Dataset Paper | Open Access

U. Skrzypczak, C. Pfau, C. Bohley, G. Seifert, S. Schweizer, "Judd-Ofelt Calculations for Nd^{3+}-Doped Fluorozirconate-Based Glasses and Glass Ceramics", *Dataset Papers in Science*, vol. 2013, Article ID 236421, 4 pages, 2013. https://doi.org/10.1155/2013/236421

# Judd-Ofelt Calculations for Nd^{3+}-Doped Fluorozirconate-Based Glasses and Glass Ceramics

**Academic Editor:**P. Kluth

#### Abstract

A Judd-Ofelt analysis is performed to calculate the optical properties of Nd^{3+} ions embedded in a fluorozirconate glass matrix. The changes in the Judd-Ofelt parameters were determined as a function of the size of BaCl_{2} nanocrystals grown inside the matrix. From these data, the radiative decay rates and the branching ratios of every transition in the energy range from 25.000 cm^{−1} to the ground state are calculated. This was accomplished for samples containing nanocrystals with average sizes ranging from 10 to 40 nm.

#### 1. Introduction

Photonic glasses doped with rare-earth ions such as erbium, neodymium, or europium gather widespread interest because of their applicability in photonic devices. Application as, for example, the active ion in a laser medium or as frequency converter in up- and downconverters [1, 2] requires efficient radiative decays of the ion with only minor losses to multiphonon relaxation (MPR). Therefore, the ion needs to be embedded in a low phonon energy environment which still remains both stable and transparent. Among appropriate materials are fluorozirconate (FZ) glasses with maximum phonon energies of less than 580 cm^{−1} [3–5]. They have already proved to be a convenient choice for several applications.

As shown previously [6, 7], a uniform growth of BaCl_{2} nanocrystals inside such glasses can be induced by thermal treatment as soon as additional chloride is introduced at the expense of fluoride. Since BaCl_{2} has a maximum phonon energy on the order of 200 cm^{−1} [3, 8], MPR is rendered even less probable and, thus, rare-earth ions tend to favor radiative decays [6, 7, 9].

The optical properties of Nd^{3+}-doped fluorochlorozirconate (FCZ) glasses with differently sized BaCl_{2} nanocrystals were studied with Judd-Ofelt theory. The sizes of the embedded nanocrystals were obtained from X-ray diffraction in combination with Scherrer analysis. It is known that Nd^{3+} ions are strongly affected by the BaCl_{2} nanocrystals, but until now only speculations were possible as to the location of rare-earth ions at the edge of nanocrystals or even the possible inclusion into them [9, 10].

From Judd-Ofelt [11–13] analysis, the phenomenological Judd-Ofelt parameters can be determined. With them a quantitative measure for the influence of BaCl_{2} nanocrystals on the Nd^{3+} can be established (see [14] for a detailed discussion). Here, the radiative decay rates for each transition were calculated and are given in a compressed form.

#### 2. Methodology

Experimental details are as follows.The FCZ glass samples [14] investigated in this study are comprised of 52ZrF_{4}-10BaF_{2}-10BaCl_{2}-19NaCl-3.5LaF_{3}-3AlF_{3}-0.5InF_{3}-1KCl-1NdF_{3} (values in mol%). The named chemicals were melted under an inert atmosphere, poured into a preheated (200°C) mold to avoid cracks, and then slowly cooled down to room temperature. Subsequently, the glasses were treated thermally at a temperature between 240°C and 270°C for 20 minutes to initiate the growth of BaCl_{2} nanocrystals.

The visible and near-infrared transmittance spectra, from which the oscillator strengths were obtained, were recorded at room temperature with a double-beam spectrophotometer (Perkin Elmer Lambda 900).

Judd-Ofelt details are as follows. From the absorption cross-section spectra, the oscillator strengths are calculated with where is the mass of the electron; , the speed of light; and , the absorption cross section.

