Tetragonal distortion field of hydrogen atoms in iron

The difference between the chemical potential μ _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 where σ _i stands for principal stress, ε _ii ^′ for the strain component along the direction of the principal stress, V for volume, and U 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 stress σ*. For a general polycrystal the formulas are, respectively, C _ten =C ₀ exp[(0.70089ε₁₁ + 0.2991lε₂₂)Vσ/R T]and C _com =C ₀ exp[(0.14956ε₁₁ + 0.85044ε₂₂)Vσ*/R T], where C _ten., C _com., and C ₀ are, respectively, the hydrogen concentrations under tensile stress, compressive stress, and without stress; R stands for the gas constant and T for absolute temperature. Hence, ε₁₁/ε₂₂ may be determined in terms of C _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 in α-Fe is nonspherical symmetry. For a torsional stress τ, U _tor = -0.55133 V _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 of α = 45 deg to torsional axis, which was observed in precharged smooth torsional or type III cracked specimens made of ultra-high strength steel.