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International Journal of Education & Applied Sciences Research

Modeling of Mn4+ doped TiO2 (Rutile) Single Crystals

Maroj Bharati, Vikram Singh, Ram Kripal

Maroj Bharati, Department of Physics, Nehru Gram Bharti (DU), Jamunipur, Prayagraj, India ORCID: https://orcid.org/0009-0007-8219-0993

Vikram Singh, Department of Physics, Nehru Gram Bharti (DU), Jamunipur, Prayagraj, India ORCID: https://orcid.org/0000-0003-3813-586X

Ram Kripal, EPR Laboratory, Department of Physics, University of Allahabad, Prayagraj-211002, India ORCID: https://orcid.org/0000-0002-3483-8704

DOI : https://doi.org/10.53882/IJEASR.2023.1001006 Page No : 59-71

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ABSTRACT

Aim of the study: The study is performed to evaluate splitting parameters of zero field and crystal field of Mn4+ doped titanium oxide, TiO2 (Rutile) single crystals to know the crystal's deformation and the placement of the Mn4+ ion. Design/Methodology: Employing the crystal field and zero field splitting parameters in the superposition model for Mn4+ ion locations in TiO2are determined. Zero fields plitting parameters in theory with good correspondence to local distortion with the experiment's values. With the aid of Using crystal field parameters and the Crystal Field Analysis Program, the optical energy bands for Mn4+ in TiO2 are estimated. Outcomes: Theoretical analysis backs the experimental result that one of the Ti4+ ions in TiO2 single crystals sites is occupied by Mn4+ ions. The experimental and calculated energy values give a fairly reasonable match. Thus theoretical study validates the results of the experimental observation. Practical Implications: The study signifies that the This can be used to numerous different ion-host systems to investigate crystals with potential uses in industry and research. Originality value: The study provides a substantial contribution to the literature on splitting parameters for Doped crystals' crystal field and zero field.

Keywords: Crystal field; Mn4+ ions in TiO2; Optical Zero-field splitting, superposition model, and spectroscopy.

Paper type: Research paper.

