Luminescence and energy transfer processes in Gd_0.99Er_0.01Al_0.995Cr_0.05O₃

Abstract

Gd_0.99Er_0.01AlO₃ and Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ samples were synthesized using a solid-state reaction method. Structural analysis revealed that the samples crystallized in an orthorhombic structure phase with a Pbnm space group. The average crystallite sizes were around 283 nm and 574 nm for Gd_0.99Er_0.01AlO₃ and Gd_0.99Er_0.01Al_0.995Cr_0.05O₃, respectively. Derivative absorption spectrum fitting (DASF) and first-derivative reflectance (dR /dλ) methods confirmed that the samples possess a direct wide band gap, with energies of 5.93 eV and 5.90 eV, respectively. The photoluminescence (PL) spectrum of Gd_0.99Er_0.01AlO₃ under λ_ex = 377 nm excitation exhibits a green emission and intense sharp red lines at 680 nm, 697 nm, 705 nm, 717 nm and 758 nm. The green emission corresponds to the transitions ²H_11/2 → ⁴I_15/2 and ⁴S_3/2 → ⁴I_15/2 of Er³⁺ ions, while the sharp red lines are attributed to transitions between intrinsic defect centers related to the GdAlO₃ host coupled to B_3g (4) and B_1g (7) vibrational modes. Efficient energy transfer via resonant phonon-assisted and cross-relaxation processes from Er³⁺ and intrinsic defect centers to Cr³⁺ is responsible for the decrease in green and red emission line intensities in Gd_0.99Er_0.01Al_0.995Cr_0.05O₃. The energy transfer from Er³⁺ and intrinsic defect centers indicates that red emission lines at 697 nm and 726 nm in Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ mainly originate from the ²T₁ (²G) → ⁴A₂ (⁴F) and ²E_g (²G) → ⁴A_2g (⁴F) transitions of Cr³⁺ ions.

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1. Introduction

Perovskite compounds serve as excellent host materials for various optical applications due to their chemical and thermal stability.^1,2 They follow the generic formula ABO₃. Rare-earth orthoaluminates (REAlO₃), such as gadolinium aluminate (GdAlO₃), possess significant optical, thermal, and mechanical properties, making them appropriate as solid-state laser hosts.³ GdAlO₃ is also known for its relatively high dielectric constant, making it valuable for electronic applications, and is being developed as a potential material for neutron absorption and control rod applications.⁴ In cubic perovskites, the tolerance factor is t_obs=1,⁵ whereas for GdAlO₃ with the Pbnm space group, t_obs = 0.986,⁶ indicating a slight distortion from the cubic structure. GdAlO₃, formed with Gd³⁺ ions having a relatively large ion radius (180.4 pm), closely approaches the ideal cubic perovskite crystal cell (Pm3̄m). GdAlO₃ with the Pbnm space group demonstrates a high accommodation capacity within the perovskite structure and assists in the modulation of its electronic and spectroscopic properties through the substitution of Gd³⁺ with various rare-earth activators (e.g., Eu³⁺, Er³⁺, Tb³⁺, Ce³⁺, Yb³⁺, Dy³⁺) and Al³⁺ with a transition metal activator ion such as Cr³⁺ and Mn⁴⁺. In this structure, the Gd³⁺ ion occupies a non-centrosymmetric site, leading to mixing of the 4fⁿ states with the first excited configuration 4fⁿ⁻¹5d. This mixing is caused by the odd terms in the crystal field, and is responsible for the strength of induced electric dipole transitions. GdAlO₃ with the Pbnm space group is appropriate for generating intense 4f electric dipole transitions, thereby enabling efficient luminescence. In recent years, trivalent rare-earth ions (RE³⁺) and transition-metal fluorescence in diverse host matrices have attracted significant attention due to their applications in persistent luminescent materials, photo-functional materials and luminescence thermometry.^7–10 Doping GdAlO₃ with transition metals and rare-earth ions is therefore of great interest for the development of advanced optical materials. Cr³⁺, in particular, is a transition-metal ion that acts as both a trapping and recombination center and has been widely studied in persistent luminescence research. Its unique properties can enhance the performance of imaging techniques, providing valuable insights into biological systems for in vivo bioimaging.^11,12 However, the concentration of Cr³⁺ must be carefully optimized: a low concentration results in weak luminescence, whereas a high concentration leads to quenching, thereby reducing both the intensity and afterglow duration. A recent study by Jinan Xu et al.¹³ demonstrated that La_0.9898Er_0.01Sm_0.0002Al_0.995Cr_0.005O₃ exhibits long-term persistent luminescence at 1553 nm due to the Er³⁺: (⁴I_13/2 → ⁴I_15/2) transition, as well as at 734 nm, due to the Cr³⁺: (²E (²G) → ⁴A₂ (⁴F)) transition. In ZnGa₂O₄ : Cr³⁺¹⁴ the persistent luminescence intensity increases with Cr³⁺ concentration up to 0.4–0.6%, after which concentration quenching reduces both intensity and lifetime. Moreover, in recent studies, the emission intensity of Cr³⁺ reaches its optimum at 0.5 mol% Cr³⁺ concentration and can be further enhanced by Li⁺ ion in Cr³⁺/Li⁺ co-doping ZnGa₂O₄ phosphor ¹⁵. The lifetimes of the ⁴T₂ (⁴F) and ²E states of Cr³⁺ decrease with increasing concentrations of Cr³⁺ and Cr³⁺/Li⁺ ions.¹⁵ Similarly, a recent study reported by Ekta Rai et al.¹⁶ demonstrated that in Cr³⁺ and Eu³⁺ co-doped LaVO₄, the emission intensity is optimal at 0.5 mol% Cr³⁺ and 1 mol% Eu³⁺ concentration. The emission intensity at 614 nm, corresponding to the ⁵D₀ → ⁷F₂ transition in the Eu³⁺ doped LaVO₄ phosphor, reduces when Cr³⁺ ion is co-doped due to energy transfer between Cr³⁺ and Eu³⁺.¹⁶ This energy transfer was confirmed by the decrease of the lifetime of the ⁵D₀ level of Eu³⁺ ions in Eu³⁺, Cr³⁺ co-doped LaVO₄ phosphor.¹⁶ Understanding the energy levels of dopant ions, traps states, in GdAlO₃ host and the energy transfer process between them is crucial for evaluating the suitability of material for optical applications such as LEDs, plant growth lighting, and in vivo optical imaging. The experimental origin of luminescence in GdAlO₃ is studied by K Dhahri et al.¹⁷ The energy levels of Cr³⁺ combined with various trivalent lanthanides in GdAlO₃ have been studied by Hongde Luo and Pieter Dorenbos ¹⁸. However, to the best of our knowledge, Er³⁺, Cr³⁺ Co-doped GdAlO₃ has not yet been explored. Taking this into account, the present work reports for the first time the synthesis and investigation of a Er³⁺, Cr³⁺ co-doped GdAlO₃. This study aims to elucidate the energy transfer process occurring between Er³⁺, Cr³⁺, and traps states (intrinsic defects). Furthermore, based on both experimental results and theoretical optical considerations, we propose a detailed mechanism for the energy transfer involving Er³⁺, Cr³⁺, and the trap states.

