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- 2. Global RE production and demand University of Belgrade OMAS group omasgroup.org
- 3. Rare-Earth elements University of Belgrade OMAS group omasgroup.org
- 4. Abundance University of Belgrade OMAS group omasgroup.org
- 5. Abudance & Usage Phosphors 5% University of Belgrade OMAS group omasgroup.org
- 6. Lanthanide Electronic Configurations • La = [Xe] 5d1 6s2 • Ce = [La] 4f1 . . . • Lu = [La] 4f14 • La3+ = [Xe] • Ce3+ = [Xe] 4f1 . . . • Lu3+ = [Xe] 4f14 - 3 e- University of Belgrade OMAS group omasgroup.org
- 7. Trivalent Lanthanides • Sharp emission & absorption lines • Transition energies independent on host E-levels independent • Long lifetimes of emitting levels • High intrinsic quantum yields A complete 4fn energy level diagram for all trivalent lanthanide ions, P.Peijzel, A. Meijerink, R. Wegh, M.F. Reid, G.W. Burdick, doi: 10.1016/j.jssc.2004.07.046
- 8. Ln3+ Energy Levels F r e e i o n Terms 7F 5L 5D 2S+1L(τ) Levels 7FJ 5DJ 0 1 2 3 4 2S+1LJ Sublevels 2S+1LJ(MJ) 4f55d1 4f6 Conf. [Xe]4f6 ℋ = ℋfree + 𝐵𝑞 𝑘𝐶𝑞 (𝑘) (𝑖) ~20000 cm-1 }~1000 cm-1 ~100 cm-1 e-e s-o CF p-e University of Belgrade OMAS group omasgroup.org
- 9. Intensities University of Belgrade OMAS group omasgroup.org
- 10. Judd-Ofelt theory – Prehistory • RE discovery: 18th – 20th century • 1937. – Van Vleck “The Puzzle of RE spectra in solids” • 1940s - Racah algebra – powerful set of tools that made possible many complex spectroscopic calculations (e.g. free ion energy levels). • 1959. - Computers – tabulation of angular momentum coupling coefficients. • 1962. – The solution to the “RE puzzle” simultaneously by Judd and Offelt. University of Belgrade OMAS group omasgroup.org
- 11. 1962.- • “The two papers of 1962 represent the paradigm that has dominated all future work…up to the present time” – B. Wybourne • Popularity rise • Very complex QM theory • Ability to predict oscillator strengths, branching ratios, lifetimes, quantum efficiencies by using only 3 parameters! 29 81 105 234 341 456 755 1200 1710 2820 3470 5490 0 1000 2000 3000 4000 5000 6000 No. of papers University of Belgrade OMAS group omasgroup.org
- 12. Ωλ Parametrization Application University of Belgrade OMAS group omasgroup.org
- 13. Ab initio Parametrization • Ω𝜆 = 2𝜆 + 1 𝑝 𝑡=1,3,5 𝐴𝑡𝑝 2 2𝑡+1 𝑌 2 𝑡, 𝜆 • Atp – parameters of the static CF expansion • Intensities of 4f-4f Transitions in Glass Materials, O.L. Malta, L.D. Carlos, doi: 10.1590/S0100- 40422003000600018 • Judd-Ofelt theory: Principles and Practices, B.M. Walsh, doi: 10.1007/1-4020-4789-4_21 • Judd-Ofelt Theory - The Golden (and the Only One) Theoretical Tool of f-Electron Spectroscopy, L. Smentek, 10.1002/9781118688304.ch10 • Spectral Intensities of f-f transitions, C.G. Walrand, K. Binnemans, doi: 10.1016/S0168- 1273(98)25006-9 • Ab-initio calculations of Judd-Ofelt intensity parameters for transitions between crystal-field levels, J.Wen et al., doi: 10.1016/j.jlumin.2013.10.055 University of Belgrade OMAS group omasgroup.org
