparatory periods: T = 5т0 (open circles) and T = 9т0 (filled circles) from [53], and the corresponding MK spectra calculated by formula (36) at T = 5т0(m2)1/2 = 1.89 (solid line) and T = 9т0( m 2)1/2 = 3.41 (dashed line). Other parameters used in the calculations: C = p2B2/m2 = 0.029, a = A2/B2 = 0.5, as well as at T = 5т0 N1 = 1/1.7, K0 = 46.9, at T = 9т0 N1 = 1/29, K0 = 403.2.

Baixar (22KB)
Metadados

Declaração de direitos autorais © Russian Academy of Sciences, 2024