While phase field models are often nondimensionalized, the inherit equations are dimensional. Thus, it is critical to understand and correctly implement the units, especially when coupling multiple physics.

# Units Analysis of Phase Field Equations

In the unit analysis, we break the equations down by units, with the following conventions:

• $$l$$$- length • $$t$$$ - time
• $$e$$$- energy • $$mol$$$ - moles

## Free Energy Functional

The driving force for evolution in the phase field method is the minimization of a free energy functional. The free energy function is written as

## Handling Units in MOOSE

There is no inherit unit system in MOOSE. Thus, the units of the phase field equations are set by the user when they define a model. Specifically, the units are set by the local free energy density and the $$\kappa$$$and mobility parameters ($$L$$$ and $$M$$\$). The units in all these terms must be consistent. Additional energy sources, such as the elastic energy, also must have consistent units. In the phase field module, all of these values are created using Material objects. Thus, the units of your system are not set by the kernels but rather by the materials.

One useful practice is to create your material objects to take SI units as input parameters. Then use length_scale, time_scale, and energy_scale input parameters to convert the actual units of the problem. As an example of this, see the PFParamsPolyFreeEnergy material, where the input file block looks like

[./Copper]
type = PFParamsPolyFreeEnergy
block = 0
c = c
T = 1000 # K
int_width = 30.0
length_scale = 1.0e-9
time_scale = 1.0e-9
D0 = 3.1e-5 # m^2/s, from Brown1980
Em = 0.71 # in eV, from Balluffi1978 Table 2
Ef = 1.28 # in eV, from Balluffi1978 Table 2
surface_energy = 0.7 # J/m^2
[../]

Taken from phase_field/tests/PolynomialFreeEnergy/split_order4_test.i