belfem::material::YBCO Class Reference

YBCO (YBa₂Cu₃O₇) high-temperature superconductor implementation. More...

#include <cl_Material_YBCO.hpp>

Inheritance diagram for belfem::material::YBCO:

Collaboration diagram for belfem::material::YBCO:

Public Member Functions
	YBCO ()
	Constructor - initializes YBCO with typical properties.
	~YBCO () override
	Destructor - deletes Bezier curve for Young's modulus.
real	test_callaway (const real T, const Vector< real > &aParams)
	Test function for Callaway model parameter fitting.
Public Member Functions inherited from belfem::material::Metal
	Metal (const string &aLabel, const MaterialType aType, const bool aBuildTables=true)
	Constructor.
	~Metal () override
	Destructor - deletes Debye integral splines.
void	set_RRR (const real RRR) override
	Set residual resistivity ratio.
virtual real	compute_debye_from_rho (const real T, const real rho, const real theta_guess=BELFEM_QUIET_NAN)
	Compute Debye temperature from measured resistivity.
real	compute_debye_from_cp (const real T, const real cp=BELFEM_QUIET_NAN, const real theta_guess=BELFEM_QUIET_NAN)
	Compute Debye temperature from specific heat capacity.
real	compute_debye_from_cv (const real T, const real cv=BELFEM_QUIET_NAN, const real theta_guess=BELFEM_QUIET_NAN)
	Compute Debye temperature from the specific heat at constant volume.
real	rho (const real T, const real B, const real beta) const override
	Electrical resistivity with magnetoresistance (Kohler's rule).
real	drhodT (const real T, const real B, const real beta) const override
real	drhodB (const real T, const real B, const real beta) const override
real	drhodbeta (const real T, const real B, const real beta) const override
real	lambda (const real T, const real B, const real beta) const override
	Thermal conductivity with magnetoresistance.
real	dlambdadT (const real T, const real B, const real beta) const override
real	dlambdadB (const real T, const real B, const real beta) const override
real	dlambdadbeta (const real T, const real B, const real beta) const override
real	l (real T) const override
	Relative length after thermal expansion.
void	set_bh_curve (const BhCurve *aCurve) override
	Assign a B-H curve to this material.
real	spline_property (const MaterialProperty aProperty, const real aX) const override
	Evaluate property using spline interpolation.
void	set_rho_i_ref (const real T_ref, const real rho_i_ref, const real theta=BELFEM_QUIET_NAN)
	Set reference intrinsic resistivity for Bloch-Grüneisen model.
real	J (const real Z) const
	Debye integral Jₙ(Z) = ∫₀^Z xⁿeˣ/(eˣ-1)² dx with n the Bloch–Grüneisen exponent ( 5 by default, see set_bloch_gruen_parameter; dispatched to J3/J4/J5/Jn ).
real	J3 (const real Z) const
	Debye integral J₃(Z) = ∫₀^Z x³eˣ/(eˣ-1)² dx.
real	J4 (const real Z) const
	Debye integral J₄(Z) = ∫₀^Z x⁴eˣ/(eˣ-1)² dx.
real	J5 (const real Z) const
	Debye integral J₅(Z) = ∫₀^Z x⁵eˣ/(eˣ-1)² dx.
real	Jn (const real Z) const
	Debye integral for arbitrary n.
real	rho_custom (const real T) const override
	Total resistivity at zero field (overrides base class).
real	rho_i_custom (const real T) const override
	Intrinsic resistivity (Bloch-Grüneisen model).
void	create_rho ()
	Initialize resistivity properties.
void	set_lambda_coefficients (const Vector< real > &aCoeffs)
	Set thermal conductivity model coefficients.
real	group_velocity (const real T) const
	Phonon group velocity.
real	grueneisen (const real T) const
	Grüneisen parameter.
void	grueneisen (const real T, real &gamma, real &c) const
	Grüneisen parameter and speed of sound.
real	cp_from_debye (const real T, const real theta) const
	Specific heat from Debye temperature.
real	cv_from_debye (const real T, const real theta) const
	Specific heat at constant volume from Debye temperature ( Sommerfeld + Debye, no dilation term ).
virtual real	kohler (const real B, const real S, const real beta) const
	Kohler function for magnetoresistance.
real	kohler_find_bs_crit (const real delta_rho_res)
	Find critical B·S for given relative resistivity increase.
void	populate_rho_database ()
real	H_bhcurve (const real B) const override
real	mu_bhcurve (real H, const real T) const override
void	dmudH_bhcurve (const real H, real &mu, real &dmudH) const override
const Vector< real > &	lambda_coefficients () const
void	set_table_flags (const bool aFlag) override
virtual real	rho (const real T) const
	Electrical resistivity (isotropic).
virtual real	lambda (const real T=gTroom) const
	Thermal conductivity (isotropic).
virtual real	lambda (const real T, const real B_par, const real B_perp, const real J) const
	Thermal conductivity for HTS materials.
virtual real	drhodT (const real T) const
virtual real	dlambdadT (const real T=gTroom) const
virtual real	dlambdadT (const real T, const real B_par, const real B_perp, const real J) const
Public Member Functions inherited from belfem::material::SplineLookupTable
	SplineLookupTable (const MaterialType aType, const bool aIsIsotropic=true)
	~SplineLookupTable () override
void	set_spline (const MaterialProperty aProperty, Spline *aSpline=nullptr)
	Assign a spline for property interpolation.
Spline *	spline (const MaterialProperty aProperty)
	Get spline for a property.
real	spline_property (const MaterialProperty aProperty, const real aX) const override
	Evaluate property using spline interpolation.
real	dspline_property (const MaterialProperty aProperty, const real aX) const override
real	ddspline_property (const MaterialProperty aProperty, const real aX) const override
real	l (real T) const override
	Relative length after thermal expansion, from integrated alpha spline.
Public Member Functions inherited from belfem::Material
