The structural phase diagram of the Pb-free ferroelectric (Na1/2Bi1/2)1−xBaxTiO3, x<0.1, has been explored by Raman spectroscopy at temperatures from 10 to 470 K. The data provide clear evidence for a proposed temperature-independent morphotropic phase boundary at x≈0.055. However, there is no evidence for a structural phase transition across T≈370 K for x>0.055, where bulk-property anomalies appear to signal a transition to a nonpolar or antiferroelectric phase. The results identify that the phase above 370 K shows short-range ionic displacements that are identical to those in the long-range-ordered phase below 370 K. These conclusions provide a natural interpretation of the weak piezoelectric response in this system and have important implications for the search for Pb-free piezoelectrics.