- FBase name of the free energy function
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Base name of the free energy function
- asublattice site fraction for the kernel variable
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:sublattice site fraction for the kernel variable
- asother sublattice site fraction in the same phase
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:other sublattice site fraction in the same phase
- csother sublattice concentration in the same phase
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:other sublattice concentration in the same phase
- variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable that this residual object operates on
SLKKSChemicalPotential
SLKKS model kernel to enforce the pointwise equality of sublattice chemical potentials in the same phase.
Implements
where and are two sublattice concentrations (for sublattices and ) in the same phase , for component .
Input 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
- coupled_variablesVector of variable arguments to the free energy function
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Vector of variable arguments to the free energy function
- displacementsThe displacements
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The displacements
- matrix_onlyFalseWhether this object is only doing assembly to matrices (no vectors)
Default:False
C++ Type:bool
Controllable:No
Description:Whether this object is only doing assembly to matrices (no vectors)
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
Contribution To Tagged Field Data 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>
Unit:(no unit assumed)
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>
Unit:(no unit assumed)
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.)
- search_methodnearest_node_connected_sidesChoice of search algorithm. All options begin by finding the nearest node in the primary boundary to a query point in the secondary boundary. In the default nearest_node_connected_sides algorithm, primary boundary elements are searched iff that nearest node is one of their nodes. This is fast to determine via a pregenerated node-to-elem map and is robust on conforming meshes. In the optional all_proximate_sides algorithm, primary boundary elements are searched iff they touch that nearest node, even if they are not topologically connected to it. This is more CPU-intensive but is necessary for robustness on any boundary surfaces which has disconnections (such as Flex IGA meshes) or non-conformity (such as hanging nodes in adaptively h-refined meshes).
Default:nearest_node_connected_sides
C++ Type:MooseEnum
Options:nearest_node_connected_sides, all_proximate_sides
Controllable:No
Description:Choice of search algorithm. All options begin by finding the nearest node in the primary boundary to a query point in the secondary boundary. In the default nearest_node_connected_sides algorithm, primary boundary elements are searched iff that nearest node is one of their nodes. This is fast to determine via a pregenerated node-to-elem map and is robust on conforming meshes. In the optional all_proximate_sides algorithm, primary boundary elements are searched iff they touch that nearest node, even if they are not topologically connected to it. This is more CPU-intensive but is necessary for robustness on any boundary surfaces which has disconnections (such as Flex IGA meshes) or non-conformity (such as hanging nodes in adaptively h-refined meshes).
- 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
- 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
Unit:(no unit assumed)
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.
Material Property Retrieval Parameters
Input Files
(modules/phase_field/examples/slkks/CrFe.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 consider diffusion (Cahn-Hilliard) and phase transformation.
