Induced Stress and Secondary Mass Transfer: Thermodynamic Basis for the Tendency toward Constant-Volume Constraint in Diffusion Metasomatism

Abstract

“Induced stress” and “secondary mass transfer” give thermodynamic sanction to Lindgren’s hypothesis that metasomatic processes tend to take place at constant volume. Owing to the finite strength of minerals and rocks, the assumption that pressure remains constant and uniform during irreversible diffusion metasomatism is generally not tenable. The migration of a nonplanar diffusion-metasomatic zone boundary induces a field of nonhydrostatic stress, except in the special case where the metasomatic reaction at the zone boundary has a zero volume-change. The stress field is created at the expense of the “primary” chemical-potential gradients caused by overstepping of whatever net reaction may be taking place in the whole system, and it is so oriented as to tend to inhibit the displacement and distortional strain that must accompany the migration of the zone boundary. “Secondary” chemical-potential gradients are induced by the stress field. To the extent that “secondary” mass transfer is driven by such gradients, the induced stress-field tends to relax towards constant and uniform pressure. If the secondary mass transfer is so efficient that the induced stress never rises to the threshold value necessary to cause irreversible distortional strain in one or the other zone, the reaction at the migrating zone boundary will be constrained to take place at virtually constant volume.

“ The fact seems to be that physical chemists are so used to consider systems inequilibrium and reactions in open space or in liquids that they give little attention to other conditions.”

W . Lindgren (1925, p.251)