# Thermodynamic model for the structure of Nd doped phosphate laser glasses and the neodymium chemistry influence on their emission properties

A. López-Grande, J. Azkargorta, I. Iparraguirre, Gregory Tricot, S. Garcia-Revilla, J. Fernández, R. Balda, F. Muñoz

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A. López-Grande, J. Azkargorta, I. Iparraguirre, Gregory Tricot, S. Garcia-Revilla, et al.. Thermodynamic model for the structure of Nd doped phosphate laser glasses and the neodymium chemistry influence on their emission properties. Journal of Non-Crystalline Solids, 2025, J. Non-Cryst. Solids, 668, pp.123779. 10.1016/j.jnoncrysol.2025.123779. hal-05340219

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# Thermodynamic model for the structure of Nd doped phosphate laser glasses and the neodymium chemistry influence on their emission properties

Alberto López-Grande<sup>a</sup>, Jon Azkargorta<sup>b</sup>, Íñaki Iparraguirre<sup>b</sup>, Gregory Tricot<sup>c</sup>,
Sara García-Revilla<sup>b</sup>, Joaquín Fernández<sup>d</sup>, Rolindes Balda<sup>b,d,e</sup>, Francisco Muñoz<sup>a,*</sup> ID

## ARTICLE INFO

### Keywords:

- Phosphate glasses

- Structure

- NMR

- Thermodynamic modeling

- Neodymium

- Laser glasses

## ABSTRACT

Development of phosphate laser glasses has focused on combining good laser emission with high mechanical performance and their structure has increasingly been of importance due to the usefulness in interpreting the behavior of functional glasses and help in the design of novel compositions. Herein we tackled the interrelationships between the structure, the nearby chemical environment of Nd<sup>3+</sup> ions and the spectroscopic and laser emission properties in a series of phosphate and alumino-phosphate Nd-doped glasses. The structure has been obtained using the associated solutions model and has been confirmed by a multinuclear NMR study in the system Na<sub>2</sub>O-K<sub>2</sub>O-BaO-Al<sub>2</sub>O<sub>3</sub>-P<sub>2</sub>O<sub>5</sub>, then correlated with the emission properties of the different glasses. Nd luminescence depends on the coordination around Nd and linear and nonlinear spectroscopic results suggest that high strength modifiers in mixed-alkali compositions increase the crystal field disorder enhancing electric-dipole transitions and promoting the presence of two broad distributions of Nd<sup>3+</sup> sites.

## 1. Introduction

Phosphate based glasses are the main system of choice for the commercial manufacturing of high energy and high-power laser glasses [1]. Among their main advantages, one of the key issues is that they can host higher content of rare-earth dopants with less clustering or precipitation than it occurs in other glass systems, thus leading to lower losses from concentration quenching. However, an increase in the rare-earth doping amount is normally correlated to a decrease of the fluorescence time due to self-quenching effect, being several the mechanisms by which relaxation losses affect the laser gain and that ultimately depend upon the glass composition and structure. The most important optical parameters that are usually evaluated in a laser glass are: the emission cross-section, the radiative decay rate and the emission band-width, where the studied compositional dependences indicate that the ionic field strength of the modifier cations, alkali or alkaline-earth, and the content of Al<sub>2</sub>O<sub>3</sub> are key issues to the performance of the glasses [2]. Many glass

compositions have so far been proposed to be suitable as laser hosts, though on an empirical basis mainly. Therefore, a more in depth knowledge of the structure of the glasses should be a must if one aims to properly design new compositions with an optimal spectroscopic activity. Additionally, since the thermal shock resistance of the glass host is the most critical aspect to handle during the laser operation, research aimed principally to the production of glasses that can attain a high thermal-mechanical loading, meanwhile it has been recognized that there is a lack of "quantitative understanding of the relationship between glass structure and performance" [1].

Another important aspect of the production of phosphate laser glasses lies in their ability to retain water during the melting process, which results in glasses with different defects, such as bubbles or stria, and so in deterioration of the rare-earth fluorescence due to non-radiative decay [3]. This has been a crucial aspect to us in our laboratory that has been solved through a new procedure of preparation that consists on the re-melting of the phosphate glass in a graphite boat under

<footnote><sup>a</sup> Institute of Ceramics and Glass (CSIC), Kelsen 5, Madrid 28049, Spain</footnote>

<footnote><sup>b</sup> Applied Physics Department, Faculty of Engineering, University of the Basque Country UPV/EHU, Bilbao 48013, Spain</footnote>

<footnote><sup>c</sup> Univ. Lille, CNRS, UMR 8516 - LASIRE - Laboratoire de Spectroscopie pour les Interactions, la Réactivité & l'Environnement F-59000 Lille, France</footnote>

<footnote><sup>d</sup> Donostia International Physics Center (DIPC), San Sebastian 20018, Spain</footnote>

<footnote><sup>e</sup> Materials Physics Center CSIC-UPV/EHU, San Sebastian 20018, Spain</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: fmunoz@icv.csic.es (F. Muñoz).</footnote>
a constant flow of N₂ [4]. Phosphate and alumino-phosphate glasses have been prepared by this method and them all present very low contents of water and a high degree of homogeneity. Actually, the structure of some of these dehydrated glasses has been also studied by nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR) techniques, through which the research group confirmed that there were no changes in the structure of the glasses submitted to the dehydration process, nor changes on their chemical composition [5].

One of the key issues in the current Glass Science is focused on adequate models able to represent the atomic structure of the glasses, which is essential for the correct prediction of properties in the design of new glass compositions. The most common existing methods are based on Molecular Dynamics or Reverse Monte-Carlo modeling, despite they are limited to the use of extremely high cooling rates and because they provide non-unique solutions [6], the ab-initio methods, that are time and computationally consuming [7] or, more recently, the modeling based on the topology constraints theory [8]. Regarding the structure of phosphate glasses doped with rare-earth elements for photonic applications, there have been attempts to correlate the structure and rare-earth chemical environment with their optical properties upon systematic variations of composition [9,10] as well as on the prediction of the glass properties based on the use of a statistical influence of glass composition throughout its structural units [11–13].

Several other models, purely based on thermodynamics, have also been developed so far, despite being not so much extended, with the aim of representing the structure of glasses and their properties, among which the ideal associated solutions model has been successfully applied in a number of glass systems [14]. These models have been used to obtain the glass structure via the estimation of the type of structural units, at the short-range order, and their associates or super-structural units at a medium-range, which are the responsible for the changes in properties that can be experimentally observed with respect to their composition. In particular, the model of ideal associated solutions was originally developed in the study of organic liquid solutions [15] and was adopted by the Glass community in the 90's on the study of glass-forming melts, notably by the pioneering works of Shakhmatkin and Vedishcheva [16]. The model assumes that the melts, and their corresponding glasses, are formed by solutions of the products of reaction of the oxide components as well as by those that remain unreacted. This ideal solution can be represented by what has been called its chemical structure, which is the sum of the crystalline structures of all salt-like products and unreacted oxides that are in equilibrium at a given composition and temperature. All chemical species will have associated a molar Gibbs free energy function, from which the total Gibbs energy of the system can be calculated, and minimized, in order to calculate their equilibrium molar fractions without the need of adjustable parameters. Once the chemical structure of the glasses is known, it is possible to calculate any property that can be a function of the thermodynamic magnitudes. In sodium borosilicate glasses, for instance, Vedishcheva et al. [17] were able to quantify both borate and silicate basic structural units at different Na₂O/B₂O₃ and Si₂O/B₂O₃ ratios and verified the accuracy of the model through comparison with available experimental measurements. The structure of glasses of the system Na₂O-CaO-MgO-SiO₂ has also been examined by Chromčíková et al. [18] through the combination of Raman spectroscopy and thermodynamic modeling. The first works in phosphate glasses by using this model appeared in binary systems by Chromčíková et al. [19], who used the method in calcium phosphate glasses to describe their structure and demonstrated that the phosphate tetrahedral units (Q³, Q² and Q¹) can be precisely correlated with the structure obtained from NMR results. Our research group has already gained some experience on the use of the model of ideal associated solutions in various glass systems, such as Li₂O-P₂O₅ [20], BaO-P₂O₅ [21] as well as in alkali aluminophosphate glasses [22]. The results on these systems have shown a quite good correlation of the chemical structure and the structural groups (Qⁿ) analyzed by Raman and NMR spectroscopies for the correlation between the experimental

values of Qⁿ structural groups with their modelled data.

Our group has previously studied two glass systems doped with 1 mol % Nd₂O₃, the 13Na₂O-13K₂O-16BaO-4Al₂O₃-54P₂O₅ [5] and the 26Li₂O-16BaO-4Al₂O₃-54P₂O₅ [23]. In the first, the structure was investigated by NMR and EPR spectroscopy and it was found that Nd³⁺ ions are fully surrounded by PO₄ groups, where part of the phosphorus is bonded to 1 or even 2 aluminums through P-O-Al bonds and with aluminum atoms in six-fold coordination with oxygens [5]. Additionally, it was concluded that Al could only be located at the third or higher coordination sphere of Nd³⁺ but not in their nearby vicinity. Given the high chemical and optical homogeneity reached in these glasses, it is assumed that Nd³⁺ ions are quite homogeneously distributed within the glass network without any indication of possible clustering or showing different chemical environment possibilities. However, a very interesting result was raised after performing the site selective laser spectroscopy, which indicated that two broad neodymium site distributions with different crystal field environment could be at play. The same has also been seen in the 26Li₂O-16BaO-4Al₂O₃-54P₂O₅ [23]. At a first sight, it does not seem plausible that the alkali modifiers could have a determinant role in the crystal field environment of neodymium, although since both studied systems contain alumina, it might be possible that its presence could have some role in this aspect, which remains then to be one of the points to clarify.

The present work has been built upon a two-fold aim: on the one hand, the work has been focused onto the structural elucidation of several Nd₂O₃ doped phosphate and alumino-phosphate glasses by means of the thermodynamic model of associated solutions as well as by NMR spectroscopy in order to experimentally validate the modeling approach. We have selected a set of phosphate as well as alumina containing phosphate systems where the two already studied compositions can also be located. On the other hand, the main spectroscopic and laser emission properties of the selected glass systems have been obtained.

## 2. Methodology of thermodynamic modeling and experimental

### 2.1. Thermodynamic modeling

The thermodynamic model of ideal associated solutions, or the so-called Shakhmatkin and Vedishcheva Thermodynamic Model (SVTDM) when applied to glasses, assumes that a glass can be considered as an ideal solution formed by the products of the reactions between the former and modifier oxides and that the respective glass obtained can be represented as an ideal solution of the products of their interaction and any unreacted residual oxides. These products are groupings of atoms with equal stoichiometry to the homologous crystalline compounds in the equilibrium phase diagram and have similar ordering to the basic units of the crystalline compounds in the short-range order, yet these products exhibit translational symmetry. The characteristic equation of the system can be written as:

$$ \Delta G = \sum_{i} n_{i} \Delta g_{i}^{(f)} + RT \sum_{j} n_{j} \ln x_{j} \quad (1) $$

where the first summation extends to the reaction products and the second to both reaction products and reactant oxides; nᵢ are the equilibrium molar amounts of the salt-like products and the remaining unreacted oxides (xᵢ is the molar fraction), and Δgᵢ⁽ᵏ⁾ the Gibbs free energies of reaction for each product. The thermodynamic properties of the system, such as heat capacity, molar volume, or thermal expansion coefficient, could also be derived from the characteristic equation (Eq. (1)).