#
# This example requires CrFe_sigma_out_var_0001.csv file, which generated by first
# running the CrFe_sigma.i input file.
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 2
nx = 160
ny = 1
nz = 0
xmin = -25
xmax = 25
ymin = -2.5
ymax = 2.5
elem_type = QUAD4
[]
[]
[AuxVariables]
[Fglobal]
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[sigma_cr0]
type = PiecewiseLinear
data_file = CrFe_sigma_out_var_0001.csv
format = columns
x_index_in_file = 5
y_index_in_file = 2
xy_in_file_only = false
[]
[sigma_cr1]
type = PiecewiseLinear
data_file = CrFe_sigma_out_var_0001.csv
format = columns
x_index_in_file = 5
y_index_in_file = 3
xy_in_file_only = false
[]
[sigma_cr2]
type = PiecewiseLinear
data_file = CrFe_sigma_out_var_0001.csv
format = columns
x_index_in_file = 5
y_index_in_file = 4
xy_in_file_only = false
[]
[]
[Variables]
# order parameters
[eta1]
order = FIRST
family = LAGRANGE
initial_condition = 0.5
[]
[eta2]
order = FIRST
family = LAGRANGE
initial_condition = 0.5
[]
# solute concentration
[cCr]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = FunctionIC
function = '(x+25)/50*0.5+0.1'
[]
[]
# sublattice concentrations
[BCC_CR]
initial_condition = 0.45
[]
[SIGMA_0CR]
[InitialCondition]
type = CoupledValueFunctionIC
function = sigma_cr0
v = cCr
variable = SIGMA_0CR
[]
[]
[SIGMA_1CR]
[InitialCondition]
type = CoupledValueFunctionIC
function = sigma_cr1
v = cCr
variable = SIGMA_1CR
[]
[]
[SIGMA_2CR]
[InitialCondition]
type = CoupledValueFunctionIC
function = sigma_cr2
v = cCr
variable = SIGMA_2CR
[]
[]
# Lagrange multiplier
[lambda]
[]
[]
[Materials]
# CALPHAD free energies
[F_BCC_A2]
type = DerivativeParsedMaterial
property_name = F_BCC_A2
outputs = exodus
output_properties = F_BCC_A2
expression = 'BCC_FE:=1-BCC_CR; G := 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*plog(BCC_FE,eps),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); G/100000'
coupled_variables = 'BCC_CR'
constant_names = 'BCC_VA T eps'
constant_expressions = '1 1000 0.01'
[]
[F_SIGMA]
type = DerivativeParsedMaterial
property_name = F_SIGMA
outputs = exodus
output_properties = F_SIGMA
expression = 'SIGMA_0FE := 1-SIGMA_0CR; SIGMA_1FE := 1-SIGMA_1CR; SIGMA_2FE := 1-SIGMA_2CR; G := '
'8.3145*T*(10.0*if(SIGMA_0CR > 1.0e-15,SIGMA_0CR*plog(SIGMA_0CR,eps),0) + '
'10.0*if(SIGMA_0FE > 1.0e-15,SIGMA_0FE*plog(SIGMA_0FE,eps),0) + 4.0*if(SIGMA_1CR > '
'1.0e-15,SIGMA_1CR*plog(SIGMA_1CR,eps),0) + 4.0*if(SIGMA_1FE > '
'1.0e-15,SIGMA_1FE*plog(SIGMA_1FE,eps),0) + 16.0*if(SIGMA_2CR > '
'1.0e-15,SIGMA_2CR*plog(SIGMA_2CR,eps),0) + 16.0*if(SIGMA_2FE > '
'1.0e-15,SIGMA_2FE*plog(SIGMA_2FE,eps),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); G/100000'
coupled_variables = 'SIGMA_0CR SIGMA_1CR SIGMA_2CR'
constant_names = 'T eps'
constant_expressions = '1000 0.01'
[]
# h(eta)
[h1]
type = SwitchingFunctionMaterial
function_name = h1
h_order = HIGH
eta = eta1
[]
[h2]
type = SwitchingFunctionMaterial
function_name = h2
h_order = HIGH
eta = eta2
[]
# g(eta)
[g1]
type = BarrierFunctionMaterial
function_name = g1
g_order = SIMPLE
eta = eta1
[]
[g2]
type = BarrierFunctionMaterial
