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The exoplanet mass radius diagram reveals that super Earths display a wide range of radii, and therefore mean densities, at a given mass. Using planet population synthesis models, we explore the key physical factors that shape this distribution: planets' solid core compositions, and their atmospheric structure. For the former, we use equilibrium disk chemistry models to track accreted minerals onto planetary cores throughout formation. For the latter, we track gas accretion during formation, and consider photoevaporation-driven atmospheric mass loss to determine what portion of accreted gas escapes after the disk phase. We find that atmospheric stripping of Neptunes and sub-Saturns at small orbital radii ($\lesssim$0.1AU) plays a key role in the formation of short-period super Earths. Core compositions are strongly influenced by the trap in which they formed. We also find a separation between Earth-like planet compositions at small orbital radii $\lesssim$0.5AU and ice-rich planets (up to 50\% by mass) at larger orbits $\sim$1AU. This corresponds well with the Earth-like mean densities inferred from the observed position of the low-mass planet radius valley at small orbital periods. Our model produces planet radii comparable to observations at masses $\sim$1-3M$_\oplus$. At larger masses, planets' accreted gas significantly increases their radii to be larger than most of the observed data. While photoevaporation, affecting planets at small orbital radii $\lesssim$0.1AU, reduces a subset of these planets' radii and improves our comparison, most planets in our computed populations are unaffected due to low FUV fluxes as they form at larger separations.