A new method is proposed for the calculation of the unrelaxed surface energy of spinel ferrite. The surface energy calculation consists of (1) setting the central and computational domains in the semi-infinite real lattice, having a specific surface, and having an infinite real lattice; (2) calculation of the lattice energies produced by the associated portion of each ion in the relative domain; and (3) dividing the difference between the semi-infinite lattice energy and the infinite lattice energy on the exposed surface area in the central domain. The surface energy was found to converge with a slight expansion of the domain in the real lattice. This method is superior to any other so far reported due to its simple concept and reduced computing burden. The unrelaxed surface energies of the (100), (110), and (111) of ZnFe2O4 and Fe3O4 were evaluated by using in the semi-infinite real lattices containing only one surface. For the normal spinel ZnFe2O4, the(100), which consisted of tetrahedral coordinated Zn2+ was electrostatically the most stable surface. But, for the inverses pinel Fe3O4, the(111), which consisted of tetrahedral coordinated Fe3+and octahedral coordinated Fe2+ was electrostatically the most stable surface.

Using reverse micelle processing, ZnAl2O4 nanopowders were synthesized from a mixed precursor(consisting of Zn(NO3)2 and Al(NO3)3). The ZnAl2O4 was prepared by mixing the aqueous solution at a molar ratio of Zn : Al = 1 : 2. The average size and distribution of the synthesized powders with heat treatment at 600 oC for 2 h were in the range of 10-20 nm and narrow, respectively. The average size of the synthesized powders increased with increasing water to surfactant molar ratio. The XRD diffraction patterns show that the phase of ZnAl2O4 was spinel(JCPDS No. 05-0669). The synthesized and calcined powders were characterized using a thermogravimetric - differential scanning calorimeter(TG-DSC), X-ray diffraction analysis (XRD), and high resolution transmission electron microscopy(HRTEM). The effects of the synthesis parameter, such as the molar ratio of water to surfactant, are discussed.