SLKKSSum

Enforce the sum of sublattice concentrations to a given phase concentration.

Overview

This kernel is used if the simulation only contains a single phase with multiple sublattices. Otherwise SLKKSMultiPhaseConcentration needs to be used.

One potential application is a static solve for the sublattice concentrations (and free energy) of a single phase. This information can be used to tabulate sublattice concentrations as functions of total concentrations to inform initial conditions of full solve simulations.

Example Input File Syntax

Input Parameters

aSublattice site fraction for the kernel variable
C++ Type:double
Controllable:No
Description:Sublattice site fraction for the kernel variable
asPhase a sublattice site fractions
C++ Type:std::vector<double>
Controllable:No
Description:Phase a sublattice site fractions
csother sublattice concentrations in the same phase
C++ Type:std::vector<VariableName>
Controllable:No
Description:other sublattice concentrations in the same phase
sumprescribed sum
C++ Type:std::vector<VariableName>
Controllable:No
Description:prescribed sum
variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
Controllable:No
Description:The name of the variable that this residual object operates on

Required Parameters

blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
displacementsThe displacements
C++ Type:std::vector<VariableName>
Controllable:No
Description:The displacements
prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Optional Parameters

absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution
C++ Type:std::vector<TagName>
Controllable:No
Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution
extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the matrices this Kernel should fill
extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the vectors this Kernel should fill
matrix_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Options:nontime, system
Controllable:No
Description:The tag for the matrices this Kernel should fill
vector_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime
C++ Type:MultiMooseEnum
Options:nontime, time
Controllable:No
Description:The tag for the vectors this Kernel should fill

Tagging Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
diag_save_inThe name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Controllable:No
Description:The name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
save_inThe name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Controllable:No
Description:The name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Controllable:No
Description:The seed for the master random number generator
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
Controllable:No
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.

Advanced Parameters

Input Files

(modules/phase_field/test/tests/slkks/sublattice_concentrations.i)
(modules/phase_field/examples/slkks/CrFe_sigma.i)

(modules/phase_field/test/tests/slkks/sublattice_concentrations.i)

#
# SLKKS two phase example for the BCC and SIGMA phases. The sigma phase contains
# multiple sublattices. Free energy from
# Jacob, Aurelie, Erwin Povoden-Karadeniz, and Ernst Kozeschnik. "Revised thermodynamic
# description of the Fe-Cr system based on an improved sublattice model of the sigma phase."
# Calphad 60 (2018): 16-28.
#
# In this simulation we solve only for the sublattice concentrations of the sigma phase
# (and consequently for the free energy of the sigma phase as function of total concentration.)
# The Cr concentration is prescribed as linear gradient. This permits us to plot
# the free energies of the BCC and sigma phases.
#

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 100
    ny = 1
    xmin = 0.01
    xmax = 0.99
    ymax = 0.1
  []
[]

[AuxVariables]
  [cCr]
    [InitialCondition]
      type = FunctionIC
      function = x
    []
  []
[]

[Variables]
  [SIGMA_0CR]
    [InitialCondition]
      type = FunctionIC
      function = x
    []
  []
  [SIGMA_1CR]
    [InitialCondition]
      type = FunctionIC
      function = x
    []
  []
  [SIGMA_2CR]
    [InitialCondition]
      type = FunctionIC
      function = x
    []
  []
[]

[Kernels]
  [chempot2a2b]
    # This kernel ties the first two sublattices in the sigma phase together
    type = SLKKSChemicalPotential
    variable = SIGMA_0CR
    a = 10
    cs = SIGMA_1CR
    as = 4
    F = F_SIGMA
    coupled_variables = SIGMA_2CR
  []
  [chempot2b2c]
    # This kernel ties the remaining two sublattices in the sigma phase together
    type = SLKKSChemicalPotential
    variable = SIGMA_1CR
    a = 4
    cs = SIGMA_2CR
    as = 16
    F = F_SIGMA
    coupled_variables = SIGMA_0CR
  []
  [sum]
    type = SLKKSSum
    variable = SIGMA_2CR
    a = 16
    cs = 'SIGMA_0CR SIGMA_1CR'
    as = '10        4'
    sum = cCr
  []
[]

