ADUPuZrPhaseLookup

Uses lookup tables to return U-Pu-Zr phase fractions, equilibrium concentrations, and chemical potentials as functions of temperature and composition.

Description

ADUPuZrPhaseLookup is part of a system used to model constituent redistribution in U-Zr and U-Pu-Zr metallic nuclear fuels. It is used in conjunction with lookup tables that describe equilibrium parameters of the fuel as functions of temperature ( $var element = document.getElementById("moose-equation-d59ec151-ad2b-4fe1-9d5e-3e1ccc79c2c7");katex.render("T", element, {displayMode:false,throwOnError:false});$ ) and the concentrations of plutonium ( $var element = document.getElementById("moose-equation-3b01f75d-0f65-4782-b15d-c884cb69203f");katex.render("X_{Pu}", element, {displayMode:false,throwOnError:false});$ ) and zirconium ( $var element = document.getElementById("moose-equation-45496b21-9737-42ef-a565-435610bcc30b");katex.render("X_{Zr}", element, {displayMode:false,throwOnError:false});$ ).

The model accounts for exactly five phases: $var element = document.getElementById("moose-equation-ba510632-c0ed-4cff-b4cf-c28ec05f527e");katex.render("\\alpha", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-1819b0d0-b19b-46e4-9531-fa918ab4c678");katex.render("\\beta", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-6aebf899-93f2-403e-9b95-5b6e4205e03f");katex.render("\\gamma", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-2e7c1326-2943-4010-aad8-187d0d536bba");katex.render("\\delta", element, {displayMode:false,throwOnError:false});$ , and $var element = document.getElementById("moose-equation-f5439156-ab92-4e60-8035-69bf510278c1");katex.render("\\zeta", element, {displayMode:false,throwOnError:false});$ . Twenty lookup tables are required to describe the equilibrium parameters of the phases. The required lookup tables include: the fraction of each phase (five total), the equilibrium concentration of zirconium in each phase (five total), the equilibrium concentration of plutonium in each phase (five total), and the chemical potential of zirconium in each phase (five total).

Due to the computational expense of generating the lookup tables, this task is performed outside of BISON using an external thermodynamic solver, e.g., ThermoCalc. The lookup tables included with BISON were generated using a thermodynamic database and the Pycalphad thermodynamic solver presented in Otis and Liu (2017). The python scripts used to build and verify the lookup tables are also included in tools/metallic (build_redistribution_tables.py and verify_redistribution_tables.py, respectively).

Existing three-dimensional functions, such as PiecewiseMultilinear, are used to read and store data from the lookup tables. These functions are supplied to ADUPuZrPhaseLookup along with three variables or auxvariables that represent $var element = document.getElementById("moose-equation-0fdefd26-6970-4a67-8963-6edb1f52be4e");katex.render("T", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-c806a40f-f326-4324-92d6-c6403dbd5585");katex.render("X_{Pu}", element, {displayMode:false,throwOnError:false});$ , and $var element = document.getElementById("moose-equation-82bf45e4-a272-48d7-97f5-e881c2c78659");katex.render("X_{Zr}", element, {displayMode:false,throwOnError:false});$ . $var element = document.getElementById("moose-equation-8be64e1c-1277-4310-b22f-6479067e003a");katex.render("T", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-4accd2c1-985f-435c-8fae-8f4d636daff0");katex.render("X_{Pu}", element, {displayMode:false,throwOnError:false});$ , and $var element = document.getElementById("moose-equation-6e77d654-bb50-4a86-b142-eeea54af7657");katex.render("X_{Zr}", element, {displayMode:false,throwOnError:false});$ are mapped to $var element = document.getElementById("moose-equation-a0789f4f-1e04-40e4-874e-81576fb55d6b");katex.render("x", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-7c915e10-5323-4178-85fc-339f7f0c4527");katex.render("y", element, {displayMode:false,throwOnError:false});$ , and $var element = document.getElementById("moose-equation-6c2b15c3-7c5b-4669-9492-eedb15458a77");katex.render("z", element, {displayMode:false,throwOnError:false});$ to sample the data stored in the functions. Temperature should be supplied in (K) and concentration should be supplied in (mol-fraction). One function must be defined for each of the required twenty lookup tables.

