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The distribution of gas-phase abundances in galaxy disks encodes the history of nucleosynthesis and transport through the interstellar medium (ISM) over cosmic time. Multi-object and high resolution integral-field spectroscopy have started to measure these distributions across hundreds of HII regions individually resolved at $lesssim 100$ pc scales in a handful of objects, but in the coming decade these studies will expand to larger samples of galaxies. This will allow us to understand the role of feedback and turbulence in driving the mixing and diffusion of metals in the ISM, and statistically assess the role of galaxy environment and disk dynamics in modifying how mixing proceeds. Detailed searches for over- and under-enriched regions can address to what extent star formation is triggered by previous generations of star formation and by pristine and recycled gas flows. Local galaxies, for which these detailed measurements will be possible within the next decade, will inform the interpretation of integrated measurements at high-z, where very different dynamical gas-rich environments are found in early disk galaxies. Currently, progress in the field is severely hampered by the 0.2-0.3 dex level systematic uncertainties plaguing nebular abundance diagnostics. Improving our detailed understanding of ionized nebulae at $<$20 pc scales will help us find a solution to this problem, which will prove key to the study of metal enrichment and mixing across the galaxy population in the next decade.
The distribution of metals within a galaxy traces the baryon cycle and the buildup of galactic disks, but the detailed gas phase metallicity distribution remains poorly sampled. We have determined the gas phase oxygen abundances for 7,138 HII regions
Element abundances in high-redshift quasar absorbers offer excellent probes of the chemical enrichment of distant galaxies, and can constrain models for population III and early population II stars. Recent observations indicate that the sub-damped Ly
The CHemical Abundances of Spirals (CHAOS) project leverages the combined power of the Large Binocular Telescope with the broad spectral range and sensitivity of the Multi Object Double Spectrograph (MODS) to measure direct abundances in large sample
Gas-phase abundances and abundance gradients provide much information on past stellar generations, and are powerful probes of how galaxies evolve. Gas abundance gradients in galaxies have been studied as functions of galaxies mass and size individual
We present SOFIA/FIFI-LS observations of the [CII] 158${mu}$m cooling line across the nearby spiral galaxy NGC 6946. We combine these with UV, IR, CO, and H I data to compare [CII] emission to dust properties, star formation rate (SFR), H$_2$, and HI