The computational methodology has to deal with a multicomponent system and so multiple chemical equilibria must occur simultaneously, that can be represented by the set of reactions:
$$ \sum_{k=1}^{r} (M_2O_m)_k \rightarrow SLP_j \qquad (2) $$

where $(M_2O_m)_k$ are the *r* network former and modifier oxides in the system and *SLP* stands for the *p* salt-like products.

The set of interdependent chemical reactions gives rise to a system of nonlinear equations that must be solved with the application of the laws of chemical equilibrium (Eq. (3)) and conservation of mass (Eq. (4)):

$$ \left\{ \begin{array}{l} K_j = \frac{x_j^i}{\prod_{k=1}^{n} x_k^i} \quad \forall j = 1, 2, \dots, p \quad (3) \\ n_k = n_k^0 + \sum_{j=1}^{p} \frac{\nu_k}{\nu_j} n_j \quad \forall k = 1, 2, \dots, r \quad (4) \end{array} \right. $$

where $K_j$ is the equilibrium constant for each reaction product, $x_i$ is the equilibrium molar fraction of each product/reactant, $\nu_i$ is the stoichiometric coefficient of each product (i=j)/reactant (i=k) in the system of equations, $n_i^0$ is the initial quantities of the reactants (oxides), and $n_i$ is the final quantities of reactants and products at chemical equilibrium.

Eqs. (3) and (4) define a system of *r* + *p* nonlinear equations with unknowns being the equilibrium quantities of each of the reactants and products participating in the equilibrium, given that the molar fractions can be rewritten as $x_i = n_i/\Sigma n$.

The salt like products together with the unreacted oxide components will determine the $Q^n$ structures present in the glass. Therefore, by knowing in what quantities each chemical species is present in the undercooled liquid, one can elucidate the structure of the resulting glass.

The glass systems that have been modelled are the following, within which it is also indicated the glass compositions that have been experimentally studied in the present work:

1. xNa₂O-(24.75-x)Li₂O-24.75BaO-49.5P₂O₅-1Nd₂O₃ (x = 0 - 24.75). Both ends of this system correspond to the 24.75Li₂O-24.75BaO-49.5P₂O₅-1Nd₂O₃ (25Li25Ba) and 24.75Na₂O-24.75BaO-49.5P₂O₅-1Nd₂O₃ (25Na25Ba) compositions for x = 0 and 24.75, respectively.

2. (15.345-5x/8)Na₂O-(15.345-5x/8)K₂O-(18.81-3x/4)BaO-xAl₂O₃-(49.5+x)P₂O₅-1Nd₂O₃ (x = 0 - 24.75). This system, that contains for x=4 the composition 12.87Na₂O-12.87K₂O-15.84BaO-3.96Al₂O₃-53.46P₂O₅-1Nd₂O₃ (NaKBa-4Al) studied in Ref. [5], has been chosen as a reference for the experimental validation of the modeled structure throughout its study by NMR up to 12 mol % alumina.

3. xLi₂O-(25.74-x)K₂O-15.84BaO-3.96Al₂O₃-53.46P₂O₅-1Nd₂O₃ (x = 0 - 24.75), which contains the last two glasses whose optical properties have been studied below: the 25.74Li₂O-15.84BaO-3.96Al₂O₃-53.46P₂O₅-1Nd₂O₃ (LiBa-4Al), studied in Ref. [23], and the 12.87Li₂O-12.87K₂O-15.84BaO-3.96Al₂O₃-53.46P₂O₅-1Nd₂O₃ (LiKBa-4Al), equivalent to NaKBa-4Al although replacing Li by Na.

The reactants are the respective oxides components of the glass formulation in every system, including Nd₂O₃. Then, we have considered the reactions involving each modifier component with P₂O₅, as in Li₂O-P₂O₅, Na₂O-P₂O₅, BaO-P₂O₅, etc. binary systems, the reactions between Al₂O₃ and P₂O₅ to produce AlPO₄ and AlP₃O₉, the reactions for existing alkali meta-, pyro- and ortho-alumino-phosphates, the reactions between Nd₂O₃ and P₂O₅ that give neodymium ultra-phosphate, metaphosphate and orthophosphate, and finally those for the formation of alkali and neodymium mixed phosphates in the form of meta-, pyro- and ortho-phosphates. The products of the above reactions are all included in the inorganic crystal structure database ICSD and the names, stoichiometric formula and number and $Q^n$-type of phosphorus in each phase have been gathered in Table 1. The $Q^n$ type groups of the compounds given in Table 1 are the type of $Q^n$ structures of the crystalline compounds and scaled to their stoichiometry. All metaphosphate phases will be composed of $Q^2$-type PO₄ tetrahedra, while pyrophosphates of $Q^1$ ones. Similarly, compositions within the polyphosphate or ultra-phosphate ranges will be composed of either $Q^2 + Q^1$ units or $Q^3 + Q^2$ ones.

<table><caption>**Table 1**

Names, formula and number of phosphorus and $Q^n$ type for the phases included into the thermodynamic calculation of equilibria.</caption><thead><tr><th>Phase</th><th>Formula</th><th>Q<sup>n</sup> per formula</th><th>Phase</th><th>Formula</th><th>Q<sup>n</sup> per formula</th></tr></thead><tbody><tr><td>LP</td><td>Li<sub>2</sub>P<sub>2</sub>O<sub>6</sub></td><td>2 Q<sup>2</sup></td><td>A3P</td><td>AlPO<sub>4</sub></td><td>1 Q<sup>0</sup></td></tr><tr><td>L2P</td><td>Li<sub>4</sub>P<sub>2</sub>O<sub>7</sub></td><td>2 Q<sup>1</sup></td><td>LAP</td><td>LiAl(PO<sub>3</sub>)<sub>4</sub></td><td>4 Q<sup>2</sup></td></tr><tr><td>L3P</td><td>Li<sub>6</sub>P<sub>2</sub>O<sub>8</sub></td><td>2 Q<sup>0</sup></td><td>LA2P</td><td>LiAlP<sub>2</sub>O<sub>7</sub></td><td>2 Q<sup>1</sup></td></tr><tr><td>NP</td><td>Na<sub>2</sub>P<sub>2</sub>O<sub>6</sub></td><td>2 Q<sup>2</sup></td><td>NaA2P</td><td>NaAlP<sub>2</sub>O<sub>7</sub></td><td>2 Q<sup>1</sup></td></tr><tr><td>N2P</td><td>Na<sub>4</sub>P<sub>2</sub>O<sub>7</sub></td><td>2 Q<sup>1</sup></td><td>NaA3P-b</td><td>Na<sub>6</sub>Al<sub>4</sub>(PO<sub>4</sub>)<sub>6</sub></td><td>6 Q<sup>0</sup></td></tr><tr><td>N3P</td><td>Na<sub>6</sub>P<sub>2</sub>O<sub>8</sub></td><td>2 Q<sup>0</sup></td><td>KAP</td><td>KAl(PO<sub>3</sub>)<sub>4</sub></td><td>4 Q<sup>2</sup></td></tr><tr><td>N5P3</td><td>Na<sub>10</sub>P<sub>6</sub>O<sub>20</sub></td><td>4 Q<sup>1</sup> + 2 Q<sup>2</sup></td><td>KA2P</td><td>KAlP<sub>2</sub>O<sub>7</sub></td><td>2 Q<sup>1</sup></td></tr><tr><td>KP</td><td>K<sub>2</sub>P<sub>2</sub>O<sub>6</sub></td><td>2 Q<sup>2</sup></td><td>KA3P-b</td><td>K<sub>6</sub>Al<sub>4</sub>(PO<sub>4</sub>)<sub>6</sub></td><td>6 Q<sup>0</sup></td></tr><tr><td>K2P</td><td>K<sub>4</sub>P<sub>2</sub>O<sub>7</sub></td><td>2 Q<sup>1</sup></td><td>NdP</td><td>Nd<sub>2</sub>P<sub>2</sub>O<sub>8</sub></td><td>2 Q<sup>0</sup></td></tr><tr><td>K3P</td><td>K<sub>6</sub>P<sub>2</sub>O<sub>8</sub></td><td>2 Q<sup>0</sup></td><td>NdP3</td><td>Nd<sub>3</sub>P<sub>2</sub>O<sub>9</sub></td><td>3 Q<sup>2</sup></td></tr><tr><td>K5P3</td><td>K<sub>10</sub>P<sub>6</sub>O<sub>20</sub></td><td>4 Q<sup>1</sup> + 2 Q<sup>2</sup></td><td>NdP5</td><td>NdP<sub>5</sub>O<sub>14</sub></td><td>2 Q<sup>3</sup> + 3 Q<sup>2</sup></td></tr><tr><td>BP</td><td>BaP<sub>2</sub>O<sub>6</sub></td><td>2 Q<sup>2</sup></td><td>LiNd</td><td>LiNd(PO<sub>3</sub>)<sub>4</sub></td><td>4 Q<sup>2</sup></td></tr><tr><td>B2P</td><td>Ba<sub>2</sub>P<sub>2</sub>O<sub>7</sub></td><td>2 Q<sup>1</sup></td><td>NaNd</td><td>NaNd(PO<sub>3</sub>)<sub>4</sub></td><td>4 Q<sup>2</sup></td></tr><tr><td>B3P</td><td>Ba<sub>3</sub>P<sub>2</sub>O<sub>8</sub></td><td>2 Q<sup>0</sup></td><td>Na3Nd</td><td>Na<sub>3</sub>Nd(PO<sub>4</sub>)<sub>2</sub></td><td>2 Q<sup>0</sup></td></tr><tr><td>B4P</td><td>Ba<sub>4</sub>P<sub>2</sub>O<sub>9</sub></td><td>2 Q<sup>0</sup></td><td>KNd</td><td>KNd(PO<sub>3</sub>)<sub>4</sub></td><td>4 Q<sup>2</sup></td></tr><tr><td>BP2</td><td>BaP<sub>4</sub>O<sub>11</sub></td><td>2 Q<sup>3</sup> + 2 Q<sup>2</sup></td><td>KNd-b</td><td>K<sub>2</sub>Nd(PO<sub>3</sub>)<sub>5</sub></td><td>5 Q<sup>2</sup></td></tr><tr><td>B3P2</td><td>Ba<sub>3</sub>P<sub>4</sub>O<sub>13</sub></td><td>2 Q<sup>2</sup> + 2 Q<sup>1</sup></td><td>K3Nd</td><td>K<sub>3</sub>Nd(PO<sub>4</sub>)<sub>2</sub></td><td>2 Q<sup>0</sup></td></tr><tr><td>AP</td><td>AlP<sub>3</sub>O<sub>9</sub></td><td>3 Q<sup>2</sup></td><td></td><td></td><td></td></tr></tbody></table>

Because the equilibrium constants have to be calculated using the free energies of reaction ($\Delta G_R$) of each compound and reactant, using the expression applicable to each reaction, $K = \exp(-\Delta G_R/RT)$, where $\Delta G_R = \nu_{prod} \cdot \Delta G_{prod}^{(f)} - \sum \nu_{react} \cdot \Delta G_{react}^{(f)}$, all energies have been taken from the FACT-sage database [24] or approximated using the methodology employed in the previous work on the modelling the alkali alumino-phosphate glasses [22]. The unknown $\Delta G_{prod}^{(f)}$ are obtained from the relationship between the electronegativity of the modifier cations in every phase compound, or its average if two or more modifiers are present, and the value of the free energy of the phosphate for each type of phosphate anion (meta-, pyro- or orthophosphate).

