# Hydrogen Diffusion in the Cladding

Calculates the diffusion of hydrogen in solid solution due to Fick's law and the Soret effect

## Description

Hydrogen in solid solution in zirconium will precipitate to form zirconium hydrides as the temperature of the sample is decreased. If the sample is then re-heated, dissolution will begin at a higher temperature than was required for precipitation. This hysteresis effect is due to a volumetric strain caused by mismatch of the density of the hydrides and the surrounding alloy. Thus, there are two terminal solid solubility (TSS) curves, denoted for precipitation and for dissolution. Bison uses the Arrhenius fits from McMinn et al. (2000) for and (1) Hydrogen in solid solution in zirconium diffuses under the influence of mass and temperature gradients by Fick's Law and the Soret effect, respectively. The mass flux is (2) where is the concentration of hydrogen in solid solution, is the mass diffusivity, and is the heat of transport for hydrogen in zirconium.

Bison uses and from Kammenzind et al. (1996): (3) Note that since the stoichiometry of the hydride phase is fixed, there is little or no driving force for diffusion of hydrogen in the hydrides. In addition, the diffusivity of hydrogen in hydrides has been measured to be at least 3 times smaller than the diffusivity of hydrogen in zirconium. Thus, we do not account for diffusion of hydrogen in the hydride phase in Bison.

## Example Input Syntax


[./hdiffusion] # diffusion of hydrogen by OC
type = HydrogenDiffusion
variable = Css
temp = temp
[../]
(test/tests/hydrogen/hydrogen.i)

## Input Parameters

• variableThe name of the variable that this Kernel operates on

C++ Type:NonlinearVariableName

Description:The name of the variable that this Kernel operates on

• tempCoupled Temperature

C++ Type:std::vector

Description:Coupled Temperature

### Required Parameters

• soret_scale1Soret effect scaling factor, 1 is default.

Default:1

C++ Type:double

Description:Soret effect scaling factor, 1 is default.

• soret1Soret effect switch, 1 is on (default).

Default:1

C++ Type:int

Description:Soret effect switch, 1 is on (default).

• 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

### Optional Parameters

• enableTrueSet the enabled status of the MooseObject.

Default:True

C++ Type:bool

Description:Set the enabled status of the MooseObject.

• save_inThe name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)

C++ Type:std::vector

Description:The name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)

• 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

• diag_save_inThe name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)

C++ Type:std::vector

Description:The name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)

• 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

• vector_tagsnontimeThe tag for the vectors this Kernel should fill

Default:nontime

C++ Type:MultiMooseEnum

Description:The tag for the vectors this Kernel should fill

• extra_vector_tagsThe extra tags for the vectors this Kernel should fill

C++ Type:std::vector

Description:The extra tags for the vectors this Kernel should fill

• matrix_tagssystemThe tag for the matrices this Kernel should fill

Default:system

C++ Type:MultiMooseEnum

Description:The tag for the matrices this Kernel should fill

• extra_matrix_tagsThe extra tags for the matrices this Kernel should fill

C++ Type:std::vector

Description:The extra tags for the matrices this Kernel should fill