# Realization of Extreme Nonstoichiometry in Gadolinium Aluminate Garnets by Glass Crystallization Synthesis

Xue Fang, Victor Castaing, Ana Isabel Becerro, Weiwei Cao, Emmanuel

Veron, Didier Zanghi, Matthew Dyer, Cécile Genevois, Mathieu Allix, Michael

J Pitcher

► To cite this version:

Xue Fang, Victor Castaing, Ana Isabel Becerro, Weiwei Cao, Emmanuel Veron, et al.. Realization of Extreme Nonstoichiometry in Gadolinium Aluminate Garnets by Glass Crystallization Synthesis. Chemistry of Materials, 2024, 36 (17), pp.8555-8563. 10.1021/acs.chemmater.4c02266. hal-04680150

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Submitted on 28 Aug 2024

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<figure><img src="image_1.png" /></figure>
# Realization of extreme nonstoichiometry in gadolinium aluminate garnets by glass crystallization synthesis

Xue Fang¹†, Victor Castaing², Ana Isabel Becerro², Weiwei Cao¹, Emmanuel Veron¹, Didier Zanghi¹, Matthew S. Dyer³, Cécile Genevois¹, Mathieu Allix¹* and Michael J. Pitcher¹*

¹CNRS, UPR3079 CEMHTI, 1D avenue de la Recherche Scientifique, 45071 Orléans, France

²Instituto de Ciencia de Materiales de Sevilla (CSIC-US), c/Américo Vespucio, 49, 41092 Seville, Spain

³Department of Chemistry, University of Liverpool, Crown Street, Liverpool L69 7ZD, UK

†Current address: Advanced Energy Storage Technology Research Center, Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China

Email: mathieu.allix@cnrs-orleans.fr, michael.pitcher@cnrs-orleans.fr

## Abstract

The garnet aluminates RE<sub>3</sub>Al<sub>5</sub>O<sub>12</sub> (RE = Gd – Lu, Y) are an important class of optical materials with a range of applications. Typically, they do not tolerate large deviations from ideal stoichiometry, and their luminescence properties are controlled by dopant selection rather than modification of the host structure. Here, we use glass crystallization as a nonequilibrium synthesis route to a new family of highly nonstoichiometric gadolinium aluminate garnets, of formula Gd<sub>3+x</sub>Al<sub>5-x</sub>O<sub>12</sub> with x ≤ 0.60. Remarkably, this range is much broader than the previously reported Y<sub>3+x</sub>Al<sub>5-x</sub>O<sub>12</sub> series (x ≤ 0.4), despite the vast size contrast between Al<sup>3+</sup> and Gd<sup>3+</sup> which are forced to share a crystallographic site in the nonstoichiometric materials: the endmember Gd<sub>3.6</sub>Al<sub>4.4</sub>O<sub>12</sub> lies half-way between ideal garnet and perovskite stoichiometries, with 30% of its octahedral Al<sup>3+</sup> sites substituted by Gd<sup>3+</sup>. In principle, this crystal chemistry should allow the synthesis of phosphor systems with rare-earth activators distributed over two different cation sublattices. To probe the response of luminescence properties to extreme nonstoichiometry in Gd<sub>3+x</sub>Al<sub>5-x</sub>O<sub>12</sub>, we synthesized three model phosphor systems by doping with Ce<sup>3+</sup>, Tb<sup>3+</sup> or Tm<sup>3+</sup>/Yb<sup>3+</sup>, and found that upconversion (Tm<sup>3+</sup>/Yb<sup>3+</sup>) phosphors have the most potential to be tuned by this approach. These results demonstrate that highly nonstoichiometric garnet aluminates are not limited to small rare-earth hosts such as YAG, opening new opportunities for development of different garnet-based optical and magnetic materials.
# 1. Introduction

The rare-earth aluminate garnets $RE_3Al_5O_{12}$ ($RE$ = Eu – Lu, Y) are attractive host materials for optical applications in solid state lasers,¹ lighting and display technologies² and scintillation detectors³, owing to their excellent optical isotropy, chemical and physical stability, and their crystal structure that offers three types of cation environments suitable for hosting wide variety of emission centres. These materials form over extremely narrow compositional ranges, and are typically represented as line phases in the $RE_2O_3 – Al_2O_3$ pseudo-binary phase equilibria diagrams. This characteristic is rooted in their crystal chemistry: their structures (general formula $A_3B_2C_3O_{12}$) feature three cation sublattices A (8-coordinate dodecahedral site), B (6-coordinate octahedral) and C (4-coordinate tetrahedral), shown in Figure 1. The resulting segregation of large ($RE^{3+}$) and small ($Al^{3+}$) cations onto the A and (B, C) sublattices respectively is associated with a low tolerance to deviation from ideal (3:5) stoichiometry. For example, in $Y_3Al_5O_{12}$ (YAG), the most energetically favourable way to deviate from the nominal stoichiometry is to substitute $Y^{3+}$ for B site $Al^{3+}$,⁴ but such substitutions are difficult to realize in appreciable concentrations, with an estimated limit of $x < 0.03$ in conventionally-synthesised YAG ceramics.⁵ This behavior is common to all members of the $RE_3Al_5O_{12}$ series⁶ and means that rare-earth dopants used to introduce and control luminescence properties are effectively constrained to a single crystallographic sublattice (A) with similar local coordination environments for each dopant ion. The luminescence properties of the phosphors are thus controlled by the identity of the dopant(s), with little scope for further property tuning via control of dopant distribution within the host structure. However, if large deviations from 3:5 stoichiometry can be imposed on the host structure, it becomes possible to distribute significant concentrations of dopant ions over multiple cation sublattices, representing an extra degree of freedom for property tuning. We recently demonstrated this effect in a series of highly nonstoichiometric YAGs ($Y_{3+x}Al_{5-x}O_{12}$ with $0 \le x \le 0.40$),⁷ which can be isolated by crystallisation of glass or deeply-undercooled melts. In these materials, excess $Y^{3+}$ substitutes up to 20% of the $Al^{3+}$ at the B sublattice. This allows small $RE^{3+}$ dopants such as $Yb^{3+}$ and $Er^{3+}$ to be distributed over the A and B sublattices, with a strong effect on the color of their upconversion emission.
<figure><img src="image_2.png" /><figcaption>**Figure 1.** Unit cell of the cubic garnet structure of Gd₃Al₅O₁₂ projected along [001] (cell edges marked by dashed line), with structural fragments showing the local A, B and C cation environments.</figcaption></figure>

