InhomogeneousBulkEnergy

construction:Undocumented Class

The InhomogeneousBulkEnergy has not been documented. The content listed below should be used as a starting point for documenting the class, which includes the typical automatic documentation associated with a MooseObject; however, what is contained is ultimately determined by what is necessary to make the documentation clear for users.

Calculates an integral whose integrand is the free energy density corresponding to the disordered materials coefficients.

Overview

Example Input File Syntax

Input Parameters

polar_xThe x component of the polarization
C++ Type:std::vector<VariableName>
Controllable:No
Description:The x component of the polarization
polar_yThe y component of the polarization
C++ Type:std::vector<VariableName>
Controllable:No
Description:The y component of the polarization
xThe concentration
C++ Type:std::vector<VariableName>
Controllable:No
Description:The concentration

Required Parameters

TThe temperature
C++ Type:double
Controllable:No
Description:The temperature
alpha01The coefficients of the Landau expansion
C++ Type:double
Controllable:No
Description:The coefficients of the Landau expansion
alpha011The coefficients of the Landau expansion
C++ Type:double
Controllable:No
Description:The coefficients of the Landau expansion
alpha0111The coefficients of the Landau expansion
C++ Type:double
Controllable:No
Description:The coefficients of the Landau expansion
alpha0112The coefficients of the Landau expansion
C++ Type:double
Controllable:No
Description:The coefficients of the Landau expansion
alpha012The coefficients of the Landau expansion
C++ Type:double
Controllable:No
Description:The coefficients of the Landau expansion
alpha0123The coefficients of the Landau expansion
C++ Type:double
Controllable:No
Description:The coefficients of the Landau expansion
alpha1111The coefficients of the Landau expansion
C++ Type:double
Controllable:No
Description:The coefficients of the Landau expansion
alpha1112The coefficients of the Landau expansion
C++ Type:double
Controllable:No
Description:The coefficients of the Landau expansion
alpha1122The coefficients of the Landau expansion
C++ Type:double
Controllable:No
Description:The coefficients of the Landau expansion
alpha1123The coefficients of the Landau expansion
C++ Type:double
Controllable:No
Description:The coefficients of the Landau expansion
b1The coupling coefficients to Sr concentration
C++ Type:double
Controllable:No
Description:The coupling coefficients to Sr concentration
b2The coupling coefficients to Sr concentration
C++ Type:double
Controllable:No
Description:The coupling coefficients to Sr concentration
b3The coupling coefficients to Sr concentration
C++ Type:double
Controllable:No
Description:The coupling coefficients to Sr concentration
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
execute_onTIMESTEP_ENDThe list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, ALWAYS.
Default:TIMESTEP_END
C++ Type:ExecFlagEnum
Options:NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, ALWAYS, TRANSFER
Controllable:No
Description:The list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, ALWAYS.
len_scale1the len_scale of the unit
Default:1
C++ Type:double
Controllable:No
Description:the len_scale of the unit
polar_zThe z component of the polarization
C++ Type:std::vector<VariableName>
Controllable:No
Description:The z component of the polarization
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
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.

Optional Parameters

allow_duplicate_execution_on_initialFalseIn the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
Default:False
C++ Type:bool
Controllable:No
Description:In the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
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.
execution_order_group0Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
Default:0
C++ Type:int
Controllable:No
Description:Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
force_postauxFalseForces the UserObject to be executed in POSTAUX
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in POSTAUX
force_preauxFalseForces the UserObject to be executed in PREAUX
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in PREAUX
force_preicFalseForces the UserObject to be executed in PREIC during initial setup
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in PREIC during initial setup
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
outputsVector of output names where you would like to restrict the output of variables(s) associated with this object
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
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

Input Files

(test/tests/relaxor/coor.i)

(test/tests/relaxor/coor.i)


[Mesh]
  type = GeneratedMesh
  dim = 2

  ############################################
  ##
  ##  Grid definition. Note that it should be
  ##  nJ = 2*(Jmax-Jmin) for J = x, y
  ##
  ############################################

  nx = 60
  ny = 60

  ############################################
  ##
  ## Actual spatial coordinates of mesh. 
  ## Jmax - Jmin = nJ/2 for J = x, y
  ##  
  ############################################

  xmin = -15
  xmax = 15
  ymin = -15
  ymax = 15

[]