## 2.2. Synthesis and characterization of glasses

In this work, a group of glasses, from which the structure has been obtained by the thermodynamic model of associated solutions, have been prepared by melting and quenching and followed by a second remelting in order to eliminate water and refining the glasses. These are glasses with the following compositions in mol %: 24.75Li₂O-24.75BaO-49.5P₂O₅-1Nd₂O₃ (25Li25Ba), 24.75Na₂O-24.75BaO-49.5P₂O₅-1Nd₂O₃ (25Na25Ba), 12.87Li₂O-12.87K₂O-15.84BaO-3.96Al₂O₃-53.46P₂O₅-1Nd₂O₃ (LiKBa-4Al), 25.74Li₂O-15.84BaO-3.96Al₂O₃-53.46P₂O₅-1Nd₂O₃ (LiBa-4Al) and 12.87Na₂O-12.87K₂O-15.84BaO-3.96Al₂O₃-53.46P₂O₅-1Nd₂O₃ (NaKBa-4Al). The main spectroscopic and laser emission properties of two of the alumina containing glasses, though different alkaline modifiers, NaKBa-4Al and LiBa-4Al, have been previously studied in Refs. [5] and [23], respectively, as mentioned in the Introduction section.

The newly prepared glasses for this study, 25Li25Ba, 25Na25Ba and LiKBa-4Al, were obtained by mixing raw materials for 80 g of glass. (NH₄)₂PO₄ (ACROS Organics, 99+%), Na₂CO₃ (Alfa Aesar, 99.5% min.), Li₂CO₃ (VWR), K₂CO₃ (Sigma Aldrich, ≥99%) Al₂O₃ (Alfa Aesar, 99.9%), BaCO₃ (Alfa Aesar, 99-101%) and Nd₂O₃ (Alfa Aesar, 99.99%) were thoroughly mixed, slowly heated up to 360°C in porcelain crucibles and then melted at temperatures of 800°C, 25Li25Ba and 25Na25Ba, and 1000°C for LiKBa-4Al. The melts were poured onto a brass plate and about 10 g of each glass were re-melted systematically at 850°C for 9 h in a graphite mold within a horizontal Mullite tube furnace under a constant N₂ flow as described in [4], so the final glasses were obtained free of bubbles and stria and well annealed.

The chemical composition of the glasses was determined through X-ray Fluorescence Spectroscopy in a PANalytical MagicX 2400
spectrometer using the pearl method mixing 0.3 g of glass with 5.5 g of Li₂Ba₄O₇, meanwhile lithium contents were obtained by Inductively Coupled Plasma-Emission Spectrometry (P₂O₅ and Al₂O₃) in a Thermo Jarrel Ash IRIS Advantage equipment. The density of the glasses was determined by the Archimedes method with ethanol as immersion liquid and the refractive index was measured by optical ellipsometry in an EC-400 equipment from J.A. Woollam Co. Inc. on 1 cm² plane-parallel and mirror-like polished samples. Table 2 gathers the density, refractive index and number density of Nd³⁺ ions in the five glass systems studied.

The ²⁷Al and ³¹P magic angle spinning nuclear magnetic resonance (MAS-NMR) experiments were performed on a 9.4 T Bruker spectrometer with a 4-mm measurement probe operating at a spinning frequency of 12.5 kHz. The ²⁷Al MAS-NMR spectra were recorded at 104.25 MHz with a 0.7 µs pulse length corresponding to a π/12 flip angle, 0.5 s recycle delays (rd) and 1024 transients. The ³¹P MAS-NMR spectra were acquired at 161.96 MHz with a 2.4 µs pulse length corresponding to a π/4 flip angle, a 120 s rd and 16 transients. The 2D ²⁷Al/³¹P correlation map was recorded with the dipolar heteronuclear multiple quantum correlation NMR sequence (D-HMQC) [25,26]. The 2048 × 24 acquisition points were recorded under rotor-synchronized conditions with ²⁷Al and ³¹P π-pulses length of 14 and 9.6 µs, respectively, 2048 transients, a 0.5 s rd and a 2*0.5 ms SR4¹ pulse scheme allowing for the reintroduction of the distance dependent dipolar interaction. The short recoupling time used in these dipolar correlation experiments allows to safely discussing the results in terms of chemical connectivity. The chemical shifts were referred at 0 ppm to 1M Al(NO₃)₃ and 85% H₃PO₄ solutions.

Conventional absorption spectra were performed with a Cary 5000 spectrophotometer. Site-selective emission and excitation spectra were recorded by using as exciting light the medium wave tuning range (765-920 nm) of a continuous wave (cw) Ti:sapphire ring laser (0.4 cm⁻¹ linewidth). The fluorescence from the sample was collected and dispersed by a 0.25 m monochromator, and the signal detected by an extended IR Hamamatsu H10330A-75 photomultiplier. The photomultiplier signal was processed by a lock-in amplifier. A continuous flow cryostat was used to perform the low-temperature (4.2 K) measurements. The decay times were obtained by exciting the sample with a Ti-sapphire laser pumped by a pulsed, frequency double Nd-YAG laser (10 ns pulse width) and detecting the emission by an extended IR Hamamatsu H10330A-75 photomultiplier. The photomultiplier signal was recorded by using a Tektronix oscilloscope.

<caption>**Table 2**</caption>

Analyzed chemical compositions in mol % of oxide components of the three new prepared glasses and the two previously studied in Refs. [5,23]. Density, refractive index by ellipsometry and number density of Nd³⁺ ions in all glass samples.

<table><thead><tr><th>Oxide</th><th>25Li25Ba</th><th>25Na25Ba</th><th>LiBa-4Al</th><th>NaKBa-4Al</th><th>LiKBa-4Al</th></tr></thead><tbody><tr><td>Li₂O</td><td>18.8</td><td>-</td><td>11</td><td>-</td><td>20.2</td></tr><tr><td>Na₂O</td><td>-</td><td>22.6</td><td>-</td><td>12.9</td><td>-</td></tr><tr><td>K₂O</td><td>-</td><td>-</td><td>11.7</td><td>13.5</td><td>-</td></tr><tr><td>BaO</td><td>26.3</td><td>25.9</td><td>16.5</td><td>14.9</td><td>17.4</td></tr><tr><td>Al₂O₃</td><td>&lt;0.2</td><td>&lt;0.2</td><td>4.2</td><td>4.4</td><td>4.1</td></tr><tr><td>P₂O₅</td><td>54</td><td>50.6</td><td>55.6</td><td>53.2</td><td>57.3</td></tr><tr><td>Nd₂O₃</td><td>0.9</td><td>0.9</td><td>0.9</td><td>0.9</td><td>1.1</td></tr><tr><td>SiO₂</td><td>1.1</td><td>0.5</td><td>0.6</td><td>0.3</td><td>-</td></tr><tr><td>Density (g.cm⁻³)</td><td>3.058</td><td>3.085</td><td>2.876</td><td>2.828</td><td>2.850</td></tr><tr><td>Refractive index<br>532 nm</td><td>1.5489</td><td>1.5256</td><td>1.5419</td><td>1.4948</td><td>1.5355</td></tr><tr><td>Nd³⁺<br>concentration<br>(x10²⁰ cm⁻³)</td><td>2.63</td><td>2.68</td><td>3.0</td><td>2.47</td><td>2.30</td></tr></tbody></table>

### 3. Results

#### 3.1. Model of the chemical structure of the phosphate and alumino-phosphate glass systems

Fig. 1a shows the results of the simulation for the chemical equilibria of the system (24.75-x)Li₂O-xNa₂O-24.75BaO-49.5P₂O₅-1Nd₂O₃, as the molar fraction of each of the phases against the mol % of Na₂O in the system. Furthermore, Fig. 1b shows the molar fraction of the neodymium containing phases that have been introduced into the model and also represented against the Na₂O content. Because the system belongs entirely to the metaphosphate composition, the dominating phases are all metaphosphates as it can be seen in Fig. 1a. The plot starts at the 24.75Li₂O-24.75BaO-49.5P₂O₅ composition, where Li₂P₂O₆ (LP) and BaP₂O₆ (BP) appear with similar fraction, though LP presents a slightly higher content. At this initial composition, a small contribution from B3P2 phases (Ba₃P₄O₁₃), L2P (Li₄P₂O₇) and BP2 (BaP₄O₁₁) can be noticed, which appear as due to the disproportionation of LP and BP metaphosphate into ultra- and polyphosphate groupings, as it has been observed previously in [20,21]. The composition is actually not purely metaphosphate due to the 1 mol % of Nd₂O₃ added; therefore, there will always be some small contributions of the stable phases within the polyphosphate region of the glasses. That disproportionation is not that

<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /></figure>

**Fig. 1.** Results of the thermodynamic calculation at 1000 K of the system of composition (24.75-x)Li₂O-xNa₂O-24.75BaO-49.5P₂O₅-1Nd₂O₃ (x = 0 - 24.75), as by the molar fraction of phases of the system against the mol % of Na₂O that replaces Li₂O (a), and separately the molar fractions of neodymium containing phases against the mol % Na₂O (b).
significant for the Li₂O-P₂O₅ system with respect the BaO-P₂O₅ one at the metaphosphate composition [20], and so LP is the dominant one at that point of the diagram. After replacing some Li₂O by Na₂O, the system evolves through a mixed alkaline system with presence of both Li₂P₂O₆ and Na₂P₂O₆ phases, showing equal amounts at 1:1 ratio of Li₂O:Na₂O. Then, the system is composed of BaP₂O₆ and Na₂P₂O₆ mainly until at the 24.75Na₂O-24.75BaO-49.5P₂O₅ composition on the right-hand side of the plot.

On the other hand, as it can be seen in Fig. 1b, Nd³⁺ is never present within a pure neodymium phosphate, but in the form of mixed alkali neodymium phosphates, either with Li or Na and with some small contribution of neodymium metaphosphate (NdP3, Nd₂P₆O₁₈). It is only for the compositions close to the one of 24.75Li₂O-24.75BaO-49.5P₂O₅ that the lithium neodymium metaphosphate (LiNd, Li₂Nd₂P₄O₁₄) is predominant. Once the Li₂O by Na₂O substitution starts, the sodium neodymium phase NaNd (Na₂Nd₂P₄O₁₄) rises and becomes predominant for even below the 5 mol % Na₂O. The presence of these Nd mixed phosphates influences the evolution of the rest of the products in Fig. 1a, particularly at 0 mol % Na₂O. Barium is present as products with higher O/P ratio: Ba₃P₄O₁₃ (O/P=3.25) and pyrophosphate (Ba₂P₂O₇, O/P=3.5). A negligible amount of BP2 (BaP₄O₁₁) with O/P=2.75, is also formed, but clearly not enough to compensate the increase in O/P introduced by the former two compounds. This no-compensation can be explained by the formation of the Nd mixed metaphosphates, that reduces the amount of phosphorus available for the rest of the oxides.

