# The Viscosity of Albitic Melt at High Pressures and Implications for the Mobility of Crust-Forming Magmas

Aaron Wolfgang Ashley, Mainak Mookherjee, Man Xu, Tony Yu, Geeth

Manthilake, Yanbin Wang

► To cite this version:

Aaron Wolfgang Ashley, Mainak Mookherjee, Man Xu, Tony Yu, Geeth Manthilake, et al.. The Viscosity of Albitic Melt at High Pressures and Implications for the Mobility of Crust-Forming Magmas. Journal of Geophysical Research: Solid Earth, 2025, 130 (5), 10.1029/2024JB030527. doi:10.1029/2024JB030527

HAL Id: hal-05356801

https://uca.hal.science/hal-05356801v1

Submitted on 10 Nov 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# The viscosity of albitic melt at high pressures and implications for the mobility of crust-forming magmas

Aaron Wolfgang Ashley¹, Mainak Mookherjee¹, Man Xu²,³, Tony Yu², Geeth Manthilake⁴,

Yanbin Wang²

¹Earth Materials Laboratory, Department of Earth, Ocean and Atmospheric Sciences, Florida

State University, Tallahassee, FL 32306, USA

²Center for Advanced Radiation Sources, The University of Chicago, Chicago, IL 60437, USA

³Shanghai Advanced Research in Physical Sciences and Center for High Pressure Science &

Technology Advanced Research, Shanghai, 201203, China

⁴Laboratoire Magmas et Volcans CNRS, IRD, OPGC, Université Clermont Auvergne, 63000,

Clermont-Ferrand, France

Corresponding author: Aaron Wolfgang Ashley (awashley@fsu.edu)

## Key Points (140 characters max)

* We tightly constrained the anomalous pressure effect on the viscosity of molten albite using experiments and rigorous error analysis.

* Modern aluminosilicate magma is more mobile at crustal depths due to a decrease in the melt viscosity at low pressures.

* Crust-forming magma in the early Earth may have ponded during ascent due to a pressure-induced minimum in the melt viscosity.
## 22 Abstract

The earliest form of continental crust was produced by tonalite-trondhjemite-granodiorite (TTG) magmas. Molten albite (NaAlSi₃O₈) is representative of TTGs and also a major component of modern crust-forming magma. The viscosity of the melt controls the magma ascent rate and hence influences the production of new continental crust. It is well known that the viscosity ($η$) of albitic melt exhibits an anomalous pressure ($P$) dependence. However, prior results on the melt $η$ at high-$P$ differ significantly which limits our ability to predict the movement of crust-forming magma at depth. In this study, we more tightly constrained the $P$-dependence on $η$ in anhydrous albitic melt via high-$P$ and high-temperature ($T$) falling sphere experiments. We limited undesirable drag effects by using small sphere-to-capsule diameter ratios ($d/D$) such that $d/D \le 0.12$, and evaluated uncertainties due to such drag using a Monte Carlo approach. Our results show that melt $η$ first decreases with $P$ (i.e., $\partialη/\partial P < 0$) and then increases with continued compression ($\partialη/\partial P > 0$) with a well-defined $η$ minimum ($η_{min}$) at ~ 6 GPa along a ~ 2000 K isotherm. We find that the viscosity of the melt can be described by an Arrhenius formalism with an activation volume that varies with $P$ and $T$. The results indicate that $η$ of aluminosilicate magmas decrease with depth and temperature in the crust, thereby mobilizing the magmas to promote rapid volcanic eruptions. The results also suggest that TTG magmas relevant for the early Earth could pond during ascent due to the anomalous $P$-effect on $η$.

## 40 Plain Language Summary

The continental crust is produced by silica-rich magma which shows a similar composition to the mineral albite. Viscosity controls the ascent rate of the magma. High-pressure experiments have shown that the viscosity of molten albite displays an anomalous pressure dependence. These
are challenging experiments and the results disagree on the exact effect of pressure. In this study, we more tightly constrain the pressure dependence of the melt viscosity using high-pressure experiments. We resolve uncertainties in our measurements using a statistical approach. Our results show that the melt viscosity decreases to a minimum at about 6 GPa and 2000 K, and then increases with continued compression. The results indicate that magma becomes less viscous with depth in the modern crust. However, magma originating from deeper or hotter conditions, such as relevant for the early Earth, may pond due to the anomalous pressure-effect on the melt viscosity.

**Keywords:** albite (NaAlSi₃O₈); melt; magma; TTG; viscosity; high pressure, multi-anvil, Synchrotron X-ray

# 1. Introduction

Melt with an albite stoichiometry (NaAlSi₃O₈) is an analog for aluminosilicate magmas which produce new continental crust. For instance, tonalite-trondhjemite-granodiorites (TTGs) characterize the continental crust of the early Earth (Moyen and Martin 2012). The TTGs are often dominated by quartz and feldspar mineralogy with high sodium (Na₂O) contents which are chemically close to the albite endmember in the albite (NaAlSi₃O₈) – anorthite (CaAl₂Si₂O₈) – K-feldspar (KAlSi₃O₈) ternary system (Laurent et al., 2024). Experiments suggest that TTG melts could be produced at ~20 to 150 km depths, i.e., ~0.5 to 4 GPa (Moyen and Martin 2012). In the present-day Earth, at conditions relevant to volcanic eruptions, albitic melts have very high viscosities (η), i.e., > 1000 Pa s (Urbain et al., 1982; Dingwell, 1987). The high η is due to a highly connected polymer network defining the melt structure (Poe et al., 1997; Allwardt et al., 2007; Ashley et al., 2024a). At the conditions relevant to producing the magma at high pressures, the connectivity of the melt structure is likely to increase. One may thus expect η to increase with
depth. However, high- *P* experiments showed that the *η* of albitic melts decreases with compression up to 2 GPa, i.e., ~ 60 km (Kushiro 1978). The effect of pressure on the *η* of albite melt contrasts our expectations that polymerization is positively correlated with *η* of melts. Later studies also found that the pressure effect on *η* reverses with continued compression, i.e., the viscosity decreases to a minimum (*η*<sub>min</sub>) and then increases with continued compression. As an ascending crustal magma is likely to follow a nearly isothermal adiabat (Ashley *et al.*, 2024a), such an anomalous pressure effect on *η* could significantly affect the ascent rate of crust-forming melts. Yet, it remains unclear whether *η*<sub>min</sub> of albitic melt occurs at ≥ 5 GPa or < 5 GPa (Mori *et al.*, 2000; Funakoshi *et al.*, 2002). Both studies constrained the melt viscosity using the falling sphere method via Stokes' Law. However, these prior studies relied on significant corrections to Stokes' Law due to additional drag effects acting on the sphere. Such corrections may significantly increase the uncertainties in the measured viscosity and hence obscure the observed trends (Ashley *et al.*, 2024b).

The anomalous pressure dependence of transport properties has also been observed in the self-diffusion of oxygen in albitic melts (Poe et al., 1997). The ionic diffusivity can be used to estimate the viscosity via the Eyring equation to further constrain the pressure of η<sub>min</sub>. However, the use of the Eyring equation to estimate the viscosity is limited since the formalism assumes certain ionic diffusing species, such as O, as the principal species affecting transport and estimates the “hopping distance” of the species, e.g., d<sub>O...O</sub> (Tinker et al., 2004). First-principles molecular dynamics (FPMD) simulations also provide insights into the behavior of albitic melt at high pressures and predict the pressure of η<sub>min</sub> changes with temperature (Bajgain and Mookherjee 2020; Ashley et al., 2024a). However, the FPMD simulations are often performed at higher
temperature isotherms. Such viscosity results at high temperatures and pressures must be extrapolated to experimental conditions (Ashley *et al.*, 2024a).

The lack of clarity on the effect pressure has on the transport properties of albitic melt prevents us from gaining fundamental insight into the mobility of aluminosilicate magmas at high pressures. Robust constraints on the variation in transport properties of magma at crustal and mantle conditions are essential for interpreting geophysical observations related to magmatism at depth (Pommier and Le-Trong, 2011; Ashley *et al.*, 2025). In this study, we conducted high-pressure falling sphere experiments in a multi-anvil press to constrain the precise pressure effect on the viscosity of albitic melts. We used white beam X-ray radiography to ensure robust constraints on the terminal velocities of the spheres (Kanzaki *et al.*, 1987). To better constrain the effect of pressure on η and more clearly identify η<sub>min</sub>, we explored higher pressures than previous experiments, i.e., P > 7 GPa. Finally, to constrain the viscosity using the falling sphere method, we ensured robust measurements by using small sphere-to-capsule diameter ratios (d/D) which minimize undesirable drag effects (Ashley *et al.*, 2024b). We also assessed uncertainties in the corrections to Stokes’ Law for such drag effects using a Monte Carlo approach. Our results allow us to examine the fundamental behavior of aluminosilicate-rich magmas which are crucial for producing continental crust.

## 2. Methods

We followed the experimental method outlined in a recent study (Ashley *et al.*, 2024b). The starting materials consisted of anhydrous, synthetic glasses with an albite stoichiometry (NaAlSi<sub>3</sub>O<sub>8</sub>). We synthesized the glasses by fusing Na<sub>2</sub>CO<sub>3</sub>, Al(OH)<sub>3</sub>, and SiO<sub>2</sub> reagent-grade powders in a 1:2:6 molar ratio at ambient pressure in a 2000 Kelvin furnace at the Laboratoire
Magmas et Volcans (LMV) at Université Clermont Auvergne, France. We crushed and re-melted the resulting glass three times to homogenize the material and remove volatiles. We confirmed that the starting glass was anhydrous using an Attenuated Total Reflectance (ATR) module with a Hyperion-1000 Bruker Fourier Transform Infrared (FTIR) spectrometer at Florida State University (FSU) (Ashley *et al.*, 2024b). To remove any adsorbed moisture from the powders, we also stored the glass powder in an oven at ≥ 373 K for at least 24 hours prior to the experiments.