[Materials]
  # CALPHAD free energy of the FeCr sigma phase
  [F_SIGMA]
    type = DerivativeParsedMaterial
    property_name = F_SIGMA
    outputs = exodus
    expression = 'SIGMA_0FE := 1-SIGMA_0CR;
                SIGMA_1FE := 1-SIGMA_1CR;SIGMA_2FE := '
               '1-SIGMA_2CR; 8.3145*T*(10.0*if(SIGMA_0CR > 1.0e-15,SIGMA_0CR*log(SIGMA_0CR),0) + '
               '10.0*if(SIGMA_0FE > 1.0e-15,SIGMA_0FE*log(SIGMA_0FE),0) + 4.0*if(SIGMA_1CR > '
               '1.0e-15,SIGMA_1CR*log(SIGMA_1CR),0) + 4.0*if(SIGMA_1FE > '
               '1.0e-15,SIGMA_1FE*log(SIGMA_1FE),0) + 16.0*if(SIGMA_2CR > '
               '1.0e-15,SIGMA_2CR*log(SIGMA_2CR),0) + 16.0*if(SIGMA_2FE > '
               '1.0e-15,SIGMA_2FE*log(SIGMA_2FE),0))/(10.0*SIGMA_0CR + 10.0*SIGMA_0FE + '
               '4.0*SIGMA_1CR + 4.0*SIGMA_1FE + 16.0*SIGMA_2CR + 16.0*SIGMA_2FE) + '
               '(SIGMA_0FE*SIGMA_1CR*SIGMA_2CR*SIGMA_2FE*(-70.0*T - 170400.0) + '
               'SIGMA_0FE*SIGMA_1FE*SIGMA_2CR*SIGMA_2FE*(-10.0*T - 330839.0))/(10.0*SIGMA_0CR + '
               '10.0*SIGMA_0FE + 4.0*SIGMA_1CR + 4.0*SIGMA_1FE + 16.0*SIGMA_2CR + 16.0*SIGMA_2FE) + '
               '(SIGMA_0CR*SIGMA_1CR*SIGMA_2CR*(30.0*if(T >= 298.15 & T < 2180.0,139250.0*1/T - '
               '26.908*T*log(T) + 157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,0) + '
               '132000.0) + SIGMA_0CR*SIGMA_1CR*SIGMA_2FE*(-110.0*T + 16.0*if(T >= 298.15 & T < '
               '1811.0,77358.5*1/T - 23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - '
               '5.89269e-8*T^3.0 + 1225.7,0) + 14.0*if(T >= 298.15 & T < 2180.0,139250.0*1/T - '
               '26.908*T*log(T) + 157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,0) + '
               '123500.0) + SIGMA_0CR*SIGMA_1FE*SIGMA_2CR*(4.0*if(T >= 298.15 & T < '
               '1811.0,77358.5*1/T - 23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - '
               '5.89269e-8*T^3.0 + 1225.7,0) + 26.0*if(T >= 298.15 & T < 2180.0,139250.0*1/T - '
               '26.908*T*log(T) + 157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,0) + '
               '140486.0) + SIGMA_0CR*SIGMA_1FE*SIGMA_2FE*(20.0*if(T >= 298.15 & T < '
               '1811.0,77358.5*1/T - 23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - '
               '5.89269e-8*T^3.0 + 1225.7,0) + 10.0*if(T >= 298.15 & T < 2180.0,139250.0*1/T - '
               '26.908*T*log(T) + 157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,0) + '
               '148800.0) + SIGMA_0FE*SIGMA_1CR*SIGMA_2CR*(10.0*if(T >= 298.15 & T < '
               '1811.0,77358.5*1/T - 23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - '
               '5.89269e-8*T^3.0 + 1225.7,0) + 20.0*if(T >= 298.15 & T < 2180.0,139250.0*1/T - '
               '26.908*T*log(T) + 157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,0) + '
               '56200.0) + SIGMA_0FE*SIGMA_1CR*SIGMA_2FE*(26.0*if(T >= 298.15 & T < '
               '1811.0,77358.5*1/T - 23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - '
               '5.89269e-8*T^3.0 + 1225.7,0) + 4.0*if(T >= 298.15 & T < 2180.0,139250.0*1/T - '
               '26.908*T*log(T) + 157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,0) + '
               '152700.0) + SIGMA_0FE*SIGMA_1FE*SIGMA_2CR*(14.0*if(T >= 298.15 & T < '
               '1811.0,77358.5*1/T - 23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - '
               '5.89269e-8*T^3.0 + 1225.7,0) + 16.0*if(T >= 298.15 & T < 2180.0,139250.0*1/T - '
               '26.908*T*log(T) + 157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,0) + '
               '46200.0) + SIGMA_0FE*SIGMA_1FE*SIGMA_2FE*(30.0*if(T >= 298.15 & T < '
               '1811.0,77358.5*1/T - 23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - '
               '5.89269e-8*T^3.0 + 1225.7,0) + 173333.0))/(10.0*SIGMA_0CR + 10.0*SIGMA_0FE + '
               '4.0*SIGMA_1CR + 4.0*SIGMA_1FE + 16.0*SIGMA_2CR + 16.0*SIGMA_2FE)'
    coupled_variables = 'SIGMA_0CR SIGMA_1CR SIGMA_2CR'
    constant_names = 'T'
    constant_expressions = '1000'
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
[]

