Dislocation creep of calcite

When the power law equation, (epsilon)over dot proportional to sigma(n) exp(-Q/RT), which relates strain rate (epsilon)over dot, stress (sigma), gas constant (R), and temperature (T), is used to describe thermally activated dislocation creep of calcite rocks, the stress sensitivity (n) and temperature sensitivity or apparent activation energy (Q) differ greatly from rock to rock. To better constrain parameters of a mechanical equation of state, we performed triaxial deformation experiments on dense synthetic aggregates of polycrystalline calcite at temperatures of 873-1073 K and strain rates between 5x10(-7) and 3x10(-3) s(-1) to strains <0.20. The strength of the marbles decreases with increasing temperature or decreasing strain rate. Combining microstructure analysis with mechanical data indicates that strength decreases with increasing grain size (d) following a Hall-Petch relation. A detailed analysis of the data revealed systematic dependence of n and Q on stress, grain size, and temperature. The variations in n and Q can be accommodated by using a Peierls law, (epsilon)over dot(P)=A(P)sigma(2) exp(sigma/sigma(P))exp(-Q(P)/RT). The resistance to glide, sigma(P), is composed of an intrinsic Peierls stress and a grain size dependent back stress and is given by sigma(P)=(Sigma(P,0)+Kd(-0.5))(T-m-T), where T-m denotes the melting temperature. The following parameters seem to apply to all calcite rocks: A(P)approximate to 10(+/- 0.5) MPa-2 s(-1), Q(P)approximate to 200 kJ/mol, Sigma(P,0)approximate to 7.8 MPa kK(-1), and K approximate to 115 MPa kK-1 mu m(0.5). Under some laboratory conditions, dislocation creep may operate simultane(ou)sly with grain size sensitive diffusion creep, complicating the quantification of the individual flow laws. More accurate flow laws will need to include the evolution of microstructure in composite flow laws, perhaps requiring a statistical description of a microstructure variable yet to be specified exactly.