This material calculates necessary parameters for the grand potential sintering model with multiple defect species coupled with electrochemistry. More...

#include <ElectrochemicalSinteringMaterial.h>

Inheritance diagram for ElectrochemicalSinteringMaterial:

[legend]

Public Types
typedef DerivativeMaterialPropertyNameInterface::SymbolName	SymbolName

Public Member Functions
	ElectrochemicalSinteringMaterial (const InputParameters &parameters)

const GenericMaterialProperty< U, is_ad > &	getDefaultMaterialProperty (const std::string &name)

const GenericMaterialProperty< U, is_ad > &	getDefaultMaterialPropertyByName (const std::string &name)

void	validateDerivativeMaterialPropertyBase (const std::string &base)

const MaterialPropertyName	derivativePropertyName (const MaterialPropertyName &base, const std::vector< SymbolName > &c) const

const MaterialPropertyName	derivativePropertyNameFirst (const MaterialPropertyName &base, const SymbolName &c1) const

const MaterialPropertyName	derivativePropertyNameSecond (const MaterialPropertyName &base, const SymbolName &c1, const SymbolName &c2) const

const MaterialPropertyName	derivativePropertyNameThird (const MaterialPropertyName &base, const SymbolName &c1, const SymbolName &c2, const SymbolName &c3) const

GenericMaterialProperty< U, is_ad > &	declarePropertyDerivative (const std::string &base, const std::vector< VariableName > &c)

GenericMaterialProperty< U, is_ad > &	declarePropertyDerivative (const std::string &base, const std::vector< SymbolName > &c)

GenericMaterialProperty< U, is_ad > &	declarePropertyDerivative (const std::string &base, const SymbolName &c1, const SymbolName &c2="", const SymbolName &c3="")

GenericMaterialProperty< U, is_ad > &	declarePropertyDerivative (const std::string &base, const std::vector< VariableName > &c)

GenericMaterialProperty< U, is_ad > &	declarePropertyDerivative (const std::string &base, const std::vector< SymbolName > &c)

GenericMaterialProperty< U, is_ad > &	declarePropertyDerivative (const std::string &base, const SymbolName &c1, const SymbolName &c2="", const SymbolName &c3="")

const GenericMaterialProperty< U, is_ad > &	getMaterialPropertyDerivative (const std::string &base, const std::vector< VariableName > &c)

const GenericMaterialProperty< U, is_ad > &	getMaterialPropertyDerivative (const std::string &base, const std::vector< SymbolName > &c)

const GenericMaterialProperty< U, is_ad > &	getMaterialPropertyDerivative (const std::string &base, const SymbolName &c1, const SymbolName &c2="", const SymbolName &c3="")

const GenericMaterialProperty< U, is_ad > &	getMaterialPropertyDerivative (const std::string &base, const SymbolName &c1, unsigned int v2, unsigned int v3=libMesh::invalid_uint)

const GenericMaterialProperty< U, is_ad > &	getMaterialPropertyDerivative (const std::string &base, unsigned int v1, unsigned int v2=libMesh::invalid_uint, unsigned int v3=libMesh::invalid_uint)

const GenericMaterialProperty< U, is_ad > &	getMaterialPropertyDerivative (const std::string &base, const std::vector< VariableName > &c)

const GenericMaterialProperty< U, is_ad > &	getMaterialPropertyDerivative (const std::string &base, const std::vector< SymbolName > &c)

const GenericMaterialProperty< U, is_ad > &	getMaterialPropertyDerivative (const std::string &base, const SymbolName &c1, const SymbolName &c2="", const SymbolName &c3="")

const GenericMaterialProperty< U, is_ad > &	getMaterialPropertyDerivative (const std::string &base, const SymbolName &c1, unsigned int v2, unsigned int v3=libMesh::invalid_uint)

const GenericMaterialProperty< U, is_ad > &	getMaterialPropertyDerivative (const std::string &base, unsigned int v1, unsigned int v2=libMesh::invalid_uint, unsigned int v3=libMesh::invalid_uint)

const GenericMaterialProperty< U, is_ad > &	getMaterialPropertyDerivativeByName (const MaterialPropertyName &base, const std::vector< VariableName > &c)

const GenericMaterialProperty< U, is_ad > &	getMaterialPropertyDerivativeByName (const MaterialPropertyName &base, const std::vector< SymbolName > &c)

const GenericMaterialProperty< U, is_ad > &	getMaterialPropertyDerivativeByName (const MaterialPropertyName &base, const SymbolName &c1, const SymbolName &c2="", const SymbolName &c3="")

const GenericMaterialProperty< U, is_ad > &	getMaterialPropertyDerivativeByName (const MaterialPropertyName &base, const std::vector< VariableName > &c)

const GenericMaterialProperty< U, is_ad > &	getMaterialPropertyDerivativeByName (const MaterialPropertyName &base, const std::vector< SymbolName > &c)

const GenericMaterialProperty< U, is_ad > &	getMaterialPropertyDerivativeByName (const MaterialPropertyName &base, const SymbolName &c1, const SymbolName &c2="", const SymbolName &c3="")

void	validateCoupling (const MaterialPropertyName &base, const std::vector< VariableName > &c, bool validate_aux=true)