[GlobalParams]

  len_scale = 1.0

  ############################################
  ##
  ## BST Landau coefficients from
  ## Y.H. Huang and L.-Q. Chen et al
  ##    Appl. Phys. Lett. 112, 102901 (2018)
  ##
  ############################################

                        #----------------#
                        #     Units      #
                        #----------------#
  T = 210               # Kelvin


  #concentration dependent coefficients

  alpha01 = 0.08        # nm^2 nN / aC^2
  alpha011 = -0.1154    # nm^6 nN / aC^4
  alpha012 = 0.653      # nm^6 nN / aC^4
  alpha0111 = -2.106    # nm^10 nN / aC^6
  alpha0112 = 4.091     # nm^10 nN / aC^6
  alpha0123 = -6.688    # nm^10 nN / aC^6

  #fixed coefficients 

  alpha1111 = 75.9      # nm^14 nN / aC^8
  alpha1112 = -21.93    # nm^14 nN / aC^8
  alpha1122 = -22.21    # nm^14 nN / aC^8
  alpha1123 = 24.16     # nm^14 nN / aC^8

  # coupling constants 
  b1 = -1.75
  b2 = 1.05
  b3 = 0.483

  polar_x = polar_x
  polar_y = polar_y
  polar_z = polar_z



  ############################################
  ##
  ## Fourier Noise implementation from 
  ## D. Schwen (INL) - see paper
  ##
  ############################################


  x = conc
 
  lambda = 5.0          # correlation length for random field (nm)
  range = 0.01          # variation of the Sr concentration (plus or minus)
  mid = 0.4             # nominal value of the Sr concentration field

  potential_E_int = potential_int

  seed = 1  #NOTE THAT THE SAME MESH GRID MUST BE USED WITH THE SAME PROCESSOR GROUPING ALWAYS TO COMPARE DOMAIN STRUCTURE EVOLUTION
[]


[Variables]

  [./polar_x]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = RandomIC
      min = -0.1e-5
      max = 0.1e-5
    [../]
  [../]
  [./polar_y]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = RandomIC
      min = -0.1e-5
      max = 0.1e-5
    [../]
  [../]
  [./polar_z]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = RandomIC
      min = -0.1e-5
      max = 0.1e-5
    [../]
  [../]
  [./potential_int]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Functions]
  [./fn]  
    type = SDFourierNoise

    # Note that FourierNoise automatically makes concentration periodic which in turn makes the Landau coefficients periodic.
    # This then makes the polarization periodic.

  [../]

  ##############################
  ##
  ## Define the electric field
  ## expression to be used below
  ##
  ##############################

  #[./bc_func_1]
  #  type = ParsedFunction
  #  value = 'amplitude*sin(freq*t)'
  #  vars = 'freq amplitude'
  #  vals = '${freq}  ${amplitude}'
  #[../]
[]

[AuxVariables]
  [./conc]
    order = FIRST
    family = LAGRANGE
    [./InitialCondition]
      type = FunctionIC
      function = fn
    [../]
  [../]

  #[./Ey]
  #  order = CONSTANT
  #  family = MONOMIAL
  #[../]

  [./fb]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxKernels]
 # [./cEy]
 #   type = ElecFieldAux
 #   component = 2
 #   variable = Ey
 # [../]
  [./fbk]
    type = SDBulkEnergyDensity
    variable = fb
  [../]
[]

[Materials]
  ############################################
  ##
  ## Gradient coefficients (assumed BTO) from
  ## Marton and Hlinka
  ##    Phys. Rev. B. 74, 104014, (2006)
  ##
  ############################################

  [./Landau_G]
    type = GenericConstantMaterial
    prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
    prop_values = '1.0 0.51 -0.02 0.02 0.0'
  [../]
  [./permitivitty_1]
     #NOTE: This is a static permittivity contribution from core-electrons.
     #      This effectively screens the electrostatic interactions.
     #      For BTO, this value is about 7*e_0, where e_0 is the permitivitty of the vacuum.
     #      See the brief discussion before sec. IV on pp. 4 of Phys. Rev. B. 74, 104014, (2006)
    type = GenericConstantMaterial
    prop_names = 'permittivity'
    prop_values = '0.0637501464'
  [../]
[]