(modules/phase_field/examples/slkks/CrFe_sigma.i)

#
# SLKKS two phase example for the BCC and SIGMA phases. The sigma phase contains
# multiple sublattices. Free energy from
# Jacob, Aurelie, Erwin Povoden-Karadeniz, and Ernst Kozeschnik. "Revised thermodynamic
# description of the Fe-Cr system based on an improved sublattice model of the sigma phase."
# Calphad 60 (2018): 16-28.
#
# In this simulation we solve only for the sublattice concentrations of the sigma phase
# (and consequently for the free energy of the sigma phase as function of total concentration.)
# The Cr concentration is prescribed as a linear gradient. This permits us to plot
# the free energies of the BCC and sigma phases.
#

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 1000
    ny = 1
    xmin = 0.01
    xmax = 0.99
    ymax = 0.1
  []
[]

[AuxVariables]
  [cCr]
    [InitialCondition]
      type = FunctionIC
      function = x
    []
  []
  [Fb]
    order = FIRST
    family = MONOMIAL
  []
  [Fs]
    order = FIRST
    family = MONOMIAL
  []
  [dFs]
    order = CONSTANT
    family = MONOMIAL
  []
  [dFs0]
    order = CONSTANT
    family = MONOMIAL
  []
  [dFs1]
    order = CONSTANT
    family = MONOMIAL
  []
  [dFs2]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Variables]
  [SIGMA_0CR]
    [InitialCondition]
      type = FunctionIC
      function = x
    []
  []
  [SIGMA_1CR]
    [InitialCondition]
      type = FunctionIC
      function = x
    []
  []
  [SIGMA_2CR]
    [InitialCondition]
      type = FunctionIC
      function = x
    []
  []
[]

[AuxKernels]
  [Fb]
    type = MaterialRealAux
    variable = Fb
    property = F_BCC_A2
  []
  [Fs]
    type = MaterialRealAux
    variable = Fs
    property = F_SIGMA
  []
  [dFs0]
    type = MaterialRealAux
    variable = dFs0
    property = dF_SIGMA/dSIGMA_0CR
  []
  [dFs1]
    type = MaterialRealAux
    variable = dFs1
    property = dF_SIGMA/dSIGMA_1CR
  []
  [dFs2]
    type = MaterialRealAux
    variable = dFs1
    property = dF_SIGMA/dSIGMA_2CR
  []
  [dFs]
    type = VariableGradientComponent
    variable = dFs
    gradient_variable = Fs
    component = x
  []
[]

[Kernels]
  [chempot2a2b]
    # This kernel ties the first two sublattices in the sigma phase together
    type = SLKKSChemicalPotential
    variable = SIGMA_0CR
    a = 10
    cs = SIGMA_1CR
    as = 4
    F = F_SIGMA
  []
  [chempot2b2c]
    # This kernel ties the remaining two sublattices in the sigma phase together
    type = SLKKSChemicalPotential
    variable = SIGMA_1CR
    a = 4
    cs = SIGMA_2CR
    as = 16
    F = F_SIGMA
  []
  [sum]
    type = SLKKSSum
    variable = SIGMA_2CR
    a = 16
    cs = 'SIGMA_0CR SIGMA_1CR'
    as = '10        4'
    sum = cCr
  []
[]

