ArrheniusDiffusionCoefMicrostructureIrradiation

Computes a two-term Arrhenius diffusion coefficient dependent on microstructure and neutron flux

Description

This material inherits from ArrheniusDiffusionCoef and computes a two-term Arrhenius diffusion coefficient that depends on the microstructure and the irradiation level (flux). The effect of microstructure and irradiation on diffusion has been investigated for Ag diffusion in SiC layer of TRISO particles in Jiang et al. (2021), Simon et al. (2022), and Aagesen et al. (2022). The diffusion coefficient is described as $var element = document.getElementById("moose-equation-2f8d1fcf-2dc7-46b8-9a1c-62f589d8dd9b");katex.render("D(T,m) = \\delta \\left(D_{th,1}(T,m) + D_{irr,1}(T,m,F) + D_{th,2}(T,m) + D_{irr,2}(T,m,F)\\right)", element, {displayMode:true,throwOnError:false});$ $var element = document.getElementById("moose-equation-e13a3cda-fad9-4b15-bfb1-f9499c7e48fa");katex.render("D_{th,i}", element, {displayMode:false,throwOnError:false});$ is the thermal contribution to the diffusion (m $var element = document.getElementById("moose-equation-a93dc8fa-89b3-4603-af3c-e20a1094928f");katex.render("^2", element, {displayMode:false,throwOnError:false});$ /s), $var element = document.getElementById("moose-equation-07a7f663-72eb-4661-8931-c5817c644a1a");katex.render("D_{irr,i}", element, {displayMode:false,throwOnError:false});$ is the irradiation-enhanced contribution to the diffusivity (m $var element = document.getElementById("moose-equation-67693c92-b651-459d-8877-2c23ddadfe6c");katex.render("^2", element, {displayMode:false,throwOnError:false});$ /s) with $var element = document.getElementById("moose-equation-686b9176-ba95-465f-a5cc-4b7397fb552b");katex.render("i=1,2", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-29aa6c47-b863-429c-a83b-3fbc521d8cd4");katex.render("m", element, {displayMode:false,throwOnError:false});$ is the microstructure variable (m), $var element = document.getElementById("moose-equation-4e6c6f9d-3b18-4b3d-a3a1-8f07a12dc017");katex.render("T", element, {displayMode:false,throwOnError:false});$ is the temperature (K), F is the flux (n/m $var element = document.getElementById("moose-equation-72a48ab1-324d-4c3d-8cd3-d4c889f800a9");katex.render("^2", element, {displayMode:false,throwOnError:false});$ /s), and $var element = document.getElementById("moose-equation-bedeeaa8-0145-4e8d-b82d-a1c48d8b003f");katex.render("\\delta", element, {displayMode:false,throwOnError:false});$ is a scalar used to scale the diffusivity to the desired value, if needed.

$var element = document.getElementById("moose-equation-29a6d479-c3d9-4498-8d2c-50c8753866e7");katex.render("D_{th,i}(T,m)", element, {displayMode:false,throwOnError:false});$ is defined as $var element = document.getElementById("moose-equation-03ea7309-d87a-473f-a273-06dafb33e323");katex.render("D_{th,i}(T,m) = \\left(D_{m,0}^i + m D_{m,1}^i \\right) \\exp\\left(-\\frac{Q_{m,0}^i + m Q_{m,1}^i }{RT}\\right),", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-ad146468-436f-4aa0-a6c1-0c28fde887a6");katex.render("\\left(D_{m,0}^i + m D_{m,1}^i \\right)", element, {displayMode:false,throwOnError:false});$ is a microstructure-dependent pre-exponential factor (m $var element = document.getElementById("moose-equation-9fdbfaea-5d2e-4460-9f60-7d3b2725ca1d");katex.render("^2", element, {displayMode:false,throwOnError:false});$ /s), $var element = document.getElementById("moose-equation-a8d5d007-2d3c-4999-9c96-353b209d61ad");katex.render("\\left(Q_{m,0}^i + m Q_{m,1}^i\\right)", element, {displayMode:false,throwOnError:false});$ is the microstructure-dependent activation energy (J/mol), and $var element = document.getElementById("moose-equation-4d5e6ee3-b443-44eb-9c60-8ca91e09985e");katex.render("R", element, {displayMode:false,throwOnError:false});$ is the universal gas constant (J/mol/K).

$var element = document.getElementById("moose-equation-55dfad2c-af77-4383-84b3-83901aae4366");katex.render("D_{irr,i}(T,m,F)", element, {displayMode:false,throwOnError:false});$ is defined as $var element = document.getElementById("moose-equation-d09e613a-f49c-4479-b0c6-21156e1e3ec7");katex.render("D_{irr,i}(T,m,F) = D_{th,i}(T,m) C_{irr,i}(T,m,F),", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-2140f7c1-7644-43f0-991e-b5fe8049db0e");katex.render("C_{irr,i}(T,m,F) = d_{irr,0}^i \\left(\\frac{F}{F_0}\\right)^{d_{irr,1}^i} \\left(1+m d_{irr,2}^i\\right) \\exp\\left(\\frac{d_{irr,3}^i}{T}\\right)", element, {displayMode:true,throwOnError:false});$ represents how irradiation affects diffusion. $var element = document.getElementById("moose-equation-18e83e83-e583-4a19-906b-2dd6d1f41283");katex.render("F_0=1", element, {displayMode:false,throwOnError:false});$ n/m $var element = document.getElementById("moose-equation-c725b904-5069-458a-a58c-74a286102687");katex.render("^2", element, {displayMode:false,throwOnError:false});$ /s ensures that $var element = document.getElementById("moose-equation-7af335ef-ebba-4661-99eb-a20edc031d06");katex.render("F/F_0", element, {displayMode:false,throwOnError:false});$ is adimensional. $var element = document.getElementById("moose-equation-934dc63c-3d75-4ccf-b3c8-08add8fb7e58");katex.render("C_{irr,i}", element, {displayMode:false,throwOnError:false});$ is therefore linearly dependent of the microstructure variable, increases exponentially with the inverse of the temperature, and evolves as a power law with respect to the flux. The coefficients $var element = document.getElementById("moose-equation-cae2d0d1-13a7-47e8-a36a-1f5ac6bca3f5");katex.render("d_{irr,j}^i", element, {displayMode:false,throwOnError:false});$ can be optimized to fit the available data. $var element = document.getElementById("moose-equation-fbd53393-3a72-40cf-bc61-9bc4e4b63140");katex.render("d_{irr,0}^i", element, {displayMode:false,throwOnError:false});$ is in (n/m $var element = document.getElementById("moose-equation-d7c0d4e7-1b41-4e91-bcd8-3d19b7c3c66a");katex.render("^2", element, {displayMode:false,throwOnError:false});$ /s) $var element = document.getElementById("moose-equation-d108c4aa-7ac3-4a60-9bae-e61b0cd5f67e");katex.render("^{-1}", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-48de3033-aeaa-4669-97a1-3a0344f9177d");katex.render("d_{irr,1}^i", element, {displayMode:false,throwOnError:false});$ is adimensional, $var element = document.getElementById("moose-equation-f371428d-0e26-4213-bb80-4c5c2300b751");katex.render("d_{irr,2}^i", element, {displayMode:false,throwOnError:false});$ is in m $var element = document.getElementById("moose-equation-3507445f-2cab-45df-a0ee-ac0b79d2a9d4");katex.render("^{-1}", element, {displayMode:false,throwOnError:false});$ , and $var element = document.getElementById("moose-equation-859fa508-1f0b-4b80-a413-ed4ca85a89e3");katex.render("d_{irr,3}^i", element, {displayMode:false,throwOnError:false});$ is in K $var element = document.getElementById("moose-equation-7380b13f-6ab9-4c62-b2fc-4d737ce05b6f");katex.render("^{-1}", element, {displayMode:false,throwOnError:false});$ .