We used spheres of rhenium less than 200 µm in diameter (Table 1) due to its high melting temperature and density in silicate melts (Ashley et al., 2024b). Furthermore, rhenium is often ideal for high-pressure and -temperature melt experiments due to its relatively inert nature. Previous falling sphere studies only noted significant reactions between silicate melt and Re spheres when the melts contain high sulfur and/or iron contents, due to the chalco- and siderophilic affinity of Re (Spice et al., 2015; Mouser et al., 2021). The lack of both Fe and S in our melt composition limits the potential for such reactions. We did not observe any obvious changes to the sphere diameter or image contrast (i.e., sphere density and hence density contrast) during the experiments. The spheres were produced by flash welding 25 µm thick strips of Re foil submerged under liquid nitrogen (Xie *et al.*, 2020, 2021). The flash electric arc was applied at 100 V.

We conducted the falling sphere experiments at the GSECARS 13-ID-D beamline at the Advanced Photon Source, Argonne National Laboratory, using the T-25 Kawai-type module and 1000-ton multi-anvil press frame (Tinker *et al.*, 2004; Wang *et al.*, 2009) (Figure 1). The press frame has five degrees of freedom and a positioning accuracy within 0.01 mm, allowing the sample to be accurately positioned relative to the incident X-ray beam, which is fixed in space. Two separate operating modes are used for the X-rays in the experiments. The first mode is a diffraction mode in which energy-dispersive X-ray diffraction patterns are collected to measure pressure and
determine the physical state of the samples. In the diffraction mode, a set of entrance slits collimates the incident X-ray beam to a cross-section 0.1 × 0.1 mm² in area. A collimator and a set of diffraction slits on the diffraction side, together with the entrance slits, define a diffraction volume with the longest dimension parallel to the incident beam. The 2θ angle was fixed at 6°. The second mode is an imaging mode in which a series of radiographic images are collected to record the falling motion of the spheres. In the imaging mode, the entrance slits of ~ 1.0 × 1.5 mm² are used so that the sample is entirely illuminated by the beam. After the X-ray beam passes through the sample, the beam is converted to visible light by fluorescence of a 200-μm thick, single-crystal of Ce-doped lutetium aluminum garnet (LuAG) phosphor on the downstream side of the multi-anvil press. This visible light is reflected by a 45° mirror into a video camera through an optical lens and a series of separate radiographic images are recorded (Figure 1). We used exposure times between 0.02 to 0.05 s to record the images.

We used 14/8 multi-anvil assemblies produced by the Consortium for Materials Properties Research in Earth Sciences (COMPRES) (Leinenweber et al., 2012). We tightly packed albitic glass powder into graphite capsules with pre-compression heights and diameters of 1.8 and 1.6 mm, respectively. We placed one Re sphere into a small indentation near the top of the glass powder within each capsule and then covered the spheres with glass powder to prevent contact with the capsule. We compressed the assemblies without heating to the target loads (Table 1). Compression typically resulted in < 30 % decrease in the capsule diameters. We heated the assemblies using an alternating current power supply and measured the temperature using Type-C tungsten-rhenium thermocouples above the sample. Thermal gradients in the assembly may increase the temperature towards the center of the assembly by at least 50 K (Hernlund et al., 2006). We do not apply correction for any such thermal gradients. A previous study showed that
uncertainties in the temperature are largely negligible in Stokes' Law viscosity measurements (Ashley et al., 2024b). We heated the assemblies incrementally below the melting curve of albite to allow thermal equilibration and monitor the pressure (Figure 1). After thermal equilibration, we began recording images and rapidly increased the temperature to ~ 2000 K (Table 1) at a heating rate of several hundred degrees per minute. This temperature exceeds the melting curve of albite at all the explored pressures (Figure 1). We note the peak temperatures of four experiments lie below the melting curve for jadeite and quartz, which may be produced by recrystallization of albite at high pressures (Williams and Kennedy 1970). However, we do not find obvious signs of crystallization in the recovered samples, i.e., the samples were glassy after quenching. This indicates that the crystallization of jadeite ± quartz was likely too slow to affect the measurement. We allowed the spheres to settle completely, i.e., either land at the bottom of the capsule or fall out of view behind one of the WC anvils, before stopping the radiographic image collection. After collecting diffraction patterns to estimate the pressure, we quenched the experiments by cutting power to the assembly.

When possible, we measured the pressures of the experiments using X-ray diffraction patterns of MgO mixed with hexagonal Boron Nitride (h-BN) in a 3:1 weight ratio and the equation of state of MgO (Tange et al., 2009). We placed compacted disks of the MgO:h-BN pressure markers directly above the sample capsules (Figure 1). We attempted to measure the pressure at the peak temperature after the spheres settled. However, the peak temperatures of the experiments promoted rapid recrystallization of the MgO in the pressure markers despite the addition of h-BN. This MgO recrystallization often obscured or distorted identifiable peaks in the diffraction patterns. Hence, the pressures could either not be determined from the patterns or were estimated to be unrealistically high. In such cases, we evaluated the pressure-temperature trends of each
experiment (Supplementary Figure S1). In multi-anvil experiments, thermal relaxation of the assemblies often occurs from heating beyond ambient temperature, which produces an initial drop in the pressure. Continued heating may then yield a thermal expansion effect, which may increase and/or stabilize the pressure (Leinenweber et al., 2012). The complex interplay between the relaxation and expansion effects can yield significant uncertainties in the extrapolated pressures of our experiments (Figure S1).

To reduce the uncertainties in our estimated pressures, we combined our data with previous experiments using the same press and a similar assembly design (Edwards 2019) to calibrate pressure to temperature and tonnage. The combined data set is well described by an empirical function given by $P \sim 5.3(\pm0.3) \ln(\Gamma) - 0.6(\pm0.2) \ln(T) - 18(\pm2)$, where P is pressure (GPa), $\Gamma$ is the applied load (tons), and T is temperature (K) (Figure 1). The calibration shows nice agreement with the separate pressure-temperature trends from each experiment (Figure S1). To note, the minimum uncertainty in our XRD-based measurements is $\pm$ 0.5 GPa. The calibration alone predicts a smaller uncertainty in the extrapolated pressures. We therefore propagated the combined uncertainties to capture the additional error due to extrapolation. For most of the experiments, we used the calibration to calculate the pressure due to the overall lower uncertainties compared to individual trends (Figure S1). Experiments T2824 and T2829 are two exceptions. The first was completed at a low load (100 tons), which we note is typically not well captured by the global calibration (Figure 1 inset). We instead take the average pressure from measurements in T2824, as this value shows better agreement with its unique pressure-temperature trends (Figure S1). For the other experiment, T2829, the final pressure was measured by XRD patterns from the pressure marker. This measured value is somewhat lower than predicted by the individual trends and global calibration, but the values still agree within $\pm$ 95 % confidence (Figure S1).
We used a MATLAB code to track the displacement of the spheres through time and determine their velocities (Ashley et al., 2024b). We identified the terminal velocities by plateaus in the velocity versus falling distance profiles of the spheres (Figure 2). All the spheres in our experiments display terminal velocities before landing. Hence, Stokes’ Law is valid and applicable in our experiments (Ashley et al., 2024b). Stokes’ Law defines the relationship between viscosity ($\eta$) and terminal velocity ($U_{\infty}$) as

$$ \eta_R = \frac{gd^2\Delta\rho}{18U_{\infty}} \qquad (1) $$
where $\eta_R$ refers to the “raw” or uncorrected $\eta$, $g$ is the acceleration due to gravity, $d$ is the diameter of the sphere, and $\Delta\rho$ is the density contrast between the sphere and the melt (Table 1). The densities of the rhenium sphere and the melt are estimated from the thermal equation of states of rhenium (Ono 2022) and albitic melts (Ashley et al., 2024b).

The finite volume of the capsules in high-pressure experiments introduces additional drag effects on the settling velocities of the spheres which must be corrected. There are multiple corrections available to account for such undesirable drag acting on the spheres (Brizard et al., 2005). For high pressure experiments, the most appropriate equation may be the Faxén correction (Ashley et al., 2024b) which considers drag due to the walls of the capsules and inertia of the falling spheres (Faxén 1922). The equation is given by

$$ \eta_w = \eta_R c_w = \eta_R \cdot \left[ 1 - \frac{3}{16} Re_n - \frac{d}{D} f\left(\frac{Re_n/4}{d/D}\right) - 2.104\left(\frac{d}{D}\right) + 2.09\left(\frac{d}{D}\right)^3 - 0.95\left(\frac{d}{D}\right)^5 \right] \quad (2) $$
where D is the inner diameter of the capsule, $Re_n$ is the Reynolds number given by $Re_n = \rho_S U_\infty d/\eta$, $\rho_S$ is the sphere density, and $f(\frac{Re_n/4}{d/D})$ is a correction function of $Re_n$ which can be solved semi-analytically (Ashley et al., 2024b). In all our experiments, we find that $Re_n \ll 10^{-3}$ and hence the drag due to inertia is negligible. A negligible inertia effect collapses $C_W$ to yield $\eta_W = \eta_R \cdot [1 - 2.104(d/D) + 2.09(d/D)^3 - 0.95(d/D)^5]$. We use the subscript “W” to distinguish the viscosity calculated by equation (2) from the uncorrected, raw viscosity, or $\eta_R$ (Table 1).

We also tested other equations for Stokes’ Law to evaluate the possible range in $\eta$. Drag effects due to the end of the capsule may be corrected by 1) $\eta_E = \eta_R/C_E = \eta_R/(1 + 9d/16z)$ (Lorentz 1907). The $z$ value may be best described by a variable distance between the sphere and capsule end (Brizard et al., 2005; Ashley et al., 2024b) (Figure 2). We recorded $z$ as a range across which the sphere fell under terminal velocity (Table 1). There are other variations of $C_E$ to account for drag due to the end of the capsule, including 2) $C_E = (1 + 3.3d/2z)$ (Ladenburg 1907) and 3) $C_E = (1 + 9d/16z + (9d/16z)^2)$ (Maude 1961). The first two variations of $C_E$ yield comparable values of $\eta_E$ while the third variation more strongly corrects the calculated viscosity (Ashley et al., 2024b). However, the third $C_E$ was also derived considering more than one sphere sinking in the melt (Maude 1961) which does not apply to our experiments. For simplicity, we consider only the first variation of $C_E$ (Lorentz 1907).

