Low-Frequency Attenuation and Transient and Steady-State Deformation...
Attenuation (Q-1) is alternatively described as "damping" or as "internal friction." It is the absorption by materials of mechanical energy (i.e., its conversion to heat). In geophysics, the interest is in using the absorption of seismic waves as a probe of the structure of the deep Earth. (In engineering systems, the interest is related to control of vibrations in structures.)
Interpreting the seismic signature requires knowledge of internal friction properties of the minerals and rocks that make up the planet; such knowledge can only come from experiments. We are engaged in the experimental evaluation of attenuation in polycrystalline olivine (magnesium-iron orthosilicate: [Mg,Fe 2SiO4), of olivine-orthopyroxene ([Mg,Fe]SiO3) aggregates (synthetic harzburgite) and of partial melts that include a crystalline olivine or olivine-orthopyroxene residuum. The research involves experiments at quite high temperatures (1100-1400oC) and at low (i.e., seismic and sub-seismic) frequencies (10-3-100 Hz). We have developed a number of unique apparatus to do this work, like the torsion rig shown schematically in Fig. 1. In the research, we have successfully (1) demonstrated the seismic signature of partial melting at the scale of the grain size, and (2) isolated the specific role of grain boundaries in effecting attenuation (e.g., Fig. 2), suggesting a way to use the earthquake record to probe the structure of actively plastically deforming regions of the mantle. Too, this discovery has allowed a physical model to be postulated concerning the origin of the "high-temperature background" absorption in engineering materials. We are exploring the validity of this postulate in experiments on solder alloys in collaboration with Prof. Rod Lakes at the University of Wisconsin-Madison. In eutectic solders, the two-phase aggregates have microstructures essentially indentical to those of ice/salt-hydrate eutectics; thus, such studies may allow understanding of the physics of tidal energy dissipation on, e.g., the Jovian moon Europa.
Figure 1: High-temperature torsional creep and attenuation apparatus for measurements of deformation at temperatures up to 1400oC. The parts above the Base Plate (piston, support rods, reference rods, spacers; all but the specimen) are fabricated from the refractory molybdenum alloy TZM. The high-temperature portion of the apparatus is placed in a controlled-oxygen-activity environment (dynamic gaseous buffer). The apparatus has torque and angular displacement resolution of 2x10-6N m and 4x10-7rad, respectively.
Figure 2: Universal Q-1 versus frequency curve for all materials deforming via grain boundary diffusional creep. t is not a standard exponential-decay loss period from linear viscoelasticity, but rather is the time necessary to dissipate stress transients by chemical diffusion along grain boundaries. Data suggest that such a universal response might also be defined for dislocation rheologies.
Gribb, T.T. and R.F. Cooper (1998b). Low frequency shear attenuation in polycrystalline olivine: Grain boundary diffusion and the physical significance of the Andrade model for viscoelastic rheology. J. Geophys. Res. 103, 27,267-27,279.
Gribb, T.T. and R.F. Cooper (2000) . The effect of an equilibrated melt phase on the shear creep and attenuation behavior of polycrystalline olivine. Geophys. Res. Lett. 27, 2341-2344.
Cooper, R.F. (2002). Seismic wave attenuation: Energy dissipation in viscoelastic crystalline solids. Rev. Mineral. Geochem. 51, 253-290.
McMillan, K.M., R.S. Lakes, R.F. Cooper and T. Lee (2003). The viscoelastic behavior of b-In3Sn and the nature of the high-temperature background. J. Mater. Sci. 38, 2747-2754.
Applying materials science experiments and theory to problems in geophysics frequently requires an extrapolation of experimental data some ten orders of magnitude (or more) in time! To do so, we must understand very well the physics of plasticity and other mechanical responses. In collaboration with Prof. Donald Stone at the University of Wisconsin, we are pursuing the unification of two descriptions of plasticity: (1) the phenomenology associated with steady-state creep (strain at constant stress) and (2) the phenomenology associated with stress relaxation (stress drop at nominally constant strain). The latter approach is often described as suggesting a "mechanical equation of state," in which a single internal state variable, i.e., one describing the deformation-effected microstructure, allows integration of the mechanical response, that is, it allows plastic strain to be considered a (path-independent) state variable. Stone's unifying model suggests that it is the distribution of subgrain sizes (as opposed to, say, the mean or median subgrain size) that is perhaps the key to the microstructural state variable; we are probing experimentally this hypothesis. We are pursuing this work with experiments on single-crystal creep and load-relaxation experiments on specimens of NaCl (where dislocation structures can be characterized over a large area through the use of surface etching) and olivine (where dislocation structures can be evaluated in three dimensions via transmitted-light microscopy of specimens where the dislocations are "decorated" via a solid-state oxidation process, Fig. 3).
Figure 3: Transmitted-light micrograph of lattice dislocation structure in an olivine single crystal deformed at 1400oC at ~150MPa differential stress. The image comprises a field of view some 225 mm across the bottom of the figure; the applied compressive stress was in a vertical orientation. One can easily resolve end-on dislocations (dots); the formation of subgrain boundaries (dislocation arrays: linear arrangements of dots) and the presence of either regions of slip concentration or of subgrain boundaries constituted of dislocations having a different crystallography than those in end view (heavy lines). What is being imaged is the precipitation of fine particles of Fe3O4 spinel and amorphous SiO2 at the cores of the dislocations as the fayalite component of the olivine is oxidized in the reaction 3/2Fe2SiO4 (fayalite) + ½O2 = Fe3O4 (magnetite) + 3/2SiO2 (silica).
Stone, D.S., T. Plookphol and R.F. Cooper (2004). Similarity and scaling in creep and load relaxation of single-crystal halite (NaCl). J. Geophys. Res. 109, B12201, doi:10.1029/2004JB003064.
Brown faculty collaborators:
Other project collaborators:
Gribb, T.T., McMillan, K.M., R.S. Lakes, T. Lee, Stone, D.S., T. Plookphol
Figure 3Back to Reid Cooper's Brown Research Profile