Estimates of differential stress and duration of annealing of crust deduced from progressive shape evolution of a mineral inclusion: Example of garnet inclusions within a granulite-facies quartzite from the Lützow-Holm Complex

Interfacial tension, γ, and differential stress, σ, affect the shape of a mineral grain included within a crystalline host. We present a simple model that predicts the progressive change in aspect ratio of an ellipsoidal inclusion. Three processes are considered in the model: dislocation creep, interface diffusion creep, and rounding by interface diffusion. The model reveals that (1) the inclusion aspect ratio (L) evolves toward a steady-state value, (2) the time taken to achieve a steady-state aspect ratio increases with increasing grain size (R), and (3) the dominant deformation mechanism varies from diffusion creep to dislocation creep with increasing grain size and/or differential stress. The L-R distribution pattern of garnets in a granulite-facies quartzite from the Lützow-Holm Complex, East Antarctica is compared with the model result. The garnet aspect ratio systematically varies with respect to grain size, and the most elongate ones are of intermediate grain size (~ 0.25 mm). Assuming γgrtqtz = 1.0 N/m, the L-R pattern of small inclusions (< 0.25 mm) is similar to the model predictions of 1.4×10-2 MPa, whereas that of coarser inclusions cannot be explained by such a small differential stress. A two-stage deformation with high and low differential stresses (stage A and B) best explains for the observed L-R pattern of garnets. The duration (tA) at stage A is determined only when the differential stress (σa) is assumed due to the size independency of dislocation creep. Assuming Dgb,A = 1.0×10-12m2s, Dgb,B} = 1.0×10-11m2/s and σA = 1.0 MPa, the garnet data is fitted to a theoretical curve under condition of σb = 1.4×10-2 MPa, tA = 0.5 Myr and tB = 14.4 Myr.