We will begin our discussion by considering the second question posed above, that is why does CaO adopt the B1 structure and why should fcc-Ca shrink when O atoms are inserted. It should be emphasized here that such questions were (if ever) rarely formulated and therefore no clear explanations have been provided.
The ELF for fcc-Ca was firstly computed at theoretical ambient conditions (a = 5.521 Å). The result is shown in Fig. 2(a) where the basins appear located around the Ca atoms and where no NNM is visible. The charge is concentrated at the atomic positions, with the valence electron contribution probably smeared-out over the unit-cell volume.
However, when the volume of the unit cell of fcc-Ca is reduced to the theoretical value of the B1 structure of CaO (a = 4.829 Å), the ELF generates basins located at the same positions as the O atoms in CaO (see Fig. 2
b). This result clearly indicates that the precise dimensions of the B1 phase are those which force the smeared valence electrons of the Ca atoms to concentrate as LPs at (½, ½, ½). In other words, the unit cell of the B1 phase has the value at which formal anions (O2−) mimic the pressure at which the LPs are formed.
These results agree with those previously obtained for Ca4
O (Savin et al.
). This compound, initially taken as the Zintl phase Ca4
(Eisenmann & Schäfer, 1974
; Hamon et al.
), was later confirmed to be the suboxide Ca4
O with the O atoms centring Ca6
octahedra (Eisenmann et al.
). The calculation of the ELF on the O-free network Ca4
(Savin et al.
) generated only one additional localization region at the position of O atoms in the experimentally observed Ca4
O oxide. They also confirm our thoughts that O2−
anions would play the role of LPs, as advanced earlier for silicate skeletons (Santamaría-Pérez et al.
) and also by X
anions in the aluminium halides (Vegas et al.
The next step was to compute the ELF for the sc
-Ca structure, stable in the pressure range 32–42 GPa (Olyjnik & Holzapfel, 1984
). When the ELF is calculated at a
= 2.645 Å, i.e.
at the theoretical volume for the B2 phase of CaO, a localization region at the cell centre is again observed, coincident with the O atom in CaO (B2; Fig. 3
). It should be remarked that the value of a
= 2.645 Å is in very good agreement with the value of a
= 2.615 Å measured for sc
-Ca at 39 GPa (Olyjnik & Holzapfel, 1984
). Again, the separation of the valence electrons to form an LP occurs at volumes identical to those of the corresponding oxide, giving additional support to the equivalence of LPs and anions. Interestingly, when the ELF is computed at a
= 2.645 Å (39 GPa), the valence electrons remain attached to the atomic cores (cf.
Figure 3 (a) ELF for the sc-Ca structure, with unit-cell parameter a = 3.498 Å (0 GPa). (b) ELF calculated with a = 2.645 Å (39 GPa), showing the charge concentration at the centre of the cell. Blue spheres represent (more ...)
We have also mentioned the existence of a bcc
-Ca. Unlike the B1 and B2 structures of CaO which reproduce the fcc
- and sc
-Ca structures, no binary nor ternary oxide of Ca with the bcc
-Ca substructure has been reported so far. A candidate for such a compound could be a perovskite with the formula CaCa(OF2
). Earlier attempts to synthesize this compound, by thermal decomposition of the mineral brenkite, Ca2
(Leufer & Tillmanns, 1980
), were unsuccessful, only leading to a mixture of CaF2
and CaO. This result was difficult to explain because if an ionic compound consists of isolated anions and cations, the formation of CaCa(OF2
) should be possible.
However, when the ELF for the bcc-Ca is computed at several volumes, the failure in the synthesis becomes meaningful as there is no charge concentration at the voids of the metal structure. The fact that even at the volume of the fcc → bcc transition, occurring at 19 GPa (a = 3.56 Å), no charge concentration was observed, which could explain the non-existence of the oxyfluoride, probably as the F atoms will not find an isolated electron to satisfy its one-electron requirement.
A final calculation was carried out on fcc
-Ca with a
= 5.408 Å. This parameter corresponds to the CaF2
structure, in which the fcc
array of Ca is compressed only 6.3% in volume. As in CaF2
) where the F atoms occupy the tetrahedral 8c
sites (¼, ¼, ¼), it should be expected that the ELF would show charge concentration at these sites. As shown in Fig. 4, the ELF shows charge concentrations at the positions of the F atoms! Thus, the location of the F atoms is clearly coincident with this model and the fluorite structure can also be justified in terms of the charge distribution of the metal matrix for each volume (pressure).
Figure 4 ELF computed for the fcc-Ca structure at a volume reduction of 6.3% (a = 5.408 Å), which is the volume of the fluorite CaF2 structure. This figure shows the presence of ELFs (isovalue of 0.5) at (¼, ¼, ¼), just (more ...)