Semi-empirical description of the regularity of change in thermal conductivity of single crystals based on the example of a concentration series of Ba1–xLaxF2+x solid solutions
DOI:
https://doi.org/10.17308/kcmf.2026.28/13561Keywords:
Barium difluoride, Lanthanum, Solid solution, Defect clusters, Thermal conductivity, Semi-empirical modelAbstract
Purpose: To study the thermal conductivity of single crystals of a Ba1–xLaxF2+x solid solution and a semi-empirical description of changes in thermal conductivity depending on the lanthanum content.
Experimental: In the temperature range of 50–300 K, the thermal conductivity of single crystal Ba1–xLaxF2+x samples with lanthanum content from x = 0.001 to x = 0.300 was determined by the experimental method of long heat flow.
Conclusions: A monotonic concentration dependence of thermal conductivity has been revealed. A semi-empirical expression has been proposed to approximate the experimental values of thermal conductivity
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1. Schotanus P., Dorenbos P., van Eijk C. W. E., Lamfers H. J. Suppression of the slow scintillation light output of BaF2 crystals by La3+ doping. Nuclear Instruments and Methods in Physics Research. A. 1989;281(1): 162–166. https://doi.org/10.1016/0168-9002(89)91229-1
2. Herweg K., Nadig V., Schulz V., Gundacker S. On the prospects of BaF2 as a fast scintillator for Time-of-Flight positron emission tomography systems. IEEE Transactions on Radiation and Plasma Medical Sciences. 2023;7(3): 241–252. https://doi.org/10.1109/TRPMS.2023.3237254
3. Belov M. V., Zavertyaev M. V., Kozlov V. A., Tskhay V. S. Scintillation properties of electromagnetic calorimeter modules based on BaF2 crystals. Bulletin of the Lebedev Physics Institute. 2024;51(8): 273–277. https://doi.org/10.3103/S1068335624600475
4. Wojtowicz J., Glodoay J., Wisniewski D., Lempicki A. Scintillation mechanism in RE-activated fluorides. Journal of Luminescence. 1997;72–74: 731–733. https://doi.org/10.1016/S0022-2313(97)80790-9
5. Vladimirov S. V., Kaftanov V. S., Nilov A. F. ... Skvortsov V. N . Characteristics of BaF2 scintillation crystals. Atomic Energy.2001;90: 55–62. https://doi.org/10.1023/A: 1011391923801
6. Shendrik R., Radzhabov E., Myasnikova A., … Pankratov V. Ultrafast core-to-core luminescence in BaF2 – LaF3 single crystals. Scientific Reports. 2025;15: 26558. https://doi.org/10.1038/s41598-025-11505-w
7. Nepomnyashchikh A. I., Radzhabov E. A., Egranov A. V., Ivashechkin V. F. Luminescence of BaF2–LaF3. Radiation Measurements. 2001;33: 759–762. https://doi.org/10.1016/S1350-4487(01)00101-9
8. Radzhabov E. A., Shalaev A., Nepomnyashikh, A. I. Exciton luminescence suppression in BaF2–LaF3 solid solutions. Radiation Measurements. 1998;29(3-4): 307–309. https://doi.org/10.1016/S1350-4487(98)00048-1
9. Madirov E. I., Kuznetsov S. V., Konyushkin V. A., Busko D., Richards B. S., Turshatov A. Pushing the limits: down-converting Er3+-doped BaF2 single crystals with photoluminescence quantum yield surpassing 100%. Advanced Optical Materials. 2024;12(16): 2303094. https://doi.org/10.1002/adom.202303094
10. Kaminskii A. A. Laser cystals, their physics and properties. In: Springer Series in Optical Sciences. Berlin: Springer; 1990, vol. 14, 2nd ed. https://doi.org/10.1007/978-3-540-70749-3
11. Lu Z., Zhang Z., Jiang D., … Su L. Thermo-mechanical properties and laser-induced damage behaviors in NYCF and NYSF crystals with different orientations. Optics Express. 2025;33(16): 33153–33168. https://doi.org/10.1364/OE.566275
12. Kuznetsov S. V., Aleksandrov A. A., Fedorov P. P. Optical fluoride nanoceramics. Inorganic Materials. 2021; 57(6): 555–578. https://doi.org/10.1134/S0020168521060078