[Materials]
  # CALPHAD free energy of the FeCr sigma phase
  [F_SIGMA]
    type = DerivativeParsedMaterial
    property_name = F_SIGMA
    expression = 'SIGMA_0FE := 1-SIGMA_0CR;
                SIGMA_1FE := 1-SIGMA_1CR;
                '
               'SIGMA_2FE := 1-SIGMA_2CR; 8.3145*T*(10.0*if(SIGMA_0CR > '
               '1.0e-15,SIGMA_0CR*log(SIGMA_0CR),0) + 10.0*if(SIGMA_0FE > '
               '1.0e-15,SIGMA_0FE*log(SIGMA_0FE),0) + 4.0*if(SIGMA_1CR > '
               '1.0e-15,SIGMA_1CR*log(SIGMA_1CR),0) + 4.0*if(SIGMA_1FE > '
               '1.0e-15,SIGMA_1FE*log(SIGMA_1FE),0) + 16.0*if(SIGMA_2CR > '
               '1.0e-15,SIGMA_2CR*log(SIGMA_2CR),0) + 16.0*if(SIGMA_2FE > '
               '1.0e-15,SIGMA_2FE*log(SIGMA_2FE),0))/(10.0*SIGMA_0CR + 10.0*SIGMA_0FE + '
               '4.0*SIGMA_1CR + 4.0*SIGMA_1FE + 16.0*SIGMA_2CR + 16.0*SIGMA_2FE) + '
               '(SIGMA_0FE*SIGMA_1CR*SIGMA_2CR*SIGMA_2FE*(-70.0*T - 170400.0) + '
               'SIGMA_0FE*SIGMA_1FE*SIGMA_2CR*SIGMA_2FE*(-10.0*T - 330839.0))/(10.0*SIGMA_0CR + '
               '10.0*SIGMA_0FE + 4.0*SIGMA_1CR + 4.0*SIGMA_1FE + 16.0*SIGMA_2CR + 16.0*SIGMA_2FE) + '
               '(SIGMA_0CR*SIGMA_1CR*SIGMA_2CR*(30.0*if(T >= 298.15 & T < 2180.0,139250.0*1/T - '
               '26.908*T*log(T) + 157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,if(T >= '
               '2180.0 & T < 6000.0,-2.88526e+32*T^(-9.0) - 50.0*T*log(T) + 344.18*T - 34869.344,0)) '
               '+ 132000.0) + SIGMA_0CR*SIGMA_1CR*SIGMA_2FE*(-110.0*T + 16.0*if(T >= 298.15 & T < '
               '1811.0,77358.5*1/T - 23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - '
               '5.89269e-8*T^3.0 + 1225.7,if(T >= 1811.0 & T < 6000.0,2.2960305e+31*T^(-9.0) - '
               '46.0*T*log(T) + 299.31255*T - 25383.581,0)) + 14.0*if(T >= 298.15 & T < '
               '2180.0,139250.0*1/T - 26.908*T*log(T) + 157.48*T + 0.00189435*T^2.0 - '
               '1.47721e-6*T^3.0 - 8856.94,if(T >= 2180.0 & T < 6000.0,-2.88526e+32*T^(-9.0) - '
               '50.0*T*log(T) + 344.18*T - 34869.344,0)) + 123500.0) + '
               'SIGMA_0CR*SIGMA_1FE*SIGMA_2CR*(4.0*if(T >= 298.15 & T < 1811.0,77358.5*1/T - '
               '23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - 5.89269e-8*T^3.0 + 1225.7,if(T >= '
               '1811.0 & T < 6000.0,2.2960305e+31*T^(-9.0) - 46.0*T*log(T) + 299.31255*T - '
               '25383.581,0)) + 26.0*if(T >= 298.15 & T < 2180.0,139250.0*1/T - 26.908*T*log(T) + '
               '157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,if(T >= 2180.0 & T < '
               '6000.0,-2.88526e+32*T^(-9.0) - 50.0*T*log(T) + 344.18*T - 34869.344,0)) + 140486.0) '
               '+ SIGMA_0CR*SIGMA_1FE*SIGMA_2FE*(20.0*if(T >= 298.15 & T < 1811.0,77358.5*1/T - '