The separate $C_W$ and $C_E$ terms have often been combined to correct the viscosity in $\eta_{WE} = \eta_R \cdot C_W/C_E$. However, combining these corrections likely overcorrects the calculated viscosity (Brizard et al., 2005). The separate corrections may instead provide a cross-comparison to ensure
an accurate value of viscosity (Ashley *et al.*, 2024b). Nevertheless, we applied the combined corrections cautiously only to gauge the lowermost possible values of η for our experiments.

We examined statistical agreement in the variations for Stokes' Law using a Monte Carlo approach (Ashley *et al.*, 2024b). We randomly varied all input parameters for Stokes' Law and its corrections $10^5$ times (Figure 2). For all parameters, we assumed normal distributions using the measured uncertainties in each parameter (Table 1). We also examined the control of each parameter on the calculated η by randomly varying one parameter while holding the others constant for $10^4$ simulations. We take the minimum uncertainties in our measurements as the standard deviation of calculated viscosities from the simulations, i.e., the propagated error by the Monte Carlo method (Table 1). However, we note that these propagated uncertainties from experiment parameters may underestimate the true uncertainties in viscosities due to the corrections themselves (Ashley *et al.*, 2024b). Therefore, we take the maximum possible uncertainty to be the change in calculated viscosity due to the correction, i.e., % uncertainty = $100 \cdot (1 - C_W)$, where $C_W = \eta_W/\eta_R$ (Table 1; Figure 2).

### 3. Results

We find that the propagated uncertainties in our values for $\eta_W$ are relatively small at $\le 10\%$ at one standard deviation (Table 1). The sphere diameters, sphere sinking velocities, and capsule diameters most strongly control the uncertainties in $\eta_W$ (Figure 2). For most of our experiments, the values for $\eta_R$ and $\eta_W$ (equations 1 and 2) typically agree within $\pm 95-99\%$ confidence based on the Monte Carlo simulations (Figure 3). The good agreement is due to a small $d/D \le 0.12$ in our experiments (Table 1). As a result, the effect of the correction is minimized. We also note that
compression of the assembly capsules does not significantly affect the calculated viscosities (Table 1).

The calculated $\eta_E$ tends to be statistically distinct from $\eta_W$ and predicts lower values of viscosity (Figure 3). Combining the corrections for $\eta_{WE}$ statistically agrees well with $\eta_E$. However, the propagated uncertainties for both $\eta_E$ and $\eta_{WE}$ are larger and more skewed than for $\eta_W$ (Figure 2). This is due to a strong control of the sinking distances of the spheres, i.e., z values, on the uncertainties for $C_E$ (Ashley et al., 2024b). The $C_E$ may also be unreliable when $d/D < 0.125$ (Sutterby 1973), as for the experiments in this study (Table 1). We further note that the Faxén correction (equation 2) may already overcorrect Stokes’ Law (Kahle et al., 2003). Therefore, calculated viscosities smaller than $\eta_W$ may not be realistic (Ashley et al., 2024b). Regardless of the correction to Stokes’ Law, we find that the melt viscosity decreases by nearly 20-fold from ~ 1 to 6 GPa (Figure 3). With increasing pressure > 6 GPa, the viscosity again increases and becomes comparable to $\eta$ at ~ 1 GPa (Table 1). We note that the trend and minimum in viscosity is robust regardless of the choice in correction for Stokes’ Law. Furthermore, propagated uncertainties in the calculation do not obscure the trend (Figure 3). The change in viscosity in our experiments is most likely due to the effect of pressure. We do not anticipate other influential factors, such as possible changes to the melt H₂O contents, due to the timescales needed for H₂O contamination (Supporting Text S1).

The effects of pressure and temperature on melt viscosity may be typically described by an Arrhenian function given by

$$ \eta(P, T) = \eta_0 \cdot \exp\left(\frac{E_a+PV_a}{RT}\right) \quad (3) $$
where $\eta(P, T)$ is the viscosity at a given pressure and temperature, $\eta_0$ is the pre-exponential term, $E_a$ is the activation energy, $P$ is the pressure, $V_a$ is the activation volume, $R$ is the ideal gas law, and $T$ is the temperature. Two separate Arrhenian functions are required to describe the observed change in trend with compression (Figure 3). The change in the pressure dependence corresponds to a change in the sign of the activation volume from negative to positive (Table 2).

## 4. Discussion

Our results provide key insights into the fundamental transport properties of aluminosilicate magmas. The anomalous pressure-dependence in the viscosity of albitic melts may be understood by pressure-induced changes to the atomistic scale structure of the melt. At low pressures, tetrahedrally coordinated units, i.e., $[TO_4]$ where $T = Si$ and/or $Al$, are often connected via “bridging” oxygens ($O_b$) to form a polymerized network, i.e., $[-O_3T - O_b - TO_3 -]_n$ where $n$ describes the number of polymer units in the chain. In contrast, a “non-bridging” ($O_{nb}$) oxygen defines a tetrahedral corner that does not connect to another tetrahedral unit, or $[-O_3T - O_{nb}]$. At low pressures, the polymer network of an aluminosilicate-rich melt dominates the structure of the melt and hinders the diffusivity of ions, resulting in enhanced viscosity relative to aluminosilicate-poor melts (Dingwell 1995). Previous studies have investigated the control of the melt structure on the viscosity of other aluminosilicate-rich melt compositions. The viscosity of molten jadeite (NaAlSi$_2$O$_6$) also decreases with compression at low pressures, based on falling sphere measurements (Suzuki et al., 2011) and FPMD simulations (Bajgain et al., 2019; Bajgain and Mookherjee, 2021). Subsequent experiments on molten jadeite based on X-ray diffraction measurements showed that compression at low pressures decreases the bonding angle between the network forming polyhedral units $(\angle T - O_b - T)$, breaks some of the bridging oxygen bonds, and
decreases available free space within the network (Wang *et al.*, 2014). A decreasing $\angle T - O_b - T$ has been also inferred from nuclear magnetic resonance (NMR) spectroscopy on aluminosilicate glasses (Kelsey *et al.*, 2009). These structural changes help to depolymerize the melt structure and thereby decrease the melt viscosity.

With continued compression, a critical packing limit of the atoms may prevent further collapse of free space. As a result, the coordination number of Si and Al begins to increase such that $TO_4$ transitions to $TO_5$ (Wang *et al.*, 2014). Previous NMR studies on quenched aluminosilicate melts have shown that compression may increase the Al coordination more effectively than that of Si (Allwardt *et al.*, 2005a, 2005b, 2007; Lee *et al.*, 2006, 2011; Malfait *et al.*, 2012). The observation based on NMR spectroscopy on glasses has also been predicted by molecular dynamics simulations on melts (Karki *et al.*, 2011; Neilson *et al.*, 2016; Bajgain *et al.*, 2019; Bajgain and Mookherjee 2020; Kobsch and Caracas 2020; Ashley *et al.*, 2024a). The concentration of Al in aluminosilicate melt may also help to increase the mean coordination of Al and Si together (Kelsey *et al.*, 2009). The $TO_5$ polyhedral unit exchanges oxygen more readily than $TO_4$ which helps to enhance the diffusion of ions and thereby also decrease the melt viscosity (Schulze and Spiekermann 2023). Previous FPMD simulations on aluminosilicate melts indicate that at relatively low pressures, where $TO_4$ is the dominant species, the lifetime ($\tau$) of $TO_4$ is significantly greater than that of $TO_5$ and $TO_6$ species, i.e., $\tau_{AlO_4} \gg \tau_{AlO_5} \gg \tau_{AlO_6}$ (Bajgain *et al.*, 2019). At pressures where $TO_5$ is the dominant species, the lifetime of $TO_5$ is similar to that of $TO_4$ and $TO_6$ species, i.e., $\tau_{AlO_4} \le \tau_{AlO_5} \ge \tau_{AlO_6}$ (Bajgain *et al.*, 2019). In addition to $\tau$, the $\angle T - O_b - T$, the fraction of $O_b$ in the albitic melt structure also decreases with compression (Bajgain and Mookherjee 2020; Ashley *et al.*, 2024a). Constraints from the previous FPMD show that the coordination of network-forming species begins to increase once atoms in the melt cannot
be packed more tightly, i.e., a critical packing limit is reached (Bajgain and Mookherjee 2020; Ashley et al., 2024a) (Figure 3). A similar effect is also observed in hydrous albitic melts. The FPMD simulations predict that continued compression of albitic melt further increases the coordination number of the network-forming species such that $TO_4 \rightarrow TO_5 \rightarrow TO_6$ (Ashley et al., 2024a). The increasing abundance of six-fold species may involve edge-sharing of the closely packed polyhedral units (Wang et al., 2014) that could slow the diffusion of ions. As a result, the melt viscosity increases at high pressures (Figure 3).

An anomalous pressure dependence of transport properties, such as diffusion and $\eta$, is not only observed in molten albite (Mori et al., 2000; Funakoshi et al., 2002; Bajgain and Mookherjee, 2020) and jadeite (Suzuki et al., 2011; Bajgain et al., 2019; Bajgain and Mookherjee, 2021). The phenomenon has also been documented in other aluminosilicate melts such as molten anorthite (CaAl$_2$Si$_2$O$_8$) (Karki et al., 2011) and in melts with mafic to intermediate silica contents, such as basaltic (Sakamaki et al., 2013; Bonechi et al., 2022; Zhou et al., 2024) and basaltic-andesitic melts (Mouser et al., 2021) (Figure S1; Figure 4). Ultramafic melts such as peridotite liquid do not typically display an obvious $\eta_{min}$ along an isotherm but could instead show $\eta_{min}$ along the liquidus (Xie et al., 2021) and/or along an adiabat (Huang et al., 2024). In the more silica-rich melts, we find that $\eta_{min}$ consistently varies with temperature and silica contents (Figure 4). The presence of $\eta_{min}$ in silicate melts suggests a complex variation in their mobility with depth and a possibility of ponding during ascent of a magma, which could explain low velocity zones as detected by geophysical surveys. Further, the variable pressure-effect on $\eta$ with composition could play an important role in large-scale crystallization processes, such as which formed the mantle from the magma ocean (Deng et al., 2024).
Our results help to resolve the disparity in previous studies on the viscosity of albitic melts at high pressures. Previous work has consistently observed a negative pressure-effect on the melt viscosity at < 4 GPa (Kushiro et al., 1978; Mori et al., 2000; Funakoshi et al., 2002). We note our data show excellent agreement with other studies at ~ 2000 K and these pressures (Figure 5). The most recent study (Funakoshi et al., 2002) also argued for a viscosity minimum at ~ 4.5 GPa at ~ 2000 K, while older experiments at the same temperature did not capture such ηmin (Mori et al., 2000). Yet, the later data (Funakoshi et al., 2002) are also at ≤ 5.2 GPa and hence cannot fully test the trend of the earlier work at higher pressures (Mori et al., 2000).