- 14. Parametrization from Absorption • M. Helhen, M. Brik, K. Kramer, 50th anniversary of the Judd-Ofelt theory: An experimentalist’s view of the formalism and its application, doi: 10.1016/j.jlumin.2012.10.035 • 𝑓 exp = 4.319 ∙ 10−9 mol∙cm 𝐿 𝜀 𝜈 𝑑𝜈 • 𝑓 𝑎𝑏𝑠 = 8𝜋2 𝑚𝑒 3ℎ 𝜈 2𝐽+1 𝜒𝐸𝐷 𝑎𝑏𝑠 𝑛 𝜆=2,4,6 𝜴𝝀 𝑙𝑁 𝑆𝐿𝐽 𝑈𝜆 𝑙𝑁 𝑆′ 𝐿′ 𝐽′ 2 + ℎ𝜈 6𝑚𝑒𝑐2 𝑛 2𝐽+1 𝑙𝑁 𝑆𝐿𝐽 𝐿 + 𝑔𝑆 𝑙𝑁 𝑆′ 𝐿′ 𝐽′ 2 • RELIC software • Problems: “This method has two drawbacks: the density of ions in the sample must be accurately measured, and absorption can only be performed on single crystals and glasses but not on crystalline powders”, Blasse, doi: 10.1063/1.457106 University of Belgrade OMAS group omasgroup.org
- 15. Parametrization from Excitation or DR • Determination of Judd-Ofelt intensity parameters from the excitation spectra for rare-earth doped luminescent materials, W. Luo et al., doi: 10.1039/b921581f • 𝑆𝑒𝑥 = 𝐶 𝜆𝜒 Γ𝑒𝑥, 𝑆𝑡ℎ = 𝜆=2,4,6 Ω𝜆 𝑙𝑁𝑆𝐿𝐽 𝑈𝜆 𝑙𝑁𝑆′𝐿′𝐽′ 2 ⇒ Ω2: Ω4: Ω6 • For absolute values calibration is needed! • 𝜏𝑟 −1 = 𝐴𝐽′ • Problem: Assumption that the non-radiative lifetime of the used level is 0! • Xue et al. Validity of Judd-Ofelt spectroscopy based on diffuse reflectance spectrum and fluorescence lifetime of phosphor, doi: 10.1016/j.jlumin.2020.117304 University of Belgrade OMAS group omasgroup.org
- 16. Parametrization from Emission: Gd3+ • The spectroscopy of Gd3+ in yttriumoxychloride: Judd-Ofelt parameters from emission data, J. Sytsma, G.F. Imusch, G. Blasse, doi: 10.1063/1.457106 • Similar to excitation, but by using AJ’ 𝐴𝑆𝐿𝐽→𝑆′𝐿′𝐽′ = 64𝜋4𝜈𝑆𝐿𝐽→𝑆′𝐿′𝐽′ 3 3ℎ 2𝐽 + 1 𝜒𝐸𝐷𝐷𝐸𝐷 + 𝜒𝑀𝐷𝐷𝑀𝐷 𝜏𝑅 = 1/ 𝐴𝑆𝐿𝐽→𝑆′𝐿′𝐽′ University of Belgrade OMAS group omasgroup.org
- 17. Parametrization from Emission: Eu3+ - Introduction • Krupke, William F. "Optical absorption and fluorescence intensities in several rare-earth-doped Y2O3 and LaF3 single crystals." Physical Review 145.1 (1966): 325. • MD – host independent – can be used for calibration. • 5D0→7F1 • Judd-Ofelt parametrization from emission spectra: The case study of the Eu3+ 5D1 emitting level, A. Ćirić, S. Stojadinović, M.G. Brik, M.D. Dramićanin, doi: 10.1016/j.chemphys.2019.110513 • New: 5D1→7F0 University of Belgrade OMAS group omasgroup.org
- 18. Parametrization from Emission: Eu3+ 𝐴𝑆𝐿𝐽→𝑆′𝐿′𝐽′ = 64𝜋4𝜈𝑆𝐿𝐽→𝑆′𝐿′𝐽′ 3 3ℎ 2𝐽 + 1 𝜒𝐸𝐷𝐷𝐸𝐷 + 𝜒𝑀𝐷𝐷𝑀𝐷 Baricenter Local field correction Dipole strength 𝐼𝑆𝐿𝐽→𝑆′𝐿′𝐽′ = 𝑖𝑆𝐿𝐽→𝑆′𝐿′𝐽′ 𝜈 𝑑𝜈 = ℎ𝜈𝑆𝐿𝐽→𝑆′𝐿′𝐽′𝑁𝑆𝐿𝐽𝐴𝑆𝐿𝐽→𝑆′𝐿′𝐽′ Population 𝐼𝜆 𝐼𝑀𝐷 = 𝜈𝜆𝐴𝜆 𝜈𝑀𝐷𝐴𝑀𝐷 = 𝜈𝜆 𝜈𝑀𝐷 4 𝜒𝐸𝐷𝐷𝐸𝐷 𝜆 𝜒𝑀𝐷𝐷𝑀𝐷 𝐷𝐸𝐷 𝜆 = 𝑒2 Ω𝜆𝑈𝜆 Ω𝜆 = 𝐷𝑀𝐷 𝑒2𝑈𝜆 𝜈𝑀𝐷 𝜈𝜆 4 9𝑛𝑀𝐷 3 𝑛𝜆 𝑛𝜆 2 + 2 2 𝐼𝜆 𝐼𝑀𝐷 RME 𝐴𝜆 = 64𝜋4 𝜈𝜆 3 3ℎ 𝜒𝐸𝐷𝐷𝐸𝐷 𝜆 , 𝜆 = 2,4,6 𝐴𝑀𝐷 = 64𝜋4 𝜈𝑀𝐷 3 3ℎ 𝜒𝑀𝐷𝐷𝑀𝐷 University of Belgrade OMAS group omasgroup.org