The extension of this concept to non-YAG garnets (*RE*₃+*_x_*Al₅-*x*O₁₂) could have significant advantages, but it also presents certain challenges. Notably, a wider range of applications can be addressed by changing *RE*³⁺. For example, as well as their photoluminescence properties, *RE*₃Al₅O₁₂ garnet aluminates based on heavier rare-earths such as Lu₃Al₅O₁₂ are particularly suitable for use as scintillators;³ while the Gd₃Al₅-*x*Ga*x*O₁₂ family hosts excellent persistent luminescence properties;⁸,⁹ and the various open-shell 4f<sup>x</sup> configurations support different magnetic phenomena and applications.¹⁰⁻¹² The challenges to this development relate mainly to synthesis and crystal chemistry: the extent of crystallographic site-sharing between Al³⁺ and Y³⁺ in Y₃+*_x_*Al₅-*x*O₁₂ is already surprising due to their large size contrast,⁷ but several of the garnet-forming rare earth ions have an even larger radius than yttrium. Conventional crystallo-chemical assumptions suggest that these should be even less amenable to non-stoichiometry. Like YAG, nonstoichiometric *RE*₃+*_x_*Al₅-*x*O₁₂ are expected to be metastable, and should require an appropriate synthesis route that avoids extended annealing times at very high temperatures. It is clear that, before the potential of *RE*₃+*_x_*Al₅-*x*O₁₂ functional materials can be realized, it is important to understand which *RE*³⁺ systems are amenable to extreme nonstoichiometry, where their compositional and thermal stability limits lie, and how to synthesize them.
Here, we focus on RE = Gd³⁺ (GAG), which has been investigated extensively for its optical properties including luminescence and scintillation,¹³,¹⁴ and for its complex low temperature magnetism.¹⁰,¹¹ Gd₃Al₅O₁₂ lies close to the stability limit of the RE₃Al₅O₁₂ series (RE = Eu – Lu, Y) and is itself metastable,¹⁵ but it is readily synthesised in polycrystalline form by sol-gel¹⁶ and glass crystallisation⁷,¹⁷ methods. Polycrystalline GAG-based phosphors are more easily prepared when the garnet phase is stabilised by decreasing the A/(B,C) ionic radius ratio (e.g. by partially substituting Lu³⁺ for Gd³⁺, or Ga³⁺ for Al³⁺).¹⁸,¹⁹ The substitution of Gd³⁺ by larger RE³⁺ ions increases this ratio and rapidly destabilises the garnet structure: Eu₃Al₅O₁₂ is significantly more challenging to synthesise,²⁰ and to the best of our knowledge there are no reports of bulk Sm₃Al₅O₁₂. As Gd³⁺ is the largest RE³⁺ ion to yield a readily-synthesisable RE₃Al₅O₁₂ garnet, compared to YAG, it may be possible to distribute a wider range of RE³⁺ dopants over multiple sublattices due to the larger B site environment induced by nonstoichiometry in a Gd₃+xAl₅-xO₁₂ system. Here, we explore the compositional limits of the highly nonstoichiometric GAG system Gd₃+xAl₅-xO₁₂ synthesised by glass crystallization, and investigate experimentally the structural and luminescence responses of three different phosphor types (upconversion and broad-/narrow-band photoluminescence) to nonstoichiometry.

## 2. Experimental

### 2.1 Glass crystallization synthesis

High purity commercial starting chemicals Gd₂O₃ (Strem, 99.99%), Al₂O₃ (Strem, 99.999%), CeO₂ (Alfa Aesar 99.99%), Tb₂O₃ (Strem, 99.999%), Tm₂O₃ (Strem, 99.95%) or Yb₂O₃ (Strem, 99.9%) were weighed according to the chemical formula and mixed well with ethanol in an agate mortar. The dried mixed powders were pelletized with a uniaxial press, then broken into fragments of approximately 50 mg. Individual fragments were loaded into the nozzle of an aerodynamic levitation furnace (see Supporting Information, Figure S1). An oxygen gas jet was used to levitate the samples, and a pair of CO₂ lasers were used to heat them, with temperatures monitored by an optical pyrometer. Melting occurred at approximately 1800°C for all samples. The levitating melts were then held for a few seconds at ~2200°C, then quenched rapidly to ambient temperature by switching off the lasers, to yield transparent glass beads of ~2 mm diameter. The formation of glass was verified by PXRD of crushed beads, which showed no Bragg peaks. The glass-transition and crystallization temperatures were determined by
differential scanning calorimetry. Crystallization was induced by heating glass powders or beads in a
muffle furnace at 950°C in air for 3 hours, or for the same temperature and time in a reducing
environment (5%H₂ and 95% argon gas flow) for the Ce³⁺-doped series (Gd₀.₉₈Ce₀.₀₂)₃⁺xAl₅⁻xO₁₂.