The parameters scalar, d1, d2, d1_coef, d2_coef, q1, q2, q1_coef, q2_coef, d1_irr_0, d1_irr_1, d1_irr_2, d1_irr_3, d2_irr_0, d2_irr_1, d2_irr_2, d2_irr_3, and grain_minor_axis_length, which respectively correspond to $var element = document.getElementById("moose-equation-c61cfac4-43e0-4a46-bc23-045788a5583a");katex.render("\\delta", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-1acf637b-1117-4eac-9c48-aecd51e8ef91");katex.render("D_{m,0}^1", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-02e75c3a-7082-4877-88a2-e2c42f847674");katex.render("D_{m,0}^2", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-25d1d016-bfcf-457b-aee1-3d7b447fbcbd");katex.render("D_{m,1}^1", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-01328e3d-ea9f-40f3-907d-0fd54e50d75e");katex.render("D_{m,1}^2", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-483fb432-886c-492a-996f-e21b833b8751");katex.render("Q_{m,0}^1", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-7f9127fc-c59e-46cc-b760-801a34e9ae07");katex.render("Q_{m,0}^2", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-773cad0e-d9d3-4fff-9687-5903915858f0");katex.render("Q_{m,1}^1", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-78f6e225-48fa-4a42-96fe-b27da677773e");katex.render("Q_{m,1}^2", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-02d07fdd-19df-4479-b2e6-2908cbd88be3");katex.render("d_{irr,0}^1", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-998cfcd1-9d1f-41d7-a3fb-3cc9e78fedf1");katex.render("d_{irr,1}^1", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-8e01242b-2587-42ef-b4dc-18216e671d4c");katex.render("d_{irr,2}^1", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-991539e6-a137-4f2c-a914-494d60c8c263");katex.render("d_{irr,3}^1", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-3e369a2d-805e-4cc2-9bee-0bb5997b85ee");katex.render("d_{irr,0}^2", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-87613f98-5f1d-4e2f-816a-e9c874902069");katex.render("d_{irr,1}^2", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-72177e92-45fd-49f2-afd2-e6c4c26ab5c5");katex.render("d_{irr,2}^2", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-9c4a231d-2e8f-410d-a2f5-420c0bec9c3c");katex.render("d_{irr,3}^2", element, {displayMode:false,throwOnError:false});$ , and $var element = document.getElementById("moose-equation-4d87b73a-e050-44a0-94fd-27ffa9d107f0");katex.render("m", element, {displayMode:false,throwOnError:false});$ are declared as controllable parameters. Their values can be modified during runtime with the Controls System. Relevant values to account for microstructure and irradiation effects on Ag diffusion in SiC, derived in Jiang et al. (2021) and Simon et al. (2022), are provided in Table 1.

Table 1: Parameters values for Ag diffusion in SiC (Aagesen et al., 2022).