void	validateCoupling (const MaterialPropertyName &base, const VariableName &c1="", const VariableName &c2="", const VariableName &c3="")

void	validateCoupling (const MaterialPropertyName &base, const std::vector< VariableName > &c, bool validate_aux=true)

void	validateCoupling (const MaterialPropertyName &base, const VariableName &c1="", const VariableName &c2="", const VariableName &c3="")

void	validateNonlinearCoupling (const MaterialPropertyName &base, const VariableName &c1="", const VariableName &c2="", const VariableName &c3="")

void	validateNonlinearCoupling (const MaterialPropertyName &base, const VariableName &c1="", const VariableName &c2="", const VariableName &c3="")

const MaterialPropertyName	propertyName (const MaterialPropertyName &base, const std::vector< SymbolName > &c) const

const MaterialPropertyName	propertyName (const MaterialPropertyName &base, const std::vector< SymbolName > &c) const

const MaterialPropertyName	propertyNameFirst (const MaterialPropertyName &base, const SymbolName &c1) const

const MaterialPropertyName	propertyNameFirst (const MaterialPropertyName &base, const SymbolName &c1) const

const MaterialPropertyName	propertyNameSecond (const MaterialPropertyName &base, const SymbolName &c1, const SymbolName &c2) const

const MaterialPropertyName	propertyNameSecond (const MaterialPropertyName &base, const SymbolName &c1, const SymbolName &c2) const

const MaterialPropertyName	propertyNameThird (const MaterialPropertyName &base, const SymbolName &c1, const SymbolName &c2, const SymbolName &c3) const

const MaterialPropertyName	propertyNameThird (const MaterialPropertyName &base, const SymbolName &c1, const SymbolName &c2, const SymbolName &c3) const

Static Public Member Functions
static InputParameters	validParams ()

Protected Member Functions
virtual void	computeQpProperties ()

Protected Attributes
const unsigned int	_neta
	number of solid phase order paramters

std::vector< const VariableValue * >	_eta
	solid phase order parameters

std::vector< VariableName >	_eta_name

const unsigned int	_ndefects
	number of defect species

std::vector< const VariableValue * >	_w
	chemical potentials for defects

std::vector< VariableName >	_w_name

const VariableValue &	_phi
	void phase order parameter

const NonlinearVariableName	_phi_name

std::vector< MaterialPropertyName >	_ns_min_names
	minima in energy wrt vacancy concentration in solid

std::vector< const MaterialProperty< Real > * >	_ns_min

std::vector< std::vector< const MaterialProperty< Real > * > >	_dns_min

std::vector< std::vector< std::vector< const MaterialProperty< Real > * > > >	_d2ns_min

const VariableValue &	_temp
	temperature

const VariableValue &	_v
	electric potential

const VariableGradient &	_grad_V
	Gradient of electric potential.

std::vector< MaterialPropertyName >	_kv_names
	Names of void energy coefficient for each defect.

std::vector< const MaterialProperty< Real > * >	_kv
	void energy coefficients for each defect

std::vector< MaterialPropertyName >	_ks_names
	Names of solid energy coefficient for each defect.

std::vector< const MaterialProperty< Real > * >	_ks
	solid energy coefficient for each defect

MaterialProperty< Real > &	_hv
	void phase switching function

MaterialProperty< Real > &	_dhv

MaterialProperty< Real > &	_d2hv

MaterialProperty< Real > &	_hs
	solid phase switching function

MaterialProperty< Real > &	_dhs

MaterialProperty< Real > &	_d2hs

MaterialProperty< Real > &	_omegav
	void phase grand potential density

std::vector< MaterialProperty< Real > * >	_domegavdw

std::vector< MaterialProperty< Real > * >	_d2omegavdw2

MaterialProperty< Real > &	_omegas
	solid phase grand potential density

std::vector< MaterialProperty< Real > * >	_domegasdw

std::vector< MaterialProperty< Real > * >	_d2omegasdw2

std::vector< MaterialProperty< Real > * >	_domegasdeta

std::vector< std::vector< MaterialProperty< Real > * > >	_d2omegasdwdeta

std::vector< std::vector< MaterialProperty< Real > * > >	_d2omegasdetadeta

MaterialProperty< Real > &	_mu
	energy barrier coefficient

MaterialProperty< Real > &	_dmu

MaterialProperty< Real > &	_d2mu

MaterialProperty< Real > &	_kappa
	gradient energy coefficient

MaterialProperty< Real > &	_dkappa

MaterialProperty< Real > &	_d2kappa

MaterialProperty< Real > &	_gamma
	interface profile coefficient

const Real	_sigma_s
	surface energy

const Real	_sigma_gb
	grain boundary energy

const Real	_int_width
	interface width

const Real	_switch
	Parameter to determine accuracy of surface/GB phase switching function.

const MooseEnum	_solid_energy
	Type of energy function to use for the solid phase.

const Real	_mu_s
	mu value on surfaces

const Real	_mu_gb
	mu value on grain boundaries

const Real	_kappa_s
	kappa value on surfaces

const Real	_kappa_gb
	kappa value on grain boundaries

const Real	_kB
	Boltzmann constant.

const Real	_e
	Electron charge.

const std::vector< int >	_z
	Defects species charges in units of e.

const Real	_v_scale
	Voltage scale.

const Real	_eps_r
	Solid phase relative permittivity.

const std::vector< Real >	_nv_min
	minima in energy wrt vacancy concentration in void

Private Member Functions
bool	haveMaterialProperty (const std::string &prop_name)

std::vector< VariableName >	buildVariableVector (const VariableName &c1, const VariableName &c2, const VariableName &c3)

void	validateCouplingHelper (const MaterialPropertyName &base, const std::vector< VariableName > &c, const System &system, std::vector< VariableName > &missing)

bool	isNotObjectVariable (const VariableName &name)

Private Attributes
FEProblemBase &	_dmi_fe_problem

Detailed Description

This material calculates necessary parameters for the grand potential sintering model with multiple defect species coupled with electrochemistry.

