Gd reference layer method for the case of two reflectometry experiments

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Abstract

The article presents an approach to determining the modulus and phase of the neutron reflectance using a gadolinium reference layer, which allows reducing the number of necessary experiments from three to two. It is shown that it is possible to reconstruct the reflection amplitude based on the results of only two reflectometric experiments. However, when conducting two experiments, calculating the reflection amplitude is complicated by the fact that there will be two solutions instead of one. Therefore, it is necessary to evaluate the obtained results, since one of these solutions will have no physical meaning. The results are evaluated based on a priori information about the sample or with the help of additional modeling of the interaction potential. The theory of the proposed approach is described in detail, and it is tested on model numerical calculations for the Al2O3//Ti film. Experimental results for the test samples Al2O3//Nb and Si//Cr/Fe/Cr are presented. A comparison of the moduli and phases of the reflectivity obtained by processing three and two experiments is carried out. It was found that under conditions of poor statistics, conducting two experiments is preferable, since the solution, in this case, contains fewer artifacts of mathematical processing.

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About the authors

Е. S. Nikova

Miheev Institute of Metal Physics UB RAS

Author for correspondence.
Email: e.nikova@mail.ru
Russian Federation, Ekaterinburg

Yu. А. Salamatov

Miheev Institute of Metal Physics UB RAS

Email: e.nikova@mail.ru
Russian Federation, Ekaterinburg

Е. А. Kravtsov

Miheev Institute of Metal Physics UB RAS

Email: e.nikova@mail.ru
Russian Federation, Ekaterinburg

References

  1. de Haan V.O., van Well A.A., Sacks P.E., Adenwalla S., Felcher G.P. // Phys. Rev. B. 1996. V. 221. P. 524.
  2. Majkrzak C.F., Berk N.F. // Phys. Rev. B.1995. V. 52. P. 10827.
  3. Никова Е.С, Саламатов Ю.А., Кравцов Е.А., Макарова М.В., Проглядо В.В., Устинов В.В., Боднарчук В.И., Нагорный А.В. // Физика металлов и металловедение. 2019. V. 120. P. 913.
  4. Никова Е.С., Саламатов Ю.А., Кравцов Е.А., Проглядо В.В., Жакетов В.Д., Миляев М.А. // Поверхность. Рентген., синхротр. и нейтрон. исслед. 2022. № 11. P. 15. https://doi.org/10.31857/S1028096022110176
  5. de Haan V.O., van Well A.A., Adenwalla S., Felcher G.P. // Phys. Rev. B. 1995. V. 52. № 15. P. 10831
  6. Majkrzak C.F., Berk N.F. // Phys. Rev. B. 1998. V. 58. P. 15416.
  7. Majkrzak C.F., Berk N.F., Silin V. // Phys. Rev. B. 2000. V. 283. P. 248.
  8. Leeb H., Grötz H., Kasper J., Lipperheide R.// Phys. Rev. B. 2001. V. 63. P. 045414
  9. Lynn J.E., Seeger P.A. // Atomic Data and Nuclear Data Tables. 1990. V. 44, Iss. 2. P. 191
  10. Никова Е.С., Саламатов Ю.А., Кравцов Е.А. // Поверхность. Рентген., синхротр. и нейтрон. исслед. 2023. № 7. P. 102. EDN: TEZEMM https://doi.org/10.31857/S1028096023070117
  11. Agranovich Z. S., Marchenkow V. S. The inverse Problem of Scattering Theory. Gordon and Breach. New York. 1963. 290 p.
  12. Chadan K., Sabatier P. C. Inverse Problems in Quantum Scattering Theory. Text and Monographs in Physics. Springer. Berlin. 2nd ed., 1989. 250 p.
  13. Kay I. // Comm. Pure and Appl. Math.1960.V. 13. P. 371.
  14. Levenberg K. A // Quart. Appl. Math. 1944. V. 2. P. 164.
  15. Marquardt D.// SIAM Journal on Applied Mathematics.1963. V. 11 (2). P.431.
  16. Majkrzak C.F., Berk N.F., Perez-Salas U.A. // Langmuir. 2003. V. 19, P. 7796.
  17. Paul E. Sacks and Tuncay Aktosun // SIAM J. Appl. Math. 2000. V. 60, № 4, P.1340.
  18. Nikova E.S., Salamatov Yu.A, Kravtsov E.A., Bodnarchuk V.I., Ustinov V.V. // Physica B. 2019. V. 552. P. 58.
  19. Nikova E.S., Salamatov Yu. A. , Kravtsov E. A. , Ustinov V. V. , Bodnarchuk V. I. , Nagorny A. V. // J. Surf. Invest.: X-Ray, Synchrotron Neutron Tech. 2020. V. 14. P. 164.

Supplementary files

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2. Fig. 1. Possible options for representing the neutron reflection amplitudes for two experiments as two circles in the complex plane.

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3. Fig. 2. Model reflectometric curves for the Al2O3//Ti(500 Å)/V(20 Å)/Gd(50 Å)V(50 Å) structure for two incidence angles of 3.3 mrad (1) and 10.1 mrad (2).

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4. Fig. 3. Moduli (a) and phases (b) of the reflection amplitude of the Al2O3//Ti(500 Å)/V(20 Å) system in comparison with model data: first solution (1), second solution (2), model data (3).

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5. Fig. 4. Experimental reflectometric curves for the Al2O3// Nb(500 Å)/V(15 Å)/ Gd(100 Å)/V(150 Å) system at neutron beam incidence angles of 5.0 mrad (1); 8.8 mrad (2).

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6. Fig. 5. Moduli (a) and phases (b) of the reflection amplitude of the Al2O3// Nb(500 Å)/V(15 Å) system in comparison with data from three reflectometric experiments: first solution (1), second solution (2), data from three experiments (3).

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7. Fig. 6. Experimental reflectometric curves for the Si//Cr(287 Å)/Fe(299 Å)/Cr(186 Å)/Gd(50 Å)/V(50 Å) system at neutron beam incidence angles of 3.1 mrad (1); 9.0 mrad (2).

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8. Fig. 7. Moduli (a) and phases (b) of the reflection amplitude of the Si//Cr(287 Å)/Fe(299 Å)/Cr(186 Å) system: first solution (1), second solution (2). Mixed solutions are shown as an example.

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9. Fig. 8. Moduli (a) and phases (b) of the reflection amplitude of the Si//Cr(287 Å)/Fe(299 Å)/Cr(186 Å) system: data from two experiments (1), data from three experiments (2).

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