Tetragonal distortion field of hydrogen atoms in iron

Abstract

The difference between the chemical potentialμ _σ of hydrogen atoms producing a nonspherical symmetry strain in a solid sample under stress and that μ₀ corresponding to the state without stress has been calculated. It is shown that μ_σ - μ₀ = -VΣiσ_iε ^′_ii =U whereσ _i stands for principal stress,ε ^′ _ii for the strain component along the direction of the principal stress,V for volume, andU is the interaction energy between the strain field and external stress field. The hydrogen atoms producing the tetragonally symmetric strain are preferentially ordered in samples under stress. As a result, the variation of hydrogen concentration with tensile stress σ will be different from that with compressive stressσ*. For a general polycrystal the formulas are, respectively,C _ten =C ₀ exp[(0.70089ε₁₁ + 0.2991lε₂₂)Vσ/RT]andC _com =C ₀ exp[(0.14956ε₁₁ + 0.85044ε₂₂)Vσ*/RT], whereC _ten.,C _com., andC ₀ are, respectively, the hydrogen concentrations under tensile stress, compressive stress, and without stress; R stands for the gas constant andT for absolute temperature. Hence, ε₁₁/ε₂₂ may be determined in terms ofC _ten/C _com which can be obtained by hydrogen permeation measurement. For example, according to Bockris' data ε₁₁/ε₂₂ = 1.27 at temperature of 27 °C which implies that the strain field of hydrogen atoms inα-Fe is nonspherical symmetry. For a torsional stressτ,U _tor = -0.55133V _τ(ε₁₁ ε₂₂. The interaction can result in the enrichment of hydrogen atoms on and hydrogen induced delayed cracking along the planes inclined at an angle ofα = 45 deg to torsional axis, which was observed in precharged smooth torsional or type III cracked specimens made of ultra-high strength steel.