cl_Material_Abundance.hpp File Reference

Natural isotope abundance database for computing alloy properties. More...

#include "typedefs.hpp"
#include "cl_Map.hpp"
#include "cl_Vector.hpp"
#include "cl_Cell.hpp"

Include dependency graph for cl_Material_Abundance.hpp:

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Classes
class	belfem::material::Abundance
	Natural isotope abundance database for alloy property calculations. More...

Namespaces
namespace	belfem
	USER GUIDES:
namespace	belfem::material

Typedefs
typedef std::pair< Vector< real >, Vector< real > >	belfem::material::AbundanceEntry
	Database entry for an element's isotopes.

Detailed Description

Natural isotope abundance database for computing alloy properties.

This file provides the Abundance class for computing effective molar masses and mass-difference impurity parameters (Γ) for alloys and composites.

Physical Background

The impurity parameter Γ quantifies phonon scattering from mass differences between isotopes and alloying elements. It appears in the mass-difference scattering rate τ_M^(-1) in thermal conductivity models (Callaway model).

For an alloy with composition {X_i} (molar fractions):

Γ = Σ_i Σ_j X_i · A_j^i · [(M_j^i - M̄_i) / M̄]²

where:

• X_i: Molar fraction of element i
• A_j^i: Natural abundance of isotope j of element i [%]
• M_j^i: Atomic mass of isotope j of element i [u]
• M̄_i: Average atomic mass of element i [u]
• M̄: Average molar mass of the alloy [u]

Database Source

All isotope masses and abundances are taken from the CRC Handbook of Chemistry and Physics. The database covers elements H (Z=1) through Bi (Z=83).

Usage

// Example: Hastelloy C-276 (Ni-Mo-Cr alloy)
Abundance db;
Cell<string> elements = {"Ni", "Mo", "Cr"};
Vector<real> mass_fractions = {0.0, 0.16, 0.155};  // fractions; the 0 marks the balance element (Ni)
real M, Gamma;
db.compute_molar_mass_and_impurity_from_masses(
    elements, mass_fractions, M, Gamma
);
// M ≈ 0.0593 kg/mol, Γ used in Callaway conductivity model

Reference: Zou & Balandin, J. Appl. Phys. 89, 2932 (2001) for τ_M formulation