An optional temperature bias ( $var element = document.getElementById("moose-equation-1ae84a8a-4988-4fe2-81ec-2088bcce8227");katex.render("T_{bias}", element, {displayMode:false,throwOnError:false});$ ) can be specified to manipulate sampling of the lookup tables. When specified, the lookup tables will be sampled at $var element = document.getElementById("moose-equation-ef47a4f8-70b3-4786-9fc0-0789e517af99");katex.render("T = T + T_{bias}", element, {displayMode:false,throwOnError:false});$ . Arbitrary dependencies can be built into the temperature bias through parsed materials, but care must be taken to ensure that the appropriate derivatives are passed through the Automatic Differentiation system.

ADUPuZrPhaseLookup evaluates the functions at the specified values and stores the results as material properties. These material properties can then be used to define phase-specific diffusion parameters in ADUPuZrMobility for modeling of constituent redistribution. The material properties could also be used to define phase-specific thermal or mechanical properties for other applications.

ADUPuZrPhaseLookup also calculates a unique numerical code to represent regions with different combinations of stable phases. Each phase is assigned an integer, as shown in Table 1. The phase region code at each location within the domain is the sum of the integers of all the phases that have a stable phase fraction greater than one percent at that location. For example, a mixture of alpha and delta would have a phase region code of nine. The resulting material property can be used to visualize how phase stabilities vary over a problem domain.

Table 1: Integers assigned to each phase, which are used to define a phase region code for visualization of phase stabilities.

Phase	Integer
$var element = document.getElementById("moose-equation-817aafce-742a-4fc6-8061-87f5c694ca65");katex.render("\\alpha", element, {displayMode:false,throwOnError:false});$	1
$var element = document.getElementById("moose-equation-25827f4c-e60f-4940-a97f-e7cda1bccfbd");katex.render("\\beta", element, {displayMode:false,throwOnError:false});$	2
$var element = document.getElementById("moose-equation-a8bd9a8d-f84f-4628-a5a8-0d6db328103f");katex.render("\\gamma", element, {displayMode:false,throwOnError:false});$	4
$var element = document.getElementById("moose-equation-8c961d39-994e-484d-b63f-5408e2581115");katex.render("\\delta", element, {displayMode:false,throwOnError:false});$	8
$var element = document.getElementById("moose-equation-fbc86977-cd98-427f-9242-d024552c30d9");katex.render("\\zeta", element, {displayMode:false,throwOnError:false});$	16

A weighted phase region code is also available. The weighted phase region code at each location within the domain is given by the sum of the integers weighted by their associated phase fractions. The phase region code and weighted phase region code have the same value in single-phase regions but have different values in multi-phase regions. The weighted phase region code can be helpful for visualizing the contributions of individual phases within multi-phase regions.

Example Input Syntax

[Functions<<<{"href": "../../syntax/Functions/index.html"}>>>]
  [f_alpha]
    type = PiecewiseMultilinear<<<{"description": "PiecewiseMultilinear performs linear interpolation on 1D, 2D, 3D or 4D data.  The data_file specifies the axes directions and the function values.  If a point lies outside the data range, the appropriate end value is used.", "href": "../functions/PiecewiseMultilinear.html"}>>>
    data_file<<<{"description": "File holding data for use with PiecewiseMultiInterpolation.  Format: any empty line and any line beginning with # are ignored, all other lines are assumed to contain relevant information.  The file must begin with specification of the grid.  This is done through lines containing the keywords: AXIS X; AXIS Y; AXIS Z; or AXIS T.  Immediately following the keyword line must be a space-separated line of real numbers which define the grid along the specified axis.  These data must be monotonically increasing.  After all the axes and their grids have been specified, there must be a line that is DATA.  Following that line, function values are given in the correct order (they may be on individual lines, or be space-separated on a number of lines).  When the function is evaluated, f[i,j,k,l] corresponds to the i + j*Ni + k*Ni*Nj + l*Ni*Nj*Nk data value.  Here i>=0 corresponding to the index along the first AXIS, j>=0 corresponding to the index along the second AXIS, etc, and Ni = number of grid points along the first AXIS, etc."}>>> = lookup_tables/alpha_frac.txt
  []
[]