Parameter name in BISON	Coefficient name	Value	Units
`scalar`	$var element = document.getElementById("moose-equation-feb4bfbf-d447-4c52-9133-98e3a2c2dde0");katex.render("\\delta", element, {displayMode:false,throwOnError:false});$	10	(unitless)
`grain_minor_axis_length`	$var element = document.getElementById("moose-equation-788bb34a-7d3f-4e7a-bbe3-9901b599c25f");katex.render("m", element, {displayMode:false,throwOnError:false});$	0.3 $var element = document.getElementById("moose-equation-71a9ef92-3b0c-4953-802f-8dbcdd31abea");katex.render("\\times", element, {displayMode:false,throwOnError:false});$ 10 $var element = document.getElementById("moose-equation-b1257459-c80e-4064-8964-9310e3cba187");katex.render("^{-6}", element, {displayMode:false,throwOnError:false});$	(m)
`d1`	$var element = document.getElementById("moose-equation-aab4da57-ad05-4e28-905c-234e590873d1");katex.render("D_{m,0}^1", element, {displayMode:false,throwOnError:false});$	6.88 $var element = document.getElementById("moose-equation-36c65dfc-6461-4a31-81d0-e73366714f0e");katex.render("\\times", element, {displayMode:false,throwOnError:false});$ 10 $var element = document.getElementById("moose-equation-80844846-3bf4-41af-8cb1-9a4671c80cd2");katex.render("^{-10}", element, {displayMode:false,throwOnError:false});$	(m $var element = document.getElementById("moose-equation-f4f85d4b-b115-4954-9a15-67cc45deb46a");katex.render("^2", element, {displayMode:false,throwOnError:false});$ /s)
`d1_coef`	$var element = document.getElementById("moose-equation-f9b4c459-3fe2-489e-8893-1a3da24eb07b");katex.render("D_{m,1}^1", element, {displayMode:false,throwOnError:false});$	-5.10 $var element = document.getElementById("moose-equation-5fb27a24-c6ba-4b67-b11c-0c66106dd1ca");katex.render("\\times", element, {displayMode:false,throwOnError:false});$ 10 $var element = document.getElementById("moose-equation-ffe5c7b6-a957-4342-b540-32c159dfa711");katex.render("^{-4}", element, {displayMode:false,throwOnError:false});$	(m/s)
`q1`	$var element = document.getElementById("moose-equation-03b79bc8-5daf-4808-bc82-909037503191");katex.render("Q_{m,0}^1", element, {displayMode:false,throwOnError:false});$	211 $var element = document.getElementById("moose-equation-ee7c091b-ad2e-477b-bf35-3ac6cf72bb57");katex.render("\\times", element, {displayMode:false,throwOnError:false});$ 10 $var element = document.getElementById("moose-equation-6f976228-b6b9-4a51-a090-6824ee283125");katex.render("^3", element, {displayMode:false,throwOnError:false});$	(J/mol)
`q1_coef`	$var element = document.getElementById("moose-equation-c4fcb1d1-7df2-4490-b956-2d6466f5ffb6");katex.render("Q_{m,1}^1", element, {displayMode:false,throwOnError:false});$	3.82 $var element = document.getElementById("moose-equation-d2c9af49-9d4b-4a1d-a01e-4bb2abafb577");katex.render("\\times", element, {displayMode:false,throwOnError:false});$ 10 $var element = document.getElementById("moose-equation-ec1c8aca-82e5-4c50-a242-bb38ae503e33");katex.render("^{9}", element, {displayMode:false,throwOnError:false});$	(J/mol/m)
`d1_irr_0`	$var element = document.getElementById("moose-equation-ded712aa-8755-46c4-adb1-b0e89a84db80");katex.render("d_{irr,0}^1", element, {displayMode:false,throwOnError:false});$	2.80 $var element = document.getElementById("moose-equation-2ac1c75e-e29a-44e0-b08c-77d8e3d84c63");katex.render("\\times", element, {displayMode:false,throwOnError:false});$ 10 $var element = document.getElementById("moose-equation-3b41db92-1b07-42b4-b628-73e711e784a2");katex.render("^{-13}", element, {displayMode:false,throwOnError:false});$	(unitless)
`d1_irr_1`	$var element = document.getElementById("moose-equation-e8535c2a-9a2d-4089-8f2d-16c1cb7b2c19");katex.render("d_{irr,1}^1", element, {displayMode:false,throwOnError:false});$	0.458	(unitless)
`d1_irr_2`	$var element = document.getElementById("moose-equation-5448fbc7-7bff-49e3-9e6c-807cb3372663");katex.render("d_{irr,2}^1", element, {displayMode:false,throwOnError:false});$	8.30 $var element = document.getElementById("moose-equation-e2aac6b3-df07-4655-b14a-94dd60b2cdc9");katex.render("\\times", element, {displayMode:false,throwOnError:false});$ 10 $var element = document.getElementById("moose-equation-de6af91b-84fc-4b87-943c-9bfd8f68a9fd");katex.render("^{6}", element, {displayMode:false,throwOnError:false});$	(m $var element = document.getElementById("moose-equation-6679f50e-c0c6-4b10-90c8-2b71f48be350");katex.render("^{-1}", element, {displayMode:false,throwOnError:false});$ )
`d1_irr_3`	$var element = document.getElementById("moose-equation-fd651194-80cd-43ed-aa99-5fd4faa009e8");katex.render("d_{irr,3}^1", element, {displayMode:false,throwOnError:false});$	9.41 $var element = document.getElementById("moose-equation-a2227d40-d2f3-450d-8213-d02d58481f11");katex.render("\\times", element, {displayMode:false,throwOnError:false});$ 10 $var element = document.getElementById("moose-equation-4bdbab99-db44-4514-b9a9-bbbda0d5767c");katex.render("^{3}", element, {displayMode:false,throwOnError:false});$	(K $var element = document.getElementById("moose-equation-fa3bc300-e8fe-4584-8bca-723d46de49c5");katex.render("^{-1}", element, {displayMode:false,throwOnError:false});$ )
`d2`	$var element = document.getElementById("moose-equation-ff405c28-67f6-425c-aa87-ee434ce2a17a");katex.render("D_{m,0}^2", element, {displayMode:false,throwOnError:false});$	0	(m $var element = document.getElementById("moose-equation-7fecfb8e-9ada-49e9-85e3-bba864bad1f8");katex.render("^2", element, {displayMode:false,throwOnError:false});$ /s)
`d2_coef`	$var element = document.getElementById("moose-equation-9a346484-a141-495b-9d87-c3608a9dd551");katex.render("D_{m,1}^2", element, {displayMode:false,throwOnError:false});$	0	(m/s)
`q2`	$var element = document.getElementById("moose-equation-67198b44-a718-4d36-9ca0-067c77c0fe92");katex.render("Q_{m,0}^2", element, {displayMode:false,throwOnError:false});$	0	(J/mol)
`q2_coef`	$var element = document.getElementById("moose-equation-7fb060f6-a3b9-4b38-be6c-08bcfa59abfc");katex.render("Q_{m,1}^2", element, {displayMode:false,throwOnError:false});$	0	(J/mol/m)
`d2_irr_0`	$var element = document.getElementById("moose-equation-a43eee9d-2c8a-4cbc-b895-6ab3ac2464cd");katex.render("d_{irr,0}^2", element, {displayMode:false,throwOnError:false});$	0	(unitless)
`d2_irr_1`	$var element = document.getElementById("moose-equation-d5b97d72-4f16-496f-994c-ea1644950f91");katex.render("d_{irr,1}^2", element, {displayMode:false,throwOnError:false});$	0	(unitless)
`d2_irr_2`	$var element = document.getElementById("moose-equation-97781c89-ce32-48dd-9a65-6c0326493ff2");katex.render("d_{irr,2}^2", element, {displayMode:false,throwOnError:false});$	0	(m $var element = document.getElementById("moose-equation-7f7ed468-f9de-4bd0-aeb6-8c4b888c6f04");katex.render("^{-1}", element, {displayMode:false,throwOnError:false});$ )
`d2_irr_3`	$var element = document.getElementById("moose-equation-8c9fdeab-b775-446e-804a-e32b528a9dc7");katex.render("d_{irr,3}^2", element, {displayMode:false,throwOnError:false});$	0	(K $var element = document.getElementById("moose-equation-1adbda70-a4f4-41e4-b4cc-efa1b9317446");katex.render("^{-1}", element, {displayMode:false,throwOnError:false});$ )