We would like to mention at this point that the (24.75-x)Na₂O-xK₂O-24.75BaO-49.5P₂O₅ glass system was also modeled, although not shown in this work, and that it shows similar results to the lithium-sodium barium phosphate one, with the main difference being the formation of the two potassium neodymium metaphosphates considered into the calculation, the KNd (KNd(PO₃)₄) and KNd-b (K₂Nd(PO₃)₅) phases. After the Na₂O by K₂O substitution, the KNd phase starts forming first though the KNd-b phase becomes the predominant even below the 5 mol % K₂O in the glass up to the final end of 24.75K₂O-24.75BaO-49.5P₂O₅ composition. After comparison of the modeling in the couples of systems 25Li25Ba-25Na25Ba and 25Na25Ba-25K25Ba, all with 1 mol % Nd₂O₃, it is worth mentioning that when the two alkali modifiers are present, the mixed alkali neodymium phosphate that is formed has preference for the alkali of higher size, i.e. Na over Li and K over Na.

The results of modeling the system (15.345-5x/8)Na₂O-(15.345-5x/8)K₂O-(18.81-3x/4)BaO-xAl₂O₃-(49.5+x)P₂O₅-1Nd₂O₃ are gathered in Fig. 2a and b, against the mol % of Al₂O₃. For x=0, the system is represented by similar proportions of the three metaphosphate phases, KP (K₂P₂O₆), BP (BaP₂O₆) and NP (Na₂P₂O₆), in order of importance, respectively. Upon introduction of Al₂O₃, the molar fractions of the above metaphosphates progressively decrease while the first aluminum-phosphate phases are formed, notably the potassium aluminum metaphosphate, KAP (KAl₂(PO₃)₄), that shows an increasing fraction up to about 10 mol % Al₂O₃. Together with the former, small fractions of two pyrophosphates can also be noticed, KA2P and NaA2P. Then, from 10 mol % Al₂O₃, the fraction of KAP starts to decrease and it is now the aluminum metaphosphate phase, AP (AlP₃O₉), the one that starts increasing at a very high rate until the end of the plot at near 25 mol % Al₂O₃. At this final content of alumina, the system would have reached the composition 24.75Al₂O₃-74.25P₂O₅-1Nd₂O₃, i.e. which approximately corresponds to the aluminum metaphosphate, if it were not because of the 1 mol % Nd₂O₃, thus in agreement with a nearly 100 % of aluminum metaphosphate in the plot. Because of that small amount of Nd₂O₃ present, that forms neodymium metaphosphate, NdP3 (NdP₃O₉), at that high alumina content because there are no more alkalis, as it can be seen in Fig. 2b, not all phosphorus is available to form aluminum metaphosphate only. Therefore, a small contribution of aluminum orthophosphate, A3P (AlPO₄), is also present at that composition of near 25 mol % Al₂O₃.

The phases containing neodymium can be seen in Fig. 2b. For Al₂O₃ below 7 mol %, only the potassium neodymium metaphosphate K₂Nd

<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /><figcaption>**Fig. 2.** Thermodynamic results at 1000 K for the system (15.345-5x/8)Na₂O-(15.345-5x/8)K₂O-(18.81-3x/4)BaO-xAl₂O₃-(49.5+x)P₂O₅-1Nd₂O₃ (x = 0 - 24.75) represented by the molar fraction of all phases against the mol % of Al₂O₃ (a) and the molar fractions of the neodymium containing phases against the alumina content (b).</figcaption></figure>

(PO₃)₅, KNd-b, is present. However, with further incorporation of Al₂O₃ into the system, i.e. decreasing K₂O content, KNd-b starts decreasing above 7 mol % Al₂O₃ and KNd appears, showing a maximum below 10 mol % Al₂O₃, then decreasing, and neodymium starts forming NaNd mainly, NaNd(PO₃)₄. Approaching the 25 mol % Al₂O₃ limit, the predominant neodymium phase becomes the metaphosphate NdP₃O₉, NdP.

Finally, the results of the modeling of the system xLi₂O-(25.74-x) K₂O-15.84BaO-3.96Al₂O₃-53.46P₂O₅-1Nd₂O₃ are gathered in Fig. 3a and b. This system has been formulated with a constant content of Al₂O₃ of ca. 4 mol %, and reaches the equimolar ratio between Li₂O and K₂O with the 12.87Li₂O-12.87K₂O-15.84BaO-3.96Al₂O₃-53.46P₂O₅-1Nd₂O₃ (LiKBa-4Al glass) composition, then ending with the 25.74Li₂O-15.84BaO-3.96Al₂O₃-53.46P₂O₅-1Nd₂O₃ (LiBa-4Al glass) composition at the left-hand side of Fig. 3a. With the last two compositions, LiKBa-4Al and LiBa-4Al, the 5 glasses whose optical properties will be shown below have been included within the modeled systems.

Upon replacement of K₂O by Li₂O in the system, Fig. 3a, the thermodynamic modeling shows an opposite behavior for the KP and LP phases, as expected by the above substitution and in agreement with the similar exchange of alkali oxides in the lithium and sodium barium phosphate system of Fig. 1a. In the present case, the BP content is also constant within the studied compositional range and, due to the constant content of a 4 mol % of Al₂O₃, the potassium aluminum metaphosphate
<figure><img src="image_8.png" /><figcaption>**Fig. 3.** Results of chemical equilibria at 1000 K in the system xLi₂O-(25.74-x) K₂O-15.84BaO-3.96Al₂O₃-53.46P₂O₅-1Nd₂O₃ (x = 0 - 24.75): molar fractions of all phases as a function of the mol % of Li₂O (a); and molar fractions of neodymium containing phases against the mol % of Li₂O (b).</figcaption></figure>

phase, KAP (KAl(PO₃)₄) is also present in a significant amount until above 20 mol % Li₂O, from where it starts decreasing until the pure lithium end composition. Fig. 3b shows that the predominant neodymium containing phase is, again in presence of potassium, the KNd-b one, (K₂Nd(PO₃)₅), up to ca. 20 mol % Li₂O, point at which it decreases at the expense of KNd first, KNd(PO₃)₄, and LiNd secondly, LiNd(PO₃)₄, near the end of the plot for the pure lithium end composition.

## 3.2. Experimental structure of the Nd₂O₃ containing (15.345-5x/8) Na₂O-(15.345-5x/8)K₂O-(18.81-3x/4)BaO-xAl₂O₃-(49.5+x)P₂O₅-1Nd₂O₃ glasses by NMR for x= 0-12

NMR spectra have been acquired in samples of the system of composition 0.99(13Na₂O-13K₂O-16BaO-xAl₂O₃-(50+x)P₂O₅)-0.01Nd₂O₃ for x= 2, 4, 8 and 12. Samples from 2 to 8 mol % Al₂O₃ have also been studied in a work by Guillet *et al.*, where the thermal shock resistance of the glasses has been evaluated against the content of alumina [27]. The glass sample for x=4, corresponds actually to the composition NaKBa-4Al. Additionally we have prepared for the present study a glass with a nominal 12 mol % of Al₂O₃, although after chemical analysis it reduces to a 10.12%; being the P₂O₅ content of 59.6%. The contents of alumina for the glasses denoted as NaKBa-2Al, NaKBa-4Al, NaKBa-8Al and NaKBa-12Al are 1.74, 4.26, 8.01 and 10.12%, respectively.

The ²⁷Al MAS-NMR spectra of the compositional line for glasses with

x = 2, 4, 8, 12, are reported in Fig. 4(a). The analysis shows the presence of six-coordinated (⁶Al) aluminate species through the main signal located at -20 ppm. This signal is accompanied by low intensity signals at 0 and 40 ppm showing the presence of [⁵Al] and [⁴Al] species at high Al₂O₃ contents. Quantification of the ²⁷Al MAS-NMR spectra confirmed that the glasses mainly contain six-coordinated aluminate species, in good agreement with the approximate metaphosphate (O/P=3) composition line. As previously reported in other alumino-phosphate systems [28–32], the overall Al coordination number decrease can be observed when the Al/P ratio increases.

The ³¹P MAS-NMR spectra are displayed in Fig. 4b. The spectra are composed by a single broad and asymmetric signal, as expected from the mixed network phosphate compositions [33]. The signal broadness also increases with the Al₂O₃ content, suggesting that the presence of Al atoms led to more complex structures, as previously observed in other alumino-phosphate systems. This complex structure is explained by the high number of possible configurations in mixed network phosphate glasses. While only 4 different Qⁿ species (Q³, Q², Q¹, Q⁰) can be observed in standard phosphate glasses (for which the glass network is only based on P tetrahedra), combination of P and Al led to a dramatic increase of the possible configurations that need to be described with an extended Qⁿ<sub>mAl</sub> notation (with n and m being the number of connected P and Al atoms, respectively). The structures of the investigated glasses are thus composed by both Qⁿ and Qⁿ<sub>mAl</sub> species, leading to the observed complex structure. The overall chemical shift of the broad and asymmetric signal evolves from -20 to -40 ppm when the Al₂O₃ content increases, in line with the evolution from a mono- and di-valent metaphosphate to an alumino-metaphosphate structure. Additional information is provided by the 2D ²⁷Al/³¹P correlation maps presented in Fig. 5. These 2D maps indicate the presence of Al-O-P linkages in the glass network through the presence of correlation signals. In addition to the dominant [⁶Al-O-P] bonds, the 2D map of the NaKBa-12Al sample also shows the presence of [⁵Al-O-P] linkages, indicating that all the different aluminate species contribute to the formation of the mixed network. The 2D map projections have been used to guide the ³¹P MAS-NMR spectra decompositions following a protocol used in previous studies [31–33]. Fig. 6 presents the ³¹P projections of the 2D maps showing the NMR signal corresponding to the P involved in P-O-Al linkage (Qⁿ<sub>mAl</sub> species). These signals have been decomposed with a single broad component centered at -24 ppm, in line with a Q²<sub>1Al</sub> assignment (Table 3). A second low intensity component has been added in the decomposition of the NaKBa-12Al sample indicating the presence of a new Qⁿ<sub>mAl</sub> species at high Al₂O₃ content. Owing to its chemical shift values (-40 ppm), this species has been assigned to Q²<sub>2Al</sub> moieties. The qualitative NMR parameters (chemical shift, broadness) of these two species have then been used as input parameters for the decompositions of the 1D ³¹P MAS-NMR, in addition to the parameters expected for the standard Qⁿ species (Table 3). The decompositions show the decrease of the initial Q² species that are replaced by Q²<sub>1Al</sub> and Q²<sub>2Al</sub> species when Al₂O₃ in introduced in the formulation. Very small amounts of Q¹ and Q³ were also observed indicating a minor Q² disproportionation. The model is then tested by comparing the O/P ratio and the number of P-O-Al linkages calculated from the nominal composition and from the NMR model. The O/P ratios calculated from the relative proportions of the different Qⁿ and Qⁿ<sub>mAl</sub> species are reported in Table 3. All the values are close to 3 and show a good agreement with the ratio of expected from the metaphosphate compositions. The number of P-O-Al linkages calculated from the Qⁿ<sub>mAl</sub> assignment and relative proportions and the number of Al-O-P linkages calculated from the overall [x]Al speciation, assuming that the Al atoms are only connected to P (and thus forming Al (OP)n units), have been compared with good agreement. The values were 20.9 and 23.7 (NaKBa-2Al), 51 and 45.1 (NaKBa-4Al), 94.7 and 82.8 (NaKBa-8Al) and 117.1 and 119.2 (NaKBa-12Al), respectively for P-O-Al and Al-O-P bonds. The good agreement between both methods indicates that the qualitative and quantitative data of the model can be trusted.
<figure><img src="image_9.png" /><figcaption>Fig. 4. $^{27}$Al (a) and $^{31}$P (b) MAS-NMR experiments of the x composition line.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 5. 2D $^{27}$Al($^{31}$P) D-HMQC correlation maps obtained on the x composition line. The 2D maps are accompanied by the $^{27}$Al and $^{31}$P projections in the horizontal and vertical axes, respectively.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>**Fig. 6.** $^{31}$P projections of the $^{27}$Al($^{31}$P) D-HMQC correlation maps obtained on the x composition line (a). 1D $^{31}$P MAS-NMR spectra decomposition based on the information provided by the 2D maps projections (b).</figcaption></figure>

