ADUPuZrMobility

Returns the chemical and thermal mobilities of U-Pu-Zr using equilibrium values from ADUPuZrPhaseLookup.

Description

ADUPuZrMobility is part of a system used to model constituent redistribution in U-Zr and U-Pu-Zr metallic nuclear fuels. Exactly five phases are considered in the model: $var element = document.getElementById("moose-equation-6d5a6fda-0938-4fbb-bcfb-c5eca795a581");katex.render("\\alpha", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-4b739b21-8fd6-4771-8e8f-98435a73725b");katex.render("\\beta", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-40556df9-0a9e-48f0-b28c-6d164b4601e4");katex.render("\\gamma", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-5ab5dc9c-1d6b-45af-99f3-b26ece6432a3");katex.render("\\delta", element, {displayMode:false,throwOnError:false});$ , and $var element = document.getElementById("moose-equation-c824fde6-3fd1-46ad-8065-3b7b2577ddfa");katex.render("\\zeta", element, {displayMode:false,throwOnError:false});$ . ADUPuZrMobility calculates the chemical ( $var element = document.getElementById("moose-equation-94e5723d-848c-4ed5-b728-7563f2256277");katex.render("M_c", element, {displayMode:false,throwOnError:false});$ ) and thermal ( $var element = document.getElementById("moose-equation-e3b75b07-6bd8-4bc3-be67-2f5d7ecc36a0");katex.render("M_T", element, {displayMode:false,throwOnError:false});$ ) mobilities of zirconium ( $var element = document.getElementById("moose-equation-5366f8b4-529c-4f58-a2bd-23eb6d849f9a");katex.render("X_{Zr}", element, {displayMode:false,throwOnError:false});$ ) in these phases, allowing for predictions of constituent redistribution using the following relationship: $var element = document.getElementById("moose-equation-024e4047-de9a-4ad6-be88-bdb07ac1c705");katex.render(" \\frac{\\partial X_{Zr}}{\\partial t} = \\nabla \\cdot \\left[M_c \\nabla \\left(\\mu - \\nabla \\cdot \\left[\\kappa \\nabla X_{Zr}\\right]\\right) - M_T \\frac{\\nabla T}{T}\\right],", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-59c17bd7-2ac8-4026-8f89-5817175ee2aa");katex.render("t", element, {displayMode:false,throwOnError:false});$ is the time, $var element = document.getElementById("moose-equation-e7b8378b-3c73-47f2-ab85-4c33d7904d60");katex.render("\\mu", element, {displayMode:false,throwOnError:false});$ is the chemical potential of zirconium, and $var element = document.getElementById("moose-equation-af497158-440c-488e-ae01-ac6056cd40e4");katex.render("T", element, {displayMode:false,throwOnError:false});$ is the temperature. Here also, $var element = document.getElementById("moose-equation-32af68ce-65e5-4891-83c8-638aa16cdaf0");katex.render("\\kappa", element, {displayMode:false,throwOnError:false});$ is a constant parameter used to maintain smoothness in $var element = document.getElementById("moose-equation-94c94fa6-9af9-44a5-97e2-f97038929f1c");katex.render("X_{Zr}", element, {displayMode:false,throwOnError:false});$ by applying a penalty to gradients in $var element = document.getElementById("moose-equation-71eba6bc-808d-4e4c-a537-70d400f507b9");katex.render("X_{Zr}", element, {displayMode:false,throwOnError:false});$ . Two combinations of kernels can be used to apply the above physics, as shown in Table 1.

Table 1: Kernel combinations that can be used to implement the constituent redistribution physics.

Forward Split	Reverse Split
ADTimeDerivative	ADCoupledTimeDerivative
ADCHSplitConcentration	ADSplitCHWRes
ADCHSplitChemicalPotential	ADSplitCHParsed
ADCHSoretMobility	ADCHSoretMobility

The chemical potential and the composition dependencies of $var element = document.getElementById("moose-equation-ebfa4547-6f2e-46ec-ae79-206a99d1ac97");katex.render("M_c", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-7ede9192-92b8-481b-bd58-286e402a5f56");katex.render("M_T", element, {displayMode:false,throwOnError:false});$ are accounted for using information from ADUPuZrPhaseLookup. The kinetic properties of the $var element = document.getElementById("moose-equation-8f530314-9493-44f9-b4e4-bbb8c8254c87");katex.render("\\alpha", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-771788ad-dd27-40dc-b5dd-b32b92502cdd");katex.render("\\beta", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-b5dcff7b-9ac0-43c6-a56e-6dd79b34b018");katex.render("\\delta", element, {displayMode:false,throwOnError:false});$ , and $var element = document.getElementById("moose-equation-db982a0d-800e-42c3-885b-9c0dd0e7b769");katex.render("\\zeta", element, {displayMode:false,throwOnError:false});$ phases are based on published interdiffusion coefficients, activation energies, and heats of transport from Hofman et al. (1996) and Kim et al. (2006). Due to a lack of experimental data, the kinetic parameters of the $var element = document.getElementById("moose-equation-00997148-7bf7-4bd1-857f-f49e7f04bf4d");katex.render("\\alpha", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-48e92e67-4b86-48b1-92c3-f36344911f40");katex.render("\\beta", element, {displayMode:false,throwOnError:false});$ phases are used to model transport in the $var element = document.getElementById("moose-equation-89bba86d-c9c3-46af-b655-6b5fd97e338a");katex.render("\\delta", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-fdbc7940-2358-4941-9706-e6ba5ce7fd72");katex.render("\\zeta", element, {displayMode:false,throwOnError:false});$ phases, respectively. The kinetic properties of the $var element = document.getElementById("moose-equation-69793707-f679-41fe-9b19-6819cff8c63f");katex.render("\\gamma", element, {displayMode:false,throwOnError:false});$ phase are based on published atomic mobilities from Li et al. (2010).

Scalar multipliers are applied to these parameters to account for uncertainties and/or irradiation effects. A default set of scalar multipliers were obtained by calibrating the model to Electron Probe Micro Analysis (EPMA) scans of U-Zr Fuel Elements DP-81 and DP-11, which were irradiated in Experimental Breeder Reactor II. These default values can be overridden by specifying different scalar multipliers in the input file. A detailed description of the model on which ADUPuZrMobility is based is available in Hirschhorn et al. (2021).

Two examples are provided in examples/constituent_redistribution. The first example, provided in 1d_thermo_composition.i, simulates tightly coupled thermo-chemical evolution of a U-Zr fuel in one dimension using empirical correlations to account for the effects of irradiation on the fuel's thermal conductivity. The second example, provided in 2d_thermo.i and 2d_composition.i, uses the MultiApps system to simulate loosely coupled thermo-chemical evolution of a U-Zr fuel clad in HT9 in two dimensions using BISON models to account for the effects of irradiation on the fuel's thermal conductivity.

Example Input Syntax

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [mobilities]
    type = ADUPuZrMobility<<<{"description": "Returns the chemical and thermal mobilities of U-Pu-Zr using equilibrium values from ADUPuZrPhaseLookup.", "href": "ADUPuZrMobility.html"}>>>
    temperature<<<{"description": "The temperature variable"}>>> = T
  []
[]

Input Parameters

temperatureThe temperature variable
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The temperature variable

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
boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
Default:True
C++ Type:bool
Controllable:No
Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
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 computeQpProperties() 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
Controllable:No
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 computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
d0_scalars1 3.5 4.5 1 3.5 The diffusion coefficient multipliers for the alpha, beta, gamma, delta, and zeta phases (in that order)
Default:1 3.5 4.5 1 3.5
C++ Type:std::vector<double>
Unit:(no unit assumed)
Controllable:No
Description:The diffusion coefficient multipliers for the alpha, beta, gamma, delta, and zeta phases (in that order)
declare_suffixAn optional suffix parameter that can be appended to any declared 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 declared properties. The suffix will be prepended with a '_' character.
q_scalars1 1 1 1 1 The activation energy multipliers for the alpha, beta, gamma, delta, and zeta phases (in that order)
Default:1 1 1 1 1
C++ Type:std::vector<double>
Unit:(no unit assumed)
Controllable:No
Description:The activation energy multipliers for the alpha, beta, gamma, delta, and zeta phases (in that order)
qstar_scalars1 1 0.56 1 1 The heat of transport multipliers for the alpha, beta, gamma, delta, and zeta phases (in that order)
Default:1 1 0.56 1 1
C++ Type:std::vector<double>
Unit:(no unit assumed)
Controllable:No
Description:The heat of transport multipliers for the alpha, beta, gamma, delta, and zeta phases (in that order)

Optional 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.
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
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

output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)
C++ Type:std::vector<std::string>
Controllable:No
Description:List of material properties, from this material, to output (outputs must also be defined to an output type)
outputsnone Vector of output names where you would like to restrict the output of variables(s) associated with this object
Default:none
C++ Type:std::vector<OutputName>
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object

Outputs 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

(examples/constituent_redistribution/2d_composition.i)
(test/tests/ad_upuzr_mobility/exact.i)
(test/tests/ad_upuzr_mobility/jacobian_test.i)
(examples/constituent_redistribution/1d_thermo_composition.i)

References

Jacob Hirschhorn, Michael Tonks, and Christopher Matthews. A CALPHAD-informed approach to modeling constituent redistribution in Zr-based metallic fuels using BISON. Journal of Nuclear Materials, 544:152657, 2021. doi:10.1016/j.jnucmat.2020.152657.