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [phases]
    type = ADUPuZrPhaseLookup<<<{"description": "Uses lookup tables to return U-Pu-Zr phase fractions, equilibrium concentrations, and chemical potentials as functions of temperature and composition.", "href": "ADUPuZrPhaseLookup.html"}>>>
    phase_function_names<<<{"description": "The names of the functions for the phase fractions of the alpha, beta, gamma, delta, and zeta phases (in that order)"}>>> = 'f_alpha         f_beta         f_gamma         f_delta         f_zeta'
    x_zr_eq_function_names<<<{"description": "The names of the functions for the equilibrium concentrations of zirconium in the alpha, beta, gamma, delta, and zeta phases (in that order)"}>>> = '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<<<{"description": "The names of the functions for the equilibrium concentrations of plutonium in the alpha, beta, gamma, delta, and zeta phases (in that order)"}>>> = '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<<<{"description": "The names of the functions for the chemical potentials of zirconium in the alpha, beta, gamma, delta, and zeta phases (in that order)"}>>> = 'f_mu_alpha      f_mu_beta      f_mu_gamma      f_mu_delta      f_mu_zeta'
    temperature<<<{"description": "The temperature variable"}>>> = T
    x_pu<<<{"description": "Plutonium atom fraction"}>>> = X_Pu
    x_zr<<<{"description": "Zirconium atom fraction"}>>> = X_Zr
    calculate_derivatives<<<{"description": "Whether to calculate AD derivatives from the lookup tables"}>>> = true # can be set to false when using PJFNK
    outputs<<<{"description": "Vector of output names where you would like to restrict the output of variables(s) associated with this object"}>>> = all
  []
[]

Input Parameters

mu_function_namesThe names of the functions for the chemical potentials of zirconium in the alpha, beta, gamma, delta, and zeta phases (in that order)
C++ Type:std::vector<FunctionName>
Unit:(no unit assumed)
Controllable:No
Description:The names of the functions for the chemical potentials of zirconium in the alpha, beta, gamma, delta, and zeta phases (in that order)
phase_function_namesThe names of the functions for the phase fractions of the alpha, beta, gamma, delta, and zeta phases (in that order)
C++ Type:std::vector<FunctionName>
Unit:(no unit assumed)
Controllable:No
Description:The names of the functions for the phase fractions of the alpha, beta, gamma, delta, and zeta phases (in that order)
temperatureThe temperature variable
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The temperature variable
x_puPlutonium atom fraction
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Plutonium atom fraction
x_pu_eq_function_namesThe names of the functions for the equilibrium concentrations of plutonium in the alpha, beta, gamma, delta, and zeta phases (in that order)
C++ Type:std::vector<FunctionName>
Unit:(no unit assumed)
Controllable:No
Description:The names of the functions for the equilibrium concentrations of plutonium in the alpha, beta, gamma, delta, and zeta phases (in that order)
x_zrZirconium atom fraction
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Zirconium atom fraction
x_zr_eq_function_namesThe names of the functions for the equilibrium concentrations of zirconium in the alpha, beta, gamma, delta, and zeta phases (in that order)
C++ Type:std::vector<FunctionName>
Unit:(no unit assumed)
Controllable:No
Description:The names of the functions for the equilibrium concentrations of zirconium in the alpha, beta, gamma, delta, and zeta phases (in that order)

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
calculate_derivativesTrueWhether to calculate AD derivatives from the lookup tables
Default:True
C++ Type:bool
Controllable:No
Description:Whether to calculate AD derivatives from the lookup tables
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
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.
temperature_bias0Value added to the temperature variable before evaluation sampling the lookup tables
Default:0
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Value added to the temperature variable before evaluation sampling the lookup tables

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/1d_thermo_composition.i)
(test/tests/ad_upuzr_phase_lookup/jacobian_test.i)
(test/tests/ad_upuzr_mobility/exact.i)
(test/tests/ad_upuzr_mobility/jacobian_test.i)
(test/tests/ad_upuzr_phase_lookup/mu_active_test.i)
(test/tests/ad_upuzr_phase_lookup/phase_region_test.i)
(test/tests/ad_upuzr_phase_lookup/3d_function_test.i)
(examples/constituent_redistribution/2d_composition.i)

References

R. Otis and Z. K. Liu. pycalphad: CALPHAD-based Computational Thermodynamics in Python. Journal of Open Research Software, 5(1):1, 2017. doi:10.5334/jors.140.

@article{otis2017,
    author = "Otis, R. and Liu, Z. K.",
    doi = "10.5334/jors.140",
    file = ":C$\backslash$:/Users/Jake/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Otis, Liu - 2017 - pycalphad CALPHAD-based Computational Thermodynamics in Python.pdf:pdf",
    journal = "Journal of Open Research Software",
    number = "1",
    pages = "1",
    title = "{pycalphad: CALPHAD-based Computational Thermodynamics in Python}",
    volume = "5",
    year = "2017"
}

(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/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/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
  []
[]

(test/tests/ad_upuzr_phase_lookup/jacobian_test.i)