**2.2 Materials characterization**

**X-ray diffraction:** Powder X-ray diffraction (PXRD) patterns were recorded from 10 to 80° (2θ) with a step size of 0.02° and a scan time of 2s per step using a D8 Advance Bruker diffractometer (Cu Kα₁,₂ radiation, LynxEye detector) at room temperature in Bragg-Brentano geometry. Finely-ground powder samples were dispersed on silicon wafers from an ethanol mull. In situ variable temperature diffraction (VT-XRD) data were collected using a Bruker D8 Advance diffractometer (CuKα₁,₂ radiation, Vantec detector) equipped with an HTK1600N Anton Paar furnace. Powder samples were deposited on a platinum ribbon from an ethanol mull, and measurements were collected in Bragg-Brentano geometry with the sample under vacuum, from room temperature up to 1600°C in the 2θ range 10-120° with a step size of 0.02° and a scan time of 2s per step. High-resolution synchrotron powder diffraction (SPD) data were recorded on 11-BM diffractometer at Argonne National Laboratory, U.S.A. in the range of 2θ from 1° to 50° with a 0.0001° step size using a wavelength of 0.4578 Å at room temperature. The measured powders were obtained by crushing one bead for each composition and loading into glass capillaries with a diameter of 0.3 - 0.5mm. Rietveld refinements were performed using TOPAS Academic version 6.²¹

**Thermal analysis:** Differential scanning calorimetry (DSC) data were acquired on heating using a Perkin Elmer Setaram MULTI HTC 1600 Thermal Analyzer with a heating rate of 10 °C.min⁻¹ under a constant argon flow (20 cm³ min⁻¹). Experiments were conducted on glass powders contained in a platinum vessel, except for x=0.6 which was conducted on a bulk (single bead) sample.

**SEM and microprobe:** An IT800SHL JEOL scanning electron microscope (FEG SEM) equipped with an SSD Ultim Max 100mm2 detector (EDS Oxford system) was used for microstructural analysis. High precision elemental analysis was examined by using a Cameca SX Five electron microprobe (EMP) (40 points per sample). All samples for SEM imaging and microprobe testing were obtained from randomly selected crystallized beads embedded in epoxy resin, polished and carbon coated under vacuum.

**EXAFS:** X-ray absorption fine structure (EXAFS) spectra were recorded at the Gd L₃-edge (7243 eV), Tm
L₃-edge (8648 eV) and Yb L₃-edge (8944 eV) using the SAMBA beamline (SOLEIL synchrotron, France). Samples were diluted with BN to give suitable absorption rates (concentrations calculated using MAX<sup>22</sup>) and pressed into pellets of 10 or 13 mm diameter. Spectra were recorded in transmission mode at ambient temperature using a Si (220) monochromator with ionization chamber detectors. For each pellet, several zones were sampled using 3 x 0.25 mm incident beam, and these were summed to produce the final spectra for analysis. Gd₂O₃, Tm₂O₃ and Yb₂O₃ were used as standards. The first coordination sphere Gd-O and Tm(Yb)-O distances were extracted by fitting each spectrum to a 1 x 1 x 1 garnet unit cell using FASTOSH<sup>23</sup> and FEFF8<sup>24</sup> to a limit of 5 Å. To support this analysis, structural models were generated from a 1 x 1 x 1 Gd₃Al₅O₁₂ unit cell (160 atoms; P1) by substituting 0, 1, 2 or 3 Gd<sup>3+</sup> ions for Al<sup>3+</sup> at the B sublattice (corresponding to x = 0, 0.125, 0.25 or 0.375), and 0, 1 or 2 Tm (Yb)<sup>3+</sup> ions at the A and/or B sublattices (corresponding to dopant concentrations of 0, 4 or 8 %). For each composition, all symmetrically-inequivalent structural configurations were generated using Supercell.<sup>25</sup> Due to the large number of inequivalent configurations for highly nonstoichiometric Tm(Yb)-doped compositions (e.g. 453 unique configurations for x = 0.25 with 8% Tm doping), a small number of representative configurations from each composition were selected for relaxation via plane-wave based DFT calculations using VASP.<sup>26</sup> These used the PBEsol functional<sup>27</sup> with the projector augmented wave method<sup>28</sup> for the treatment of core electrons. Structures were optimized with a 600 eV plane-wave cutoff and a 5×5×5 k-point grid until forces fell below 10<sup>-3</sup> eV Å<sup>-1</sup>.

**Luminescence:** Photoluminescence (PL), upconversion (UC), and photoluminescence excitation (PLE) spectra of samples at room temperature were recorded using an FLS1000 photoluminescence spectrometer (Edinburgh Instruments) equipped with a 980 nm laser (2 W of optical power) and a Xe-lamp as excitation sources. The luminescence decay curves of UC phosphors were measured in the same instrument at room temperature under excitation by the 980 nm laser in pulsed mode. The dependence of the peak intensity of UC luminescence was recorded by varying the pump power of the 980 nm laser using an iris filter. All samples tested were placed in a fused silica sample holder. The disk-shaped samples used for PL and UC measurements were obtained from crystallized beads by polishing two parallel faces.
### 3. Results