13. Sorokin N. I., Breiter M. W. Anionic conductivity and thermal stability of single crystals of solid solutions based on barium fluoride. Solid State Ionics. 1997;99(3-4): 241–250. https://doi.org/10.1016/S0167-2738(97)00190-2
14. Ivanov-Shits A. K., Sorokin N. I., Fedorov P. P., Sobolev B. P. Specific features of ion transport in nonstoichiometric fluorite-type Ba1–xRxF2+x (R=La−Lu phases). Solid State Ionics. 1989; 31(4): 269–280. https://doi.org/10.1016/0167-2738(89)90466-9
15. Preishuber-Pflűgl F., Bottke P., Pregartner V., Bitschnauc B., Wilkening M. Correlated fluorine diffusion and ionic conduction in the nanocrystalline F- solid electrolyte Ba0.6La0.4F2.4–19F T1(ρ) NMR relaxation vs. conductivity measurements. Physical Chemistry Chemical Physics. 2014;16(20): 9580–9590. https://doi.org/10.1039/C4CP00422A
16. Rammutla K. E., Comins J. D. High temperature raman scattering studies of Ba1–xLaxF2+x. Radiation Effects and Defects in Solids. 1999;150(1–4): 347–353. https://doi.org/10.1080/10420159908226255
17. Den Hartog H. W., Langevoort J. C. Ionic thermal current of concentrated cubic solid solutions of SrF2: LaF3 and BaF2: LaF3. Physical Review B. 1981;24(6): 3547–3554. https://doi.org/10.1103/PhysRevB.24.3547
18. Den Hartog H. W., Pen K. F., Meuldijk J. Defect structure and charge transport in solid solutions Ba1–xLaxF2+x. Physical Review B. 1983;28(10): 6031–6040. https://doi.org/10.1103/PhysRevB.28.6031
19. Laredo E., Suarez N., Bello A., Puma M., Figueroa D., Schoonman J. Dislocation polarization and space-charge relaxation in solid solutions Ba1–xLaxF2+x. Physical Review B. 1985;32(12): 8325–8331. https://doi.org/10.1103/Phys-RevB.32.8325
20. Wapenaar K. E. D., Koesveld J. L., Schoonmam J. Conductivity enhancement in fluorite-structured Ba1–xLaxF2+x solid solutions. Solid State Ionics. 1981;2(3): 145–154. https://doi.org/10.1016/0167-2738(81)90172-7
21. Ivanov-Shits A. K., Sorokin N. I., Fedorov P. P., Sobolev B. P. Specific features of ion transport in nonstoichiometric Sr1–xRxF2+x phases (R=La-Lu, Y) with the fluorite-type structure. Solid State Ionics. 1989;31(4): 253–268. https://doi.org/10.1016/0167-2738(89)90465-7
22. Trnovcova V., Sorokin N. I., Fedorov P. P., Krivandina E. A., Šramkova T., Sobolev B. P. Electrical properties of heavily doped fluorite-structured BaF2:RF3 (R=rare earth element, Y, Sc) single crystals. Ionics. 2000;6(5): 351–358. https://doi.org/10.1007/BF02374152
23. Munnangi R., Mohammad I., Fichtner M. Room temperature fluoride ion batteries. ECS Meeting Abstracts, Vol. MA2019-01, A02-Lithium Ion Batteries and Beyond. 346. https://doi.org/10.1149/MA2019-01/2/346
24. Rongeat C., Munnangi A. R., Witter R., Fichtner M. Nanostructured fluorite-type fluorides as electrolytes for fluoride ion batteries. The Journal of Physical Chemistry C. 2013;117(10): 4943–4950. https://doi.org/10.1021/jp3117825
25. Astruc A., Celerier S., Pavon E., Mamede A.-S., Delevoye L., Brunet S. Mixed Ba1-xLaxF2+x fluoride materials as catalyst for the gas phase fluorination of 2-chloropyridine by HF. Applied Catalysis B: Environmental. 2017;204: 107–118. https://doi.org/10.1016/j.apcatb.2016.11.019
26. Akchurin M. Sh., Gainutdinov R. V., Smolyanskii P. L., Fedorov P. P. Anomalously high fracture toughness of polycrystalline optical fluorite from the Suran deposit (South Urals). Doklady Physics. 2006;51(1): 10–12. https://doi.org/10.1134/S1028335806010034
27. Aminov L. K., Kurkin I. N., Kurzin S. P., Gromov I. A., Mamin G. V. Identification of the La6F37 cubooctahedral clusters in mixed crystals (BaF2)1−x(LaF3)x by the electron paramagnetic resonance method. Physics of the Solid State. 2007;49 (11): 2086–2090. https://doi.org/10.1134/S1063783407110121