2. Experimental procedures (synthesis and characterization)

The GdAlO₃, Gd_0.99Er_0.01AlO₃ and Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ samples were prepared using a conventional solid-state reaction method. Gd₂O₃ (99%), Al₂O₃ (99%), Cr₂O₃ (99%), and Er₂O₃ (99%) were used as starting raw materials in stoichiometric amounts. The precursor materials were ground into fine powders using an agate mortar. The powders were initially annealed at 700 °C and then reground, pestled, and gradually heated to 1200 °C in an alumina crucible, where they were sintered for four hours. Finally, the powders were pressed into pellets with an 8 mm diameter. Several techniques were employed to characterize the physical and structural properties of the compounds. The phase compositions of Gd_0.99Er_0.01AlO₃ and Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ were identified by X-ray diffraction (XRD) measurements using a Siemens D5000 X-ray powder diffractometer utilizing CuK_α radiation (λ = 1.5406 Å) over a range of 20°–100°, with a step size of 0.02°. The powder morphology and chemical homogeneity were studied by scanning electron microscopy (SEM) using a TESCAN VEGA3 SBH instrument equipped with an energy dispersive microscopy (EDS) detector. Raman spectra were recorded in the range of 50–1100 cm⁻¹ using a Horiba LabRam HR Evolution micro-Raman confocal system, with wavelength laser excitations at λ = 532 nm, 633 nm, and 785 nm. Absorption and reflectance spectra were recorded using a (SHIMADZU, UV-3101PC) UV–vis–IR spectrophotometer. Photoluminescence emission (PL) and excitation (PLE) measurements were recorded using a Horiba–Jobin–Yvon Fluorolog 322 spectrometer in time-resolved mode, using a pulsed lamp with a 0.05 ms post-flash delay.

3. Results and discussions

3.1. Structural analysis

3.1.1. Crystal structure and X-ray diffraction patterns. The XRD pattern analysis of the GdAlO₃, Gd_0.99Er_0.01AlO₃, and Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ samples was performed at room temperature and is shown in Fig. 1(a)–(c). The XRD data were refined using the Rietveld method in the Full Prof software suite.¹⁹ The diffraction peaks align closely with the crystal planes of the orthorhombic GdAlO₃ structure all diffraction peaks are indexed according to the PDF card no. 46-0395.²⁰ Refinement results indicate that all samples crystallize in the orthorhombic GdAlO₃ structure phase with the Pbnm space group.²⁰ The estimated Rietveld refinement parameters, including the goodness of fit (χ²), reliability factors (R-profile factor, R-Bragg factor, and R-crystallographic factor), lattice parameters, cell volumes (V), and interatomic distances, are listed in Table 1. The crystal structure of Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ and Gd_0.99Er_0.01AlO₃ compounds using VESTA software is presented in Fig. 2. The average crystallite size (D_sc) was estimated from the line broadening of the peak with the highest intensity associated with the plane (112), using the Debye–Scherrer formula.²¹where K = 0.9 for spherical shape, λ is the wavelength of X-ray used, β is the full width at half maximum (FWHM) of the diffraction peak, and λ is the Bragg angle for the most intense peak. Furthermore, XRD peak broadening also has a contribution from the self-induced strain (ε) developed in crystallites during the growth that is effective in the nanoparticles.²² We additionally used the Williamson–Hall equation:²³to determine the crystallite size and strain, taking into account the contribution of crystallites and strain to peak broadening. Where K is a constant (K = 0.9 for spherical shape), λ is the wavelength of the used X-ray, β is the full width at half maximum (FWHM) of the diffraction peak, and ε is the effective strain and θ is the Bragg angle for the most intense peak. Eqn (2) represents the Uniform Deformation Model (UDM), which assumes uniform strain in all crystallographic directions. The term (β cos θ) is plotted with respect to (4 sin θ) in Fig. 3 for the preferred orientation peaks (hkl) of Gd_0.99Er_0.01AlO₃ and Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ samples showing that with the y-intercept and slope of the fitted line determining the crystallite size and related strain, respectively. The lattice strain observed is attributed to defects concentrated along the amorphous grain boundaries. These defects create a stress field within the grain boundary region, thereby inducing strain in the system.²⁴ Table 1 displays the crystallite size estimated from Debye Scherrer's formula and W–H plot as well as the related strain. The crystallite size increases considerably with Cr³⁺ doping. Cr³⁺ incorporation can increase both crystallite and particle size in certain oxide materials. When small amounts of Cr³⁺ ions substitute the cation Al³⁺ in the Gd₀.₉₉AlEr₀.₀₁O₃ host lattice, they can induce lattice strain, modify the crystal growth process, and reduce the number of nucleation sites, leading to larger crystallites and particles. This effect is noticeable at low doping levels, as seen in Cr³⁺-doped gadolinium aluminum garnet and doped Mn₃O₄ systems.^25–28 This fact explains the considerable increase of both crystallite and particle size of Gd_0.99AlEr_0.01O₃ by Cr³⁺ doping with low concentrations. However, as the doping concentration increases further, excessive lattice distortion can inhibit growth, resulting in smaller crystallites and particles, a trend seen in several oxide systems.^25,26,28

Fig. 1 Rietveld refinement of X-ray diffraction pattern of (a) GdAlO₃ (b) Gd_0.99Er_0.01AlO₃ and (c) Gd_0.99Er_0.01Al_0.995Cr_0.05O_3.

Table 1 Refined crystallographic parameters, average particle size and average strain value of GdAlO₃, Gd_0.99AlEr_0.01O₃ and Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ samples

Compounds	GdAlO3	Gd0.99AlEr0.01O3	Gd0.99Er0.01Al0.995Cr0.05O3
a (Å)	5.253(2)	5.253(8)	5.253(6)
b (Å)	5.302(5)	5.303(7)	5.302(5)
c (Å)	7.447(2)	7.448(6)	7.447(8)
v (Å^3)	207.442(4)	207.552(1)	207.474(9)
d(Gd–Gd)	—	3.736(7)	3.804(8)
d(Gd–Al)	—	3.072(3)	3.266(8)
χ^2	1.853	1.389	1.46
RP (%)	12.3	11.7	14.8
Rwp (%)	11.5	10.4	12.0
Re (%)	8.43	8.81	9.93
Dsc (nm)	—	108.5(6)	111.0(2)
DW–H (nm)	—	283.1(4)	574.3(8)
DSEM (nm)	—	300	639
ε	—	0.00076(1)	0.00086(6)

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Fig. 2 The Crystal structure using VESTA software for (a) Gd_0.99Er_0.01AlO₃ and (b) Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ compounds.