@article{HIRSCHHORN2021152657,
    author = "Hirschhorn, Jacob and Tonks, Michael and Matthews, Christopher",
    doi = "10.1016/j.jnucmat.2020.152657",
    journal = "Journal of Nuclear Materials",
    publisher = "Elsevier",
    title = "{A CALPHAD-informed approach to modeling constituent redistribution in Zr-based metallic fuels using BISON}",
    volume = "544",
    pages = "152657",
    year = "2021"
}

G. L. Hofman, S. L. Hayes, and M. C. Petri. Temperature gradient driven constituent redistribution in U-Zr alloys. Journal of Nuclear Materials, 227:277–286, 1996. doi:10.1016/0022-3115(95)00129-8.

@article{hofman1996,
    author = "Hofman, G. L. and Hayes, S. L. and Petri, M. C.",
    doi = "10.1016/0022-3115(95)00129-8",
    issn = "00223115",
    journal = "Journal of Nuclear Materials",
    pages = "277-286",
    publisher = "Elsevier",
    title = "{Temperature gradient driven constituent redistribution in U-Zr alloys}",
    volume = "227",
    year = "1996"
}

Yeon Soo Kim, S. L. Hayes, G. L. Hofman, and A. M. Yacout. Modeling of constituent redistribution in U-Pu-Zr metallic fuel. Journal of Nuclear Materials, 359:17–28, 2006. doi:10.1016/j.jnucmat.2006.07.013.

@article{kim2006a,
    author = "Kim, Yeon Soo and Hayes, S. L. and Hofman, G. L. and Yacout, A. M.",
    doi = "10.1016/j.jnucmat.2006.07.013",
    issn = "00223115",
    journal = "Journal of Nuclear Materials",
    pages = "17-28",
    publisher = "Elsevier",
    title = "{Modeling of constituent redistribution in U-Pu-Zr metallic fuel}",
    volume = "359",
    year = "2006"
}

W. Li, R. Hu, Y. Cui, H. Zhong, H. Chang, J. Li, and L. Zhou. Computational study of atomic mobility for the bcc phase of the u-pu-zr ternary system. Journal of Nuclear Materials, 407(3):220–227, 2010. doi:10.1016/j.jnucmat.2010.10.035.

@article{li_et_al_2010,
    author = "Li, W. and Hu, R. and Cui, Y. and Zhong, H. and Chang, H. and Li, J. and Zhou, L.",
    title = "Computational study of atomic mobility for the bcc phase of the U-Pu-Zr ternary system",
    journal = "Journal of Nuclear Materials",
    year = "2010",
    volume = "407",
    number = "3",
    pages = "220-227",
    doi = "10.1016/j.jnucmat.2010.10.035"
}

(examples/constituent_redistribution/1d_thermo_composition.i)

# This example demonstrates how to properly model metallic fuel constituent
# redistribution using ADUPuZrPhaseLookup and ADUPuZrMobility.  It sets up a
# simplified simulation of Experimental Breeder Reactor II Fuel Element DP81
# using an empirical thermal conductivity correction based on data in Ref. [2].
# The predicted zirconium profile (X_Zr) can be compared to the experimental
# EPMA scan stored in (X_Zr_ref) [1].  This example runs in about 1 minute on 1
# processor using the Newton method.

# References
# [1]: Hofman, G. L., Hayes, S. L., and Petri, M. C.  Temperature Gradient
#      Driven Constituent Redistribution in U-Zr Alloys.  Journal of Nuclear
#      Materials 227 (1996).  277-286.
# [2]: Fink, J. K. and Leibowitz, L.  Thermodynamic and Transport Properties of
#      Sodium Liquid and Vapor.  ANL/RE-95/2 (1995).
# [3]: Bauer, T. H. and Holland J. W.  In-Pile Measurement of the Thermal
#      Conductivity of Irradiated Metallic Fuel.  Nuclear Technology 110 (1995)
#      407-421.

[Mesh]
  coord_type = RZ
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 200
    xmax = 2.192e-03
  []
[]

[Variables]
  [T]
    initial_condition = 298
  []
  [X_Zr]
    initial_condition = 0.225
  []
  [w_Zr]
  []
[]

[BCs]
  [T_surf]
    type = ADFunctionDirichletBC
    variable = T
    function = f_T_surf
    boundary = right
  []
[]

[Kernels]
  # Transient heat generation and conduction
  [heat_dt]
    type = ADHeatConductionTimeDerivative
    variable = T
    specific_heat = specific_heat
    density_name = density
  []
  [heat_conduction]
    type = ADHeatConduction
    variable = T
    thermal_conductivity = irradiated_thermal_conductivity
  []
  [heat_source]
    type = ADFissionRateHeatSource
    variable = T
    fission_rate = fission_rate
  []

  # Constituent redistribution using reverse Cahn-Hilliard
  [X_Zr_dt]
    type = ADCoupledTimeDerivative
    variable = w_Zr
    v = X_Zr
  []
  [X_Zr_chemical]
    type = ADSplitCHWRes
    variable = w_Zr
    mob_name = m_c_active
  []
  [X_Zr_thermal]
    type = ADCHSoretMobility
    variable = w_Zr
    T = T
    mobility = m_t_active
  []
  [w_Zr_bulk_int]
    type = ADSplitCHParsed
    variable = X_Zr
    w = w_Zr
    f_name = F
    kappa_name = 1e-6
  []
[]

[AuxVariables]
  [X_Pu]
  []
  [X_Zr_ref]
    [InitialCondition]
      type = FunctionIC
      function = f_X_Zr_ref
    []
  []
[]