28. Aminov L. K., Abdulsabirov R. Y., Korableva S. L., Kurkin I. N., Kurzin S. P. EPR of rare-earth ion clusters in mixed crystals Ba1–xLaxF2+x doped with Yb3+ Ion. Applied Magnetic Resonance. 2005;29(4): 561–568. https://doi.org/10.1007/BF03166332
29. Fedorov P. P. Association of point defects in non-stoichiometric M1–xRxF2+x fluorite-type solid solutions. Butlletí de les Societats Catalanes de Física, Química, Matemàtiques i Tecnologia. 1991;12(2): 349–381. Режим доступа: https://raco.cat/index.php/ButlletiSCFQMT/article/view/221696
30. Moore D. S., Wright J. C. Laser spectroscopy of defect chemistry in CaF2:Er. The Journal of Chemical Physics. 1981;74: 1626–1636. https://doi.org/10.1063/1.441303
31. Kazanskii S. A., Ryskin A. I., Nikiforov A. E., Zaharov A. Y., Ougrumov M. Y., Shakurov G. S. EPR spectra and crystal field of hexamer rare-earth clusters in fluorites. Physical Review B. 2005;72(1): 014127. https://doi.org/10.1103/PhysRevB.72.014127
32. Liu K., Bian G., Zhang Z., Ma F., Su L. Modelling and analyzing the glass-like heat transfer behavior of rare-earth doped alkaline earth fluoridecrystals. CrystEngComm. 2022;24(37): 6468–6476. https://doi.org/10.1039/D2CE00698G
33. Popov P. A., Shchelokov A. V., Fedorov P. P. Numerical model of temperature-dependent thermal conductivity in M1–xRxF2+x heterovalent solid Solution nanocomposites, where M stands for alkaline-earth metals and R for rare-earth Metals. Nanosystems: Physics, Chemistry, Mathematics. 2024;15(2): 255–259. https://doi.org/10.17586/2220-8054-2024-15-2-255-259
34. Kaczmarek S. M., Tsuboi T., Ito M., Boulon G., Leniec G. Optical study of Yb 3+/Yb2+ conversion in CaF2 crystals. Journal of Physics: Condensed Matter. 2005;17(25): 3771–3786. https://doi.org/10.1088/0953-8984/17/25/005
35. Angervaks A. E., Shcheulin A. S., Ryskin A. I., … Fedorov P. P. Di- and trivalent ytterbium distributions along a melt-grown CaF2 crystal. Inorganic Materials. 2014;50(7): 733–737. https://doi.org/10.1134/S0020168514070024
36. Savchuk R. N., Omelchuk A. A., Kompanichenko N. M., Nagorny P. G. Reduction of rare earth element fluorides with zirconium. Russian Journal of Inorganic Chemistry. 2003;48(10): 1454–1458. Available at: https://elibrary.ru/item.asp?id=27970487
37. Azarov V. V., Skorobogatov B. S. Reduction of rareearth ions in LaF3 single crystals. Izvestiya Akademii Nauk SSSR. Neorganicheskiye Materialy (Inorganic Materials) 1968;4(10): 1748–1749.
38. Kaminskii A. A., Osico V. V., Prokhorov A. M., Voronko Yu. K. Spectral investigation of the timulated radiation of Nd3+ in CaF2–YF3. Physics Letters. 1966;22(4): 419–421. https://doi.org/10.1016/0031-9163(66)91208-X
39. Kitajima S., Yamakado K., Shirakawa A., Ueda K., Ezura Y., Ishizawa H. Yb3+-doped CaF2–LaF3 ceramics laser. Optics Letters. 2017;42(9): 1724–1727. https://doi.org/10.1364/OL.42.001724
40. Novikov V. V., Matovnikov A. V., Avdashchenko D. V., … Shevelkov A. V. Low-temperature structure and lattice Dynamics of the thermoelectric clathrate Sn24P19.3I8. Journal of Alloys and Compounds. 2012;520: 174–179. https://doi.org/10.1016/j.jallcom.2011.12.171
41. Popov P. A., Sidorov А. А., Kul’chenkov Е. А., … Fedorov P. P. Thermal conductivity and expansion of PbF2 single crystal. Ionics. 2017;23(1): 233–239. https://doi.org/10.1007/s11581-016-1802-2
42. Sobolev B. P., Tkachenko N. L. Phase diagrams of BaF2-(Y, Ln)F3 systems. Journal of the Less Common Metals. 1982;85: 155–170. https://doi.org/10.1016/0022-5088(82)90067-4
43. Sidorov A. A., Popov P. A., Aksenov S. V., Begunov A. I., Fedorov P. P. Thermal expansion of solid solutions based on calcium and barium fluorides. Inorganic Materials. 2013;49(5): 525–527. https://doi.org/10.1134/S0020168513040146
