1：Experimental Design and Method Selection:

The study involved synthesizing Ba2 –

2：5xCaNbO5 – xFx solid solutions via solid-state synthesis from BaCO3, CaCO3, Nb2O5, and BaF2, with stepwise temperature increases and repeated grinding. X-ray diffraction (XRD) analysis was performed to confirm phase purity and structure, using the Rietveld method for full-profile analysis. Scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDS) were used to examine morphology and chemical composition. Pycnometric density measurements were conducted. Electrical conductivity was studied using electrochemical impedance spectroscopy in atmospheres of varying humidity (dry and wet), with gas humidity monitored and CO2 removed. Sample Selection and Data Sources:

Samples were synthesized for x values in the range 0 ≤ x ≤

3：15, based on the formula Ba2 – 5xCaNbO5 – xFx. Data were collected from synthesized ceramic tablets. List of Experimental Equipment and Materials:

Equipment included a Bruker Advance D8 diffractometer for XRD, AURIGA CrossBeam and JEOL JSM-6390LA scanning electron microscopes with JEOL JED-2300 X-ray energy dispersive micro-analyzer for SEM/EDS, an IVG-1 MK-S meter for gas humidity monitoring, and an Ellins Z-1000P impedance meter for conductivity measurements. Materials included BaCO3, CaCO3, Nb2O5, BaF2, ethanol for grinding, platinum for electrodes, and chemicals for gas treatment (NaOH, Ascarite, P2O5, KBr).

4：Experimental Procedures and Operational Workflow:

Synthesis involved mixing and heating reagents at 800–1300°C with 24 h annealing per stage, followed by grinding. Tablets were sintered at 1400°C for 24 h, with platinum electrodes burned-in at 900°C for 3 h. XRD was done in CuKα radiation, SEM/EDS for surface analysis, pycnometry for density, and impedance measurements in frequency range 1 Hz to 1 MHz at various temperatures and humidities.

5：Data Analysis Methods:

Data were analyzed using FullProf software for lattice parameters, Zview software for impedance fitting, and statistical methods for composition and conductivity trends.