Definition at line 19 of file ElectrochemicalSinteringMaterial.h.

Constructor & Destructor Documentation

◆ ElectrochemicalSinteringMaterial()

ElectrochemicalSinteringMaterial::ElectrochemicalSinteringMaterial ( const InputParameters & parameters )

Definition at line 71 of file ElectrochemicalSinteringMaterial.C.

  : DerivativeMaterialInterface<Material>(parameters),
    _neta(coupledComponents("etas")),
    _eta(_neta),
    _eta_name(_neta),
    _ndefects(coupledComponents("chemical_potentials")),
    _w(coupledValues("chemical_potentials")),
    _w_name(_ndefects),
    _phi(coupledValue("void_op")),
    _phi_name(coupledName("void_op", 0)),
    _ns_min_names(getParam<std::vector<MaterialPropertyName>>("min_vacancy_concentrations_solid")),
    _ns_min(_ndefects),
    _dns_min(_ndefects),
    _d2ns_min(_ndefects),
    _temp(coupledValue("Temperature")),
    _v(coupledValue("electric_potential")),
    _grad_V(coupledGradient("electric_potential")),
    _kv_names(getParam<std::vector<MaterialPropertyName>>("void_energy_coefficients")),
    _kv(_ndefects),
    _ks_names(getParam<std::vector<MaterialPropertyName>>("solid_energy_coefficients")),
    _ks(_ndefects),
    _hv(declareProperty<Real>("hv")),
    _dhv(declarePropertyDerivative<Real>("hv", _phi_name)),
    _d2hv(declarePropertyDerivative<Real>("hv", _phi_name, _phi_name)),
    _hs(declareProperty<Real>("hs")),
    _dhs(declarePropertyDerivative<Real>("hs", _phi_name)),
    _d2hs(declarePropertyDerivative<Real>("hs", _phi_name, _phi_name)),
    _omegav(declareProperty<Real>("omegav")),
    _domegavdw(_ndefects),
    _d2omegavdw2(_ndefects),
    _omegas(declareProperty<Real>("omegas")),
    _domegasdw(_ndefects),
    _d2omegasdw2(_ndefects),
    _domegasdeta(_neta),
    _d2omegasdwdeta(_ndefects),
    _d2omegasdetadeta(_neta),
    _mu(declareProperty<Real>("mu")),
    _dmu(declarePropertyDerivative<Real>("mu", _phi_name)),
    _d2mu(declarePropertyDerivative<Real>("mu", _phi_name, _phi_name)),
    _kappa(declareProperty<Real>("kappa")),
    _dkappa(declarePropertyDerivative<Real>("kappa", _phi_name)),
    _d2kappa(declarePropertyDerivative<Real>("kappa", _phi_name, _phi_name)),
    _gamma(declareProperty<Real>("gamma")),
    _sigma_s(getParam<Real>("surface_energy")),
    _sigma_gb(getParam<Real>("grainboundary_energy")),
    _int_width(getParam<Real>("int_width")),
    _switch(getParam<Real>("surface_switch_value")),
    _solid_energy(getParam<MooseEnum>("solid_energy_model")),
    _mu_s(6.0 * _sigma_s / _int_width),
    _mu_gb(6.0 * _sigma_gb / _int_width),
    _kappa_s(0.75 * _sigma_s * _int_width),
    _kappa_gb(0.75 * _sigma_gb * _int_width),
    _kB(8.617343e-5), // eV/K
    _e(1.0),          // to put energy units in eV
    _z(getParam<std::vector<int>>("defect_charges")),
    _v_scale(getParam<Real>("voltage_scale")),
    _eps_r(getParam<Real>("solid_relative_permittivity")),
    _nv_min(getParam<std::vector<Real>>("min_vacancy_concentrations_void"))
{
  if (_ndefects != _z.size())
    paramError("defect_charges", "Need to pass in as many defect_charges as chemical_potentials");
  if (_ndefects != _ns_min_names.size())
    paramError("min_vacancy_concentrations_solid",
               "Need to pass in as many min_vacancy_concentrations_solid as chemical_potentials");
  if (_ndefects != _nv_min.size())
    paramError("min_vacancy_concentrations_void",
               "Need to pass in as many min_vacancy_concentrations_void as chemical_potentials");
  if (_ndefects != _kv_names.size())
    paramError("void_energy_coefficients",
               "Need to pass in as many void_energy_coefficients as chemical_potentials");
  if (_ndefects != _ks_names.size())
    paramError("solid_energy_coefficients",
               "Need to pass in as many solid_energy_coefficients as chemical_potentials");
 
