This data was collected to study the growth behavior of faceted Si particles in an Al-Si-Cu liquid, upon continuous cooling. The as-cast, hyper-eutectic sample consisted of primary Si particles in a eutectic matrix. Upon heating to above the liquidus temperature for Si (here, we heat to 910 C), the Si particles melted, leaving behind a featureless liquid. Then, the sample temperature was lowered at a rate of 1 C per minute while projections were recorded. After a brief incubation period, the Si particles grew from the oxide skin of the sample into the liquid. The weight fraction of Si particles at temperature was consistent with predictions from equilibrium, indicating that the growth of solid Si can keep up with the quench rate. Nevertheless, the morphologies of the Si particles were not given by the equilibrium shape of Si due to the prevalence of defects during the growth process. Identifying the crystallography and dynamics of these defects (including twin boundaries that intersect the solid-liquid interfaces) was central to this work. The raw data were obtained in the following sequence: for the first 20 min, projections were collected continuously, providing a temporal resolution of 30 s between subsequent 3D reconstructions; for the next 120 minutes, 40 more tomographic scans with the same parameters were spaced 150 s apart. Thus, 80 scans were collected over the course of over 2 hours. The motivation for collecting the X-ray projections in this manner was that the system-average length-scale increased logarithmically with time during bulk diffusion-limited growth. Therefore, this data collection scheme adequately captured the interfacial dynamics. The data here includes the raw projections. Note that dark field and flat field measurements, which are used to normalize the data, are in a separate file. For details on the data processing and quantitative analysis, the reader is pointed to the following publication. Correspondence should be directed to Ashwin J. Shahani (shahani@u.northwestern.edu).