Crucially, the older study relied on *ex-situ* determination of the sphere velocity after quenching (Mori et al., 2000). This *ex-situ* tactic prevents accurate measurement of the terminal velocities, which are essential to ensuring Stokes' Law is valid (Ashley et al., 2024b). Our *in-situ* data, based on radiographic videos, show that the post-quench measurements may indeed underestimate the melt viscosity at > 5.2 GPa (Figure 5). Yet, this does not explain the discrepancy between our observed ηmin at ~ 6 GPa and that of previous *in-situ* work at ~ 4.5 GPa (Funakoshi et al., 2002). We note that the previously constrained ηmin depends largely on a single data point at 5.2 GPa. Furthermore, the previous work estimated very small uncertainties in their measurements, i.e., ≤ 0.001 Pa s or ≤ 0.1 % error (Funakoshi et al., 2002). More recent consideration of the inherent uncertainties to falling sphere experiments suggests these previous experiments show ≤ 21 % uncertainty due to corrections to Stokes' Law (Ashley et al., 2024b). Hence, we find that the previous ηmin may not be robustly defined. Our work extends on these previous efforts by providing more *in-situ* data at > 5.2 GPa. The additional data more clearly resolve the effect of pressure on the melt viscosity and hence the pressure of ηmin (Figure 5).
Notably, these experiments are several hundred degrees hotter than temperatures expected for geologically realistic production or storage of aluminosilicate magmas (Huang and Wyllie 1975; Skjerlie and Johnston 1993; Collins et al., 2020; Moyen et al., 2021). We evaluated the melt viscosity across a range of pressures and temperatures relevant to subduction zones and the deep Earth (Figure 5). We also examined the viscosity at more extreme conditions (> 2000 K) to better understand the controls of pressure and temperature. Our results agree well with previous experiments at ≤ 2000 K and FPMD simulations at higher temperatures (Figure 5). We note that the FPMD simulations predict ηmin at > 6 GPa for ≥ 2500 K. This suggests that the anomalous pressure effect on viscosity is also dependent on temperature.

We find that all the experiment data (Kushiro 1978; Urbain et al., 1982; Brearley et al., 1986; Brearley and Montana 1989; Mori et al., 2000; Funakoshi et al., 2002; Suzuki et al., 2002; this study) and FPMD predictions (Bajgain et al., 2020; Ashley et al., 2024a) at < 4000 K are well described by allowing the activation volume in equation (3) to vary with pressure and temperature, or $V_a(P, T)$ (Figure 5). The function is given by

$$V_a(P,T) = (V_1 + V_2T) + P(V_3 + V_4T + \frac{V_5}{T}) \quad (4)$$
where $V_1$ to $V_5$ are empirical terms to capture the pressure and/or temperature effects on $V_a$ (Table 2). We note that this model predicts $\eta_{min}$ at $6 \pm 1$ GPa and $\sim 2000$ K.

At temperatures below 2000 K, the model predicts that the pressure of $\eta_{min}$ shifts by roughly 0.2 to 0.4 GPa per 100 K (Figures 4 and 5). This suggests that $\eta_{min}$ may occur around 2.5 GPa by 1000 K. Such pressures are relevant for incipient melting in subduction zones (Syracuse et al., 2010). However, the necessary temperature for this pressure of $\eta_{min}$ is at least a
couple hundred degrees cooler than typical for such melting. We also note that the melting curve for source rocks increases dramatically with compression. For instance, the melting temperature of anhydrous albite may be ~1650 K by 2.5 GPa (Boyd and England 1963; Tenner et al., 2007; Makhluf et al., 2020) (Figure 1). To better examine the pressure and temperature conditions of η<sub>min</sub>, we calculated the melt viscosity (equations 3 and 4) along the melting curve of albite (Figure 5). The viscosity along the melting curve agrees well with the values determined at the maximum pressures explored by previous experiments (Kushiro, 1978; Urbain et al., 1982; Brearley et al., 1986; Brearley and Montana, 1989; Mori et al., 2000; Funakoshi et al., 2002; Suzuki et al., 2002). Considering the viscosity along an isotherm shows that the pressures required to produce η<sub>min</sub> should typically stabilize solid jadeite + quartz (Figure 5).

Crucially, it is important to recognize that this study constrains the pressure and temperature effects on the viscosity of anhydrous melts. However, realistic magmas in subduction zones commonly contain several weight percent H₂O. The presence of H₂O will significantly lower the melting temperatures of source rocks by several hundred degrees (Makhluf et al., 2020) (Figure 5) and is well associated with the origin of continental crust (Campbell and Taylor 1983). Investigating the combined pressure, temperature, and water effects on the melt viscosity is technically challenging due to the fast diffusion kinetics of hydrogen (Ashley et al., 2024a) in silicate melts and thus the possibility of rapid escape of hydrogen during the timescale of the experiments. It is well known that dissolved H₂O in the melt dramatically lowers the melt viscosity even at high pressures (Dingwell 1987; Schulze et al., 1996; Holtz et al., 1999; Poe et al., 2006; Ardia et al., 2008). However, these earlier experimental studies on hydrous magmas were conducted at relatively low pressures (≤ 2.5 GPa) and temperatures (≤ 1823 K) and did not document η<sub>min</sub>. Complementary FPMD simulations have documented η<sub>min</sub> in hydrous
aluminosilicate magmas with compression (Bajgain et al., 2019; Ashley et al., 2024a). The combined effects of pressure, temperature, and water could shift η$_{min}$ to conditions relevant to subduction zones or the deep crust. To further investigate the effect of water on the η and η$_{min}$ of aluminosilicate magma at high pressures, we combine experimental results from this study and ∂η/∂X$_{H_2O}$ from FPMD simulations which investigated albitic melts with ~5 wt% H$_2$O (Ashley et al., 2024a; Table 2). We find that the melt viscosity should dramatically decrease with H$_2$O at conditions relevant to magma production (Figure 5). Our models also predict that the conditions which may produce η$_{min}$ move upward in depth by ~3 km per wt% H$_2$O (Figure 5). Hence, the combined effects of H$_2$O on crustal melting temperatures and the viscosity of the resulting melts likely enhance the potential for ascending aluminosilicate magmas to encounter η$_{min}$.

We further evaluated the potential for ponding of magma via the melt mobility, i.e., the contrast in density of a melt with a host matrix (Δρ = ρ$_{matrix}$ − ρ$_{melt}$) to the melt viscosity, or Δρ/η (Figure 5). For magma ascending in the early Earth, we used an equation of state (EoS) for crystalline albite (Stewart and Limbach 1967; Benusa et al., 2005) as a proxy for the crustal rock matrix. We also assumed that the matrix follows an Archean geothermal gradient (Moyen and Martin 2012) (Figure S4). We note the exact mineralogical composition of the host rock will influence its density (Figure S5). We calculate the melt ρ using the EoS for anhydrous albitic melts (Ashley et al., 2024b) with the parameters adjusted to 5 wt% H$_{2}$O based on FPMD (Ashley et al., 2024a) (Table S1). The anhydrous albitic melt displays a density crossover with the host matrix (ρ$_{melt}$ = ρ$_{matrix}$) due to the higher compressibility of melt compared to its solid counterpart (Jing and Karato 2011; Mookherjee et al., 2016; Bajgain and Mookherjee 2020). The neutral buoyancy would enable ponding of the magma (Figure S5). However, adding H$_{2}$O to the melt significantly lowers the melt density and helps to prevent the density crossover at conditions
relevant to the crustal melting (Figure S5). This yields a positive Δρ (ρ<sub>melt</sub> < ρ<sub>matrix</sub>) at lithospheric conditions which drives the ascent of the magma. Yet, the Δρ is typically ≤ 0.8 g cm<sup>-3</sup>. In contrast, the change in η with depth can span orders of magnitude along an isotherm and hence dominates the trend in mobility (Figure 5). The η<sub>min</sub> yields a maximum in the calculated mobility. Hence, ascending melts may accelerate to the depth of the maximum and begin to slow with continued ascent. As η increases with ascent beyond η<sub>min</sub>, the slowing melt may pond or ultimately freeze (Stolper et al., 1981). Notably, silicate melts in nature are produced by partial melting and modified by reactive transport, both of which will also influence the host matrix. Corresponding changes to the melt and host rock composition will affect Δρ/η but likely also the conditions of η<sub>min</sub> (Figure 4), which will further influence the depths for potential ponding. Notably, the diffusion of network-forming ions also often shows opposite pressure-trends to the viscosity (Poe et al 1997; Ashley et al., 2024a). The enhanced diffusivity would likely promote crystallization and/or chemical partitioning (Mollo and Hammer 2017), which may influence geochemical and petrologic interpretation of exhumed rock.