Example Input Syntax

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [SiC_conc_Ag]
    type = ArrheniusDiffusionCoefMicrostructureIrradiation<<<{"description": "Computes a two-term Arrhenius diffusion coefficient dependent on microstructure and neutron flux", "href": "ArrheniusDiffusionCoefMicrostructureIrradiation.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = SiC
    scalar<<<{"description": "Scalar to multiply the diffusion coefficient (unitless)"}>>> = 10
    d1<<<{"description": "First coefficient (m**2/s)"}>>> = 6.88e-10 # m^2/s
    d1_coef<<<{"description": "Coefficient of the first coefficient (m/s)"}>>> = -5.10e-4 # m/s
    q1<<<{"description": "First activation energy (J/mol)"}>>> = 211e3 # J/mol
    q1_coef<<<{"description": "Coefficient of the first activation energy (J/mol/m)"}>>> = 3.82e9 # J/mol/m
    grain_minor_axis_length<<<{"description": "Average minor axis length of the grain (perpendicular to diffusion direction) (m)"}>>> = 0.3e-6 # m
    d1_irr_0<<<{"description": "First Arrhenius law: First coefficient for irradiation effects - scale (unitless)"}>>> = 2.80e-13 # (n/m^2/s)^-1
    d1_irr_1<<<{"description": "First Arrhenius law: Second coefficient for irradiation effects - flux (unitless)"}>>> = 0.458 # (-)
    d1_irr_2<<<{"description": "First Arrhenius law: Third coefficient for irradiation effects - grain size (1/m)"}>>> = 8.30e6 # m^-1
    d1_irr_3<<<{"description": "First Arrhenius law: Forth coefficient for irradiation effects - temperature (1/K)"}>>> = 9.41e3 # K^-1
    temperature<<<{"description": "Coupled temperature"}>>> = temperature # K
    flux<<<{"description": "Coupled flux (n/m^2/2)."}>>> = flux # n/m^2/s
    arrhenius_prpty_name<<<{"description": "Property name for the Arrhenius diffusion coefficient."}>>> = arrhenius_diffusion_coef_Ag
  []
[]

Input Parameters

d1First coefficient (m**2/s)
C++ Type:double
Unit:(no unit assumed)
Controllable:Yes
Description:First coefficient (m**2/s)
d1_coefCoefficient of the first coefficient (m/s)
C++ Type:double
Unit:(no unit assumed)
Controllable:Yes
Description:Coefficient of the first coefficient (m/s)
q1First activation energy (J/mol)
C++ Type:double
Unit:(no unit assumed)
Controllable:Yes
Description:First activation energy (J/mol)
q1_coefCoefficient of the first activation energy (J/mol/m)
C++ Type:double
Unit:(no unit assumed)
Controllable:Yes
Description:Coefficient of the first activation energy (J/mol/m)
temperatureCoupled temperature
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled temperature

Required Parameters

R8.31446Universal gas constant.
Default:8.31446
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Universal gas constant.
arrhenius_prpty_namearrhenius_diffusion_coefProperty name for the Arrhenius diffusion coefficient.
Default:arrhenius_diffusion_coef
C++ Type:std::string
Controllable:No
Description:Property name for the Arrhenius diffusion coefficient.
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
d1_irr_00First Arrhenius law: First coefficient for irradiation effects - scale (unitless)
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:Yes
Description:First Arrhenius law: First coefficient for irradiation effects - scale (unitless)
d1_irr_10First Arrhenius law: Second coefficient for irradiation effects - flux (unitless)
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:Yes
Description:First Arrhenius law: Second coefficient for irradiation effects - flux (unitless)
d1_irr_20First Arrhenius law: Third coefficient for irradiation effects - grain size (1/m)
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:Yes
Description:First Arrhenius law: Third coefficient for irradiation effects - grain size (1/m)
d1_irr_30First Arrhenius law: Forth coefficient for irradiation effects - temperature (1/K)
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:Yes
Description:First Arrhenius law: Forth coefficient for irradiation effects - temperature (1/K)
d20Second coefficient (m**2/s)
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:Yes
Description:Second coefficient (m**2/s)
d2_coef0Coefficient of the second coefficient (m/s)
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:Yes
Description:Coefficient of the second coefficient (m/s)
d2_functionFunction to be multiplied by d2
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Function to be multiplied by d2
d2_function_variableVariable to be used when evaluating d2_function. If not given, time will be used.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Variable to be used when evaluating d2_function. If not given, time will be used.
d2_irr_00Second Arrhenius law: First coefficient for irradiation effects - scale (unitless)
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:Yes
Description:Second Arrhenius law: First coefficient for irradiation effects - scale (unitless)
d2_irr_10Second Arrhenius law: Second coefficient for irradiation effects - flux (unitless)
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:Yes
Description:Second Arrhenius law: Second coefficient for irradiation effects - flux (unitless)
d2_irr_20Second Arrhenius law: Third coefficient for irradiation effects - grain size (1/m)
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:Yes
Description:Second Arrhenius law: Third coefficient for irradiation effects - grain size (1/m)
d2_irr_30Second Arrhenius law: Forth coefficient for irradiation effects - temperature (1/K)
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:Yes
Description:Second Arrhenius law: Forth coefficient for irradiation effects - temperature (1/K)
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.
fluxCoupled flux (n/m^2/2).
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled flux (n/m^2/2).
gas_constant8.31446Universal gas constant (J/mol-K)
Default:8.31446
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Universal gas constant (J/mol-K)
grain_minor_axis_length0Average minor axis length of the grain (perpendicular to diffusion direction) (m)
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:Yes
Description:Average minor axis length of the grain (perpendicular to diffusion direction) (m)
q1_functionFunction to be multiplied by q1
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Function to be multiplied by q1
q1_function_variableVariable to be used when evaluating q1_function. If not given, time will be used.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Variable to be used when evaluating q1_function. If not given, time will be used.
q20Second activation energy (J/mol)
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:Yes
Description:Second activation energy (J/mol)
q2_coef0Coefficient of the second activation energy (J/mol/m)
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:Yes
Description:Coefficient of the second activation energy (J/mol/m)
q2_functionFunction to be multiplied by q2
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Function to be multiplied by q2
q2_function_variableVariable to be used when evaluating q2_function. If not given, time will be used.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Variable to be used when evaluating q2_function. If not given, time will be used.
scalar1Scalar to multiply the diffusion coefficient (unitless)
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:Yes
Description:Scalar to multiply the diffusion coefficient (unitless)

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

(assessment/TRISO/validation/AGR-2/AGR-2_Ag_Microstructure_Irradiation.i)
(assessment/TRISO/validation/AGR-1/AGR-1_Ag_Microstructure_Irradiation.i)
(assessment/TRISO/validation/AGR-1/AGR-1_Ag_Microstructure.i)
(assessment/TRISO/validation/AGR-2/AGR-2_Ag_Microstructure.i)

References

Larry K. Aagesen, Chao Jiang, Wen Jiang, Jia-Hong Ke, Pierre-Clément A. Simon, and Lin Yang. Demonstrate improved Ag diffusion and describe the basis for Pd penetration modeling in SiC. Technical Report INL/RPT-22-02769, Idaho National Laboratory, 9 2022.