# This template is to verify the accuracy of the AD Jacobian calculated by
# ADUPuZrPhaseLookup material.
#
# This tests uses the material to calculate Jacobian contributions for material
# properties generated from lookup tables.  An analytical function is used in
# place of the lookup tables to define the material properties such that
# property = f(T, X_Pu, X_Zr)

[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 = ADMatDiffusion
    variable = T
    diffusivity = alpha
  []
  [X_Zr_dt]
    type = ADTimeDerivative
    variable = X_Zr
  []
  [X_Zr_diff]
    type = ADMatDiffusion
    variable = X_Zr
    diffusivity = alpha
  []
[]

[Functions]
  [f_lookup]
    type = ParsedFunction
    expression = 'x + 2 * y + 3 * z'
  []
[]

[Materials]
  [phases]
    type = ADUPuZrPhaseLookup
    phase_function_names = 'f_lookup f_lookup f_lookup f_lookup f_lookup'
    x_zr_eq_function_names = 'f_lookup f_lookup f_lookup f_lookup f_lookup'
    x_pu_eq_function_names = 'f_lookup f_lookup f_lookup f_lookup f_lookup'
    mu_function_names = 'f_lookup f_lookup f_lookup f_lookup f_lookup'
    temperature = T
    x_pu = X_Pu
    x_zr = X_Zr
  []
[]

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

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

(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
[]

(test/tests/ad_upuzr_phase_lookup/mu_active_test.i)

# This test is to verify the implementation of ADUPuZrPhaseLookup material.
# ADUPuZrPhaseLookup material determines the active chemical potential from
# the stable phase or combination of stable phases present at each location.
#
# This test uses the material to determine the active chemical potential in
# five regions with different combinations of stable phases.
#
# point mu_active_value stable_phase(s)
# 1     1               alpha
# 2     9               alpha, delta
# 3     2               beta
# 4     10              beta, delta
# 5     8               delta

[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, 9.0,
                   if(z <= 0.5, 0.0,
                      if(z < 0.75, 10.0,
                         8.0))))'
  []
  [f_mu_alpha]
    type = ParsedFunction
    expression = 'if(z <= 0.25 & x <= 823, 1.0,
                if(z < 0.75 & x <= 823, 9.0,
                   0.0))'
  []
  [f_mu_beta]
    type = ParsedFunction
    expression = 'if(z <= 0.5 & x > 823, 2.0,
                if(z < 0.75 & x > 823, 10.0,
                   0.0))'
  []
  [f_mu_delta]
    type = ParsedFunction
    expression = 'if(z <= 0.25 & x <= 823, 0.0,
                if(z < 0.75 & x <= 823, 9.0,
                   if(z <= 0.5, 0.0,
                      if(z < 0.75, 10.0,
                         8.0))))'
  []
[]

[Materials]
  [phases]
    type = ADUPuZrPhaseLookup
    phase_function_names = 'f_alpha    f_beta    0.0 f_delta    0.0'
    x_zr_eq_function_names = '0.0        0.0       0.0 0.0        0.0'
    x_pu_eq_function_names = '0.0        0.0       0.0 0.0        0.0'
    mu_function_names = 'f_mu_alpha f_mu_beta 0.0 f_mu_delta 0.0'
    temperature = T
    x_pu = 0.0
    x_zr = X_Zr
    outputs = 'all'
    output_properties = mu_active
  []
[]

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

[Postprocessors]
  [point_1]
    type = PointValue
    variable = mu_active
    point = '0.125 0.25 0.0'
    outputs = csv
  []
  [point_2]
    type = PointValue
    variable = mu_active
    point = '0.5 0.25 0.0'
    outputs = csv
  []
  [point_3]
    type = PointValue
    variable = mu_active
    point = '0.25 0.75 0.0'
    outputs = csv
  []
  [point_4]
    type = PointValue
    variable = mu_active
    point = '0.625 0.75 0.0'
    outputs = csv
  []
  [point_5]
    type = PointValue
    variable = mu_active
    point = '0.875 0.5 0.0'
    outputs = csv
  []
[]

[Outputs]
  csv = true
[]

(test/tests/ad_upuzr_phase_lookup/phase_region_test.i)

# This test is to verify the implementation of ADUPuZrPhaseLookup material.
# ADUPuZrPhaseLookup material assigns a unique phase_region code for each
# combination of stable phases.  The spatial variation of this number can be
# used to visualize how phase stability varies between different regions of the
# problem domain.  A weighted_phase_region code is also calculated to aid in
# visualization of multi-phase regions.
#
# This test uses the material to calculate these parameters for five regions
# with different combinations of stable phases.
#
# point stable_phase(s)
# 1     alpha
# 2     alpha, delta
# 3     beta
# 4     beta, delta
# 5     delta

