The determination of the partial molar volume of hydrogen in zirconium in a simple stress gradient using comparative microcalorimetry

In a simple stress gradient using comparative micro-calorimetry the role of stress in the diffusion of mobile atomic species in solids was established by Li, Oriani and darken. They showed that to a very good approximation the chemical potential of a mobile species in a stressed solid is given by: {mu}{sub A} = {mu}{sub 0} {minus} p{bar V}{sub A} where {mu}{sub 0} is the chemical potential at zero stress, p is the average principal stress which is positive if tensile, and {bar V}{sub A} is the partial molar volume of the mobile atom species A, and reflects the volume change per mole of species A when an atom of A enters the solid region under consideration. They also showed that for equilibrium between stressed and unstressed regions the concentration varies with respect to p in the following way: C{sup P}{sub A} = C{sup 0}{sub A} exp p{bar V}{sub A}/RT where C{sup 0}{sub A} is the concentration at zero stress and C{sup p}{sub A} that at the stress p. Consider a specimen which is at equilibrium with respect to diffusion and which contains a stress gradient. It we can measure the concentration of the species A in regions within which pmore » varies but is well-characterized, then the value of {bar V}{sub A} can be determined. We shall return to this equation later in the paper as it is key to our development. The flux of mobile species under a gradient in free energy is given by: J = {minus}Dc/kT {del}{mu} which in combination yields the flux of a mobile species in a stress gradient: J = {minus}Dc{bar V}{sub A}/kT {del}p where D is the diffusion coefficient, c is the concentration of the species, k is Boltzmann's constant and T is the absolute temperature.« less