<caption>**Table 3**</caption>

$^{31}$P NMR parameters: chemical shift ($\delta_{iso}$, +/- 0.1 ppm), full width at half maximum (FWHM, +/- 0.2 ppm) and relative proportions (rel. prop., +/- 2%). The NMR parameters deduced from the simulations of the $^{31}$P projections of the $^{27}$Al/$^{31}$P 2D maps are reported into brackets.

<table><thead><tr><th>Al<sub>2</sub>O<sub>3</sub> (mol %)</th><th>Q<sup>b</sup><sub>naAl</sub></th><th>δ<sub>iso</sub> (ppm)</th><th>FWHM (ppm)</th><th>Rel. prop. (%)</th><th>Q<sup>i</sup></th><th>δ<sub>iso</sub> (ppm)</th><th>FWHM (ppm)</th><th>Rel. prop. (%)</th><th>O/P (±0.02)</th></tr></thead><tbody><tr><td rowspan="3">2</td><td rowspan="3">Q<sup>2</sup><sub>lAl</sub></td><td rowspan="3">-26.0 (-25.9)</td><td rowspan="3">13.5 (13.4)</td><td rowspan="3">23</td><td>Q<sup>3</sup></td><td>-34.3</td><td>10.1</td><td>3</td><td rowspan="3">2.99</td></tr><tr><td>Q<sup>2</sup></td><td>-22.0</td><td>8.7</td><td>72</td></tr><tr><td>Q<sup>i</sup></td><td>-10.6</td><td>8.2</td><td>2</td></tr><tr><td rowspan="3">4</td><td rowspan="3">Q<sup>2</sup><sub>lAl</sub></td><td rowspan="3">-27.0 (-26.5)</td><td rowspan="3">13.6 (13.5)</td><td rowspan="3">42</td><td>Q<sup>3</sup></td><td>-36.3</td><td>10.2</td><td>5</td><td rowspan="3">2.98</td></tr><tr><td>Q<sup>2</sup></td><td>-23.2</td><td>9.2</td><td>51</td></tr><tr><td>Q<sup>i</sup></td><td>-11.5</td><td>8.3</td><td>2</td></tr><tr><td rowspan="3">8</td><td rowspan="3">Q<sup>2</sup><sub>lAl</sub></td><td rowspan="3">-29.2 (-28.6)</td><td rowspan="3">14.5 (14.4)</td><td rowspan="3">73</td><td>Q<sup>3</sup></td><td>-42.0</td><td>12.0</td><td>6</td><td rowspan="3">2.97</td></tr><tr><td>Q<sup>2</sup></td><td>-23.7</td><td>8.8</td><td>20</td></tr><tr><td>Q<sup>i</sup></td><td>-11.7</td><td>8.3</td><td>1</td></tr><tr><td rowspan="3">12</td><td>Q<sup>2</sup><sub>lAl</sub></td><td>-30.5 (-30.4)</td><td>14.5 (14.4)</td><td>74</td><td>Q<sup>3</sup></td><td>-50.0</td><td>11.9</td><td>3</td><td rowspan="3">2.99</td></tr><tr><td>Q<sup>2</sup><sub>2Al</sub></td><td>-40.8 (-41.3)</td><td>12.7 (12.7)</td><td>13</td><td>Q<sup>2</sup></td><td>-23.5</td><td>8.8</td><td>9</td></tr><tr><td></td><td></td><td></td><td></td><td>Q<sup>i</sup></td><td>-11.8</td><td>8.5</td><td>1</td></tr></tbody></table>

### 3.3. Spectroscopic properties of modeled phosphate and alumino-phosphate glasses

#### 3.3.1. Absorption spectra. Judd-Ofelt parameters

The room temperature absorption spectra for the group of five different glass compositions were recorded in the 200-950 nm spectral range. The spectra show the bands corresponding to the transitions from the $^{4}$I$_{9/2}$ ground state to the excited states of Nd$^{3+}$ ion. Fig. 7 shows the absorption coefficient of the glasses. The transitions were assigned by comparing with energy levels of previously reported Nd$^{3+}$ glass systems [5]. The absorption bands were integrated and used together with the Nd$^{3+}$ concentrations to calculate the experimental oscillator strengths according to the relation:

$$f_{\text{exp}} = \frac{mc^2}{\pi e^2 N} \int_{\text{band}} \alpha(\nu) d\nu \qquad (5)$$

where m and e are the mass and charge of the electron, respectively, c is the speed of light, $\alpha(\nu)$ is the absorption coefficient, $\nu$ is the frequency and N is the rare-earth concentration. The obtained values for the oscillator strength are displayed in Table 4. The results show that the hypersensitive transition $^{4}$I$_{9/2}$→$^{4}$G$_{5/2}$+$^{2}$G$_{7/2}$ always shows higher values when compared with other bands. It is also observed that the oscillator strengths of most of the transitions are higher in LiKBa-4Al,

25Na25Ba and 25Li25Ba glasses and that the highest values correspond to LiKBa-4Al glass which could indicate a higher asymmetry compared to the other glasses.

The values of the oscillator strengths were used to calculate the Judd-Ofelt parameters (JO) by using a least square fit method [34,35]. The matrix elements used in the fitting procedure were those reported by Carnall et al. [36]. In the case of overlapping transitions, the corresponding matrix elements were summed. The JO parameters obtained for the glasses investigated in this work are displayed in Table 5. The value of $\Omega_2$ generally indicates the covalence between Nd$^{3+}$ ions and ligand anions and also reflects the asymmetry of the local environment at the Nd$^{3+}$ site while the $\Omega_4$ and $\Omega_6$ are associated to the rigidity of the host medium. As it can be seen, among all the glass matrices studied, the highest values of $\Omega_2$ correspond to glasses containing K (NaKBa-4Al and LiKBa-4Al glasses) suggesting that the Nd$^{3+}$ site shows higher asymmetry for these glass compositions, i.e. the lower the value of $\Omega_2$ parameter the higher the centro-symmetrical ion site and more ionic in nature of rare earth ligand bond [37]. In the present work, lithium barium glass matrices (LiBa-4Al and 25Li25Ba) show lower $\Omega_2$ parameter than the other glasses indicating more centro-symmetrical ion site. In the case of the $\Omega_4$ and $\Omega_6$ parameters, the lowest values correspond to NaKBa-4Al and LiBa-4Al glasses which indicate lower rigidity compared to the other compositions investigated. The obtained values for the JO intensity parameters are similar to those of commercial glass lasers such
<figure><img src="image_12.png" /><figcaption>**Fig. 7.** Room temperature absorption spectra for the five glass compositions doped with 1 mol % Nd₂O₃.</figcaption></figure>

as Hoya et al. [1]. The values for the spectroscopic quality factor, Ω₄/Ω₆, are less than 1 for all glasses, having the lowest values for NaKBa-4Al and LiBa-4Al glasses.

### 3.3.2. Near infrared emission and radiative properties

The ⁴F₃/₂⁻⁴I₁₁/₂,¹³/₂ emission spectra were measured at room temperature by exciting the samples at 803 nm in resonance with the ⁴I₉/₂→⁴F₅/₂,²H₉/₂ absorption band. Fig. 8 shows the emission spectra for the studied glasses. The emission intensity of the ⁴F₃/₂⁻⁴I₁₁/₂ laser transition is only dependent on the Ω₄ and Ω₆ parameters and can be expressed in terms of the spectroscopic quality factor χ = Ω₄/Ω₆. To maximize the fluorescence intensity to the ⁴I₁₁/₂ level the requirement is

<caption>**Table 5**</caption>

JO intensity parameters for the five glass compositions doped with 1 mol % Nd₂O₃.

<table><thead><tr><th>Glass</th><th>Ω₂(× 10<sup>-20</sup>cm²)</th><th>Ω₄(× 10<sup>-20</sup>cm²)</th><th>Ω₆(× 10<sup>-20</sup>cm²)</th><th>Ω₄/Ω₆</th></tr></thead><tbody><tr><td>NaKBa-4Al [5]</td><td>4.5</td><td>3.5</td><td>5.6</td><td>0.60</td></tr><tr><td>LiBa-4Al [23]</td><td>3.96</td><td>3.62</td><td>5.33</td><td>0.68</td></tr><tr><td>LiKBa-4Al</td><td>4.84</td><td>4.98</td><td>6.63</td><td>0.75</td></tr><tr><td>25Li25Ba</td><td>3.92</td><td>4.32</td><td>5.92</td><td>0.73</td></tr><tr><td>25Na25Ba</td><td>4.04</td><td>4.40</td><td>6.07</td><td>0.72</td></tr></tbody></table>

<figure><img src="image_13.png" /><figcaption>**Fig. 8.** Room temperature emission spectrum of the ⁴F₃/₂→⁴I₁₁/₂ transition of Nd³⁺ ions in the studied glasses obtained under excitation in the ⁴I₉/₂→⁴F₅/₂,²H₉/₂ absorption band.</figcaption></figure>

Ω₄<Ω₆. In these glasses, the spectroscopic quality factor is less than 1 which means that the most efficient emission from the ⁴F₃/₂ state corresponds to the ⁴F₃/₂→⁴I₁₁/₂ transition. As it can be seen, the emission bands are inhomogeneously broadened due to site-to-site variations in the local ligand field and the peak position is practically the same for all samples. The highest emission intensity for the ⁴F₃/₂→⁴I₁₁/₂,¹³/₂ transitions corresponds to the LiKBa-4Al glass. The emission band for the ⁴F₃/₂→⁴I₁₁/₂ transition was integrated and divided by the peak intensity to yield an effective linewidth in order to estimate the stimulated emission cross-section of this transition by using [37]:

$$ \sigma_p(\lambda_p) = \frac{\lambda_p^4}{8\pi c n^2 \Delta\lambda_{eff}} A[(^4F_{3/2}) \cdot (^4I_{11/2})] \quad (6) $$

where λₚ is the peak fluorescence wavelength, n is the refractive index, Δλₐff is the effective linewidth, and A[(⁴F₃/₂);(⁴I₁₁/₂)] is the radiative transition probability for this transition [38]. The JO intensity parameters were used to calculate the radiative transition probabilities, branching ratios and radiative lifetimes shown in Table 6.