	Material (const MaterialType aType, const bool aIsIsotropic=true)
	Constructor.
virtual	~Material ()
	Destructor - deletes owned B-H curves and Jc/n functions.
	Material (const Material &)=delete
Material &	operator= (const Material &)=delete
	Material (Material &&)=delete
Material &	operator= (Material &&)=delete
bool	have (const MaterialProperty aProperty) const
	Check if a material property is available.
bool	have_defect () const
	Check if the material has a defect.
bool	have_heating () const
	Check if the material has a heating function.
bool	use_piecewise () const
	Check if we use piecewise instead of power-law.
bool	depends (const MaterialProperty aProperty, const MaterialDependency aDependency) const
	Check if a property depends on a specific variable.
const MaterialDependencyBitset *	dependencies (const MaterialProperty aProperty) const
	Get all dependencies for a property.
bool	is_isotropic () const
	Check if material is isotropic.
MaterialType	type () const
	Get the material type.
const string &	label () const
	Get material label.
const string &	number () const
	Get material number/identifier.
void	load_bh_curve (const material::BhCurve *aCurve)
	Activate a B-H curve as the permeability source (ferromagnets).
void	flag (const uint8_t aIndex=0)
	Set flag (multi-purpose flag used by Kernel).
void	unflag (const uint8_t aIndex=0)
	Clear flag.
bool	is_flagged (const uint8_t aIndex=0) const
	Check if material is flagged.
bool	is_constant (const MaterialProperty aProperty) const
	Check if a property is constant (temperature-independent).
virtual real	density (const real T=gTroom) const
	Density as a function of temperature.
real	ref_density () const
	Reference density at reference temperature.
real	M () const
	Molar mass.
virtual real	cp (const real T=gTroom) const
	Specific heat capacity.
virtual real	dcpdT (const real T=gTroom) const
virtual real	d2cpdT2 (const real T=gTroom) const
real	rho_powerlaw (const real normJ) const
	Power law resistivity for HTS (constant jc and n).
real	rho_powerlaw (const real normJ, const real x, const real y, const real z, const real t) const
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. Constant \(J_c\) / \(n\) with spatially-dependent defect modulation \(J_c \rightarrow J_c \cdot d(x,y,z,t)\).
real	rho_powerlaw (const real normJ, real normB, const real angleNxB) const
	Power law resistivity for HTS (field-dependent jc, constant n).
real	rho_powerlaw (const real normJ, real normB, const real angleNxB, const real x, const real y, const real z, const real t) const
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. Field-dependent \(J_c(|B|, \angle)\) with spatial defect modulation.
real	rho_powerlaw (const real normJ, const real T, real normB, const real angleNxB) const
	Power law resistivity for HTS (full temperature and field dependence).
real	rho_powerlaw (const real normJ, const real T, real normB, const real angleNxB, const real x, const real y, const real z, const real t) const
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. Fully \((|B|, \angle, T)\)-dependent variant with spatial defect modulation applied to \(J_c\).
real	rho_powerlaw (const real normJ, const real T) const
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. Temperature-only variant.
real	rho_powerlaw (const real normJ, const real T, const real x, const real y, const real z, const real t) const
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. Temperature-only custom-callback variant with spatial defect modulation.
real	rho_piecewise (const real normJ) const
	Piecewise resistivity for HTS (constant jc and n).
real	rho_piecewise (const real normJ, const real x, const real y, const real z, const real t) const
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. Constant \(J_c\) / \(n\) with spatially-dependent defect modulation \(J_c \rightarrow J_c \cdot d(x,y,z,t)\).
real	rho_piecewise (const real normJ, real normB, const real angleNxB) const
	Piecewise resistivity for HTS (field-dependent jc, constant n).
real	rho_piecewise (const real normJ, real normB, const real angleNxB, const real x, const real y, const real z, const real t) const
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. Field-dependent \(J_c(|B|, \angle)\) with spatial defect modulation.
real	rho_piecewise (const real normJ, const real T, real normB, const real angleNxB) const
	Piecewise resistivity for HTS (full temperature and field dependence).
real	rho_piecewise (const real normJ, const real T, real normB, const real angleNxB, const real x, const real y, const real z, const real t) const
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. Fully \((|B|, \angle, T)\)-dependent variant with spatial defect modulation applied to \(J_c\).
real	rho_piecewise (const real normJ, const real T) const
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. Temperature-only variant: \(J_c(T)\) and \(n(T)\) from the user-supplied callbacks Material::jc_custom() / Material::n_custom().
real	rho_piecewise (const real normJ, const real T, const real x, const real y, const real z, const real t) const
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. Temperature-only custom-callback variant with spatial defect modulation.
real	rho_riva (const real normJ, const real T, const real normB, const real angleNxB) const
	Riva-law resistivity: the superconducting power-law channel in parallel with the normal-state channel.
real	rho_riva (const real normJ, const real T, const real normB, const real angleNxB, const real x, const real y, const real z, const real t) const
	defect overload: jc_eff = D(x,y,z,t)·jc throughout
real	drho_riva_dJ (const real normJ, const real T, const real normB, const real angleNxB) const
