A critical assessment of estimation methods for activation volume

Abstract

We have compared estimates of the activation volume V* based on several theoretical models with measured values in metals, alkali halides, and olivine. The theoretical methods tested include one based upon the empirical correlation between activation energy and melting temperature and several which are based upon simple elastic models for the defect structure. For metals and olivine, the melting relation works well, but for alkali halides, the melting model predicts too large a V* by an approximate factor of 1.5. Of the elastic models, the dilatational strain energy model introduced by Zener (1942) provides reasonable estimates of V* for metals and olivine, but it also overestimates V* for alkali halides. Zener's assertion that the experimental value of V* should be bounded by theoretical values calculated from strain energy models which assume pure shear (Keyes, 1963) and pure dilatation is supported by the available data for metals, oxides, and alkali halides. These provide upper and lower estimates for the variation of viscosity with depth in the mantle.

On the mechanism of dislocation creep of calcite at high temperature: Inferences from experimentally measured pressure sensitivity and strain rate sensitivity of flow stress

“…Apparent activation volume Δ V calculated applying (1) to the experimental data of each individual experiment, using the n ‐values of Table 3. Solid lines represent theoretical values for Δ V determined using (8) and (9) [after Sammis et al , 1981]. …”

“…The apparent values for Δ V can be compared with theoretical values for the activation volume for creep controlled by diffusion of vacancies calculated on the basis of elastic (dilatational) strain energy models for point defects [see Keyes , 1963; Sammis et al , 1981; Poirier and Lieberman , 1984]. The strain energy associated with a point defect exists in two forms, as energy of dilatation and as energy of shear [ Sammis et al , 1981]. Accordingly, theoretical values for Δ V can be calculated assuming the strain energy is all shear and if the strain energy is all dilatational, respectively: where K and μ are the bulk‐ and shear modulus, β* is the volume coefficient of thermal expansion, and Δ U is the activation energy for volume diffusion.…”

“…Accordingly, theoretical values for Δ V can be calculated assuming the strain energy is all shear and if the strain energy is all dilatational, respectively: where K and μ are the bulk‐ and shear modulus, β* is the volume coefficient of thermal expansion, and Δ U is the activation energy for volume diffusion. Analysis of experimental values of the activation volume of a number of materials has shown that Δ V lies between the shear and dilatational model estimates ((8) and (9), respectively), though (9) provides the best estimate of Δ V [ Sammis et al , 1981]. Predicted values for calcite are shown in Figure 10, taking β* = 1.65 × 10 −5 [ Carmichael , 1984] and Δ U = 382 kJ/mol [ Farver and Yund , 1996].…”

Laboratory Constraints on the Rheology of the Upper Mantle

“…A large range in V*, from ~0 to 27 × 10 -6 m 3 /mol, has been reported in the literature based on a combination of experimental and theoretical analyses (e.g., Sammis et al 1981;Borch and Green 1989;Karato and Rubie 1997;Karato and Jung 2002;Hirth and Kohlstedt 2003;Wang et al (in preparation). In addition, there are very few data available to evaluate V* for the diffusion creep regime (Kohlstedt et al 2000).…”

Qp‐melting temperature relation in peridotite at high pressure and temperature: Attenuation mechanism and implications for the mechanical properties of the upper mantle

“…;Sherby and Sirehad, 1961;Shewmon, 1963] and for creep rate of rocks[Weertman, 1970; Weertman and Weert•nan, 1975]. The parameter g of the diffusion coefficient is approximately constant for metals that have the same crystal structure[Sherby and Sirehad, 1961;Sammis et al, 1981]; it is approximately equal to 18 for metals and 30 for silicates[Poirier, 1985]. Changes in chem-…”