[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))))'
  []
[]

[Materials]
  [phases]
    type = ADUPuZrPhaseLookup
    phase_function_names = 'f_alpha f_beta  0.0 f_delta 0.0'
    x_zr_eq_function_names = '0.0     0.0     0.0 0.0     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
    outputs = 'all'
    output_properties = 'phase_regions weighted_phase_regions'
  []
[]

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

[Postprocessors]
  [unweighted_1]
    type = PointValue
    variable = phase_regions
    point = '0.125 0.25 0.0'
    outputs = csv
  []
  [unweighted_2]
    type = PointValue
    variable = phase_regions
    point = '0.5 0.25 0.0'
    outputs = csv
  []
  [unweighted_3]
    type = PointValue
    variable = phase_regions
    point = '0.25 0.75 0.0'
    outputs = csv
  []
  [unweighted_4]
    type = PointValue
    variable = phase_regions
    point = '0.625 0.75 0.0'
    outputs = csv
  []
  [unweighted_5]
    type = PointValue
    variable = phase_regions
    point = '0.875 0.5 0.0'
    outputs = csv
  []
  [weighted_1]
    type = PointValue
    variable = weighted_phase_regions
    point = '0.125 0.25 0.0'
    outputs = csv
  []
  [weighted_2]
    type = PointValue
    variable = weighted_phase_regions
    point = '0.5 0.25 0.0'
    outputs = csv
  []
  [weighted_3]
    type = PointValue
    variable = weighted_phase_regions
    point = '0.25 0.75 0.0'
    outputs = csv
  []
  [weighted_4]
    type = PointValue
    variable = weighted_phase_regions
    point = '0.625 0.75 0.0'
    outputs = csv
  []
  [weighted_5]
    type = PointValue
    variable = weighted_phase_regions
    point = '0.875 0.5 0.0'
    outputs = csv
  []
[]

[Outputs]
  csv = true
[]

(test/tests/ad_upuzr_phase_lookup/3d_function_test.i)

# This test is to verify the implementation of ADUPuZrPhaseLookup material.
# ADUPuZrPhaseLookup material accepts:
# - three-dimensional functions defined in terms of x, y, and z
# - three variables (T, X_Pu, and X_Zr)
# The material maps (T,X_Pu,X_Zr) to a three-dimensional point (x,y,z) and then
# evaluates the functions at that point.  The results are stored as material
# properties.
#
# This test uses the material to evaluate a three-dimensional analytical
# function (f_lookup) at three points defined by time-dependent values
# (T, X_Pu, and X_Zr).
# The resulting material property is then compared to the analytical solution.
#
# f_lookup = x + y^2 + z^3
# time (T,Pu,Zr) solution
# 0    (0,0,0)   0
# 1    (1,2,3)   32
# 2    (2,4,6)   234

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

[Problem]
  solve = false
[]

[AuxVariables]
  [T]
  []
  [X_Pu]
  []
  [X_Zr]
  []
[]

[AuxKernels]
  [define_T]
    type = FunctionAux
    variable = T
    function = 't'
  []
  [define_X_Pu]
    type = FunctionAux
    variable = X_Pu
    function = '2 * t'
  []
  [define_X_Zr]
    type = FunctionAux
    variable = X_Zr
    function = '3 * t'
  []
[]

[Functions]
  [f_lookup]
    type = ParsedFunction
    expression = 'x + y^2 + z^3'
  []
[]

[Materials]
  [phases]
    type = ADUPuZrPhaseLookup
    phase_function_names = 'f_lookup f_lookup f_lookup f_lookup f_lookup'
    x_zr_eq_function_names = 'f_lookup f_lookup f_lookup f_lookup f_lookup'
    x_pu_eq_function_names = 'f_lookup f_lookup f_lookup f_lookup f_lookup'
    mu_function_names = 'f_lookup f_lookup f_lookup f_lookup f_lookup'
    temperature = T
    x_pu = X_Pu
    x_zr = X_Zr
    outputs = 'all'
    output_properties = alpha
  []
[]

[Executioner]
  type = Transient
  dt = 1
  num_steps = 2
[]

[Postprocessors]
  [alpha_fraction]
    type = PointValue
    variable = alpha
    point = '0.5 0.0 0.0'
    outputs = csv
  []
[]

[Outputs]
  csv = true
[]

(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
  []
[]

Description
Example Input Syntax
Input Parameters
Input Files
References