# Two-phase models

MOOSE provides capabilities that enable the easy development of multiphase field model. A free energy expression has to be provided for each individual phase. Two different systems exist to combine those phase free energies into a global free energy.

Material objects that internally derive from DerivativeFunctionMaterialBase (Doxygen), like the materials for the Parsed Function Kernels are used to provide the free energy expressions for each phase.

The simplified two-phase model uses a single order parameter to switch between the two phases. A global free energy is constructed using a meta material class that combines the phase free energies.

For two phase models the DerivativeTwoPhaseMaterial (Doxygen) can be used to combine two phase free energies into a global free energy (which the Allen-Cahn and Cahn-Hilliard kernels use to evolve the system) as

(1)

## Input Parameters

• etaOrder parameter

C++ Type:std::vector

Options:

Description:Order parameter

• fa_namePhase A material (at eta=0)

C++ Type:MaterialPropertyName

Options:

Description:Phase A material (at eta=0)

• fb_namePhase A material (at eta=1)

C++ Type:MaterialPropertyName

Options:

Description:Phase A material (at eta=1)

### Required Parameters

• computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the Material via MaterialPropertyInterface::getMaterial(). Non-computed Materials are not sorted for dependencies.

Default:True

C++ Type:bool

Options:

Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the Material via MaterialPropertyInterface::getMaterial(). Non-computed Materials are not sorted for dependencies.

• ggBarrier Function Material that provides g(eta)

Default:g

C++ Type:MaterialPropertyName

Options:

Description:Barrier Function Material that provides g(eta)

C++ Type:std::vector

Options:

• f_nameFBase name of the free energy function (used to name the material properties)

Default:F

C++ Type:std::string

Options:

Description:Base name of the free energy function (used to name the material properties)

• argsArguments of fa and fb - use vector coupling

C++ Type:std::vector

Options:

Description:Arguments of fa and fb - use vector coupling

• derivative_order3Maximum order of derivatives taken (2 or 3)

Default:3

C++ Type:unsigned int

Options:

Description:Maximum order of derivatives taken (2 or 3)

• W0Energy barrier for the phase transformation from A to B

Default:0

C++ Type:double

Options:

Description:Energy barrier for the phase transformation from A to B

• hhSwitching Function Material that provides h(eta)

Default:h

C++ Type:MaterialPropertyName

Options:

Description:Switching Function Material that provides h(eta)

• boundaryThe list of boundary IDs from the mesh where this boundary condition applies

C++ Type:std::vector

Options:

Description:The list of boundary IDs from the mesh where this boundary condition applies

• blockThe list of block ids (SubdomainID) that this object will be applied

C++ Type:std::vector

Options:

Description:The list of block ids (SubdomainID) that this object will be applied

### Optional Parameters

• enableTrueSet the enabled status of the MooseObject.

Default:True

C++ Type:bool

Options:

Description:Set the enabled status of the MooseObject.

• use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Default:False

C++ Type:bool

Options:

Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

• control_tagsAdds user-defined labels for accessing object parameters via control logic.

C++ Type:std::vector

Options:

Description:Adds user-defined labels for accessing object parameters via control logic.

• seed0The seed for the master random number generator

Default:0

C++ Type:unsigned int

Options:

Description:The seed for the master random number generator

• implicitTrueDetermines whether this object is calculated using an implicit or explicit form

Default:True

C++ Type:bool

Options:

Description:Determines whether this object is calculated using an implicit or explicit form

• constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped

Default:NONE

C++ Type:MooseEnum

Options:NONE ELEMENT SUBDOMAIN

Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped

• output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)

C++ Type:std::vector

Options:

Description:List of material properties, from this material, to output (outputs must also be defined to an output type)

• outputsnone Vector of output names were you would like to restrict the output of variables(s) associated with this object

Default:none

C++ Type:std::vector

Options:

Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object

Check out the example input at modules/phase_field/tests/MultiPhase/derivativetwophasematerial.i to see it in action.

## Example

An example material block looks like this (materials for phase field mobilities omitted for clarity).


[Materials]
# Free energy for phase A

[./free_energy_A]
type = DerivativeParsedMaterial
block = 0
f_name = Fa
args = 'c'
function = '(c-0.1)^2'
third_derivatives = false
enable_jit = true
[../]

# Free energy for phase B

[./free_energy_B]
type = DerivativeParsedMaterial
block = 0
f_name = Fb
args = 'c'
function = '(c-0.9)^2'
third_derivatives = false
enable_jit = true
[../]

[./switching]
type = SwitchingFunctionMaterial
block = 0
eta = eta
h_order = SIMPLE
[../]

[./barrier]
type = BarrierFunctionMaterial
block = 0
eta = eta
g_order = SIMPLE
[../]

# Total free energy F = h(phi)*Fb + (1-h(phi))*Fa

[./free_energy]
type = DerivativeTwoPhaseMaterial
block = 0
f_name = F    # Name of the global free energy function (use this in the Parsed Function Kernels)
fa_name = Fa  # f_name of the phase A free energy function
fb_name = Fb  # f_name of the phase B free energy function
args = 'c'
eta = eta     # order parameter that switches between A and B phase
third_derivatives = false
outputs = exodus
[../]
[]


Note that the phase free energies are single wells. The global free energy landscape will however have a double well character in this example.