               '23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - 5.89269e-8*T^3.0 + 1225.7,if(T >= '
               '1811.0 & T < 6000.0,2.2960305e+31*T^(-9.0) - 46.0*T*log(T) + 299.31255*T - '
               '25383.581,0)) + 10.0*if(T >= 298.15 & T < 2180.0,139250.0*1/T - 26.908*T*log(T) + '
               '157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,if(T >= 2180.0 & T < '
               '6000.0,-2.88526e+32*T^(-9.0) - 50.0*T*log(T) + 344.18*T - 34869.344,0)) + 148800.0) '
               '+ SIGMA_0FE*SIGMA_1CR*SIGMA_2CR*(10.0*if(T >= 298.15 & T < 1811.0,77358.5*1/T - '
               '23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - 5.89269e-8*T^3.0 + 1225.7,if(T >= '
               '1811.0 & T < 6000.0,2.2960305e+31*T^(-9.0) - 46.0*T*log(T) + 299.31255*T - '
               '25383.581,0)) + 20.0*if(T >= 298.15 & T < 2180.0,139250.0*1/T - 26.908*T*log(T) + '
               '157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,if(T >= 2180.0 & T < '
               '6000.0,-2.88526e+32*T^(-9.0) - 50.0*T*log(T) + 344.18*T - 34869.344,0)) + 56200.0) + '
               'SIGMA_0FE*SIGMA_1CR*SIGMA_2FE*(26.0*if(T >= 298.15 & T < 1811.0,77358.5*1/T - '
               '23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - 5.89269e-8*T^3.0 + 1225.7,if(T >= '
               '1811.0 & T < 6000.0,2.2960305e+31*T^(-9.0) - 46.0*T*log(T) + 299.31255*T - '
               '25383.581,0)) + 4.0*if(T >= 298.15 & T < 2180.0,139250.0*1/T - 26.908*T*log(T) + '
               '157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,if(T >= 2180.0 & T < '
               '6000.0,-2.88526e+32*T^(-9.0) - 50.0*T*log(T) + 344.18*T - 34869.344,0)) + 152700.0) '
               '+ SIGMA_0FE*SIGMA_1FE*SIGMA_2CR*(14.0*if(T >= 298.15 & T < 1811.0,77358.5*1/T - '
               '23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - 5.89269e-8*T^3.0 + 1225.7,if(T >= '
               '1811.0 & T < 6000.0,2.2960305e+31*T^(-9.0) - 46.0*T*log(T) + 299.31255*T - '
               '25383.581,0)) + 16.0*if(T >= 298.15 & T < 2180.0,139250.0*1/T - 26.908*T*log(T) + '
               '157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,if(T >= 2180.0 & T < '
               '6000.0,-2.88526e+32*T^(-9.0) - 50.0*T*log(T) + 344.18*T - 34869.344,0)) + 46200.0) + '
               'SIGMA_0FE*SIGMA_1FE*SIGMA_2FE*(30.0*if(T >= 298.15 & T < 1811.0,77358.5*1/T - '
               '23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - 5.89269e-8*T^3.0 + 1225.7,if(T >= '
               '1811.0 & T < 6000.0,2.2960305e+31*T^(-9.0) - 46.0*T*log(T) + 299.31255*T - '
               '25383.581,0)) + 173333.0))/(10.0*SIGMA_0CR + 10.0*SIGMA_0FE + 4.0*SIGMA_1CR + '
               '4.0*SIGMA_1FE + 16.0*SIGMA_2CR + 16.0*SIGMA_2FE)'
    coupled_variables = 'SIGMA_0CR SIGMA_1CR SIGMA_2CR'
    constant_names = 'T'
    constant_expressions = '1000'
  []