  for (unsigned int i = 0; i < _ndefects; ++i)
  {
    _w_name[i] = coupledName("chemical_potentials", i);
    _ns_min[i] = &getMaterialPropertyByName<Real>(_ns_min_names[i]);
    _dns_min[i].resize(_neta);
    _d2ns_min[i].resize(_neta);
    _d2omegasdwdeta[i].resize(_neta);
    _kv[i] = &getMaterialPropertyByName<Real>(_kv_names[i]);
    _ks[i] = &getMaterialPropertyByName<Real>(_ks_names[i]);
    _domegavdw[i] = &declarePropertyDerivative<Real>("omegav", _w_name[i]);
    _d2omegavdw2[i] = &declarePropertyDerivative<Real>("omegav", _w_name[i], _w_name[i]);
    _domegasdw[i] = &declarePropertyDerivative<Real>("omegas", _w_name[i]);
    _d2omegasdw2[i] = &declarePropertyDerivative<Real>("omegas", _w_name[i], _w_name[i]);
    for (unsigned int j = 0; j < _neta; ++j)
    {
      _dns_min[i][j] = &getMaterialPropertyDerivativeByName<Real>(_ns_min_names[i], _eta_name[j]);
      _d2ns_min[i][j].resize(_neta);
 
      for (unsigned int k = 0; k < _neta; ++k)
        _d2ns_min[i][j][k] = &getMaterialPropertyDerivativeByName<Real>(
            _ns_min_names[i], _eta_name[j], _eta_name[k]);
    }
  }
 
  for (unsigned int i = 0; i < _neta; ++i)
  {
    _eta[i] = &coupledValue("etas", i);
    _eta_name[i] = coupledName("etas", i);
    _domegasdeta[i] = &declarePropertyDerivative<Real>("omegas", _eta_name[i]);
    _d2omegasdetadeta[i].resize(_neta);
 
    for (unsigned int j = 0; j <= i; ++j)
      _d2omegasdetadeta[j][i] = _d2omegasdetadeta[i][j] =
          &declarePropertyDerivative<Real>("omegas", _eta_name[j], _eta_name[i]);
  }
 
  for (unsigned int i = 0; i < _ndefects; ++i)
    for (unsigned int j = 0; j < _neta; ++j)
      _d2omegasdwdeta[i][j] = &declarePropertyDerivative<Real>("omegas", _w_name[i], _eta_name[j]);
}

Member Function Documentation

◆ computeQpProperties()

void ElectrochemicalSinteringMaterial::computeQpProperties ( )

protectedvirtual

Definition at line 188 of file ElectrochemicalSinteringMaterial.C.

{
  // Calculate phase switching functions
  _hv[_qp] = 0.0;
  _dhv[_qp] = 0.0;
  _d2hv[_qp] = 0.0;
 
  if (_phi[_qp] >= 1.0)
    _hv[_qp] = 1.0;
  else if (_phi[_qp] > 0.0)
  {
    _hv[_qp] = _phi[_qp] * _phi[_qp] * _phi[_qp] * (10.0 + _phi[_qp] * (-15.0 + _phi[_qp] * 6.0));
    _dhv[_qp] = 30.0 * _phi[_qp] * _phi[_qp] * (_phi[_qp] - 1.0) * (_phi[_qp] - 1.0);
    _d2hv[_qp] = 60.0 * _phi[_qp] * (2.0 * _phi[_qp] - 1.0) * (_phi[_qp] - 1.0);
  }
 
  _hs[_qp] = 1.0 - _hv[_qp];
  _dhs[_qp] = -_dhv[_qp];
  _d2hs[_qp] = -_d2hv[_qp];
 
  // Calculate interface switching function
  Real phi = _phi[_qp] / _switch;
  Real f = 0.0;
  Real df = 0.0;
  Real d2f = 0.0;
  if (phi >= 1.0)
    f = 1.0;
  else if (phi > 0.0)
  {
    f = phi * phi * phi * (10.0 + phi * (-15.0 + phi * 6.0));
    df = 30.0 / _switch * phi * phi * (phi - 1.0) * (phi - 1.0);
    d2f = 60.0 * phi / (_switch * _switch) * (2.0 * phi - 1.0) * (phi - 1.0);
  }
 
  // Permittivity in the void phase (permittivity of free space)
  Real eps_0 = 5.52e-2 * _v_scale * _v_scale; // units eV/V^2/nm, change with V_scale if needed
 
  // Calculate grand potential of void phase
  Real sum_omega_v = 0.0;
  for (unsigned int i = 0; i < _ndefects; ++i)
    sum_omega_v += -0.5 / (*_kv[i])[_qp] * ((*_w[i])[_qp] - _z[i] * _e * _v[_qp] * _v_scale) *
                       ((*_w[i])[_qp] - _z[i] * _e * _v[_qp] * _v_scale) -
                   _nv_min[i] * ((*_w[i])[_qp] - _z[i] * _e * _v[_qp] * _v_scale);
 
  _omegav[_qp] = sum_omega_v - 0.5 * eps_0 * _grad_V[_qp] * _grad_V[_qp];
 
