The dynamics and mechanical behavior of Earth's upper mantle depend in large part on the solid-state flow of olivine. Flow in olivine, as for many phenomena in crystalline materials, can be best understood as the result of structural perturbations at or near the atomic scale. Therefore, it is essential that the scale at which these phenomena are investigated approach the length scale of the perturbations themselves. This dissertation presents nanoscale information on two common structural perturbations in olivine, dislocations and low-angle grain boundaries, obtained using high-resolution transmission electron microscopy coupled with geometric phase analysis.; The analysis of displacements and strain around a perfect [100] dislocation in olivine was the first measurement of its kind made for a mineral. An accuracy of 9 picometers was attained for the displacement fields as compared to the displacements predicted using elastic theory. The displacements were used to map the strain fields and rotation field around the dislocation. The rotation measurement was extended to study a low-angle grain boundary in olivine. Analysis revealed that the boundary plane is wavy rather than flat, and the waviness is in strong agreement with predictions based on elastic theory. This agreement prompted the question of whether this is an intrinsic boundary property independent of the host material. Derivation of the rotation across infinite arrays of dislocations starting from the displacements given by elastic theory confirmed that waviness is indeed intrinsic to grain boundaries containing more than one family of dislocations. The waviness was incorporated into the Read-Shockley model of low-angle grain boundaries, thereby extending the model to the nanoscale. Finally, the strain fields and strain-energy density around dissociated dislocations and a perfect [100] dislocation were determined. Interactions between weakly dissociated partial dislocations were inferred from the measured strain fields. The observed strain-energy distribution in the region close to the dislocation core suggests that estimates regarding dislocation stabilities must be re-examined at the nanoscale.
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