  # single sublattice BCC phase (no sublattice concentration solve necessary)
  [F_BCC_A2]
    type = DerivativeParsedMaterial
    property_name = F_BCC_A2
    expression = 'BCC_CR:=cCr; BCC_FE:=1-BCC_CR; 8.3145*T*(1.0*if(BCC_CR > '
               '1.0e-15,BCC_CR*log(BCC_CR),0) + 1.0*if(BCC_FE > 1.0e-15,BCC_FE*log(BCC_FE),0) + '
               '3.0*if(BCC_VA > 1.0e-15,BCC_VA*log(BCC_VA),0))/(BCC_CR + BCC_FE) + 8.3145*T*if(T < '
               '548.2*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - 932.5*BCC_CR*BCC_FE*BCC_VA + '
               '311.5*BCC_CR*BCC_VA - '
               '1043.0*BCC_FE*BCC_VA,-8.13674105561218e-49*T^15/(0.525599232981783*BCC_CR*BCC_FE*BCC_'
               'VA*(BCC_CR - BCC_FE) - 0.894055608820709*BCC_CR*BCC_FE*BCC_VA + '
               '0.298657718120805*BCC_CR*BCC_VA - BCC_FE*BCC_VA + 9.58772770853308e-13)^15 - '
               '4.65558036243985e-30*T^9/(0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - '
               '0.894055608820709*BCC_CR*BCC_FE*BCC_VA + 0.298657718120805*BCC_CR*BCC_VA - '
               'BCC_FE*BCC_VA + 9.58772770853308e-13)^9 - '
               '1.3485349181899e-10*T^3/(0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - '
               '0.894055608820709*BCC_CR*BCC_FE*BCC_VA + 0.298657718120805*BCC_CR*BCC_VA - '
               'BCC_FE*BCC_VA + 9.58772770853308e-13)^3 + 1 - '
               '0.905299382744392*(548.2*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - '
               '932.5*BCC_CR*BCC_FE*BCC_VA + 311.5*BCC_CR*BCC_VA - 1043.0*BCC_FE*BCC_VA + '
               '1.0e-9)/T,if(T < -548.2*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) + '
               '932.5*BCC_CR*BCC_FE*BCC_VA - 311.5*BCC_CR*BCC_VA + '
               '1043.0*BCC_FE*BCC_VA,-8.13674105561218e-49*T^15/(-0.525599232981783*BCC_CR*BCC_FE*BCC'
               '_VA*(BCC_CR - BCC_FE) + 0.894055608820709*BCC_CR*BCC_FE*BCC_VA - '
               '0.298657718120805*BCC_CR*BCC_VA + BCC_FE*BCC_VA + 9.58772770853308e-13)^15 - '
               '4.65558036243985e-30*T^9/(-0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) '
               '+ 0.894055608820709*BCC_CR*BCC_FE*BCC_VA - 0.298657718120805*BCC_CR*BCC_VA + '
               'BCC_FE*BCC_VA + 9.58772770853308e-13)^9 - '
               '1.3485349181899e-10*T^3/(-0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) + '
               '0.894055608820709*BCC_CR*BCC_FE*BCC_VA - 0.298657718120805*BCC_CR*BCC_VA + '
               'BCC_FE*BCC_VA + 9.58772770853308e-13)^3 + 1 - '
               '0.905299382744392*(-548.2*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) + '
               '932.5*BCC_CR*BCC_FE*BCC_VA - 311.5*BCC_CR*BCC_VA + 1043.0*BCC_FE*BCC_VA + '
               '1.0e-9)/T,if(T > -548.2*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) + '
               '932.5*BCC_CR*BCC_FE*BCC_VA - 311.5*BCC_CR*BCC_VA + 1043.0*BCC_FE*BCC_VA & '
               '548.2*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - 932.5*BCC_CR*BCC_FE*BCC_VA + '
               '311.5*BCC_CR*BCC_VA - 1043.0*BCC_FE*BCC_VA < '
               '0,-79209031311018.7*(-0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) + '
               '0.894055608820709*BCC_CR*BCC_FE*BCC_VA - 0.298657718120805*BCC_CR*BCC_VA + '