The theoretical oscillator strengths feature contributions from electric, , and magnetic dipole transitions, . Quadrupole effects are very weak and have been neglected. The dipolar oscillator strengths are of the following form: where is the mean frequency and is the total angular momentum quantum number. From these, the line strengths, are calculated, in which are the doubly reduced matrix elements of the electric dipole tensor operator and are the elements of the magnetic dipole operator. These values do not depend much on the host and are given in the literature [13, 15–19]. The local field correction factors are and [20]. The Gaussian least-squares minimization of yields the evaluation of the intensity parameters (with ).

The effective refractive index of a composite material made of an FCZ glass matrix with inclusion of nanometric BaCl_{2} crystallites has been calculated involving a Maxwell-Garnett approach [21]:
where and are the dielectric constants of matrix and inclusion (data taken from [22, 23]).

The radiative emission rates are calculated [14] with When is not only the ground state, the branching ratios define the percentage of the rate for each possible relaxation channel.

The tabular data given here are sectioned into samples with different BaCl_{2} nanocrystal sizes. This starts with a determination for FZ glass and an untreated FCZ glass for reference and comparison. Then in order of increasing nanocrystal sizes, the different samples are given. For each source level , the target levels of the transition along with the radiative decay rates and the corresponding branching ratio are given. This is repeated for each sample.

#### 3. Dataset Description

The dataset associated with this Dataset Paper consists of 6 items which are described as follows.

*Dataset Item 1 (Table)*. Data of the radiative decay parameters in the FZ glass matrix.

*Column 1:**Column 2:**Column 3:*(s^{-1})*Column 4:*

*Dataset Item 2 (Table)*. Data of the radiative decay parameters in the untreated FCZ glass matrix.

*Column 1:**Column 2:**Column 3:*(s^{-1})*Column 4:*

*Dataset Item 3 (Table)*. Data of the radiative decay parameters in the FCZ glass matrix, thermally treated at 240°C. The average nanocrystal size was determined to be 12 nm [14].

*Column 1:**Column 2:**Column 3:*(s^{-1})*Column 4:*

*Dataset Item 4 (Table)*. Data of the radiative decay parameters in the FCZ glass matrix, thermally treated at 250°C. The average nanocrystal size was determined to be 14 nm [14].

*Column 1:**Column 2:**Column 3:*(s^{-1})*Column 4:*

*Dataset Item 5 (Table)*. Data of the radiative decay parameters in the FCZ glass matrix, thermally treated at 260°C. The average nanocrystal size was determined to be 25 nm [14].

*Column 1:**Column 2:**Column 3:*(s^{-1})*Column 4:*

*Dataset Item 6 (Table)*. Data of the radiative decay parameters in the FCZ glass matrix, thermally treated at 270°C. The average nanocrystal size was determined to be 42 nm [14].

*Column 1:**Column 2:**Column 3:*(s^{-1})*Column 4:*

#### 4. Concluding Remarks

A Judd-Ofelt analysis under consideration of the effective- matrix in an FZ-based glass ceramic with BaCl_{2} nanocrystals of different sizes has been performed in order to evaluate the optical properties of Nd^{3+} ions embedded therein. The radiative decay rates and the branching ratios of every transition in the energy range from 25.000 cm^{−1} to the ground state are calculated. This is accomplished for samples containing nanocrystals with average sizes ranging from 10 to 40 nm. Using these data, the dynamics of these systems can be studied using rate equations.

#### Dataset Availability

The dataset associated with this Dataset Paper is dedicated to the public domain using the CC0 waiver and is available at http://dx.doi.org/10.1155/2013/236421/dataset.

#### Acknowledgments

This work was supported by the FhG Internal Programs under Grant no. Attract 692 034. In addition, the authors would like to thank the German Federal Ministry for Education and Research (Bundesministerium für Bildung und Forschung) for the financial support within the Centre for Innovation Competence SiLi-nano (Project no. 03Z2HN11).