Our results highlight the importance of understanding the effect of pressure on the viscosity of aluminosilicate magma. At the surface, aluminosilicate-rich melt tends to be extremely viscous (> 1000 Pa s) (Dingwell 1995) due to the high degree of polymerization in the melt structure by Si and Al. We would expect such high viscosity to make the magma very sluggish before injection into magma chambers or eruption onto the surface at volcanoes. Yet very rapid volcanic eruption of aluminosilicate-rich lava, with little forewarning activity, has shown the opposite case in which the magma is significantly more mobile than expected (Castro and Dingwell 2009). Previous FPMD studies, which examined the viscosity of aluminosilicate magma at depth in the crust, found that the decrease in melt viscosity with depth helps to mobilize the magma in such eruptions
(Ashley et al., 2024a). Our experiment results confirm that the effect of pressure on the melt viscosity steepens at cooler temperatures (Figure 5). The viscosity of magma produced or stored at ≤ 50 km depth (~ 1.7 GPa) and < 1400 K, as typical for modern magma (Huang and Wyllie 1975; Skjerlie and Johnston 1993; Collins et al., 2020) and perhaps ancient TTG melts (Laurent et al., 2024), may be an order of magnitude lower at depth compared to the surface. Hence, the magma will be significantly more mobile close to its source. Our results also shed insight into the mobilization of aluminosilicate magma originating from deeper and/or hotter conditions within the Earth, as is relevant for subduction zones or perhaps TTG magma in the early Earth (Moyen and Martin 2012; Laurent et al., 2024). Under such conditions, the changing pressure effect on viscosity could promote slowing or ponding of ascending magma (Figure 5). Our results indicate it may be crucial to consider the anomalous pressure-dependence on silicate melt viscosity to fully evaluate magmatic processes at depth.

## 5. Conclusions

Our study expands on previous efforts to constrain the viscosity of anhydrous albitic melt at high pressures and temperatures. We resolve disagreements in previous studies by carefully evaluating the inherent uncertainties in falling sphere experiments and exploring a greater pressure range than previous work. Regardless of the type of correction for drag acting on falling sphere, we find robust and clear evidence for a changing pressure-effect on the melt viscosity. Compression acts to first decrease and then increase the viscosity, which yields a viscosity minimum ($\eta_{min}$) at ~ 6 GPa and ~ 2000 K. The anomalous pressure effect is most likely due to multiple changes in the atomistic-scale structure of the melt, including decreasing bond angles, breaking of the network forming bonds, and increases in the packing and coordination numbers of network-forming species, namely silicon and aluminum. We find that the viscosity of albitic melt
across a wide range of temperatures and pressures can be well described by a modified Arrhenius function (equations 3 and 4; **Table 2**). We further extend this function to explore the effect of H₂O on the melt viscosity using constraints from previous studies. Our results indicate that aluminosilicate-rich magma in the modern crust will become less viscous, and hence more mobile, with depth. The enhanced mobility should promote extraction of the melt from its source at depth. However, magma originating from deeper or hotter conditions, such as may be relevant for crust-forming magmas in the early Earth, may also encounter viscosity minima during ascent. Such minima may promote ponding and potential freezing of the magma.

## Acknowledgments

A.W.A. acknowledges the Buie, DeVore, and Watkins Fund from the Department of Earth, Ocean and Atmospheric Sciences, Florida State University. M.M. acknowledges the National Science Foundation grant (EAR-2246802) for funding this research. A.W.A. and M.M. also acknowledge the Extreme Science and Engineering Discovery (XSEDE) and Advanced Cyberinfrastructure Coordination Ecosystem: Services & Support (ACCESS) supercomputing facilities (TG-GEO170003) and the Research Computing Center (RCC) at Florida State University (FSU) for computing resources for the FPMD simulations. G.M. acknowledges funding and resources supported by INSU and the LabEx ClerVolc (contribution number XXX), which were used to synthesize the spheres and starting albitic glass. Y.W. acknowledges NSF support via EAR-2246803. The experiments were performed at GeoSoilEnviroCARS (The University of Chicago, Sector 13), Advanced Photon Source (APS), Argonne National Laboratory. GeoSoilEnviroCARS is supported by the National Science Foundation – Earth Sciences via SEES: Synchrotron Earth and Environmental Science (EAR-2223273). This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility,
operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357.

Declaration of Interest

The authors report there are no competing interests to declare.

Open Research

All final experiment data and model parameters are provided in the main tables or supporting information. Image sequence stacks and Monte Carlo simulation files are available in a Zenodo repository (Ashley et al., 2025).

Figure Captions

**Figure 1.** (a) The pressure-temperature space of the experiments in this study. Circles display experiment conditions from this study while squares show previous experiment conditions (Edwards, 2019). For this study, solid circles show pressures estimated from energy-dispersive X-ray diffraction (XRD) patterns on a pressure marker. The hollow circles with “+” symbols show the final estimated pressure for experiments where the pressure could not be measured at the peak temperature (Figure S1). The faded arrows provide general guides for the change in pressure of each experiment. Note that only the final pressure of experiment T2828 is shown due to a blowout during heating (Table 1; Figure S1). Error bars show ± 1 standard deviation of uncertainty and are omitted for clarity from the previous experiments (Edwards, 2019). Lines show relevant phase boundaries for our experiments, including the anhydrous albite melting curve (Boyd and England 1963; Shimada 1972; Anovitz and Blencoe 1999; Tenner et al., 2007), phase transition from albite to jadeite (Jd) ± quartz (Qtz) and their melting relations (Williams and Kennedy 1970), and the melting curve of rhenium (Re) (Yang et al., 2012). The melting of platinum (Pt) (Anzellini et al., 2019) is also shown for reference. (b) The top shows a diagram of the experiment assembly. The bottom shows an image of the assembly in the secondary stage anvils on the T-25 module.

**Figure 2.** Results from experiment T2859 as an example. (a) Sequential radiographic images of rhenium sphere falling in anhydrous albitic melt. (b) The measured velocity of the sphere versus sinking distance. The sphere reaches terminal velocity, i.e., $U_\infty$, at the plateau indicated by an arrow and thick black line. The faded green band highlights the range over which $U_\infty$ occurs. The landing of the sphere is identified by a rapid decrease in the velocity at a constant sinking distance (vertical line labeled “end of fall”). The z values show the distance between the sphere during $U_\infty$ to the bottom of the capsule. (c) Histograms and probability distribution functions (PDFs) of $10^5$ randomized Monte Carlo simulations for calculations of Stokes’ Law. Abbreviations are “R” for uncorrected ($\eta_R$), “W” for wall-effect corrected ($\eta_W$), “E” for end-effect corrected ($\eta_E$), and “WE” for “Weibull”.
for combined wall- and end-effect corrections ($\eta_{WE}$). (d) Overlain PDFs for R, W and WE. Colored histograms show Monte Carlo simulations for one randomized variable. Outer black lines indicate the PDFs from panel (c). Abbreviations *d* and *D* are for the sphere and inner capsule diameters, respectively. The recorded mean viscosity is assumed to be $\eta_W$ and is indicated by an arrow (Table 1). Dashed lines and the faded gray background show the uncertainty due to the $\eta_W$. The separate end correction results (E) are not shown in (d) for clarity.

**Figure 3.** (a) Probability distribution functions (PDFs) from Monte Carlo results on the viscosity ($\eta$) of albitic melts from this study. Lines show the PDFs for simulations which randomly varied all parameters $10^5$ times. The PDFs are color-coded for correction scheme. The abbreviations follow the description of Figure 2. The end effect corrections (E and WE) for experiment T2827 are dashed as the landing of the sphere could not be directly observed (Table 1). Numbers above and below the symbol-sets indicate the approximate $d/D$ of the experiment after compression. (b) The average $\eta$ of the melts from panel (a). Symbols indicate the type of correction applied to Stokes' Law. Error bars show $\pm 1$ standard deviation of uncertainty as estimated from Monte Carlo simulations and are typically smaller than the marker size shown. The dashed lines show two separate Arrhenian functions to describe the viscosity (fit to $\eta_W$) below and above 6 GPa (Table 2). The inset schematic diagram in (b) illustrates changes in the melt structure which help to decrease the viscosity with pressure. Red spheres show oxygen while blue spheres indicate Si and/or Al. The faded arrow provides a general guide for the effect of pressure on the melt structure and viscosity. (c-d) The average coordination number of network forming species, i.e., $TO_x$ where $T$ = Si and/or Al, as a function of the molar volume of melt ($\bar{V}$) normalized by the number of oxygen atoms in the melt per mole. The panels separate FPMD results for (c) anhydrous and (d) hydrous albitic melts, respectively (Ashley *et al.*, 2024a). The “LDA” and “GGA” refer to local density and generalized gradient approximations, respectively, and are types of energy exchange-correlation functionals used for FPMD simulations. The upper horizontal axes give approximate pressures based on the GGA simulations (Ashley *et al.*, 2024a). The $\bar{V}/(O\ atoms) \ge 16$ and $\ge 12$ $cm^3\ mol^{-1}$ for the anhydrous and hydrous melts, respectively, correspond to an extensional regime in which the melts may begin to vaporize (Kobsch and Caracas, 2020; Ashley *et al.*, 2024a). Smaller values of $\bar{V}/(O\ atoms)$ correspond to a compressional regime relevant to the crust and mantle. The shaded gray areas are guides for changes in trend of the data with compression. Arrows labeled “critical packing limits” highlight inflection points where atoms can no longer be packed together, and the coordination number of $TO_x$ increases in response (Wang *et al.*, 2014; Bajgain *et al.*, 2019; Bajgain and Mookherjee 2020).

