Thermodynamics of stress-induced interstitial redistribution in body-centered cubic metals
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10/30/03
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Thermodynamics of Stress-induced Interstitial Redistribution in Body-Centered Cubic Metals WILLIAM C. JOHNSON and J.Y. HUH A set of open-system elastic constants used to approximate the redistribution of interstitial atoms among the three different interstitial sublattices in a body-centered cubic (bcc) metal is derived accounting for the tetragonal nature of the compositional strain in the presence of a nonhydrostatic stress. Predictions of the stress-induced composition change are calculated and compared to the actual solution and to two other approximation schemes, one based on a hydrostatic compositional strain and one based on ignoring the compositional self-stress. The open-system elastic constants give a qualitatively and quantitatively accurate representation of the composition changes when the far-field composition is greater than a few percent. For very small far-field compositions, less than about 104, the compositional self-stress can be ignored in calculating the stress-induced interstitial redistribution. However, for larger far-field compositions, neglecting the compositional self-stress can overestimate significantly the degree of interstitial redistribution.
I. INTRODUCTION
THE elastic stress field associated with material defects in crystals can affect the equilibrium distribution of the individual component species. For example, dislocations,[1,2] precipitates,[3] interfaces,[4] and cracks[5,6] can redistribute solute atoms owing to the elastic interaction between the defect and the compositional strain of the component species. This interaction can have a significant influence on the mechanical[7] and electrical[8] properties of the crystal. The body-centered-cubic (bcc) crystal contains two substitutional atoms and six octahedral sites for interstitials per cubic unit cell. Common interstitial elements occupying octahedral sites in bcc metals, including hydrogen and carbon, induce a tetragonal distortion or compositional strain in the crystal lattice. The tetragonal distortion frequently displays a strong asymmetry with a large positive strain along the tetragonal axis and a significant compressive strain along the two perpendicular directions. The tetragonal axis of the compositional strain is oriented along one of the directions parallel to the three edges of the cubic unit cell. The interstitial lattice of the bcc crystal can be viewed as consisting of three sublattices, which, in the absence of an external stress field, are degenerate in their energy. If the interstitial occupies all three sublattices of a volume element equally, as is expected for a stress-free or hydrostatically stressed system, the net compositional strain of a volume element averages to a uniform or isotropic dilatational field. This isotropic compositional strain has been used to calculate the equilibrium distribution of interstitial species in iron.[9,10] However, the averaged compositional strain can be several times smaller in magnitude than the individual strain components of the co
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