Skip to main content
SpringerLink
Log in

Analysis of Substitutional Hydrogen Diffusional Coefficient in LiNbO3 under Anharmonic Potential

  • Original Contribution
  • Published:
Journal of The Institution of Engineers (India): Series D Aims and scope Submit manuscript

Abstract

The dynamic of hydrogen in Lithium niobate is explained by adopting Morse potential. The diffused hydrogen substitutes Lithium, and it makes bonding with one oxygen atom of a facet of oxygen triangle. Bonds will be stretched to set up anharmonic vibration. Damped anharmonic oscillation is derived to explain the dynamics of hydrogen as an impurity. The thermal fluctuation is studied by Fokker–Planck equation (FPE) has an important role to determine the diffusion constant for substitutional hydrogen. Relaxation time is the result of diffusion coefficient. Probability of substitutional hydrogens in different quantum state is studied with help of Boltzmann distribution. Arrhenius expressions have been derived from analysis of FPE. The derivation of absorption coefficient of absorption band of stretching vibration of OH bond with damping constant is nearly equal to experimental result.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. M E Lines and A M Glass, Principles and Applications of Ferroelectrics and Related Materials.OUP Oxford (1977).

  2. S. Kim, V. Gopalan, A. Gruverman, Coercive fields in ferroelectrics: a case study in lithium niobate and lithium tantalite. Appl. Phys. Lett. 80, 2740 (2002)

    Article  Google Scholar 

  3. K.T. Gahagan et al., Integrated electro-optic lens/scanner in a LiTaO3 single crystal. Appl. Opt. 38, 1186–1190 (1999)

    Article  Google Scholar 

  4. S. Kim, V. Gopalan, K. Kitamura, Y. Furukawa, Domain reversal and nonstoichiometry in lithium tantalite. J. Appl. Phys. 90, 2949 (2001)

    Article  Google Scholar 

  5. M. Dawber, K.M. Rabe, J.F. Scott, Physics of thin-film ferroelectric oxides. Rev. Mod. Phys. 77(4), 1083 (2005)

    Article  Google Scholar 

  6. A.M. Prokhorov, Y.S. Kuzminov, Physics and Chemistry of Crystalline Lithium Niobate (Adam Hilger, New York, 1990)

    Google Scholar 

  7. Y.N. Korkishko, V.A. Fedorov, Relationship between refractive indices and hydrogen concentration in proton exchanged LiNbO3 waveguides. J. Appl. Phys. 82(3), 1010 (1997)

    Article  Google Scholar 

  8. R. Hunsperger, Integrated Optics: Theory and Technology (Spinger, New York, 2009)

    Book  Google Scholar 

  9. R.G. Smith, D.B. Fraser, R.T. Denton, T.C. Rich, Correlation of reduction in optically induced refractive index inhomogeneity with OH content in LiTaO3 and LiNbO3. J. Appl. Phys. 39(10), 4600 (1968)

    Article  Google Scholar 

  10. J.M. Zavada, H.C. Casey, CH Chem and ALono, Correlation of refractive index profiles with substitutional hydrogen concentrations in annealed proton-exchanged LiNbO3 waveguides. Appl. Phys. Lett. 62(22), 2769 (1993)

    Article  Google Scholar 

  11. I. Nee, K. Buse, F. Avenmer, R.A. Rupp, M. Fally, R.P. May, Neutron diffraction from thermally fixed gratings in photorefractive lithium niobate crystals. Phys. Rev. B 60(14), R9896 (1999)

    Article  Google Scholar 

  12. R. Liyong, L. Liren, L. Dean, Z Jifeng andL Zhu, Recording and fixing dynamics of nonvolatile photorefractive holograms in LiNbO3:Fe: Mn crystals. Opt. Soc. Am. J. B 20(10), 2162–2173 (2003)

    Article  Google Scholar 

  13. L. Kovacs, M. Wohlecke, A. Jovanovic, K. Polgar, S. Kapphan, Infrared absorption study of the OH vibrational band in LiNbO3 crystals. J. Phys. Chem. Solids 52(6), 797 (1991)

    Article  Google Scholar 

  14. C.E. Rice, The structure and properties of Li1−xHxNbO3. J. Solid State Chem. 64(2), 188 (1986)

    Article  Google Scholar 

  15. T. Volk, M. Wohlecke, Lithium Niobate (Spinger, New York, 2008)

    Google Scholar 

  16. V. Bermudez, L. Huang, D. Hui, S. Field, E. Dieguez, Role of stoichiometric point defect in electric-field-poling lithium niobate. Appl. Phys. A 70, 591–594 (2000)

