Stars in open clusters are expected to share an identical abundance pattern. Establishing the level of chemical homogeneity in a given open cluster deserves further study as it is the basis of the concept of chemical tagging to unravel the history of the Milky Way. M67 is particularly interesting given its solar metallicity and age as well as being a dense cluster environment. We conducted a strictly line-by-line differential chemical abundance analysis of two solar twins in M67: M67-1194 and M67-1315. Stellar atmospheric parameters and elemental abundances were obtained with high precision using Keck/HIRES spectra. M67-1194 is essentially identical to the Sun in terms of its stellar parameters. M67-1315 is warmer than M67-1194 by ~ 150 K as well as slightly more metal-poor than M67-1194 by ~ 0.05 dex. M67-1194 is also found to have identical chemical composition to the Sun, confirming its solar twin nature. The abundance ratios [X/Fe] of M67-1315 are similar to the solar abundances for elements with atomic number Z <= 30, while most neutron-capture elements are enriched by ~ 0.05 dex, which might be attributed to enrichment from a mixture of AGB ejecta and r-process material. The distinct chemical abundances for the neutron-capture elements in M67-1315 and the lower metallicity of this star compared to M67-1194, indicate that the stars in M67 are likely not chemically homogeneous. This poses a challenge for the concept of chemical tagging since it is based on the assumption of stars forming in the same star-forming aggregate.
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