420
T. L. Tsaregradskaya et al.
The change in the total energy and volume of the supercell during annealing at a
temperature of 300 K is shown in Fig. 7. At the initial stages of molecular dynamics,
insignificant fluctuations of the total energy of the supercell (imperceptible on the
scale of Fig. 7) are observed, which are not accompanied by noticeable changes in
the electronic spectra. Further, a sharp decrease in the total energy of the supercell
is observed (N = 9 in Fig. 7), which is accompanied by a decrease in the supercell
volume and a noticeable change in the electronic spectrum of the supercell (Fig. 6c).
Figure 6c shows the density of electronic states of the supercell of the “amorphous” phase after annealing at 300 K. Compared with the electronic spectrum of
the initial “liquid” phase (Fig. 6b), one can notice the appearance of a local minimum
in the vicinity of the Fermi level. It is precisely this behavior of electronic spectra
characteristic of amorphization [14] that allows us to call the resulting supercell an
“amorphous” phase. The latter correlates with the experimentally obtained stability
criterion of amorphous metal alloys Nagel–Tauc [15, 16]; a decrease in the density
of electronic states at the Fermi level stabilizes the amorphous state.
It should be noted that the obtained electronic spectrum of the “amorphous” phase
does not coincide with the electronic spectra of the stable crystalline phases of the
Fe–Zr system at a temperature of 300 K (α-Fe and the Fe 2 Zr intermetallic alloy). In
addition, if we calculate the total energy of the mixture of stable crystalline phases
(23(α-Fe) + 3(Fe 2 Zr) = Fe 29 Zr 3 ), which corresponds to the supercell chosen by us,
then we obtain a value of ~−680 Hartree. The latter, of course, is much less than the
total energy of the obtained supercell of the “amorphous” phase, which is metastable.
It should be noted that during numerical annealing at a temperature of 300 K we
did not observe signs of crystallization of our system: for example, the order of the
mutual arrangement of atoms in the supercell did not change (atoms did not transfer
from one coordination sphere to another). The latter correlates with the results of
an experimental study of the amorphization and crystallization process in the Fe–Zr
system: in [8], it was shown that the temporary annealing of the amorphous Fe 90 Zr 10
alloy at temperatures below 500 K does not lead to crystallization.
It was possible to simulate processes similar to crystallization of amorphous alloys
with increasing temperature of numerical annealing of our disordered supercell. For
example, upon annealing at a temperature of 600 K, the formation of a local minimum
is first observed in the vicinity of the Fermi level, similar to that discussed above
for the “amorphous” phase. Then a more large-scale restructuring of the electronic
spectra is observed (Fig. 8), which is accompanied by a change in the order of
the mutual arrangement of atoms in the supercell—coordination spheres are mixed.
Such a change in the arrangement of atoms allows us to talk about the beginning of
crystallization processes in the structure under consideration.
Figure 8 shows the energy dependences of the electronic states density of the
Fe 29 Zr 3 supercell annealed at temperatures of 300 K (a), 450 K (b), and 600 K (c).
It is seen that with increasing temperature of numerical annealing, the electronic
spectrum of the system undergoes significant changes. With a further increase in the
annealing temperature, the electronic spectra do not qualitatively differ from those
T. L. Tsaregradskaya et al.
The change in the total energy and volume of the supercell during annealing at a
temperature of 300 K is shown in Fig. 7. At the initial stages of molecular dynamics,
insignificant fluctuations of the total energy of the supercell (imperceptible on the
scale of Fig. 7) are observed, which are not accompanied by noticeable changes in
the electronic spectra. Further, a sharp decrease in the total energy of the supercell
is observed (N = 9 in Fig. 7), which is accompanied by a decrease in the supercell
volume and a noticeable change in the electronic spectrum of the supercell (Fig. 6c).
Figure 6c shows the density of electronic states of the supercell of the “amorphous” phase after annealing at 300 K. Compared with the electronic spectrum of
the initial “liquid” phase (Fig. 6b), one can notice the appearance of a local minimum
in the vicinity of the Fermi level. It is precisely this behavior of electronic spectra
characteristic of amorphization [14] that allows us to call the resulting supercell an
“amorphous” phase. The latter correlates with the experimentally obtained stability
criterion of amorphous metal alloys Nagel–Tauc [15, 16]; a decrease in the density
of electronic states at the Fermi level stabilizes the amorphous state.
It should be noted that the obtained electronic spectrum of the “amorphous” phase
does not coincide with the electronic spectra of the stable crystalline phases of the
Fe–Zr system at a temperature of 300 K (α-Fe and the Fe 2 Zr intermetallic alloy). In
addition, if we calculate the total energy of the mixture of stable crystalline phases
(23(α-Fe) + 3(Fe 2 Zr) = Fe 29 Zr 3 ), which corresponds to the supercell chosen by us,
then we obtain a value of ~−680 Hartree. The latter, of course, is much less than the
total energy of the obtained supercell of the “amorphous” phase, which is metastable.
It should be noted that during numerical annealing at a temperature of 300 K we
did not observe signs of crystallization of our system: for example, the order of the
mutual arrangement of atoms in the supercell did not change (atoms did not transfer
from one coordination sphere to another). The latter correlates with the results of
an experimental study of the amorphization and crystallization process in the Fe–Zr
system: in [8], it was shown that the temporary annealing of the amorphous Fe 90 Zr 10
alloy at temperatures below 500 K does not lead to crystallization.
It was possible to simulate processes similar to crystallization of amorphous alloys
with increasing temperature of numerical annealing of our disordered supercell. For
example, upon annealing at a temperature of 600 K, the formation of a local minimum
is first observed in the vicinity of the Fermi level, similar to that discussed above
for the “amorphous” phase. Then a more large-scale restructuring of the electronic
spectra is observed (Fig. 8), which is accompanied by a change in the order of
the mutual arrangement of atoms in the supercell—coordination spheres are mixed.
Such a change in the arrangement of atoms allows us to talk about the beginning of
crystallization processes in the structure under consideration.
Figure 8 shows the energy dependences of the electronic states density of the
Fe 29 Zr 3 supercell annealed at temperatures of 300 K (a), 450 K (b), and 600 K (c).
It is seen that with increasing temperature of numerical annealing, the electronic
spectrum of the system undergoes significant changes. With a further increase in the
annealing temperature, the electronic spectra do not qualitatively differ from those