We present ultrasonic measurements of elastic anisotropy in gallium undergoing directional solidification in the presence of imposed thermal gradients, rotation, convection, turbulence, and magnetic fields. Simultaneous in situ measurements of temperature and compressional wave speed are used to track the crystallization front during solidification. We find that individual solidified gallium samples are always polycrystalline and elastically anisotropic, with grains elongated in the solidification direction. The measured compressional wave anisotropy in individual solid samples ranges from 20 to 80% of the single crystal values, depending on experimental conditions. We also find the amount of elastic anisotropy varies with position in an individual sample. Based on ensemble averages from multiple experiments made under similar environmental conditions, we find the direction of elastic anisotropy in the solid is sensitive to the thermal: gradient direction, while the amount of anisotropy is most sensitive to the presence or absence of initial nucleation in the melt. Experiments that show average anisotropy have the ultrasonically fast axis aligned with gravity and the thermal gradient. Strongly anisotropic solids result when nucleation grains are present in the initial melt, whereas smaller or zero average anisotropy results when nucleation grains are initially absent. Other externally imposed factors we have examined, such as turbulence and magnetic fields, have either no measurable influence or tend to reduce the amount of anisotropy of the solid. Our results suggest that during crystallization of Earth's inner core, the orientation of average anisotropy in the newly formed solid is controlled primarily by radial solidification, while the amount of anisotropy may be influenced by pre-existing inner core texture. (C) 2002 Elsevier Science B.V All rights reserved.