High-pressure electrical resistance measurements have been performed on single crystal Ba0.5Sr0.5Fe2As2 platelets to pressures of 16 GPa and temperatures down to 10 K using designer diamond anvils under quasi-hydrostatic conditions with an insulating steatite pressure medium. The resistance measurements show evidence of pressure-induced superconductivity with an onset transition temperature at ~31 K and zero resistance at ~22 K for a pressure of 3.3 GPa. The transition temperature decreases gradually with increasing in pressure before completely disappearing for pressures above 12 GPa. The present results provide experimental evidence that a solid solution of two 122-type materials, e.g., Ba1-x.SrxFe2As2 (0 < x <1), can also exhibit superconductivity under high pressure
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