44. White G. K. Thermal eExpansion at low temperatures of the alkaline earth fluorides and PbF2. Journal of Physics C: Solid State Physics.1980;13(26): 4905–4913. https://doi.org/10.1088/0022-3719/13/26/012
45. Cahill D. G., Pohl R. O. Low-energy excitations in the mixed crystal Ba1–xLaxF2+x. Physical Review B. 1989;39: 10477–10480. https://doi.org/10.1103/PhysRevB.39.10477
46. Cahill D. G., Watson S. K., Pohl R. O. Lower limit to the thermal conductivity of disordered crystals. Physical Review B, 1992;46(10): 6131–6140. https://doi.org/10.1103/PhysRevB.46.6131
47. Popov P A., Moiseev N. V., Filimonova A. V., … Mironov I. Thermal conductivity of LaF3-based single crystals and ceramics. Inorganic Materials. 2015;48(3): 304–308. https://doi.org/10.1134/S0020168512030120
48. Popov P. A., Fedorov P. P., Kuznetsov S. V., Konyushkin V. A., Osiko V. V., Basiev T. T. Thermal conductivity of single crystals of Вa1-xYbxF2+x solid solution. Doklady Physics. 2008;53(7): 353–355. https://doi.org/10.1134/S1028335808070045
49. Moiseev N. V., Popov P. A., Reiterov V.M., Fedorov P. P. Heat Capacity and Thermodynamic Functions of Ba0.70La0.30F2.30 heterovalent solid solution. Condensed Matter and Interphases. 2010;12(3): 243–246. Available at: https://journals.vsu.ru/kcmf/article/view/1121
50. Andeen N. H., Clausen K. N., Kjems J. K., Schoonman J. A Study of the Disorder in Heavy Doped Ba1−xLaxF2+x by Neutron Scattering. Journal of Physics C: Solid State Physics. 1986;19(14): 2377–2389. https://doi.org/10.1088/0022-3719/19/14/004
51. Popov P. A., Fedorov P. P., Konyushkin V. A. Thermal conductivity of single crystals of Ba1-xRxF2+x (R=La, Ce, Nd, Gd) solid solutions. Crystallography Reports. 2017;62(2): 283–287. https://doi.org/10.1134/S1063774517020225
52. Popov P. A., Fedorov P. P., Konyushkin V. A., Nakladov A. N., Kuznetsov S. V., Osiko V. V., Basiev T. T. Thermal conductivity of single crystals of Sr1-xYbxF2+x solid solution. Doklady Physics. 2008;53(8): 413–415. https://doi.org/10.1134/S1028335808080016
53. Popov P. A., Fedorov P. P., Kuznetsov S. V., Konyushkin V. A., Osiko V. V., Basiev T. T. Thermal conductivity of single crystals of Ca1–xYbxF2+x solid solutions. Doklady Physics. 2008;53(4): P. 198-200. https://doi.org/10.1134/S102833580804006X
54. Popov P. A., Fedorov P. P., Osiko V. V., Reiterov V. M., Garibin E. A., Demidenko A. A., Mironov I. A. Thermal conductivity of single crystals of Ca1-хErхF2+х and Ca1-хTmхF2+х solid solutions. Doklady Physics. 2012;57(3): 97–99. https://doi.org/10.1134/S1028335812030111
55. Popov P. A., Fedorov P. P., Garibin E. A., Smirnov A. N., Gusev P. E., Krutov M. A. Thermal conductivity of Ca1-хHoхF2+х optical ceramics. Inorganic Materials. 2012;48(8): 857–860. https://doi.org/10.1134/S002016851207014X
56. Popov P. A., Fedorov P. P., Osiko V. V. Thermal conductivity of single crystals of the Ca1-xYxF2+x solid solution. Doklady Physics. 2014;59(5): 199–202. https://doi.org/10.1134/S1028335814050036
57. Popov P. A., Fedorov P. P., Konyushkin V. A. Heat conductivity of Ca1-xRxF2+x (R = La, Ce, Pr, 0 ≤ x ≤ 0.25) heterovalent solid solutions. Crystallography Reports. 2015; 60(5): 744–748. https://doi.org/10.1134/S1063774515050107
58. Sergeev O. A., Shashkov A. G., Umanskii A. S. Thermophysical properties of quartz glass. Journal of Engineering Physics. 1982;43(6): 1375–1383. https://doi.org/10.1007/BF00824797
59. Wapenaar K. E. D., Van Koesveld J. L., Schoonman J. Conductivity enhancement in fluorite-structured Ba1−xLaxF2+x solid solutions. Solid State Ionics. 1981;2(3): 145–154. https://doi.org/10.1016/0167-2738(81)90172-7