@techreport{INLRPT-22-02769,
    author = "Aagesen, Larry K. and Jiang, Chao and Jiang, Wen and Ke, Jia-Hong and Simon, Pierre-Cl\'ement A. and Yang, Lin",
    institution = "Idaho National Laboratory",
    number = "INL/RPT-22-02769",
    title = "Demonstrate improved {A}g diffusion and describe the basis for {P}d penetration modeling in {S}i{C}",
    year = "2022",
    month = "9"
}

C. Jiang, J.-H. Ke, P.-C. A. Simon, W. Jiang, and L. K. Aagesen. Atomistic and mesoscale simulations to determine effective diffusion coefficient of fission products in SiC. Technical Report INL/EXT-21-64633, Idaho National Laboratory, September 2021.

@TECHREPORT{INLEXT-21-64633,
    author = "Jiang, C. and Ke, J.-H. and Simon, P.-C. A. and Jiang, W. and Aagesen, L. K.",
    title = "Atomistic and mesoscale simulations to determine effective diffusion coefficient of fission products in {SiC}",
    year = "2021",
    number = "INL/EXT-21-64633",
    month = "September",
    publisher = "INL Technical Report",
    institution = "Idaho National Laboratory"
}

P.-C.A. Simon, L. K. Aagesen, C. Jiang, W. Jiang, and J.-H. Ke. Mechanistic calculation of the effective silver diffusion coefficient in polycrystalline silicon carbide: application to silver release in AGR-1 TRISO particles. Journal of Nuclear Materials, 563:153669, 2022. doi:10.1016/j.jnucmat.2022.153669.

@article{SIMON2022153669,
    author = "Simon, P.-C.A. and Aagesen, L. K. and Jiang, C. and Jiang, W. and Ke, J.-H.",
    title = "Mechanistic calculation of the effective silver diffusion coefficient in polycrystalline silicon carbide: Application to silver release in {AGR-1 TRISO} particles",
    journal = "Journal of Nuclear Materials",
    volume = "563",
    pages = "153669",
    year = "2022",
    issn = "0022-3115",
    doi = "10.1016/j.jnucmat.2022.153669"
}

(assessment/TRISO/validation/AGR-1/AGR-1_Ag_Microstructure_Irradiation.i)

[Variables]
  [conc_Ag]
    initial_condition = 0.0
    scaling = 1e14
  []
[]

[AuxVariables]
  [Ag_diff_coef]
    order = CONSTANT
    family = MONOMIAL
  []
  [flux]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [flux]
    type = PiecewiseLinear
    #data_file = DATA_FILE
    x_index_in_file = 0
    y_index_in_file = 5
    xy_in_file_only = false
    format = columns
  []
[]

[Kernels]
  [mass_Ag_dt]
    type = TimeDerivative
    variable = conc_Ag
  []
  [mass_Ag]
    type = ArrheniusDiffusion
    variable = conc_Ag
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
    extra_vector_tags = 'ref'
  []
  [mass_source_Ag]
    type = SpeciesSourceRate
    variable = conc_Ag
    property_name = Ag_generation
    block = 'fuel OPyC'
    extra_vector_tags = 'ref'
  []
[]

[AuxKernels]
  [Ag_diff_coef]
    type = MaterialRealAux
    variable = Ag_diff_coef
    property = arrhenius_diffusion_coef_Ag
    execute_on = timestep_end
  []
  [flux]
    type = FunctionAux
    variable = flux
    function = flux
    block = 'fuel buffer IPyC SiC OPyC'
    execute_on = timestep_begin
  []
[]

[BCs]
  [freesurf_conc_Ag]
    type = DirichletBC
    variable = conc_Ag
    boundary = exterior
    value = 0.0
  []
[]

[Materials]

  # Arrhenius diffusion coefficients for kernel, PyC, and SiC
  #   come from IAEA TECDOC-978, French parameters.
  [fuel_conc_Ag]
    type = ArrheniusDiffusionCoef
    block = fuel
    d1 = 6.7e-9               # m^2/s
    q1 = 165e3                # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
  []
  [mass_source_Ag_property]
    type = SpeciesSourceMaterial
    property_name = Ag_generation
    kind = Ag
    block = fuel
  []

### Buffer Properties

  [buffer_conc_Ag]
    type = ArrheniusDiffusionCoef
    block = buffer
    d1 = 1e-8             # m^2/s
    q1 = 0.0
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
  []

### IPyC  properties

  [IPyC_conc_Ag]
    type = ArrheniusDiffusionCoef
    block = IPyC
    d1 = 5.3e-9                   # m^2/s
    q1 = 154e3                    # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
  []

### SiC properties

  [SiC_conc_Ag]
    type = ArrheniusDiffusionCoefMicrostructureIrradiation
    block = SiC
    scalar = 10
    d1 = 6.88e-10                     # m^2/s
    d1_coef = -5.10e-4                # m/s
    q1 = 211e3                        # J/mol
    q1_coef = 3.82e9                  # J/mol/m
    grain_minor_axis_length = 0.3e-6  # m
    d1_irr_0 = 2.80e-13               # (n/m^2/s)^-1
    d1_irr_1 = 0.458                  # (-)
    d1_irr_2 = 8.30e6                 # m^-1
    d1_irr_3 = 9.41e3                 # K^-1
    temperature = temperature         # K
    flux = flux                       # n/m^2/s
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
  []

###  OPyC properties

  [OPyC_conc_Ag]
    type = ArrheniusDiffusionCoef
    block = OPyC
    d1 = 5.3e-9                   # m^2/s
    q1 = 154e3                    # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
  []
  [mass_source_Ag_property_OPyC]
    type = SpeciesSourceMaterial
    property_name = Ag_generation
    kind = Ag
    block = OPyC
    #value = impurities * vol_kernel / vol_opyc
    #value = 1.59e-6 * 4.07e-11 / 9.16e-11 # for UCO
    #value = 1.57e-6 * 6.85e-11 / 1.18e-10 # for UO2
    value = ${mass_source_property_OPyC}
  []
[]