- 19. Parametrization from Emission: Eu3+ - Software • Judd-Ofelt from emission Spectra: JOES • All that is needed is single emission spectrum • Choose material from the list of >150 different hosts or • Enter refractive index values manually • And outputs the results to a text file Judd-Ofelt Parameters: Ω2 = 1.1465194020534921E-19 cm² Ω4 = 2.9751146626870955E-20 cm² Ω6 = NaN cm² == Derived Quantities == Radiative Transition Probabilities A(5D0->7F1) = 68.17799738106247 s^-1 A(5D0->7F2) = 490.78769879104266 s^-1 A(5D0->7F4) = 63.78022107243416 s^-1 A(5D0->7F6) = NaN s^-1 Experimental Branching Ratios and Theoretical Branching Ratios β(5D0->7F1) = 0.11452264749042913; 0.10947963767105741 β(5D0->7F2) = 0.7938046817756628; 0.7881026357629585 β(5D0->7F4) = 0.09167267073390804; 0.10241772656598405 β(5D0->7F6) = 0.0; 0.0 Barycenters v(5D0->7F1) = 16858.597021525726 cm^-1 v(5D0->7F2) = 16232.818864281908 cm^-1 v(5D0->7F4) = 14425.398497300715 cm^-1 v(5D0->7F6) = NaN cm^-1 Total Radiative transition probability = 622.7459172445393 s^-1 Nonradiative transition probability = 0.0 s^-1 Lifetimes Theoretical radiative lifetime = 0.0016530641897090424 s Calculated radiative lifetime = 0.0016057913385039838 s DOWNLOAD from: https://omasgroup.org/joes-software/ Assistance: aleksandar.ciric@ff.bg.ac.rs
- 20. Nanomaterials • Correction for nanocrystals << λ • 𝑛𝑒𝑓𝑓 = 𝑛 𝜆 𝑛𝑝𝑥 + 1 − 𝑥 𝑛𝑚𝑒𝑑 • 𝑥 – filling factor – fraction of space occupied by the nanoparticles • 𝑛 𝜆 𝑛𝑝 - refractive index of nanoparticles as they would be in bulk • 𝑛𝑚𝑒𝑑 - refractive index of surrounding media (e.g. 𝑛𝑎𝑖𝑟 ≈ 1) University of Belgrade OMAS group omasgroup.org
- 21. Luminescence thermometry Steady State Luminescence Intensity Ratio (LIR) Bandshift Bandwidth Time Resolved Lifetime & Risetime Phase-shift University of Belgrade OMAS group omasgroup.org
- 22. Luminescence Intensity Ratio (LIR) The most widely used method! IH IL LI R 𝐿𝐼𝑅 = 𝐼𝐻 𝐼𝐿 = 𝑁𝐻 𝑁𝐿 = 𝑔𝐻 𝑔𝐿 𝑒−Δ𝐸 𝑘𝑇 = 𝐵𝑒−Δ𝐸/𝑘𝑇 University of Belgrade OMAS group omasgroup.org
- 23. LIR & Ln • Abundance of sharp emissions to chose from, from UV to IR! • Many of them are intense! • Many well thermalized levels!
- 24. Judd-Ofelt and LIR: Acknowledgments • Can JO be applied to LIR thermometry? • Upconverting Nanoparticles Working As Primary Thermometers in Different Media, S. Balabhadra, M.L. Debasu, C.Brites, R.Ferreira, L.D. Carlos, doi:10.1021/acs.jpcc.7b04827 • A Novel Multifunctional Upconversion Phosphor: Yb3+/Er3+ Codoped La2S3, Y.Yang et al., doi: 10.1111/jace.12822 University of Belgrade OMAS group omasgroup.org
