## 1 Introduction  
Scintillator materials are indispensable in a broad range of radiation detection applications, including medical imaging (e.g., positron emission tomography, PET), high-energy physics experiments, security screening, and environmental monitoring. The fundamental role of a scintillator is to absorb incoming high-energy photons or charged particles and re-emit the absorbed energy as visible or near-visible light. The ideal scintillator material therefore requires a high density (for effective stopping power), strong luminescence intensity (for good energy discrimination), and fast decay time (for high-count-rate applications) [1, 2]. Moreover, excellent optical transparency, good mechanical properties, and chemical stability are crucial for practical deployment in large-area detectors and harsh operating environments [3, 4]. Within the family of scintillator materials, rare-earth doped garnets stand out due to their robust crystal structure, high thermal and chemical stability, and favorable optical properties. Garnets of the general formula A\({}_{3}\)B\({}_{5}\)O\({}_{12}\) (where A is typically Y, Lu, or Gd, and B is Al or Ga) offer a tunable host lattice for accommodating various rare-earth activator ions [5, 6, 7]. By carefully selecting and tailoring the host's composition, one can optimize critical scintillation characteristics such as the band gap, density, and energy transfer dynamics [8]. For instance, partially substituting Lu\({}^{3+}\) with Y\({}^{3+}\) can balance material density and cost, while replacing Al\({}^{3+}\) with Ga\({}^{3+}\) can modify the conduction and valence bands to enhance luminescence efficiency [9, 10]. Although cerium (Ce\({}^{3+}\)) is widely employed in garnet scintillators (e.g., Ce:LuAG, Ce:GAGG) due to its fast emission (tens of nanoseconds), other rare-earth ions also exhibit promising properties. Terbium (Tb\({}^{3+}\)) has garnered increasing interest in recent years because of its characteristic green emission (\({}^{5}\)D\({}_{4}\)\({}^{\prime}\)F\({}_{5}\) at around 545 nm), relatively high light yield potential, and long-lived excited states. The specific electronic configuration of Tb\({}^{3+}\) (4f) gives rise to a series of intra-4f transitions that can be effectively excited by both UV photons and high-energy radiation, making Tb-doped materials suitable for certain imaging modalities or detection schemes where green luminescence is advantageous [3, 11, 12, 13, 14]. Moreover, Tb\({}^{3+}\) can sometimes offer higher quantum yields under specific excitation conditions compared to other rare-earth dopants, depending on the host lattice environment and doping concentration. Despite these advantages, the scintillation performance of Tb-doped garnets can be sensitive to a range of factors, including dopant concentration, crystal growth conditions, and the presence of defects or charge-compensating ions [15, 16]. At low Tb concentrations, luminescence intensity may be suboptimal due to insufficient activator centers. Conversely, at very high concentrations, concentration quenching and non-radiative energy transfer between Tb ions may degrade the light yield and lengthen decay times. Hence, a systematic investigation of Tb concentration is crucial to identify the doping level that maximizes light output without sacrificing decay time or transparency [15, 17]. In the present work, we focus on the synthesis and characterization of Tb-doped Lu\({}_{2.5}\)Y\({}_{0.5}\)(Al\({}_{2.5}\)Ga\({}_{2.5}\))O\({}_{12}\) (LuYAGG) single crystals, aiming to explore the impact of Tb content (0.5, 1, 5, and 10 mol%) on the luminescent and scintillation properties. High-purity oxide precursors (Al\({}_{2}\)O\({}_{3}\), Y\({}_{2}\)O\({}_{3}\), Lu\({}_{2}\)O\({}_{3}\), Ga\({}_{2}\)O\({}_{3}\), and Tb\({}_{4}\)O\({}_{7}\)) were carefully weighed according to the stoichiometric ratios and subsequently processed to grow single crystals.