Skip to main content
Log in

Entropic crossovers in superionic fluorites from specific heat

  • Short Communication
  • Published:
Ionics Aims and scope Submit manuscript

Abstract

Neutron scattering/diffraction experiments and atomistic simulations reveal that anions in fluorite superionic conductors show rapid disordering at a characteristic temperature T α, which is distinct from the superionic or λ transition temperature T λ that is associated with a quasi-divergent behavior of the thermodynamic response functions. We demonstrate that both crossovers are unmistakably captured by the variation of the ratio of specific heat to the temperature (c/T)—a surprisingly seldom-used thermodynamic metric representing the rate of change of entropy with temperature (ds/dT). With increasing temperature, c/T decreases and portrays a minimum near T α; it then increases and depicts a maximum near T λ. The minimum in c/T corresponds to the onset of superionic state characterized by a rapid increase in the ionic conductivity while the maximum represents a quasi-second-order thermodynamic phase transition. The simple c/T metric appears to be a useful experimental indicator for entropic crossovers that arise from complex disordering in a wider class of superionic conductors.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2

References

  1. Kamaya N, Homma K, Yamakawa Y, Hirayama M, Kanno R, Yonemura M, Kamiyama T, Kato Y, Hama S, Kawamoto K, Mitsui A (2011) A lithium superionic conductor. Nat Mater 10(9):682–686

    Article  CAS  Google Scholar 

  2. Nishimura S-i, Kobayashi G, Ohoyama K, Kanno R, Yashima M, Yamada A (2008) Experimental visualization of lithium diffusion in LixFePO4. Nat Mater 7(9):707–711

  3. Liang X, Wang L, Jiang Y, Wang J, Luo H, Liu C, Feng J (2015) In-channel and in-plane Li ion diffusions in the superionic conductor Li10GeP2S12 probed by solid-state NMR. Chem Mater 27(16):5503–5510

    Article  CAS  Google Scholar 

  4. Deng Y, Eames C, Chotard J-N, Lalére F, Seznec V, Emge S, Pecher O, Grey CP, Masquelier C, Islam MS (2015) Structural and mechanistic insights into fast lithium-ion conduction in Li4SiO4-Li3PO4 solid electrolytes. J Am Chem Soc 137(28):9136–9145

    Article  CAS  Google Scholar 

  5. Wang Y, Richards WD, Ong SP, Miara LJ, Kim JC, Mo Y, Ceder G (2015) Design principles for solid-state lithium superionic conductors. Nat Mater 14(10):1026–1031

    Article  CAS  Google Scholar 

  6. Hull S, Norberg ST, Ahmed I, Eriksson SG, Mohn CE (2011) High temperature crystal structures and superionic properties of SrCl2, SrBr2, BaCl2 and BaBr2. J Solid State Chem 184(11):2925–2935

    Article  CAS  Google Scholar 

  7. Hutchings MT, Clausen K, Dickens MH, Hayes W, Kjems JK, Schnabel PG, Smith C (1984) Investigation of thermally induced anion disorder in fluorites using neutron scattering techniques. J Phys C Solid State Phys 17(22):3903–3940

    Article  CAS  Google Scholar 

  8. Clausen K, Hayes W, Macdonald JE, Osborn R, Hutchings MT (1984) Observation of oxygen Frenkel disorder in uranium dioxide above 2000 K by use of neutron-scattering techniques. Phys Rev Lett 52(14):1238–1241

    Article  CAS  Google Scholar 

  9. Kuhn A, Duppel V, Lotsch BV (2013) Tetragonal Li10GeP2S12 and Li7GePS8—exploring the Li ion dynamics in LGPS Li electrolytes. Energy Environ Sci 6(12):3548–3552

    Article  CAS  Google Scholar 

  10. Annamareddy A, Eapen J (2015) Mobility propagation and dynamic facilitation in superionic conductors. J Chem Phys 143(19):194502

    Article  Google Scholar 

  11. Annamareddy VA, Nandi PK, Mei X, Eapen J (2014) Waxing and waning of dynamical heterogeneity in the superionic state. Phys Rev E 89(1):010301(R)

    Article  Google Scholar 

  12. Xu M, Ding J, Ma E (2012) One-dimensional stringlike cooperative migration of lithium ions in an ultrafast ionic conductor. Appl Phys Lett 101(3):031901

    Article  Google Scholar 

  13. Voronin BM, Volkov SV (2001) Ionic conductivity of fluorite type crystals CaF2, SrF2, BaF2, and SrCl2 at high temperatures. J Phys Chem Solids 62(7):1349–1358

    Article  CAS  Google Scholar 

  14. Gray-Weale A, Madden PA (2004) Dynamical arrest in superionic crystals and supercooled liquids. J Phys Chem B 108(21):6624–6633

    Article  CAS  Google Scholar 

  15. Dworkin AS, Bredig MA (1968) Diffuse transition and melting in fluorite and anti-fluorite type of compounds: heat content of potassium sulfide from 298 to 1260o K. J Phys Chem 72(4):1277–1281

    Article  CAS  Google Scholar 

  16. Hull S (2004) Superionics: crystal structures and conduction processes. Rep Prog Phys 67(7):1233–1314

    Article  CAS  Google Scholar 

  17. Gillan MJ (1986) Collective dynamics in superionic CaF2: I. Simulation compared with neutron-scattering experiment. J Phys C Solid State Phys 19(18):3391–3411

    Article  CAS  Google Scholar 

  18. Gillan MJ (1986) Collective dynamics in super-ionic CaF2: II. Defect interpretation. J Phys C Solid State Phys 19(19):3517–3533

    Article  CAS  Google Scholar 

  19. Roberts RB, White GK (1986) Thermal expansion of fluorites at high temperatures. J Phys C Solid State Phys 19(36):7167–7172

    Article  CAS  Google Scholar 

  20. Dickens MH, Hayes W, Hutchings MT, Smith C (1982) Investigation of anion disorder in PbF2 at high temperatures by neutron diffraction. J Phys C Solid State Phys 15(19):4043–4060

    Article  CAS  Google Scholar 

  21. Bonne RW, Schoonman J (1977) The ionic conductivity of beta lead fluoride. J Electrochem Soc 124(1):28–35

    Article  CAS  Google Scholar 

  22. Annamareddy A, Eapen J (2017) Disordering and dynamic self-organization in stoichiometric UO2 at high temperatures. J Nucl Mater 483:132–141

    Article  CAS  Google Scholar 

  23. Annamareddy A, Eapen J (2017) Low dimensional string-like relaxation underpins superionic conduction in fluorites and related structures. Sci Rep. doi:10.1038/srep44149

Download references

Acknowledgement

Support from US Department of Energy through the Nuclear Energy University Program (NEUP) is gratefully acknowledged.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jacob Eapen.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Eapen, J., Annamareddy, A. Entropic crossovers in superionic fluorites from specific heat. Ionics 23, 1043–1047 (2017). https://doi.org/10.1007/s11581-017-2007-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11581-017-2007-z

Keywords

Navigation