  // Calculate derivatives of grand potential wrt chemical potential
  for (unsigned int i = 0; i < _ndefects; ++i)
  {
    (*_domegavdw[i])[_qp] =
        -((*_w[i])[_qp] - _z[i] * _e * _v[_qp] * _v_scale) / (*_kv[i])[_qp] - _nv_min[i];
    (*_d2omegavdw2[i])[_qp] = -1.0 / (*_kv[i])[_qp];
  }
 
  // Calculate solid phase density and potential
  switch (_solid_energy)
  {
    case 0: // PARABOLIC
    {
      // Calculate grand potential of solid phase and derivatives wrt chemical potentials
      Real sum_omega_s = 0.0;
      for (unsigned int i = 0; i < _ndefects; ++i)
      {
        sum_omega_s += -0.5 / (*_ks[i])[_qp] * ((*_w[i])[_qp] - _z[i] * _e * _v[_qp] * _v_scale) *
                           ((*_w[i])[_qp] - _z[i] * _e * _v[_qp] * _v_scale) -
                       (*_ns_min[i])[_qp] * ((*_w[i])[_qp] - _z[i] * _e * _v[_qp] * _v_scale);
        (*_domegasdw[i])[_qp] =
            -((*_w[i])[_qp] - _z[i] * _e * _v[_qp] * _v_scale) / (*_ks[i])[_qp] -
            (*_ns_min[i])[_qp];
        (*_d2omegasdw2[i])[_qp] = -1.0 / (*_ks[i])[_qp];
      }
 
      _omegas[_qp] = sum_omega_s - 0.5 * _eps_r * eps_0 * _grad_V[_qp] * _grad_V[_qp];
 
      // Calculate derivatives of grand potential wrt order parameters and mixed derivatives
      for (unsigned int i = 0; i < _neta; ++i)
      {
        Real sum_domegasdeta = 0.0;
        for (unsigned int j = 0; j < _ndefects; ++j)
        {
          sum_domegasdeta +=
              -(*_dns_min[j][i])[_qp] * ((*_w[j])[_qp] - _z[j] * _e * _v[_qp] * _v_scale);
          (*_d2omegasdwdeta[j][i])[_qp] = -(*_dns_min[j][i])[_qp];
        }
        (*_domegasdeta[i])[_qp] = sum_domegasdeta;
 
        for (unsigned int j = i; j < _neta; ++j)
        {
          Real sum_d2omegadeta2 = 0.0;
          for (unsigned int k = 0; k < _ndefects; ++k)
            sum_d2omegadeta2 +=
                -(*_d2ns_min[k][i][j])[_qp] * ((*_w[k])[_qp] - _z[k] * _e * _v[_qp] * _v_scale);
 
          (*_d2omegasdetadeta[i][j])[_qp] = (*_d2omegasdetadeta[j][i])[_qp] = sum_d2omegadeta2;
        }
      }
      break;
    } // case 0; // PARABOLIC
    case 1: // DILUTE
    {
      // Calculate grand potential of solid phase and derivatives wrt chemical potentials
      Real sum_omega_s = 0.0;
      for (unsigned int i = 0; i < _ndefects; ++i)
      {
        Real n_exp = std::exp(((*_w[i])[_qp] - _z[i] * _e * _v[_qp] * _v_scale) / _kB / _temp[_qp]);
        sum_omega_s += -_kB * _temp[_qp] * (*_ns_min[i])[_qp] * n_exp;
        (*_domegasdw[i])[_qp] = -(*_ns_min[i])[_qp] * n_exp;
        (*_d2omegasdw2[i])[_qp] = -(*_ns_min[i])[_qp] * n_exp / _kB / _temp[_qp];
      }
 
      _omegas[_qp] = sum_omega_s - 0.5 * _eps_r * eps_0 * _grad_V[_qp] * _grad_V[_qp];
 
      // Calculate derivatives of grand potential wrt order parameters and mixed derivatives
      for (unsigned int i = 0; i < _neta; ++i)
      {
        Real sum_domegasdeta = 0.0;
        for (unsigned int j = 0; j < _ndefects; ++j)
        {
          Real n_exp =
              std::exp(((*_w[j])[_qp] - _z[j] * _e * _v[_qp] * _v_scale) / _kB / _temp[_qp]);
          sum_domegasdeta += -_kB / _temp[_qp] * (*_dns_min[j][i])[_qp] * n_exp;
          (*_d2omegasdwdeta[j][i])[_qp] = -(*_dns_min[j][i])[_qp] * n_exp;
        }
        (*_domegasdeta[i])[_qp] = sum_domegasdeta;
 
        for (unsigned int j = i; j < _neta; ++j)
        {
          Real sum_d2omegadeta2 = 0.0;
          for (unsigned int k = 0; k < _ndefects; ++k)
          {
            Real n_exp =
                std::exp(((*_w[k])[_qp] - _z[k] * _e * _v[_qp] * _v_scale) / _kB / _temp[_qp]);
            sum_d2omegadeta2 += -_kB / _temp[_qp] * (*_d2ns_min[k][i][j])[_qp] * n_exp;
          }
 
          (*_d2omegasdetadeta[i][j])[_qp] = (*_d2omegasdetadeta[j][i])[_qp] = sum_d2omegadeta2;
        }
      }
 
      break;
    } // case 1: // DILUTE
    case 2: // IDEAL
    {
      mooseError(
          "Ideal solution in solid is not yet supported in ElectrochemicalSinteringMaterial");
      break;
    } // case 2: // IDEAL
  } // switch (_solid_energy)
 