Fig. 3 W–H plots of Gd_0.99Er_0.01AlO₃ and Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ compounds.

3.1.2. SEM and EDS analysis. The morphological characterization of Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ and Gd_0.99Er_0.01AlO₃ compounds was carried out using scanning electron microscopy (SEM), as illustrated in Fig. 4(a) and (b), respectively. The SEM images show that the particles are approximately spherical. Due to the high surface energy of the nanoparticles, the synthesized samples exhibit noticeable aggregation at the annealing temperature.²⁹ The grain size distribution, shown in the inset of Fig. 4(a) and (b), was analyzed using Image J software, and the resulting histograms were fitted to a Lorentzian function. The average grain size distribution revealed peaks around 300 nm for Gd_0.99Er_0.01AlO₃ and 639 nm for Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ as presented in Fig. 4(a) and (b), and summarized in Table 1. Furthermore, energy dispersive spectra (EDS) were recorded for both samples, as illustrated in Fig. 4(c) and (d). The EDS spectra confirm the existence of the expected constituent elements: Gd, Er, Al, Cr, and O. These results further confirm the compositional purity of the synthesized compound.

Fig. 4 (a and b) SEM micrographs, with the inset showing the size distribution histogram for Gd_0.99Er_0.01AlO₃ and Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ compounds, (c and d) spectra of chemical analysis for Gd_0.99Er_0.01AlO₃ and Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ compounds.

3.1.3. Raman spectra analysis of Gd_0.99AlEr_0.0O₃ and Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ compounds. Raman spectroscopy is a powerful technique that extracts information on the development of the desired phase, detecting impurities, and identifying structural defects by examining Raman active phonon modes. The Raman spectra of GdAlO₃ in the orthorhombic (Pbnm) perovskite structure have been studied both theoretically and experimentally by Anastasia Chopelas.³⁰ For GdAlO₃ with the orthorhombic (Pbnm) structure, group theory predicts the following optical modes in the Brillouin zone center.³⁰

Γ′ = 7Ag® + 5B_1g® + 7B_2g® + 5B_3g® + 8A_u(1) + 7B_1u® + 9B_2u(IR) + 9B_3u(IR) (3)

where R and IR denote, respectively, their Raman and infrared spectral activity. Fig. 5 and 6 display the Raman spectra of Gd_0.99Er_0.01AlO₃ and Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ respectively, recorded using excitation wavelengths of 532 nm, 633 nm, and 785 nm. By comparing the spectra obtained with various excitation wavelengths, it is possible to distinguish between Raman scattering and luminescence based on their distinct natures: bands with fixed locations are true Raman bands, whereas bands that shift in position are associated with luminescence.³¹ By extending the collection range to 1100 cm⁻¹, our measurement revealed several intense and clearly non-vibrational extra bands above 579 cm⁻¹. These bands were attributed to fluorescence as they resemble the characteristic f–f transitions of trivalent lanthanide ions. The appearance of resonance Raman, resonance fluorescence and relaxed fluorescence can be attributed to the excitation energies of the wavelength's excitation 532 nm, 633 nm, and 785 nm which are resonant with the transitions ⁴I_15/2 → ⁴S_3/2, ⁴I_15/2 → ⁴F_9/2, ⁴I_15/2 → ⁴I_9/2 of Er³⁺, respectively.³² Raman spectra of Gd_0.99Er_0.01AlO₃ and Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ collected with 532 nm laser excitation are shown in Fig. 5 (a) and 6(a). They present prominent peaks at 330 cm⁻¹, 355 cm⁻¹, 403 cm⁻¹, 468 cm⁻¹, 507 cm⁻¹, 545 cm⁻¹, 579 cm⁻¹ assigned respectively to Resonance Raman and resonance fluorescence associated to the vibrations modes B_3g(3), Ag(5), B_3g (4), B_2g (4), B_1g(6), B_3g(5), B_1g(7).³⁰ The peaks at 281 cm⁻¹, 625 cm⁻¹, 677 cm⁻¹, 734 cm⁻¹, 807 cm⁻¹, 892 cm⁻¹, 947 cm⁻¹, 1026 cm⁻¹ are assigned to the vibration modes 2B_2g(1), 2A_g(4), 2B_3g(3), 2A_g(5), 2B_3g(4), 2A_g(6), 2B_2g (4), 2B_1g(6)³⁰ related to relaxed fluorescence. The bands of Raman spectra of Gd_0.99Er_0.01AlO₃ and Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ recorded with 785 nm laser excitation in the vicinity of 1000 cm⁻¹ are clearly due to relaxed fluorescence. Some vibration modes such Ag(3) at 235 cm⁻¹ (ref. 30) occur only under 785 nm excitation, the vibrations mode B_1g(3) at 220 cm⁻¹ appear only under 633 nm excitation, whereas the vibrations mode at Ag(4) at 314 cm⁻¹ appear only under 633 nm excitation. The bands at 403 cm⁻¹ and 579 cm⁻¹ due to B_3g(4) and B_1g(7) vibration modes are true Raman bands since they have fixed locations and do not depend on the wavelength excitation. They appear under all the wavelengths excitations of 532 nm, 633 nm, and 785 nm.

Fig. 5 Raman spectra of Gd_0.99AlEr_0.01O₃ under different excitation wavelengths: (a) 532 nm, (b) 633 nm, and (c) 785 nm.

Fig. 6 Raman spectra of Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ under different excitation wavelengths: (a) 532 nm, (b) 633 nm, and (c) 785 nm.

3.2. Optical properties

3.2.1. Absorbance, reflectance spectra and band gap determination. The wavelength–dependent absorbance spectra of Gd_0.99Er_0.0AlO₃ and Gd_0.99Er_0.01Al_0.995Cr_0.05O₃, recorded in the 200–2500 nm range, are illustrated in Fig. 7. Both spectra exhibit an intense absorption band at 246 nm and two weaker bands at 975 nm and 1535 nm. With Cr³⁺ co-doping, an additional broad band appears at 565 nm. The absorption band at 246 nm is assigned to ⁸S_7/2 → ⁶D_7/2 transition of Gd³⁺ ions,³³ whereas the peaks at 975 nm and 1535 nm correspond to the ⁴I_15/2 →⁴I_11/2 and ⁴I_15/2 →⁴I_13/2, transitions of Er³⁺ ions,³² respectively. The additional broad band in the absorbance spectrum of Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ at 565 nm is assigned to the ⁴A₂ (⁴F) → ⁴T₂ (⁴F) transition of Cr³⁺ ions. The band gap energy of the samples needs to be correctly determined in order to predict semiconductor optical properties. The derivation of absorption spectrum fitting (DASF), a precise method developed by Souri and Tahan,³⁴ was used to ascertain the band gap's value and nature. The main advantage of this method is that it does not require any presumption of the nature of the optical transition and linear extrapolation. The absorption coefficient can be expressed as a function of the optical gap and the energy of photons as follows:^35,36

α(ν)hν = B(hν − E_g)^m (4)

Fig. 7 Absorbance spectra of Gd_0.99Er_0.01AlO₃ and Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ samples at room temperature in the wavelength range 200–2500 nm.