- 25. Judd-Ofelt and LIR 𝐿𝐼𝑅 = 𝐼𝐻 𝐼𝐿 𝐴𝑆𝐿𝐽→𝑆′𝐿′𝐽′ = 64𝜋4𝜈𝑆𝐿𝐽→𝑆′𝐿′𝐽′ 3 3ℎ 2𝐽 + 1 𝜒𝐸𝐷𝐷𝐸𝐷 + 𝜒𝑀𝐷𝐷𝑀𝐷 𝐵 = 𝑔𝐻ℎ𝜈𝐻𝐴𝐻 𝑔𝐿ℎ𝜈𝐿𝐴𝐿 𝐵 = 𝜈𝐻 𝜈𝐿 4 𝜒𝐸𝐷 𝐻 𝐷𝐸𝐷 𝐻 + 𝜒𝑀𝐷 𝐻 𝐷𝑀𝐷 𝐻 𝜒𝐸𝐷 𝐿 𝐷𝐸𝐷 𝐿 + 𝜒𝑀𝐷 𝐿 𝐷𝑀𝐷 𝐿 𝐷𝐸𝐷 𝜆 = 𝑒2 𝜆 Ω𝜆𝑈𝜆 Uλ and DMD are tabulated and host independent = 𝑔𝐻ℎ𝜈𝐻𝐴𝐻 𝑔𝐿ℎ𝜈𝐿𝐴𝐿 𝑩 𝑒− Δ𝐸 𝑘𝑇 = ℎ𝜈𝐻𝑁𝐻𝐴𝐻 ℎ𝜈𝐿𝑁𝐿𝐴𝐿 = 𝐼 = ℎ𝜈𝑁𝐴, 𝑁𝐻 𝑁𝐿 = 𝑔𝐻 𝑔𝐿 𝑒− Δ𝐸 𝑘𝑇 University of Belgrade OMAS group omasgroup.org
- 26. Figures of Merit via Ωλ 𝑆 𝑇 = Δ𝐸 𝑘𝑇2 𝐵 exp − Δ𝐸 𝑘𝑇 = Δ𝐸 𝑘𝑇2 𝜈𝐻 𝜈𝐿 4 𝜒𝐸𝐷 𝐻 𝐷𝐸𝐷 𝐻 + 𝜒𝑀𝐷 𝐻 𝐷𝑀𝐷 𝐻 𝜒𝐸𝐷 𝐿 𝐷𝐸𝐷 𝐿 + 𝜒𝑀𝐷 𝐿 𝐷𝑀𝐷 𝐿 exp − Δ𝐸 𝑘𝑇 𝑆max = 4𝑘 𝑒2Δ𝐸 𝜈𝐻 𝜈𝐿 4 𝜒𝐸𝐷 𝐻 𝐷𝐸𝐷 𝐻 + 𝜒𝑀𝐷 𝐻 𝐷𝑀𝐷 𝐻 𝜒𝐸𝐷 𝐿 𝐷𝐸𝐷 𝐿 + 𝜒𝑀𝐷 𝐿 𝐷𝑀𝐷 𝐿 Δ𝑇 = 𝑘𝑇2 𝜎 𝜒𝐸𝐷 𝐿 𝐷𝐸𝐷 𝐿 + 𝜒𝑀𝐷 𝐿 𝐷𝑀𝐷 𝐿 Δ𝐸 𝜒𝐸𝐷 𝐻 𝐷𝐸𝐷 𝐻 + 𝜒𝑀𝐷 𝐻 𝐷𝑀𝐷 𝐻 exp − Δ𝐸 𝑘𝑇 An Extension of the Judd-Ofelt theory to the field of lanthanide thermometry, A. Ćirić, S. Stojadinović, M.D. Dramićanin, doi: 10.1016/j.jlumin.2019.116749 University of Belgrade OMAS group omasgroup.org
- 27. Significance • Ωλ is easier to obtain (single spectrum @ RT) • Large number of Ωλ in literature • Largest #: Spectral Intensities of f-f transitions, C.G. Walrand, K. Binnemans, doi: 10.1016/S0168-1273(98)25006-9 JO-LIR Experimental Setup Price Low High Speed High Low Knowledge Level Mid High Accuracy Mid High
- 28. Explicit equations for each Ln3+ Sensing Temperature via downshifting emissions of of lanthanide-doped metal oxides and salts. A review, M.D. Dramićanin, doi: 10.1088/2050- 6120/4/4/042001 An Extension of the Judd-Ofelt theory to the field of lanthanide thermometry, A. Ćirić, S. Stojadinović, M.D. Dramićanin, doi: 10.1016/j.jlumin.2019.116749
- 29. JOLIR applet Magnetic dipole and electric quadrupole transitions in the trivalent lanthanide series: Calculated emission rates and oscillator strengths, doi: 10.1103/PhysRevB.86. 125102 https://omasgroup.org/jolir-interactive-software/ University of Belgrade OMAS group omasgroup.org
- 30. Testing on Y2O3:Eu3+ • LIR of 5D1→7F1,2 and 5D0→7F1,2,4 • 𝐿𝐼𝑅 = 𝐶 𝛼𝐴𝑅+𝑀𝜌𝑔2𝑛𝑝 𝛽𝐴𝑅+𝑀𝜌𝑔1 1+𝑛 𝑝 • R. Geitenbeek, H.W. de Wijn, A. Meijerink, doi: 10.1103/PhysRevApplied. 10.064006 University of Belgrade OMAS group omasgroup.org
- 31. Dual-excited single band LIR • A.Souza,…, R. Ferreira, L.D. Carlos, O.L. Malta, High-sensitive Eu3+ ratiometric thermometers based on excited state absorption with predictable calibration, doi: 10.1039/C6NR00158K • At 0 K all optical centers are at ground. • T > 0K : thermal population. • Excitation from Ex1 and Ex2. • Single emission is monitored. • LIR of two emissions by excitations from Ex1 and Ex2. • Dual-excited – much larger ΔE larger Sr Ex1 Ex2 Em University of Belgrade OMAS group omasgroup.org IEx1 IEx2 𝐿𝐼𝑅 = 𝐼𝐸𝑥1 𝐼𝐸𝑥2 } ΔE