#### Dataset Files

- 236421.item.1.xlsx
*Dataset Item 1 (Table)*. Data of the radiative decay parameters in the FZ glass matrix.*Column 1:**Column 2:**Column 3:*(s^{-1})*Column 4:*

- 236421.item.2.xlsx
*Dataset Item 2 (Table)*. Data of the radiative decay parameters in the untreated FCZ glass matrix.*Column 1:**Column 2:**Column 3:*(s^{-1})*Column 4:*

- 236421.item.3.xlsx
*Dataset Item 3 (Table)*. Data of the radiative decay parameters in the FCZ glass matrix, thermally treated at 240°C. The average nanocrystal size was determined to be 12 nm [14].*Column 1:**Column 2:**Column 3:*(s^{-1})*Column 4:*

- 236421.item.4.xlsx
*Dataset Item 4 (Table)*. Data of the radiative decay parameters in the FCZ glass matrix, thermally treated at 250°C. The average nanocrystal size was determined to be 14 nm [14].*Column 1:**Column 2:**Column 3:*(s^{-1})*Column 4:*

- 236421.item.5.xlsx
*Dataset Item 5 (Table)*. Data of the radiative decay parameters in the FCZ glass matrix, thermally treated at 260°C. The average nanocrystal size was determined to be 25 nm [14].*Column 1:**Column 2:**Column 3:*(s^{-1})*Column 4:*

- 236421.item.6.xlsx
*Dataset Item 6 (Table)*. Data of the radiative decay parameters in the FCZ glass matrix, thermally treated at 270°C. The average nanocrystal size was determined to be 42 nm [14].*Column 1:**Column 2:**Column 3:*(s^{-1})*Column 4:*