60. Trnovcova V., Garashina L. S., Skubla A., … Sobolev B. P. Structural aspects of fast ionic conductivity of rare earth fluorides. Solid State Ionics. 2003;157(1-4): 195–201. https://doi.org/10.1016/S0167-2738(02)00209-6
61. Hull S. Superionics: crystal structures and conduction. Reports on Progress in Physics. 2004;67(7): 1233–1314. https://doi.org/10.1088/0034-4885/67/7/R05
62. Düvel A., Bednarcik J., Šepelák V., Heitjans P. Mechanosynthesis of the fast fluoride ion conductor Ba1–xLaxF2+x: from the fluorite to the tysonite structure. The Journal of Physical Chemistry С. 2014;118(13): 7117–7129. https://doi.org/10.1021/jp410018t
63. Sobolev B. P., Sorokin N. I., Bolotina N. B. Nonstoichiometric single crystals M1–xRxF2+x and R1–yMyF3–y (M = Ca, Sr, Ba: R = rare earth elements) as fluorine-ionic conductive solid electrolytes. In: Photonic & Electronic Properties of Fluoride Materials. Tressaud A., Poeppelmeier K. (ed.). Elsevier; 2016. pp. 465–491. https://doi.org/10.1016/B978-0-12-801639-8.00021-0
64. Gschwind F., Rodrigues-Garsia G., … Hörmann N. Fluoride ion batteries: theoretical performance, safety, toxicity, and a combinatorial screening of new electrodes. Journal of Fluorine Chemistry. 2016;182: 76–90. https://doi.org/10.1016/j.jfluchem.2015.12.002
65. Cheng X., Wang S., Lin X. Preparation and electrochemical properties of Ba1-xLaxF2+x fluoride electrolyte. IOP Conference Series: Materials Science and Engineering. 2019;678: 012148. https://doi.org/10.1088/1757-899X/678/1/012148
66. Nikolaichik V. I., Sobolev B. P., Sorokin N. I., Avilov A. S. Electron diffraction study and ionic conductivity of fluorite Ba1-xLaxF2+x and tysonite La1–yBayF3–y phases in the BaF2-LaF3 system. Solid State Ionics. 2022;386: 116052. https://doi.org/10.1016/j.ssi.2022.116052
67. Sorokin N. I. Concentration and mobility of charge carriers in the superionic conductor Ba1–xLaxF2+x (0.05 ≤ x ≤ 0.5). Physics of the Solid State. 2024;66(1): 53–58https://doi.org/10.61011/PSS.2024.01.57854.253 Available at: https://journals.ioffe.ru/articles/viewPDF/57854
68. Andersen N. H., Clausen K. N., Kjems J. K., Schoonman J. A study of the disorder in heavily doped Ba1–xLaxF2+x by neutron scattering, ionic conductivity and specific heat measurements. Journal of Physics C: Solid State Phys ics. 1986; 19(14): 2377–2389. https://doi.org/10.1088/0022-3719/19/14/004
69. Fedorov P. P., Sorokin N. I., Popov P. A. Inverse correlation between the ionic and thermal conductivities of single crystals of M1–xRxF2+x (M = Ca, Ba; R–rare-earth element) fluorite solid solutions. Inorganic Materials. 2017; 53(6): 626–632. https://doi.org/10.1134/S0020168517060036
70. Sorokin N. I., Karimov D. N. Crystallophysical model of ion transport in single crystals of Ba1−xLaxF2+x and Ca1–xYxF2+x superionics сonductors. Physics of the Solid State. 2021;63(12): 1821–1832. https://doi.org/10.1134/S106378342110036X
71. Popov P. A., Shchelokov A. V., Konyushkin V. A., Nakladov A. N., Fedorov P. P. Application of the numerical model of temperature-dependent thermal conductivity in Ca1–xYxF2+x heterovalent solid solution nanocomposites. Nanosystems: Physics, Chemistry, Mathematics. 2024;16(1): 67–73. https://doi.org/10.17586/2220-8054-2025-16-1-67-73
72. Shannon R. D. Revised effective ionic radii and systematic studies of interaction distance in halides
end chalcogenides. Acta Crystallographica Section A. 1976;32(5): 751–767. https://doi.org/10.1107/S0567739476001551
73. Popov P. A., Shchelokov A. V., Zentsova A. A., Fedorov P. P. Thermal conductivity of single crystals of Ca1–x–ySrxNdyF2+y solid solution. Inorganic Materials. 2024;60(5): 590–600. https://doi.org/10.31857/S0002337X24050082
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