On the orthosilicate join, Li4SiO4-Mn2SiO4, the new phase Li3Mn0.5SiO4 and a range of Li2+2xMn1-xSiO4 solid solutions with similar to 0.76 <= x <= 1 have been prepared by high-temperature, solid-state reaction and characterized. Li3Mn0.5SiO4 is orthorhombic, space group Pnma, with a = 10.722(3) angstrom, b = 6.239(2) angstrom, and c = 5.052(3) angstrom. A combined analysis of X-ray and neutron powder diffraction data show that its structure is derived from the gamma(11) tetrahedral structural family typified by Li3PO4, but with additional Li+ in partially occupied, distorted octahedral sites. These octahedral sites are linked by a combination of edge- and face-sharing, similar to that in the nickel arsenide structure and their partial occupancy is responsible for an Li+ ion conductivity of, for example, similar to 1 x 10(-8) S cm(-1) at 60 degrees C, with activation energy 0.93(1) eV, which is many orders of magnitude higher than that of Li2MnSiO4.