二氧化鈰奈米粒子被廣泛應用在光催化、固態氧化燃料電池、三元觸媒轉換器，和有機催化中。目前已發表的論文中皆使用高濃度的氫氧化鈉在高溫環境下以長時間合成正立方體的二氧化鈰奈米粒子。在此研究中，我們利用濃度較低的氨水與硫酸鈉在100°C反應5小時得到尺寸均勻的正立方體二氧化鈰奈米粒子，加入硫酸鈉可在反應過程中產生白色的硫酸鈰中間產物，以此來控制反應速率，進而調整奈米粒子的形狀，並藉由改變前驅物的濃度與反應溫度來合成特定尺寸(9、13、18 nm)的正立方體二氧化鈰奈米粒子。
透過吸收光譜可觀察到隨著奈米粒子的尺寸增加，吸收光譜的鋒值紅位移。由此我們得知當奈米粒子的尺寸超過其波爾半徑時，仍然可觀察到光譜的位移，這一現象刷新了我們對於量子侷限的認知。進一步將不同尺寸的正立方體二氧化鈰奈米粒子之吸收光譜，與之前製備的正八面體二氧化鈰奈米粒子之吸收光譜對照之下，可發現在同一尺寸但不同晶面之奈米粒子有不同的吸收。上述現象證明了光學上的尺寸與晶面效應。在電化學量測中，透過莫特-肖特基量測可以發現尺寸效應對導帶與價帶能階的影響。透過電化學產氧的量測,可發現尺寸效應造成的導帶位置不同對產氧的電位會有影響。

Ceria nanoparticles can be applied in photocatalysis, solid oxide fuel cell (SOFC), three-way catalysts (TWCs), and organic catalysis. A very concentrated base and high temperature are normally employed to make CeO2 particles. In this research, mild synthesis of 1-bound cubic ceria nanoparticles with tunable sizes has been developed by heating cerium(III) nitrate hexahydrate, sodium sulfate, and dilute ammonia at 100 ºC for 4 hours. Adding sodium sulfate can produce a white precipitate, Ce2(SO4)3, which possibly reduces the rate of reaction to yield CeO2 nano-cubes with sizes of 9, 13, and 18 nm. The maximum absorption wavelength red-shifts as the size of ceria nanoparticles increases. Comparing to the {111}-bound CeO2 octahedra of similar volume with a band gap of 3.46 eV, the 18 nm CeO2 cubes show a band gap of 3.45 eV. This equates to a band wavelength separation of about 10 nm. Thus, CeO2 nanocrystals exhibit both optical size and facet effects. From Mott–Schottky measurements, the energy levels of conduction band and valence band show size dependence. Notably, the size-dependent valence band energy difference gives onset potential variation in the electrochemical oxygen evolution reaction.

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