[Postprocessors]
  [release_Ag_inc]
    type = SideIntegralMassFlux
    variable = conc_Ag
    boundary = exterior
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
    execute_on = 'initial timestep_end'
  []
  [released_Ag]
    type = TimeIntegratedPostprocessor
    value = release_Ag_inc
    execute_on = 'initial timestep_end'
  []
  [total_Ag]
    type = ElementIntegralMaterialProperty
    mat_prop = Ag_generation_total
    block = 'fuel OPyC'
    execute_on = 'initial timestep_end'
  []
  [x_Ag_released]
    type = FractionalRelease
    released = released_Ag
    total = total_Ag
    execute_on = 'initial timestep_end'
  []
  [x_Ag_released_safety]
    type = FractionalRelease
    released = released_Ag
    total = total_Ag
    execute_on = 'initial timestep_end'
    start_time = 55209600
    safety_fraction_type = net
  []
  [retained_Ag]
    type = ElementIntegralVariablePostprocessor
    variable = conc_Ag
    execute_on = 'initial timestep_end'
  []
[]

(assessment/TRISO/validation/AGR-2/AGR-2_Ag_Microstructure_Irradiation.i)

[Variables]
  [conc_Ag]
    initial_condition = 0.0
  []
[]

[AuxVariables]
  [Ag_diff_coef]
    order = CONSTANT
    family = MONOMIAL
  []
  [flux]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [flux]
    type = PiecewiseLinear
    #data_file = DATA_FILE
    x_index_in_file = 0
    y_index_in_file = 5
    xy_in_file_only = false
    format = columns
  []
[]

[Kernels]
  [mass_Ag_dt]
    type = TimeDerivative
    variable = conc_Ag
  []
  [mass_Ag]
    type = ArrheniusDiffusion
    variable = conc_Ag
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
    extra_vector_tags = 'ref'
  []
  [mass_source_Ag]
    type = SpeciesSourceRate
    variable = conc_Ag
    property_name = Ag_generation
    block = 'fuel OPyC'
    extra_vector_tags = 'ref'
  []
[]

[AuxKernels]
  [Ag_diff_coef]
    type = MaterialRealAux
    variable = Ag_diff_coef
    property = arrhenius_diffusion_coef_Ag
    execute_on = timestep_end
  []
  [flux]
    type = FunctionAux
    variable = flux
    function = flux
    block = 'fuel buffer IPyC SiC OPyC'
    execute_on = timestep_begin
  []
[]

[BCs]
  [freesurf_conc_Ag]
    type = DirichletBC
    variable = conc_Ag
    boundary = exterior
    value = 0.0
  []
[]

[Materials]

  # Arrhenius diffusion coefficients for kernel, PyC, and SiC
  #   come from IAEA TECDOC-978, French parameters.
  [fuel_conc_Ag]
    type = ArrheniusDiffusionCoef
    block = fuel
    d1 = 6.7e-9 # m^2/s
    q1 = 165e3 # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
  []
  [mass_source_Ag_property]
    type = SpeciesSourceMaterial
    property_name = Ag_generation
    kind = Ag
    block = fuel
  []

  ### Buffer Properties

  [buffer_conc_Ag]
    type = ArrheniusDiffusionCoef
    block = buffer
    d1 = 1e-8 # m^2/s
    q1 = 0.0
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
  []

  ### IPyC  properties

  [IPyC_conc_Ag]
    type = ArrheniusDiffusionCoef
    block = IPyC
    d1 = 5.3e-9 # m^2/s
    q1 = 154e3 # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
  []

  ### SiC properties

  [SiC_conc_Ag]
    type = ArrheniusDiffusionCoefMicrostructureIrradiation
    block = SiC
    scalar = 10
    d1 = 6.88e-10 # m^2/s
    d1_coef = -5.10e-4 # m/s
    q1 = 211e3 # J/mol
    q1_coef = 3.82e9 # J/mol/m
    grain_minor_axis_length = 0.4e-6 # m
    d1_irr_0 = 2.80e-13 # (n/m^2/s)^-1
    d1_irr_1 = 0.458 # (-)
    d1_irr_2 = 8.30e6 # m^-1
    d1_irr_3 = 9.41e3 # K^-1
    temperature = temperature # K
    flux = flux # n/m^2/s
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
  []

  ###  OPyC properties

  [OPyC_conc_Ag]
    type = ArrheniusDiffusionCoef
    block = OPyC
    d1 = 5.3e-9 # m^2/s
    q1 = 154e3 # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
  []
  [mass_source_Ag_property_OPyC]
    type = SpeciesSourceMaterial
    property_name = Ag_generation
    kind = Ag
    block = OPyC
    #value = impurities * vol_kernel / vol_opyc
    #value = 1.59e-6 * 4.07e-11 / 9.16e-11 # for UCO
    #value = 1.57e-6 * 6.85e-11 / 1.18e-10 # for UO2
    value = ${mass_source_property_OPyC}
  []
[]

[Postprocessors]
  [release_Ag_inc]
    type = SideIntegralMassFlux
    variable = conc_Ag
    boundary = exterior
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
    execute_on = 'initial timestep_end'
  []
  [released_Ag]
    type = TimeIntegratedPostprocessor
    value = release_Ag_inc
    execute_on = 'initial timestep_end'
  []
  [total_Ag]
    type = ElementIntegralMaterialProperty
    mat_prop = Ag_generation_total
    block = 'fuel OPyC'
    execute_on = 'initial timestep_end'
  []
  [x_Ag_released]
    type = FractionalRelease
    released = released_Ag
    total = total_Ag
    execute_on = 'initial timestep_end'
  []
  [x_Ag_released_safety]
    type = FractionalRelease
    released = released_Ag
    total = total_Ag
    execute_on = 'initial timestep_end'
    start_time = 55209600
    safety_fraction_type = net
  []
  [retained_Ag]
    type = ElementIntegralVariablePostprocessor
    variable = conc_Ag
    execute_on = 'initial timestep_end'
  []
[]

(assessment/TRISO/validation/AGR-1/AGR-1_Ag_Microstructure_Irradiation.i)

[Variables]
  [conc_Ag]
    initial_condition = 0.0
    scaling = 1e14
  []
[]

[AuxVariables]
  [Ag_diff_coef]
    order = CONSTANT
    family = MONOMIAL
  []
  [flux]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [flux]
    type = PiecewiseLinear
    #data_file = DATA_FILE
    x_index_in_file = 0
    y_index_in_file = 5
    xy_in_file_only = false
    format = columns
  []
[]