The stimulated emission cross-section is one of the most important laser glass properties since together with the quantum yield control the

<caption>**Table 4**</caption>

Experimental oscillator strengths for the five glass compositions doped with 1 mol % Nd₂O₃.

<table><thead><tr><th>Transition from the <sup>4</sup>I<sub>9/2</sub> to:</th><th>f<sub>exp</sub>(10<sup>-6</sup>) NaKBa-4Al [5]</th><th>f<sub>exp</sub>(10<sup>-6</sup>) LiBa-4Al</th><th>f<sub>exp</sub>(10<sup>-6</sup>) LiKBa-4Al</th><th>f<sub>exp</sub>(10<sup>-6</sup>) 25Na25Ba</th><th>f<sub>exp</sub>(10<sup>-6</sup>) 25Li25Ba</th></tr></thead><tbody><tr><td><sup>4</sup>F<sub>3/2</sub></td><td>1.90</td><td>1.86</td><td>2.38</td><td>2.14</td><td>2.16</td></tr><tr><td><sup>4</sup>F<sub>5/2</sub> + <sup>2</sup>H<sub>9/2</sub></td><td>7.24</td><td>6.69</td><td>8.92</td><td>8.1</td><td>8.04</td></tr><tr><td><sup>4</sup>F<sub>7/2</sub> + <sup>4</sup>S<sub>3/2</sub></td><td>6.93</td><td>7.24</td><td>8.65</td><td>7.8</td><td>7.8</td></tr><tr><td><sup>4</sup>F<sub>9/2</sub></td><td>0.49</td><td>0.53</td><td>0.62</td><td>0.55</td><td>0.55</td></tr><tr><td><sup>2</sup>H<sub>11/2</sub></td><td>0.13</td><td>0.15</td><td>0.15</td><td>0.14</td><td>0.14</td></tr><tr><td><sup>4</sup>G<sub>5/2</sub> + <sup>2</sup>G<sub>7/2</sub></td><td>16.58</td><td>15.8</td><td>20.4</td><td>17.4</td><td>17.3</td></tr><tr><td><sup>2</sup>K<sub>13/2</sub> + <sup>4</sup>G<sub>7/2</sub> + <sup>4</sup>G<sub>9/2</sub></td><td>5.79</td><td>4.32</td><td>7.19</td><td>6.55</td><td>6.29</td></tr><tr><td><sup>2</sup>K<sub>15/2</sub> + <sup>2</sup>G<sub>9/2</sub> + <sup>2</sup>D<sub>3/2</sub> + <sup>4</sup>G<sub>11/2</sub></td><td>1.59</td><td>1.13</td><td>1.96</td><td>1.79</td><td>1.79</td></tr><tr><td><sup>2</sup>P<sub>1/2</sub></td><td>0.35</td><td>0.51</td><td>0.41</td><td>0.38</td><td>0.38</td></tr><tr><td><sup>4</sup>D<sub>3/2</sub> + <sup>4</sup>D<sub>5/2</sub> + <sup>2</sup>I<sub>11/2</sub> + <sup>4</sup>D<sub>1/2</sub></td><td>8.33</td><td>7.8</td><td>10.8</td><td>9.39</td><td>9.44</td></tr></tbody></table>
<caption>**Table 6**</caption>

Radiative transition probabilities $A_R$ (s⁻¹), branching ratios $\beta_R$ (%) and radiative lifetimes $\tau_R$ (µs) of the studied glasses doped with 1 mol % Nd₂O₃.

<table><caption>**Table 7**</caption><thead><tr><th>Glass</th><th>⁴I<sub>15/2</sub>→</th><th>A<sub>R</sub> (s<sup>-1</sup>)</th><th>β<sub>R</sub> (%)</th><th>τ<sub>R</sub> (µs)</th></tr></thead><tbody><tr><td rowspan="4">NaKBa-4Al [5]</td><td>⁴I<sub>15/2</sub></td><td>12</td><td>0.5</td><td rowspan="4">416</td></tr><tr><td>⁴I<sub>13/2</sub></td><td>272.4</td><td>11.3</td></tr><tr><td>⁴I<sub>11/2</sub></td><td>1279.2</td><td>53.2</td></tr><tr><td>⁴I<sub>9/2</sub></td><td>837.6</td><td>34.9</td></tr><tr><td rowspan="4">LiBa-4Al [23]</td><td>⁴I<sub>15/2</sub></td><td>12.5</td><td>0.48</td><td rowspan="4">384</td></tr><tr><td>⁴I<sub>13/2</sub></td><td>284.7</td><td>11</td></tr><tr><td>⁴I<sub>11/2</sub></td><td>1367.8</td><td>52.6</td></tr><tr><td>⁴I<sub>9/2</sub></td><td>936.4</td><td>36</td></tr><tr><td rowspan="4">LiKBa-4Al</td><td>⁴I<sub>15/2</sub></td><td>15.4</td><td>0.46</td><td rowspan="4">301</td></tr><tr><td>⁴I<sub>13/2</sub></td><td>349.5</td><td>10.5</td></tr><tr><td>⁴I<sub>11/2</sub></td><td>1713.8</td><td>51.6</td></tr><tr><td>⁴I<sub>9/2</sub></td><td>1246.6</td><td>37.5</td></tr><tr><td rowspan="4">25Li25Ba</td><td>⁴I<sub>15/2</sub></td><td>14.1</td><td>0.46</td><td rowspan="4">332</td></tr><tr><td>⁴I<sub>13/2</sub></td><td>320.7</td><td>10.6</td></tr><tr><td>⁴I<sub>11/2</sub></td><td>1563.6</td><td>51.9</td></tr><tr><td>⁴I<sub>9/2</sub></td><td>1115</td><td>37</td></tr><tr><td rowspan="4">25Na25Ba</td><td>⁴I<sub>15/2</sub></td><td>13.8</td><td>0.47</td><td rowspan="4">340</td></tr><tr><td>⁴I<sub>13/2</sub></td><td>313.5</td><td>10.7</td></tr><tr><td>⁴I<sub>11/2</sub></td><td>1526.2</td><td>53.2</td></tr><tr><td>⁴I<sub>9/2</sub></td><td>1084.4</td><td>36.9</td></tr></tbody></table>

Room temperature emission properties of Nd³⁺ in the studied glasses doped with 1 mol % Nd₂O₃ for the ⁴F₃/₂→⁴I₁₁/₂ transition.

<table><thead><tr><th>Glass</th><th>λ<sub>p</sub> (nm)</th><th>Δλ<sub>eff</sub> (nm)</th><th>σ<sub>p</sub> (nm) x10<sup>-20</sup> cm<sup>2</sup></th><th>τ<sub>exp</sub> (μs)</th><th>σ<sub>p</sub> x τ<sub>exp</sub> cm<sup>2</sup>s</th></tr></thead><tbody><tr><td>NaKBa-4Al [5]</td><td>1053</td><td>23.2</td><td>3.9</td><td>370</td><td>144.3 x 10<sup>-25</sup></td></tr><tr><td>LiBa-4Al [23]</td><td>1053</td><td>25.6</td><td>3.6</td><td>350</td><td>125 x 10<sup>-25</sup></td></tr><tr><td>LiKBa-4Al</td><td>1053</td><td>24.0</td><td>4.9</td><td>344</td><td>167.2 x 10<sup>-25</sup></td></tr><tr><td>25Li25Ba</td><td>1054</td><td>24.8</td><td>4.3</td><td>320</td><td>137.6 x 10<sup>-25</sup></td></tr><tr><td>25Na25Ba</td><td>1054</td><td>23.9</td><td>4.4</td><td>325</td><td>145.2 x 10<sup>-25</sup></td></tr></tbody></table>

energy storage, gain coefficient, and extraction efficiency of the laser glass. The stimulated emission cross-section for the ⁴F₃/₂→⁴I₁₁/₂ transition is presented in Table 7, together with the peak position ($\lambda_p$), effective fluorescence linewidth ($\Delta\lambda_{eff}$), and experimental lifetime ($\tau_{exp}$) measured by exciting at 803 nm. The value of the experimental lifetime corresponds to the fit to a single exponential function. The quantum efficiency values can be estimated from the experimental and calculated radiative lifetimes ($\eta=\tau_{exp}/\tau_R$).

The values of the stimulated emission cross-section are in the range of the commercial Nd-phosphate glass which are currently used for high average power Nd-phosphate lasers [1,39]. In the studied glasses, the highest value for the stimulated emission cross-section corresponds to the glass composition containing Li and K (LiKBa-4Al) in agreement with the highest emission intensity observed in this glass.

The experimental decays of the ⁴F₃/₂ state were obtained by exciting the samples with a pulsed Ti-sapphire laser at 803 nm in the ⁴I₉/₂→⁴F₅/₂ absorption band at room temperature. In all cases the decays can be described by a single exponential function and the lifetime values are similar to those reported for commercial glasses (Schott, Hoya, Kigre) [1,40]. The product of the stimulated emission cross-section and experimental lifetime, known as a figure of merit, should be as large as possible to attain high optical gain. In these glasses the values are between 125 and 167.2 x 10⁻²⁵ cm²s, which are higher than in other phosphate glasses [41]. The spectroscopic and laser parameters of these glass compositions close of the commercial glass lasers show its suitability for laser amplification around 1053 nm as it has already been demonstrated for NaKBa-4Al and LiBa-4Al glasses [5,23].

