“…As observed from the radial distribution function R ( r ) in Figure , with increasing firing temperature, the crystalline quality improves for the isolated Ru ( P 6 3 / mmc ) particle phase. This is identified by the sharpening of the short-range correlations in the R ( r ), which results from the decrease in atomic disorder due to lattice defects, strain, and size effects as the mean diameter of the nanoparticles grows. , As size increases, the total surface area to volume ratio and number of surface defects decrease, which typically results in poorer HER performance as the total concentration of reaction sites is reduced. , This trend, however, is not observed, and as a result, the phase purity of the nanoparticle must be taken into consideration. To accomplish this, a single parameter was calculated by multiplying the surface area to volume ratio by the Ru ( P 6 3 / mmc ) phase fraction.…”