References

Açıkgöz, M. A. (2012), study of the impurity structure for 3d3 (Cr3+ and Mn4+) ions doped into rutile TiO2 crystal, Spectrochim. Acta A 86(2): 417-422.
Acikgoz, M., Kripal R., Misra, M.G., Yadav, A. K., Gnutek, P.,Rudowicz, C. (2023), Theoretical analysis of crystal field parameters and zero field splitting parameters for Mn2+ ions in tetrame thy lammonium tetrachlorozincate, Polyhedron 235: 116341.
Adachi S. (2019),Photo luminescence Spectroscopy and Crystal-Field Parameters of Cr3+ Ion in Red and Deep Red-Emitting Phosphors. ECS J Solid State Sci. Tech. 8 (12): R164-R168.
Adachi S. (2021), Review—Photoluminescence Properties of Cr3+-Activated Oxide Phosphors. ECS J Solid State Sci. Tech. 10: 026001(21 pages).
Andresen, H. G. (1960), Electron Paramagnetic Resonance of Manganese in TiO2, Phys. Rev. 120(5): 1606-1611.
Bansal, R. S., Seth, V. P., Chand, P., Gupta, S. K. (1991),EPR and optical spectra of vanadyl ion (impurities) in three polycrystalline solids, J. Phys. Chem. Solids 52: 389-392.
Bharati, M., Singh, V., Kripal, R. (2023),Zero Field Splitting Parameter of Mn2+ in PMN Single Crystals, Int. J. of Eng. Tech. Res. Man. (IJETRM), 7:43-52.
Bharati, M., Singh, V., Kripal, R. (2023), Modeling of Mn2+ doped CdGa2Se4 single crystals,Int. J. Eng. Inv. (IJEI), 12:170-175.
Bharati,M., Singh, V., Kripal,R.(2024), Modeling of Cr3+ doped Cassiterite (SnO2) Single Crystals, IgMin Res., 2(6):484-489.
Boca, R., Rajnak, C., Titis, J. (2023),Zero-Field Splitting in Hexacoordinate Co(II) Complexes, Magnetochem. 9: 100(31 pages).
Brik, M. G., Avram, C. N., Avram, N. M. (2006), Calculations of spin Hamiltonian parameters and analysis of trigonal distortions in LiSr (Al, Ga) F6: Cr3+ crystals, Physica B.384: 78-81. doi.org/10.1016/j.physb.2006.05.155.
Cantero-Lo´pez, . P., Hidalgo-Rosa, Y., Sandoval-Olivares, Z., Santoyo-Flores, J., Mella, P., Arrue´, L., Zu´n˜ iga, C.,Arratia-Pe´rez, R., Pa´ez-Herna´ndez, D. (2021), The role of zero-field splitting and p-stacking interaction of different nitrogen-donor ligands on the optical properties of luminescent rhenium tricarbonyl complexes, New J. Chem. 45: 11192-11201.
Chang, Y. M., Rudowicz, C., Yeung, Y. Y. (1994), Crystal field analysis of the 3dN ions at low symmetry sites including the ‘imaginary’ terms, Comp. Phys. 8(5): 583-588.
Figgis, B. N., Hitchman, M. A. (2000), Ligand Field Theory and its Applications, Wiley,New York.
Gopal, N. O., Narsimhulu, K.V., Sunandan, C. S., Rao, J. L. (2004), EPR and optical absorption spectral studies of Cr3+ ions doped in nickel maleate tetrahydrate single crystals. Physica B 348(1-4): 335-340.
Halder,D., Jana,Y., Piwowarska,D., Gnutek, P., Rudowicz, C.(2024),Tailoring single-ion magnet properties of coordination polymer C11H18DyN3O9 (Dy-CP) using the radial effective charge model (RECM) and superposition model (SPM),Phys. Chem. Chem. Phys.26: 19947-19959.
Hanaor, D. A. H., Sorrell, C. C.(2011). Review of the anatase to rutile phase transformation J. Mater. Sci. 2011, 46, 855-874.
Kripal, R.(2022),Zero Field Splitting Parameter Study of Fe3+ in RbCdF3 Single Crystals at Axial Symmetry Site, Int. J. of Eng. Tech. Res. Man. (IJETRM), 6: 47-53.
Kripal, R. (2022),Theoretical Investigation of Zero field splitting parameter of Fe3+ in CsCdF3, IJIRSES 2(10)(2022)9-13.
Kripal, R. (2023), Zero Field Splitting Parameter of Mn2+-Doped Tl2Cd2(SO4)3 Single Crystals at Axial Symmetry Site, Acta Phys. Polon. A 143: 217-220.