    Article  Google Scholar 

  17. V. Gopalan, T.E. Mitchell, K.E. Sicakfus, Switching kinetics of 180° domains in congruent LiNbO3 and LiTaO3 crystals. Solid State Commun. 109(2), 111–117 (1999)

    Article  Google Scholar 

  18. A.K. Bandyopadhyay, P.C. Roy, V. Gopalan, An approach to the Klein-Gordon equation for a dynamic study in ferroelectric materials. J. Phys. Condens. Matter 18(16), 4093 (2006)

    Article  Google Scholar 

  19. P. Giri, K. Choudhary, A. Dey, A. Biswas, A. Ghosal, A.K. Bandyopadhyay, Discrete energy levels of bright solitons in lithium niobate ferroelectrics. Phys. Rev. B 86(18), 184101 (2012)

    Article  Google Scholar 

  20. P. Giri, M.K. Mandal, Dark soliton based frequency dependent dielectric constant of ferroelectric materials. AIP Adv. 4, 107140 (2014)

    Article  Google Scholar 

  21. W.B. Yan et al., The H+ related defects in near-stoichiometric lithium niobate crystals investigated by domain reversal. Phys. Stat. Solidi 201(9), 2013–2020 (2004)

    Article  Google Scholar 

  22. H.H. Nahm, C.H. Park, Microscopic structure of hydrogen impurity in LiNbO3. Appl. Phys. Lett. 78(24), 3812 (2001)

    Article  Google Scholar 

  23. P.M. Morse, Diatomic molecules according to the wave mechanics II vibrational levels. Phys. Rev. 34(1), 57 (1929)

    Article  Google Scholar 

  24. H. Risken, The Fokker Planck Equation: Methods of Solution and Applications (Springer, New York, 1996)

    Book  Google Scholar 

  25. S. Viktor, L. Krisztian, K. Laszlo, T. Vicente, H. Alfonso, Vibrations of H+(D+) in stoichiometric LiNbO3 single crystal. J. Chem. Phys. 135(12), 124501 (2011)

    Article  Google Scholar 

  26. J.B. Bates, J.C. Wang, R.A. Perkins, Mechanisms for hydrogen diffusion in TiO2. Phys. Rev. B 19(8), 4130 (1979)

    Article  Google Scholar 

  27. F. Freytag, G. Corradi, M. Imlau, Atomic insight to lattice distortions caused by carrier self-trapping in oxide materials. Nat. Sci. Rep. 6, 36929 (2016)

    Article  Google Scholar 

  28. G.R. Paz-Pujait, D.D. Tuschel, S.T. Lee, L.M. Salter, Characterization of proton exchange lithium niobate waveguides. J. Appl. Phys. 76(7), 3981 (1994)

    Article  Google Scholar 

  29. H.C. Casey, C.H. Chen, J.M. Zavada, S.W. Novak, Analysis of hydrogen diffusion from proton-exchanged layers in LiNbO3. Appl. Phys. Lett. 63(6), 718 (1993)

    Article  Google Scholar 

  30. M.M. Howerton, W.K. Burns, P.R. Skeath, A.S. Greenblatt, Dependence of refractive index on hydrogen concentration in proton exchanged LiNbO3. IEEE J. Quantum Electron. 27(3), 593–601 (1991)

    Article  Google Scholar 

  31. A. Grone, S. Kapphan, Sharp temperature dependent OH/OD IR-absorption bands in nearly stoichiometric LiNbO3. J. Phys. Chem. Solids 56, 687–701 (1995)

    Article  Google Scholar 

  32. S. Klauer, M. Wohlecke, S. Kapphan, Influence of H-D isotopic substitution on the protonic conductivity of LiNbO3. Phys. Rev. B 45(6), 2786 (1992)

    Article  Google Scholar 

  33. W. Bollmann, Diffusion of hydrogen (OH− Ions) in LiNbO3 crystals. Phys. Stat. Sol. A 104(2), 643–648 (1987)

    Article  Google Scholar 

Download references

Funding

There is no external funding for this research work.

Author information

Authors and Affiliations

  1. Department of Physics, National Institute of Technology, Durgapur, 713209, India

    Pradipta Giri & M. K. Mandal

  2. School of Mines and Metallurgy, Kazi Nazrul University, Asansol, 713340, India

    A. Biswas

Authors
  1. Pradipta Giri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Biswas
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. K. Mandal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Biswas.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Giri, P., Biswas, A. & Mandal, M.K. Analysis of Substitutional Hydrogen Diffusional Coefficient in LiNbO3 under Anharmonic Potential. J. Inst. Eng. India Ser. D 102, 283–289 (2021). https://doi.org/10.1007/s40033-021-00275-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40033-021-00275-0

Keywords

Search

Navigation