### 3.3.3. Site selective laser spectroscopy

In the two previous works [5,23], we have investigated the crystal field inhomogeneity of Nd³⁺ ions in NaKBa-4Al and LiBa-4Al glasses, respectively, by using site selective laser spectroscopy. Low temperature (4.2 K) emission spectra were performed by exciting the samples at different wavelengths along the low energy component of the ⁴I₉/₂→⁴F₉/₂ transition whereas the excitation spectra were obtained by collecting the luminescence along the ⁴F₃/₂→⁴I₁₁/₂ laser transition. The results showed that the shape, peak position and linewidth of the emission band depend on the excitation wavelength. In both glasses the spectra narrow and red shift from 1051.5 to 1059.5 nm in the case of NaKBa-4Al glass, and from 1050 to 1058.5 nm in LiBa-4Al one. Moreover, the excitation spectra obtained at different emission wavelengths showed more than one peak in the low energy component of the doublet ⁴F₃/₂. All these results point out to the presence of two (or more) spectrally overlapped site distributions for Nd³⁺ ions in these glasses. In order to check the influence of glass composition on the crystal inhomogeneity at the Nd³⁺ site we also have performed the low temperature emission and excitation spectra for LiKBa-4Al and 25Li25Ba glasses, one of the two without alumina. The excitation spectra were obtained by collecting the luminescence between 1042.5 nm and 1080 nm. As an example, Fig. 9 shows the spectra for LiKBa-4Al and 25Li25Ba glasses obtained between 1042.5 nm and 1058 nm. As it can be seen, in both cases two peaks are clearly observed in the low energy component

<figure><img src="image_14.png" /><figcaption>**Fig. 9.** Normalized excitation spectra of the ⁴I₉/₂→⁴F₉/₂ transition obtained by collecting the Nd³⁺ luminescence at different emission wavelengths along the ⁴F₃/₂→⁴I₁₁/₂ transition. Data correspond to 4.2 K.</figcaption></figure>
of the $ ^{4}\text{I}_{9/2} \rightarrow ^{4}\text{F}_{9/2} $ transition (only one peak should appear for a low symmetry site) by collecting the luminescence at the high energy side of the $ ^{4}\text{F}_{3/2} \rightarrow ^{4}\text{I}_{11/2} $ transition. As the emission wavelength increases, the low energy component broadens and red shift. The same behaviour is observed for the glass without $\text{Al}_2\text{O}_3$, which indicates that the presence of $\text{Al}_2\text{O}_3$ at the given concentration in these compositions (4 mol %) does not have a significant influence on the site distributions.

The site-selective emission spectra were obtained by exciting between 874 and 882 nm. For all the studied glasses the spectra narrow and red shift as the excitation wavelength increases. The effective linewidth is reduced from 19.7 nm to 9.5 nm in the case of LiKBa-4Al glass and from 19.3 to 11 nm in the case of 25Li25Ba glass. A red shift from 1050.5 to 1058.1 nm is observed for LiKBa-4Al glass and from 1052.5 to 1061 in the case of 25Li25Ba glass. Fig. 10 shows the normalized emission spectra obtained at 4.2 K at different excitation wavelengths.

### 3.3.4. Laser emission

The crystal field inhomogeneities observed in the spontaneous emission are also reflected in the stimulated emission obtained under selective excitation in the $ ^{4}\text{F}_{5/2} $ level. The suitability of these glasses for laser emission has been demonstrated in previous works for NaKBa-4Al [5] and LiBa-4Al glasses [23]. Account taken of the highest stimulated emission and figure of merit of the LiBaK-4Al glass, we have performed

<figure><img src="image_15.png" /><figcaption>**Fig. 10.** Normalized emission spectra of the $ ^{4}\text{F}_{3/2} \rightarrow ^{4}\text{I}_{11/2} $ transition obtained by exciting $\text{Nd}^{3+}$ ions along the low energy component of the $ ^{4}\text{I}_{9/2} \rightarrow ^{4}\text{F}_{9/2} $ transition. Data correspond to 4.2 K.</figcaption></figure>

laser experiments by using a pulsed tunable Ti-sapphire laser of 0.1 nm spectral width and 9 ns pulse width. The 4.4 mm thick plate sample was placed at Brewster angle inside a 15 cm long confocal resonator as described previously [23].

The laser output spectra were recorded as a function of pumping wavelength along the $ ^{4}\text{I}_{9/2} \rightarrow ^{4}\text{F}_{5/2} $ absorption band. As an example, Fig. 11 shows three series of laser emission spectra obtained at different excitation wavelengths. The effective linewidth of the laser emission changes with the excitation wavelength from 0.73 nm at 793 nm increasing to 1.85 nm as the excitation wavelength increases up to 807 nm and decreasing again for longer excitation wavelengths showing the high crystal field inhomogeneity of the glass matrix. The laser emission obtained by exciting at the shortest excitation wavelengths between 793 and 798 nm is centered around 1053.3 nm with another component at

<figure><img src="image_16.png" /><figcaption>**Fig. 11.** $ ^{4}\text{F}_{3/2} \rightarrow ^{4}\text{I}_{11/2} $ laser emission obtained at different excitation wavelengths along the $ ^{4}\text{I}_{9/2} \rightarrow ^{4}\text{F}_{5/2} $ absorption band.</figcaption></figure>
1053.9 nm (see Fig. 11a). As the excitation wavelength increases up to 803 nm, the spectra slightly blue shift being the mean peak situated around 1052.8 nm (Fig. 11b). The emission slightly red-shifts for longer excitation wavelengths and presents two peaks at 1053.4 and 1054.1 nm. A similar behavior has also been observed in NaKBa-4Al [5] and LiBa-4Al [23] phosphate glasses and attributed to the existence of well-defined inhomogeneous Nd³⁺ site distributions.

Regarding the energy threshold, which depends on the emission cross-section, and in accordance with the highest value obtained for the stimulated emission cross section, LiBaK-4Al glass composition presents the lowest laser threshold value, of 11 mJ, among the three glasses studied (LiBa-4Al (15 mJ) and NaKBa-4Al (26 mJ).

As it has been seen, the laser emission is inhomogeneously broadened due to the slightly different local environments for Nd³⁺ ions in the glass matrix. The inhomogeneity of the gain medium leads to a gain profile that can be much broader than the axial mode spacing of the laser cavity, allowing multiple axial modes to oscillate. A practical procedure to obtain a narrowed laser output is to insert a thin etalon inside the laser cavity [42]. The use of an intracavity etalon allows selecting a single longitudinal mode or a narrow group of modes tuning the laser frequency by changing its tilt angle.

Following previous results obtained for LiBa-4Al glass [23], we have also explored the possibility of tuning the laser emission in LiBaK-4Al glass by using an intracavity etalon (a 0.15 mm thick microscope coverslip), first placed perpendicular to the resonator axis (θ = 0°), and then slightly tilted, and measuring the corresponding laser emission spectra.

Fig. 12 shows the laser emission for different angles. As it can be seen, the laser emission presents a strong narrowing when compared

<figure><img src="image_17.png" /><figcaption>Fig. 12. $^{4}$F$_{3}$$_{/}$$_{2}$→$^{4}$I$_{11}$$_{/}$$_{2}$ laser emission obtained by exciting the LiKBa-4Al glass at 803 nm as a function of the tilt angle θ of the intracavity glass plate.</figcaption></figure>

with those obtained without the glass plate (Fig. 11). Moreover, depending on the angle, one or two laser lines with a spectral width lower that the resolution of the system (0.4 nm) are observed. The observed behavior is similar to that found in LiBa-4Al glass [23].

The wavelength λ corresponding to a maximum transmitted intensity of the order m is given by

$$2ne\sqrt{1 - \frac{\sin^2\theta}{n^2}} = m\lambda \qquad (7)$$

being e the thickness of the plate, n its refractive index and θ the angle between the incident laser beam and the perpendicular to the plate. In our case, for a 0.15 mm thick intracavity plate (n = 1.50), a difference of approximately 2.5 nm is expected at small angles between two successive orders of etalon transmission, which coincides with that observed in Fig. 12. This figure also shows a blue-shift of the emission when increasing the tilt angle in agreement with Eq. (7). Therefore, the etalon allows the laser emission wavelength to be fixed and tuned, in addition to making it much narrower which is useful for precision applications.

# 4. Discussion

## 4.1. The model of the structure in the alumino-phosphate glasses

The results of the thermodynamic modeling of the three different systems of composition that have been developed in this work, allow us to fully describe the chemical structure of the glasses as a function of their compositions, i.e. a representation of the structure of the glasses throughout a distribution of chemical groupings with the same short-range order structure and chemical composition as the ones present in the stable stoichiometric phases. The last are the phases that can be formed by the reaction of the oxides components of the system. As it was pointed out above, this modeling has worked very fine in the representation of the structure, in terms of the Qn units, in binary phosphate systems, such the Li₂O-P₂O₅ [20], Na₂O-P₂O₅ [44], BaO-P₂O₅ [21] and the ZnO-P₂O₅ [43]. Furthermore, the results of the model may not only be useful to obtain the quantitative Qn distribution of phosphate units along the modifier to former ratio, but also to obtain the values of the proportion of species that result from disproportionation reactions. This result is actually remarkable in the case of the BaO-P₂O₅ system at the metaphosphate composition [21] and particularly for the ZnO-P₂O₅ system [43] for glasses formulated near the pyrophosphate composition, which were first synthesized and their structure analyzed by NMR by Brow et al. [44]. The thermodynamic modeling permits the quantification of all structural Qn groups only with the resolution of the system of equilibria that give rise to the thermodynamically stable phases at the given temperature without any adjustable parameters. In more complex glasses, like the alumino-phosphates, a complete modeling has been recently obtained in the system 50M₂O-xAl₂O₃-(50-x)P₂O₅ (M=Li,K) [22], where it is possible to get the type of Qn units of the network, as well as the type of aluminum coordination depending on the chemical environment of aluminum in the structure of the phases involved.

Regarding the systems of composition in the present work, despite their high number of components, the results should be relatively easy to analyze given that all compositions modeled are of the metaphosphate type. This actually simplifies the solution of the system and notably the interpretation of the results. For instance, the results plotted in Fig. 1, and that correspond to the line between 25Li₂O-25BaO-50P₂O₅ and 25Na₂O-25BaO-50P₂O₅, exception of the 1 mol % of Nd₂O₃ added, represent a near metaphosphate composition that is formed by lithium, sodium and barium metaphosphate phases, in stoichiometric amounts depending on the oxides contents. Because of the small amount of neodymium added, the glasses are not purely metaphosphate and so some very small contribution of polyphosphate phases could be found. Additionally, it can also be seen the preference of neodymium to associate with different metaphosphate type compounds depending on what
is the major modifier present, lithium-neodymium metaphosphate or sodium-neodymium metaphosphate in the system of Fig. 1.

If one now looks at the results in Fig. 2a, regarding the aluminum-phosphate glasses of the system (15.345-5x/8)Na₂O-(15.345-5x/8)K₂O-(18.81-3x/4)BaO-xAl₂O₃-(49.5+x)P₂O₅-1Nd₂O₃, also metaphosphate glasses, it can be seen that the majority of phases are metaphosphates, although their molar fraction seem also to depend on what if the type of neodymium phase formed. Fig. 2a shows that for alumina contents 10 mol %, the potassium metaphosphate (KP) phase decreases much faster than the sodium and barium ones. This is due to the fact that, with the addition of alumina, the main aluminum containing phase is a potassium aluminum metaphosphate, so part of potassium goes from the KP phase to the KAP one and, furthermore, because the main Nd containing phase at that alumina content is a potassium neodymium metaphosphate. Above 10 mol % Al₂O₃, however, there is not any more potassium to form a K-Nd-P phase, so the new Nd phase formed is the sodium neodymium metaphosphate, which in parallel induces the formation of other pyrophosphate species, such NaA2P at the expenses of a higher decreasing rate of the sodium metaphosphate. It is then remarkable that the formation of any of the phases included in the equilibria is fully balanced.

