Dominguez et al. reply

Abstract

Replying to D. J. Lacks, J. A. Van Orman & C. E. Lesher Nature 482, (2012)

Lacks et al.¹ argue that our model of isotopic fractionation in thermal gradients in silicate melts² does not agree with measurements of the ratio of diffusivities seen in silicate melts. This statement is based on an over-interpretation of our model into non-steady-state applications, such as chemical fractionation, because the model we presented treats the quantized energy levels of the transition state as being equal to each other (the partition function Z(TS) = 1). This was warranted, as our main interest was in finding the steady-state solution to isotopic fractionation in a closed system (which is insensitive to the transition state). The potential importance of the transition state in determining the ratios of diffusivities of He isotopes in a geologic system has previously been noted³, and future work will need to clarify the importance of the transition state for kinetic isotopic fractionation in silicate systems, particularly the ratio of diffusivities.

Main

Lacks et al.¹ point out that isotopic fractionation due to temperature gradients in the gas phase have been observed (for example, ref. 4), but they do not provide proof that classical mechanics quantitatively explains these observations. Furthermore, Lacks et al.¹ (and references therein) provide no evidence that molecular dynamics simulations reproduce the isotopic fractionations observed in real gas systems, much less high-temperature condensed phases. A full understanding of isotopic fractionation for complex (diatomic, polyatomic) species, even in the gas phase, is likely to require quantum mechanics because of the involvement of quantized vibrations⁵.

No evidence is presented by Lacks et al.¹ that molecular dynamics simulations, based on Lennard-Jones interactions, are capable of reproducing the isotopic fractionations of elements and of capturing the strong potential energy interactions that characterize silicate melts and other systems where diffusion is a strong function of temperature. Because of the magnitude of the activation energies involved, only a very small fraction (f) of all particles acquire enough energy to overcome activation energy barriers: f ≈ exp−(−E_a/k_BT). Here E_a is activation energy, k_B Boltzmann’s constant, and T temperature. For typical activation energies of 2–3 eV, this fraction is rather small (∼10⁻⁸), thus making it difficult for molecular dynamics simulations, which typically employ ∼10³ particles, to realistically capture the thermodynamics associated with isotopic fractionation in a highly interacting condensed matter system. We suggest caution in interpreting simple binary mixture molecular dynamics simulations that rely on ‘unphysical’ means of implementing heat transport⁶.

Last, Lacks et al.¹ point out that the vibrational frequencies needed to explain the steady-state fractionations are physically unrealistic. We note that this frequency may or may not correspond to a physical frequency, as the initial reactant state consists of three independent vibrational components that we, for the sake of clarity and simplicity, incorporated into one effective frequency (thus the effective frequency would be higher than each of the independent components)⁷. The infrared vibrational features that are observed in natural systems are sensitive only to differences in energy levels, not the zero-point energy. We also note that, as infrared vibrational features in a silicate melt are overwhelmingly dominated by modes associated with Si–O stretching and bending, it is unclear whether Raman or vibrational infrared spectra include features associated with diffusing interstitial species such as Mg, Fe and Ca.

In short, Lacks et al.¹ have provided no new data or physical model that quantitatively explains the empirical observations of steady-state isotopic fractionation in silicate melts. Furthermore, over 50 years of work in isotope effects in physical chemistry and isotope geochemistry support the role of quantum mechanics in isotopic fractionation processes.