#### References

- C. Paßlick, B. Henke, I. Császár et al., “Advances in up-and down-converted fluorescence for high efficiency solar cells using rare-earth doped fluorozirconate-based glasses and glass ceramics,” in
*Next Generation (Nano) Photonic and Cell Technologies for Solar Energy Conversion*, vol. 7772 of*Proceedings of SPIE*, August 2010. View at: Publisher Site | Google Scholar - B. Ahrens, P. T. Miclea, and S. Schweizer, “Upconverted fluorescence in Nd
^{3+}-doped barium chloride single crystals,”*Journal of Physics: Condensed Matter*, vol. 210, no. 12, p. 125501, 2009. View at: Publisher Site | Google Scholar - C. Pfau, C. Bohley, P. T. Miclea, and S. Schweizer, “Structural phase transitions of barium halide nanocrystals in fluorozirconate glasses studied by Raman spectroscopy,”
*Journal of Applied Physics*, vol. 109, no. 8, Article ID 083545, 2011. View at: Publisher Site | Google Scholar - B. Bendow, P. K. Banerjee, M. G. Drexhage, J. Goltman, S. S. Mitra, and C. T. Moynihan, “Comparative study of vibrational characteristics of fluorozirconate and fluorohafnate glasses,”
*Journal of the American Ceramic Society*, vol. 65, no. 1, pp. C-8–C-9, 1982. View at: Publisher Site | Google Scholar - B. Bendow, M. G. Drexhage, and H. G. Lipson, “Infrared absorption in highly transparent fluorozirconate glass,”
*Journal of Applied Physics*, vol. 52, no. 3, pp. 1460–1461, 1981. View at: Publisher Site | Google Scholar - B. Ahrens, P. Löper, J. C. Goldschmidt et al., “Neodymium-doped fluorochlorozirconate glasses as an upconversion model system for high efficiency solar cells,”
*Physica Status Solidi A*, vol. 205, no. 12, pp. 2822–2830, 2008. View at: Publisher Site | Google Scholar - C. Pfau, U. Skrzypczak, M. Miclea, C. Bohley, P. T. Miclea, and S. Schweizer, “Low phonon energy BaCl
_{2}nanocrystals in Nd^{3+}-doped fluorozirconate glasses and their influence on the photoluminescence properties,” in*Proceedings of the Materials Research Society Symposium*, vol. 1404, 2012. View at: Google Scholar - C. Bohley, J.-M. Wagner, C. Pfau, P.-T. Miclea, and S. Schweizer, “Raman spectra of barium halides in orthorhombic and hexagonal symmetry: an ab initio study,”
*Physical Review B*, vol. 83, no. 2, Article ID 024107, 6 pages, 2011. View at: Publisher Site | Google Scholar - U. Skrzypczak, M. Miclea, A. Stalmashonak et al., “Time-resolved investigations of erbium ions in ZBLAN-based glasses and glass ceramics,”
*Physica Status Solidi C*, vol. 8, no. 9, pp. 2649–2652, 2011. View at: Publisher Site | Google Scholar - G. Soundararajan, C. Koughia, A. Edgar, C. Varoy, and S. Kasap, “Optical properties of erbium-doped fluorochlorozirconate glasses,”
*Journal of Non-Crystalline Solids*, vol. 357, no. 11–13, pp. 2475–2479, 2011. View at: Publisher Site | Google Scholar - B. R. Judd, “Optical absorption intensities of rare-earth ions,”
*Physical Review*, vol. 127, no. 3, pp. 750–761, 1962. View at: Publisher Site | Google Scholar - G. S. Ofelt, “Intensities of crystal spectra of rare-earth ions,”
*Journal of Chemical Physics*, vol. 37, no. 3, p. 511, 1962. View at: Publisher Site | Google Scholar - B. Walsh, “Judd-Ofelt Theory: Principles and Practices,” in
*Advances in Spectroscopy For Lasers and Sensing*, pp. 403–433, Springer, New York, NY, USA, 2006. View at: Google Scholar - U. Skrzypczak, C. Pfau, C. Bohley, G. Seifert, and S. Schweizer, “Particle size monitoring of BaCl
_{2}nanocrystals in fluorozirconate glasses,”*Journal of Non-Crystalline Solids*, vol. 363, pp. 205–208, 2013. View at: Publisher Site | Google Scholar - T. Suzuki, H. Kawai, H. Nasu et al., “Spectroscopic investigation of Nd
^{3+}-doped ZBLAN glass for solar-pumped lasers,”*Journal of the Optical Society of America B*, vol. 28, no. 8, pp. 2001–2006, 2011. View at: Publisher Site | Google Scholar - R. Caspary,
*Applied rare-earth spectroscopy for fiber laser optimization [Ph.D. thesis]*, Technische Universität Braunschweig, 2002. - A. A. Kaminskii, G. Boulon, M. Buonchristiani, B. di Bartolo, A. Kornienko, and V. Mironov, “Spectroscopy of a new laser garnet Lu
_{3}Sc_{2}Ga_{3}O_{12}:Nd^{3+},”*Physica Status Solidi A*, vol. 141, no. 2, pp. 471–494, 1994. View at: Google Scholar - W. T. Carnall, P. R. Fields, and K. Rajnak, “Electronic energy levels of the trivalent lanthanide aquo ions. I. Pr
^{3+}, Nd^{3+}, Pm^{3+}, Sm^{3+}, Dy^{3+}, Ho^{3+}, Er^{3+}, and Tm^{3+},”*Journal of Chemical Physics*, vol. 49, no. 10, pp. 4424–4442, 1968. View at: Google Scholar - X. Qiao, X. Fan, J. Wang, and M. Wang, “Luminescence behavior of Er
^{3+}ions in glass-ceramics containing CaF_{2}nanocrystals,”*Journal of Non-Crystalline Solids*, vol. 351, no. 5, pp. 357–363, 2005. View at: Publisher Site | Google Scholar - W. B. Fowler and D. L. Dexter, “Relation between absorption and emission probabilities in luminescent centers in ionic solids,”
*Physical Review*, vol. 128, no. 5, pp. 2154–2165, 1962. View at: Publisher Site | Google Scholar - C. F. Bohren and D. R. Huffmann,
*Absorption and Scattering of Light by Small Particles*, John Wiley & Sons, New York, NY, USA, 1983. - H. H. Li, “Refractive index of alkaline earth halides and its wavelength and temperature derivatives,”
*Journal of Physical and Chemical Reference Data*, vol. 9, no. 1, p. 161, 1980. View at: Google Scholar - L. Wetenkamp, T. Westendorf, G. West, and A. Kober, “The effect of small composition changes on the refractive index and material dispersion in ZBLAN heavy-metal fluoride glass,”
*Materials Science Forum*, vol. 32-33, pp. 471–476, 1991. View at: Google Scholar

#### Copyright

Copyright © 2013 U. Skrzypczak et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.