## 2 Materials and Methods  
The Cu\({}_{x}\)Zn\({}_{1-x}\)Ti\({}_{0.2}\)Zr\({}_{0.8}\)Nb\({}_{2}\)O\({}_{8}\) ceramics (0.0 \(\leq\)\(x\)\(\leq\) 0.4) were synthesized using analytical-grade ZnO (Makclin Biochemical Technology, Shanghai, China), CuO, ZrO\({}_{2}\), TiO\({}_{2}\), and Nb\({}_{2}\)O\({}_{5}\) (Aladdin Biochemical Technology, Shanghai, China) via the conventional solid-state reaction method. This method includes ball milling and subsequent high-temperature treatment (calcination and sintering). Ball milling allows for the uniform mixing of different types of powders or compounds and high-temperature treatment provides sufficient energy to overcome reaction barriers and enable the reaction to proceed. In comparison to other chemical synthesis methods, despite its time-consuming nature and high energy consumption, the solid-state reaction method offers a multitude of advantages, including simplicity in operation, ease of control, excellent crystallinity of the resulting ceramics, strong customizability, and the capability to easily achieve large-scale production [19]. In the context of the present research, a typical experimental procedure is detailed as outlined below. The raw powders, weighing a total of 28 g and proportion according to the stoichiometric requirements, were ball-milled in a Teflon jar containing zirconia balls of various sizes (specifically, 2 pieces of 20 mm, 10 pieces of 15 mm, 40 pieces of 10 mm, 120 g of 5 mm, and 80 g of 3 mm) and 33 milliliters of ethanol. The milling process was conducted on a horizontal ball mill operating at a speed of 25 rpm for a duration of 24 h. The slurry was subsequently dried at 85 \({}^{\circ}\)C for 4 h followed by calcination at 900 \({}^{\circ}\)C for 3 h. The calcined powders underwent a secondary milling process, employing the same parameters as the initial stage, for an additional 24 h in order to achieve a finer powder consistency. Subsequently, they were dried at 85 \({}^{\circ}\)C for another 4 h and sifted through a 40-mesh sieve. Finally, after grinding with 5 wt.% PVA (as the organic binder) in an agate mortar and sifting through a 200-mesh sieve, the resulting powders were pressed into cylindrical disks of 10 mm in diameter and 5 mm in height under a pressure of 100 MPa. To extract the organic binder, the green pellets were firstly heated at 600 \({}^{\circ}\)C for 2 h, followed by sintering at a temperature range of 1050-1300 \({}^{\circ}\)C for 4 h. To further decrease the sintering temperature, various amounts of LiF (0.0 mol-50.0 mol%, 99.9%, Makclin Biochemical Technology, Shanghai, China) were added during the second ball milling, and a similar procedure to that described above was performed, except the green pellets were sintered at 950 \({}^{\circ}\)C for 4 h.  
The relative densities of sintered specimens were determined using the Archimedes method, employing DI water as the buoyancy medium. The phase composition and purity were analyzed using an X-ray diffractometer (XRD; Rigaku SmartLab SE, Tokyo, Japan) equipped with Cu K\(\alpha\) radiation. The XRD testing parameters were precisely defined: the 20 range was set from 10\({}^{\circ}\) to 90\({}^{\circ}\), with a step size of 0.01\({}^{\circ}\) and a scanning speed of 2\({}^{\circ}\) per minute. Additionally, the operating voltage and current were adjusted to 40 kV and 40 mA, respectively. The crystal structure of all compositions was further analyzed by using the TOPAS-Academic Rietveld refinement method and Raman spectrometer (LabRam HR Evolution, HORIBA Scientific, Kyoto, Japan) with an argon laser (532 nm). The microstructure of the polished and thermally etched (conducted at 100 \({}^{\circ}\)C below the optimum sintering temperature for 1 h) samples was observed using scanning electron microscopy (SEM; Zeiss Sigma 300, Oberkochen, Germany), and compositional analysis was performed using an energy-dispersive spectroscopic (EDS; Oxford UltimMax40, UK) attached to the SEM. The average grain sizes were estimated using ImageJ software (v1.8.0).