[Functions]
  [f_alpha]
    type = PiecewiseMultilinear
    data_file = lookup_tables/alpha_frac.txt
  []
  [f_beta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/beta_frac.txt
  []
  [f_gamma]
    type = PiecewiseMultilinear
    data_file = lookup_tables/gamma_frac.txt
  []
  [f_delta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/delta_frac.txt
  []
  [f_zeta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/zeta_frac.txt
  []
  [f_X_Zr_eq_alpha]
    type = PiecewiseMultilinear
    data_file = lookup_tables/zr_in_alpha.txt
  []
  [f_X_Zr_eq_beta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/zr_in_beta.txt
  []
  [f_X_Zr_eq_gamma]
    type = PiecewiseMultilinear
    data_file = lookup_tables/zr_in_gamma.txt
  []
  [f_X_Zr_eq_delta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/zr_in_delta.txt
  []
  [f_X_Zr_eq_zeta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/zr_in_zeta.txt
  []
  [f_X_Pu_eq_alpha]
    type = PiecewiseMultilinear
    data_file = lookup_tables/pu_in_alpha.txt
  []
  [f_X_Pu_eq_beta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/pu_in_beta.txt
  []
  [f_X_Pu_eq_gamma]
    type = PiecewiseMultilinear
    data_file = lookup_tables/pu_in_gamma.txt
  []
  [f_X_Pu_eq_delta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/pu_in_delta.txt
  []
  [f_X_Pu_eq_zeta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/pu_in_zeta.txt
  []
  [f_mu_alpha]
    type = PiecewiseMultilinear
    data_file = lookup_tables/mu_zr_alpha.txt
  []
  [f_mu_beta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/mu_zr_beta.txt
  []
  [f_mu_gamma]
    type = PiecewiseMultilinear
    data_file = lookup_tables/mu_zr_gamma.txt
  []
  [f_mu_delta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/mu_zr_delta.txt
  []
  [f_mu_zeta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/mu_zr_zeta.txt
  []
  [f_power]
    type = PiecewiseLinear
    x = '0 100000 4420000 5111200 11504800 18157600 24969600'
    y = '0 31816 30504 29848 30504 29192 29192'
  []
  [f_T_surf]
    type = PiecewiseLinear
    x = '0 100000 4420000 5111200 11504800 18157600 24969600'
    y = '298.0 910.4 901.4 896.1 904.5 894.8 895.3'
  []
  [f_X_Zr_ref]
    type = SplineFunction
    x = '0.000e+00 1.099e-05 2.197e-05 3.296e-05 4.394e-05 5.493e-05 6.591e-05 7.690e-05 8.788e-05 9.887e-05 1.099e-04 1.208e-04 1.318e-04 1.428e-04 1.538e-04 1.648e-04 1.758e-04 1.867e-04 1.977e-04 2.087e-04 2.197e-04 2.307e-04 2.417e-04 2.527e-04 2.636e-04 2.746e-04 2.856e-04 2.966e-04 3.076e-04 3.186e-04 3.296e-04 3.405e-04 3.515e-04 3.625e-04 3.735e-04 3.845e-04 3.955e-04 4.064e-04 4.174e-04 4.284e-04 4.394e-04 4.504e-04 4.614e-04 4.724e-04 4.833e-04 4.943e-04 5.053e-04 5.163e-04 5.273e-04 5.383e-04 5.493e-04 5.602e-04 5.712e-04 5.822e-04 5.932e-04 6.042e-04 6.152e-04 6.261e-04 6.371e-04 6.481e-04 6.591e-04 6.701e-04 6.811e-04 6.921e-04 7.030e-04 7.140e-04 7.250e-04 7.360e-04 7.470e-04 7.580e-04 7.690e-04 7.799e-04 7.909e-04 8.019e-04 8.129e-04 8.239e-04 8.349e-04 8.458e-04 8.568e-04 8.678e-04 8.788e-04 8.898e-04 9.008e-04 9.118e-04 9.227e-04 9.337e-04 9.447e-04 9.557e-04 9.667e-04 9.777e-04 9.887e-04 9.996e-04 1.011e-03 1.022e-03 1.033e-03 1.044e-03 1.055e-03 1.066e-03 1.077e-03 1.088e-03 1.099e-03 1.109e-03 1.120e-03 1.131e-03 1.142e-03 1.153e-03 1.164e-03 1.175e-03 1.186e-03 1.197e-03 1.208e-03 1.219e-03 1.230e-03 1.241e-03 1.252e-03 1.263e-03 1.274e-03 1.285e-03 1.296e-03 1.307e-03 1.318e-03 1.329e-03 1.340e-03 1.351e-03 1.362e-03 1.373e-03 1.384e-03 1.395e-03 1.406e-03 1.417e-03 1.428e-03 1.439e-03 1.450e-03 1.461e-03 1.472e-03 1.483e-03 1.494e-03 1.505e-03 1.516e-03 1.527e-03 1.538e-03 1.549e-03 1.560e-03 1.571e-03 1.582e-03 1.593e-03 1.604e-03 1.615e-03 1.626e-03 1.637e-03 1.648e-03 1.659e-03 1.670e-03 1.681e-03 1.692e-03 1.703e-03 1.714e-03 1.725e-03 1.736e-03 1.747e-03 1.758e-03 1.769e-03 1.780e-03 1.791e-03 1.802e-03 1.813e-03 1.824e-03 1.834e-03 1.845e-03 1.856e-03 1.867e-03 1.878e-03 1.889e-03 1.900e-03 1.911e-03 1.922e-03 1.933e-03 1.944e-03 1.955e-03 1.966e-03 1.977e-03 1.988e-03 1.999e-03 2.010e-03 2.021e-03 2.032e-03 2.043e-03 2.054e-03 2.065e-03 2.076e-03 2.087e-03 2.098e-03 2.109e-03 2.120e-03 2.131e-03 2.142e-03 2.153e-03 2.164e-03 2.175e-03 2.186e-03'
    y = '3.885e-01 3.885e-01 3.734e-01 3.590e-01 3.453e-01 3.801e-01 4.422e-01 4.596e-01 4.215e-01 3.965e-01 3.933e-01 4.167e-01 4.431e-01 4.037e-01 4.095e-01 4.104e-01 4.010e-01 3.799e-01 3.995e-01 4.261e-01 4.421e-01 4.450e-01 4.256e-01 4.510e-01 5.115e-01 4.718e-01 4.138e-01 4.158e-01 4.454e-01 3.952e-01 2.708e-01 1.811e-01 2.932e-01 3.956e-01 4.010e-01 4.438e-01 4.706e-01 4.574e-01 3.943e-01 3.271e-01 3.642e-01 4.024e-01 3.875e-01 3.970e-01 4.123e-01 4.326e-01 4.353e-01 4.202e-01 3.674e-01 3.546e-01 3.746e-01 4.111e-01 4.174e-01 3.858e-01 3.380e-01 3.172e-01 3.418e-01 3.884e-01 4.080e-01 3.816e-01 3.655e-01 3.654e-01 3.654e-01 3.677e-01 3.751e-01 3.649e-01 3.557e-01 3.597e-01 3.655e-01 3.656e-01 3.542e-01 3.659e-01 3.575e-01 3.202e-01 2.908e-01 3.047e-01 3.069e-01 3.287e-01 3.847e-01 3.949e-01 3.514e-01 3.297e-01 3.263e-01 3.546e-01 3.581e-01 3.608e-01 3.121e-01 2.694e-01 2.931e-01 3.235e-01 2.970e-01 2.552e-01 2.159e-01 1.917e-01 2.040e-01 2.168e-01 1.825e-01 1.284e-01 7.370e-02 4.785e-02 1.842e-02 7.600e-03 7.420e-03 1.751e-02 6.518e-02 7.871e-02 7.470e-02 6.046e-02 1.203e-01 2.068e-01 1.903e-01 8.591e-02 4.031e-02 2.911e-02 5.307e-02 8.001e-02 1.061e-01 1.072e-01 7.464e-02 4.104e-02 3.966e-02 7.244e-02 8.140e-02 7.180e-02 9.492e-02 1.281e-01 1.213e-01 1.188e-01 1.617e-01 2.258e-01 2.321e-01 1.980e-01 1.650e-01 1.621e-01 2.045e-01 2.132e-01 1.669e-01 1.865e-01 2.431e-01 2.144e-01 1.597e-01 1.821e-01 1.962e-01 1.905e-01 2.026e-01 2.446e-01 2.788e-01 2.705e-01 2.518e-01 2.454e-01 2.472e-01 2.465e-01 2.963e-01 3.190e-01 2.726e-01 2.280e-01 2.382e-01 2.713e-01 2.889e-01 2.408e-01 2.094e-01 2.454e-01 2.894e-01 2.808e-01 2.695e-01 2.769e-01 2.813e-01 2.802e-01 2.810e-01 3.856e-01 4.359e-01 3.762e-01 4.293e-01 4.049e-01 3.155e-01 2.501e-01 2.662e-01 3.887e-01 4.248e-01 3.808e-01 3.120e-01 2.897e-01 2.816e-01 2.762e-01 2.350e-01 2.032e-01 2.147e-01 2.246e-01 3.273e-01 3.938e-01 3.301e-01 2.641e-01 2.351e-01 2.482e-01 2.716e-01 2.403e-01 2.083e-01 1.802e-01 1.772e-01 2.982e-01'
  []
[]

[Materials]
  [density]
    type = ADGenericConstantMaterial
    prop_names = density
    prop_values = 1.580e+04
  []

  # Heat generation and conduction
  [fission_rate]
    type = ADUPuZrFissionRate
    X_Pu_function = 0.0
    initial_X_Zr = 0.225
    X_Zr = X_Zr
    rod_linear_power = f_power
    axial_power_profile = 0.927
    pellet_radius = 2.192e-03
  []
  [burnup]
    type = ADUPuZrBurnup
    initial_X_Pu = 0.0
    initial_X_Zr = 0.225
    density = 1.580e+04
    outputs = 'all'
  []
  [fresh_thermal_conductivity]
    type = ADUPuZrThermal
    temperature = T
    X_Zr = X_Zr
    X_Pu = X_Pu
    thcond_model = lanl
    porosity = 0.0
    spheat_model = savage
  []
  [k_sodium]
    # Empirical correlation from Ref. 2.
    type = ADParsedMaterial
    property_name = k_sodium
    coupled_variables = T
    expression = '124.67 - 0.11381 * T + 5.5226e-5 * T^2 - 1.1842e-8*T^3'
  []
  [porosity]
    # Empirical correlation for solid and gaseous fission product swelling to
    # burnup based on Ref. 3.  Gaseous porosity increases linearly with burnup
    # to porosity_max vol% at burnup_contact at%.  Contact and fission gas
    # release occur at burnup_contact at%.  Gaseous porosity then decreases
    # linearly at a rate of porosity_decrease vol% per at% burnup until
    # burnup_max at%.
    type = ADParsedMaterial
    property_name = porosity
    material_property_names = burnup
    constant_names = 'burnup_contact porosity_max porosity_decrease'
    constant_expressions = '0.0075         0.33         0.011'
    expression = 'min(porosity_max / burnup_contact * burnup, porosity_max) - porosity_decrease * 100 * max(0.0, burnup - burnup_contact)'
    outputs = 'all'
  []
  [logged_sodium]
    # Empirical correlation for sodium infiltration to burnup based on Ref. 3.
    # Sodium begins to infiltrate the fuel at burnup_contact at%.  It proceeds
    # linearly until it reaches a maximum value of sodium_max vol% at
    # burnup_infil at%.
    type = ADParsedMaterial
    property_name = logged_sodium
    material_property_names = burnup
    constant_names = 'burnup_contact burnup_infil sodium_max'
    constant_expressions = '0.0075         0.0150       0.13'
    expression = 'min(sodium_max / (burnup_infil - burnup_contact) * max(0.0, burnup - burnup_contact), sodium_max)'
    outputs = 'all'
  []
  [gas_porosity]
    type = ADParsedMaterial
    property_name = gas_porosity
    material_property_names = 'porosity logged_sodium'
    expression = 'porosity - logged_sodium'
    outputs = 'all'
  []
  [thermal_conductivity_correction]
    # Empirical correlation for the effects of solid and gaseous fission
    # product swelling and sodium infiltration on the thermal conductivity of
    # the fuel based on Ref. 3.
    type = ADParsedMaterial
    property_name = thermal_conductivity_correction
    material_property_names = 'k_sodium thermal_conductivity gas_porosity logged_sodium'
    expression = '(1 - 3 * ((1 - k_sodium / thermal_conductivity) / (2 / 1.72 + (3 - 2 / 1.72) * k_sodium / thermal_conductivity)) * logged_sodium / (1 - gas_porosity)) * (1 - gas_porosity)^(3 / 2)'
    outputs = 'all'
  []
  [irradiated_thermal_conductivity]
    type = ADParsedMaterial
    property_name = irradiated_thermal_conductivity
    material_property_names = 'thermal_conductivity thermal_conductivity_correction'
    expression = 'thermal_conductivity * thermal_conductivity_correction'
  []