	dρ/d|J| of rho_riva: w²·dρ_PL/dJ with w = ρ_n/(ρ_PL+ρ_n)
real	drho_riva_dJ (const real normJ, const real T, const real normB, const real angleNxB, const real x, const real y, const real z, const real t) const
real	drho_riva_dB (const real normJ, const real T, const real normB, const real angleNxB) const
	dρ/d|B| of rho_riva: w²·dρ_PL/dB ( dρ_n/dB = 0 on this path )
real	drho_riva_dB (const real normJ, const real T, const real normB, const real angleNxB, const real x, const real y, const real z, const real t) const
real	drho_riva_dT (const real normJ, const real T, const real normB, const real angleNxB) const
	dρ/dT of rho_riva: w²·dρ_PL/dT + (1−w)²·dρ_n/dT
real	drho_riva_dT (const real normJ, const real T, const real normB, const real angleNxB, const real x, const real y, const real z, const real t) const
real	n (const real normB, const real angleNxB, const real T) const
	Direct evaluation of the n-value as a function of \(|B|\), \(\angle(n,B)\) and \(T\).
real	n (const real normB, const real angleNxB) const
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. Field-dependent \(n(|B|, \angle(n,B))\) without temperature dependence.
real	jc (const real normB, const real angleNxB, const real T) const
	Direct evaluation of the critical current density \(J_c(|B|, \angle(n,B), T)\).
real	jc (const real normB, const real angleNxB) const
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. Field-dependent \(J_c(|B|, \angle(n,B))\) without temperature dependence.
real	jc (const real normB, const real angleNxB, const real T, const real x, const real y, const real z, const real t) const
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. Variant with spatial defect modulation \(J_c \rightarrow J_c \cdot d(x,y,z,t)\).
real	jc (const real normB, const real angleNxB, const real x, const real y, const real z, const real t) const
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. Field-dependent \(J_c(|B|, \angle(n,B))\) with spatial defect modulation \(J_c \rightarrow J_c \cdot d(x,y,z,t)\).
real	drho_powerlaw_dJ (const real normJ, const real T, const real normB, const real angleNxB) const
	Derivative of power-law resistivity with respect to current density magnitude.
real	drho_powerlaw_dJ (const real normJ, const real T, const real normB, const real angleNxB, const real x, const real y, const real z, const real t) const
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. Fully \((|B|, \angle, T)\)-dependent variant with spatial defect modulation applied to \(J_c\).
real	drho_powerlaw_dJ (const real normJ) const
	Analytic Jacobian \(d\rho_{eff}/dJ\) of the power-law model.
real	drho_powerlaw_dJ (const real normJ, const real x, const real y, const real z, const real t) const
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. Constant \(J_c\) / \(n\) with spatial defect modulation applied to \(J_c\).
real	drho_powerlaw_dJ (const real normJ, const real T) const
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. Temperature-only variant: \(J_c(T)\) and \(n(T)\) from Material::jc_custom() / Material::n_custom().
real	drho_powerlaw_dJ (const real normJ, const real T, const real x, const real y, const real z, const real t) const
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. Temperature-only custom-callback variant with spatial defect modulation.
real	drho_powerlaw_dJ (const real normJ, const real normB, const real angleNxB) const
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. Field-dependent \(J_c(|B|, \angle)\) via mJcFunction; \(n\) remains constant.
real	drho_powerlaw_dJ (const real normJ, const real normB, const real angleNxB, const real x, const real y, const real z, const real t) const
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. Field-dependent \(J_c(|B|, \angle)\) with spatial defect modulation; \(n\) remains constant.
real	drho_piecewise_dJ (const real normJ, const real T, const real normB, const real angleNxB) const
	Derivative of piecewise resistivity with respect to current density magnitude.
real	drho_piecewise_dJ (const real normJ, const real T, const real normB, const real angleNxB, const real x, const real y, const real z, const real t) const
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. Fully \((|B|, \angle, T)\)-dependent variant with spatial defect modulation applied to \(J_c\).
real	drho_powerlaw_dB (const real normJ, const real T, const real normB, const real angleNxB) const
	Derivative of power-law resistivity with respect to |B| at fixed J, T, θ ( jc = jc(T,|B|,θ), n = n(T,|B|,θ) ).
real	drho_powerlaw_dB (const real normJ, const real T, const real normB, const real angleNxB, const real x, const real y, const real z, const real t) const
	defect overload: jc_eff = D(x)·jc throughout, djc_eff = D·djc
real	drho_powerlaw_dT (const real normJ, const real T, const real normB, const real angleNxB) const
	Derivative of power-law resistivity with respect to T at fixed J, |B|, θ ( T-leg: jc(T), n(T) AND ρ_n(T) all move — the quench-feedback tangent ).
real	drho_powerlaw_dT (const real normJ, const real T, const real normB, const real angleNxB, const real x, const real y, const real z, const real t) const
	defect overload: jc_eff = D(x)·jc throughout, djc_eff = D·djc
real	drho_piecewise_dB (const real normJ, const real T, const real normB, const real angleNxB) const
	Derivative of piecewise resistivity with respect to |B| at fixed J, T, θ
real	drho_piecewise_dB (const real normJ, const real T, const real normB, const real angleNxB, const real x, const real y, const real z, const real t) const
	defect overload: jc_eff = D(x)·jc throughout, djc_eff = D·djc
real	drho_piecewise_dT (const real normJ, const real T, const real normB, const real angleNxB) const
