# Zirconium Diffusivities

Property that determines Fickian and Soret Diffusivity.

## Description

Zirconium redistribution in U-Zr and U-Pu-Zr based fuels impacts both fuel mechanical and thermal performance. For the detailed theoretical information of the calculation of the UPuZr phase diffusivity and impact on redistribution, refer to the Zirconium Redistribution page.

## Numerical Implementation in Bison

Using the phase fractions calculated in PhaseUPuZr, ZrDiffusivityUPuZr calculates the Fickian and Soret diffusion coefficients using (1) The artificial two-phase diffusivity parameter is used to set the diffusivity in the two-phase regions, and is typically set to . A scalar factor is also included to tune the diffusivities within each phase. It should be noted that is multiplied against all diffusivity values, including the Soret calculation, except for the artificial two-phase regions. In these regions, the only scalar utilized is the values.

## Example Input Syntax


[./zr_diff]
type = ZrDiffusivityUPuZr
block = 0
temp = temp
X_Pu = 0.16
X_Zr = X_Zr
outputs = csv
#output_properties = ''
[../]
(test/tests/zrdiffusivity_upuzr/patch.i)

## Input Parameters

• X_ZrCoupled zirconium atom fraction.

C++ Type:std::vector

Description:Coupled zirconium atom fraction.

• tempCoupled temperature.

C++ Type:std::vector

Description:Coupled temperature.

• X_PuCoupled plutonium atom fraction.

C++ Type:std::vector

Description:Coupled plutonium atom fraction.

### Required Parameters

• Qstar_gamma-200000Gamma phase heat of transport

Default:-200000

C++ Type:double

Description:Gamma phase heat of transport

• p_beta0.2Artificial diffusion coefficient for beta phase

Default:0.2

C++ Type:double

Description:Artificial diffusion coefficient for beta phase

• computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the Material via MaterialPropertyInterface::getMaterial(). Non-computed Materials are not sorted for dependencies.

Default:True

C++ Type:bool

Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the Material via MaterialPropertyInterface::getMaterial(). Non-computed Materials are not sorted for dependencies.

• Q_scale_gamma1Beta diffusion activation energy multiplier

Default:1

C++ Type:double

Description:Beta diffusion activation energy multiplier

• Qstar_alpha200000Alpha phase heat of transport

Default:200000

C++ Type:double

Description:Alpha phase heat of transport

• Qstar_beta450000Beta phase heat of transport

Default:450000

C++ Type:double

Description:Beta phase heat of transport

• D0_scale_alpha1Alpha diffusion coefficient multiplier

Default:1

C++ Type:double

Description:Alpha diffusion coefficient multiplier

• Q_scale_beta1Delta diffusion activation energy multiplier

Default:1

C++ Type:double

Description:Delta diffusion activation energy multiplier

• p_gamma0.2Artificial diffusion coefficient for gamma phase

Default:0.2

C++ Type:double

Description:Artificial diffusion coefficient for gamma phase

• p_delta0.2Artificial diffusion coefficient for delta phase

Default:0.2

C++ Type:double

Description:Artificial diffusion coefficient for delta phase

• D0_scale_gamma1Beta diffusion coefficient multiplier

Default:1

C++ Type:double

Description:Beta diffusion coefficient multiplier

• verboseFalsePrint diagnostic information

Default:False

C++ Type:bool

Description:Print diagnostic information

• D0_scale_delta1Gamma diffusion coefficient multiplier

Default:1

C++ Type:double

Description:Gamma diffusion coefficient multiplier

• Qstar_delta160000Delta phase heat of transport

Default:160000

C++ Type:double

Description:Delta phase heat of transport

• D0_scale_beta1Delta diffusion coefficient multiplier

Default:1

C++ Type:double

Description:Delta diffusion coefficient multiplier

• Q_scale_alpha1Alpha diffusion activation energy multiplier

Default:1

C++ Type:double

Description:Alpha diffusion activation energy multiplier

• Q_scale_delta1Gamma diffusion activation energy multiplier

Default:1

C++ Type:double

Description:Gamma diffusion activation energy multiplier

• boundaryThe list of boundary IDs from the mesh where this boundary condition applies

C++ Type:std::vector

Description:The list of boundary IDs from the mesh where this boundary condition applies

• blockThe list of block ids (SubdomainID) that this object will be applied

C++ Type:std::vector

Description:The list of block ids (SubdomainID) that this object will be applied

• p_alpha0.2Artificial diffusion coefficient for alpha phase

Default:0.2

C++ Type:double

Description:Artificial diffusion coefficient for alpha phase

### Optional Parameters

• enableTrueSet the enabled status of the MooseObject.

Default:True

C++ Type:bool

Description:Set the enabled status of the MooseObject.

• 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

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.

• control_tagsAdds user-defined labels for accessing object parameters via control logic.

C++ Type:std::vector

Description:Adds user-defined labels for accessing object parameters via control logic.

• seed0The seed for the master random number generator

Default:0

C++ Type:unsigned int

Description:The seed for the master random number generator

• implicitTrueDetermines whether this object is calculated using an implicit or explicit form

Default:True

C++ Type:bool

Description:Determines whether this object is calculated using an implicit or explicit form

• 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 computeSubdomainProperties() 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

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 computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped

• output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)

C++ Type:std::vector

Description:List of material properties, from this material, to output (outputs must also be defined to an output type)

• outputsnone Vector of output names were you would like to restrict the output of variables(s) associated with this object

Default:none

C++ Type:std::vector

Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object