76
M. Senami and A. Fukushima
(a)
(b)
(c)
(d)
Fig. 3.15 Calculation models. Panel (a) is La 2 O 3 , panel (b) is m-HfO 2 , panel (c) is c-HfO 2 , and
panel (d) is HfLaO x . Red spheres represent O atoms, green spheres represent La atoms, and yellow
spheres represent Hf atoms. All models were rendered by VESTA [58]
Table 3.2 The averaged value of the polarizability density tensor and the dielectric constant
density tensor around the certain region obtained according to Eq. (3.14–3.15). The definition of
the region is in the text
Materials
Polarizability
Dielectric constant
La 2 O 3
0.057
4.72
m-HfO 2
0.041
2.40
c-HfO 2
0.058
3.57
HfLaO x
0.047
2.50
the result for HfLaO x was 0.047, which is smaller than those of La 2 O 3 (0.057) and
c-HfO 2 (0.058). This value was quite close to that of m-HfO 2 (0.041). In the case of
the dielectric constant, the result for HfLaO x was 2.50, which is smaller than those
of La 2 O 3 (4.72) and c-HfO 2 (3.57). Similar to the polarizability density, this value
is quite close to that of m-HfO 2 (2.40).
We next focused on averaged values in the bond region. In this case, we employed
a cylindrical region whose axis corresponded to the bond axis with a radius of 1