- 32. How? Optical centers redistribution • Eu3+ ion example. • 7FJ are thermally excited. • Number of optical centers follows Boltzmann distribution. • Excitation can be executed on higher levels of the ground multiplet. 𝑋𝐴(𝑇) = 𝑁𝐴 𝑁 = 𝑔𝐴 exp(− 𝐸𝐴 𝑘𝑇) 𝑔𝑖 exp(− 𝐸𝑖 𝑘𝑇) 𝑖 University of Belgrade OMAS group omasgroup.org
- 33. How? Excitations and emission • Excitations from 7F1 and 7F2 • Monitor emission to 7F4 University of Belgrade OMAS group omasgroup.org
- 34. Judd-Ofelt model • Prediction of the B parameter. • 𝐷𝐸𝐷 𝜆 = 𝑒2 Ω𝜆𝑈𝜆 • 𝐷𝑀𝐷 = 9.6 ∙ 10−42 𝑒𝑠𝑢2 𝑐𝑚2 • ∆E can be obtained from spectrum. 𝐿𝐼𝑅 = 𝐼1 𝐼2 = 𝐵 exp Δ𝐸 𝑘𝑇 𝐼𝑆𝐿𝐽→𝑆′𝐿′𝐽′ = ℎ𝜈𝑆𝐿𝐽→𝑆′𝐿′𝐽′𝑁𝑆𝐿𝐽𝐴𝑆𝐿𝐽→𝑆′𝐿′𝐽′ 𝐴𝜆 = 64𝜋4𝜈𝜆 3 3ℎ 𝜒𝐸𝐷𝐷𝐸𝐷 𝜆 𝐴𝑀𝐷 = 64𝜋4 𝜈𝑀𝐷 3 3ℎ 𝜒𝑀𝐷𝐷𝑀𝐷 University of Belgrade OMAS group omasgroup.org
- 35. Corrections • Excitations are performed in some Stark sublevels. • Correction factors are needed: 𝜑1 = 𝐼1,1 𝑗=1 3 𝐼1,𝑗 , 𝜑2 = 𝑗=4 6 𝐼2,𝑗 𝑗=4 8 𝐼2,𝑗 • 𝐿𝐼𝑅𝐽𝑂 = 𝜑1 𝜑2 𝐵𝐽𝑂 exp Δ𝐸𝑠𝑝 𝑘𝑇 University of Belgrade OMAS group omasgroup.org Judd-Ofelt modelling of the dual-excited single band ratiometric luminescence thermometry, A. Ćirić, I. Zeković, M. Medić, Ž. Antić, M.D. Dramićanin, doi: 10.1016/j.jlumin.2020.117369
- 36. TEST ON Lu2O3:Eu3+ • 𝐵 = 0.04773 • 𝜑1 = 0.304, 𝜑2 = 0.873 • JOES: Ω2 = 9.605 ∙ 10−20 𝑐𝑚2 , Ω4 = 2.928 ∙ 10−20 𝑐𝑚2 ℎ𝑡𝑡𝑝𝑠://𝑜𝑚𝑎𝑠𝑔𝑟𝑜𝑢𝑝. 𝑜𝑟𝑔/𝑗𝑜𝑒𝑠 − 𝑠𝑜𝑓𝑡𝑤𝑎𝑟𝑒/ • 𝐵𝐽𝑂 = 0.137 • 𝐵𝐽𝑂 𝜑1 𝜑2 = 0.04770 • 99.9% match between 𝐵 and 𝐵𝐽𝑂 𝜑1 𝜑2 Exp JO University of Belgrade OMAS group omasgroup.org
- 37. CONCLUSIONS • Temperature invariant B parameter for LIR can be predicted • Prediction of Sensitivities! • Needed: 1 RT spectrum or Ω from literature! • Test showed high matching between experimental and theoretical B parameters. • Applicability: tool for initial selection of phosphors! • Applies to other Lanthanides. University of Belgrade OMAS group omasgroup.org
Editor's Notes
- Good afternoon to everyone on this Friday 13th. I will give you the presentation on how to use the theoretical tools to predict the thermometric lanthanide phosphor performances.
- It is not an overstatement to claim that Rare-earths are revolutionizing modern science and technology. *They can be found in almost every type of device, which is why both the demand, production and their price are rapidly rising.
- They consist of the 17 chemical elements with rather similar chemical properties: *15 lanthanides and *Yttrium and Scandium.
- *Some of them deserve the name rare-earth, but some like Ce do not, as it is more abundant than copper.
- However, their mining and subsequent chemical extraction is anything but easy. For these reasons China is currently dominating the rare-earth production, while other countries who realized their importance are aiming to step up despite the difficulties. *They have many applications, *out of which what interests us, phosphors, account only for approximately 5%.
