 Phase Field Modeling 
Definition:  A computational
method
for simulating
microstructure
evolution. 
Explanation:  A central challenge
in the modeling of
microstructure
formation is the
fact that the
position of the
interfaces is not
known in advance and
it is regarded as
the
part of the solution
of the problem. This
is obvious during
solidification,
where latent heat is
emitted at freezing
fronts and
solute is also
partitioned. On the
other hand, the
motion of these
interfaces depends
on the local
concentration and
heat fluxes; i.e.
diffusive transport
couples with
boundary conditions
and front
propagation
conditions at the
a
priori unknown
interface
positions.
In contrast to sharp
interface methods
where complex
interface tracking
is pursued, phase
field modeling
follows an
alternative strategy
by introducing an
order
parameter or
phase field,
which discriminates
among different
phases. For example,
a
value of 1 would
correspond to a
local solid state,
whereas 0 represents
the melt phase. At
the interfaces, the
order parameter
changes smoothly
over a certain
length scale. The
crucial point is now
that the evolution
of the order
parameter is
described via
partial differential
equations in the
entire computational
domain, and a
tracking of the
interfaces is no
longer needed.
Typical applications
are related to
solidification and
solid state
transformations.
More recently,
aspects as
fracture have also
been
studied. Further
recent extensions
are the phase
field crystal
model, which
resolves
an atomic structure
and are therefore
capable to simulate
grain boundaries.
Moreover,
amplitude
equations
methods contain
atomic resolution,
but are able
to simulate large
systems as entire
polycrystalline
structures. 
Picture / Figure / Diagram: 

Left: Phase field modeling of dendritic solidification. Right: Polycrystalline solidification of iron, simulated with amplitude equations.


SFBLink:  In the project A5 and A9, phase field models are used for the description of hydrogen embrittlement. Solidification modeling using phase field techniques is done in project A8. Amplitude equations are used for modeling of grain boundary premelting and solidmelt gamma surfaces in project A9. 
References:  I. Steinbach, Modelling Simul. Mater. Sci. Eng. 17 (2009) 073001. L.Q. Chen, Annu. Rev. Mater. Res. 32 (2002) 113. R. Spatschek, E. Brener, A. Karma, Phil. Mag. 91 (2010), 75. K.R. Elder, M. Katakowski, M. Haataja, M. Grant, Phys. Rev. Lett. 88 (2001) 245701 R. Spatschek, A. Karma, Phys. Rev. B, 214201 (2010). 