	Derivative of piecewise resistivity with respect to T at fixed J, |B|, θ ( T-leg ).
real	drho_piecewise_dT (const real normJ, const real T, const real normB, const real angleNxB, const real x, const real y, const real z, const real t) const
	defect overload: jc_eff = D(x)·jc throughout, djc_eff = D·djc
real	drho_piecewise_dJ (const real normJ) const
	Branch-aware Jacobian \(d\rho/dJ\) of the three-regime piecewise model.
real	drho_piecewise_dJ (const real normJ, const real x, const real y, const real z, const real t) const
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. Constant \(J_c\) / \(n\) with spatial defect modulation applied to \(J_c\).
real	drho_piecewise_dJ (const real normJ, const real T) const
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. Temperature-only variant: \(J_c(T)\) and \(n(T)\) from Material::jc_custom() / Material::n_custom().
real	drho_piecewise_dJ (const real normJ, const real T, const real x, const real y, const real z, const real t) const
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. Temperature-only custom-callback variant with spatial defect modulation.
real	drho_piecewise_dJ (const real normJ, const real normB, const real angleNxB) const
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. Field-dependent \(J_c(|B|, \angle)\) via mJcFunction; \(n\) remains constant.
real	drho_piecewise_dJ (const real normJ, const real normB, const real angleNxB, const real x, const real y, const real z, const real t) const
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. Field-dependent \(J_c(|B|, \angle)\) with spatial defect modulation; \(n\) remains constant.
virtual real	rho_i (const real T) const
	Intrinsic (phonon) electrical resistivity of a metal, ρ = ρ_i(T) + ρ_0.
virtual real	H (const real B) const
	Magnetic field strength from flux density.
virtual real	mu (const real H, const real T=BELFEM_QUIET_NAN) const
	Magnetic permeability.
virtual void	dmudH (const real H, real &mu, real &dmudH) const
	Magnetic permeability and its derivative.
virtual real	E (real T=gTroom) const
	Young's modulus.
virtual real	nu (real T=gTroom) const
	Poisson's ratio.
virtual real	G (real T=gTroom) const
	Shear modulus.
virtual real	K (real T=gTroom) const
	Bulk modulus.
virtual real	alpha (real T=gTroom) const
	Thermal expansion coefficient.
virtual real	Rp02 (real T=gTroom) const
	Yield stress (0.2% offset).
virtual real	debye (const real T) const
	Debye temperature.
void	set_jc_function (const material::JcFunction *aFunction)
	Assign a critical current density function.
void	set_n_function (const material::JcFunction *aFunction)
	Assign a power law exponent function.
void	set_piecewise (const bool aUsePiecewise)
void	set_resistivity_law (const ResistivityLaw aLaw)
ResistivityLaw	resistivity_law () const
bool	use_riva () const
virtual void	set_user_defined_function (const MaterialProperty Property, const MaterialDependency Dependency, MatFunc1 *Function)
	Set a user-defined function with one dependency (for UserDefinedMaterial).
virtual void	set_user_defined_function (const MaterialProperty Property, const MaterialDependency Dependency1, const MaterialDependency Dependency2, MatFunc2 *Function)
	Set a user-defined function with two dependencies (for UserDefinedMaterial).
virtual void	set_user_defined_function (const MaterialProperty Property, const MaterialDependency Dependency1, const MaterialDependency Dependency2, const MaterialDependency Dependency3, MatFunc3 *Function)
	Set a user-defined function with three dependencies (for UserDefinedMaterial).
void	set_user_defined_defect (DefectFunc *Function)
	Set a user-defined defect function with x, y, z, t dependencies.
void	read_defect (const string &aLibraryPath, const string &aLabel)
	Read a defect from the library.
void	set_user_defined_heating (HeatFunc *Function)
	Set a user-defined volumetric heat load [ W/m³ ] as a function of x, y, z [ m ] and t [ s ].
void	read_heating (const string &aLibraryPath, const string &aLabel)
	Read a heating function from a plugin library.
virtual real	evaluate_polynomial (const MaterialProperty Property, const real T) const
	Evaluate a polynomial for a given property (for UserDefinedMaterial).
virtual real	evaluate_derivative_of_polynomial (const MaterialProperty Property, const real T) const
virtual void	set_user_defined_polynomial (const MaterialProperty Property, const std::vector< real > &Coefficients)
	Set a polynomial function for a property (for UserDefinedMaterial).
virtual void	set_user_defined_polynomial (const MaterialProperty Property, const Cell< real > &Coefficients)
void	set_label (const string &aLabel)
	PROTECTED INTERFACE FOR DERIVED MATERIALS.
void	set_number (const string &aNumber)
	Set material number/identifier (for derived classes).
void	set_have (const MaterialProperty aProperty, const bool aHave=true)
	Mark a property as available.
void	reset_dependencies (const MaterialProperty aProperty)
	Reset all dependencies for a property.
void	set_dependency (const MaterialProperty aProperty, const MaterialDependency aDependency)
	Add a dependency to a property.
void	set_constant (const MaterialProperty aProperty, const real aValue)
	Define a property as constant.
void	set_custom (const MaterialProperty aProperty)
	Mark property as using custom evaluation function.
real	constant_property (const MaterialProperty aProperty) const
	Get constant property value.
virtual real	jc_custom (const real T) const
virtual real	n_custom (const real T) const
real	volumetric_heatload (const real x, const real y, const real z, const real time) const
	Artificial volumetric heat load [ W/m³ ] from the heating plugin.