**Figure 4.** (a) The viscosity ($\eta$) of albitic (this study), jadeitic (Suzuki *et al.*, 2011 and references therein), basaltic-andesitic (bas.-and.) (Mouser *et al.*, 2021), basaltic (Sakamaki *et al.*, 2013), picro-basaltic (Zhou *et al.*, 2024), and peridotitic (Xie *et al.*, 2021) melts as a function of pressure and temperature. The solid circles show data from this study using the wall correction ($\eta_W$) and the corresponding error bars indicate $\pm 1$ standard deviation of uncertainty based on the wall correction scheme (Table 1). The open symbols highlight the possible positions for $\eta_{min}$ in the other melt compositions. For clarity, data from previous work is not shown (see Figure S3). For the jadeitic melts, empirical second-order polynomial functions are used to describe the data along each isotherm and constrain the position $\eta_{min}$ by interpolation. For the bas.-and., basaltic, and picro-basaltic melts, the $\eta_{min}$ are taken directly from the data. The faded solid line shows the $\eta$ of peridotite melt along its liquidus as calculated from previous work (Xie *et al.*, 2021). The thin,
solid to dashed lines show the calculated peridotite melt η at super- and sub-liquidus conditions, respectively. For these isothermal η, we applied a previous Arrhenian model with E_a = 116 kJ mol⁻¹ and V_a = 0.63 cm³ mol⁻¹ (Xie et al., 2021). We adjusted the previous η₀ to 70 µPa s, based on comparison to a dimensionless temperature η model which agrees well with the liquidus prediction (Xie et al., 2021). (b) The pressure of η_min (P(η_min)) as a function of temperature and color-coded by melt composition for the basaltic to albitic melts. The dashed lines are linear regressions for the η_min. The solid line for albitic melts is calculated using equations (3) and (4) (Table 2). (c) The P(η_min) as a function of SiO₂ contents and color-coded to temperature. The dashed lines are general guides for the non-linear trends suggested by the data and are calculated by P(η_min, T, X_SiO₂) ~ 0.013X<sub>wtsiO₂</sub><sup>2</sup> - 1.4X<sub>wtsiO₂</sub> + 0.0056T + 32, where X<sub>wtsiO₂</sub> is the weight % of SiO₂. The circles for albitic melts are again calculated as in (b). In (b) and (c), the η_min for basaltic and jadeitic melts are taken from (a).

**Figure 5.** The viscosity of albitic melts (η) as a function of pressure and temperature based on experiments (“exp.”) (Kushiro 1978; Urbain *et al.*, 1982; Brearley *et al.*, 1986; Brearley and Montana 1989; Mori *et al.*, 2000; Funakoshi *et al.*, 2002; Suzuki *et al.*, 2002) and FPMD simulations (Bajgain and Mookherjee 2020; Ashley *et al.*, 2024a). Data above 10 GPa are not shown for clarity. Hollow symbols are values from previous work. Solid symbols are data from this study (see description in **Figure 3**). The solid lines show models using equations (3) and (4) (**Table 2**). The faded gray line highlights η_min for reference. The stippled line labeled “dry melt curve” displays the η calculated along the liquidus of albite (Boyd and England 1963; Tenner *et al.*, 2007; Makhluf *et al.*, 2020) (see inset). Error bars show ± 1 standard deviation of uncertainty. The uncertainties for previous experiments are estimated from the reported corrections for Stokes’ Law (Ashley *et al.*, 2024b). All symbols and isothermal models are color-coded by temperature. (b) The η of albitic melt with 0 and 5 wt% H₂O as a function of depth and temperature using equations (3) and (4) (**Table 2**). We assume 1 GPa for every 30 km depth. Faded gray lines highlight the predicted η_min. The lower depth for producing modern aluminosilicate magma is ~ 50 km (Huang and Wyllie 1975; Skjerlie and Johnston 1993; Collins *et al.*, 2020). The lowermost boundaries for TTG production lie at 100 to 150 km (Moyen and Martin 2012; Laurent *et al.*, 2024). (c) The mobility (Δρ/η) of the hydrous melts along several isotherms. We assume the ρ of solid albite along an Archean geothermal gradient (**Figures S1, S2**).
<table><thead><tr><th rowspan="2">Exp. No.</th><th rowspan="2">Load (tons)</th><th rowspan="2">Peak T (K)<sup>a</sup></th><th rowspan="2">P at peak T (GPa)</th><th rowspan="2">d (μm)</th><th rowspan="2">post-Exp. D (μm)<sup>b</sup></th><th rowspan="2">z range (μm)<sup>c</sup></th><th rowspan="2">Mean z (μm)<sup>c</sup></th><th rowspan="2">Δρ at T (g cm<sup>-3</sup>)<sup>d</sup></th><th rowspan="2">U<sub>∞</sub> (μm s<sup>-1</sup>)</th><th colspan="4">η<sub>W</sub> (Pa s)<sup>b</sup></th></tr><tr><th>pre-Exp. D</th><th>post-Exp. D</th><th>prop. ± 1 σ</th><th>C<sub>W</sub> ± 1 σ</th></tr></thead><tbody><tr><td>T2824<sup>e</sup></td><td>100</td><td>1871</td><td>1.3 ± 0.6</td><td>127 ± 1</td><td>1130 ± 60</td><td>65 to 132</td><td>90 ± 20</td><td>18.98</td><td>5.43 ± 0.09</td><td>25.6</td><td>23.6</td><td>0.7</td><td>6</td></tr><tr><td>T2827</td><td>120</td><td>2028</td><td>2.5 ± 0.6</td><td>94 ± 3</td><td>1350 ± 60</td><td>&gt; 2 to 152<sup>f</sup></td><td>70 ± 50<sup>f</sup></td><td>18.85</td><td>6.8 ± 0.1</td><td>11.8</td><td>11.6</td><td>0.6</td><td>2</td></tr><tr><td>T2861</td><td>160</td><td>1945</td><td>4.1 ± 0.6</td><td>172 ± 2</td><td>1330 ± 20</td><td>31 to 84</td><td>60 ± 20</td><td>18.59</td><td>45 ± 2</td><td>5.2</td><td>4.9</td><td>0.3</td><td>1</td></tr><tr><td>T2829</td><td>250</td><td>1997</td><td>5.2 ± 0.5<sup>g</sup></td><td>101 ± 1</td><td>1270 ± 40</td><td>105 to 151</td><td>130 ± 30</td><td>18.48</td><td>27.1 ± 0.3</td><td>3.3</td><td>3.2</td><td>0.2</td><td>0.5</td></tr><tr><td>T2859</td><td>225</td><td>1999</td><td>5.9 ± 0.7</td><td>145 ± 2</td><td>1640 ± 40</td><td>46 to 104</td><td>70 ± 20</td><td>18.38</td><td>125 ± 5</td><td>1.36</td><td>1.37</td><td>0.06</td><td>0.3</td></tr><tr><td>T2828<sup>h</sup></td><td>263</td><td>1916</td><td>6.7 ± 0.7</td><td>102 ± 2</td><td>1090 ± 40</td><td>211 to 312</td><td>260 ± 30</td><td>18.25</td><td>52 ± 2</td><td>1.74</td><td>1.62</td><td>0.07</td><td>0.3</td></tr><tr><td>T2860</td><td>275</td><td>2077</td><td>6.9 ± 0.8</td><td>131 ± 2</td><td>1580 ± 40</td><td>107 to 225</td><td>160 ± 40</td><td>18.27</td><td>24.7 ± 0.7</td><td>5.8</td><td>5.8</td><td>0.2</td><td>1</td></tr><tr><td>T2826</td><td>300</td><td>2021</td><td>7.4 ± 0.8</td><td>131 ± 1</td><td>1300 ± 60</td><td>26 to 84</td><td>50 ± 20</td><td>18.18</td><td>5.45 ± 0.04</td><td>25.7</td><td>24.6</td><td>0.4</td><td>5</td></tr></tbody></table>

620 Notes:

621 Abbreviations and symbols are "Exp." for experiment, P for pressure, T for temperature, d for sphere diameter, D for the inner diameter of the
622 graphite capsules, z for falling distance between sphere and capsule bottom during terminal velocity, Δρ for density contrast between sphere and
623 melt, U<sub>∞</sub> for terminal velocity, η for viscosity, "prop." indicates propagated uncertainty by the Monte Carlo method, and C<sub>W</sub> ± 1 σ indicates the
624 uncertainty based on the wall correction scheme (calculated by η<sub>W</sub> × (1 − C<sub>W</sub>)). For clarity, the experiments are organized with increasing pressure
625 downward.

626 <sup>a</sup> Uncertainty in measured temperature is estimated to be ≤ 10 K.

627 <sup>b</sup> We estimate D before compression (pre-Exp.) to be 1600 µm with ± 10 % uncertainty. Values for D after the experiment (post-Exp.) were measured
628 from back-scattered electron (BSE) images.

629 <sup>c</sup> The z range shows the minimum and maximum values for z. The mean z gives the average and standard deviation within the range.

630 <sup>d</sup> Average density contrast from Monte Carlo simulations. We estimate the uncertainty in the sphere and melt densities to be ≤ 1 % and ≤ 3 %,
631 respectively, using Monte Carlo simulations on the equations of state of rhenium (Ono 2022) and albitic melt (Ashley et al., 2024b).

632 <sup>e</sup> Data previously reported (Ashley et al., 2024b).

633 <sup>f</sup> Sphere landing was blocked from view by anvil. The z value is estimated from the lowest position of the sphere prior to falling behind the anvil and
634 is hence a minimum estimate.

635 <sup>g</sup> Pressure estimated from X-ray diffraction pattern collected at the peak temperature. Diffraction patterns collected from other experiments either
636 did not have resolvable peaks corresponding to MgO or yielded unrealistically high pressures. In such cases, the pressures at the peak temperatures
637 were estimated from other data (Figure 1).
The initial load was 400 tons, but a sudden decrease in the load, i.e., a “blowout”, occurred upon heating to the target temperature (Figure S1).

The temperature and load stabilized prior to the sphere fall.