Kripal, R., Shukla, L. C. (2021),Superposition model analysis for Cr3+ ions at orthorhombic sites in Sr3Ga2Ge4O14,Int. J. Sci. Res. Phys. Appl. Sci. (IJSRPAS), 9: 44-48.
Kripal, R., Shukla, L. C. (2021), Zero Field Splitting Study of Cr3+ Doped Nickel Maleate Tetrahydrate, Int. J. Sci. Dev. Res. (IJSDR),6: 99-100.
Kripal, R., Tripathi, U. M. (2022), Superposition Model Investigation of Mn2+ doped Ni[C4H304]2.6H20 Crystal, Int. J. Res. Eng. Sci. (IJRES), 10:72-76.
Liu, B. E., Aydil, S.(2009),Growth of Oriented Single-Crystalline Rutile TiO2 Nanorods on Transparent Conducting Substrates for Dye-Sensitized Solar Cells,J. Am. Chem. Soc. 131, 3985-3990.
Liu, G., Pan, J., Yin, L., Irvine, J. T. S., Li, F., Tan, J., Wormald, P., Cheng, H.-M. (2012), Heteroatom-Modulated Switching of Photocatalytic Hydrogen and Oxygen Evolution Preferences of Anatase TiO2 Microspheres,Adv. Funct. Mater. 22: 3233 –3238.
Mabbs, F. E., Collison, D., Gatteschi, D. (1992), Electron Paramagnetic Resonance of the Transition Metal Compounds, Elsevier, Amsterdam.
Marcinkowski, D., Adamski, A., Kubicki, M., Consiglio, G., Patroniak, V., Ślusarski, T., Açıkgöz, M., Szeliga, D., Vadra, N., Karbowiak, M., Stefaniuk, I., Rudowicz, C., Gorczyński, A., Korabik, M.(2022), Understanding the effect of structural changes on slow magnetic relaxation in mononuclear octahedral copper(II) complexes, Dalton Trans. 51:12041-12055.
Müller, K. A.(1959),Electron Paramagnetic Resonance of Manganese IV in SrTiO3, Phys. Rev. Lett. 2:341-343.
Müller, K. A., Berlinger, W., Albers, J. (1985), Paramagnetic resonance and local position of Cr3+ in ferroelectric BaTiO3. Phys. Rev. B 32(9): 5837-5850.
Müller, K. A., Berlinger, W. (1983),Superposition model for six fold-coordinated Cr3+ in oxide crystals (EPR study). J. Phys. C: Solid State Phys. 16(35): 6861-6874.
Newman, D. J., Ng, B. (2000), Superposition model. Ch. 5 in: Newman D J, Ng B. (Eds.). Crystal Field Handbook, Cambridge University Press, UK, pp. 83–119.
Newman, D. J., Ng, B. (1989), The Superposition model of crystal fields. Rep. Prog. Phys. 52: 699-763.
Nikitin, S.I., Kutashova, E.M., Yusupov, R.V., Karimov, R.I., Kiiamov, A.G. (2024),Laser spectroscopy and crystal field analysis of energy level structure of Tm3+ ions in SrY2O4 crystal J. Lumin. 272(8):120616.
Pandey, S., Kripal, R., Yadav, A. K., Açıkg¨oz, M., Gnutek, P., Rudowicz, C.(2021), Implications of direct conversions of crystal field parameters into zero-field splitting ones - Case study: Superposition model analysis for Cr3+ ions at orthorhombic sites in LiKSO4, J. Lumin. 230: 117548 (10 pages).
Pilbrow, J. R. (1990), Transition Ion Electron Paramagnetic Resonance, Clarendon Press,Oxford.
Rathee, S.P., Hooda, S.S. (2024), EPR and superposition-model analysis of zero-field splitting parameters for Mn2+ doped in ZnNbOF5.6(H2O) and CoNbOF5.6(H2O) single crystals, Indian J Phys .https://doi.org/10.1007/s12648-024-03268-3
Rudowicz, C., Karbowiak, M. (2015),Disentangling intricate web of interrelated notions at the interface between the physical (crystal field) Hamiltonians and the effective (spin) Hamiltonians, Coord. Chem. Rev. 287: 28-63.
Rudowicz, C. 1987),(Concept of spin Hamiltonian, forms of zero field splitting and electronic Zeeman Hamiltonians and relations between parameters used in EPR. A critical review, Magn.
Rudowicz, C., Misra, S. K. (2001), Spin-Hamiltonian formalisms in electron magnetic resonance (EMR) and related spectroscopies, Appl. Spectrosc. Rev. 36(1): 11-63.