#### 3.1 Synthesis conditions for nonstoichiometric Gd<sub>3+x</sub>Al<sub>5-x</sub>O<sub>12</sub> (GAG)

Rapid quenching of aerodynamically levitated melts was used to synthesize a range of Gd<sub>3+x</sub>Al<sub>5-x</sub>O<sub>12</sub> precursor glasses with nominal compositions 0 ≤ x ≤ 0.7. For all compositions, transparent glass beads were obtained most reliably by using an oxygen gas jet, which affords a faster cooling rate than levitation in argon<sup>7</sup>. A representative cooling curve for the formation of Gd<sub>3.2</sub>Al<sub>4.8</sub>O<sub>12</sub> glass in an oxygen gas jet is shown in Figure 2a, with a photograph (inset) of a typical glass bead. The slower cooling rates afforded by quenching in an argon jet produced fully-crystallized opaque beads with perovskite (GdAlO<sub>3</sub>) as the majority phase (see Supporting Information, Figure S2). We did not observe any intermediate quenching conditions that lead consistently and reproducibly to direct crystallization of garnet on quenching (in contrast to the YAG system where such a mechanism is readily accessed<sup>7</sup>). The glass transition and crystallization temperatures of 850(2) and 925(2) °C respectively were extracted from DSC curves (see Figure 2b and Supporting Information, Figures S4-S8). With the exception of x = 0.7 (see section 3.2), the glass beads crystallized fully into the garnet structure after heating for three hours in a muffle furnace at 950°C, as shown by the PXRD patterns in Figure 2c, and had typical ceramic-type microstructures with no apparent residual glass at the micron scale (see Supporting Information S12). The crystallization step causes a loss of bead transparency (see Figure 2(b) inset): this is typical behavior for garnet vitroceramics, where large differences in density between glass and crystalline states cause fractures and pores to form upon crystallization.<sup>29</sup> For compositions 0 ≤ x ≤ 0.5, the same crystallization products were obtained from bulk (as-made, non-pulverized) glass beads and their powders, suggesting that surface crystallization is not dominant in this system. For compositions x > 0.5, high quality garnet samples could only be obtained by crystallizing bulk (as-made, non-pulverized) glass beads rather than powders, due to competition from surface crystallization of perovskite.
<figure><img src="image_3.png" /></figure>

**Figure 2.** Synthesis of Gd₃.₂Al₄.₈O₁₂ by glass crystallization. (a) Temperature profile of a Gd₃.₂Al₄.₈O₁₂ melt free-cooled in an oxygen jet, resulting in a glass bead (see photograph, inset). (b) DSC scan recorded on Gd₃.₂Al₄.₈O₁₂ glass powder (crushed beads) on heating at 10 °C min⁻¹, showing a glass transition (T_g) at ~850 °C and the onset of crystallization (T_c) at ~925 °C. Inset, photograph of a crystallized Gd₃.₂Al₄.₈O₁₂ bead. (c) Laboratory PXRD scans of glass powder before (upper panel) and after (lower panel) thermal treatment at 950°C for 3 hours, with the crystalline phase indexed to a cubic garnet structure (blue stick diagram, base of frame).

**3.2 Crystal structures of nonstoichiometric Gd<sub>3+x</sub>Al<sub>5-x</sub>O<sub>12</sub>**

The laboratory PXRD patterns of Gd₃+xAl₅-xO₁₂ with nominal compositions 0 ≤ x ≤ 0.6, after crystallization, are shown in Figure 3. The patterns from 0 ≤ x ≤ 0.5 are phase-pure with a cubic garnet as the sole crystalline phase. The patterns of x = 0.55 and 0.60 are dominated by the same cubic garnet, but contain a set of weak Bragg peaks corresponding to a perovskite impurity phase (GdAlO₃), with the x = 0.6 member containing 16.3(9) wt.% of this phase. An abrupt change was observed at x = 0.7, which yielded a complex multiphase mixture, indicating the end of the solid solution (see Supporting Information, Figure S3). Across the series, the lattice parameter of the garnet phase shows a clear evolution, with a systematic peak shift towards lower 2θ angle (see trend in the (420) peak position, expanded in Figure 3a) corresponding to a linear expansion of the unit cell in the range 0 ≤ x ≤ 0.60
(Figure 3b). Based on this analysis, the compositional limit of the garnet phase in Gd₃+xAl₅-xO₁₂ lies close to x = 0.60.

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

**Figure 3.** Structural analysis of Gd₃+xAl₅-xO₁₂ in the range 0 ≤ x ≤ 0.60. (a) Laboratory PXRDs showing the retention of the garnet structure with a systematic shift in peak position as x increases (* = GdAlO₃, † = Gd₄Al₂O₉), and (b) the corresponding lattice parameters derived from profile fitting. (c) Rietveld fit to SXRD data from composition x = 0.40 (red points = yobs, green line = ycalc, gray line = yobs-ycalc, blue ticks = garnet, magenta ticks = 0.50(1) wt.% GdAlO₃, cyan ticks = 0.09(1) wt.% Gd₄Al₂O₉). (d) Refined structural parameters from SXRD showing refined site occupancy parameter of Gd³⁺ at the BO₆ sites (black squares, top panel) with the nominal trend indicated by the dashed red line; and normalized metal-oxygen distances at the three different cation sites (colored triangles, lower panels).

Structural evolution and detailed structural information were obtained by Rietveld refinement against high-resolution SPD data for the nominal compositions x = 0, 0.20, 0.40 and 0.60. The starting models were based on the Gd₃Al₅O₁₂ garnet structure for nonstoichiometric compositions (x = 0.20, 0.40 and 0.60). The refined models were based upon the Y₃+xAl₅-xO₁₂ family<sup>7</sup>, with excess Gd³⁺ included by replacing a nominal amount of Al³⁺ at the B sublattice. The Gd³⁺/Al³⁺ occupancy ratio at this site was then allowed to refine freely. The lattice parameter was refined, in addition to the oxygen atomic coordinates and isotropic atomic displacement parameters for each site. Figure 3c shows the
refinement profile of Gd₃.₄Al₄.₆O₁₂ (see Supporting Information S13-18 for fits to x = 0, 0.2 and 0.6 and table of refined parameters for all samples). The occupancy by Gd³⁺ of the B sublattice was found to increase linearly with x, consistent with the theoretical solid solution formula (Figure 3d, upper panel).