  # Thermodynamic parameters
  [phases]
    type = ADUPuZrPhaseLookup
    phase_function_names = 'f_alpha         f_beta         f_gamma         f_delta         f_zeta'
    x_zr_eq_function_names = 'f_X_Zr_eq_alpha f_X_Zr_eq_beta f_X_Zr_eq_gamma f_X_Zr_eq_delta f_X_Zr_eq_zeta'
    x_pu_eq_function_names = 'f_X_Pu_eq_alpha f_X_Pu_eq_beta f_X_Pu_eq_gamma f_X_Pu_eq_delta f_X_Pu_eq_zeta'
    mu_function_names = 'f_mu_alpha      f_mu_beta      f_mu_gamma      f_mu_delta      f_mu_zeta'
    temperature = T
    x_pu = X_Pu
    x_zr = X_Zr
    calculate_derivatives = true # can be set to false when using PJFNK
    outputs = all
  []
  [F]
    # This material renames the chemical potential to accomodate the naming
    # scheme used in ADSplitCHParsed.
    type = ADParsedMaterial
    property_name = 'dF/dX_Zr'
    material_property_names = mu_active
    expression = mu_active
  []

  # Kinetic parameters
  [mobilities]
    type = ADUPuZrMobility
    temperature = T
  []
[]

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

[Executioner]
  type = Transient
  solve_type = NEWTON
  automatic_scaling = true
  compute_scaling_once = false
  scheme = bdf2
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  line_search = none
  l_max_its = 15
  l_tol = 1e-3
  nl_max_its = 15
  nl_rel_tol = 1e-6
  nl_abs_tol = 1e-6
  dtmin = 1e-2
  dtmax = 1e6
  end_time = 24969600
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 1e5
    iteration_window = 2
    optimal_iterations = 9
    growth_factor = 1.1
    cutback_factor = 0.5
  []
[]

[Postprocessors]
  [T_cl]
    type = PointValue
    variable = T
    point = '0 0 0'
  []
  [burnup_avg]
    type = ElementAverageValue
    variable = burnup
  []
  [porosity_avg]
    type = ElementAverageValue
    variable = porosity
  []
  [logged_sodium_avg]
    type = ElementAverageValue
    variable = logged_sodium
  []
  [gas_porosity_avg]
    type = ElementAverageValue
    variable = gas_porosity
  []
  [correction_avg]
    type = ElementAverageValue
    variable = thermal_conductivity_correction
  []
[]

[VectorPostprocessors]
  [profiles]
    type = LineValueSampler
    variable = 'T X_Pu X_Zr X_Zr_ref alpha beta gamma delta zeta'
    sort_by = x
    start_point = '0 0 0'
    end_point = '2.192e-03 0 0'
    num_points = 201
  []
[]

[Outputs]
  perf_graph = true
  exodus = true
  [console]
    type = Console
  []
  [csv]
    type = CSV
    execute_vector_postprocessors_on = final
  []
[]

(examples/constituent_redistribution/2d_composition.i)

# This example demonstrates how to loosely couple the metallic fuel constituent
# redistribution model provided by ADUPuZrPhaseLookup and ADUPuZrMobility to a
# thermo solve using the MultiApps system.  This file contains the composition
# solve, which is executed as a SubApp by 2d_thermo.i.

[Mesh]
  coord_type = RZ
  [smeared_pellet_mesh]
    type = FuelPinMeshGenerator
    clad_thickness = 3.810e-04
    pellet_outer_radius = 2.192e-03
    pellet_height = 3.428e-01
    clad_top_gap_height = 2.714e-01
    clad_gap_width = 3.480e-04
    bottom_clad_height = 2.240e-03
    top_clad_height = 2.240e-03
    clad_bot_gap_height = 3.100e-04
    clad_mesh_density = customize
    pellet_mesh_density = customize
    nx_p = 20
    ny_p = 260
    include_clad = false
    pellet_quantity = 1
    elem_type = QUAD8
  []
[]

[Variables]
  [X_Zr]
    initial_condition = 0.225
  []
  [w_Zr]
  []
[]

[Kernels]
  # Constituent redistribution using reverse Cahn-Hilliard
  [X_Zr_dt]
    type = ADCoupledTimeDerivative
    variable = w_Zr
    v = X_Zr
  []
  [X_Zr_chemical]
    type = ADSplitCHWRes
    variable = w_Zr
    mob_name = m_c_active
  []
  [X_Zr_thermal]
    type = ADCHSoretMobility
    variable = w_Zr
    T = T
    mobility = m_t_active
  []
  [w_Zr_bulk_int]
    type = ADSplitCHParsed
    variable = X_Zr
    w = w_Zr
    f_name = F
    kappa_name = 5e-5
  []
[]

[AuxVariables]
  [X_Pu]
  []
  [X_Zr_ref]
    [InitialCondition]
      type = FunctionIC
      function = f_X_Zr_ref
    []
  []
  [T]
    order = SECOND
    family = LAGRANGE
  []
[]