Rudowicz, C. (1985), Transformation relations for the conventional Okq and normal ised O'kq Stevens operator equivalents with k=1 to 6 and –k ≤ q ≤ k, J. Phys. C Solid State Phys. 18( 7) : 1415-1430; Erratum: Rudowicz C. (1985), J. Phys. C Solid State Phys. 18(19): 3837.
Rudowicz, C., Chung, C. Y. (2004), The generalization of the extended Stevens operators to higher ranks and spins, and a systematic review of the tables of the tensor operators and their matrix elements, J. Phys. Condens. Matter 16(32): 5825-5847.
Rudowicz, C. (1987), On the derivation of the superposition-model formulae using the transformation relations for the Stevens operators. J. Phys. C: Solid State Phys. 20(35): 6033-6037.
Rudowicz, C., Gnutek, P., Açıkgöz, M. (2019), Superposition model in electron magnetic resonance spectroscopy – a primer for experimentalists with illustrative applications and literature database. Appl. Spectroscopy Rev. 54: 673-718.
Rudowicz, C., Bramley, R. (1985), On standardization of the spin Hamiltonian and the ligand field Hamiltonian for orthorhombic symmetry. J. Chem. Phys. 83(10): 5192-5197.
Shao, G. S., Deng, Q. R., Wan, L., Guo, M. L., Xia, X. H., Gao, Y. (2010), Molecular Design of TiO2 for Gigantic Red Shift via Sublattice Substitution,J.Nanosci. Nanotechnol. 10: 7092 –7096.
Shao, G. (2009),Red Shift in Manganese- and Iron-Doped TiO2: A DFT+U Analysis J. Phys. Chem. C 113: 6800 –6808.
Siegel, E., Muller, K. A. (1979), Structure of transition-metal—oxygen-vacancy pair centers. Phys. Rev. B 19(1): 109-120.
Stefaniuk, I., Rudowicz, C.,Gnutek,P., Suchocki,A.(2009),EPR Study of Cr3+ and Fe3+ Impurity Ions in Nominally Pure and Co2+-Doped YAlO3 Single Cry stals. Appl. Magn. Reson. 36:371–380.
Tang, H., Levy, F., Berger, H., Schmid, P. E. (1995), Urbach tail of anatase TiO2, Phys. Rev. B 52: 7771-7774.
Von Werner H B. (1956), Uber die Verfeinerung der Kristallstrukturbestimmunge in iger Vertreterdes Rutiltyps: TiO2, SnO2, GeO2 und MgF2. Acta Cryst. 9: 515-520.
Wang,L.,Fan,J., Cao,Z., Zheng,Y.,Yao,Z.,Shao,G.,Hu, J.(2014),Fabrication of Predominantly Mn4+-Doped TiO2 Nanoparticles under Equilibrium Conditions and Their Application as Visible-Light Photo catalyts, Chem. Asian J. 9: 1904 – 1912.DOI: 10.1002/asia.201402114
Wang, J.-H., Li, Z.-Y., Yamashita, M., Bu, X.-H.(2021), Recent progress on cyano-bridged transition-metal-based single-molecule magnets and single-chain magnets. Coord. Chem. Rev. 428: 213617 (21 pages).
Weil, J. A., Bolton, J. R. (2007), Electron Paramagnetic Resonance: Elementary Theory and Practical Applications, 2nd ed., Wiley, New York.
Wybourne, B. G. (1965), Spectroscopic Properties of Rare Earth. Wiley, New York, USA.
Yamaga, M., Singh, A. K., Cameron, D., Edwards, P. R., Boćkowski, M. (2024),Crystal-field analysis of photoluminescence from orthorhombic Eu centers and energy transfer from host to Eu in GaN co-doped with Mg and Eu,J. Lumin. 270(6):120557.
Yeom,T. H., Chang,Y. M., Rudowicz,C.(1993), Cr3+ centres in LiNbO3: Experimental and theoretical investigation of spin Hamiltonian parameters, Solid State Commun.87(3):245-249.
Yeung,Y.Y., Newman,D. J.(1986), Superposition-model analyses for the Cr3+4A2ground state,Phys. Rev. B34(4):2258-2265.
Yeung,Y.Y., Rudowicz,C.(1992), Ligand field analysis of the 3dN ions at orthorhombic or higher symmetry sites. Comp. Chem.16(3):207-216.
Yeung,Y.Y., Rudowicz,C.(1993), Crystal Field Energy Levels and State Vectors for the 3dN Ions at Orthorhombic or Higher Symmetry Sites, J. Comput. Phys.109(1):150-152.

