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Phase Field Modeling of Melting of Aluminum Nanoparticles
K. Samani and V. I. Levitas
Departments of Mechanical Engineering
Iowa State University, Ames, Iowa
Surface pre-melting and melting of nanoparticles are fundamental problems, which are currently under
intense study. For aluminum nanoparticles, this study also has applied aspects. Aluminum nanoparticles
represent important class of nanoenergetic materials that are used in rocket propellant mixtures and
other energetic applications. They posses significantly enhanced burning rate and reduced ignition
delay time. Aluminum nanoparticles usually have a several nanometers thick oxide layer.
According to the recently developed melt-dispersion mechanism of reaction of Al anoparticles,
one of the processes that determines the reactivity of Al nanoparticles is melting of Al and stress
development in Al core–shell system due to volume increase during melting. Melt nucleation, melting
temperature and rate of melting at high heating rates (10 8 K/s and above) determine mechanics of
deformation and fracture of alumina shell, which are important for the melt-dispersion mechanism.
We expanded a phase field approach for the pre-melting (surface melting) and melting of
nanoparticles by introducing correct expression for surface tension at the solid-melt interface and
correct description of variation of surface energy of the external surface. New definition of surface
tension yields results that are consistent with sharp interface approach, in contrast to previous theories.
Suggested description of variation of surface energy eliminates drawbacks of known approaches to
surface melting.
Coupled phase field and mechanical equations are solved using finite element method and COMSOL
code. Melting, without and with mechanics, is considered. Calculated results for the thickness of the
molten layer versus temperature (Fig. 1) and melting temperature versus particle size are in good
correspondence with known experiments. Surprisingly, for the particles with radius from 2 to 5 nm,
melting temperatures are even in better agreement with experiments than the molecular dynamics
results (see Fig. 2). For heating rates greater than 10 13 K/s, homogeneous nucleation competes with
interface propagation. It is also found that classical expression for the interface velocity based on sharpinterface
equation is well reproduced in our calculations even for temperatures for which solid is
completely unstable and for particle radiuses exceeding interface width, which is approximately 4 nm.
For spherical particle, interface energy is independent of interface radius down to 4 nm.
Classical relationship for pressure jump across the interface, Δσ = 2Γ/r, where Γ is interface energy and
r is the interface radius, is confirmed for r > 5nm and neglected internal stresses. The effect of alumina
shell is also considered. Alumina shell increases melting time and melting temperature considerably.
Large hoop stresses and strain rates developed in the shell can yield spallation of the shell.
Society of Engineering Science ▪ 47 th Annual Technical Meeting 48