# Phase Determination for UPuZr Fuel

Property that determines the phase for a given temperature and Zr atom concentration from the pseudo-binary phase diagram for U-Pu-Zr fuel.

## 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 phases and impact on redistribution, refer to the Zirconium Redistribution page.

## Numerical Implementation in Bison

The diffusivity of zirconium in UPuZr fuel is heavily dependent on the current phase. This is true for both Fickian and Soret type diffusion. As such, it is essential to know where the current mesh point lies within the pseudo two-phase diagram as a function of temperature and zirconium concentration . This is achieved using the solubility curve solution (1) to calculate the solvus lines, typically with the default parameters, however each parameter can be set at run-time. Once each solvus line is calculated, the point described by (, ) will explicitly give the phase diagram region, either in the single phase regions (, , , ) or the two-phase regions (, ).

While determination of the phase region is important, it does not provide the necessary composition fractions of each single phase in the two-phase region. In addition, the smoothing of the diffusion coefficients and is necessary to ensure adequate convergence. As such, PhaseUPuZr explicitly tracks the fraction of each single phase type for any combination of (, ), determining each phase's contribution in the 2-phase region using the lever-rule, and artificially smoothing the transitions between phases by using an artificial smoothing width.

Two types of smoothing are required. The first occurs when the zirconium concentration is held constant, and temperature increases (or decreases) across a phase-transition line described by the transition temperatures between points A and B () and points C and D () in the simplified phase diagram. A mixing width (typically 2 K) is utilized such that if the temperature falls within of a temperature transition , the relative fraction of the upper and lower phases are smoothed across the transition region so that abrupt changes are avoided. Similar smoothing is required as temperature is held constant and moves across solvus lines. Smoothing occurs across the region of the solvus line, with typically 0.02.

After the lever rule is applied to the two-phase region and all smoothing is calculated, PhaseUPuZr returns the fraction of each single phase region at any given point. This information can then be used to calculate any phase dependent properties.

## Example Input Syntax

[./phase]
type = PhaseUPuZr
block = 0
temp = temp
X_Pu = 0.16
X_Zr = X_Zr
outputs = csv
lever_weight_coeffs = '.1 .9' # different for testing, usually '0 1'
[../]
(test/tests/phase_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

• H_values100000 -50000 -100000 -3000 Phase H values. Must have four values: Alpha, Beta, Gamma, Delta

Default:100000 -50000 -100000 -3000

C++ Type:std::vector

Description:Phase H values. Must have four values: Alpha, Beta, Gamma, Delta

• D_conc0.43Zirconium concentration at point D in the psuedo-binary phase diagram.

Default:0.43

C++ Type:double

Description:Zirconium concentration at point D in the psuedo-binary phase diagram.

• B_conc0.7Zirconium concentration at point B in the psuedo-binary phase diagram.

Default:0.7

C++ Type:double

Description:Zirconium concentration at point B in the psuedo-binary phase diagram.

• verboseFalsePrint diagnostic information

Default:False

C++ Type:bool

Description:Print diagnostic information

• calc_HTrueFlag to automatically calculate H values

Default:True

C++ Type:bool

Description:Flag to automatically calculate H values

• CD_temp923.15Material property name for the horizontal temperature line between points C and D in the pseudo-binary phase diagram.

Default:923.15

C++ Type:MaterialPropertyName

Description:Material property name for the horizontal temperature line between points C and D in the pseudo-binary phase diagram.

• lever_weight_coeffs0 1 Weighting factor coefficients (2 total) for modifying default linear lever rule in two-phase region (default: linear [0, 1])

Default:0 1

C++ Type:std::vector

Description:Weighting factor coefficients (2 total) for modifying default linear lever rule in two-phase region (default: linear [0, 1])

• lower_concentrations0.002 0.05 0.98 0.76 Lower zirconium concentration points used to calculate H values. Must have four values: Alpha, Beta, Gamma, Delta

Default:0.002 0.05 0.98 0.76

C++ Type:std::vector

Description:Lower zirconium concentration points used to calculate H values. Must have four values: Alpha, Beta, Gamma, Delta

• AB_temp868.15Material property name for the horizontal temperature line between points A and B in the pseudo-binary phase diagram.

Default:868.15

C++ Type:MaterialPropertyName

Description:Material property name for the horizontal temperature line between points A and B in the pseudo-binary phase diagram.

• A_conc0.04Zirconium concentration at point A in the psuedo-binary phase diagram.

Default:0.04

C++ Type:double

Description:Zirconium concentration at point A in the psuedo-binary phase diagram.

• temp_mixing_width2Width of mixing gap used when crossing phase boundaries by changinga temperature.

Default:2

C++ Type:double

Description:Width of mixing gap used when crossing phase boundaries by changinga temperature.

• 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.

• 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

• C_conc0.033Zirconium concentration at point C in the psuedo-binary phase diagram.

Default:0.033

C++ Type:double

Description:Zirconium concentration at point C in the psuedo-binary phase diagram.

• conc_mixing_width0.02Width of mixing gap used when crossing phase boundaries by changing Zr concentration.

Default:0.02

C++ Type:double

Description:Width of mixing gap used when crossing phase boundaries by changing Zr concentration.

• 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.

• 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