Cite this Article as: Bharati M, Singh V & Kripal R (2023), “Modeling of Mn4+ doped TiO2 (Rutile) Single Crystals”, International Journal of Education & Applied Sciences Research, Volume 10, Issue 1, 2023, pp 59-71. DOI : https://doi.org/10.53882/IJEASR.2023.1001006

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References

Açıkgöz, M. A. (2012), study of the impurity structure for 3d3 (Cr3+ and Mn4+) ions doped into rutile TiO2 crystal, Spectrochim. Acta A 86(2): 417-422.
Acikgoz, M., Kripal R., Misra, M.G., Yadav, A. K., Gnutek, P.,Rudowicz, C. (2023), Theoretical analysis of crystal field parameters and zero field splitting parameters for Mn2+ ions in tetrame thy lammonium tetrachlorozincate, Polyhedron 235: 116341.
Adachi S. (2019),Photo luminescence Spectroscopy and Crystal-Field Parameters of Cr3+ Ion in Red and Deep Red-Emitting Phosphors. ECS J Solid State Sci. Tech. 8 (12): R164-R168.
Adachi S. (2021), Review—Photoluminescence Properties of Cr3+-Activated Oxide Phosphors. ECS J Solid State Sci. Tech. 10: 026001(21 pages).
Andresen, H. G. (1960), Electron Paramagnetic Resonance of Manganese in TiO2, Phys. Rev. 120(5): 1606-1611.
Bansal, R. S., Seth, V. P., Chand, P., Gupta, S. K. (1991),EPR and optical spectra of vanadyl ion (impurities) in three polycrystalline solids, J. Phys. Chem. Solids 52: 389-392.
Bharati, M., Singh, V., Kripal, R. (2023),Zero Field Splitting Parameter of Mn2+ in PMN Single Crystals, Int. J. of Eng. Tech. Res. Man. (IJETRM), 7:43-52.
Bharati, M., Singh, V., Kripal, R. (2023), Modeling of Mn2+ doped CdGa2Se4 single crystals,Int. J. Eng. Inv. (IJEI), 12:170-175.
Bharati,M., Singh, V., Kripal,R.(2024), Modeling of Cr3+ doped Cassiterite (SnO2) Single Crystals, IgMin Res., 2(6):484-489.
Boca, R., Rajnak, C., Titis, J. (2023),Zero-Field Splitting in Hexacoordinate Co(II) Complexes, Magnetochem. 9: 100(31 pages).
Brik, M. G., Avram, C. N., Avram, N. M. (2006), Calculations of spin Hamiltonian parameters and analysis of trigonal distortions in LiSr (Al, Ga) F6: Cr3+ crystals, Physica B.384: 78-81. doi.org/10.1016/j.physb.2006.05.155.
Cantero-Lo´pez, . P., Hidalgo-Rosa, Y., Sandoval-Olivares, Z., Santoyo-Flores, J., Mella, P., Arrue´, L., Zu´n˜ iga, C.,Arratia-Pe´rez, R., Pa´ez-Herna´ndez, D. (2021), The role of zero-field splitting and p-stacking interaction of different nitrogen-donor ligands on the optical properties of luminescent rhenium tricarbonyl complexes, New J. Chem. 45: 11192-11201.
Chang, Y. M., Rudowicz, C., Yeung, Y. Y. (1994), Crystal field analysis of the 3dN ions at low symmetry sites including the ‘imaginary’ terms, Comp. Phys. 8(5): 583-588.
Figgis, B. N., Hitchman, M. A. (2000), Ligand Field Theory and its Applications, Wiley,New York.
Gopal, N. O., Narsimhulu, K.V., Sunandan, C. S., Rao, J. L. (2004), EPR and optical absorption spectral studies of Cr3+ ions doped in nickel maleate tetrahydrate single crystals. Physica B 348(1-4): 335-340.
Halder,D., Jana,Y., Piwowarska,D., Gnutek, P., Rudowicz, C.(2024),Tailoring single-ion magnet properties of coordination polymer C11H18DyN3O9 (Dy-CP) using the radial effective charge model (RECM) and superposition model (SPM),Phys. Chem. Chem. Phys.26: 19947-19959.
Hanaor, D. A. H., Sorrell, C. C.(2011). Review of the anatase to rutile phase transformation J. Mater. Sci. 2011, 46, 855-874.
Kripal, R.(2022),Zero Field Splitting Parameter Study of Fe3+ in RbCdF3 Single Crystals at Axial Symmetry Site, Int. J. of Eng. Tech. Res. Man. (IJETRM), 6: 47-53.
Kripal, R. (2022),Theoretical Investigation of Zero field splitting parameter of Fe3+ in CsCdF3, IJIRSES 2(10)(2022)9-13.