<table><caption>**Table 2.** Parameters for Arrhenian functions.</caption><thead><tr><th rowspan="2">Parameters</th><th colspan="2">This study only</th><th>Exp. & FPMD</th><th colspan="3">V<sub>a</sub>(P, T) based on FPMD<sup>c</sup></th><th rowspan="2">Exp. & FPMD model adjusted to 5 wt% H<sub>2</sub>O<sup>e</sup></th></tr><tr><th>V<sub>a</sub><sup>a</sup></th><th></th><th>V<sub>a</sub>(P, T)<sup>b</sup></th><th>Anhydrous<sup>c</sup></th><th>~ 5 wt% H<sub>2</sub>O<sup>c</sup></th><th>∂M/∂X<sub>wtH<sub>2</sub>O</sub><sup>d</sup></th></tr></thead><tbody><tr><td>log<sub>10</sub> η<sub>0</sub> (Pa s)</td><td>-3.8 ± 0.2</td><td>-10</td><td>-8.2 ± 0.6</td><td>-6.00 ± 0.09</td><td>-5.4 ± 0.2</td><td>0.10 ± 0.02</td><td>-7.7 ± 0.7</td></tr><tr><td>E<sub>a</sub> (kJ mol<sup>-1</sup>)</td><td>200</td><td>200</td><td>410 ± 20</td><td>265 ± 5</td><td>200 ± 20</td><td>-12 ± 4</td><td>350 ± 20</td></tr><tr><td>V<sub>a</sub> (cm<sup>3</sup> mol<sup>-1</sup>)</td><td>-8 ± 2</td><td>31 ± 2</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>V<sub>1</sub> (cm<sup>3</sup> mol<sup>-1</sup>)</td><td>-</td><td>-</td><td>-64 ± 8</td><td>-30 ± 1</td><td>-22 ± 3</td><td>1.5 ± 0.6</td><td>-57 ± 8</td></tr><tr><td>V<sub>2</sub> (×10<sup>-3</sup> cm<sup>3</sup> mol<sup>-1</sup> K<sup>-1</sup>)</td><td>-</td><td>-</td><td>18 ± 4</td><td>8.3 ± 0.4</td><td>7 ± 1</td><td>-0.3 ± 0.2</td><td>17 ± 4</td></tr><tr><td>V<sub>3</sub> (cm<sup>3</sup> mol<sup>-1</sup> GPa<sup>-1</sup>)</td><td>-</td><td>-</td><td>-4.7 ± 0.6</td><td>0.9 ± 0.3</td><td>-0.5 ± 0.1</td><td>-0.29 ± 0.06</td><td>-6.2 ± 0.6</td></tr><tr><td>V<sub>4</sub> (×10<sup>-3</sup> cm<sup>3</sup> mol<sup>-1</sup> GPa<sup>-1</sup> K<sup>-1</sup>)</td><td>-</td><td>-</td><td>0.3 ± 0.2</td><td>-0.30 ± 0.05</td><td>-0.04 ± 0.04</td><td>0.05 ± 0.01</td><td>0.6 ± 0.2</td></tr><tr><td>V<sub>5</sub> (cm<sup>3</sup> K mol<sup>-1</sup> GPa<sup>-1</sup>)</td><td>-</td><td>-</td><td>12530.13 ± 0.03</td><td>1000 ± 400</td><td>2328.56 ± 0.04</td><td>280 ± 80</td><td>13950 ± 80</td></tr></tbody></table>

**Notes:**

<sup>a</sup> The results for V<sub>a</sub> describe two separate trends with equation (3) to capture the anomalous pressure dependence of viscosity in only our results at ~ 2000 K.

These fit parameters are based on the viscosity calculated from equation (2), i.e., η<sub>w</sub>.

<sup>b</sup> The V<sub>a</sub>(P, T) is given by equation (4) and describes all considered experiment and simulation results (Figure 5).

<sup>c</sup> Model parameters taken from previous FPMD simulations (Ashley et al., 2024a).

<sup>d</sup> The symbol M indicates the model parameters in the first column. The X<sub>wtH<sub>2</sub>O</sub> indicates the concentration of H<sub>2</sub>O per weight %. The values for ∂M/∂X<sub>wtH<sub>2</sub>O</sub> are calculated from the parameters based on previous FPMD simulations (Ashley et al., 2024a), following ∂M/∂X<sub>wtH<sub>2</sub>O</sub> = (M<sub>w</sub> - M<sub>d</sub>)/(4.9 wt% H<sub>2</sub>O), where M<sub>w</sub> and M<sub>d</sub> indicate the parameter values for the “wet” (hydrous) and “dry” (anhydrous) melts, respectively. The 4.9 wt% H<sub>2</sub>O is taken from the precise water contents of the hydrous albitic melts in the previous work (Ashley et al., 2024a).

<sup>e</sup> Model parameters for V<sub>a</sub>(P, T) based on experiments and simulations, adjusted using the ∂M/∂X<sub>wtH<sub>2</sub>O</sub> values set to 5 wt% H<sub>2</sub>O.
652 References

653 Allwardt, J.R., Stebbins, J.F., Schmidt, B.C., Frost, D.J., Withers, A.C., and Hirschmann, M.M.
654 (2005a) Aluminum coordination and the densification of high-pressure aluminosilicate
glasses. *American Mineralogist*, 90, 1218–1222.

656 Allwardt, J.R., Poe, B.T., and Stebbins, J.F. (2005b) The effect of fictive temperature on Al
657 coordination in high-pressure (10 GPa) sodium aluminosilicate glasses. *American
Mineralogist*, 90, 1453–1457.

659 Allwardt, J.R., Stebbins, J.F., Terasaki, H., Du, L.S., Frost, D.J., Withers, A.C., Hirschmann,
660 M.M., Suzuki, A., and Ohtani, E. (2007) Effect of structural transitions on properties of high-
661 pressure silicate melts: 27 Al NMR, glass densities, and melt viscosities. *American
Mineralogist*, 92, 1093–1104.

663 Anovitz, L. M. and Blencoe, J. G. (1999). Dry melting of high albite. *American Mineralogist* 84, 1830–1842.

665 Anzellini, S., Monteseguro, V., Bandiello, E., Dewaele, A., Burakovsky, L. and Errandonea, D.
666 (2019). In situ characterization of the high pressure – high temperature melting curve of
667 platinum. *Scientific Reports* 9, 1–10.

668 Ardia, P., Giordano, D., and Schmidt, M.W. (2008) A model for the viscosity of rhyolite as a
669 function of H₂O-content and pressure: A calibration based on centrifuge piston cylinder
670 experiments. *Geochimica et Cosmochimica Acta*, 72, 6103–6123.

671 Ashley, A.W., Bajgain, S., and Mookherjee, M. (2024a) Mobility of magmas within the Earth: Insights from the elasticity and transport properties of hydrous albitic melts. *Geochemistry, Geophysics, Geosystems*, 25, e2024GC011510.
674 Ashley, A.W., Mookherjee, M., Xu, M., Yu, T., Manthilake, G., and Wang, Y. (2024b) Viscosity
675 Measurements at High Pressures: A Critical Appraisal of Corrections to Stokes' Law. *Journal
676 of Geophysical Research: Solid Earth*, 129, e2023JB028489.

677 Ashley, A. W., Manthilake, G., Schiavi, F., and Mookherjee, M. (2025). Insights into the chemical
678 evolution of sub-arc magmas from the high-pressure electrical conductivity of basaltic and
679 andesitic magmas. *Geology*, https://doi.org/10.1130/G52545.1

680 Ashley, A. W., Mookherjee, M., Xu, M., Yu, T., Manthilake, G., & Wang, Y. (2025). The viscosity
681 of albitic melt at high pressures and implications for the mobility of crust-forming magmas
682 [Dataset]. *Zenodo*. https://doi.org/10.5281/zenodo.15066705

683 Bajgain, S. K., Ashley, A. W., Mookherjee, M., Ghosh, D. B., and Karki, B. B. (2022). Insights
684 into magma ocean dynamics from the transport properties of basaltic melt. *Nature
685 Communications*, 13, 7590.

686 Bajgain, S.K., and Mookherjee, M. (2020) Structure and properties of albite melt at high pressures.
687 *ACS Earth and Space Chemistry*, 4, 1-13, DOI: 10.1021/acsearthspacechem.9b00187.

688 Bajgain, S. K., and Mookherjee, M. (2021). Carbon bearing aluminosilicate melt at high
689 pressure. *Geochimica et Cosmochimica Acta*, 312, 106-123.

690 Bajgain, S.K., Peng, Y., Mookherjee, M., Jing, Z., and Solomon, M. (2019) Properties of hydrous
691 aluminosilicate melt at high pressures. *ACS Earth and Space Chemistry*, 3, 390-402, DOI:
692 10.1021/acsearthspacechem.8b00157.

693 Bonechi, B., Stagno, V., Kono, Y., Hrubiak, R., Ziberna, L., Andreozzi, G. B., ... and Gaeta, M.
694 (2022). Experimental measurements of the viscosity and melt structure of alkali basalts at
695 high pressure and temperature. *Scientific Reports*, 12, 2599.
696 Boyd, F.R., and England, J.L. (1963) Effect of pressure on the melting of diopside, CaMgSi₂O₆,
697 and albite, NaAlSi₃O₈, in the range up to 50 kilobars. *Journal of Geophysical Research*, 68,
698 311–323.

699 Brearley, M., Dickinson, J. E. & Scarfe, C. M. (1986) Pressure dependence of melt viscosities on the join
700 diopside-albite. *Geochimica et Cosmochimica* 50, 2563–2570.

701 Brearley, M. & Montana, A. (1989) The effect of CO₂ on the viscosity of silicate liquids at high pressure.
702 *Geochimica et Cosmochimica Acta* 53, 2609–2616.

703 Brizard, M., Megharfi, M., Mahé, E., and Verdier, C. (2005) Design of a high precision falling-
704 ball viscometer. *Review of Scientific Instruments*, 76.

705 Campbell, I.H., and Taylor, S.R. (1983) No water, no granites - No oceans, no continents.
706 *Geophysical Research Letters*, 10, 1061–1064.

707 Castro, J.M., and Dingwell, D.B. (2009) Rapid ascent of rhyolitic magma at Chaitén volcano,
708 Chile. *Nature*, 461, 780–783.

709 Collins, W.J., Murphy, J.B., Johnson, T.E., and Huang, H.Q. (2020) Critical role of water in the
710 formation of continental crust. *Nature Geoscience*, 13, 331–338.

711 Benusa, M. D., Angel, R. J. and Ross, N. L. (2005). Compression of albite, NaAlSi₃O₈. *American
712 Mineralogist*, 90, 1115–1120.

713 Deng, J., Hu, J., Shi, Y., Lee, J., Niu, H., and Stixrude, L. (2024). Bridgmanite megacrysts drive
714 segregation of the terrestrial magma ocean. *Preprint under review at Nature Portfolio*. DOI:
715 10.21203/rs.3.rs-3108549/v1.