- When we speak of their applications for phosphors, we are interested in the luminescent properties of lanthanides. Luminescent properties depend on their electronic structure. *Xenon for example has completely filled 5p shell. We then keep filling the shells with electrons, and see that for Lanthanum, the 4f shells did not start filling up, but rather we have the higher energy 5d electron. *If we would continue to add electrons, the 4f shells *would start filling *up to Lutetium, which has 14 4f electrons The luminescent properties strongly depend on their valence in a host and they are most commonly found in trivalent state. *Instead of 4f electrons, the energetically higher 5d and 6s electrons are first being removed. Trivalent lanthanum is thus isoelectronic with Xenon. In other words it does not have 4f electrons. ** *Thus, Lanthanum and Lutetium do not luminescence, and the luminescent trivalent lanthanides are 13 elements from Cerium to Ytterbium, *and we can rule out Promethium as a phosphor since it is very radioactive.
- What makes trivalent lanthanides so special? In two words, it can be said their spectroscopic properties, which can be summed as: *Sharp lines as we can see on this Europium spectrum, *energy levels independent on the host, and a plethora of them, from IR to UV, as summarized in the famous Dieke diagram. Here the presented diagram is from the article by prof. Meijerink and Reid as they greatly extended it up to 200 cm^-1. *And Long emission lifetimes and high intrinsic quantum yields.
- How is that possible, why their spectra are nothing like that of transition metals? *The key is again in their unusual electronic structure. 4f electrons are shielded by the 5s and 5p electrons. So, when trivalent lanthanide is incorporated in the host matrix, the host ions will have only weak effect. To take a closer look into this 4f configuration let us take trivalent Eu as an example. *Firstly, we take only interactions between the core and the electrons, and we get 4f6 configuration as Eu3+ has 6 electrons in its 4f shell. *Then, we add repulsion between electrons, and we get LS terms with relatively large splitting. *When s-o interaction is included and the terms further split into levels. *All this accounts for the trivalent lanthanide as a free ion, and so the free ion Hamiltonian holds. *The outer CF can be regarded as a perturbation that depends on the crystal field parameters. This perturbation is giving rise to yet another splitting.
- So due to the shielding, the positions of energy levels are weakly dependent on the host matrix. This has a consequence that the transition energies are also mostly independent, and we can calculate that from Dieke diagram. The levels split into different number of peaks depending on the symmetry the rare-earth ion takes in the host matrix. What was troubling are the origins of their intensities, and at this point we have come to the introduction of the Judd-Ofelt theory.
- **From the standpoint of quantum theory developed in the 1920s and 30s, their spectral properties were puzzling. Their sharp lines were known to originate from interconfigurational 4f transitions, but their origin was unknown as they violated the parity selection rule, known as the Laporte rule. *Then In 1940s Racah developed his famous algebra, and with the dawn of computers it was finally possible to do many complex calculations. *The solution came soon after: in noncentrosymmetric crystal field the coupling between odd and even parity states is forced, resulting in mixed parity states that mitigates Laporte’s rule. *In 1962. this solution to the very complex Schroedinger equation came simultaneously by Judd, and Ofelt who worked under the instructions of Wybourne.
- *And these two papers have become the centerpiece in spectroscopy of rare earths from that moment. *As it is the only theory behind 4f-4f luminescence, with increasing need for rare-earths, its popularity rapidly rises each year, *no matter that it is a very complex Quantum Mechanical theory. *What is this theory capable of? From only 3 parameters (labelled Omega) it has ability to predict derived quantities such as transition probabilities, branching ratios, lifetimes and quantum efficiencies.
- There are numerous ways and methods to get the JO parameters. *The first one is what is called ab initio, and it includes the calculation from the CF parameters. *The most conventional is parametrization from the absorption spectra. *There are some novel methods that make use of the diffuse-reflectance or excitation spectra. *Last, but not the least, is the method I prefer, parametrization from emission spectra, as it is both the most accurate and the simplest method. *When we have omega parameters, we directly get derived quantities, the point where we have reached the practical applicative importance of the JO theory.
- The theory behind ab initio parametrization, an exact solution, is very complex, so I will not get into it at all. *Whoever is interested, I can point you to these articles. *The last of these references describes parametrization that can be used on even Ce and Yb. However, this method it is often of limited accuracy, *as pointed by Smetnek in her reference.
- Traditionally, JO parameters are extracted by a fitting procedure from the absorption spectrum, which is an approximate solution. *The procedure is best described in article by Hehlen, Brik and Kramer. *From the absorption spectrum we get the experimental oscillator strengths. *JO parameters are obtained by fitting of theoretical equation, with the experimental equation. *As it is a complex estimation, RELIC software is published to ease the process. However, I must warn you that it is not user friendly. *But there are some problems. The density of ions must be accurately measured. The absorption spectrum is difficult to get to for powder or non-transparent materials.
- *It is possible to extract JO parameters from the excitation spectrum of most of the lanthanides. *By fitting the relative values of Omega are obtained. *They need to be calibrated in order to get the absolute values. *This can be done via the radiative lifetime. *And there is its problem, it requires that the radiative lifetime is the only mechanism for the depopulation of the level in which the excitations are performed. This criteria holds well for some ions where the gap between two levels is large. *Equivalent parametrization is performed by diffuse-reflectance spectra and lifetime in this paper published only two months ago.