Kripal, R. (2023), Zero Field Splitting Parameter of Mn2+-Doped Tl2Cd2(SO4)3 Single Crystals at Axial Symmetry Site, Acta Phys. Polon. A 143: 217-220.
Kripal, R., Shukla, L. C. (2021),Superposition model analysis for Cr3+ ions at orthorhombic sites in Sr3Ga2Ge4O14,Int. J. Sci. Res. Phys. Appl. Sci. (IJSRPAS), 9: 44-48.
Kripal, R., Shukla, L. C. (2021), Zero Field Splitting Study of Cr3+ Doped Nickel Maleate Tetrahydrate, Int. J. Sci. Dev. Res. (IJSDR),6: 99-100.
Kripal, R., Tripathi, U. M. (2022), Superposition Model Investigation of Mn2+ doped Ni[C4H304]2.6H20 Crystal, Int. J. Res. Eng. Sci. (IJRES), 10:72-76.
Liu, B. E., Aydil, S.(2009),Growth of Oriented Single-Crystalline Rutile TiO2 Nanorods on Transparent Conducting Substrates for Dye-Sensitized Solar Cells,J. Am. Chem. Soc. 131, 3985-3990.
Liu, G., Pan, J., Yin, L., Irvine, J. T. S., Li, F., Tan, J., Wormald, P., Cheng, H.-M. (2012), Heteroatom-Modulated Switching of Photocatalytic Hydrogen and Oxygen Evolution Preferences of Anatase TiO2 Microspheres,Adv. Funct. Mater. 22: 3233 –3238.
Mabbs, F. E., Collison, D., Gatteschi, D. (1992), Electron Paramagnetic Resonance of the Transition Metal Compounds, Elsevier, Amsterdam.
Marcinkowski, D., Adamski, A., Kubicki, M., Consiglio, G., Patroniak, V., Ślusarski, T., Açıkgöz, M., Szeliga, D., Vadra, N., Karbowiak, M., Stefaniuk, I., Rudowicz, C., Gorczyński, A., Korabik, M.(2022), Understanding the effect of structural changes on slow magnetic relaxation in mononuclear octahedral copper(II) complexes, Dalton Trans. 51:12041-12055.
Müller, K. A.(1959),Electron Paramagnetic Resonance of Manganese IV in SrTiO3, Phys. Rev. Lett. 2:341-343.
Müller, K. A., Berlinger, W., Albers, J. (1985), Paramagnetic resonance and local position of Cr3+ in ferroelectric BaTiO3. Phys. Rev. B 32(9): 5837-5850.
Müller, K. A., Berlinger, W. (1983),Superposition model for six fold-coordinated Cr3+ in oxide crystals (EPR study). J. Phys. C: Solid State Phys. 16(35): 6861-6874.
Newman, D. J., Ng, B. (2000), Superposition model. Ch. 5 in: Newman D J, Ng B. (Eds.). Crystal Field Handbook, Cambridge University Press, UK, pp. 83–119.
Newman, D. J., Ng, B. (1989), The Superposition model of crystal fields. Rep. Prog. Phys. 52: 699-763.
Nikitin, S.I., Kutashova, E.M., Yusupov, R.V., Karimov, R.I., Kiiamov, A.G. (2024),Laser spectroscopy and crystal field analysis of energy level structure of Tm3+ ions in SrY2O4 crystal J. Lumin. 272(8):120616.
Pandey, S., Kripal, R., Yadav, A. K., Açıkg¨oz, M., Gnutek, P., Rudowicz, C.(2021), Implications of direct conversions of crystal field parameters into zero-field splitting ones - Case study: Superposition model analysis for Cr3+ ions at orthorhombic sites in LiKSO4, J. Lumin. 230: 117548 (10 pages).
Pilbrow, J. R. (1990), Transition Ion Electron Paramagnetic Resonance, Clarendon Press,Oxford.
Rathee, S.P., Hooda, S.S. (2024), EPR and superposition-model analysis of zero-field splitting parameters for Mn2+ doped in ZnNbOF5.6(H2O) and CoNbOF5.6(H2O) single crystals, Indian J Phys .https://doi.org/10.1007/s12648-024-03268-3
Rudowicz, C., Karbowiak, M. (2015),Disentangling intricate web of interrelated notions at the interface between the physical (crystal field) Hamiltonians and the effective (spin) Hamiltonians, Coord. Chem. Rev. 287: 28-63.
Rudowicz, C. 1987),(Concept of spin Hamiltonian, forms of zero field splitting and electronic Zeeman Hamiltonians and relations between parameters used in EPR. A critical review, Magn.
Rudowicz, C., Misra, S. K. (2001), Spin-Hamiltonian formalisms in electron magnetic resonance (EMR) and related spectroscopies, Appl. Spectrosc. Rev. 36(1): 11-63.