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

**Figure 4.** In-situ PXRD of Gd₃.₄Al₄.₆O₁₂ collected on heating from room temperature to 1600°C. (a) Two dimensional plot of the region 15 ≤ 2θ ≤ 70°. Expected peaks/intensities from Gd₃.₄Al₄.₆O₁₂ “GAG(ns)” are shown by the black stick diagram at the base of the frame. Peaks due to GdAlO₃ “Perov.” are indicated by magenta arrows at the top of the frame. The peaks corresponding to stoichiometric Gd₃Al₅O₁₂ “GAG(s)” are indicated by yellow arrows in the zoomed panel. Peaks from the platinum sample holder are marked by asterisks. (b) Rietveld-refined weight percentages of Gd₃.₄Al₄.₆O₁₂, Gd₃Al₅O₁₂ and GdAlO₃ as a function of temperature (top panel) and the lattice parameter evolution of Gd₃.₄Al₄.₆O₁₂ (bottom panel) showing abrupt changes at ~1200°C. The dashed line is a guide to the eye.

The trends in refined M-O distances are shown in the lower panels of Figure 3d. A strong linear increase of the B-O distance with x in the range 0 ≤ x ≤ 0.6 is observed, which is associated with the larger
Gd<sup>3+</sup>(0.94 Å) occupying the Al<sup>3+</sup>(0.535 Å) at this site. At the same time, the A-O and C-O distance trends show a much weaker dependence with x, consistent with these sites being populated entirely by Gd<sup>3+</sup> and Al<sup>3+</sup> respectively. These trends are consistent with those observed in the nonstoichiometric YAG system (Supporting Information, Figure S16).

### 3.3 Thermal stability

The thermal stability of Gd<sub>3+x</sub>Al<sub>5-x</sub>O<sub>12</sub> was evaluated by in situ PXRD, for compositions x = 0, 0.2, 0.4 and 0.6. The nonstoichiometric members (x > 0) showed similar decomposition behaviors, exemplified by the x = 0.4 member in Figure 4 (x = 0.2 and 0.6 members are shown in Supporting Information S10-11). Here, it can be seen that the Bragg peaks shift systematically on heating from 30 – 1150°C due to thermal expansion, with garnet retained as the only crystalline phase. Between 1150 and 1200°C, two new sets of Bragg peaks appear, indicating the onset of decomposition into perovskite GdAlO<sub>3</sub> and stoichiometric garnet Gd<sub>3</sub>Al<sub>5</sub>O<sub>12</sub>, as shown in Figure 4a and the upper panel of 4b. The lattice parameter evolution of the nonstoichiometric garnet phase from RT to 1600°C is shown in Figure 4b (lower), demonstrating first a linear increase due to thermal expansion from room temperature up to ~1200°C, followed by an abrupt change in gradient associated with the onset of decomposition into Gd<sub>3</sub>Al<sub>5</sub>O<sub>12</sub> and GdAlO<sub>3</sub>, which are the only observed crystalline phases at 1400°C. The decomposition onset temperature decreases slightly with increasing x, from 1200 – 1250°C for x = 0.2, to 1050 – 1100°C for x = 0.6. In contrast, the stoichiometric member (x = 0) is stable until 1350°C, before decomposing into GdAlO<sub>3</sub> and Al<sub>2</sub>O<sub>3</sub>, consistent with previous ex situ studies.<sup>17,19</sup>

### 3.4 Dopant distribution and UC properties of (Gd<sub>0.89</sub>Yb<sub>0.1</sub>Tm<sub>0.01</sub>)<sub>3+x</sub>Al<sub>5-x</sub>O<sub>12</sub>

The distribution of RE<sup>3+</sup> activators over two cation sublattices may have important implications for the luminescence properties<sup>7</sup>, but very few bulk probes are adapted to this problem in Gd<sub>3+x</sub>Al<sub>5-x</sub>O<sub>12</sub>. Notably, there is negligible X-ray contrast between Gd<sup>3+</sup> and other RE<sup>3+</sup> ions; neutron diffraction is inhibited by the presence of highly absorbing <sup>157</sup>Gd; and NMR techniques are inhibited by paramagnetism. However, X-ray absorption spectroscopy allows some combinations of Gd<sup>3+</sup> and RE<sup>3+</sup> to be studied without interference between their spectra: this is the case for RE = Tm<sup>3+</sup> or Yb<sup>3+</sup>, whose L<sub>3</sub>-edges are sufficiently far in energy from that of Gd<sup>3+</sup> to allow them to be resolved by EXAFS.
Three series Gd<sub>3+x</sub>Al<sub>5-x</sub>O<sub>12</sub>, (Gd<sub>0.9</sub>Tm<sub>0.1</sub>)<sub>3+x</sub>Al<sub>5-x</sub>O<sub>12</sub> and (Gd<sub>0.9</sub>Yb<sub>0.1</sub>)<sub>3+x</sub>Al<sub>5-x</sub>O<sub>12</sub> were prepared with x = 0, 0.2 and 0.4, and their EXAFS spectra were recorded at the Gd, Tm and Yb L<sub>3</sub> edges. The first coordination sphere Gd-O and Tm(Yb)-O distances were extracted from fits to the EXAFS spectra, and these were compared with theoretical M-O distances calculated by DFT relaxation of 1 x 1 x 1 garnet cells (see Section 2.2). The experimental and theoretical M-O distances are plotted together in Figure 5, and the