By rewriting the eqn (1) as a function of the wavelength (λ): eqn (4) become:

where α(λ), is the absorption coefficient defined by the Beer–Lambert's law as:where d and A as film thickness and film absorbance. Using (5) and (6); the absorbance can be rewritten as: where:

According to eqn (7) we have:

Eqn (8) can be reformulated as follows:

By differentiating with respect to we obtained the following equation:

The band gap's value can be determined using the following expression for absorbance.³⁷

A(λ), λ, and λ_g are, respectively, absorbance, the incident wavelength, and the wavelength corresponding to the band gap energy. m and D are constants. The plot left side of eqn (11) for Gd_0.99AlEr_0.01O₃ and Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ samples is shown in Fig. 8. The peak maxima can be used to determine the band gap energy, as seen in Fig. 8, at the peak maximum discontinuity occurs. The optical band gap is computed as Using the obtained λg, the resulting values are (5.93 ± 0.01) eV and (5.90 ± 0.01) eV for Gd_0.99Er_0.01AlO₃ and Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ respectively. Marotti et al. showed that for direct band gap semiconductors, dR/dλ peaks close to E_g, whereas for indirect band gap compounds, it approaches zero. Fig. 9 confirms the direct character of the optical band gap Gd_0.99Er_0.01AlO₃ and Gd_0.99Er_0.01Al_0.995Cr_0.05O₃, indicating that dR/dλ reaches a maximum at about 5.93 eV and 5.90 eV for Gd_0.99Er_0.01AlO₃ and Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ samples. The optical band gap values determined via the derivation of absorption spectrum fitting (DASF) and the first derivative of reflectance, dR/dλ, are the same. This supports the correctness of the band gap energy values found. The decrease in the band gap of Gd_0.99AlEr_0.01O₃ when doped with low concentration of Cr³⁺ ions introduces localized energy levels within the band gap which act as both deep electron and deep hole traps within the Gd_0.99AlEr_0.01O₃ band gap. These traps are localized and do not merge with the conduction or valence bands at low doping levels. At low concentrations, these levels do not significantly alter the overall electronic structure or the positions of the conduction and valence bands.¹⁸ The increased hybridization Cr–O between the Cr-3d and O-2p orbitals due Cr³⁺ incorporation modifies slightly the top of the valence band which may shift upward (due to Cr 3d–O 2p interactions) or the bottom of the conduction band may shift downward.³⁸ So, the band gap remains nearly unchanged.

Fig. 8 The variation of for Gd_0.99AlEr_0.01O₃ and Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ samples.

Fig. 9 The room temperature reflectance spectrum R(λ) of (a) Gd_0.99AlEr_0.01O₃ and (b) Gd_0.99Er_0.01Al_0.995Cr_0.05O₃. The inset shows the evolution of dR/dλ with λ.

3.2.2. Photoluminescence (PL) and photoluminescence excitation (PLE) spectra. The PL spectra of the GdAlO₃ and Gd_0.99Er_0.01AlO₃ samples, excited at 377 nm with a 0.05 ms delay after flash, in the wavelength range of 400–800 nm, are presented in Fig. 10. At room temperature, the PL spectrum of undoped GdAlO₃ exhibits distinct sharp red emission lines at 680 nm (14 705 cm⁻¹), 697 nm (14 347 cm⁻¹), 705 nm (14 184 cm⁻¹) 717 nm (13 947 cm⁻¹), and 758 nm (13 192 cm⁻¹). Upon Er³⁺ doping, these red emission lines persist, while additional bands appear in the wavelength ranges of 521–535 nm, 542–562 nm, and 655–657 nm, corresponding to the ²H_11/2 → ⁴I_15/2, ⁴S_3/2 → ⁴I_15/2 and ⁴F_9/2 → ⁴I_15/2 transitions of Er³⁺ ions, respectively.³² These bands are the result of intra-configurational 4f–4f transitions of Er³⁺ ions that appear within the 4f shell. According to the Laporte selection rule, 4f–4f transitions in rare-earth ions are parity-forbidden. The appearance of sharp spectral characteristics in Er³⁺ spectra could be explained by a non–central crystalline field's odd-order terms, which can create a coupling between odd and even states. Thus, resulting in mixed states of the 4fn with the first excited 4fⁿ⁻¹ 5d configuration, which mitigates Laporte's rule. This fact is responsible for the high intensity of induced electric dipole transitions observed in the PL and PLE spectra.³⁹ The red lines at 680, 697, 717, 705 and 758 nm are superimposed in both GdAlO₃ and Gd_0.99Er_0.01AlO₃, indicating that Er³⁺ doping does not modify the structure of the sharp lines and their energy locations confirms that these sharp red lines originate from the host GdAlO₃ matrix. The red lines cannot originate from intraconfigurational transitions of Gd³⁺ ions since the excitation wavelength is 377 nm and the first excited state is ⁶P_7/2 at 314 nm. In order for 4f–4f transitions of Gd³⁺ to take place under 377 nm excitation, two photons of 377 nm absorption must happen. Since we used a pulsed lamp with low intensity rather than a high-power laser, this is not possible. Similar sharp red emission lines under 320 nm excitation were also reported in undoped GdAlO₃ by Kh. Dhahri et al.¹⁷ Based on their findings, the red emission in GdAlO₃ is attributed to the presence of oxygen vacancies, singly ionized Vo⁺. In CaGdAlO₄-type layered perovskites,⁴⁰ deep red luminescence (emission around 711 nm) under 338 nm excitation is attributed to oxygen defects, especially oxygen interstitials. These defects create localized energy states within the bandgap, enabling radiative recombination that results in red light emission when the material is excited by UV or visible light. The origin of red luminescence in undoped GdAlO₃ is primarily linked to intrinsic crystal defects, specifically oxygen-related defects, rather than the presence of intentional dopants. In addition, under 532 nm excitation, undoped YAlO₃ single crystals exhibit emission bands in the wavelength range 670–800 nm, including peaks at ∼688, 703, 715, 732, and 750 nm,⁴¹ similar to those observed in GdAlO₃ (ref. 17) and to the red lines found in the present work. The PLE spectrum monitored at the emission wavelength 715 nm in YAlO₃ shows the strong excitation bands at ∼320 nm and 315 nm.⁴¹ In the distorted perovskite structure of GdAlO₃, cation vacancies such as Vo⁺ and Vo⁺⁺ are the dominant intrinsic defects to neutralize the minor amount of Cr³⁺ and Er³⁺.⁴² Taking this into account, the photoluminescence (PL) process responsible for the red emission under 377 nm excitation can be described as follows: under excitation at 377 nm, electrons are excited from the valence band and subsequently trapped by intrinsic defect. These trapped electrons then relax and are captured by deep acceptor states associated with intrinsic defects. According to the configuration coordinate model, the resulting red emission peaks can be ascribed to electron transitions between donor and acceptor levels associated with vibrational modes B_3g(4) and B_1g(7) as shown in Fig. 11. With chrome co-doping, an additional intense red emission line appears at 726 nm, and a weak peak at 693 nm, as shown in the room-temperature PL spectrum of Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ in Fig. 12. The 726 nm emission corresponds to the ²E (²G) → ⁴A₂(⁴F) transition of Cr³⁺ ions.⁴³ The co-doping by chrome induces a significant decrease in the emission intensity of the Er³⁺ ions, a dramatic decrease in the emission line intensity at 680 nm, 697 nm, 717 nm, 705 nm. A low intensity peak at 693 nm occurs assigned to the transition from the fundamental state ⁴A₂(⁴F) to the sublevel of ²T₁(²G) split by spin–orbit coupling. An intense emission line emerges at 726 nm Fig. 13. Photoluminescence excitation (PLE) spectra of Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ and Gd_0.99Er_0.01AlO₃ monitored at 542 nm are presented in Fig. 14a and b, respectively. The room-temperature PLE spectrum of Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ monitored at 542 nm, corresponding to an Er³⁺ transition, shows typical Er³⁺ excitation lines peaking at around (357 nm, 366 nm), 377 nm, 406 nm, 443 nm, 450 nm, 487 nm, and 521 nm. These lines are attributed to the following transitions: ⁴I_15/2 → ⁴G_7/2, ⁴I_15/2 → ⁴G_11/2, ⁴I_15/2 → ²H_9/2, ⁴I_15/2 → ⁴F_3/2, ⁴I_15/2 → ⁴F_5/2, ⁴I_15/2 → ⁴F_7/2, ⁴I_15/2 → ²H_11/2, respectively.³² The intensity I (N, τ) of the emission lines depends on both the population density N of the excited state and the radiative lifetime τ of the emitting level. The strongest excitation peak at 377 nm, corresponding to the transition⁴I_15/2 → ⁴G_11/2, can be justified by the fact that the transition ⁴I_15/2 → ⁴G_11/2 obeys the selection rule for an electronic–dipole transition in the context of Judd–Oeffelt theory.³⁹