function_name = g2
g_order = SIMPLE
eta = eta2
[]
# constant properties
[constants]
type = GenericConstantMaterial
prop_names = 'D L kappa'
prop_values = '10 1 0.1 '
[]
# Coefficients for diffusion equation
[Dh1]
type = DerivativeParsedMaterial
material_property_names = 'D h1(eta1)'
expression = D*h1
property_name = Dh1
coupled_variables = eta1
derivative_order = 1
[]
[Dh2a]
type = DerivativeParsedMaterial
material_property_names = 'D h2(eta2)'
expression = D*h2*10/30
property_name = Dh2a
coupled_variables = eta2
derivative_order = 1
[]
[Dh2b]
type = DerivativeParsedMaterial
material_property_names = 'D h2(eta2)'
expression = D*h2*4/30
property_name = Dh2b
coupled_variables = eta2
derivative_order = 1
[]
[Dh2c]
type = DerivativeParsedMaterial
material_property_names = 'D h2(eta2)'
expression = D*h2*16/30
property_name = Dh2c
coupled_variables = eta2
derivative_order = 1
[]
[]
[Kernels]
#Kernels for diffusion equation
[diff_time]
type = TimeDerivative
variable = cCr
[]
[diff_c1]
type = MatDiffusion
variable = cCr
diffusivity = Dh1
v = BCC_CR
args = eta1
[]
[diff_c2a]
type = MatDiffusion
variable = cCr
diffusivity = Dh2a
v = SIGMA_0CR
args = eta2
[]
[diff_c2b]
type = MatDiffusion
variable = cCr
diffusivity = Dh2b
v = SIGMA_1CR
args = eta2
[]
[diff_c2c]
type = MatDiffusion
variable = cCr
diffusivity = Dh2c
v = SIGMA_2CR
args = eta2
[]
# enforce pointwise equality of chemical potentials
[chempot1a2a]
# The BCC phase has only one sublattice
# we tie it to the first sublattice with site fraction 10/(10+4+16) in the sigma phase
type = KKSPhaseChemicalPotential
variable = BCC_CR
cb = SIGMA_0CR
kb = '${fparse 10/30}'
fa_name = F_BCC_A2
fb_name = F_SIGMA
args_b = 'SIGMA_1CR SIGMA_2CR'
[]
[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'
[]
[phaseconcentration]
# This kernel ties the sum of the sublattice concentrations to the global concentration cCr
type = SLKKSMultiPhaseConcentration
variable = SIGMA_2CR
c = cCr
ns = '1 3'
as = '1 10 4 16'
cs = 'BCC_CR SIGMA_0CR SIGMA_1CR SIGMA_2CR'
h_names = 'h1 h2'
eta = 'eta1 eta2'
[]
# Kernels for Allen-Cahn equation for eta1
[deta1dt]
type = TimeDerivative
variable = eta1
[]
[ACBulkF1]
type = KKSMultiACBulkF
variable = eta1
Fj_names = 'F_BCC_A2 F_SIGMA'
hj_names = 'h1 h2'
gi_name = g1
eta_i = eta1
wi = 0.1
coupled_variables = 'BCC_CR SIGMA_0CR SIGMA_1CR SIGMA_2CR eta2'
[]
[ACBulkC1]
type = SLKKSMultiACBulkC
variable = eta1
F = F_BCC_A2
c = BCC_CR
ns = '1 3'
as = '1 10 4 16'
cs = 'BCC_CR SIGMA_0CR SIGMA_1CR SIGMA_2CR'
h_names = 'h1 h2'
eta = 'eta1 eta2'
[]
[ACInterface1]
type = ACInterface
variable = eta1
kappa_name = kappa
[]
[lagrange1]
type = SwitchingFunctionConstraintEta
variable = eta1
h_name = h1
lambda = lambda
coupled_variables = 'eta2'
[]
# Kernels for Allen-Cahn equation for eta1
[deta2dt]
type = TimeDerivative
variable = eta2
[]
[ACBulkF2]
type = KKSMultiACBulkF
variable = eta2
Fj_names = 'F_BCC_A2 F_SIGMA'
hj_names = 'h1 h2'
gi_name = g2
eta_i = eta2
wi = 0.1
coupled_variables = 'BCC_CR SIGMA_0CR SIGMA_1CR SIGMA_2CR eta1'
[]
[ACBulkC2]
type = SLKKSMultiACBulkC
variable = eta2
F = F_BCC_A2
c = BCC_CR
ns = '1 3'
