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Solids
On self-diffusion and surface energy under compression of diamond, silicon, and germanium
M. N. Magomedov Institute of Geothermy Problems, Makhachkala
Abstract:
The dependences of activation (vacancy formation and self-diffusion) parameters, specific surface energy
$\sigma$, and its isochoric temperature derivative versus relative volume
$(V/V_0)$ are calculated for diamond, silicon, and germanium along two isotherms at 300 and 3000 K. Here, V 0 is the crystal volume under pressure
$P$ = 0 at temperature
$T$ = 0 K. It is shown that under a compression to
$V/V_0>(V/V_0)_{\mathrm{min}}$, activation processes are suppressed during isothermal compression and enhanced during isochoric heating. However, for
$V/V_0=(V/V_0)_{\mathrm{min}}$, the self-diffusion coefficient attains its minimal value. And for
$V/V_0<(V/V_0)_{\mathrm{min}}$, self-diffusion is intensified; in this case, the self-diffusion coefficient is independent of temperature. This is due to the quantum effect: under superstrong compression, the atomic spacing becomes comparable with the amplitude of atomic vibrations, which leads to the tunnel transport of atoms over the crystal. It is shown that upon an isothermal decrease in
$V/V_0$, the surface energy, which attains is maximal value at
$(V/V_0)_{\mathrm{max}}$, sharply decreases upon a further compression. For
$V/V_0\le(V/V_0)_{fr}$, the surface energy becomes negative (
$\sigma(V/V_0)_{fr}$ = 0), which must stimulate fragmentation of the crystal, i.e., an increase in the surface (per atom) intercrystallite surface. It is shown that
$(V/V_0)_{fr}\gg(V/V_0)_{\mathrm{min}}$.
Received: 05.12.2012
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