Protected Member Functions
real	E_custom (const real T) const override
	Young's modulus (custom evaluation).
real	nu_custom (const real T) const override
	Poisson's ratio (custom evaluation).
real	alpha_custom (const real T) const override
	Thermal expansion coefficient (custom evaluation).
real	cp_custom (const real T) const override
	Specific heat capacity (custom evaluation).
real	lambda_custom (const real T) const override
	Thermal conductivity using Callaway model.
Protected Member Functions inherited from belfem::material::Metal
Spline *	create_J_spline (const real aExponent)
	Create spline for Debye integral J_n(Z).
real	rho_table (const real T, const real B, const real beta) const override
real	drhodT_table (const real T, const real B, const real beta) const override
real	drhodB_table (const real T, const real B, const real beta) const override
real	drhodbeta_table (const real T, const real B, const real beta) const override
real	rho_kohler (const real T, const real B, const real beta) const override
real	drhodT_kohler (const real T, const real B, const real beta) const override
real	drhodB_kohler (const real T, const real B, const real beta) const override
real	drhodbeta_kohler (const real T, const real B, const real beta) const override
real	dcpdT_custom (const real T) const override
real	d2cpdT2_custom (const real T) const override
void	set_kohler_dependencies ()
void	set_bloch_gruen_parameter (const real n)
void	create_cp (const Vector< real > &Px, const Vector< real > &Py, const Vector< real > &Qx, const Vector< real > &Qy, const Vector< real > &Rx={}, const Vector< real > &Ry={})
real	dEdT_custom (const real T) const override
void	create_mech (const real E0, const real b, const real T1, const real T2, const real nu2)
Protected Member Functions inherited from belfem::material::SplineLookupTable
void	reset_spline (const MaterialProperty aProperty) override
void	create_spline (real(Material::*aFunction)(const real aT) const, const MaterialProperty aProperty, const uint aStartBC, const uint aEndBC, const real adYdX0, const real adYdX1) override
void	create_cryo_expansion (const Bezier *aThermalExpansion, Vector< real > &aThermalExpansionCryo, const real aTSwitch=BELFEM_QUIET_NAN)
void	create_cryo_expansion (const real alpha, const real dalphadT, const real d2alphadT2, Vector< real > &aThermalExpansionCryo)
	cryogenic branch from alpha and its derivatives at the split temperature, for materials whose alpha( T ) is not a dL/L Bezier
void	create_cryo_expansion_anchored (const real alpha, Vector< real > &aThermalExpansionCryo, const real aTSwitch=BELFEM_QUIET_NAN)
	cryogenic branch anchored on the VALUE of alpha at the split only.
real	alpha_composite (const Bezier *aBezier, const Vector< real > &aPoly, const real T) const
	composite thermal expansion for a Material::alpha_custom() override: the Grueneisen polynomial aPoly below the switch temperature, the Bezier aBezier above it.
real	set_alpha_switch_temperature (const real aTSwitch=BELFEM_QUIET_NAN)
	Fix the split temperature of the cryogenic expansion branch.
void	create_low_temperature_alpha (const Bezier *aBezier, Vector< real > &aPoly, const real aTSwitch=BELFEM_QUIET_NAN)
	Fit the cryogenic branch alpha = C( T ) cp( T ) below the split temperature from a dL/L Bezier ( the pure metals ).
void	create_low_temperature_alpha (const real alpha, const real dalphadT, const real d2alphadT2, Vector< real > &aPoly, const bool aCheckGuard=true)
	Same fit from alpha and its first two derivatives at the split temperature, which the caller evaluated from any alpha( T ) source after set_alpha_switch_temperature().
void	create_spline (const MaterialProperty aProperty, const real adYdX0=BELFEM_QUIET_NAN, const real adXdX1=BELFEM_QUIET_NAN)
	PROPERTY EVALUATION FUNCTIONS.
Protected Member Functions inherited from belfem::Material
real	jc_eval (const real T, const real normB, const real angleNxB) const
	O1 "full-signature policy" helpers: the assembly path always passes the full ( T, normB, angleNxB ) set; the material consumes what its Jc / n functions depend on and ignores the rest.
real	djc_eval_dB (const real T, const real normB, const real angleNxB) const
real	dn_eval_dB (const real T, const real normB, const real angleNxB) const
	d(n)/d|B|, same routing as djc_eval_dB
real	djc_eval_dT (const real T, const real normB, const real angleNxB) const
real	dn_eval_dT (const real T, const real normB, const real angleNxB) const
	d(n)/dT, same routing as djc_eval_dT
real	n_eval (const real T, const real normB, const real angleNxB) const
void	check_riva_n_source () const
real	n_eval_raw (const real T, const real normB, const real angleNxB) const
bool	riva_rho_pl (const real normJ, const real jc, const real n, const real ec, real &rhoPL) const
void	create_spline (const MaterialProperty aProperty, const real adYdX0=BELFEM_QUIET_NAN, const real adXdX1=BELFEM_QUIET_NAN)
	PROPERTY EVALUATION FUNCTIONS.
real	alpha_switch_temperature () const
	Temperature below which alpha is taken from the Grueneisen branch.
real	density_const (const real T) const
virtual real	density_custom (const real T) const
real	return_zero (const real T) const
	Shared binding for derivative channels that are identically zero.
real	cp_const (const real T) const
real	dcpdT_finite_difference (const real T) const
real	d2cpdT2_finite_difference (const real T) const
real	cp_spline (const real T) const
real	dcpdT_spline (const real T) const
real	d2cpdT2_spline (const real T) const
real	lambda_const (const real T) const
real	dlambdadT_finite_difference (const real T) const
real	lambda_spline (const real T) const
real	dlambdadT_spline (const real T) const
virtual real	dlambdadT_custom (const real T) const
real	drhodT_finite_difference (const real T) const
real	rho_const (const real T) const
virtual real	drhodT_custom (const real T) const
virtual real	rho_spline (const real T) const
virtual real	drhodT_spline (const real T) const
virtual real	lambda_custom (const real T, const real normB, const real angle) const
virtual real	lambda_table (const real T, const real normB, const real angle) const
real	H_const (const real B) const
real	mu_const (const real H, const real T) const
virtual real	mu_custom (const real H, const real T) const
void	dmudH_const (const real H, real &mu, real &dmudH) const
real	E_const (const real T) const
real	E_spline (const real T) const
real	nu_const (const real T) const
real	nu_spline (const real T) const
real	alpha_const (const real T) const
real	alpha_spline (const real T) const
real	Rp02_const (const real T) const
real	Rp02_spline (const real T) const
virtual real	Rp02_custom (const real T) const
real	debye_const (const real T) const
real	debye_spline (const real T) const
virtual real	debye_custom (const real T) const
real	rho_i_spline (const real T) const

