Mirrors made of silicon have been proposed for use in future cryogenic gravitational-wave detectors, which will be significantly more sensitive than current room-temperature detectors. These mirrors are planned to have diameters of ≈ 50 ,cm and a mass of ≈ 200 ,kg. While single-crystalline float zone silicon meets the requirements of low optical absorption and low mechanical loss, the production of this type of material is restricted to sizes much smaller than required. Here we present studies of silicon produced by directional solidification. This material can be grown as quasi-monocrystalline ingots in sizes larger than currently required. We present measurements of a low room-temperature and cryogenic mechanical loss comparable t...