[Functions]
  [f_alpha]
    type = PiecewiseMultilinear
    data_file = lookup_tables/alpha_frac.txt
  []
  [f_beta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/beta_frac.txt
  []
  [f_gamma]
    type = PiecewiseMultilinear
    data_file = lookup_tables/gamma_frac.txt
  []
  [f_delta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/delta_frac.txt
  []
  [f_zeta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/zeta_frac.txt
  []
  [f_X_Zr_eq_alpha]
    type = PiecewiseMultilinear
    data_file = lookup_tables/zr_in_alpha.txt
  []
  [f_X_Zr_eq_beta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/zr_in_beta.txt
  []
  [f_X_Zr_eq_gamma]
    type = PiecewiseMultilinear
    data_file = lookup_tables/zr_in_gamma.txt
  []
  [f_X_Zr_eq_delta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/zr_in_delta.txt
  []
  [f_X_Zr_eq_zeta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/zr_in_zeta.txt
  []
  [f_X_Pu_eq_alpha]
    type = PiecewiseMultilinear
    data_file = lookup_tables/pu_in_alpha.txt
  []
  [f_X_Pu_eq_beta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/pu_in_beta.txt
  []
  [f_X_Pu_eq_gamma]
    type = PiecewiseMultilinear
    data_file = lookup_tables/pu_in_gamma.txt
  []
  [f_X_Pu_eq_delta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/pu_in_delta.txt
  []
  [f_X_Pu_eq_zeta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/pu_in_zeta.txt
  []
  [f_mu_alpha]
    type = PiecewiseMultilinear
    data_file = lookup_tables/mu_zr_alpha.txt
  []
  [f_mu_beta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/mu_zr_beta.txt
  []
  [f_mu_gamma]
    type = PiecewiseMultilinear
    data_file = lookup_tables/mu_zr_gamma.txt
  []
  [f_mu_delta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/mu_zr_delta.txt
  []
  [f_mu_zeta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/mu_zr_zeta.txt
  []
  [f_X_Zr_ref]
    type = SplineFunction
    x = '0.000e+00 1.099e-05 2.197e-05 3.296e-05 4.394e-05 5.493e-05 6.591e-05 7.690e-05 8.788e-05 9.887e-05 1.099e-04 1.208e-04 1.318e-04 1.428e-04 1.538e-04 1.648e-04 1.758e-04 1.867e-04 1.977e-04 2.087e-04 2.197e-04 2.307e-04 2.417e-04 2.527e-04 2.636e-04 2.746e-04 2.856e-04 2.966e-04 3.076e-04 3.186e-04 3.296e-04 3.405e-04 3.515e-04 3.625e-04 3.735e-04 3.845e-04 3.955e-04 4.064e-04 4.174e-04 4.284e-04 4.394e-04 4.504e-04 4.614e-04 4.724e-04 4.833e-04 4.943e-04 5.053e-04 5.163e-04 5.273e-04 5.383e-04 5.493e-04 5.602e-04 5.712e-04 5.822e-04 5.932e-04 6.042e-04 6.152e-04 6.261e-04 6.371e-04 6.481e-04 6.591e-04 6.701e-04 6.811e-04 6.921e-04 7.030e-04 7.140e-04 7.250e-04 7.360e-04 7.470e-04 7.580e-04 7.690e-04 7.799e-04 7.909e-04 8.019e-04 8.129e-04 8.239e-04 8.349e-04 8.458e-04 8.568e-04 8.678e-04 8.788e-04 8.898e-04 9.008e-04 9.118e-04 9.227e-04 9.337e-04 9.447e-04 9.557e-04 9.667e-04 9.777e-04 9.887e-04 9.996e-04 1.011e-03 1.022e-03 1.033e-03 1.044e-03 1.055e-03 1.066e-03 1.077e-03 1.088e-03 1.099e-03 1.109e-03 1.120e-03 1.131e-03 1.142e-03 1.153e-03 1.164e-03 1.175e-03 1.186e-03 1.197e-03 1.208e-03 1.219e-03 1.230e-03 1.241e-03 1.252e-03 1.263e-03 1.274e-03 1.285e-03 1.296e-03 1.307e-03 1.318e-03 1.329e-03 1.340e-03 1.351e-03 1.362e-03 1.373e-03 1.384e-03 1.395e-03 1.406e-03 1.417e-03 1.428e-03 1.439e-03 1.450e-03 1.461e-03 1.472e-03 1.483e-03 1.494e-03 1.505e-03 1.516e-03 1.527e-03 1.538e-03 1.549e-03 1.560e-03 1.571e-03 1.582e-03 1.593e-03 1.604e-03 1.615e-03 1.626e-03 1.637e-03 1.648e-03 1.659e-03 1.670e-03 1.681e-03 1.692e-03 1.703e-03 1.714e-03 1.725e-03 1.736e-03 1.747e-03 1.758e-03 1.769e-03 1.780e-03 1.791e-03 1.802e-03 1.813e-03 1.824e-03 1.834e-03 1.845e-03 1.856e-03 1.867e-03 1.878e-03 1.889e-03 1.900e-03 1.911e-03 1.922e-03 1.933e-03 1.944e-03 1.955e-03 1.966e-03 1.977e-03 1.988e-03 1.999e-03 2.010e-03 2.021e-03 2.032e-03 2.043e-03 2.054e-03 2.065e-03 2.076e-03 2.087e-03 2.098e-03 2.109e-03 2.120e-03 2.131e-03 2.142e-03 2.153e-03 2.164e-03 2.175e-03 2.186e-03'
    y = '3.885e-01 3.885e-01 3.734e-01 3.590e-01 3.453e-01 3.801e-01 4.422e-01 4.596e-01 4.215e-01 3.965e-01 3.933e-01 4.167e-01 4.431e-01 4.037e-01 4.095e-01 4.104e-01 4.010e-01 3.799e-01 3.995e-01 4.261e-01 4.421e-01 4.450e-01 4.256e-01 4.510e-01 5.115e-01 4.718e-01 4.138e-01 4.158e-01 4.454e-01 3.952e-01 2.708e-01 1.811e-01 2.932e-01 3.956e-01 4.010e-01 4.438e-01 4.706e-01 4.574e-01 3.943e-01 3.271e-01 3.642e-01 4.024e-01 3.875e-01 3.970e-01 4.123e-01 4.326e-01 4.353e-01 4.202e-01 3.674e-01 3.546e-01 3.746e-01 4.111e-01 4.174e-01 3.858e-01 3.380e-01 3.172e-01 3.418e-01 3.884e-01 4.080e-01 3.816e-01 3.655e-01 3.654e-01 3.654e-01 3.677e-01 3.751e-01 3.649e-01 3.557e-01 3.597e-01 3.655e-01 3.656e-01 3.542e-01 3.659e-01 3.575e-01 3.202e-01 2.908e-01 3.047e-01 3.069e-01 3.287e-01 3.847e-01 3.949e-01 3.514e-01 3.297e-01 3.263e-01 3.546e-01 3.581e-01 3.608e-01 3.121e-01 2.694e-01 2.931e-01 3.235e-01 2.970e-01 2.552e-01 2.159e-01 1.917e-01 2.040e-01 2.168e-01 1.825e-01 1.284e-01 7.370e-02 4.785e-02 1.842e-02 7.600e-03 7.420e-03 1.751e-02 6.518e-02 7.871e-02 7.470e-02 6.046e-02 1.203e-01 2.068e-01 1.903e-01 8.591e-02 4.031e-02 2.911e-02 5.307e-02 8.001e-02 1.061e-01 1.072e-01 7.464e-02 4.104e-02 3.966e-02 7.244e-02 8.140e-02 7.180e-02 9.492e-02 1.281e-01 1.213e-01 1.188e-01 1.617e-01 2.258e-01 2.321e-01 1.980e-01 1.650e-01 1.621e-01 2.045e-01 2.132e-01 1.669e-01 1.865e-01 2.431e-01 2.144e-01 1.597e-01 1.821e-01 1.962e-01 1.905e-01 2.026e-01 2.446e-01 2.788e-01 2.705e-01 2.518e-01 2.454e-01 2.472e-01 2.465e-01 2.963e-01 3.190e-01 2.726e-01 2.280e-01 2.382e-01 2.713e-01 2.889e-01 2.408e-01 2.094e-01 2.454e-01 2.894e-01 2.808e-01 2.695e-01 2.769e-01 2.813e-01 2.802e-01 2.810e-01 3.856e-01 4.359e-01 3.762e-01 4.293e-01 4.049e-01 3.155e-01 2.501e-01 2.662e-01 3.887e-01 4.248e-01 3.808e-01 3.120e-01 2.897e-01 2.816e-01 2.762e-01 2.350e-01 2.032e-01 2.147e-01 2.246e-01 3.273e-01 3.938e-01 3.301e-01 2.641e-01 2.351e-01 2.482e-01 2.716e-01 2.403e-01 2.083e-01 1.802e-01 1.772e-01 2.982e-01'
  []
[]

[Materials]
  # Thermodynamic parameters
  [phases]
    type = ADUPuZrPhaseLookup
    phase_function_names = 'f_alpha         f_beta         f_gamma         f_delta         f_zeta'
    x_zr_eq_function_names = 'f_X_Zr_eq_alpha f_X_Zr_eq_beta f_X_Zr_eq_gamma f_X_Zr_eq_delta f_X_Zr_eq_zeta'
    x_pu_eq_function_names = 'f_X_Pu_eq_alpha f_X_Pu_eq_beta f_X_Pu_eq_gamma f_X_Pu_eq_delta f_X_Pu_eq_zeta'
    mu_function_names = 'f_mu_alpha      f_mu_beta      f_mu_gamma      f_mu_delta      f_mu_zeta'
    temperature = T
    x_pu = X_Pu
    x_zr = X_Zr
    calculate_derivatives = true # can be set to false when using PJFNK
    outputs = 'all'
  []
  [F]
    # This material renames the chemical potential to accomodate the naming
    # scheme used in ADSplitCHParsed.
    type = ADParsedMaterial
    property_name = 'dF/dX_Zr'
    material_property_names = mu_active
    expression = mu_active
  []

  # Kinetic parameters
  [mobilities]
    type = ADUPuZrMobility
    temperature = T
  []
[]

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

[Executioner]
  type = Transient
  solve_type = NEWTON
  automatic_scaling = true
  compute_scaling_once = false
  scaling_group_variables = 'X_Zr w_Zr'
  scheme = bdf2
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  line_search = none
  l_max_its = 15
  l_tol = 1e-3
  nl_max_its = 15
  nl_rel_tol = 1e-6
  nl_abs_tol = 1e-6
  dtmin = 10
  dtmax = 1e6
  end_time = 24969600
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 1e5
    iteration_window = 2
    optimal_iterations = 9
    growth_factor = 1.1
    cutback_factor = 0.5
  []
[]

[VectorPostprocessors]
  [profiles]
    type = LineValueSampler
    variable = 'T X_Pu X_Zr X_Zr_ref alpha beta gamma delta zeta'
    sort_by = x
    start_point = '0 2.689e-01 0'
    end_point = '2.192e-03 2.689e-01 0'
    num_points = 21
  []
[]

[Outputs]
  perf_graph = true
  exodus = true
  [console]
    type = Console
  []
  [csv]
    type = CSV
    execute_vector_postprocessors_on = final
  []
[]

(test/tests/ad_upuzr_mobility/exact.i)

# This test is to verify the implementation of ADUPuZrMobility material.
# ADUPuZrMobility material accepts phase stability information from
# ADUPuZrPhaseLookup material and uses it to evaluate chemical and thermal
# mobilities.
#
# This test uses the material to calculate mobilities for eight different
# compositions, temperatures, and combinations of stable phases.
#
# point stable_phase(s)
# 1     beta
# 2     beta (different composition)
# 3     beta, delta
# 4     beta, delta (different temperature)
# 5     alpha, delta
# 6     alpha, delta (different composition)
# 7     delta
# 8     delta (different temperature)