Rudowicz, C. (1985), Transformation relations for the conventional Okq and normal ised O'kq Stevens operator equivalents with k=1 to 6 and –k ≤ q ≤ k, J. Phys. C Solid State Phys. 18( 7) : 1415-1430; Erratum: Rudowicz C. (1985), J. Phys. C Solid State Phys. 18(19): 3837.
Rudowicz, C., Chung, C. Y. (2004), The generalization of the extended Stevens operators to higher ranks and spins, and a systematic review of the tables of the tensor operators and their matrix elements, J. Phys. Condens. Matter 16(32): 5825-5847.
Rudowicz, C. (1987), On the derivation of the superposition-model formulae using the transformation relations for the Stevens operators. J. Phys. C: Solid State Phys. 20(35): 6033-6037.
Rudowicz, C., Gnutek, P., Açıkgöz, M. (2019), Superposition model in electron magnetic resonance spectroscopy – a primer for experimentalists with illustrative applications and literature database. Appl. Spectroscopy Rev. 54: 673-718.
Rudowicz, C., Bramley, R. (1985), On standardization of the spin Hamiltonian and the ligand field Hamiltonian for orthorhombic symmetry. J. Chem. Phys. 83(10): 5192-5197.
Shao, G. S., Deng, Q. R., Wan, L., Guo, M. L., Xia, X. H., Gao, Y. (2010), Molecular Design of TiO2 for Gigantic Red Shift via Sublattice Substitution,J.Nanosci. Nanotechnol. 10: 7092 –7096.
Shao, G. (2009),Red Shift in Manganese- and Iron-Doped TiO2: A DFT+U Analysis J. Phys. Chem. C 113: 6800 –6808.
Siegel, E., Muller, K. A. (1979), Structure of transition-metal—oxygen-vacancy pair centers. Phys. Rev. B 19(1): 109-120.
Stefaniuk, I., Rudowicz, C.,Gnutek,P., Suchocki,A.(2009),EPR Study of Cr3+ and Fe3+ Impurity Ions in Nominally Pure and Co2+-Doped YAlO3 Single Cry stals. Appl. Magn. Reson. 36:371–380.
Tang, H., Levy, F., Berger, H., Schmid, P. E. (1995), Urbach tail of anatase TiO2, Phys. Rev. B 52: 7771-7774.
Von Werner H B. (1956), Uber die Verfeinerung der Kristallstrukturbestimmunge in iger Vertreterdes Rutiltyps: TiO2, SnO2, GeO2 und MgF2. Acta Cryst. 9: 515-520.
Wang,L.,Fan,J., Cao,Z., Zheng,Y.,Yao,Z.,Shao,G.,Hu, J.(2014),Fabrication of Predominantly Mn4+-Doped TiO2 Nanoparticles under Equilibrium Conditions and Their Application as Visible-Light Photo catalyts, Chem. Asian J. 9: 1904 – 1912.DOI: 10.1002/asia.201402114
Wang, J.-H., Li, Z.-Y., Yamashita, M., Bu, X.-H.(2021), Recent progress on cyano-bridged transition-metal-based single-molecule magnets and single-chain magnets. Coord. Chem. Rev. 428: 213617 (21 pages).
Weil, J. A., Bolton, J. R. (2007), Electron Paramagnetic Resonance: Elementary Theory and Practical Applications, 2nd ed., Wiley, New York.
Wybourne, B. G. (1965), Spectroscopic Properties of Rare Earth. Wiley, New York, USA.
Yamaga, M., Singh, A. K., Cameron, D., Edwards, P. R., Boćkowski, M. (2024),Crystal-field analysis of photoluminescence from orthorhombic Eu centers and energy transfer from host to Eu in GaN co-doped with Mg and Eu,J. Lumin. 270(6):120557.
Yeom,T. H., Chang,Y. M., Rudowicz,C.(1993), Cr3+ centres in LiNbO3: Experimental and theoretical investigation of spin Hamiltonian parameters, Solid State Commun.87(3):245-249.
Yeung,Y.Y., Newman,D. J.(1986), Superposition-model analyses for the Cr3+4A2ground state,Phys. Rev. B34(4):2258-2265.
Yeung,Y.Y., Rudowicz,C.(1992), Ligand field analysis of the 3dN ions at orthorhombic or higher symmetry sites. Comp. Chem.16(3):207-216.
Yeung,Y.Y., Rudowicz,C.(1993), Crystal Field Energy Levels and State Vectors for the 3dN Ions at Orthorhombic or Higher Symmetry Sites, J. Comput. Phys.109(1):150-152.

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