The main issue in the results shown in Fig. 2, is the fact that the aluminum becomes involved mainly in the potassium aluminum metaphosphate (KAP), that shows a maximum at near 10 mol % Al₂O₃, and above that, aluminum forms aluminum metaphosphate, that progressively increases reaching a near to 1 molar fraction at the maximum of the alumina content plotted. This is actually in full agreement with the stoichiometric variation of the composition of the system, since at the 25 mol % of Al₂O₃ in a pure Al₂O₃-P₂O₅ system, the composition would correspond exactly to the AlP₃O₉, the aluminum metaphosphate, thus confirming the results of the model. In practice, the results of the model including the 1 mol % Nd₂O₃ do not allow the formation of a 100 % AlP₃O₉ since part of the Nd now forms the neodymium metaphosphate (NdP3) (Fig. 2b) and so there is a smaller amount of P₂O₅ than the 75 % needed for the AlP₃O₉, which additionally gives rise to formation of a small amount of aluminum orthophosphate as well. Regarding the aluminum environment in both KAP and AP phases, this should be in six-fold coordination in both phases, as it has been seen in the ²⁷Al NMR spectra (Fig. 4), particularly for lower than 8 mol % Al₂O₃ glasses, where the aluminum atoms are mainly in six-fold coordination as well.

In the first work on the glasses of the same system, though with a 4 mol % Al₂O₃ only, the neodymium structure was studied by Electron Paramagnetic Resonance [5], where it was concluded that only phosphorus could be in the second coordination sphere around Nd³⁺ ions, with the probability of aluminum being near Nd very low. This actually fits well with the results from the structural model that account for neodymium involved in metaphosphate phases with other alkali cations.

As it was presented above, the thermal mechanical properties of similar glasses of the same system Na₂O-K₂O-BaO-Al₂O₃-P₂O₅ with 1 mol % Nd₂O₃, were studied recently by Guillet et al. [27]. The structure of these glasses, together with a higher alumina containing one, has been studied though ³¹P and ²⁷Al NMR whose results have been presented in Figs. 4 to 6. Through the quantification of the different resonances, attributed to signals of phosphorus with and without bonding to aluminum, one can obtain the relative content of phosphorus in P-O-Al bonds over the total phosphorus for each alumina composition. Similarly, using the thermodynamic modeling and the data of moles of phases in the equilibria, it is possible to get the percentage of phosphorus present in alumina containing phases over the total phosphorus for each composition. The results of these calculations, from both NMR and the model, have been plotted in Fig. 13 against the analyzed mol % of Al₂O₃. The regular increase of P-O-Al bonds with the alumina in the network denotes a good agreement between both methodologies and demonstrates the validity of the model in the representation of the structure of the glass networks under study. However, both sets of values show some difference and the systematic higher % of P involved in P-O-Al linkages

<figure><img src="image_18.png" /><figcaption>Fig. 13. Comparison of the percentage of phosphorus involved in the formation of mixed P-O-Al linkages represented by those obtained experimentally by NMR analysis (black squares) and the ones obtained from the thermodynamic calculations (red circles).</figcaption></figure>

obtained by NMR are still not perfectly understood. We believe that some type of heterogeneity could be missed by the thermodynamic model or that the NMR protocol overestimates the number of P involved in the mixed linkages.

## 4.2. Influence of the Nd chemical environment on the laser emission properties of the glasses

It is then assumed that the chemical groupings of the phases containing neodymium atoms will also be valid to represent the chemical environment of the Nd³⁺ ions in the glasses. The results of the calculations of the Nd phases shown in Figs. 1b–3b, allow one to study which phosphate phases are formed in terms of the glass composition and that would be relevant for their relationship with the optical and laser emission properties of the glass samples studied in this work. Fig. 1b, as noted above, shows that Nd is present in the form of LiNd(PO₃)₄ for the glass 25Li25Ba and in the form of NaNd(PO₃)₄ for the glass 25Na25Ba (Fig. 1b). The three other glasses of the study are all containing 4 mol % Al₂O₃, and the Nd is present in the phase K₂Nd(PO₃)₅ for the glass NaKBa-4Al (Fig. 2b), LiNd(PO₃)₄ in LiBa-4Al (Fig. 3b at 25.74 mol % Li₂O) and K₂Nd(PO₃)₅ in LiKBa-4Al (Fig. 3b at 12.87 mol % Li₂O). These results indicate that always that K is present above a threshold content, the Nd phase will mostly be the K₂Nd(PO₃)₅. Actually, when Li and Na are together (Fig. 1b), the LiNd(PO₃)₄ phase is only predominant over the NaNd(PO₃)₄ up to values of less than 2 or even 1 mol % Na₂O which indicates a higher stability of the Na phase over the Li one. Overall, it could be derived from the results that the stability of the Nd containing phases, relative to the alkali modifier, increases in the order Li<Na<K. However, this apparent preference for the Nd to be within metaphosphate phases with one or another alkaline modifier should not be regarded as the predominant factor for its stability since it will all depend on what is the stability of the rest of phosphate and aluminum-phosphate species between each other, and how much of each modifier is left to be able to form any phase with neodymium.

Actually, the comparison between the spectroscopic results shown here allowed us to reach the conclusion that amongst all five studied glasses, those in which neodymium is in similar chemical environments as in the K₂Nd(PO₃)₅ and NaNd(PO₃)₄ metaphosphates show the best results. From the values of the Judd-Ofelt parameters presented in Table 5, the highest value of Ω₂ has been found for the LiKBa-4Al and NaKBa-4Al glass samples, both containing 4 % Al₂O₃ and also both where the Nd containing phase is the K₂Nd(PO₃)₅. This indicates that
Nd-O bonds would be more covalent and that the asymmetry of the NdO₈ coordination polyhedra will be higher, giving rise to an enhancement of the electric-dipole transitions. Furthermore, the product of emission cross-section and fluorescence lifetime shown in Table 7 do also give the best values for the glasses LiKBa-4Al, NaKBa-4Al and 25Na25Ba glasses, being notably the LiKBa-4Al the best amongst all five samples.

Therefore, it is the nearby chemical environment around Nd³⁺ ions the one which determines the better or worse performance of the laser host. Additionally, the two mixed-alkali glasses, NaKBa-4Al and LiKBa-4Al, are those with lower Nd³⁺ density (Table 2) which will also enhance their fluorescence properties since the non-radiative losses by concentration quenching would be lower than in the rest of samples. Although not strictly comparable with the rest of compositions due to the absence of alumina and higher BaO content, the glass sample 25Na25Ba, where Nd belongs to NaNd(PO₃)₄ chemical environment, does also show a good σₚ × τₑₚ figure of merit, which indicates that emission properties are indeed enhanced in compositions with lower field strength modifiers nearby the Nd³⁺ ions following the order Li<Na<K.

On the other hand, the two site distributions of Nd³⁺ with different crystal field environments that have been suggested from the site selective laser spectroscopy and laser emission cannot finally been attributed to different chemical environments in either phosphate or alumino-phosphate glasses, since it appears regardless of the alkaline modifiers as well as alumina content. The same effect has been observed in the two first studied systems containing alumina [5,23], the LiKBa-4Al glass of the present work also with 4 mol % Al₂O₃, as well as in the 25Li25Ba newly studied glass, without alumina and lithium instead of potassium. However, the thermodynamic modeling of the Nd containing phases has shown that the NaKBa-4Al and LiKBa-4Al systems have Nd with chemical environment as in K₂Nd(PO₃)₅ phase, while the Nd enters the LiNd(PO₃)₄ in LiBa-4Al and 25Li25Ba glasses or NaNd(PO₃)₄ in the 25Na25Ba glass sample. In the respective crystal structures of K₂Nd(PO₃)₅ [45], LiNd(PO₃)₄ [46] and NaNd(PO₃)₄ phases [47], (space groups Cc, C2/c and P2₁/c, respectively) the neodymium octupies the center of NdO₈ dodecahedra, than in the case of K₂Nd(PO₃)₅ lacks of local inversion symmetry around Nd³⁺, as also shown in its equivalent structure KNd(PO₃)₄ (space group P2₁) [48]. This acentric perturbation of the crystal field symmetry present in Nd³⁺ site polyhedra, particularly in K₂Nd(PO₃)₅ type structures, and which enhances f-f dipolar forbidden transitions, could also be related to the influence of the structural disorder facilitated by alkali ions which in turn, may also be responsible for the Nd³⁺ site distributions observed by site-selective laser spectroscopy and which is common to the different composition systems studied. Finally, it is also worth mentioning that the Nd coordination polyhedra in the above chemical environment must be isolated from each other, not sharing oxygen atoms, additionally giving rise to their reduced concentration quenching of the neodymium fluorescence.

## 5. Conclusions

The structure of the Nd-doped alumino-phosphate glasses is composed of a network of metaphosphate groupings, of the alkaline and barium metaphosphates, as well as the mixed alkali-aluminum metaphosphates that transform to aluminum-metaphosphate at high Al₂O₃ contents and ending at the pure AlP₃O₉ phase for the highest alumina composition. When two alkalis are present, there is a preference for the mixed metaphosphate to incorporate the lower ionic field strength modifier where the PO₄ building units have one phosphorus bonded to an AlO₆ polyhedra. At the point where AlP₃O₉ appears, new PO₄ are formed having two of its phosphorus bonded to aluminum. Throughout the evolution of the number of phosphorus bonded to aluminum in the form of P-O-Al bonds, we have been able to verify by NMR experiments the modeled structure in the Na₂O-K₂O-BaO-Al₂O₃-P₂O₅ glasses for increasing contents of alumina along the metaphosphate line. Furthermore, the thermodynamic model approach is also useful to obtain the

most stable phase in which Nd is contained, so that the spectroscopic properties of the glasses can be interpreted in terms of the chemical environment of Nd that is found for every system of composition. It has been found that glasses in which Nd is in the sodium or potassium neodymium metaphosphates are those with best emission properties, whose electric-dipole transitions are enhanced due to the higher covalency of the Nd-O bonds as well as by the higher asymmetry of the Nd environment. Therefore, it can be concluded that, despite the difficulties in achieving a full descriptive picture of the structure and environment of rare-earth active ions in the phosphate laser glasses, the structural study by the thermodynamic modeling method permits a direct correlation between the local structure around the active element and its optical properties.

## CRediT authorship contribution statement

**Alberto López-Grande:** Writing – review & editing, Writing – original draft, Software, Methodology, Investigation, Conceptualization.

**Jon Azkargorta:** Writing – review & editing, Writing – original draft, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Inaki Iparraguirre:** Writing – review & editing, Writing – original draft, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Gregory Tricot:** Writing – review & editing, Writing – original draft, Visualization, Methodology, Funding acquisition, Formal analysis, Data curation, Conceptualization. **Sara García-Revilla:** Writing – review & editing, Writing – original draft, Visualization, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. **Joaquín Fernández:** Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Software, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. **Francisco Muñoz:** Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Software, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization.

**Rolindes Balda:** Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Software, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. **Joaquín Fernández:** Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Software, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. **Francisco Muñoz:** Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Software, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgments

This work has been funded by MICINN (grant number PID2020-115419GBC-21/C-22/AEI/10.13039/501100011033), the University of the Basque Country with GIU21/006 grant and the Basque Country Government through project PIBA2023_1_006. GT would like to thank Region Nord Pas de Calais, Europe (FEDER), CNRS, University of Lille for funding of the NMR spectrometer.

## Data availability

Data will be made available on request.

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