[Kernels]

  #########################################
  ##
  ## Landau's problem (no elastic coupling:
  ##
  #########################################

  [./bed_x]
    type = InhomogeneousBulkEnergyDerivP
    variable = polar_x
    component = 0
  [../]
  [./bed_y]
    type = InhomogeneousBulkEnergyDerivP
    variable = polar_y
    component = 1
  [../]
  [./bed_z]
    type = InhomogeneousBulkEnergyDerivP
    variable = polar_z
    component = 2
  [../]
  [./walled_x]
    type = WallEnergyDerivative
    variable = polar_x
    component = 0
 [../]
 [./walled_y]
    type = WallEnergyDerivative
    variable = polar_y
    component = 1
  [../]
  [./walled_z]
     type = WallEnergyDerivative
     variable = polar_z
     component = 2
  [../]

  #########################################
  ##
  ## Poisson's equation and P*E interaction
  ##
  #########################################

  [./polar_x_electric_E]
     type = PolarElectricEStrong
     variable = potential_int
  [../]
  [./FE_E_int]
     type = Electrostatics
     variable = potential_int
  [../]
  [./polar_electric_px]
     type = PolarElectricPStrong
     variable = polar_x
     component = 0
  [../]
  [./polar_electric_py]
     type = PolarElectricPStrong
     variable = polar_y
     component = 1
  [../]
  [./polar_electric_pz]
     type = PolarElectricPStrong
     variable = polar_z
     component = 2
  [../]

  #########################################
  ##
  ## Time dependence
  ##
  #########################################

  [./polar_x_time]
     type = TimeDerivativeScaled
     variable = polar_x
     # Time scale estimate for BTO, from Hlinka (2007)
     # We use seconds here
     time_scale = 1.0
  [../]
  [./polar_y_time]
     type = TimeDerivativeScaled
     variable = polar_y
     time_scale = 1.0
  [../]
  [./polar_z_time]
     type = TimeDerivativeScaled
     variable = polar_z
     time_scale = 1.0
  [../]
[]


[BCs]

  ##############################
  ##
  ## Boundary Condition System
  ##
  ## This corresponds to a small
  ## ac field along the direction
  ## of the spontaneous polarization
  ## that was ostensibly put there
  ## by a strong dc bias.
  ##
  ##############################

  [./top_pot]
    type = DirichletBC
    variable = potential_int
    boundary = 'top'
    value = 0.0
  [../]

  [./back_pot]
    type = DirichletBC
    variable = potential_int
    boundary = 'bottom'
    value = 0.0
  [../]


  [./Periodic]
    [./xy]
      auto_direction = 'x y'
      variable = 'polar_x polar_y polar_z'
    [../]
  [../]

[]

[Postprocessors]
  [./Fgrad]
    type = WallEnergy
    execute_on = 'initial timestep_end'
  [../]

  [./Fsdbulk]
    type = InhomogeneousBulkEnergy
    execute_on = 'initial timestep_end'
    block = '0'
  [../]
  [./Ftot]
    type = LinearCombinationPostprocessor 
    pp_names = 'Fgrad Fsdbulk'
    pp_coefs = ' 1 1 ' 
    execute_on = 'initial timestep_end'
  [../]
  [./perc_change]
    type = PercentChangePostprocessor
    postprocessor = Ftot
    execute_on = 'initial timestep_end'
  [../]
[]

[UserObjects]
  [./kill]
   type = Terminator
   expression = 'perc_change <= 5.0e-5'
  [../]
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_gmres_restart  -snes_atol -ksp_rtol -pc_type'
    petsc_options_value = '    121                1e-10     1e-8     bjacobi'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  scheme = 'implicit-euler'
  dtmin = 1e-10
  dt = 3.0
  dtmax = 10.0
  num_steps = 2
[]

[Outputs]
  print_linear_residuals = false
  [./out]
    type = Exodus
    file_base = out_test
    elemental_as_nodal = true
  [../]
  [./outCSV]
    type = CSV
    new_row_tolerance = 1e-16
    file_base = out_test
  [../]
[]