  // thermodynamic parameters
  _mu[_qp] = _mu_gb + (_mu_s - _mu_gb) * f;
  _kappa[_qp] = _kappa_gb + (_kappa_s - _kappa_gb) * f;
  _dmu[_qp] = (_mu_s - _mu_gb) * df;
  _dkappa[_qp] = (_kappa_s - _kappa_gb) * df;
  _d2mu[_qp] = (_mu_s - _mu_gb) * d2f;
  _d2kappa[_qp] = (_kappa_s - _kappa_gb) * d2f;
  _gamma[_qp] = 1.5;
} // void ElectrochemicalSinteringMaterial::computeQpProperties()

◆ validParams()

InputParameters ElectrochemicalSinteringMaterial::validParams ( )

static

Definition at line 17 of file ElectrochemicalSinteringMaterial.C.

{
  InputParameters params = Material::validParams();
  params.addClassDescription("Includes switching and thermodynamic properties for the grand "
                             "potential sintering model coupled with electrochemistry");
  params.addRequiredCoupledVarWithAutoBuild(
      "etas", "var_name_base", "op_num", "Array of order parameters that describe solid phase");
  params.addRequiredCoupledVar("chemical_potentials",
                               "The name of the chemical potential variables for defects");
  params.addRequiredCoupledVar("void_op", "The name of the void phase order parameter");
  params.addRequiredCoupledVar("Temperature", "Name of the temperature variable with units of K");
  params.addRequiredCoupledVar("electric_potential",
                               "Name of the electric potential variable with units of V");
  params.addParam<std::vector<MaterialPropertyName>>(
      "solid_energy_coefficients",
      "Vector of parabolic solid energy coefficients (energy*volume) for "
      "each defect species. Only used for parabolic energy. Place in same order as "
      "chemical_potentials!");
  params.addRequiredParam<std::vector<MaterialPropertyName>>(
      "void_energy_coefficients",
      "Vector of parabolic void energy coefficients (energy*volume) for each defect species. Place "
      "in same order as chemical_potentials!");
  params.addParam<Real>("surface_energy", 19.7, "Surface energy in units of problem (energy/area)");
  params.addParam<Real>(
      "grainboundary_energy", 9.86, "Grain boundary energy in units of problem (energy/area)");
  params.addParam<Real>("int_width", 1, "Interface width in units of problem (length)");
  params.addRangeCheckedParam<Real>(
      "surface_switch_value",
      0.3,
      "surface_switch_value >= 0 & surface_switch_value <= 1.0",
      "Value between 0 and 1 that determines when the interface begins to switch "
      "from surface to GB. Small values give less error while large values "
      "converge better.");
  params.addRequiredParam<std::vector<MaterialPropertyName>>(
      "min_vacancy_concentrations_solid",
      "Vector of names of materials that determine the minimum in energy wrt defect concentrations "
      "in the solid phase. Place in same order as chemical_potentials!");
  params.addRequiredParam<std::vector<Real>>("min_vacancy_concentrations_void",
                                             "Vector of minima in energy wrt defect concentrations "
                                             "in the void phase. Place in same order as "
                                             "chemical_potentials!");
  MooseEnum solid_energy_model("PARABOLIC DILUTE IDEAL", "PARABOLIC");
  params.addParam<MooseEnum>("solid_energy_model",
                             solid_energy_model,
                             "Type of energy function to use for the solid phase.");
  params.addRequiredParam<std::vector<int>>(
      "defect_charges",
      "Vector of charges of defect species. Place in same order as chemical_potentials!");
  params.addRequiredParam<Real>("solid_relative_permittivity",
                                "Solid phase relative permittivity (dimensionless)");
  params.addParam<Real>("voltage_scale", 1, "Voltage scale (default is for voltage in V)");
  return params;
}

Member Data Documentation

◆ _d2hs

MaterialProperty<Real>& ElectrochemicalSinteringMaterial::_d2hs

protected

Definition at line 79 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _d2hv

MaterialProperty<Real>& ElectrochemicalSinteringMaterial::_d2hv

protected

Definition at line 74 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _d2kappa

MaterialProperty<Real>& ElectrochemicalSinteringMaterial::_d2kappa

protected

Definition at line 102 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _d2mu

MaterialProperty<Real>& ElectrochemicalSinteringMaterial::_d2mu

protected

Definition at line 97 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _d2ns_min

std::vector<std::vector<std::vector<const MaterialProperty<Real> *> > > ElectrochemicalSinteringMaterial::_d2ns_min

protected

Definition at line 51 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties(), and ElectrochemicalSinteringMaterial().

◆ _d2omegasdetadeta

std::vector<std::vector<MaterialProperty<Real> *> > ElectrochemicalSinteringMaterial::_d2omegasdetadeta

protected

Definition at line 92 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties(), and ElectrochemicalSinteringMaterial().

◆ _d2omegasdw2

std::vector<MaterialProperty<Real> *> ElectrochemicalSinteringMaterial::_d2omegasdw2

protected

Definition at line 89 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties(), and ElectrochemicalSinteringMaterial().

