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Experiments show that temperature gradients in silicate melts lead to isotope fractionation, where the heavier isotopes concentrate in cold regions and light isotopes concentrate in hot regions1,2,3,4. Dominguez et al.5 present a phenomenological model based on quantum effects that provides a good fit to these experimental results, and argue that “consideration of the quantum mechanical zero-point energy of diffusing species is essential for understanding diffusion at the isotopic level”. However, we point out that the zero-point energy required to fit their model to experimental results is unphysically large, and that isotopic fractionation similar to that observed in silicate melts is found in systems where quantum effects are absent. Therefore, the conclusion that quantum effects underlie isotope fractionation in silicate melts with temperature gradients is not justified.

To fit experimental data, the Dominguez et al.5 model requires a zero-point energy (ZPE) for 26Mg of ∼0.4 eV. The atomic motion giving rise to the ZPE is vibrational, and can be modelled by a harmonic oscillator for which ZPE = (1/2)hν, where h is Planck’s constant and ν is the vibrational frequency. (Here for convenience we consider = ν/c, where c is the velocity of light.) The value ZPE ≈ 0.4 eV corresponds to ≈ 6,500 cm−1, which is much larger than the highest vibrational frequencies (∼1,300 cm−1) observed in anhydrous silicate melts6. In fact, ≈ 6,500 cm−1 is larger than the vibrational frequency in any material whatsoever (the highest vibrational frequency we are aware of is that for H2, where ≈ 4,395 cm−1)7. Thus a ZPE of ∼0.4 eV is not physically relevant.

The unphysically large ZPE in the model of Dominguez et al.5 leads to predictions of relative diffusivities of isotopes that are in poor agreement with experiments. For example, their model (equations (11) and (12), and ZPE(26Mg) = 0.4 eV) predicts D(24Mg)/D(26Mg) = 1.13 at 1,500 K. In contrast, experiments on silicate melts find D(24Mg)/D(26Mg) = 1.004 (ref. 2). Thus, the Dominguez et al. model predicts an isotope effect for relative diffusivities that is more than 30 times larger than found experimentally (13% versus 0.4%).

Finally, we note that isotope fractionation in temperature gradients occurs in systems where quantum effects are not relevant; this implies that quantum effects are not a necessary condition for isotope fractionation to occur (whereas they are a necessary condition in the Dominguez et al.5 model). For example, significant fractionation of isotopes is seen in gases held in a temperature gradient8,9,10. In gases, quantum ZPE (arising from confinement) plays no role because molecules typically are far apart. Thermal fractionation of isotopes is also observed in molecular dynamics simulations of condensed phase systems11 based on classical mechanics—these simulations ignore quantum effects, and in contrast to the model of Dominguez et al.5 include no phenomenological considerations. In both of these cases, heavier isotopes concentrate in cold regions and light isotopes concentrate in hot regions, consistent with experimental observations on silicate melts and all other condensed phase systems that have been studied. This effect is understood theoretically in terms of classical mechanics12, and quantitative agreement is obtained between this theory and experiment13.