( a ) ( b )
Fig.1
Ball and stick representation of normal SnZn
2
O
4
spinel structure, (a) showing the position of the O atoms
(red balls) bonded to the Sn atoms (grey balls) at the tetrahedral sites, (b) showing the position of the O atoms
(red balls) bonded to the Zn atoms (blue balls) at the octahedral sites.
The effective
u
parameter in the inverse spinel structure is obtained using the averaged tetrahedral and
octahedral bond lengths and the formula given above.
MEDTHOD OF CALCULATIONS
Zinc stannate belong to the group of “4-2” cubic oxide spinel, with space group of Fd3m (O
7
h
) or number
227. The structural parameters was used in this calculation are taken from Segev and Wei (Su-Huai Wei
et al
., 2001),
as a starting point for geometry relaxation. In particular, the lattice constant in ours calculation is
a
= 8.657 Å and the
oxygen parameter
u
= 0.361. The cubic unit cell contain one molecule with the atom positions are Zn(0.652, 0.652,
0.652), Sn(0, 0, 0), O(0.361, 0.361, 0.361) (R. Dekkert
et al
., 2002). All calculations were performed in density
functional theory (DFT) framework. The exchange-correlation potential is described in term of local density
approximation (LDA), with the Ceperley-Alder and Perdew–Zunger functional. The core level atoms are represented
by ultrasoft pseudopotential. Note that a plane-wave basis set energy cutoff was set 380 eV, whereas the Monkhorst-
Pack scheme k-point grid sampling was set to 12
12
12 for the Brillouin zone of both normal and inverses spinel
structures. The electronic configuration of Sn(5s
2
5p
2
), Zn(3d
10
4s
2
), and O(2s
2
2p
4
) are treated as valence state. The
structural parameters of SnZn
2
O
4
were determined using Broyden-Fletcher-Goldfarb-Shenno (BFGS) minimization
technique, with the threshold for converged structure: energy per atom less than 0.5x10
-5
eV, residual force less than
0.01 eV/Å, stress below 0.02 GPa and displacement of atoms during the structural relaxation less than 0.0005 Å.