Fig. 10 Room temperature PL emission spectra of the GdAlO₃ and Gd_0.99Er_0.01AlO₃ samples collected with excitation at 377 nm with flash-lamp and 0.05 ms delay after flash.

Fig. 11 Configuration coordinate diagram showing the transition responsible for red emission lines which takes place between vibrational levels at (T = 300 K) in Gd_0.99Er_0.01AlO₃ and Gd_0.99Er_0.01Al_0.995Cr_0.05O₃.

Fig. 12 Room temperature PL spectrum of Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ in the wavelength range of 400–740 nm under 377 nm excitation.

Fig. 13 Room temperature PL spectra of Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ and Gd_0.99Er_0.01AlO₃ samples under 377 nm excitation.

Fig. 14 Room-temperature photoluminescence excitation (PLE) spectra monitored at 542 nm of (a) Gd_0.99Er_0.01AlO₃ and (b) Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ (⁴S_3/2 →⁴I_15/2: Er³⁺).

The intensity of 4f–4f transitions of rare-earth elements within a host matrix can be described using the standard Judd–Ofelt (J–O) theory. According to this theory, the expressions for the electric dipolar line strength S_JJ′^ED and electric dipolar oscillator strength f_cal(J,J′) of transitions from the state |S, L, J> to the state |S′, L′, J′> are given by:³⁹

where Ω_λ are the Judd–Ofelt intensity parameters. The terms in brackets represent the doubly reduced matrix elements in intermediate coupling. J is the total angular momentum of the initial state, h is the Planck constant, c is the speed of light, [small lambda, Greek, macron] is the mean wavelength corresponding to the specific absorption band of a transition |S, L, J> to the state|S′, L′, J′> and n is the refractive index of GdAlO₃. Assuming that the host matrix has minimal influence on these values, we take this value as the value of Er³⁺ in aqueous solutions (aq), or Er³⁺ in LaF₃ crystal as mentioned in ref. 44. The transitions from the ground state ⁴I_15/2 to the excited states ²H_11/2 and ⁴G_11/2 are characterized by large reduced matrix elements of the unit tensor.³² Thus, they present a high population densities of Er³⁺ ions in these excited state ⁴G_11/2 and ²H_11/2. According to eqn (5) and (6), this may result in strong absorption exhibited in the PLE spectrum.³² The existence of a significant electric dipole transition ⁴I_15/2 → ⁴G_11/2 implies that Er³⁺ ions occupy non-centrosymmetric sites in the GdAlO₃ lattice. The appearance of the emission line at 542 nm (⁴S_3/2 → ⁴I_15/2) transition under 377 nm excitation can be attributed to three factors: firstly, strong absorption to the ⁴G_11/2 state since λ_ex = 377 nm is a resonant excitation, secondly the rate of multiphonon relaxation ⁴G_11/2 → ²H_9/2 → ⁴F_3/2 → ⁴F_5/2 → ⁴F_7/2 → ²H_11/2 → ⁴S_3/2 exceeds the probability of radiative decay transitions to the ground state ⁴I_15/2; finally, the high energy separation between the emitted level ⁴S_3/2 and ⁴F_9/2 level. However, the high intensity of the emission line at 542 nm under 521 nm excitation (⁴I_15/2 → ²H_11/2) can be attributed to the large reduced matrix elements of the unit tensor of this transition, leading to high cross-absorption to the ²H_11/2 state. Moreover, the lowest energy separation (approximately 1000 cm⁻¹) between the emitted level ⁴S_3/2 and ²H_11/2 levels increases the multiphonon relaxation. Hence, the multiphonon relaxation from ²H_11/2 to ⁴S_3/2 level is efficient, which induces the population of ⁴S_3/2 level. The increase of the intensity of the 542 nm emission line (⁴S_3/2 → ⁴I_15/2) with decreasing wavelength excitation from 406 nm to 487 nm can be explained by the multi-phonon relaxation between the excited level and the emitting level ⁴S_3/2, which is governed by the energy-gap law or phonon law.⁴⁵ The multi-phonon relaxation rate (W_nr) increases with decreasing energy separation between the excited levels and the emitting level ⁴S_3/2. Hence, the emission at 542 nm increases with decreasing wavelength excitation from 406 nm (⁴I_15/2 → ²H_9/2) to 487 nm (⁴I_15/2 →⁴F_7/2). The energy separation between the ⁴S_3/2 and ⁴F_9/2 levels is approximately 3100 cm⁻¹,³² requiring five phonons (579 cm⁻¹ each) to bridge the gap. Therefore, the non-radiative relaxation from ⁴S_3/2 to ⁴F_9/2 highly inefficient. As a result, the red emission intensity at 655 nm is lower than the green emission intensity at 542 nm under 377 nm excitation in Gd_0.99Er_0.01AlO₃ (Fig. 10). The Photoluminescence process at 542 nm under 377 nm excitation in Gd_0.99Er_0.01AlO₃ is shown in Fig. 15.

