Fig. 4. Porous structures during oxidation.

a A 2.4 Å-thick slice from the reconstructed volume of Zr1, with vacancy (triangle), nano-pores (rectangle) and the largest pore (circle) highlight. b Volume distribution of all the voids. We define the voids with volume no larger than filling two Zr atoms (125 ų, Methods) as vacancies, the voids with volume between 125 and 4500 ų as nano-pores. We consider the largest pore with volume of 34,000 ų independently as it touches and separates all three phases. Dashed lines show the boundaries between three types of voids we define. c The surface renderings of all vacancies in c-ZrO₂ (in green) and a-ZrO₂ (in blue). The outline of whole NP is plotted with gray contour. d, e Statistics of vacancies. The fractions of vacancies in c-ZrO₂ and a-ZrO₂ show in (d). The radially normalized density distributions of vacancies as a function of distance from the surface core to the surface show in (e). f The surface renderings of all nano-pores in c-ZrO₂ (in green), in a-ZrO₂ (in blue) and in between c-ZrO₂ and a-ZrO₂ (in orange). g The surface rendering of the largest pore. The boundary atoms composed of amorphous and crystalline atoms are colored by blue and green, respectively. h One interface between two c-ZrO₂ regions with distorted interfacial Zr-Zr bonds, amorphous region and nano-pores. The crystal and amorphous atoms distinguished by BOO analysis are colored as green and blue, respectively. The contour of the nano-pore is colored as orange. i One representative slice shows a 7.8 Å-thick (≈ five atomic layers) cross section of the nano-pores and surrounding atoms. Source data are provided as a Source Data file.