as = '1 10 4 16'
cs = 'BCC_CR SIGMA_0CR SIGMA_1CR SIGMA_2CR'
h_names = 'h1 h2'
eta = 'eta1 eta2'
[]
[ACInterface2]
type = ACInterface
variable = eta2
kappa_name = kappa
[]
[lagrange2]
type = SwitchingFunctionConstraintEta
variable = eta2
h_name = h2
lambda = lambda
coupled_variables = 'eta1'
[]
# Lagrange-multiplier constraint kernel for lambda
[lagrange]
type = SwitchingFunctionConstraintLagrange
variable = lambda
h_names = 'h1 h2'
etas = 'eta1 eta2'
epsilon = 1e-6
[]
[]
[AuxKernels]
[GlobalFreeEnergy]
type = KKSMultiFreeEnergy
variable = Fglobal
Fj_names = 'F_BCC_A2 F_SIGMA'
hj_names = 'h1 h2'
gj_names = 'g1 g2'
interfacial_vars = 'eta1 eta2'
kappa_names = 'kappa kappa'
w = 0.1
[]
[]
[Executioner]
type = Transient
solve_type = 'NEWTON'
line_search = none
petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -ksp_gmres_restart'
petsc_options_value = 'asm lu nonzero 30'
l_max_its = 100
nl_max_its = 20
nl_abs_tol = 1e-10
end_time = 10000
[TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 12
iteration_window = 2
growth_factor = 1.5
cutback_factor = 0.7
dt = 0.1
[]
[]
[VectorPostprocessors]
[var]
type = LineValueSampler
start_point = '-25 0 0'
end_point = '25 0 0'
variable = 'cCr eta1 eta2 SIGMA_0CR SIGMA_1CR SIGMA_2CR'
num_points = 151
sort_by = id
execute_on = 'initial timestep_end'
[]
[mat]
type = LineMaterialRealSampler
start = '-25 0 0'
end = '25 0 0'
property = 'F_BCC_A2 F_SIGMA'
sort_by = id
execute_on = 'initial timestep_end'
[]
[]
[Postprocessors]
[F]
type = ElementIntegralVariablePostprocessor
variable = Fglobal
execute_on = 'initial timestep_end'
[]
[cmin]
type = NodalExtremeValue
value_type = min
variable = cCr
execute_on = 'initial timestep_end'
[]
[cmax]
type = NodalExtremeValue
value_type = max
variable = cCr
execute_on = 'initial timestep_end'
[]
[ctotal]
type = ElementIntegralVariablePostprocessor
variable = cCr
execute_on = 'initial timestep_end'
[]
[]
[Outputs]
exodus = true
print_linear_residuals = false
csv = true
perf_graph = true
[]
(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
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
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
[]
(modules/phase_field/test/tests/slkks/full_solve.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 consider diffusion (Cahn-Hilliard) and phase transformation.
#
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 1
nx = 30
ny = 1
xmin = -25
xmax = 25
[]
[]
[AuxVariables]
[Fglobal]
order = CONSTANT
family = MONOMIAL
[]
[]
[Variables]
# order parameters
[eta1]
initial_condition = 0.5
[]
[eta2]
initial_condition = 0.5
[]
# solute concentration
[cCr]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = FunctionIC
function = '(x+25)/50*0.5+0.1'
[]
[]
# sublattice concentrations (good guesses are needed here! - they can be obtained
# form a static solve like in sublattice_concentrations.i)
[BCC_CR]
[InitialCondition]
type = FunctionIC
function = '(x+25)/50*0.5+0.1'
[]
[]
[SIGMA_0CR]
[InitialCondition]
type = FunctionIC
function = '(x+25)/50*0.17+0.01'
[]
[]
[SIGMA_1CR]
[InitialCondition]
type = FunctionIC
function = '(x+25)/50*0.36+0.02'