Fig. 15 The Photoluminescence process at 542 nm under 377 nm in Gd_0.99Er_0.01AlO₃ and Gd_0.99Er_0.01Al_0.995Cr_0.05O₃.

The room-temperature PLE spectrum of Gd_0.99Er_0.01AlO₃ monitored at 542 nm, shows the same characteristic excitation lines as those observed in Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ with two additional bands at 241 nm and 275 nm. These bands are attributed to the ⁸S_7/2 → ⁶D_7/2 and ⁸S_7/2 → ⁶I_7/2 transitions of Gd³⁺ ions, respectively.⁴⁶ The disappearance of these emission bands in the Cr-doped sample (Gd_0.99Er_0.01Al_0.995Cr_0.05O₃), under 542 nm monitoring, suggests the absence of energy transfer from Gd³⁺ to Er³⁺ in the presence of Cr³⁺. The room-temperature PLE spectrum of Gd_0.99Er_0.01AlO₃ and Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ monitored at 697 nm are shown in (Fig. 16). The spectrum of Gd_0.99Er_0.01AlO₃ exhibits two intense peaks at 322 nm and 275 nm, which assigned to the excitation of the electron from the valence band which trapped by the defect within the forbidden bandgap and the ⁸S_7/2 → ⁶I_7/2 transitions of Gd³⁺ ions, respectively. In contrast, the photoluminescence spectrum of Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ monitored at 697 nm reveals intense peaks at 329 nm and 276 nm, assigned to the excitation of the electron from the valence band which trapped by the defect and the ⁸S_7/2 → ⁶I_7/2 transitions of Gd³⁺ ions, respectively. Additionally, four extra bands are observed at 565 nm, 413 nm, 314 nm, and 241 nm. The broad bands around 565 nm and 413 nm are assigned to transitions from the ground state ⁴A₂ (⁴F) to the excited states ⁴T₂ (⁴F) and ⁴T₁(⁴F) of Cr³⁺.⁴⁷ The peaks at 314 nm and 241 nm are assigned to the (⁸S_7/2 → ⁶P_7/2:Gd³⁺) and (⁸S_7/2 → ⁶D_7/2: Gd³⁺) transitions, respectively.⁴⁶

Fig. 16 Room temperature PLE spectra in Gd_0.99Er_0.01AlO₃ and Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ monitored at 697 nm.

3.2.3. Crystal field analysis and energy level schemes of Cr³⁺ ions in Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ nanoparticles. The energy levels of Cr³⁺ ions in Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ nanoparticles were calculated using the total Hamiltonian⁴⁸

H = H₀ + H_ee(B, C) + H_Trees(α) + H_CF(D_q) + H_SO(ξ) (14)

Eqn (14) describes the entire Hamiltonian H, where H₀ is the configuration Hamiltonian term, and H_ee(B, C), representing the electron–electron repulsion Hamiltonian. This term gives rise to the eight Russell–Saunders terms ^2S+1L, including ⁴F, ⁴P, ²G, ²P, ²H, ²F, (²_aD) and (²_bD) for Cr³⁺ ions with 3 d³ configuration. H_CF(D_q) is the crystal field Hamiltonian, and H_SO (ξ) represents the spin–orbit coupling Hamiltonian. Using Racah algebraic techniques, the energy levels of the Russell–Saunders terms for the 3 d³ configuration are expressed in terms of Racah parameters A, B, and C, which depend on the double radial integrals F and G. The relative energies are those measured by optical spectroscopy. The quantity related to the A parameter is eliminated since it is the same for all the Russell–Saunders terms. Cr³⁺ ions (3 d³) are assumed to substitute Al³⁺ ions at the octahedral [AlO₆] site in an intermediate crystal field (CF) strength. The basic function in the LS coupling scheme are expressed as:^49,50

|ψ〉 = |α, SM_s, LM〉 (15)

The crystal field energy levels can then be obtained by diagonalizing the entire Hamiltonian H = H₀ +H_ee (B,C) + H_CF (D_q) + H_SO (ξ). The crystal field Hamiltonian (H_CF) in Wybourne notation is the spin–orbit hamiltonian and the Trees hamiltonian are expressed as follow:

H_Trees = αL (L+ 1) (18)

where ξ_3d is the spin–orbit coupling constant, α is the Trees parameter. The Racah and crystal field parameters B, C, and D_q are determined using the Newton–Raphson method by fitting the experimental energies levels to the theoretical ones ⁴A₂ (⁴F) → ⁴T₂ (⁴F) (565 nm), ⁴A₂(⁴F) → ⁴T₁(⁴F) (413 nm), and ²E(²G) →⁴A₂(⁴F) (726 nm). The adjusted spin–orbit coupling ξ_3d and Trees parameter α are calculated as follows:

B₀ = 918 cm⁻¹, C₀ = 4133 cm⁻¹,⁴⁸ ξ₀ = 275 cm⁻¹ and α₀ = 30 cm⁻¹,⁴⁸ which refer to the free ion parameters of Cr³⁺. The matrix elements of the crystal field, spin–orbit, and Trees Hamiltonians in the basics are provided by Y. Y. Yeung and C. Rudowicz.⁵⁰ The full Hamiltonian matrix H (as defined in eqn (14)) was diagonalized to derive the energy levels as a function of the Racah parameters B and C, the crystal field parameter D_q, and the spin–orbit coupling constant. This diagonalization was performed using unique code developed in our lab with the Maple program. The theoretical computed values are B = 635 cm⁻¹, C = 3008 cm⁻¹ and D_q = 1776 cm⁻¹ with (D_q/B = 2.79). The calculated parameters were used to calculate the energy levels at room temperature, as listed in Table 2. The Tanabe–Sugano diagram for Cr³⁺ ions in octahedral site symmetry, shown for the ratio C/B = 4.73 in Fig. 17, illustrates the overall behavior of Cr³⁺ energy levels in terms of D_q/B relative to the local field intensity. The vertical line corresponds to the calculated D_q/B value from our theoretical computation of Cr³⁺ levels in Gd₀.₉₉Er₀.₀₁Al₀.₉₉₅Cr₀.₀₅O₃. It is well known that when D_q/B < 2.3, Cr³⁺ ions experience a weak crystal field, resulting in broad-band emission. However, when D_q/B > 2.3, the ions exhibit strong and narrow peak emission through the ²E(²G) → ⁴A₂(⁴F) transitions.⁵¹ In our case, the calculated D_q/B = 2.9, confirms that the energy of the ²E state is the lowest excited energy level. These results demonstrate that Cr³⁺ ions experience a strong crystal field, exhibiting sharp ²E(²G) → ⁴A₂(⁴F) emission at 726 nm.

