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H-Solubility

Evaluates the energetics of inserting a single hydrogen atom into octahedral and tetrahedral interstitial sites of a BCC host, and reports the lowest-energy (preferred) site.

Overview

Interstitial solubility of hydrogen governs hydrogen embrittlement and storage behavior in metals. In a BCC lattice the two candidate interstitial families are octahedral sites (6 per conventional cell, each with 2 nearest neighbors close and 4 farther away, the geometry relevant to H trapping in ferritic steels) and tetrahedral sites (12 per conventional cell, 4 equidistant nearest neighbors). HSolubilityAnalyzer inserts a hydrogen atom at each candidate site of each requested family, relaxes (or, with is_relaxed=True, single-point evaluates) the resulting host+H structure, and compares its energy against the clean host and a hydrogen reference. The host itself can be supplied directly or generated for a given composition via SqsGenerator (through HSolubilityTransformation). When the host is relaxed from scratch (is_relaxed=False), interstitial sites are re-generated on the relaxed host so site positions reflect the relaxed lattice, not the initial guess.

Theory

For a host of energy \(E_{\text{host}}\) and a host-plus-hydrogen structure of energy \(E_{\text{host+H}}\), the insertion energy at that site is

\[ E_{\text{ins}} = E_{\text{host+H}} - E_{\text{host}} - E_{\text{H}}^{\text{ref}} \]

where \(E_{\text{H}}^{\text{ref}}\) is the hydrogen_reference_energy supplied at construction: typically half the energy of an isolated H\(_2\) molecule, \(\tfrac{1}{2} E(\text{H}_2)\), so that \(E_{\text{ins}}\) measures the energy cost of moving a hydrogen atom from the gas-phase molecule into the lattice. \(E_{\text{ins}}\) is computed for every generated site of every requested site_types family, and the minimum within each family is kept:

\[ E_{\text{ins}}^{\text{min}} = \min_{\text{sites}} E_{\text{ins}} \]

The overall solution_energy is the smaller of the octahedral and tetrahedral minima, and preferred_site_type records which family it came from. Octahedral sites win when their minimum is less than or equal to the tetrahedral one. A lower solution energy means hydrogen more readily dissolves into that site family.

References