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In order to study quartz-coesite transition under the conditions of differential stress, experiments of quartzite deformation were carried out using a triaxial testing system with a Griggs type solid medium pressure vessel. Analyses on the plastically-deformed samples under optical microscope and Raman spectra show that fine-grained coesite was present in the region of samples adjacent to the pistons at temperatures of 950-1000℃, confining pressure of 1.3 GPa, differential stress of 1.5-1.67 GPa, and total strain of 75%-81%. It is evident that the transition pressure of quartz-coesite at differential stress and intensely-strained conditions is far lower than the pressure for coesite stability at isostatic pressure. In other words, the stress condition of coesite occurrence is not unique. The decrease in confining pressure for quartz-coesite transition under differential stress conditions is controlled by a combined effect of the maximum principal stress that provides a high stress environment, and differential stress that causes sample deformation. Coesite was produced in the plastically-deformed samples in this study, but it can occur in both semi-brittle and plastic deformation regimes as seen in previous studies. Phase transition in semi-brittle deformation regime is caused by local mechanical instability induced by shear deformation, and phase transition in plastic flow regime is due to strain instability induced by the presence of a high dislocation density within intensely-deformed quartz crystals.