[]
[]
[SIGMA_2CR]
[InitialCondition]
type = FunctionIC
function = '(x+25)/50*0.33+0.20'
[]
[]
# Lagrange multiplier
[lambda]
[]
[]
[Materials]
# CALPHAD free energies
[F_BCC_A2]
type = DerivativeParsedMaterial
property_name = F_BCC_A2
outputs = exodus
output_properties = F_BCC_A2
expression = 'BCC_FE:=1-BCC_CR; G := 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*plog(BCC_FE,eps),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); G/100000'
coupled_variables = 'BCC_CR'
constant_names = 'BCC_VA T eps'
constant_expressions = '1 1000 0.01'
[]
[F_SIGMA]
type = DerivativeParsedMaterial
property_name = F_SIGMA
outputs = exodus
output_properties = F_SIGMA
expression = 'SIGMA_0FE := 1-SIGMA_0CR; SIGMA_1FE := 1-SIGMA_1CR; SIGMA_2FE := 1-SIGMA_2CR; G := '
'8.3145*T*(10.0*if(SIGMA_0CR > 1.0e-15,SIGMA_0CR*plog(SIGMA_0CR,eps),0) + '
'10.0*if(SIGMA_0FE > 1.0e-15,SIGMA_0FE*plog(SIGMA_0FE,eps),0) + 4.0*if(SIGMA_1CR > '
'1.0e-15,SIGMA_1CR*plog(SIGMA_1CR,eps),0) + 4.0*if(SIGMA_1FE > '
'1.0e-15,SIGMA_1FE*plog(SIGMA_1FE,eps),0) + 16.0*if(SIGMA_2CR > '
'1.0e-15,SIGMA_2CR*plog(SIGMA_2CR,eps),0) + 16.0*if(SIGMA_2FE > '
'1.0e-15,SIGMA_2FE*plog(SIGMA_2FE,eps),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); G/100000'
coupled_variables = 'SIGMA_0CR SIGMA_1CR SIGMA_2CR'
constant_names = 'T eps'
constant_expressions = '1000 0.01'
[]
# h(eta)
[h1]
type = SwitchingFunctionMaterial
function_name = h1
h_order = HIGH
eta = eta1
[]
[h2]
type = SwitchingFunctionMaterial
function_name = h2
h_order = HIGH
eta = eta2
[]
# g(eta)
[g1]
type = BarrierFunctionMaterial
function_name = g1
g_order = SIMPLE
eta = eta1
[]
[g2]
type = BarrierFunctionMaterial
function_name = g2
g_order = SIMPLE
eta = eta2
[]
# constant properties
[constants]
type = GenericConstantMaterial
prop_names = 'D L kappa'
prop_values = '10 1 0.1 '
[]
# Coefficients for diffusion equation
[Dh1]
type = DerivativeParsedMaterial
material_property_names = 'D h1(eta1)'
expression = D*h1
property_name = Dh1
coupled_variables = eta1
derivative_order = 1
[]
[Dh2a]
type = DerivativeParsedMaterial
material_property_names = 'D h2(eta2)'
expression = D*h2*10/30
property_name = Dh2a
coupled_variables = eta2
derivative_order = 1
[]
[Dh2b]
type = DerivativeParsedMaterial
material_property_names = 'D h2(eta2)'
expression = D*h2*4/30
property_name = Dh2b
coupled_variables = eta2
derivative_order = 1
[]
[Dh2c]
type = DerivativeParsedMaterial
material_property_names = 'D h2(eta2)'
expression = D*h2*16/30
property_name = Dh2c
coupled_variables = eta2
derivative_order = 1
[]
[]
[Kernels]
#Kernels for diffusion equation
[diff_time]
type = TimeDerivative
variable = cCr
[]
[diff_c1]
type = MatDiffusion
variable = cCr
diffusivity = Dh1
v = BCC_CR
args = eta1
[]
[diff_c2a]
type = MatDiffusion
variable = cCr
diffusivity = Dh2a
v = SIGMA_0CR
args = eta2
[]
[diff_c2b]
type = MatDiffusion
variable = cCr
diffusivity = Dh2b
v = SIGMA_1CR
args = eta2
[]
[diff_c2c]
type = MatDiffusion
variable = cCr
diffusivity = Dh2c
v = SIGMA_2CR
args = eta2
[]
# enforce pointwise equality of chemical potentials
[chempot1a2a]