               'BCC_FE*BCC_VA + 9.58772770853308e-13)^5/T^5 - '
               '3.83095660520737e+42*(-0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) + '
               '0.894055608820709*BCC_CR*BCC_FE*BCC_VA - 0.298657718120805*BCC_CR*BCC_VA + '
               'BCC_FE*BCC_VA + 9.58772770853308e-13)^15/T^15 - '
               '1.22565886734485e+72*(-0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) + '
               '0.894055608820709*BCC_CR*BCC_FE*BCC_VA - 0.298657718120805*BCC_CR*BCC_VA + '
               'BCC_FE*BCC_VA + 9.58772770853308e-13)^25/T^25,if(T > '
               '548.2*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - 932.5*BCC_CR*BCC_FE*BCC_VA + '
               '311.5*BCC_CR*BCC_VA - 1043.0*BCC_FE*BCC_VA & 548.2*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - '
               'BCC_FE) - 932.5*BCC_CR*BCC_FE*BCC_VA + 311.5*BCC_CR*BCC_VA - 1043.0*BCC_FE*BCC_VA > '
               '0,-79209031311018.7*(0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - '
               '0.894055608820709*BCC_CR*BCC_FE*BCC_VA + 0.298657718120805*BCC_CR*BCC_VA - '
               'BCC_FE*BCC_VA + 9.58772770853308e-13)^5/T^5 - '
               '3.83095660520737e+42*(0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - '
               '0.894055608820709*BCC_CR*BCC_FE*BCC_VA + 0.298657718120805*BCC_CR*BCC_VA - '
               'BCC_FE*BCC_VA + 9.58772770853308e-13)^15/T^15 - '
               '1.22565886734485e+72*(0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - '
               '0.894055608820709*BCC_CR*BCC_FE*BCC_VA + 0.298657718120805*BCC_CR*BCC_VA - '
               'BCC_FE*BCC_VA + 9.58772770853308e-13)^25/T^25,0))))*log((2.15*BCC_CR*BCC_FE*BCC_VA - '
               '0.008*BCC_CR*BCC_VA + 2.22*BCC_FE*BCC_VA)*if(2.15*BCC_CR*BCC_FE*BCC_VA - '
               '0.008*BCC_CR*BCC_VA + 2.22*BCC_FE*BCC_VA <= 0,-1.0,1.0) + 1)/(BCC_CR + BCC_FE) + '
               '1.0*(BCC_CR*BCC_VA*if(T >= 298.15 & T < 2180.0,139250.0*1/T - 26.908*T*log(T) + '
               '157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,if(T >= 2180.0 & T < '
               '6000.0,-2.88526e+32*T^(-9.0) - 50.0*T*log(T) + 344.18*T - 34869.344,0)) + '
               'BCC_FE*BCC_VA*if(T >= 298.15 & T < 1811.0,77358.5*1/T - 23.5143*T*log(T) + 124.134*T '
               '- 0.00439752*T^2.0 - 5.89269e-8*T^3.0 + 1225.7,if(T >= 1811.0 & T < '
               '6000.0,2.2960305e+31*T^(-9.0) - 46.0*T*log(T) + 299.31255*T - 25383.581,0)))/(BCC_CR '
               '+ BCC_FE) + 1.0*(BCC_CR*BCC_FE*BCC_VA*(500.0 - 1.5*T)*(BCC_CR - BCC_FE) + '
               'BCC_CR*BCC_FE*BCC_VA*(24600.0 - 14.98*T) + BCC_CR*BCC_FE*BCC_VA*(9.15*T - '
               '14000.0)*(BCC_CR - BCC_FE)^2)/(BCC_CR + BCC_FE)'

    coupled_variables = 'cCr'
    constant_names = 'BCC_VA T'
    constant_expressions = '1 1000'
  []
[]

[VectorPostprocessors]
  [var]
    type = LineValueSampler
    variable = 'SIGMA_0CR SIGMA_1CR SIGMA_2CR cCr Fb Fs dFs dFs0 dFs1 dFs2'
    start_point = '0.01 0 0'
    end_point = '0.99 0 0'
    sort_by = x
    num_points = 1000
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Steady
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
  csv = true
[]

Overview
Example Input File Syntax
Input Parameters
Input Files