1：Experimental Design and Method Selection:

The study aimed to elucidate the correlation between particle size of tetrahedron-shaped Ag3PO4 crystals and their photocatalytic water-oxidation activity and carrier dynamics. Methods included synthesis of Ag3PO4 particles with controlled sizes, photocatalytic O2 evolution tests, and time-resolved transient diffuse reflection spectroscopy with global analysis to study carrier dynamics.

2：Sample Selection and Data Sources:

Ag3PO4 particles were prepared with varying particle sizes (Ag-S, Ag-M, Ag-L) by controlling the H2O/EtOH ratio in the AgNO3 solution during synthesis. Samples were characterized using SEM, XRD, and diffuse reflection spectroscopy.

3：List of Experimental Equipment and Materials:

Equipment included a Pyrex side-irradiation reactor, 500 W high-pressure Hg lamp, UV cut-off filter, magnetic stirrer, gas chromatograph (Shimadzu GC-8A), SEM (Hitachi S-4800), XRD diffractometer (Rigaku MiniFlex II), diffuse reflection spectrophotometer (JASCO V-770), and a sub-nanosecond time-resolved transient diffuse reflection spectroscopy system (Ultrafast Systems EOS with Spectra Physics Hurricane-X and OPA800C). Materials included AgNO3, H3PO4, ethanol, and deionized water from Wako Pure Chemical Industries, Ltd.

4：Experimental Procedures and Operational Workflow:

Ag3PO4 particles were synthesized by dropping AgNO3 solution into H3PO4/EtOH mixture under stirring, followed by filtration, washing, and drying. Photocatalytic O2 evolution was measured in a reactor with Ag3PO4 powder and AgNO3 solution under Ar atmosphere and light irradiation, with O2 analyzed by gas chromatography. Time-resolved spectra were measured using pump-probe spectroscopy with 355 nm excitation under vacuum or oxygen atmosphere.

5：Data Analysis Methods:

Data were analyzed using global analysis of transient diffuse reflection spectra to extract decay-associated spectra (DAS) and lifetimes of carrier components. Rates of O2 evolution were determined from maximum rates during irradiation.