◆ _d2omegasdwdeta

std::vector<std::vector<MaterialProperty<Real> *> > ElectrochemicalSinteringMaterial::_d2omegasdwdeta

protected

Definition at line 91 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties(), and ElectrochemicalSinteringMaterial().

◆ _d2omegavdw2

std::vector<MaterialProperty<Real> *> ElectrochemicalSinteringMaterial::_d2omegavdw2

protected

Definition at line 84 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties(), and ElectrochemicalSinteringMaterial().

◆ _dhs

MaterialProperty<Real>& ElectrochemicalSinteringMaterial::_dhs

protected

Definition at line 78 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _dhv

MaterialProperty<Real>& ElectrochemicalSinteringMaterial::_dhv

protected

Definition at line 73 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _dkappa

MaterialProperty<Real>& ElectrochemicalSinteringMaterial::_dkappa

protected

Definition at line 101 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _dmu

MaterialProperty<Real>& ElectrochemicalSinteringMaterial::_dmu

protected

Definition at line 96 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _dns_min

std::vector<std::vector<const MaterialProperty<Real> *> > ElectrochemicalSinteringMaterial::_dns_min

protected

Definition at line 50 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties(), and ElectrochemicalSinteringMaterial().

◆ _domegasdeta

std::vector<MaterialProperty<Real> *> ElectrochemicalSinteringMaterial::_domegasdeta

protected

Definition at line 90 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties(), and ElectrochemicalSinteringMaterial().

◆ _domegasdw

std::vector<MaterialProperty<Real> *> ElectrochemicalSinteringMaterial::_domegasdw

protected

Definition at line 88 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties(), and ElectrochemicalSinteringMaterial().

◆ _domegavdw

std::vector<MaterialProperty<Real> *> ElectrochemicalSinteringMaterial::_domegavdw

protected

Definition at line 83 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties(), and ElectrochemicalSinteringMaterial().

◆ _e

const Real ElectrochemicalSinteringMaterial::_e

protected

Electron charge.

Definition at line 138 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _eps_r

const Real ElectrochemicalSinteringMaterial::_eps_r

protected

Solid phase relative permittivity.

Definition at line 147 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _eta

std::vector<const VariableValue *> ElectrochemicalSinteringMaterial::_eta

protected

solid phase order parameters

Definition at line 33 of file ElectrochemicalSinteringMaterial.h.

Referenced by ElectrochemicalSinteringMaterial().

◆ _eta_name

std::vector<VariableName> ElectrochemicalSinteringMaterial::_eta_name

protected

Definition at line 34 of file ElectrochemicalSinteringMaterial.h.

Referenced by ElectrochemicalSinteringMaterial().

◆ _gamma

MaterialProperty<Real>& ElectrochemicalSinteringMaterial::_gamma

protected

interface profile coefficient

Definition at line 105 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _grad_V

const VariableGradient& ElectrochemicalSinteringMaterial::_grad_V

protected

Gradient of electric potential.

Definition at line 60 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _hs

MaterialProperty<Real>& ElectrochemicalSinteringMaterial::_hs

protected

solid phase switching function

Definition at line 77 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _hv

MaterialProperty<Real>& ElectrochemicalSinteringMaterial::_hv

protected

void phase switching function

Definition at line 72 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _int_width

const Real ElectrochemicalSinteringMaterial::_int_width

protected

interface width

Definition at line 114 of file ElectrochemicalSinteringMaterial.h.

◆ _kappa

MaterialProperty<Real>& ElectrochemicalSinteringMaterial::_kappa

protected

gradient energy coefficient

Definition at line 100 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _kappa_gb

const Real ElectrochemicalSinteringMaterial::_kappa_gb

protected

kappa value on grain boundaries

Definition at line 132 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _kappa_s

const Real ElectrochemicalSinteringMaterial::_kappa_s

protected

kappa value on surfaces

Definition at line 129 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _kB

const Real ElectrochemicalSinteringMaterial::_kB

protected

Boltzmann constant.

Definition at line 135 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _ks

std::vector<const MaterialProperty<Real> *> ElectrochemicalSinteringMaterial::_ks

protected

solid energy coefficient for each defect

Definition at line 69 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties(), and ElectrochemicalSinteringMaterial().

◆ _ks_names

std::vector<MaterialPropertyName> ElectrochemicalSinteringMaterial::_ks_names

protected

Names of solid energy coefficient for each defect.

Definition at line 67 of file ElectrochemicalSinteringMaterial.h.

Referenced by ElectrochemicalSinteringMaterial().

◆ _kv

std::vector<const MaterialProperty<Real> *> ElectrochemicalSinteringMaterial::_kv

protected

void energy coefficients for each defect

Definition at line 65 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties(), and ElectrochemicalSinteringMaterial().

◆ _kv_names

std::vector<MaterialPropertyName> ElectrochemicalSinteringMaterial::_kv_names

protected

Names of void energy coefficient for each defect.

Definition at line 63 of file ElectrochemicalSinteringMaterial.h.

Referenced by ElectrochemicalSinteringMaterial().