Additional Inherited Members
Protected Attributes inherited from belfem::material::Metal
Spline *	mSplineJ3 = nullptr
Spline *	mSplineJ4 = nullptr
Spline *	mSplineJ5 = nullptr
Spline *	mSplineJn = nullptr
Cell< Vector< real > >	mCpPolys
Vector< real >	mTCpSwitch
Bezier *	mCpBezierLow = nullptr
Bezier *	mCpBezierMedium = nullptr
Bezier *	mCpBezierHigh = nullptr
Vector< real >	mWachtmanYoung
Protected Attributes inherited from belfem::material::SplineLookupTable
Cell< Spline * >	mSplines
Protected Attributes inherited from belfem::Material
real(Material::*)	mFunctionRhoKohler (const real T, const real normB, const real angle) const = nullptr
real(Material::*)	mFunctiondRhoKohlerdT (const real T, const real normB, const real angle) const = nullptr
real(Material::*)	mFunctiondRhoKohlerdB (const real T, const real normB, const real angle) const = nullptr
real(Material::*)	mFunctiondRhoKohlerdbeta (const real T, const real normB, const real angle) const = nullptr
real(Material::*)	mFunctionH (const real B) const = nullptr
real(Material::*)	mFunctionMu (const real H, const real T) const = nullptr
void(Material::*)	mFunctionDMuDH (double, double &, double &) const = nullptr
const material::JcFunction *	mJcFunction = nullptr
const material::JcFunction *	mNFunction = nullptr