# The BCC phase has only one sublattice
# we tie it to the first sublattice with site fraction 10/(10+4+16) in the sigma phase
type = KKSPhaseChemicalPotential
variable = BCC_CR
cb = SIGMA_0CR
kb = '${fparse 10/30}'
fa_name = F_BCC_A2
fb_name = F_SIGMA
args_b = 'SIGMA_1CR SIGMA_2CR'
[]
[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'
[]
[phaseconcentration]
# This kernel ties the sum of the sublattice concentrations to the global concentration cCr
type = SLKKSMultiPhaseConcentration
variable = SIGMA_2CR
c = cCr
ns = '1 3'
as = '1 10 4 16'
cs = 'BCC_CR SIGMA_0CR SIGMA_1CR SIGMA_2CR'
h_names = 'h1 h2'
eta = 'eta1 eta2'
[]
# Kernels for Allen-Cahn equation for eta1
[deta1dt]
type = TimeDerivative
variable = eta1
[]
[ACBulkF1]
type = KKSMultiACBulkF
variable = eta1
Fj_names = 'F_BCC_A2 F_SIGMA'
hj_names = 'h1 h2'
gi_name = g1
eta_i = eta1
wi = 0.1
coupled_variables = 'BCC_CR SIGMA_0CR SIGMA_1CR SIGMA_2CR eta2'
[]
[ACBulkC1]
type = SLKKSMultiACBulkC
variable = eta1
F = F_BCC_A2
c = BCC_CR
ns = '1 3'
as = '1 10 4 16'
cs = 'BCC_CR SIGMA_0CR SIGMA_1CR SIGMA_2CR'
h_names = 'h1 h2'
eta = 'eta1 eta2'
[]
[ACInterface1]
type = ACInterface
variable = eta1
kappa_name = kappa
[]
[lagrange1]
type = SwitchingFunctionConstraintEta
variable = eta1
h_name = h1
lambda = lambda
coupled_variables = 'eta2'
[]
# Kernels for Allen-Cahn equation for eta1
[deta2dt]
type = TimeDerivative
variable = eta2
[]
[ACBulkF2]
type = KKSMultiACBulkF
variable = eta2
Fj_names = 'F_BCC_A2 F_SIGMA'
hj_names = 'h1 h2'
gi_name = g2
eta_i = eta2
wi = 0.1
coupled_variables = 'BCC_CR SIGMA_0CR SIGMA_1CR SIGMA_2CR eta1'
[]
[ACBulkC2]
type = SLKKSMultiACBulkC
variable = eta2
F = F_BCC_A2
c = BCC_CR
ns = '1 3'
as = '1 10 4 16'
cs = 'BCC_CR SIGMA_0CR SIGMA_1CR SIGMA_2CR'
h_names = 'h1 h2'
eta = 'eta1 eta2'
[]
[ACInterface2]
type = ACInterface
variable = eta2
kappa_name = kappa
[]
[lagrange2]
type = SwitchingFunctionConstraintEta
variable = eta2
h_name = h2
lambda = lambda
coupled_variables = 'eta1'
[]
# Lagrange-multiplier constraint kernel for lambda
[lagrange]
type = SwitchingFunctionConstraintLagrange
variable = lambda
h_names = 'h1 h2'
etas = 'eta1 eta2'
epsilon = 1e-6
[]
[]
[AuxKernels]
[GlobalFreeEnergy]
type = KKSMultiFreeEnergy
variable = Fglobal
Fj_names = 'F_BCC_A2 F_SIGMA'
hj_names = 'h1 h2'
gj_names = 'g1 g2'
interfacial_vars = 'eta1 eta2'
kappa_names = 'kappa kappa'
w = 0.1
[]
[]
[Executioner]
type = Transient
solve_type = 'NEWTON'
line_search = none
petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -ksp_gmres_restart'
petsc_options_value = 'asm lu nonzero 30'
l_max_its = 100
nl_max_its = 20
nl_abs_tol = 1e-10
end_time = 1000
[TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 12
iteration_window = 2
growth_factor = 2
cutback_factor = 0.5
dt = 0.1
[]
[]
[Postprocessors]
[F]
type = ElementIntegralVariablePostprocessor
variable = Fglobal
[]
[cmin]
type = NodalExtremeValue
value_type = min
variable = cCr
[]
[cmax]
type = NodalExtremeValue
value_type = max
variable = cCr
[]
[]
[Outputs]
exodus = true
print_linear_residuals = false
# exclude lagrange multiplier from output, it can diff more easily
hide = lambda
[]