[Mesh]
  uniform_refine = 2
  [mesh]
    type = GeneratedMeshGenerator
    dim = 2
  []
[]

[Problem]
  solve = false
[]

[AuxVariables]
  [T]
    [InitialCondition]
      type = FunctionIC
      function = '100 * y + 773'
    []
  []
  [X_Zr]
    [InitialCondition]
      type = FunctionIC
      function = x
    []
  []
[]

[Functions]
  [f_alpha]
    type = ParsedFunction
    expression = 'if(z <= 0.25 & x <= 823, 1.0,
                if(z < 0.75 & x <= 823, 1.0 - ((1.0 - 0.0) / (0.75 - 0.25) * z - 0.5),
                   0.0))'
  []
  [f_beta]
    type = ParsedFunction
    expression = 'if(z <= 0.5 & x > 823, 1.0,
                if(z < 0.75 & x > 823, 1.0 - ((1.0 - 0.0) / (0.75 - 0.5) * z - 2.0),
                   0.0))'
  []
  [f_delta]
    type = ParsedFunction
    expression = 'if(z <= 0.25 & x <= 823, 0.0,
                if(z < 0.75 & x <= 823, (1.0 - 0.0) / (0.75 - 0.25) * z - 0.5,
                   if(z <= 0.5, 0.0,
                      if(z < 0.75, (1.0 - 0.0) / (0.75 - 0.5) * z - 2.0,
                         1.0))))'
  []
  [f_X_Zr_eq_alpha]
    type = ParsedFunction
    expression = 'if(z <= 0.25 & x <= 823, z,
                if(z < 0.75 & x <= 823, 0.25,
                   0.0))'
  []
  [f_X_Zr_eq_beta]
    type = ParsedFunction
    expression = 'if(z <= 0.5 & x > 823, z,
                if(z < 0.75 & x > 823, 0.5,
                   0.0))'
  []
  [f_X_Zr_eq_delta]
    type = ParsedFunction
    expression = 'if(z <= 0.25 & x <= 823, 0.0,
                if(z < 0.75 & x <= 823, 0.75,
                   if(z <= 0.5, 0.0,
                      if(z < 0.75, 0.75,
                         z))))'
  []
[]

[Materials]
  [phases]
    type = ADUPuZrPhaseLookup
    phase_function_names = 'f_alpha         f_beta         0.0 f_delta         0.0'
    x_zr_eq_function_names = 'f_X_Zr_eq_alpha f_X_Zr_eq_beta 0.0 f_X_Zr_eq_delta 0.0'
    x_pu_eq_function_names = '0.0             0.0            0.0 0.0             0.0'
    mu_function_names = '0.0             0.0            0.0 0.0             0.0'
    temperature = T
    x_pu = 0.0
    x_zr = X_Zr
  []
  [mobilities]
    type = ADUPuZrMobility
    temperature = T
    outputs = 'all'
  []
[]

[Executioner]
  type = Transient
  dt = 1
  num_steps = 1
[]

[Postprocessors]
  [m_c_active_point_1]
    type = PointValue
    variable = m_c_active
    point = '0.125 0.625 0.0'
    outputs = csv
  []
  [m_c_active_point_2]
    type = PointValue
    variable = m_c_active
    point = '0.375 0.625 0.0'
    outputs = csv
  []
  [m_c_active_point_3]
    type = PointValue
    variable = m_c_active
    point = '0.625 0.875 0.0'
    outputs = csv
  []
  [m_c_active_point_4]
    type = PointValue
    variable = m_c_active
    point = '0.625 0.625 0.0'
    outputs = csv
  []
  [m_c_active_point_5]
    type = PointValue
    variable = m_c_active
    point = '0.375 0.375 0.0'
    outputs = csv
  []
  [m_c_active_point_6]
    type = PointValue
    variable = m_c_active
    point = '0.625 0.375 0.0'
    outputs = csv
  []
  [m_c_active_point_7]
    type = PointValue
    variable = m_c_active
    point = '0.875 0.875 0.0'
    outputs = csv
  []
  [m_c_active_point_8]
    type = PointValue
    variable = m_c_active
    point = '0.875 0.125 0.0'
    outputs = csv
  []
  [m_t_active_point_1]
    type = PointValue
    variable = m_t_active
    point = '0.125 0.625 0.0'
    outputs = csv
  []
  [m_t_active_point_2]
    type = PointValue
    variable = m_t_active
    point = '0.375 0.625 0.0'
    outputs = csv
  []
  [m_t_active_point_3]
    type = PointValue
    variable = m_t_active
    point = '0.625 0.875 0.0'
    outputs = csv
  []
  [m_t_active_point_4]
    type = PointValue
    variable = m_t_active
    point = '0.625 0.625 0.0'
    outputs = csv
  []
  [m_t_active_point_5]
    type = PointValue
    variable = m_t_active
    point = '0.375 0.375 0.0'
    outputs = csv
  []
  [m_t_active_point_6]
    type = PointValue
    variable = m_t_active
    point = '0.625 0.375 0.0'
    outputs = csv
  []
  [m_t_active_point_7]
    type = PointValue
    variable = m_t_active
    point = '0.875 0.875 0.0'
    outputs = csv
  []
  [m_t_active_point_8]
    type = PointValue
    variable = m_t_active
    point = '0.875 0.125 0.0'
    outputs = csv
  []
[]

[Outputs]
  csv = true
[]

(test/tests/ad_upuzr_mobility/jacobian_test.i)

# This template sets up tests to verify the accuracy of the AD Jacobian
# calculated by ADUPuZrMobility material when the material properties supplied
# by ADUPuZrPhaseLookup do and do not have variable dependencies
#
# These tests use the material to calculate Jacobian contributions for two
# mobilities (m_c_active and m_t_active) using AD.  These resulting Jacobian
# is compared to a Jacobian calculated using finite difference.  Two cases are
# considered:
# - material properties supplied by ADUPuZrPhaseLookup have variable
#   dependencies: mobilities = f(T,X_Zr,X_Pu)
# - material properties supplied by ADUPuZrPhaseLookup are constant:
#   mobilities = f(T)

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 1
  []
[]

[Variables]
  [dummy]
  []
  [T]
  []
  [X_Zr]
  []
[]

[AuxVariables]
  [X_Pu]
  []
[]

[ICs]
  [T]
    type = RampIC
    variable = T
    value_left = 500
    value_right = 1000
  []
  [X_Zr]
    type = RampIC
    variable = X_Zr
    value_left = 0
    value_right = 0.5
  []
  [X_Pu]
    type = RampIC
    variable = X_Pu
    value_left = 0
    value_right = 0.5
  []
[]

[Kernels]
  [dummy_dt]
    type = ADTimeDerivative
    variable = dummy
  []
  [T_dt]
    type = ADTimeDerivative
    variable = T
  []
  [T_diff]
    type = ADDiffusion
    variable = T
  []
  [X_Zr_dt]
    type = ADTimeDerivative
    variable = X_Zr
  []
  [X_Zr_diff]
    type = ADMatDiffusion
    variable = X_Zr
    diffusivity = m_c_active
  []
[]

[Functions]
  [f_dependent]
    type = ParsedFunction
    expression = 'x + 2 * y + 3 * z'
  []
  [f_constant]
    type = ParsedFunction
    expression = 0.2
  []
[]

[Materials]
  [phases]
    type = ADUPuZrPhaseLookup
    x_zr_eq_function_names = '0.1 0.1 0.1 0.1 0.1'
    x_pu_eq_function_names = '0.1 0.1 0.1 0.1 0.1'
    mu_function_names = '0.0 0.0 0.0 0.0 0.0'
    temperature = T
    x_pu = X_Pu
    x_zr = X_Zr
  []
  # scalar multipliers ensure that T, X_Pu, and X_Zr evolve at similar rates
  [mobilities]
    type = ADUPuZrMobility
    d0_scalars = '5e16 5e16 5e16 5e16 5e16'
    qstar_scalars = '1e-5 1e-5 1e-5 1e-5 1e-5'
    temperature = T
  []
[]

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

[Executioner]
  type = Transient
  dt = 1
  num_steps = 1
[]

(examples/constituent_redistribution/1d_thermo_composition.i)

# This example demonstrates how to properly model metallic fuel constituent
# redistribution using ADUPuZrPhaseLookup and ADUPuZrMobility.  It sets up a
# simplified simulation of Experimental Breeder Reactor II Fuel Element DP81
# using an empirical thermal conductivity correction based on data in Ref. [2].
# The predicted zirconium profile (X_Zr) can be compared to the experimental
# EPMA scan stored in (X_Zr_ref) [1].  This example runs in about 1 minute on 1
# processor using the Newton method.

# References
# [1]: Hofman, G. L., Hayes, S. L., and Petri, M. C.  Temperature Gradient
#      Driven Constituent Redistribution in U-Zr Alloys.  Journal of Nuclear
#      Materials 227 (1996).  277-286.
# [2]: Fink, J. K. and Leibowitz, L.  Thermodynamic and Transport Properties of
#      Sodium Liquid and Vapor.  ANL/RE-95/2 (1995).
# [3]: Bauer, T. H. and Holland J. W.  In-Pile Measurement of the Thermal
#      Conductivity of Irradiated Metallic Fuel.  Nuclear Technology 110 (1995)
#      407-421.