- The large gap from emissive level to the ground level was used by Blasse to get the parametrization scheme from the emission spectrum of Gd3+. In essence, all he needed to do is match radiative transition probability with the radiative lifetime, and he was able to obtain the JO parameters.
- This method for Eu3+ was first introduced by Krupke in 1966. Its derivation is very simple. *Eu is unique element in a way that it has a pure MD transition: 5D0->7F1. MD strengths can be exactly calculated and are independent on the host, thus we can use them for the spectrum calibration. *In this article we demonstrated that Eu3+ has another pure MD transition, 5D1->7F0, which can be used for parametrization. It is preferable in the rare case of very low concentrations and low phonon matrices, when emissions from 5D1 are of relatively high intensity, *and here we see that on example of two glasses with 0.01% Eu content.
- *Starting from the radiative transition probability equation. *Eu has pure MD and ED transitions, thus these are the forms of radiative transition probabilities for pure transitions. *We now add the expression for emission intensity. *And we take the ratio of ED transition to the MD transition. * *And since ED strength in Eu depends only on the single JO parameter, *we get the final, very simple equation for parametrization. No fitting is needed.
- The first software available for this was Lumpac. It can do many calculations, but we found that it is not as accurate nor complete for JO analysis. *Thus, we decided to make our own application, called JOES, which is an abbreviation of the Judd-Ofelt from emission spectra. *The user just needs to import a single emission spectrum file, *choose among 150 different materials from the list or enter the refractive index values in the table manually, *enter the range for each transition and click on calculate. ***Video*** *Output of JO analysis is in the text file we can se here. The app can be freely downloaded from our website, and if you have any questions on how to use it you can contact me via this email.
- With nanoparticles the things get a bit more complex. If the particles are much smaller than the wavelength of light, then the effective refractive index must be used instead. It is not difficult to do this correction, one just needs to know the fraction of space that is occupied by the nanoparticles, but it is an approximative solution to the problem. The exact solution can come with Ab Initio calculations.
- Let us now jump to luminescence thermometry. As we know, there are two general classes of methods for readout, depending on the temporal nature of measurements, and Luminescence intensity ratio is the most widely used method for luminescent temperature readout.
- The reason behind this lies in the simplicity and low equipment cost, *we need a single excitation to monitor two emissions at different wavelengths, and from the ratio of their intensities we get a calibration curve. *If two levels are well thermalized, then their emissions follow the Boltzmann distribution.
- Why are lanthanides so important for thermometry? *Their emissions are sharp. There are many of them in all regions. Energy levels are at positions almost independent on the host, so we know what to expect. *Many of them are intense. *Many of the levels are thermalized. *And that is why there are plenty of research papers describing the thermometry of various lanthanides by using various thermalized levels.
- So we asked ourselves, *can JO theory be useful for LIR thermometry, since it explains well lanthanide luminescence intensities, while the energy gaps can be obtained from Dieke diagram or from the barycenters in the spectrum? *Before going any further, it must be stated that after we have developed the model that will be described now, and after the publication, we saw this paper in which prof. Carlos mentioned that temperature independent parameter can be calculated via the Judd-Ofelt parameters, *while Yang gave the incomplete and very approximate equation for the specific transitions of Er3+.
- *Let us return to the equation for Luminescence intensity ratio. *As we recall, the intensities depend on the photon energy, emitting level population and radiative transition probability. We can substitute that in equation for LIR with Boltzmann distribution. *And we get the ratios of populations of the two emitting levels we are using for LIR. *Again, substitute that in equation for LIR and we get the equation that is well known. As the radiative transition probabilities and the energy level positions are approximately independent on temperature, B is approximately temperature invariant and we consider it constant for a given material and selected levels for LIR. dE can be extracted from the spectra. *So by substitution of radiative transition probabilities from the JO theory, we get the explicit equation for temperature invariant parameter B, obtained directly from the Judd-Ofelt parameters. *We note that the squared reduced matrix elements, abbreviated as U to the power of λ, and MD strengths are tabulated and host independent values.
- Now we know that if we have B and dE parameters, we can get absolute sensitivity by simply differentiating LIR equation. Thus, from JO parameters we get the equation for the absolute sensitivity, where and what is its maximum and if we have an instrumental uncertainty, temperature resolution as well. All this was reported in our article published in Journal of Luminescence titled: An extension of the Judd-Ofelt theory to the field of lanthanide thermometry
- So, what are the benefits? There are many lanthanides that we can incorporate in infinite number of hosts in various concentrations. There are many levels for each lanthanide to chose from. At the same time, the thermometric experimental procedure is lengthy and requires an expensive equipment, knowledge and experience in the field, and a lot of time to process. *In contrast, JO parameters can be obtained from single spectrum at room temperature or in literature. *The number of papers that report on JO analysis by far outnumbers the number of papers on luminescent thermometry. The largest selection is reported in the book chapter by Warland and Binnemans. So one does not even have to do any experiments if the JO parameters are already reported. *Thus, one can use JO to approximately estimate LIR theoretically and select the best phosphor for application, before doing the conventional thermometric analysis for precise calibration.