Detailed Description

YBCO (YBa₂Cu₃O₇) high-temperature superconductor implementation.

YBa₂Cu₃O₇ is a cuprate superconductor with Tc ≈ 92.5 K (typical). This implementation includes both normal-state and superconducting properties.

Composition: YBa₂Cu₃O₇ (13 atoms per formula unit) Critical temperature: ~92.5 K (typical, can vary with oxygen content) Density: ~6300 kg/m³

Key features:

• Mechanical: Based on Lei & Ledbetter 1991 (NISTIR 3980)
• Thermal expansion: Salomons et al. 1987 (10.1016/0378-4363(87)90092-1)
• Specific heat: Baak 1989, Lang et al. 1988
• Electrical: Bloch-Grüneisen model with RRR ≈ 50
• Thermal conductivity: Callaway model with e-ph and umklapp scattering including d-wave superconducting gap effects

IMPORTANT: For HTS materials, use rho_powerlaw() for resistivity calculations in the superconducting state, not rho(T).

MaterialType: HTS (ρ, λ depend on j, T, n×B and n·B)

References:

• Sommerfeld et al. 2003 (10.1103/PhysRevB.67.174520) - fitted parameters
• Raman data: 10.1103/PhysRevB.80.064505

Constructor & Destructor Documentation

YBCO()

belfem::material::YBCO::YBCO

(

)

Constructor - initializes YBCO with typical properties.

YBCO (YBa₂Cu₃O₇) material property implementation.