◆ _mu

MaterialProperty<Real>& ElectrochemicalSinteringMaterial::_mu

protected

energy barrier coefficient

Definition at line 95 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _mu_gb

const Real ElectrochemicalSinteringMaterial::_mu_gb

protected

mu value on grain boundaries

Definition at line 126 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _mu_s

const Real ElectrochemicalSinteringMaterial::_mu_s

protected

mu value on surfaces

Definition at line 123 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _ndefects

const unsigned int ElectrochemicalSinteringMaterial::_ndefects

protected

number of defect species

Definition at line 37 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties(), and ElectrochemicalSinteringMaterial().

◆ _neta

const unsigned int ElectrochemicalSinteringMaterial::_neta

protected

number of solid phase order paramters

Definition at line 30 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties(), and ElectrochemicalSinteringMaterial().

◆ _ns_min

std::vector<const MaterialProperty<Real> *> ElectrochemicalSinteringMaterial::_ns_min

protected

Definition at line 49 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties(), and ElectrochemicalSinteringMaterial().

◆ _ns_min_names

std::vector<MaterialPropertyName> ElectrochemicalSinteringMaterial::_ns_min_names

protected

minima in energy wrt vacancy concentration in solid

Definition at line 48 of file ElectrochemicalSinteringMaterial.h.

Referenced by ElectrochemicalSinteringMaterial().

◆ _nv_min

const std::vector<Real> ElectrochemicalSinteringMaterial::_nv_min

protected

minima in energy wrt vacancy concentration in void

Definition at line 150 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties(), and ElectrochemicalSinteringMaterial().

◆ _omegas

MaterialProperty<Real>& ElectrochemicalSinteringMaterial::_omegas

protected

solid phase grand potential density

Definition at line 87 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _omegav

MaterialProperty<Real>& ElectrochemicalSinteringMaterial::_omegav

protected

void phase grand potential density

Definition at line 82 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _phi

const VariableValue& ElectrochemicalSinteringMaterial::_phi

protected

void phase order parameter

Definition at line 44 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _phi_name

const NonlinearVariableName ElectrochemicalSinteringMaterial::_phi_name

protected

Definition at line 45 of file ElectrochemicalSinteringMaterial.h.

◆ _sigma_gb

const Real ElectrochemicalSinteringMaterial::_sigma_gb

protected

grain boundary energy

Definition at line 111 of file ElectrochemicalSinteringMaterial.h.

◆ _sigma_s

const Real ElectrochemicalSinteringMaterial::_sigma_s

protected

surface energy

Definition at line 108 of file ElectrochemicalSinteringMaterial.h.

◆ _solid_energy

const MooseEnum ElectrochemicalSinteringMaterial::_solid_energy

protected

Type of energy function to use for the solid phase.

Definition at line 120 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _switch

const Real ElectrochemicalSinteringMaterial::_switch

protected

Parameter to determine accuracy of surface/GB phase switching function.

Definition at line 117 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _temp

const VariableValue& ElectrochemicalSinteringMaterial::_temp

protected

temperature

Definition at line 54 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _v

const VariableValue& ElectrochemicalSinteringMaterial::_v

protected

electric potential

Definition at line 57 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _v_scale

const Real ElectrochemicalSinteringMaterial::_v_scale

protected

Voltage scale.

Definition at line 144 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _w

std::vector<const VariableValue *> ElectrochemicalSinteringMaterial::_w

protected

chemical potentials for defects

Definition at line 40 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties().

◆ _w_name

std::vector<VariableName> ElectrochemicalSinteringMaterial::_w_name

protected

Definition at line 41 of file ElectrochemicalSinteringMaterial.h.

Referenced by ElectrochemicalSinteringMaterial().

◆ _z

const std::vector<int> ElectrochemicalSinteringMaterial::_z

protected

Defects species charges in units of e.

Definition at line 141 of file ElectrochemicalSinteringMaterial.h.

Referenced by computeQpProperties(), and ElectrochemicalSinteringMaterial().

The documentation for this class was generated from the following files:

phase_field/include/materials/ElectrochemicalSinteringMaterial.h
phase_field/src/materials/ElectrochemicalSinteringMaterial.C

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ ElectrochemicalSinteringMaterial()

Member Function Documentation

◆ computeQpProperties()

◆ validParams()

Member Data Documentation

◆ _d2hs

◆ _d2hv

◆ _d2kappa

◆ _d2mu

◆ _d2ns_min

◆ _d2omegasdetadeta

◆ _d2omegasdw2

◆ _d2omegasdwdeta

◆ _d2omegavdw2

◆ _dhs

◆ _dhv

◆ _dkappa

◆ _dmu

◆ _dns_min

◆ _domegasdeta

◆ _domegasdw

◆ _domegavdw

◆ _e

◆ _eps_r

◆ _eta

◆ _eta_name

◆ _gamma

◆ _grad_V

◆ _hs

◆ _hv

◆ _int_width

◆ _kappa

◆ _kappa_gb

◆ _kappa_s

◆ _kB

◆ _ks

◆ _ks_names

◆ _kv

◆ _kv_names

◆ _mu

◆ _mu_gb

◆ _mu_s

◆ _ndefects

◆ _neta

◆ _ns_min

◆ _ns_min_names

◆ _nv_min

◆ _omegas

◆ _omegav

◆ _phi

◆ _phi_name

◆ _sigma_gb

◆ _sigma_s

◆ _solid_energy

◆ _switch

◆ _temp

◆ _v

◆ _v_scale

◆ _w

◆ _w_name

◆ _z