[Kernels]
  [mass_Ag_dt]
    type = TimeDerivative
    variable = conc_Ag
  []
  [mass_Ag]
    type = ArrheniusDiffusion
    variable = conc_Ag
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
    extra_vector_tags = 'ref'
  []
  [mass_source_Ag]
    type = SpeciesSourceRate
    variable = conc_Ag
    property_name = Ag_generation
    block = 'fuel OPyC'
    extra_vector_tags = 'ref'
  []
[]

[AuxKernels]
  [Ag_diff_coef]
    type = MaterialRealAux
    variable = Ag_diff_coef
    property = arrhenius_diffusion_coef_Ag
    execute_on = timestep_end
  []
  [flux]
    type = FunctionAux
    variable = flux
    function = flux
    block = 'fuel buffer IPyC SiC OPyC'
    execute_on = timestep_begin
  []
[]

[BCs]
  [freesurf_conc_Ag]
    type = DirichletBC
    variable = conc_Ag
    boundary = exterior
    value = 0.0
  []
[]

[Materials]

  # Arrhenius diffusion coefficients for kernel, PyC, and SiC
  #   come from IAEA TECDOC-978, French parameters.
  [fuel_conc_Ag]
    type = ArrheniusDiffusionCoef
    block = fuel
    d1 = 6.7e-9               # m^2/s
    q1 = 165e3                # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
  []
  [mass_source_Ag_property]
    type = SpeciesSourceMaterial
    property_name = Ag_generation
    kind = Ag
    block = fuel
  []

### Buffer Properties

  [buffer_conc_Ag]
    type = ArrheniusDiffusionCoef
    block = buffer
    d1 = 1e-8             # m^2/s
    q1 = 0.0
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
  []

### IPyC  properties

  [IPyC_conc_Ag]
    type = ArrheniusDiffusionCoef
    block = IPyC
    d1 = 5.3e-9                   # m^2/s
    q1 = 154e3                    # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
  []

### SiC properties

  [SiC_conc_Ag]
    type = ArrheniusDiffusionCoefMicrostructureIrradiation
    block = SiC
    scalar = 10
    d1 = 6.88e-10                     # m^2/s
    d1_coef = -5.10e-4                # m/s
    q1 = 211e3                        # J/mol
    q1_coef = 3.82e9                  # J/mol/m
    grain_minor_axis_length = 0.3e-6  # m
    d1_irr_0 = 2.80e-13               # (n/m^2/s)^-1
    d1_irr_1 = 0.458                  # (-)
    d1_irr_2 = 8.30e6                 # m^-1
    d1_irr_3 = 9.41e3                 # K^-1
    temperature = temperature         # K
    flux = flux                       # n/m^2/s
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
  []

###  OPyC properties

  [OPyC_conc_Ag]
    type = ArrheniusDiffusionCoef
    block = OPyC
    d1 = 5.3e-9                   # m^2/s
    q1 = 154e3                    # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
  []
  [mass_source_Ag_property_OPyC]
    type = SpeciesSourceMaterial
    property_name = Ag_generation
    kind = Ag
    block = OPyC
    #value = impurities * vol_kernel / vol_opyc
    #value = 1.59e-6 * 4.07e-11 / 9.16e-11 # for UCO
    #value = 1.57e-6 * 6.85e-11 / 1.18e-10 # for UO2
    value = ${mass_source_property_OPyC}
  []
[]

[Postprocessors]
  [release_Ag_inc]
    type = SideIntegralMassFlux
    variable = conc_Ag
    boundary = exterior
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
    execute_on = 'initial timestep_end'
  []
  [released_Ag]
    type = TimeIntegratedPostprocessor
    value = release_Ag_inc
    execute_on = 'initial timestep_end'
  []
  [total_Ag]
    type = ElementIntegralMaterialProperty
    mat_prop = Ag_generation_total
    block = 'fuel OPyC'
    execute_on = 'initial timestep_end'
  []
  [x_Ag_released]
    type = FractionalRelease
    released = released_Ag
    total = total_Ag
    execute_on = 'initial timestep_end'
  []
  [x_Ag_released_safety]
    type = FractionalRelease
    released = released_Ag
    total = total_Ag
    execute_on = 'initial timestep_end'
    start_time = 55209600
    safety_fraction_type = net
  []
  [retained_Ag]
    type = ElementIntegralVariablePostprocessor
    variable = conc_Ag
    execute_on = 'initial timestep_end'
  []
[]

(assessment/TRISO/validation/AGR-1/AGR-1_Ag_Microstructure.i)

[Variables]
  [conc_Ag]
    initial_condition = 0.0
    scaling = 1e14
  []
[]

[AuxVariables]
  [Ag_diff_coef]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Kernels]
  [mass_Ag_dt]
    type = TimeDerivative
    variable = conc_Ag
  []
  [mass_Ag]
    type = ArrheniusDiffusion
    variable = conc_Ag
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
    extra_vector_tags = 'ref'
  []
  [mass_source_Ag]
    type = SpeciesSourceRate
    variable = conc_Ag
    property_name = Ag_generation
    block = 'fuel OPyC'
    extra_vector_tags = 'ref'
  []
[]

[AuxKernels]
  [Ag_diff_coef]
    type = MaterialRealAux
    variable = Ag_diff_coef
    property = arrhenius_diffusion_coef_Ag
    execute_on = timestep_end
  []
[]

[BCs]
  [freesurf_conc_Ag]
    type = DirichletBC
    variable = conc_Ag
    boundary = exterior
    value = 0.0
  []
[]

[Materials]

  # Arrhenius diffusion coefficients for kernel, PyC, and SiC
  #   come from IAEA TECDOC-978, French parameters.
  [fuel_conc_Ag]
    type = ArrheniusDiffusionCoef
    block = fuel
    d1 = 6.7e-9               # m^2/s
    q1 = 165e3                # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
  []
  [mass_source_Ag_property]
    type = SpeciesSourceMaterial
    property_name = Ag_generation
    kind = Ag
    block = fuel
  []

### Buffer Properties

  [buffer_conc_Ag]
    type = ArrheniusDiffusionCoef
    block = buffer
    d1 = 1e-8             # m^2/s
    q1 = 0.0
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
  []

### IPyC  properties

  [IPyC_conc_Ag]
    type = ArrheniusDiffusionCoef
    block = IPyC
    d1 = 5.3e-9                   # m^2/s
    q1 = 154e3                    # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
  []

