Biomedical Engineering Reference
In-Depth Information
of dislocations accelerates dissolution, because dislocations give rise
to continuous steps on the surface (Fig. 7.2D) and the strain energy
they cause in crystals favors etch pit formation. Thus, the dissolution
process of solids is induced by formation of pits (Fig. 7.3) and
continues with spreading of their stepwaves [107, 108]. As a result,
the surface of apatite becomes rough and the total edge length and
edge free energy increases [37-43]. These pits provide dissolution
sites and the entire reaction proceeds via nucleation and growth of
the pits accompanying step flow. The pits appear at the dislocation
outlets, usually they are 0.1-10 µm in size (their dimensions depend
on dissolution kinetics and dissolution time: they increase when the
dissolution progresses; furthermore, the crystals must be sufficiently
big to provide enough room for large pits to form). For dissolution
of apatites, the pits have a hexagonal shape (Fig. 7.3) according
to the crystal symmetry P6
/m of pure HA and FA [97-102, 109-
112]. Furthermore, their walls and bottom consist of crystal faces
possessing the highest dissolution rates.
However, in the case of nearly physiological conditions and
sufficiently low solution undersaturation, a free energy barrier
becomes too high for vacancy nucleation to occur on a time scale
that is competitive with other processes. Thus, the dissolution
process of apatites becomes spontaneous only when etch pits of
critical sizes (determined by the Gibbs-Thomson effect, a well-known
thermodynamic principle) are reached [37-43]. At this critical size,
the free energy change goes through a maximum that defines an
energy barrier to a pit formation. Therefore, only relatively large
pits (of sizes greater than a critical value) appear to be active, with
stepwaves contributing to dissolution, while the spreading velocities
are also dependent on the pit sizes, decreasing with pit size decreasing.
Moreover, during dissolution, the crystals become smaller and the
average lengths of dissolution steps decrease (which leads to a
decrease in dissolution rates), and approach the critical value. When
dimensions of dissolving crystals is sufficiently reduced, in some
cases dissolution is thought to be dynamically stabilized (dissolution
suppression) due to a lack of space for active pits/defects formation
on the very small crystallite surfaces [37-43]. Although, the authors
claim this effect as “a new dissolution model incorporating particle
size considerations” [37-43], in fact, they just have introduced some
boundary conditions (the minimal pit sizes and crystal dimensions)
to the etch pit formation process. One should remind, that a similar
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