Can spinodal decomposition occur during decompression-induced vesiculation of magma?

TL;DR

The paper addresses whether spinodal decomposition can occur during decompression-induced vesiculation of magma. It adopts a simple thermodynamic model that treats hydrous magma as a two-component regular solution of silicate and water, and it maps the water solubility data to binodal and spinodal curves in composition–pressure space, yielding $P_{bi}$ and $P_{spi}$. The main finding is that $P_{spi}$ lies far below $P_{bi}$ in the pressure range relevant to crustal magmatic processes, and observed decompression experiments fall between these curves, supporting nucleation-and-growth as the primary vesiculation mechanism rather than spinodal decomposition. The work also shows how the calculated $P_{spi}$ can be used with non-classical nucleation theory to estimate the microscopic melt–bubble surface tension $\sigma$, providing a practical link between thermodynamics and interfacial properties. Overall, the results challenge the spinodal-vesiculation hypothesis for continental-crust magmas and offer a straightforward method to infer interfacial parameters from decompression data.

Abstract

Volcanic eruptions are driven by decompression-induced vesiculation of supersaturated volatile components in magma. The initial phase of this phenomenon has long been described as nucleation and growth. Recently, it was proposed that spinodal decomposition (an energetically spontaneous phase separation that does not require the formation of a distinct interface) may occur during decompression-induced magma vesiculation. This suggestion has attracted attention, but is currently based only on textural observations of decompression experiment products (e.g., independence of bubble number density on decompression rate and homogeneous spatial distribution of bubbles). In this study, I used a simple thermodynamic approach to investigate whether spinodal decomposition can occur during decompression-induced vesiculation of magma. I plotted binodal and spinodal curves on the chemical composition-pressure plane by approximating hydrous magmas under several temperature and compositional conditions as two-component symmetric regular solutions of silicate and water, using experimentally determined water solubility values. The spinodal curve was consistently much lower than the binodal curve at pressures sufficiently below the second critical endpoint. In addition, the final pressure of all decompression experiments performed to date fell between these two curves. This suggests that spinodal decomposition is unlikely to occur in the pressure range of magmatic processes in the continental crust, and that decompression-induced vesiculation results from nucleation and subsequent growth, as previously considered. Furthermore, by substituting the determined spinodal pressure into the formula of non-classical nucleation theory, the surface tension between silicate melt and bubble nucleus can be estimated.

Figures (8)

• Figure 1: Schematic diagrams of the molar Gibbs energy for regular solutions of two components A and B: (a) symmetric regular solution and (b) asymmetric regular solution. The green curve represents that of an ideal solution $g^\mathrm{ideal}$, which is common to both regular solution models. The orange curve represents the molar excess Gibbs energy for a regular solution $g^\mathrm{excess}$, and the two models are differentiated based on its shape. The bold black curve represents the sum of these: the molar Gibbs energy of mixing $g^\mathrm{real}$. The interaction parameters $w_\mathrm{A}$ and $w_\mathrm{B}$ are represented by the slopes of the $g^\mathrm{excess}$ curve at the endpoints on the B side and A side, respectively. In the symmetric model (a), $w_\mathrm{A} = w_\mathrm{B}$, which is referred to as $w_\mathrm{sym}$ in the text.
• Figure 2: Schematic molar Gibbs energy of mixing $g^\mathrm{real}$ (upper panel) and corresponding phase diagram (lower panel) for a general two-component symmetric regular solution. In the interval where the $g^\mathrm{real}$ curve is convex downwards, the system is metastable, and nucleation occurs with clear phase boundaries (surfaces) appearing randomly in space. On the other hand, when the $g^\mathrm{real}$ curve is convex upward, the system is unstable, and spinodal decomposition occurs, in which the two phases start to separate at a specific wavelength with unclear phase boundaries.
• Figure 3: The relation between $x_\mathrm{bi}$ and $x_\mathrm{spi}$ at an arbitrary fixed temperature, derived from a series of Eqs. (\ref{['sym-binodal']}) and (\ref{['sym-spinodal']}), which represent the first- and second-order derivatives of $g^\mathrm{real}$ by $x$. $x_\mathrm{bi}$ and $x_\mathrm{spi}$ are the $x$ values that constitute the binodal and spinodal curves, respectively. The range $0 < x < 0.5$ corresponds to the left half of Fig. \ref{['Fig1']}. The relation $x_\mathrm{spi} > x_\mathrm{bi}$ holds for all the ranges.
• Figure 4: (a) Schematic diagram of the molar Gibbs energy for a realistic hydrous magma, when it was assumed as an asymmetric regular solution of anhydrous silicate (melt) and water (vapor). The meaning of each curve is the same as in Fig. 1. Components A and B correspond to silicate and water, respectively. (b) The relationship between $x_\mathrm{bi}$ and $x_\mathrm{spi}$ in a two-component asymmetric regular solution model. An example is shown for the case where $T = 1,000^\circ$C, $w_\mathrm{A} = 345.7$ kJ/mol, and $w_\mathrm{B} = -1.0$ kJ/mol.
• Figure 5: Binodal (blue) and spinodal (red) curves for hydrous 1,050$^{\circ}$C K-phonolitic (solid line), 1,100$^{\circ}$C basaltic (dashed line), and 900$^{\circ}$C albite (dotted line) melts in the pressure range 0.1--1000 MPa. The left panel shows an enlargement of the right panel at pressures below 400 MPa. The binodal curves correspond to the water solubility curves in the melt for each chemical composition (Moore et al., 1998; Hamilton et al., 1964; Burnham and Jahns, 1962). The position of spinodal curves was determined from the position of binodal curves and Eq. (\ref{['bi-spi-relation']}).