Sets up:

• Tc = 92.5 K (typical)
• RRR = 50 (typical for thin films)
• Debye temperature θD = 275 K (fitted)
• Layer thickness = 1 μm (default)
• Young's modulus = 210 GPa @ RT (typical for thin films)
• Poisson's ratio = 0.25 @ RT (assumed reasonable value)

This is the most complex material in the database, combining:

• Normal-state metallic properties (Bloch-Grüneisen resistivity)
• Superconducting properties (d-wave gap, power law resistivity)
• Advanced thermal conductivity (Callaway model with multiple scattering mechanisms)

Key implementation features:

• Mechanical: Normalized curves from Lei & Ledbetter scaled to user values
• Thermal expansion: Polynomial with constant tail at high T
• Specific heat: 4 piecewise regions (polynomial, log-log fits)
• Electrical: Bloch-Grüneisen + RRR model (fitted to Sommerfeld 2003)
• Thermal conductivity: Callaway model including:
  • Phonon-phonon umklapp scattering
  • Boundary scattering (layer thickness dependent)
  • Electron-phonon scattering
  • Optical phonon scattering (Raman active mode at 501 cm⁻¹)
  • D-wave superconducting gap effects

Data sources:

• Lei & Ledbetter 1991 (NISTIR 3980) - mechanical
• Salomons et al. 1987 (10.1016/0378-4363(87)90092-1) - thermal expansion
• Baak 1989, Lang et al. 1988 - specific heat
• Sommerfeld et al. 2003 (10.1103/PhysRevB.67.174520) - fitted parameters

~YBCO()

belfem::material::YBCO::~YBCO ( )

override

Destructor - deletes Bezier curve for Young's modulus.

Member Function Documentation

alpha_custom()

real belfem::material::YBCO::alpha_custom ( const real T ) const

overrideprotectedvirtual

Thermal expansion coefficient (custom evaluation).

Parameters

T	Temperature [K]

Returns

Thermal expansion coefficient [1/K]

Reimplemented from belfem::Material.

cp_custom()

real belfem::material::YBCO::cp_custom ( const real T ) const

overrideprotectedvirtual

Specific heat capacity (custom evaluation).

Parameters

T	Temperature [K]

Returns

Specific heat capacity [J/(kg·K)]

Reimplemented from belfem::material::Metal.

E_custom()

real belfem::material::YBCO::E_custom ( const real T ) const

overrideprotectedvirtual

Young's modulus (custom evaluation).

Parameters

T	Temperature [K]

Returns

Young's modulus [Pa]

Reimplemented from belfem::material::Metal.

lambda_custom()

real belfem::material::YBCO::lambda_custom ( const real T ) const

overrideprotectedvirtual

Thermal conductivity using Callaway model.

Parameters

T	Temperature [K]

Returns

Thermal conductivity [W/(m·K)]

Implements λ = λ_e + λ_ph where:

• λ_e: Electronic contribution (Wiedemann-Franz law)
• λ_ph: Phonon contribution (Callaway model with umklapp, boundary, electron-phonon scattering, and d-wave gap)

Parameters fitted to Sommerfeld et al. 2003 data.

Implements λ = λ_e + λ_ph where:

• λ_e: Electronic contribution via Wiedemann-Franz law
• λ_ph: Phonon contribution via Callaway model

The Callaway model includes:

1. Umklapp scattering (phonon-phonon): τ_U ∝ exp(θD/(b·T))
2. Boundary scattering: τ_B = v·L (layer thickness dependent)
3. Electron-phonon scattering: temperature and carrier dependent
4. Optical phonon scattering: Raman mode at 501 cm⁻¹
5. D-wave superconducting gap: Δ₀/(kB·Tc) factor

All parameters fitted to Sommerfeld et al. 2003 (10.1103/PhysRevB.67.174520)

Reimplemented from belfem::material::Metal.

nu_custom()

real belfem::material::YBCO::nu_custom ( const real T ) const

overrideprotectedvirtual

Poisson's ratio (custom evaluation).

Parameters

T	Temperature [K]

Returns

Poisson's ratio [-]

Reimplemented from belfem::Material.

test_callaway()

real belfem::material::YBCO::test_callaway	(	const real	T,
		const Vector< real > &	aParams )

Test function for Callaway model parameter fitting.

Parameters

T	Temperature [K]
aParams	Model parameters to test

Returns

Thermal conductivity [W/(m·K)]

Used for calibrating the Callaway thermal conductivity model.

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

• src/physics/materials/cl_Material_YBCO.hpp
• src/physics/materials/cl_Material_YBCO.cpp