<figure><img src="image_6.png" /><figcaption>**Figure 5.** Site preferences of Tm<sup>3+</sup> and Yb<sup>3+</sup> dopants by EXAFS and DFT (a) Two representative unit cells relaxed by DFT, from Scenario 1 (Tm/Yb<sup>3+</sup> populates A sites) and Scenario 2 (Tm/Yb<sup>3+</sup> populates B sites) respectively, both with x = 0.25. The C sites are omitted for clarity. (b, c) DFT-calculated trends in Gd-O and Tm-O distances, according to Scenario 1 and Scenario 2. (d, e) Experimental trends in R-O distances (R = Gd, Tm or Yb) derived from EXAFS spectra, exhibiting Scenario 2-like behavior.</figcaption></figure>

corresponding EXAFS fits and DFT-relaxed models are shown in Supporting Information S19-23. For the Tm<sup>3+</sup> and Yb<sup>3+</sup> doped series, two opposing scenarios are considered: Scenario 1, where Tm<sup>3+</sup> or Yb<sup>3+</sup> populate only the AO<sub>8</sub> sites (displacing Gd<sup>3+</sup> to the BO<sub>6</sub> sublattice when x > 0), and Scenario 2 which maximises the population of Tm<sup>3+</sup> or Yb<sup>3+</sup> at the BO<sub>6</sub> sites (Figure 5a). These two scenarios give very different expected trends in (Tm, Yb)-O distance (Figure 5c), either negligible change with x (Scenario 1) or a strong decrease followed by a plateau at higher x values when the number of available B sites becomes greater than the number of (Tm, Yb) ions (Scenario 2). The corresponding experimental data show decreasing trends for both Tm-O and Yb-O distance with x, with a similar magnitude to that predicted for Scenario 2 (Figure 5d, e). This indicates that Tm and Yb both tend to occupy the BO<sub>6</sub> sites
in $(Gd_{0.9}RE_{0.1})_{3+x}Al_{5-x}O_{12}$ when $x > 0$. The weak variation of Gd-O distance with $x$ in both scenarios is consistent with the undoped $Gd_{3+x}Al_{5-x}O_{12}$ series, where the prevailing lattice parameter increase is countered by an increasing population of octahedral $Gd^{3+}$ (see Supporting Information S23).

Powder samples of $(Gd_{0.89}Tm_{0.01}Yb_{0.10})_{3+x}Al_{5-x}O_{12}$ with $x = 0, 0.2$ and $0.4$ were prepared by the same protocol as for the parent $Gd_{3+x}Al_{5-x}O_{12}$ series, and confirmed to crystallize into the garnet structure by

<figure><img src="image_7.png" /><figcaption>**Figure 6.** (a) Upconversion emission spectra of single beads of $(Gd_{0.89}Tm_{0.01}Yb_{0.10})_{3+x}Al_{5-x}O_{12}$ for $x = 0, 0.2$ and $0.4$ in the near-infrared, using an excitation wavelength of 980 nm. (b) Luminescence decay curves of the 780 nm emission line, with single- ($x = 0$) or double- ($x = 0.2, 0.4$) exponential fits overlaid in red.</figcaption></figure>

PXRD (Supporting Information S24). Bead samples were then prepared for the same compositions and polished into disks of ~2mm diameter for luminescence measurements. Electron microprobe analysis of the disks (Supporting Information S25-28) showed a homogeneous distribution of Gd, Tm and Yb at the micron scale. The normalized UC responses of these samples under 980 nm excitation are shown
in Figure 6a. Here, the near-IR emission band arising from the ¹G₄⁻³H₅/³H₄⁻³H₆ transition of Tm³⁺ (region 720 – 820 nm) shows marked changes in fine structure with increasing x, with the most intense emission peaks in x = 0.2 and x = 0.4 located at 806 nm and 795 nm, rather than 783 nm for x = 0. The x = 0.4 spectrum is strongly modified with respect to the x = 0 and 0.2 spectra, with a marked collapse in the intensity of the 783 nm emission line. This may reflect a switch from a regime where (Tm³⁺, Yb³⁺) are distributed between the A- and B-sublattices, to one where they can be accommodated at the B-sublattice only (see Discussion, Section 4). At the same time, the luminescence lifetimes (measured at 780 nm) are progressively shortened as nonstoichiometry increases (Figure 6b). The emission mechanism does not vary with nonstoichiometry, with all compositions exhibiting a two-electron transfer process determined by measurements of luminescence intensity vs pump power (Supporting Information Figure S31). These behaviors are qualitatively similar to those of the nonstoichiometric YAG:(Er³⁺, Yb³⁺) upconversion phosphors⁷.

### 3.5 Nonstoichiometric (Gd₀.98Ce₀.02)₃+xAl₅-xO₁₂ and (Gd₀.9Tb₀.1)₃+xAl₅-xO₁₂ phosphors

To explore the response of other classes of phosphor to nonstoichiometry, we prepared two representative systems showing (i) broad-band emission by Ce³⁺ doping (Gd₀.98Ce₀.02)₃+xAl₅-xO₁₂ and (ii) narrow-band emission by Tb³⁺ doping (Gd₀.9Tb₀.1)₃+xAl₅-xO₁₂. In contrast with the Tm/Yb upconversion system, and due to the difficulties in contrasting Gd³⁺ and other RE³⁺ ions by different techniques (see Section 3.4), the luminescence responses of these phosphors are presented here without precise experimentally-determined information on the dopant distribution within the crystal structures (although atomic scale STEM-EDS data do suggest an unquantified amount of Tb³⁺ at the BO₆ sites in (Gd₀.9Tb₀.1)₃.₄Al₄.₆O₁₂ – see Supporting Information S36). The emission spectra and luminescence lifetimes of the Ce³⁺ and Tb³⁺ phosphors are shown together in Figure 7, and their structural and compositional analyses are detailed in Supporting Information S32-35 and S36-38 respectively.

