1：Experimental Design and Method Selection:

The study involved synthesizing Na-doped PbTe compounds using different milling processes (hand milling and ball milling) and sintering methods (hot press and spark plasma sintering) to investigate their effects on microstructure and thermoelectric properties. Theoretical models included the Williamson-Hall equation for lattice strain analysis and Gibbs free energy considerations for grain growth mechanisms.

2：Sample Selection and Data Sources:

Crystalline ingots of Pb0.96Na0.04Te were synthesized by direct melting of high-purity elements (Pb, Na, Te). Powders were prepared by hand milling and ball milling (10 min and 30 min), followed by sintering via HP or SPS. Data sources included XRD, SEM, TEM, EBSD, EDX, and thermoelectric property measurements.

3：96Na04Te were synthesized by direct melting of high-purity elements (Pb, Na, Te). Powders were prepared by hand milling and ball milling (10 min and 30 min), followed by sintering via HP or SPS. Data sources included XRD, SEM, TEM, EBSD, EDX, and thermoelectric property measurements. List of Experimental Equipment and Materials:

3. List of Experimental Equipment and Materials: Equipment included a planetary ball mill (Pulverisette-5, Fritsch), XRD with Cu Kα radiation, SEM (MERLIN, Carl Zeiss), TEM (JEOL 2100F), FIB (Nova 600 nanolab), thermoelectric measurement system (ZEM-3 ULVAC), laser flash apparatus (LFA-457, NETZSCH), and PPMS (Quantum Design). Materials included high-purity Pb (99.999%), Na (99.95%), Te (99.999%), and stainless steel balls.

4：999%), Na (95%), Te (999%), and stainless steel balls. Experimental Procedures and Operational Workflow:

4. Experimental Procedures and Operational Workflow: Ingots were melted, annealed, pulverized by milling, and sintered under specific conditions (HP: 40 min at 873 K, 50 MPa; SPS: 5 min at 873 K, 50 MPa). Characterization involved XRD for phase identification, SEM and TEM for microstructure analysis, EBSD for grain size distribution, and measurements of electrical conductivity, Seebeck coefficient, thermal diffusivity, and Hall carrier concentration.

5：Data Analysis Methods:

Data analysis included lattice parameter calculation from XRD, lattice strain estimation using the Williamson-Hall equation, Hall carrier density calculation from Hall coefficient, thermal conductivity derivation from density, thermal diffusivity, and specific heat, and power factor and ZT calculation from measured properties.