Biomedical Engineering Reference
In-Depth Information
where A is the surface area (doubled, because two faces are generated), E
bulk
and E
slab
are the
calculated energies of the related models and n is an integer number, required to match the
chemical potentials of the two systems. Astala and Stott adopted a clever and rather
involved scheme to evaluate the phase existence conditions for the two non-stoichiometric
surfaces, showing that the region of their stability is outside the stability window defined by
bulk HA, Ca(OH)
2
and -Ca
3
(PO
4
)
2
(Astala & Stott, 2008).
The typology of the exposed layers differentiates the (010) stoichiometric surface from the
non-stoichiometric ones. Indeed, the (010) Ca-rich surface exposes the OH
-
ions belonging to
the B layer, while both the stoichiometric and the P-rich surfaces contain the OH ions in an
inner layer (see the structures displayed in Fig. 3 for details).
Stoichiometric Ca-rich P-rich
a (Å) 6.98 6.93 7.00
b (Å) 9.28 9.27 9.33
γ (°) 89.87 90.01 90.02
Area (Å
2
) 64.83 64.24 65.24
* Thickness (Å) 13.28 20.05 20.23
<Ca-O> (Å) 2.41 2.39 2.40
<P-O> (Å) 1.55 1.55 1.55
<O-H> (Å) 0.97 0.97 0.97
<OPO> (°) 109.5 109.4 109.4
Band Gap (eV) 6.21 6.80 6.65
Dipole (Debye) 3.5·10
-3
4.0·10
-3
1.4·10
-2
* The slab thickness is the perpendicular distance between the most exposed Ca ions on
the upper and lower faces of the slab.
Table 1. Most important geometrical parameters of the HA (010) surfaces. The values in <
…
>
correspond to the arithmetical averages of the considered feature.
In Fig. 3, the most exposed layers of the three terminations are reported, superimposed on
the isodensity surface colorcoded with the electrostatic potential. The isodensity value is
fixed to 10
-6
electrons and the electrostatic potential spans from -0.02 a.u. (red) to +0.02 a.u.
(blue). Positive values of the potential are visible in correspondence of the Ca ions while
negative potential zones are mostly located upon superficial phosphate ions.
In Table 1, a geometrical analysis of the three surfaces is reported. The cell parameters are
slightly different between the three cases, but the rectangular shape is mostly maintained.
The slab thickness is not comparable, because of a different number of layers for each
surface model. The interatomic distances and angles are, however, very similar.
Two important intensive parameters can classify the stability of a slab structure, the
electronic band gap and the total dipole moment across the slab: each surface has a dipole
moment close to zero and a band gap typical of electrical insulators. The three surfaces are,
then, stable and can be adopted as a substrate to study the adsorption of molecules.
2.1.2 Adsorption of H
2
O and CO upon the most exposed Ca ions of the (010) surfaces
The chemical reactivity of the most exposed cations of a surface is experimentally studied
with the IR technique by monitoring the perturbation of the vibrational frequency of the
probe molecule, which is compared to the value for the free molecule. Of the possible probe