In (Gd₀.98Ce₀.02)₃+xAl₅-xO₁₂, the main emission line centered at ~600 nm undergoes a slight broadening with an associated red-shift as nonstoichiometry (x) increases. At the same time, its luminescence lifetimes decrease, with average decay times of 49, 35 and 31 ns for x = 0, 0.2 and 0.4 respectively. These trends are very similar to those exhibited by nonstoichiometric YAG:Ce³⁺, where Ce³⁺ populates the AO₈ sublattice only, and the line broadening is ascribed to increasing disorder in the second
coordination sphere of Ce³⁺. In contrast, the PL spectra and lifetimes of the narrow-band (Gd₀.₉ Tb₀.₁)₃+xAI₅-xO₁₂ phosphors are essentially insensitive to nonstoichiometry, representing typical behavior for this class of activator.

<figure><img src="image_8.png" /><figcaption>**Figure 7.** Luminescence properties of some other nonstoichiometric phosphor types. (a,b) PL of (Gd₀.₉₈ Ce₀.₀₂)₃+xAI₅-xO₁₂ and (Gd₀.₉ Tb₀.₁)₃+xAI₅-xO₁₂ with x = 0, 0.2 and 0.4 excited at 470 nm and 270 nm respectively, shown together with their lifetimes (fits overlaid in red).</figcaption></figure>

**4. Discussion**

The compositional range established here for gadolinium aluminate garnet is extraordinary. At its extreme, the composition Gd₃.₆Al₄.₄O₁₂ (Gd/Al = 0.82) is closer to the adjacent perovskite phase GdAlO₃ (Gd/Al = 1) than it is to its parent garnet phase Gd₃Al₅O₁₂ (Gd/Al = 0.6). Rare-earth aluminates have long been considered to behave as line phases, and major departures from this behaviour (e.g. x > 0.03) have only recently been demonstrated in the analogous YAG system (stable up to x = 0.4)⁷. In the related rare-earth gallate garnets RE₃+xAI₅-xO₁₂, nonstoichiometries of a similar magnitude have very recently been reported with x < 0.2 (for RE = Gd³⁺) and x < 0.6 (for the smallest rare-earth members Er, Yb and Lu)³⁰,³¹ by conventional ceramic synthesis, but nonstoichiometric aluminates could not be made by this synthesis route: these are summarized in the Supporting Information (S39 – 40). By a simple ionic radius argument, the Gd₃+xAI₅-xO₁₂ (GAG) solid solution is expected to be less amenable than YAG
or $Gd_{3+x}Ga_{5-x}O_{12}$ (GGG) to this type of nonstoichiometry. YAG and GGG have ionic radius ratios $r_A/r_B$ of 1.68 and 1.51 respectively (using ionic radii of 6-coordinated $Y^{3+}$, $Gd^{3+}$ and $Ga^{3+}$),³² but GAG has the greatest size mis-match between A and B cations with $r_{Gd}/r_{Al} = 1.75$. Indeed, compared to YAG, the nonstoichiometric GAG system exhibits a more pronounced volume expansion with increasing x because $Gd^{3+}$ is larger than $Y^{3+}$, as shown in Supporting Information Figure S16.

It is notable that, even though precursor glasses can be formed with $x > 0.6$ by rapid containerless quenching of the melt, the solid solution $Gd_{3+x}Al_{5-x}O_{12}$ is limited by strongly increasing competition from the surface crystallization of the adjacent perovskite (ABO$_3$-type) phases beyond $Gd_{3.5}Al_{4.5}O_{12}$, and finally by the rapid crystallization of a $Gd_4Al_2O_9$-type phase beyond $Gd_{3.6}Al_{4.4}O_{12}$. In contrast, nonstoichiometry in the $Y_{3+x}Al_{5-x}O_{12}$ system appears to be limited by the extent of the $Y_2O_3 – Al_2O_3$ glass-forming domain (at $x = 0.4$), rather than the proximity of competing phases. This also suggests that the local atomic arrangements in the precursor glasses (composed mainly of AlO$_4$ and AlO$_5$ species at $x = 0$)³³ have an important role in phase selection, offering a more facile route to the crystallization of garnets (where at least 60% of $Al^{3+}$ is in tetrahedral coordination) than to perovskites (where $Al^{3+}$ is exclusively in octahedral coordination). Together, these factors should work to define the compositional limits for different $RE^{3+}$ across the 4f series: for each $RE^{3+}$, the accessible nonstoichiometric range should depend on the preparation of a suitable activated precursor of the desired composition (glass, or other types such as a solution-derived precursor), up to an intrinsic limit of $x \approx 0.6$. In addition to the interest of such materials for optical properties (discussed below), this could also open a new range of compounds of interest for their low temperature magnetic or magnetocaloric properties.¹⁰,¹¹,³⁰,³¹

