RESULTS AND DISCUSSION
The optimized lattices constant are shown in Table I, in comparison with the results of experiment and other
available calculations for SnZn
2
O
4
. As seen from the Table I, our present results are rather reliable with other
calculation results and experiment data.
TABLE I:
Demonstration of calculated and experimental results of structural parameters: a and u for normal (N)
and inverse (I) spinel.
Sources of data
Exp.
a
N (cal.
b
)
N (cal.
c
)
N (cal.
d
)
I (cal.
b
)
I (cal.
c
)
I (cal.
d
)
a, b, c (Å)
8.66
8.52
8.63
8.55
8.69
8.66
8.58
u
0.390
0.382
0.383
0.383
0.389
0.383
0.383
a
ref. ( R. J. Hill
et al
., 1979)
b
our work
c
ref. (Su-Huai Wei
et al
., 2001)
d
ref. (D. Segev
et al
., 2005)
The tetrahedral (R
tetra
) and octahedral (R
octa
) bond lengths between the cation and oxygen atoms (i.e. Zn-O and Sn-O),
shown in Table II, exhibited in agreement with the other calculations (D. Segev et al., 2005). We noted that the bond
length increases as the cation valence decreases or as atomic number increases. We found that the octahedral bond
length (
R
octa
) is systematically larger by about 0.1 Å than tetrahedral bond length
(
R
tetra
), due to the larger space
available at the octahedral site.
Calculated band structure of normal spinel and inverse spinel SnZn
2
O
4
are shown in Fig. 2(a) and 2(b),
respectively. Coordinates of the special points of the Brillouin zone are as follows (in terms of unit vectors of the
reciprocal lattice): L(0.5, 0.5, 0.5), G(0,0,0), X(0.5, 0, 0.5). The energy band gaps,
E
g
, are 0.826 eV for normal spinel
and 1.089 eV for inverse spinel, whereas the corresponding experimental values are 3.6 eV.
However, it is well known
that LDA calculations provide underestimated energy gap in comparison with experimental values.
As seen from
Figures 2, such compound has direct band gap at G point, which is in agreement with other calculations (Su-Huai Wei
et al., 2001 , D. Segev et al., 2005).
TABLE II
: Demonstration the tetrahedral (R
tetra
) and the octahedral (R
octa
) bond length between the cations and their
oxygen atoms nearest neighbors, for normal and inverse spinel SnZn
2
O
4
.