[Mesh]
  coord_type = RZ
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 200
    xmax = 2.192e-03
  []
[]

[Variables]
  [T]
    initial_condition = 298
  []
  [X_Zr]
    initial_condition = 0.225
  []
  [w_Zr]
  []
[]

[BCs]
  [T_surf]
    type = ADFunctionDirichletBC
    variable = T
    function = f_T_surf
    boundary = right
  []
[]

[Kernels]
  # Transient heat generation and conduction
  [heat_dt]
    type = ADHeatConductionTimeDerivative
    variable = T
    specific_heat = specific_heat
    density_name = density
  []
  [heat_conduction]
    type = ADHeatConduction
    variable = T
    thermal_conductivity = irradiated_thermal_conductivity
  []
  [heat_source]
    type = ADFissionRateHeatSource
    variable = T
    fission_rate = fission_rate
  []

  # Constituent redistribution using reverse Cahn-Hilliard
  [X_Zr_dt]
    type = ADCoupledTimeDerivative
    variable = w_Zr
    v = X_Zr
  []
  [X_Zr_chemical]
    type = ADSplitCHWRes
    variable = w_Zr
    mob_name = m_c_active
  []
  [X_Zr_thermal]
    type = ADCHSoretMobility
    variable = w_Zr
    T = T
    mobility = m_t_active
  []
  [w_Zr_bulk_int]
    type = ADSplitCHParsed
    variable = X_Zr
    w = w_Zr
    f_name = F
    kappa_name = 1e-6
  []
[]

[AuxVariables]
  [X_Pu]
  []
  [X_Zr_ref]
    [InitialCondition]
      type = FunctionIC
      function = f_X_Zr_ref
    []
  []
[]

[Functions]
  [f_alpha]
    type = PiecewiseMultilinear
    data_file = lookup_tables/alpha_frac.txt
  []
  [f_beta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/beta_frac.txt
  []
  [f_gamma]
    type = PiecewiseMultilinear
    data_file = lookup_tables/gamma_frac.txt
  []
  [f_delta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/delta_frac.txt
  []
  [f_zeta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/zeta_frac.txt
  []
  [f_X_Zr_eq_alpha]
    type = PiecewiseMultilinear
    data_file = lookup_tables/zr_in_alpha.txt
  []
  [f_X_Zr_eq_beta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/zr_in_beta.txt
  []
  [f_X_Zr_eq_gamma]
    type = PiecewiseMultilinear
    data_file = lookup_tables/zr_in_gamma.txt
  []
  [f_X_Zr_eq_delta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/zr_in_delta.txt
  []
  [f_X_Zr_eq_zeta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/zr_in_zeta.txt
  []
  [f_X_Pu_eq_alpha]
    type = PiecewiseMultilinear
    data_file = lookup_tables/pu_in_alpha.txt
  []
  [f_X_Pu_eq_beta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/pu_in_beta.txt
  []
  [f_X_Pu_eq_gamma]
    type = PiecewiseMultilinear
    data_file = lookup_tables/pu_in_gamma.txt
  []
  [f_X_Pu_eq_delta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/pu_in_delta.txt
  []
  [f_X_Pu_eq_zeta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/pu_in_zeta.txt
  []
  [f_mu_alpha]
    type = PiecewiseMultilinear
    data_file = lookup_tables/mu_zr_alpha.txt
  []
  [f_mu_beta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/mu_zr_beta.txt
  []
  [f_mu_gamma]
    type = PiecewiseMultilinear
    data_file = lookup_tables/mu_zr_gamma.txt
  []
  [f_mu_delta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/mu_zr_delta.txt
  []
  [f_mu_zeta]
    type = PiecewiseMultilinear
    data_file = lookup_tables/mu_zr_zeta.txt
  []
  [f_power]
    type = PiecewiseLinear
    x = '0 100000 4420000 5111200 11504800 18157600 24969600'
    y = '0 31816 30504 29848 30504 29192 29192'
  []
  [f_T_surf]
    type = PiecewiseLinear
    x = '0 100000 4420000 5111200 11504800 18157600 24969600'
    y = '298.0 910.4 901.4 896.1 904.5 894.8 895.3'
  []
  [f_X_Zr_ref]
    type = SplineFunction
    x = '0.000e+00 1.099e-05 2.197e-05 3.296e-05 4.394e-05 5.493e-05 6.591e-05 7.690e-05 8.788e-05 9.887e-05 1.099e-04 1.208e-04 1.318e-04 1.428e-04 1.538e-04 1.648e-04 1.758e-04 1.867e-04 1.977e-04 2.087e-04 2.197e-04 2.307e-04 2.417e-04 2.527e-04 2.636e-04 2.746e-04 2.856e-04 2.966e-04 3.076e-04 3.186e-04 3.296e-04 3.405e-04 3.515e-04 3.625e-04 3.735e-04 3.845e-04 3.955e-04 4.064e-04 4.174e-04 4.284e-04 4.394e-04 4.504e-04 4.614e-04 4.724e-04 4.833e-04 4.943e-04 5.053e-04 5.163e-04 5.273e-04 5.383e-04 5.493e-04 5.602e-04 5.712e-04 5.822e-04 5.932e-04 6.042e-04 6.152e-04 6.261e-04 6.371e-04 6.481e-04 6.591e-04 6.701e-04 6.811e-04 6.921e-04 7.030e-04 7.140e-04 7.250e-04 7.360e-04 7.470e-04 7.580e-04 7.690e-04 7.799e-04 7.909e-04 8.019e-04 8.129e-04 8.239e-04 8.349e-04 8.458e-04 8.568e-04 8.678e-04 8.788e-04 8.898e-04 9.008e-04 9.118e-04 9.227e-04 9.337e-04 9.447e-04 9.557e-04 9.667e-04 9.777e-04 9.887e-04 9.996e-04 1.011e-03 1.022e-03 1.033e-03 1.044e-03 1.055e-03 1.066e-03 1.077e-03 1.088e-03 1.099e-03 1.109e-03 1.120e-03 1.131e-03 1.142e-03 1.153e-03 1.164e-03 1.175e-03 1.186e-03 1.197e-03 1.208e-03 1.219e-03 1.230e-03 1.241e-03 1.252e-03 1.263e-03 1.274e-03 1.285e-03 1.296e-03 1.307e-03 1.318e-03 1.329e-03 1.340e-03 1.351e-03 1.362e-03 1.373e-03 1.384e-03 1.395e-03 1.406e-03 1.417e-03 1.428e-03 1.439e-03 1.450e-03 1.461e-03 1.472e-03 1.483e-03 1.494e-03 1.505e-03 1.516e-03 1.527e-03 1.538e-03 1.549e-03 1.560e-03 1.571e-03 1.582e-03 1.593e-03 1.604e-03 1.615e-03 1.626e-03 1.637e-03 1.648e-03 1.659e-03 1.670e-03 1.681e-03 1.692e-03 1.703e-03 1.714e-03 1.725e-03 1.736e-03 1.747e-03 1.758e-03 1.769e-03 1.780e-03 1.791e-03 1.802e-03 1.813e-03 1.824e-03 1.834e-03 1.845e-03 1.856e-03 1.867e-03 1.878e-03 1.889e-03 1.900e-03 1.911e-03 1.922e-03 1.933e-03 1.944e-03 1.955e-03 1.966e-03 1.977e-03 1.988e-03 1.999e-03 2.010e-03 2.021e-03 2.032e-03 2.043e-03 2.054e-03 2.065e-03 2.076e-03 2.087e-03 2.098e-03 2.109e-03 2.120e-03 2.131e-03 2.142e-03 2.153e-03 2.164e-03 2.175e-03 2.186e-03'
    y = '3.885e-01 3.885e-01 3.734e-01 3.590e-01 3.453e-01 3.801e-01 4.422e-01 4.596e-01 4.215e-01 3.965e-01 3.933e-01 4.167e-01 4.431e-01 4.037e-01 4.095e-01 4.104e-01 4.010e-01 3.799e-01 3.995e-01 4.261e-01 4.421e-01 4.450e-01 4.256e-01 4.510e-01 5.115e-01 4.718e-01 4.138e-01 4.158e-01 4.454e-01 3.952e-01 2.708e-01 1.811e-01 2.932e-01 3.956e-01 4.010e-01 4.438e-01 4.706e-01 4.574e-01 3.943e-01 3.271e-01 3.642e-01 4.024e-01 3.875e-01 3.970e-01 4.123e-01 4.326e-01 4.353e-01 4.202e-01 3.674e-01 3.546e-01 3.746e-01 4.111e-01 4.174e-01 3.858e-01 3.380e-01 3.172e-01 3.418e-01 3.884e-01 4.080e-01 3.816e-01 3.655e-01 3.654e-01 3.654e-01 3.677e-01 3.751e-01 3.649e-01 3.557e-01 3.597e-01 3.655e-01 3.656e-01 3.542e-01 3.659e-01 3.575e-01 3.202e-01 2.908e-01 3.047e-01 3.069e-01 3.287e-01 3.847e-01 3.949e-01 3.514e-01 3.297e-01 3.263e-01 3.546e-01 3.581e-01 3.608e-01 3.121e-01 2.694e-01 2.931e-01 3.235e-01 2.970e-01 2.552e-01 2.159e-01 1.917e-01 2.040e-01 2.168e-01 1.825e-01 1.284e-01 7.370e-02 4.785e-02 1.842e-02 7.600e-03 7.420e-03 1.751e-02 6.518e-02 7.871e-02 7.470e-02 6.046e-02 1.203e-01 2.068e-01 1.903e-01 8.591e-02 4.031e-02 2.911e-02 5.307e-02 8.001e-02 1.061e-01 1.072e-01 7.464e-02 4.104e-02 3.966e-02 7.244e-02 8.140e-02 7.180e-02 9.492e-02 1.281e-01 1.213e-01 1.188e-01 1.617e-01 2.258e-01 2.321e-01 1.980e-01 1.650e-01 1.621e-01 2.045e-01 2.132e-01 1.669e-01 1.865e-01 2.431e-01 2.144e-01 1.597e-01 1.821e-01 1.962e-01 1.905e-01 2.026e-01 2.446e-01 2.788e-01 2.705e-01 2.518e-01 2.454e-01 2.472e-01 2.465e-01 2.963e-01 3.190e-01 2.726e-01 2.280e-01 2.382e-01 2.713e-01 2.889e-01 2.408e-01 2.094e-01 2.454e-01 2.894e-01 2.808e-01 2.695e-01 2.769e-01 2.813e-01 2.802e-01 2.810e-01 3.856e-01 4.359e-01 3.762e-01 4.293e-01 4.049e-01 3.155e-01 2.501e-01 2.662e-01 3.887e-01 4.248e-01 3.808e-01 3.120e-01 2.897e-01 2.816e-01 2.762e-01 2.350e-01 2.032e-01 2.147e-01 2.246e-01 3.273e-01 3.938e-01 3.301e-01 2.641e-01 2.351e-01 2.482e-01 2.716e-01 2.403e-01 2.083e-01 1.802e-01 1.772e-01 2.982e-01'
  []
[]