- For conventional LIR of thermally coupled levels of lanthanides, the used energy levels are best illustrated in Sensing temperature via downshifting emissions article by prof. Dramicanin. *For those levels, in the previously mentioned article, *we enlisted the explicit equations for each combination of levels for each lanthanide.
- Based on this, we built an universal and interactive app in Wolfram language. The user needs to input the desired temperature range, refractive index values, reduced matrix elements, energy gap, magnetic dipole strength (which are tabulated in article by Dodson), and JO parameters, and optionally, measurement uncertainty. The output is the predicted luminescence intensity ratio, absolute and relative sensitivities and temperature resolution graphs. *If I would to raise omega4 parameter, I can see that the scale for LIR has changed. *And lower the O2 parameter. The shape naturally stayed the same as it depends on the energy gap. *So lets now reduce it to 510 cm^-1 and we will see how the LIR and sensitivity shapes have changed. *At the bottom left you see the maximum absolute sensitivity, at which temperature it is obtained, and the predicted temperature independent B parameter in LIR equation. The applet can be downloaded from out website as well.
- Naturally, we had to test this JO thermometric model. *for all combinations of the two most intense transitions from 5D1 and three from 5D0 levels. Then we applied the model, which prediction is represented by the dashed blue line in this figure. As we can see, there is a very good match between experimentally obtained values and the predicted by the JO theory. *However, this model we presented works with Boltzmann distribution. If the Boltzmann distribution holds, the model will give good predictions. *For Eu3+ ion there are expected discrepancies from the ideal Boltzmann distribution at lower temperatures, but they are spot on at higher temperatures. *We can see that the theoretical and experimental B parameters and absolute sensitivities are also very close, as obtained by the LIR from JO parameters and experimental fit to the Boltzmann distribution. Thus, the prediction of LIR from JO works. *In the case of the non-Boltzmann distribution, other theoretical models can be applied, like the one given by prof. Meijerink. In that case, the modified versions of the model could also work simply because the expression for the radiative transition probability estimated from JO parameters always holds.
- One novel LIR technique is to observe a single emission while exciting into the ground level and its thermalized level. It is firstly introduced by prof. Carlos and prof. Malta. *At 0 K all optical centers are at the ground level. *As we increase T, higher levels get thermally populated *Thus, the excitation from the higher levels is possible. *And we can observe a single emission for LIR. *LIR is obtained by ratio of a single emission, but with two different excitation pathways. *And we get larger sensitivities
- *The basis of the dual excitation thermometry can be explained on the ground multiplet of Eu3+ ion. *7FJ levels are thermally excited, *and the number of optical centers in each level depends on the temperature, according to the Boltzmann distribution. *Then, excitation can be performed from the higher levels of the ground multiplet
- *We chose to excite from 7F1 and 7F2 levels, because they have a large absorption cross-sections comparing to the 7F0 and can be explained by the Judd-Ofelt theory. *Monitored emission is to 7F4. Any choice of levels for excitation or emission would work.
- Where we wondered if it was possible to do the same as we did for the LIR from two emissions: *can we predict the LIR for this method via the JO parameters? The B parameter is calculated in analogous manner, this time by taking Judd-Ofelt for 7F1 and 7F2 levels, while dE is obtained from the spectrum.
- *However, as professors Malta and Carlos have shown, the correction factors must be included for accounting on the fractions of the Stark sublevels involved in the excitation process. **Thus, the corrected LIR is given by these equations. All this is explained in this article we published.
- With theory set, it was time for testing. *First B is obtained experimentally. *The correction factors are obtained from the spectrum. *Judd-Ofelt parameters are obtained by the JOES app from the emission spectrum. *Judd-Ofelt B parameter is estimated by the equation shown previously. *And after application of the correction factors, the value of B matches the experimentally obtained value by lucky 99.9%. And it is obtained from the single spectrum at room temperature. *Now this unrealistically good matching means just one thing, that we were very lucky! *If we got our B parameter from JO with some probability distribution, *and a bit more accurately we got it from the experimental data, *we must have hit it somewhere in this section by both methods. Nevertheless our luck on this example, this method should always give an adequately good matching.
- What are the conclusions? *The temperature invariant B parameter for LIR of two-excitations or of conventional LIR by using two emissions can be predicted by the JO thermometric model This means that the sensitivities can be also predicted. *A single spectrum at room temperature is sufficient, from which the needed parameters can be calculated. *Our testing with Eu3+ showed high matching with experimentally obtained values. *This theoretical model can as well have applications for initial selection of phosphors, before doing the arduous task of measuring many spectra at various temperatures, data processing and subsequent theoretical analysis. Judd-Ofelt parameters can be calculated from the single spectrum, or they can be obtained from the vast literature. *The model is applicable to other Lanthanides beyond Eu3+, with slight modifications to the equation for Judd-Ofelt B parameter.