Table 2 Experimental and calculated energies levels (cm⁻¹) of Cr³⁺ ion in octahedral symmetry in Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ nanoparticles

Oh	Eobs	[this work]	[this work]
^4A2g(^4F)	0	0	0
^2Eg(^2G)	13 774	13 772	13 902 (4)
^2T1g(^2G)		14 312	14 434 (4)
			14 493 (2)
^4T2g(^4F)	17 760	17 760	17 666 (2)
			17 722 (4)
			17 832 (2)
			17 836 (4)
^2T2g(^2G)	—	20 906	20 974 (4)
			21 083 (2)
^4T1g(^4F)		24 276	24 165 (4)
			24 173 (2)
			24 185 (4)
			24 187(2)
^2A1g(^2G)	—	29 324	29 507 (2)
^2T1g(^2P)	—	31 382	31 582 (2)
			31 629 (4)
^2T1g(^2H)	—	31 712	31 803 (2)
			31 978 (4)
^2Eg(^2H)	—	33 325	33 458 (2)
^2T1g(^2H)	—	36 266	36 324 (2)
			36 360 (4)
^4T1g(^4P)	—	38 528	38 388 (2)
			38 403 (4)
			38 503 (4)
			38 535 (2)
^2T2g(^2H)	—	40 671	40 574 (2)
			40 674(4)
^2A2g(^2F)	—	42 024	42 033 (2)
^2T2g(^2aD)	—	49 088	49 341 (2)
			49 451 (4)
^2T2g(^2F)	—	50 505	50 543 (2)
			50 652 (4)
^2Eg(^2aD)	—	50 661	50 662(4)
^2T1g(^2F)	—	55 225	55 122 (2)
			55 246 (4)
^2T2g(^2bD)	—	69 140	69 008 (4)
			69 204(2)
^2Eg(^2bD)	—	72 823	72 879 (4)

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Fig. 17 Tanabe–Sugano diagram for Cr³⁺ ions with C/B = 4.73. The vertical line at D_q/B = 2.79 represents the energy levels identified for Cr³⁺in Gd_0.99Er_0.01Al_0.995Cr_0.05O₃.

3.2.4. Energy transfer process from Gd³⁺, Er³⁺ and oxygen defects to Cr³⁺ ions in Gd₀.₉₉Er₀.₀₁Al₀.₉₉₅Cr₀.₀₅O₃. The lack of Gd³⁺ transitions in the PLE spectrum of the Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ sample monitored at 542 nm proves the weak efficiency of energy transfer between Gd³⁺ and Er³⁺ ions. This can be attributed, first, to the shorter distance between Gd³⁺ and Cr³⁺ ions (d_Gd–Cr = 3.26683 Å, Table 1) compared to the distance between Gd³⁺ and Er³⁺ ions (d_Gd–Er = 3.80481 Å, Table 1) in Gd_0.99Er_0.01Al_0.995Cr_0.05O₃. Second, the dominance of the higher energy transfer efficacy from Gd³⁺ to Cr³⁺ ions, which is explained by the higher trapping efficiency of the migrating excitation energy levels ⁶P_J and ⁶I_J of Gd³⁺ by Cr³⁺ activators in Gd₀.₉₉Er₀.₀₁Al₀.₉₉₅Cr₀.₀₅O₃. Which is greater than by Er³⁺.⁵² This higher trapping efficiency is further explained by the spectral overlaps between the Cr³⁺ excitation band (⁴T₁ (⁴P)) and the ⁶I_7/2 level of Gd³⁺ ions.⁵² Notably, the peaks at 314 nm and 275 nm in the PLE spectrum of Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ monitored at 697 nm, present high intensities comparable to the peak at 329 nm. This experimental fact points out that under 314 nm and 275 nm, Gd³⁺ ions also act as donors of energy to the intrinsic defects via resonant phonon-assisted energy transfer. The decay PL curves at 697 nm and 542 nm under 377 nm excitation are shown in Fig. 18 (a) and (b) for Gd_0.99Er_0.01AlO₃ and in Fig. 18 (c) and (d), for Gd_0.99Er_0.01Al_0.995Cr_0.05O₃. The decay PL curves at 542 nm under λ_ex = 377 nm in Gd_0.99Er_0.01AlO₃ is fitted to a monoexponential equation I(t) = Aexp(−t/τ) with fluorescence lifetimes The decay of the emission at 542 nm under 377 nm excitation in Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ is bi-exponential with lifetimes τ′ = 0.13 ms and K_r is the emissive rate constant, K_nr is the non-radiative rate and K_T is the transfer rate constant. The decay curve shows two lifetimes: an unchanged longer time 0.13 ms (no transfer), a shorter time 0.03 ms (efficient transfer) which indicates an efficient energy transfer from a part of Er³⁺ ions to Cr³⁺ is taken place. The decay rate of Er³⁺ emission in Gd_0.99Er_0.01AlO₃ and Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ samples as well as the ET efficiency from Er³⁺ to Cr³⁺ can be calculated using eqn (21)–(23),

K_r + K_nr = (τ_Er)⁻¹ (21)

K_r + K_nr + K_T = (τ_Er,Cr)⁻¹ (22)

Fig. 18 Decay PL curves under 377 nm excitation for Gd_0.99Er_0.01AlO₃ at (a) 697 nm and (b) 542 nm, and for Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ at (c) 697 nm and (d) 542 nm.

