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Configurational entropy of basaltic melts in Earth's mantle.

ABSTRACT: Although geophysical observations of mantle regions that suggest the presence of partial melt have often been interpreted in light of the properties of basaltic liquids erupted at the surface, the seismic and rheological consequences of partial melting in the upper mantle depend instead on the properties of interstitial basaltic melt at elevated pressure. In particular, basaltic melts and glasses display anomalous mechanical softening upon compression up to several GPa, suggesting that the relevant properties of melt are strongly pressure-dependent. A full understanding of such a softening requires study, under compression, of the atomic structure of primitive small-degree basaltic melts at their formation depth, which has proven to be difficult. Here we report multiNMR spectra for a simplified basaltic glass quenched at pressures up to 5 GPa (corresponding to depths down to ?150 km). These data allow quantification of short-range structural parameters such as the populations of coordination numbers of Al and Si cations and the cation pairs bonded to oxygen atoms. In the model basaltic glass, the fraction of ^[5,6]Al is ?40% at 5 GPa and decreases to ?3% at 1 atm. The estimated fraction of nonbridging oxygens at 5 GPa is ?84% of that at ambient pressure. Together with data on variable glass compositions at 1 atm, these results allow us to quantify how such structural changes increase the configurational entropy of melts with increasing density. We explore how configurational entropy can be used to explain the anomalous mechanical softening of basaltic melts and glasses.

SUBMITTER: Lee SK

PROVIDER: S-EPMC7486762 | biostudies-literature | 2020 Sep

REPOSITORIES: biostudies-literature

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Configurational entropy of basaltic melts in Earth's mantle.

Lee Sung Keun SK Mosenfelder Jed L JL Park Sun Young SY Lee A Chim AC Asimow Paul D PD

Proceedings of the National Academy of Sciences of the United States of America 20200824 36

Although geophysical observations of mantle regions that suggest the presence of partial melt have often been interpreted in light of the properties of basaltic liquids erupted at the surface, the seismic and rheological consequences of partial melting in the upper mantle depend instead on the properties of interstitial basaltic melt at elevated pressure. In particular, basaltic melts and glasses display anomalous mechanical softening upon compression up to several GPa, suggesting that the relev ...[more]

PMID: 32839310

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Project description:Entropy and the second law of thermodynamics are fundamental concepts that underlie all natural processes and patterns. Recent research has shown how the entropy of a landscape mosaic can be calculated using the Boltzmann equation, with the entropy of a lattice mosaic equal to the logarithm of the number of ways a lattice with a given dimensionality and number of classes can be arranged to produce the same total amount of edge between cells of different classes. However, that work seemed to also suggest that the feasibility of applying this method to real landscapes was limited due to intractably large numbers of possible arrangements of raster cells in large landscapes. Here I extend that work by showing that: (1) the proportion of arrangements rather than the number with a given amount of edge length provides a means to calculate unbiased relative configurational entropy, obviating the need to compute all possible configurations of a landscape lattice; (2) the edge lengths of randomized landscape mosaics are normally distributed, following the central limit theorem; and (3) given this normal distribution it is possible to fit parametric probability density functions to estimate the expected proportion of randomized configurations that have any given edge length, enabling the calculation of configurational entropy on any landscape regardless of size or number of classes. I evaluate the boundary limits (4) for this normal approximation for small landscapes with a small proportion of a minority class and show it holds under all realistic landscape conditions. I further (5) demonstrate that this relationship holds for a sample of real landscapes that vary in size, patch richness, and evenness of area in each cover type, and (6) I show that the mean and standard deviation of the normally distributed edge lengths can be predicted nearly perfectly as a function of the size, patch richness and diversity of a landscape. Finally, (7) I show that the configurational entropy of a landscape is highly related to the dimensionality of the landscape, the number of cover classes, the evenness of landscape composition across classes, and landscape heterogeneity. These advances provide a means for researchers to directly estimate the frequency distribution of all possible macrostates of any observed landscape, and then directly calculate the relative configurational entropy of the observed macrostate, and to understand the ecological meaning of different amounts of configurational entropy. These advances enable scientists to take configurational entropy from a concept to an applied tool to measure and compare the disorder of real landscapes with an objective and unbiased measure based on entropy and the second law.

Dataset Information

Configurational entropy of basaltic melts in Earth's mantle.

Publications

Configurational entropy of basaltic melts in Earth's mantle.

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