# Judd-Ofelt Calculations for Nd3+-Doped Fluorozirconate-Based Glasses and Glass Ceramics

Authors: U. Skrzypczak; C. Pfau; C. Bohley; G. Seifert; S. Schweizer
Journal: Dataset Papers in Physics
 (2013)

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## Abstract

A Judd-Ofelt analysis is performed to calculate the optical properties of Nd3+ ions embedded in a fluorozirconate glass matrix. The changes in the Judd-Ofelt parameters were determined as a function of the size of BaCl2 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.


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## Body

## 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 BaCl2 nanocrystals inside such glasses can be induced by thermal treatment as soon as additional chloride is introduced at the expense of fluoride. Since BaCl2 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 Nd3+-doped fluorochlorozirconate (FCZ) glasses with differently sized BaCl2 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 Nd3+ ions are strongly affected by the BaCl2 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 BaCl2 nanocrystals on the Nd3+ 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 52ZrF4-10BaF2-10BaCl2-19NaCl-3.5LaF3-3AlF3-0.5InF3-1KCl-1NdF3 (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 BaCl2 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 strengthsfmeas  are calculated with
(1)fmeas=4πε0e2mec2π∫k1k2‍σ(k)dk,
where me is the mass of the electron; c, the speed of light; and σ(k), the absorption cross section.The theoretical oscillator strengths feature contributions from electric,fed, and magnetic dipole transitions, fmd. Quadrupole effects are very weak and have been neglected. The dipolar oscillator strengths are of the following form:
(2)fed=4πε0e28π2meν3h(2J+1)χedSed,fmd=4πε0e28π2meν3h(2J+1)χmdSmd,
where ν is the mean frequency and J is the total angular momentum quantum number. From these, the line strengths,
(3)Sed=∑λ‍Ωλ|〈i∥Uλ∥j〉|2,Smd=(eh4πmec)2|〈i∥L+2S∥j〉|2,
are calculated, in which 〈i∥Uλ∥j〉 are the doubly reduced matrix elements of the electric dipole tensor operator and 〈i∥L+2S∥j〉 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 χed=(n2+2)2 and χmd=n [20]. The Gaussian least-squares minimization of
(4)fmeas-fmd=fed(λ)Ωλ
yields the evaluation of the intensity parameters Ωλ (with λ=2,4,6).The effective refractive indexn of a composite material made of an FCZ glass matrix with inclusion of nanometric BaCl2 crystallites has been calculated involving a Maxwell-Garnett approach [21]:
(5)εeff=εm(εi(1+2δi)-εm(2δi-2))εm(2+δi)+εi(1-δi),
where εm and εi are the dielectric constants of matrix and inclusion (data taken from [22, 23]).The radiative emission rates are calculated [14] with
(6)Aji=64π4ν33hc3(2Jj+1)(χedSed+χmdSmd).
When i is not only the ground state, the branching ratios βji=τjAji define the percentage of the rate for each possible relaxation channel.The tabular data given here are sectioned into samples with different BaCl2 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 |i〉, the target levels of the transition |j〉 along with the radiative decay rates Arad and the corresponding branching ratio βij 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.1
Data of the radiative decay parameters in the FZ glass matrix.
226
4
4
|
i
〉
|
j
〉
A
rad
β
i
j2
Data of the radiative decay parameters in the untreated FCZ glass matrix.
226
4
4
|
i
〉
|
j
〉
A
rad
β
i
j3
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].
226
4
4
|
i
〉
|
j
〉
A
rad
β
i
j4
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].
226
4
4
|
i
〉
|
j
〉
A
rad
β
i
j5
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].
226
4
4
|
i
〉
|
j
〉
A
rad
β
i
j6
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].
226
4
4
|
i
〉
|
j
〉
A
rad
β
i
j


## 4. Concluding Remarks

A Judd-Ofelt analysis under consideration of the effective-n matrix in an FZ-based glass ceramic with BaCl2 nanocrystals of different sizes has been performed in order to evaluate the optical properties of Nd3+ 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.



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*Source: 236421-2013-04-11.xml*