τ_Er and τ_Er,Cr, are the life times of the Er³⁺ : ⁴S_3/2 level in Gd_0.99Er_0.01AlO₃ and Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ respectively. The ET efficiency (η_ET) from Er³⁺ : ⁴S_3/2 to the Cr³⁺: as indicated from the energy level diagram in Fig. 19 can be estimated to be 76%. Which indicate highly efficient energy transfer from Er³⁺ : ⁴S_3/2 to the Cr³⁺ : ⁴T_2g(⁴F). In rare-earth ion systems, energy transfer exchange interactions are generally negligible due to the small spatial extent of 4f orbitals, making multipolar mechanisms dominant. Specifically, in GdAlO₃, efficient trapping of excitation energy by Cr³⁺ and rare earth ions like Er³⁺ is attributed to multipolar interactions when there is spectral overlap, while exchange interactions play a minor role and are only significant for rare earth ions lacking allowed absorption bands.⁵² Therefore, for Er³⁺–Cr³⁺ pairs in GdAlO₃, multipolar interactions are expected to dominate the energy transfer process, provided there is suitable spectral overlap between their energy levels. The non-radiative energy transfer in Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ is taken place through the following cross-relaxations: (²H_11/2 + ⁴A₂(⁴F) → ⁴I_15/2 + ⁴T₂(⁴F)), (⁴S_3/2 + ⁴A₂(⁴F) → ⁴I_15/2 + ⁴T₂(⁴F)) transitions and via resonant phonon-assisted energy transfer (Fig. 19). This energy transfer process involving Er³⁺ ions explain the strong luminescence quenching of the emission bands at 542 nm, 521 nm and the appearance of an intense emission line at 726 nm when Cr³⁺ is incorporated. The decay of the emission at 697 nm under 377 nm excitation in Gd_0.99Er_0.01AlO₃ is bi-exponential with lifetimes τ′ = 2.61 ms. and τ′′ = 1.18 ms. Biexponential decay indicates that there are two different mechanisms that affect the decay dynamics and energy transfer may be one of these mechanisms. The decay curve shows two lifetimes: a longer time 2.61 ms (no transfer), a shorter time 1.18 (efficient transfer). This fact indicates that there is energy transfer from intrinsic defects to Er³⁺ ions in Gd_0.99Er_0.01AlO₃. However, the decay curve at 697 nm under 377 nm excitation in Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ is described by a double-exponential equation I(t) = I₀₁ exp(−t/τ₁) + I₀₂ exp (−t/τ₂), where I is the luminescence intensity; I₀₁ = 1844 and I₀₂ = 1258 are constants; t represents time, τ₁ = 1.69 ms and τ₂ = 10.77 ms are decay times for the respective exponential components. The absence of the bands at 565 nm and 413 nm in the PLE spectrum of Gd₀.₉₉Er₀.₀₁AlO₃ monitored at 697 nm indicates that the 697 nm emission line arise not only from electron transition between intrinsic defects centers, but also from the transition ²T₁(²G)→⁴A₂(⁴F) of Cr³⁺. This assignment is justified since the experimental value 697 nm (14 347 cm⁻¹) is well reproduced by theoretical value of the transition in Table 2. Moreover, the highest-value lifetime τ₂ = 10.77 ms is characteristic of the spin-forbidden transition. τ₁ = 1.69 ms is fluorescence lifetime of 697 nm emission coming from the electron transition between two defects centers. The co-doping with chromium leads to a reduction of fluorescence lifetime of 697 nm emission from 2.61 ms to 1.69 ms, indicating that there is an increase in the transfer rate K_T constant. A dramatic decrease in the 697 nm emission line intensity and the appearance of an intense emission line at 726 nm support the energy transfer from oxygen-vacancies to Cr³⁺ ions via resonant phonon-assisted energy transfer from oxygen defect to Cr³⁺ : ⁴T₂(⁴F) level and cross-relaxation processes (Fig. 19). The value of the constants I₀₁ and τ₁ in the PL decay at 697 nm under 377 nm excitation in Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ indicate that a very low part I₀₁ exp(−t/τ₁) of the emission at 697 nm is originating from electron transition between two intrinsic defects centers coupled to the B_3g (4) and B_1g(7) vibrational modes. The highest part I₀₂ exp (−t/τ₂) of the emission at 697 nm inGd_0.99Er_0.01Al_0.995Cr_0.05O₃ is originating from the transition ²T₁ (²G) →⁴A₂ (⁴F) of Cr³⁺. The energy transfer from Er³⁺, defects centers to Cr³⁺ and the high multiphonon relaxation from ²T₁ (²G) to the ²E (²G) level, induces the intense line at 726 nm through the transition ²E (²G) →⁴A₂ (⁴F) of Cr³⁺ (Fig. 19). Based on the experimental results and the theoretical optical considerations, the energy transfer process between Er³⁺, Cr³⁺ and oxygen-vacancies under λ_ex = 377 nm is presented in Fig. 19 and (Table 3).

Fig. 19 Energy level diagram and energy transfer mechanism in Gd_0.99Er_0.01Al_0.995Cr_0.05O₃.

Table 3 Fluorescence lifetime of Gd_0.99Er_0.01AlO₃ and Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ samples, monitored at Er³⁺ emission wavelengths of λ_em = 542 nm and λ_em = 697 nm under λ_ex = 377 nm

Samples	Gd0.99Er0.01AlO3		Gd0.99Er0.01Al0.995Cr0.05O3
The recorded wavelength	697 nm	542 nm	697 nm	542 nm
	Double-exponential	Mono-exponential	Double-exponential	Double-exponential
	2.61–1.18	0.13	—	—
	—	—	1.69–10.77	0.13–0.03

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4. Conclusion

Gd_0.99Er_0.01AlO₃ and Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ samples were successfully synthesized using the solid-state reaction method. XRD analysis confirmed that both samples crystallize in an orthorhombic structure with a Pbnm space group. Using the Derivation of absorption spectrum fitting (DASF) and the first derivative of reflectance dR/dλ methods, the optical band gaps were determined to be 5.93 eV and 5.90 eV, respectively. Red emission peaks at 680, 697, 705, 717, and 758 nm were observed in both samples and are ascribed transition involving intrinsic defects coupled with the B_3g (4) and B_1g(7) vibrational modes. Co-doping with Cr³⁺ induced a significant decrease in Er³⁺ emission intensity, particularly the intensity of red lines at 680, 697, 705, 717 nm. The weak peak at 693 nm and the intense peak at 726 nm are assigned to the ²T₁ (²G) → ⁴A₂ (⁴F) and ²E_g (²G) → ⁴A_2g (⁴F) transitions of Cr³⁺. PL spectra and decay curves at 697 nm and 542 nm under 377 nm excitation confirmed efficient non-radiative energy transfer from Er³⁺ and intrinsic defects to Cr³⁺ ions. The energy transfer occurs via resonant phonon-assisted processes from the Er^{3+ 2}H_11/2 and ⁴S_3/2 levels to the Cr³⁺ : ⁴T₂ (⁴F) level, followed by cross-relaxations (²H_11/2+⁴A₂(⁴F) → ⁴I_15/2+⁴T₂(⁴F)),(⁴S_3/2+⁴A₂(⁴F) → ⁴I_15/2+⁴T₂(⁴F)). Decay curves at 697 nm indicate that the lower part of this emission originates from transition involving intrinsic defects coupled with vibrational modes, while the highest part of the emission at 697 nm in Gd_0.99Er_0.01Al_0.995Cr_0.05O₃ is due to the Cr^{3+ 2}T₁ (²G) →⁴A₂ (⁴F) transition. Finally, energy transfer from Er³⁺, defect to Cr³⁺and the high relaxation from ²T₁ (²G) to the ²E (²G) level induce the intense line at 726 nm due to the transition ²E (²G) →⁴A₂ (⁴F) of Cr³⁺.

Author contributions

F. Mselmi: Conceptualization, methodology, writing – original draft, formal analysis. Abir Hadded: Writing – original draft, formal analysis, software. Hajer Souissi: Investigation, validation. Souha Kammoun: Investigation, validation, supervision. J. Pina: Software, investigation. B. F. O. Costa: Investigation, validation, supervision.

Conflicts of interest

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Data availability

All the data for the manuscript is available in the manuscript.

Acknowledgements

This work was supported by the Tunisian National Ministry of Higher Education, Scientific Research and Technology.

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