[Materials]
  [density]
    type = ADGenericConstantMaterial
    prop_names = density
    prop_values = 1.580e+04
  []

  # Heat generation and conduction
  [fission_rate]
    type = ADUPuZrFissionRate
    X_Pu_function = 0.0
    initial_X_Zr = 0.225
    X_Zr = X_Zr
    rod_linear_power = f_power
    axial_power_profile = 0.927
    pellet_radius = 2.192e-03
  []
  [burnup]
    type = ADUPuZrBurnup
    initial_X_Pu = 0.0
    initial_X_Zr = 0.225
    density = 1.580e+04
    outputs = 'all'
  []
  [fresh_thermal_conductivity]
    type = ADUPuZrThermal
    temperature = T
    X_Zr = X_Zr
    X_Pu = X_Pu
    thcond_model = lanl
    porosity = 0.0
    spheat_model = savage
  []
  [k_sodium]
    # Empirical correlation from Ref. 2.
    type = ADParsedMaterial
    property_name = k_sodium
    coupled_variables = T
    expression = '124.67 - 0.11381 * T + 5.5226e-5 * T^2 - 1.1842e-8*T^3'
  []
  [porosity]
    # Empirical correlation for solid and gaseous fission product swelling to
    # burnup based on Ref. 3.  Gaseous porosity increases linearly with burnup
    # to porosity_max vol% at burnup_contact at%.  Contact and fission gas
    # release occur at burnup_contact at%.  Gaseous porosity then decreases
    # linearly at a rate of porosity_decrease vol% per at% burnup until
    # burnup_max at%.
    type = ADParsedMaterial
    property_name = porosity
    material_property_names = burnup
    constant_names = 'burnup_contact porosity_max porosity_decrease'
    constant_expressions = '0.0075         0.33         0.011'
    expression = 'min(porosity_max / burnup_contact * burnup, porosity_max) - porosity_decrease * 100 * max(0.0, burnup - burnup_contact)'
    outputs = 'all'
  []
  [logged_sodium]
    # Empirical correlation for sodium infiltration to burnup based on Ref. 3.
    # Sodium begins to infiltrate the fuel at burnup_contact at%.  It proceeds
    # linearly until it reaches a maximum value of sodium_max vol% at
    # burnup_infil at%.
    type = ADParsedMaterial
    property_name = logged_sodium
    material_property_names = burnup
    constant_names = 'burnup_contact burnup_infil sodium_max'
    constant_expressions = '0.0075         0.0150       0.13'
    expression = 'min(sodium_max / (burnup_infil - burnup_contact) * max(0.0, burnup - burnup_contact), sodium_max)'
    outputs = 'all'
  []
  [gas_porosity]
    type = ADParsedMaterial
    property_name = gas_porosity
    material_property_names = 'porosity logged_sodium'
    expression = 'porosity - logged_sodium'
    outputs = 'all'
  []
  [thermal_conductivity_correction]
    # Empirical correlation for the effects of solid and gaseous fission
    # product swelling and sodium infiltration on the thermal conductivity of
    # the fuel based on Ref. 3.
    type = ADParsedMaterial
    property_name = thermal_conductivity_correction
    material_property_names = 'k_sodium thermal_conductivity gas_porosity logged_sodium'
    expression = '(1 - 3 * ((1 - k_sodium / thermal_conductivity) / (2 / 1.72 + (3 - 2 / 1.72) * k_sodium / thermal_conductivity)) * logged_sodium / (1 - gas_porosity)) * (1 - gas_porosity)^(3 / 2)'
    outputs = 'all'
  []
  [irradiated_thermal_conductivity]
    type = ADParsedMaterial
    property_name = irradiated_thermal_conductivity
    material_property_names = 'thermal_conductivity thermal_conductivity_correction'
    expression = 'thermal_conductivity * thermal_conductivity_correction'
  []

  # Thermodynamic parameters
  [phases]
    type = ADUPuZrPhaseLookup
    phase_function_names = 'f_alpha         f_beta         f_gamma         f_delta         f_zeta'
    x_zr_eq_function_names = 'f_X_Zr_eq_alpha f_X_Zr_eq_beta f_X_Zr_eq_gamma f_X_Zr_eq_delta f_X_Zr_eq_zeta'
    x_pu_eq_function_names = 'f_X_Pu_eq_alpha f_X_Pu_eq_beta f_X_Pu_eq_gamma f_X_Pu_eq_delta f_X_Pu_eq_zeta'
    mu_function_names = 'f_mu_alpha      f_mu_beta      f_mu_gamma      f_mu_delta      f_mu_zeta'
    temperature = T
    x_pu = X_Pu
    x_zr = X_Zr
    calculate_derivatives = true # can be set to false when using PJFNK
    outputs = all
  []
  [F]
    # This material renames the chemical potential to accomodate the naming
    # scheme used in ADSplitCHParsed.
    type = ADParsedMaterial
    property_name = 'dF/dX_Zr'
    material_property_names = mu_active
    expression = mu_active
  []

  # Kinetic parameters
  [mobilities]
    type = ADUPuZrMobility
    temperature = T
  []
[]

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

[Executioner]
  type = Transient
  solve_type = NEWTON
  automatic_scaling = true
  compute_scaling_once = false
  scheme = bdf2
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  line_search = none
  l_max_its = 15
  l_tol = 1e-3
  nl_max_its = 15
  nl_rel_tol = 1e-6
  nl_abs_tol = 1e-6
  dtmin = 1e-2
  dtmax = 1e6
  end_time = 24969600
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 1e5
    iteration_window = 2
    optimal_iterations = 9
    growth_factor = 1.1
    cutback_factor = 0.5
  []
[]

[Postprocessors]
  [T_cl]
    type = PointValue
    variable = T
    point = '0 0 0'
  []
  [burnup_avg]
    type = ElementAverageValue
    variable = burnup
  []
  [porosity_avg]
    type = ElementAverageValue
    variable = porosity
  []
  [logged_sodium_avg]
    type = ElementAverageValue
    variable = logged_sodium
  []
  [gas_porosity_avg]
    type = ElementAverageValue
    variable = gas_porosity
  []
  [correction_avg]
    type = ElementAverageValue
    variable = thermal_conductivity_correction
  []
[]

[VectorPostprocessors]
  [profiles]
    type = LineValueSampler
    variable = 'T X_Pu X_Zr X_Zr_ref alpha beta gamma delta zeta'
    sort_by = x
    start_point = '0 0 0'
    end_point = '2.192e-03 0 0'
    num_points = 201
  []
[]

[Outputs]
  perf_graph = true
  exodus = true
  [console]
    type = Console
  []
  [csv]
    type = CSV
    execute_vector_postprocessors_on = final
  []
[]

Description
Example Input Syntax
Input Parameters
Input Files
References