Recent astronomical observations obtained with the Kepler and TESS missions and their related ground-based follow-ups revealed an abundance of exoplanets with a size intermediate between Earth and Neptune (1 R ⊕ ≤ R ≤ 4 R ⊕). A low occurrence rate of planets has been identified at around twice the size of Earth (2 × R ⊕), known as the exoplanet radius gap or radius valley. We explore the geometry of this gap in the mass–radius diagram, with the help of a Mathematica plotting tool developed with the capability of manipulating exoplanet data in multidimensional parameter space, and with the help of visualized water equations of state in the temperature–density (T–ρ) graph and the entropy–pressure (s–P) graph. We show that the radius valley can be explained by a compositional difference between smaller, predominantly rocky planets (<2 × R ⊕) and larger planets (>2 × R ⊕) that exhibit greater compositional diversity including cosmic ices (water, ammonia, methane, etc.) and gaseous envelopes. In particular, among the larger planets (>2 × R ⊕), when viewed from the perspective of planet equilibrium temperature (T eq), the hot ones (T eq ≳ 900 K) are consistent with ice-dominated composition without significant gaseous envelopes, while the cold ones (T eq ≲ 900 K) have more diverse compositions, including various amounts of gaseous envelopes.

Early silicate differentiation events for the terrestrial planets can be traced with the short-lived146Sm-142Nd system (∼100-My half-life). Resulting early Earth-produced142Nd/144Nd variations are an excellent tracer of the rate of mantle mixing and thus a potential tracer of plate tectonics through time. Evidence for early silicate differentiation in the Hadean (4.6 to 4.0 Ga) has been provided by142Nd/144Nd measurements of rocks that show both higher and lower (±20 ppm) values than the present-day mantle, demonstrating major silicate Earth differentiation within the first 100 My of solar system formation. We have obtained an external 2σ uncertainty at 1.7 ppm for142Nd/144Nd measurements to constrain its homogeneity/heterogeneity in the mantle for the last 2 Ga. We report that most modern-day mid-ocean ridge basalt and ocean island basalt samples as well as continental crustal rocks going back to 2 Ga are within 1.7 ppm of the average Earth142Nd/144Nd value. Considering mafic and ultramafic compositions, we use a mantle-mixing model to show that this trend is consistent with a mantle stirring time of about 400 My since the early Hadean. Such a fast mantle stirring rate supports the notion that Earth’s thermal and chemical evolution is likely to have been largely regulated by plate tectonics for most of its history. Some young rocks have142Nd/144Nd signatures marginally resolved (∼3 ppm), suggesting that the entire mantle is not equally well homogenized and that some silicate mantle signatures from an early differentiated mantle (>4.1 Ga ago) are preserved in the modern mantle.

We present an optimized α-HIBA column chromatography method for Nd for high-precision isotope analyses (±2–5 ppm). It produces consistently high yields (>95%) and extremely good separation of Ce, Pr and Sm from Nd.