The measurement of the PL spectra of several nonstoichiometric GAG phosphor types, along with previous study of the nonstoichiometric YAG system, allows a general picture to emerge about the luminescence responses of this materials class. It is the case in both GAG and YAG that upconversion phosphors are most strongly affected by increasing nonstoichiometry. In both examples, these phosphors follow complex emission schemes (two-photon absorption), contain small rare-earth activators ($Er^{3+}$ or $Tm^{3+}$) that populate two cation sublattices in the host material, and a high concentration of small rare-earth sensitizer ($Yb^{3+}$) with a similar crystallographic distribution to the activators. The nonstoichiometric YAG-based upconversion phosphors were previously studied to a
limit of x = 0.2 and their spectra showed an approximately linear evolution with x.⁷ Here, the behaviour
of $(Gd_{0.89}Tm_{0.01}Yb_{0.1})_{3+x}Al_{5-x}O_{12}$ over a more extended range $0 \le x \le 0.4$, indicates that this evolution will
not necessarily remain linear as x increases to very high values, possibly due to different local structural
configurations that can arise at such compositions. For example, the collapse in intensity of the 780
nm emission line between x = 0.2 and 0.4 (Figure 6a) coincides with a crossover-point where the
number of $Al^{3+}$ ions removed from the B sublattice becomes larger than the number of dopant ($Tb^{3+}$,
$Yb^{3+}$) ions in the unit cell (see Supporting Information S29), permitting configurations with the
optically-active species accommodated exclusively at the B sublattice. In-depth studies at low
temperature may help to unravel the physical origin of the spectral changes observed here, for
example a relaxation of selection rules to favor emission from electric dipole transitions (such as $^1G_4$-
$^4H_5$) over magnetic dipole transitions (such as $^3H_4$-$^3H_6$).³⁴ The exploration of other $RE_{3+x}Al_{5-x}O_{12}$ systems
may help to clarify such links between crystal chemistry and luminescence properties, and may be
expected to yield a significant number of new modified upconversion phosphors.

In both GAG and YAG the Ce³⁺ phosphors are only weakly perturbed by nonstoichiometry, associated
with Ce³⁺ retaining an 8-fold first-coordination sphere (shown experimentally for nonstoichiometric
YAG:Ce³⁺). The PL response of Ce³⁺ is highly sensitive to its local coordination environment, and the
incorporation of significant concentrations of Ce³⁺ at the BO₆ sublattice might be expected to produce
strong changes in emission properties. Strategies to achieve this may include development of highly
nonstoichiometric Eu₃+xAl₅-xO₁₂:Ce³⁺ hosts. In such a system, the smaller ionic size contrast between
Eu³⁺ and Ce³⁺ may help to homogenize their distribution between A and B sites. Finally, whilst the
indifference of the narrow-band emitter Tb³⁺ to nonstoichiometry suggests that there is little interest
in pursuing other highly nonstoichiometric phosphors of this type, there is scope for other types of
nonstoichiometric phosphor (beyond those reported here) to be developed, for example in Gd₃Al₅O₁₂
– Gd₃Ga₅O₁₂ (GAG-GGG) solid solutions which are an important class of persistent luminescence
host.⁸,³⁵

**5. Conclusions**

The crystallization of glass precursors at a moderate temperature of 950°C can be used to isolate highly
nonstoichiometric gadolinium aluminate garnets $Gd_{3+x}Al_{5-x}O_{12}$ with $0 \le x \le 0.60$, which are described
here for the first time. Once formed, these materials are highly stable, with composition-dependent
thermal decomposition temperatures in the range 1050 – 1200°C. Despite the major size contrast
between the two cation species, the garnet structure accommodates excess Gd³⁺ by replacement of
Al³⁺ at the octahedral BO₆ sublattice: 30% of these sites are occupied by Gd³⁺ in the end-member
Gd₃.₆Al₄.₄O₁₂. The nonstoichiometric range is more extensive than the analogous Y₃+xAl₅-xO₁₂ system (0
≤ x ≤ 0.4) due to a broader glass-forming domain in the Gd₂O₃ – Al₂O₃ binary system, with the
compositional limit of x = 0.6 lying half-way between ideal garnet and perovskite stoichiometries. In
common with the nonstoichiometric YAG system, nonstoichiometry has a marked effect on the
emission spectra of upconversion phosphors where dopants can occupy two cation sublattices (AO₈
and BO₆), demonstrated here in the Tm/Yb-substituted system (Gd₀.₈₉Yb₀.₁Tm₀.₀₁)₃+xAl₅-xO₁₂, while the
impact of nonstoichiometry on Ce³⁺ and Tb³⁺ substituted systems is much smaller. This implies that the
exploration of other nonstoichiometric RE₃+xAl₅-xO₁₂ hosts may be particularly interesting for the
development of new upconversion systems with small rare-earth dopants, and should motivate the
exploration of other applications such as persistent luminescence and magnetism.

**Supporting Information**

Aerodynamic levitator details; DSC; PXRD; Rietveld analysis; EXAFS analysis; SEM imaging; electron
microprobe; HAADF-STEM imaging; STEM-EDS analysis; luminescence
## Acknowledgements

Funding was provided by the French National Research Agency (ANR) under projects 20-CE08-0007 CAPRE and ANR-23-CE08-0013-01 HighFive, and by the I + D + I Grant PID2021-122328OB-I00 funded by MCIN/AEI/10.13039/501100011033 and by "ERDF A way of making Europe". Electron microscopy facilities were provided by the Platform MACLE - CVL, co-funded by the European Union and the Centre-Val de Loire Region (FEDER). Xue Fang acknowledges the China Scholarship Council (CSC) for a PhD scholarship (project 202008450026). Victor Castaing thanks Junta de Andalucía for financial support (POSTDOC_21_00694). Use of the Advanced Photon Source at Argonne National Laboratory was supported by the U. S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357. This work used the Cirrus UK National Tier-2 HPC Service at EPCC (http://www.cirrus.ac.uk) funded by the University of Edinburgh and EPSRC (EP/P020267/1). Access to the SAMBA beamline (SOLEIL synchrotron, Gif-sur-Yvette, France) was granted under proposal 20211197. We thank Dr. Emiliano Fonda for assistance with EXAFS data collection, Sandra Ory (CEMHTI, Orléans) for DSC measurements and TEM sample preparation, and Pierre-Loup Savary (CEMHTI, Orléans) for preparation of additional glass precursors.
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