## 3 Results and Discussion  
Figure 1 shows the XRD patterns of the as-synthesized and calcined samples. The vertical lines indicate the respective Joint Committee on Powder Diffraction Standards (JCPDS) card no. 37-1484, which can be related to monoclinic phase of zirconia. As can be seen in Figure 1, all the samples exhibited the characteristic diffraction peaks of monoclinic zirconia. No diffraction peaks of any other crystal phase can be observed in the samples, which indicates that all the samples are of pure monoclinic phase. With the increase of calcination temperature, the intensity of the diffraction peaks gradually increases, and the shape of the peaks becomes sharper. According to the Scherrer equation [20], the crystal size of the as-synthesized and calcined samples are 5.1 nm, 7.5 nm (calcined at 723 K) and 17.5 nm (calcined at 923 K), which indicates that the increase of calcination temperature can result in the increase the crystallinity and the crystal size of the materials. Figure 2 shows FESEM images of as-synthesized and calcined samples. The as-synthesized sample is composed of highly dispersed cube-like particles of 50-150 nm in size (Figure 2a,b). On the contrary, the sample synthesized without DTAB (Figure S1) shows obvious agglomeration, which indicates that  
Figure 3 shows TEM images and electron diffraction patterns of as-synthesized and calcined samples. As can be seen in Figure 3a,b, the as-synthesized sample possesses cube-like morphology and each cube-like particle is made up of numerous crystals of about 5 nm in size. Under the compact accumulation of these nanocrystals, wormhole-like channels with a pore size of about 2 nm were formed for the as-synthesized sample. The color of the center of the particle (Figure 3b) is slightly lighter than that around it, which indicates that the sample may have a hollow structure. An array of blurred lattice fringes can be observed in Figure 3c, which indicates that the sample is in semi-crystallized state. Consistently with the SEM results, the sample synthesized without DTAB (Figure S2a) also shows obvious agglomeration. In addition, the shape of the particles is also not regular (Figure S2b). It can be seen that the introduction of DTAB can improve the dispersion and regularity of the as-synthesized sample. After calcination at 723 K, the morphology of the sample does not show obvious changes, but the edges of the corners become rounded. The size of the crystals increased to about 12 nm, which is a little bigger than the calculated value according to the Scherrer equation [20]. The pore size of the sample also accordingly increases to about 4 nm. The color difference between the center and the surroundings of the particle becomes more obvious, revealing that the sample has a hollow structure. When the calcination temperature increases to 923 K, the sample exhibits a hollow spherical structure and the crystal size increases to about 25 nm. Both the samples after calcination (Figure 3j,k) show clear lattice fringes, which indicates that the samples are in a highly crystallized state. As can be seen in Figure 3d,h,l, all the samples show characteristic diffraction pattern of monoclinic zirconia. The patterns undergo from blur to clarity, which suggests again that calcination can improve crystallinity. N\({}_{2}\) adsorption-desorption isotherms and the pore size distributions of as-synthesized and calcined samples are plotted in Figures 4 and 5. The as-synthesized sample shows a transitional type isotherm between the Type I (b) and Type II [21]. The hump in the range of P/P\({}_{0}\) = 0-0.2 can be related to the micropore filling, and the steep uptake between P/P\({}_{0}\) = 0.9-1.0 is due to the existence of the macropores in the sample, which indicates that the sample contains both micropores and macropores. The pore size distributions (Figure 5a,d, due to the limitation of BJH model in micropore calculation, we have added the DFT pore size distribution of the as-synthesized sample) of the as-synthesized sample proved the above conclusions.