### SiC properties

  [SiC_conc_Ag]
    type = ArrheniusDiffusionCoefMicrostructureIrradiation
    block = SiC
    scalar = 10
    d1 = 6.88e-10                     # m^2/s
    d1_coef = -5.10e-4                # m/s
    q1 = 211e3                        # J/mol
    q1_coef = 3.82e9                  # J/mol/m
    grain_minor_axis_length = 0.3e-6  # m
    temperature = temperature         # K
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
  []

###  OPyC properties

  [OPyC_conc_Ag]
    type = ArrheniusDiffusionCoef
    block = OPyC
    d1 = 5.3e-9                   # m^2/s
    q1 = 154e3                    # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
  []
  [mass_source_Ag_property_OPyC]
    type = SpeciesSourceMaterial
    property_name = Ag_generation
    kind = Ag
    block = OPyC
    #value = impurities * vol_kernel / vol_opyc
    #value = 1.59e-6 * 4.07e-11 / 9.16e-11 # for UCO
    #value = 1.57e-6 * 6.85e-11 / 1.18e-10 # for UO2
    value = ${mass_source_property_OPyC}
  []
[]

[Postprocessors]
  [release_Ag_inc]
    type = SideIntegralMassFlux
    variable = conc_Ag
    boundary = exterior
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
    execute_on = 'initial timestep_end'
  []
  [released_Ag]
    type = TimeIntegratedPostprocessor
    value = release_Ag_inc
    execute_on = 'initial timestep_end'
  []
  [total_Ag]
    type = ElementIntegralMaterialProperty
    mat_prop = Ag_generation_total
    block = 'fuel OPyC'
    execute_on = 'initial timestep_end'
  []
  [x_Ag_released]
    type = FractionalRelease
    released = released_Ag
    total = total_Ag
    execute_on = 'initial timestep_end'
  []
  [x_Ag_released_safety]
    type = FractionalRelease
    released = released_Ag
    total = total_Ag
    execute_on = 'initial timestep_end'
    start_time = 55209600
    safety_fraction_type = net
  []
  [retained_Ag]
    type = ElementIntegralVariablePostprocessor
    variable = conc_Ag
    execute_on = 'initial timestep_end'
  []
[]

(assessment/TRISO/validation/AGR-2/AGR-2_Ag_Microstructure.i)

[Variables]
  [conc_Ag]
    initial_condition = 0.0
  []
[]

[AuxVariables]
  [Ag_diff_coef]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Kernels]
  [mass_Ag_dt]
    type = TimeDerivative
    variable = conc_Ag
  []
  [mass_Ag]
    type = ArrheniusDiffusion
    variable = conc_Ag
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
    extra_vector_tags = 'ref'
  []
  [mass_source_Ag]
    type = SpeciesSourceRate
    variable = conc_Ag
    property_name = Ag_generation
    block = 'fuel OPyC'
    extra_vector_tags = 'ref'
  []
[]

[AuxKernels]
  [Ag_diff_coef]
    type = MaterialRealAux
    variable = Ag_diff_coef
    property = arrhenius_diffusion_coef_Ag
    execute_on = timestep_end
  []
[]

[BCs]
  [freesurf_conc_Ag]
    type = DirichletBC
    variable = conc_Ag
    boundary = exterior
    value = 0.0
  []
[]

[Materials]

  # Arrhenius diffusion coefficients for kernel, PyC, and SiC
  #   come from IAEA TECDOC-978, French parameters.
  [fuel_conc_Ag]
    type = ArrheniusDiffusionCoef
    block = fuel
    d1 = 6.7e-9               # m^2/s
    q1 = 165e3                # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
  []
  [mass_source_Ag_property]
    type = SpeciesSourceMaterial
    property_name = Ag_generation
    kind = Ag
    block = fuel
  []

### Buffer Properties

  [buffer_conc_Ag]
    type = ArrheniusDiffusionCoef
    block = buffer
    d1 = 1e-8             # m^2/s
    q1 = 0.0
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
  []

### IPyC  properties

  [IPyC_conc_Ag]
    type = ArrheniusDiffusionCoef
    block = IPyC
    d1 = 5.3e-9                   # m^2/s
    q1 = 154e3                    # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
  []

### SiC properties

  [SiC_conc_Ag]
    type = ArrheniusDiffusionCoefMicrostructureIrradiation
    block = SiC
    scalar = 10
    d1 = 6.88e-10                     # m^2/s
    d1_coef = -5.10e-4                # m/s
    q1 = 211e3                        # J/mol
    q1_coef = 3.82e9                  # J/mol/m
    grain_minor_axis_length = 0.4e-6  # m
    temperature = temperature         # K
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
  []

###  OPyC properties

  [OPyC_conc_Ag]
    type = ArrheniusDiffusionCoef
    block = OPyC
    d1 = 5.3e-9                   # m^2/s
    q1 = 154e3                    # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
  []
  [mass_source_Ag_property_OPyC]
    type = SpeciesSourceMaterial
    property_name = Ag_generation
    kind = Ag
    block = OPyC
    #value = impurities * vol_kernel / vol_opyc
    #value = 1.59e-6 * 4.07e-11 / 9.16e-11 # for UCO
    #value = 1.57e-6 * 6.85e-11 / 1.18e-10 # for UO2
    value = ${mass_source_property_OPyC}
  []
[]

[Postprocessors]
  [release_Ag_inc]
    type = SideIntegralMassFlux
    variable = conc_Ag
    boundary = exterior
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
    execute_on = 'initial timestep_end'
  []
  [released_Ag]
    type = TimeIntegratedPostprocessor
    value = release_Ag_inc
    execute_on = 'initial timestep_end'
  []
  [total_Ag]
    type = ElementIntegralMaterialProperty
    mat_prop = Ag_generation_total
    block = 'fuel OPyC'
    execute_on = 'initial timestep_end'
  []
  [x_Ag_released]
    type = FractionalRelease
    released = released_Ag
    total = total_Ag
    execute_on = 'initial timestep_end'
  []
  [x_Ag_released_safety]
    type = FractionalRelease
    released = released_Ag
    total = total_Ag
    execute_on = 'initial timestep_end'
    start_time = 50284800
    safety_fraction_type = net
  []
  [retained_Ag]
    type = ElementIntegralVariablePostprocessor
    variable = conc_Ag
    execute_on = 'initial timestep_end'
  []
[]

Description
Example Input Syntax
Input Parameters
Input Files
References