We present a high-precision differential abundance analysis of 16 solar-type stars in the Hyades open cluster based on high resolution, high signal-to-noise ratio (S/N ~ 350 - 400) spectra obtained from the McDonald 2.7m telescope. We derived stellar parameters and differential chemical abundances for 19 elements (C, O, Na, Mg, Al, Si, S, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, and Ba) with uncertainties as low as ~ 0.01 - 0.02 dex. Our main results include: (1) there is no clear chemical signature of planet formation detected among the sample stars, i.e., no correlations in abundances versus condensation temperature; (2) the observed abundance dispersions are a factor of ~ 1.5 - 2 larger than the average measurement errors for most elements; (3) there are positive correlations, of high statistical significance, between the abundances of at least 90% of pairs of elements. We demonstrate that none of these findings can be explained by errors due to the stellar parameters. Our results reveal that the Hyades is chemically inhomogeneous at the 0.02 dex level. Possible explanations for the abundance variations include (1) inhomogeneous chemical evolution in the proto-cluster environment, (2) supernova ejection in the proto-cluster cloud, and (3) pollution of metal-poor gas before complete mixing of the proto-cluster cloud. Our results provide significant new constraints on the chemical composition of open clusters and a challenge to the current view of Galactic archeology.
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