Electronic Material Properties - und Geowissenschaften ...

In order to assess the influence of the uncertainty of the twin boundary energy, a
more versatile continuum description of particle energies has been employed. In this
continuum model, the energy of a nanoparticle is approximated by the sum of
volume, surface and twin boundary energy terms:
E( N)
= N E + W + A ( N)
γ + A ( N)
γ . (1)
( c ) twin twin ∑
hkl hkl
hkl
Here, Ec is the cohesive energy per atom in the bulk phase and W is an average
strain energy per atom, which is zero for single crystalline particles. Atwin and γtwin
denote the twin boundary area and its energy. Furthermore, Ahkl and γhkl denote the
total area and energies of the hkl facets terminating the particle surface. For
validating the continuum model, its predictions on particle energies when provided
with materials parameters from the interatomic potential are compared with the
atomistic calculations in Fig. 1, where an excellent agreement is found.
By varying the surface and twin boundary energies, Eq. (1) has now been used for
evaluating the boundaries between stability domains of decahedral, icosahedral and
single crystalline particles as is shown in Fig. 2.
Fig. 2:.Stability of FePt particles in multiply twinned and single crystalline morphologies as
obtained from Eq. (1) by varying surface and twin boundary energies. The vertical lines
indicate surface and twin boundary energies predicted by the interatomic potential used in
Fig. 1 and values estimated on the basis of first principles calculations.
For estimating which set of surface and twin boundary energies best describes
reality, reference values from first principles calculations have been considered,
which amount to 100 meV/Å 2 and 6.5 meV/Å 2 , respectively. For this set of energies,
Fig. 2 reveals that icosahedral particles are stable up to a diameter of 2.6 nm.
The calculations on particle energies provide a reasonable explanation for the
predominance of icosahedral FePt nanoparticles prepared by inert gas condensation.
Since icosahedral particles are energetically most stable for small sizes below 2.6
nm, it is likely that icosahedral seeds evolve during the nucleation stage of inert gas
condensation. When growing further, kinetic trapping of the particles in the
metastable morphology can then lead to the presence of icosahedral particles even
at larger sizes.
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