belfem::material::Abundance Class Reference

Natural isotope abundance database for alloy property calculations. More...

#include <cl_Material_Abundance.hpp>

Public Member Functions
	Abundance ()
	Constructor - initializes isotope database.
	~Abundance ()=default
	Destructor.
void	compute_molar_mass_and_impurity_from_volumes (const Cell< string > &aElements, const Vector< real > &aVolumeFractions, real &aMolarMass, real &aImpurity) const
	Compute molar mass and impurity parameter from volume fractions.
void	compute_molar_mass_and_impurity_from_masses (const Cell< string > &aElements, const Vector< real > &aMassFractions, real &aMolarMass, real &aImpurity) const
	Compute molar mass and impurity parameter from mass fractions.
real	compute_molar_mass (const string &aElement) const
	Get molar mass of a single element.

Detailed Description

Natural isotope abundance database for alloy property calculations.

Provides isotope mass and abundance data for computing effective molar masses and mass-difference impurity parameters (Γ) used in phonon scattering models.

The database contains isotope data for all stable elements from H (Z=1) through Bi (Z=83), sourced from the CRC Handbook of Chemistry and Physics.

Applications

1. Molar Mass Calculation: M̄ = Σ_i X_i · M̄_i
   • Used for density calculations
   • Required for Callaway thermal conductivity
2. Impurity Parameter (Γ): Quantifies mass-difference scattering
   • Appears in τ_M^(-1) ∝ ω⁴ · Γ (Callaway model)
   • Accounts for both isotope and alloy scattering

Usage Patterns

For single elements:

Abundance db;
real M_Cu = db.compute_molar_mass("Cu");  // 0.06355 kg/mol

For alloys with mass fractions:

Cell<string> elements = {"Ni", "Cr", "Fe"};
Vector<real> wt_percent = {70.0, 20.0, 10.0};  // Can sum to 100
real M, Gamma;
db.compute_molar_mass_and_impurity_from_masses(
    elements, wt_percent, M, Gamma
);

For composites with volume fractions:

Cell<string> elements = {"Y", "Ba", "Cu", "O"};
Vector<real> vol_fractions = {1.0, 2.0, 3.0, 7.0};  // YBCO stoichiometry ( not normalized )
real M, Gamma;
db.compute_molar_mass_and_impurity_from_volumes(
    elements, vol_fractions, M, Gamma
);

Constructor & Destructor Documentation

Abundance()

belfem::material::Abundance::Abundance

(

)

Constructor - initializes isotope database.

Loads natural isotope masses and abundances for all elements from H (Z=1) through Bi (Z=83) from CRC Handbook data.

~Abundance()

belfem::material::Abundance::~Abundance ( )

default

Destructor.

Member Function Documentation

compute_molar_mass()

real belfem::material::Abundance::compute_molar_mass

(

const string &

aElement

)

const

Get molar mass of a single element.

Parameters

aElement

Element symbol (e.g., "Cu", "Ni", "O")

Returns

Molar mass [kg/mol]

Returns the average molar mass weighted by natural isotope abundances: M̄ = Σ_j A_j · M_j

Example:

Abundance db;
real M_Cu = db.compute_molar_mass("Cu");
// Returns 0.063546 kg/mol (natural Cu: 69.17% ⁶³Cu, 30.83% ⁶⁵Cu)

Used by: Material constructors for pure elements

compute_molar_mass_and_impurity_from_masses()

void belfem::material::Abundance::compute_molar_mass_and_impurity_from_masses	(	const Cell< string > &	aElements,
		const Vector< real > &	aMassFractions,
		real &	aMolarMass,
		real &	aImpurity ) const

Compute molar mass and impurity parameter from mass fractions.

Parameters

[in]	aElements	Element symbols (e.g., {"Ni", "Mo", "Cr"})
[in]	aMassFractions	Mass fractions [wt%] or [fraction] Can sum to 100 (wt%), 1.0 (fraction), or be unbalanced
[out]	aMolarMass	Average molar mass [kg/mol]
[out]	aImpurity	Mass-difference impurity parameter Γ [-]

Computes effective properties for alloys where weight percentages are known from composition specifications.

Input handling:

• If Σ(wt%) ≈ 100: Treats as percentages, normalizes to fractions
• If Σ(frac) ≈ 1.0: Treats as fractions
• If unbalanced: Exactly one element must be zero (balance element)

Algorithm:

1. Convert mass fractions Y_i to molar fractions: X_i = Y_i / M̄_i
2. Normalize: X_i ← X_i / Σ(X_i)
3. Compute M̄ = Σ_i X_i · M̄_i
4. Compute Γ = Σ_i Σ_j X_i · A_j^i · [(M_j^i - M̄_i) / M̄]²

Example (Hastelloy C-276):

Cell<string> elem = {"Ni", "Mo", "Cr", "Fe", "W"};
Vector<real> wt = {0.0, 0.16, 0.155, 0.055, 0.04};  // fractions, Ni = balance
// percent lists must sum to exactly 100; an unbalanced list needs exactly one 0
real M, Gamma;
db.compute_molar_mass_and_impurity_from_masses(elem, wt, M, Gamma);

Used by: HastelloyC276::set_constants()

compute_molar_mass_and_impurity_from_volumes()

void belfem::material::Abundance::compute_molar_mass_and_impurity_from_volumes	(	const Cell< string > &	aElements,
		const Vector< real > &	aVolumeFractions,
		real &	aMolarMass,
		real &	aImpurity ) const

Compute molar mass and impurity parameter from volume fractions.

Parameters

[in]	aElements	Element symbols (e.g., {"Ni", "Cr", "Fe"})
[in]	aVolumeFractions	Stoichiometric counts per formula unit ( NOT normalized: the returned molar mass is Σ X_i·M̄_i, i.e. the formula-unit mass when the counts are integers )
[out]	aMolarMass	Average molar mass [kg/mol]
[out]	aImpurity	Mass-difference impurity parameter Γ [-]

Computes effective properties for composites where volume fractions are known (e.g., from stoichiometry or microstructure).

Algorithm:

1. Compute M̄_i for each element from isotope abundances
2. Compute alloy molar mass: M̄ = Σ_i X_i · M̄_i
3. Compute Γ = Σ_i Σ_j X_i · A_j^i · [(M_j^i - M̄_i) / M̄]²

Example (YBCO: Y₁Ba₂Cu₃O₇):

Cell<string> elem = {"Y", "Ba", "Cu", "O"};
Vector<real> vol = {1.0, 2.0, 3.0, 7.0};  // Stoichiometric ratios
real M, Gamma;
db.compute_molar_mass_and_impurity_from_volumes(elem, vol, M, Gamma);
// M ≈ 0.6658 kg/mol (for YBa₂Cu₃O₇)

Used by: the YBCO constructor ( cl_Material_YBCO.cpp )

---

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

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