716 Dingwell, D.B. (1987) Melt viscosities in the system NaAlSi₃O₈-H₂O-F₂O. *Magmatic Processes:
717 *Physicochemical Principles*, 1, 423–433.
718 Dingwell, D.B. (1995) Viscosity and anelasticity of melts, 209–216 p. *Mineral physics and crystallography: a handbook of physical constraints*.

719
Ducea, M. N., Saleeby, J. B., and Bergantz, G. (2015) The architecture, chemistry, and evolution
of continental magmatic arcs. *Annual Review of Earth and Planetary Sciences*, 43, 1, 299-
331.

723 Edwards, P.M. (2019) Viscosity of Iron-Rich Silicate Melts by Falling Sphere Viscometry at High
Pressure: Implications for the Mobility of Pyroxenitic Melts in the Mantle. University of
California: Davis.

725
Faxén, H. (1922) Der Widerstand gegen die Bewegung einer starren Kugel in einer zahen
Flussigkeit, die zwischen zwei parallelen ebenen Wanden eingeschlossen is. *Annalen der
Physik*, 373, 89–119.

725
California: Davis.
726
Faxén, H. (1922) Der Widerstand gegen die Bewegung einer starren Kugel in einer zahen
727
Flussigkeit, die zwischen zwei parallelen ebenen Wanden eingeschlossen is. *Annalen der
728
Physik*, 373, 89–119.
729
Funakoshi, K.I., Suzuki, A., and Terasaki, H. (2002) In situ viscosity measurements of albite melt
730
under high pressure. *Journal of Physics Condensed Matter*, 14, 11343–11347.

731 Hernlund, J., Leinenweber, K., Locke, D., and Tyburczy, J.A. (2006) A numerical model for
732
steady-state temperature distributions in solid-medium high-pressure cell assemblies.
733
*American Mineralogist*, 91, 295–305.

731
Hernlund, J., Leinenweber, K., Locke, D., and Tyburczy, J.A. (2006) A numerical model for
732
steady-state temperature distributions in solid-medium high-pressure cell assemblies.
733
*American Mineralogist*, 91, 295–305.
734
Holtz, F., Roux, J., Ohlhorst, S., Behrens, H., and Schulze, F. (1999) The effects of silica and water
735
on the viscosity of hydrous quartzofeldspathic melts. *American Mineralogist*, 84, 27–36.

734
Holtz, F., Roux, J., Ohlhorst, S., Behrens, H., and Schulze, F. (1999) The effects of silica and water
735
on the viscosity of hydrous quartzofeldspathic melts. *American Mineralogist*, 84, 27–36.
736
Huang, W.-L., and Wyllie, P.J. (1975) Melting reactions in the system NaAlSi₃O₈-KAlSi₃O₈-SiO₂
737
to 35 kilobars, dry and with excess water. *The Journal of Geology*, 83, 737–748.

736
Huang, W.-L., and Wyllie, P.J. (1975) Melting reactions in the system NaAlSi₃O₈-KAlSi₃O₈-SiO₂
737
to 35 kilobars, dry and with excess water. *The Journal of Geology*, 83, 737–748.
738
Huang, D., Li, Y., and Murakami, M. (2024) Low Viscosity of Peridotite Liquid: Implications for
739
Magma Ocean Dynamics. *Geophysical Research Letters*, 51.
740 Jing, Z., and Karato, S. I. (2011). A new approach to the equation of state of silicate melts: An
741 application of the theory of hard sphere mixtures. *Geochimica et Cosmochimica Acta*, **75**,
742 6780-6802.

743 Kahle, A., Winkler, B., and Hennion, B. (2003) Is Faxén's correction function applicable to
744 viscosity measurements of silicate melts with the falling sphere method? *Journal of Non-
745 Newtonian Fluid Mechanics*, **112**, 203–215.

746 Kanzaki, M., Kurita, K., Fujii, T., Kato, T., Shimomura, O., and Akimoto, S. (1987) A new
747 technique to measure the viscosity and density of silicate melts at high pressure. *High-
748 Pressure Research in Mineral Physics*, **195–200**.

749 Karki, B.B., Bohara, B., and Stixrude, L.P. (2011) First-principles study of diffusion and viscosity
750 of anorthite (CaAl₂Si₂O₈) liquid at high pressure. *American Mineralogist*, **96**, 744–751.

751 Kelsey, K.E., Stebbins, J.F., Mosenfelder, J.L., and Asimow, P.D. (2009) Simultaneous aluminum,
752 silicon, and sodium coordination changes in 6 GPa sodium aluminosilicate glasses. *American
753 Mineralogist*, **94**, 1205–1215.

754 Kobsch, A., and Caracas, R. (2020) The Critical Point and the Supercritical State of Alkali
755 Feldspars: Implications for the Behavior of the Crust During Impacts. *Journal of Geophysical
756 Research: Planets*, **125**, e2020JE006412.

757 Kushiro, I. (1978) Viscosity and structural changes of albite (NaAlSi₃O₈) melt at high pressures.
758 *Earth and Planetary Science Letters*, **41**, 87–90.

759 Ladenburg, R. (1907) Über den Einfluß von Wänden auf die Bewegung einer Kugel in einer
760 reibenden Flüssigkeit. *Annalen der Physik*, **328**, 447–458.

761 Laurent, O., Guitreau, M., Bruand, E., and Moyen, J. F. (2024) At the dawn of continents: Archean
762 tonalite-trondhjemite-granodiorite suites. *Elements*, **20**, 174–179.
763 Lee, S.K., Cody, G.D., Fei, Y., and Mysen, B.O. (2006) The effect of Na/Si on the structure of
764 sodium silicate and aluminosilicate glasses quenched from melts at high pressure: A multi-
765 nuclear (Al-27, Na-23, O-17) 1D and 2D solid-state NMR study. *Chemical Geology*, 229,
766 162–172.

767 Lee, S.K., Yi, Y.S., Cody, G.D., Mibe, K., Fei, Y., and Mysen, B.O. (2011) Effect of Network
768 Polymerization on the Pressure-Induced Structural Changes in Sodium Aluminosilicate
769 Glasses and Melts: $ ^{27}Al $ and $ ^{17}O $ Solid-State NMR Study. *Journal of Physical Chemistry C*,
770 116, 2183–2191.

771 Leinenweber, K.D., Tyburczy, J.A., Sharp, T.G., Soignard, E., Diedrich, T., Petuskey, W.B.,
772 Wang, Y., and Mosenfelder, J.L. (2012) Cell assemblies for reproducible multi-anvil
773 experiments (the COMPRES assemblies). *American Mineralogist*, 97, 353–368.

774 Lorentz, H.A. (1907) Ein allgemeiner Satz, die Bewegung einer reibenden Flüssigkeit betreffend,
775 nebst einigen Anwendungen desselben. *Abhandlungen über Theoretische Physik.*, 1, 23.

776 Makhluf, A.R., Newton, R.C., and Manning, C.E. (2020) Experimental investigation of phase
777 relations in the system NaAlSi₃O₈–H₂O at high temperatures and pressures: liquidus relations,
778 liquid–vapor mixing, and critical phenomena at deep crust–upper mantle conditions.
779 *Contributions to Mineralogy and Petrology*, 175, 1–20.

780 Malfait, W.J., Verel, R., Ardia, P., and Sanchez-Valle, C. (2012) Aluminum coordination in
781 rhyolite and andesite glasses and melts: Effect of temperature, pressure, composition and
782 water content. *Geochimica et Cosmochimica Acta*, 77, 11–26.

783 Maude, A.D. (1961) End effects in a falling-sphere viscometer. *Journal of Applied Physics*, 12,
784 293–295.
Mollo, S., and Hammer, J. (2017) Dynamic crystallization in magmas. *European Mineralogical Union Notes in Mineralogy*, 16, 373-418.

Mookherjee, M., Mainprice, D., Maheshwari, K., Heinonen, O., Patel, D., and Hariharan, A. (2016) Pressure induced elastic softening in framework aluminosilicate-albite (NaAlSi₃O₈). *Scientific Reports*, 6, No. 34815.

Mori, S., Ohtani, E., and Suzuki, A. (2000) Viscosity of the albite melt to 7 GPa at 2000 K. *Earth and Planetary Science Letters*, 175, 87-92.

Mouser, M.D., Dygert, N., Anzures, B.A., Grambling, N.L., Hrubiak, R., Kono, Y., Shen, G. and Parman, S.W. (2021) Experimental investigation of Mercury's magma ocean viscosity: Implications for the formation of Mercury's cumulate mantle, its subsequent dynamic evolution, and crustal petrogenesis. *Journal of Geophysical Research: Planets*, 126, e2021JE006946.

Moyen, J.F., and Martin, H. (2012) Forty years of TTG research. Lithos, 148, 312-336.

Moyen, J.F., Janoušek, V., Laurent, O., Bachmann, O., Jacob, J.B., Farina, F., Fiannacca, P., and Villaros, A. (2021) Crustal melting vs. fractionation of basaltic magmas: Part 1, granites and paradigms. *Lithos*, 402-403.

Neilson, R.T., Spera, F.J., and Ghiorso, M.S. (2016) Thermodynamics, self-diffusion, and structure of liquid NaAlSi3O8 to 30 GPa by classical molecular dynamics simulations. *American Mineralogist*, 101, 2029-2040.

Ono, S. (2022) Equation of state determination for rhenium using first-principles molecular dynamics calculations and high-pressure experiments. *Advances in Condensed Matter Physics*, 2022, 1-6.
807 Poe, B.T., McMillan, P.F., Rubie, D.C., Chakraborty, S., Yarger, J., and Diefenbacher, J. (1997)
808 Silicon and oxygen self-diffusivities in silicate liquids measured to 15 gigapascals and 2800
809 Kelvin. *Science*, 276, 1245-1248.

810 Poe, B.T., Romano, C., Liebske, C., Rubie, D.C., Terasaki, H., Suzuki, A., and Funakoshi, K.
811 (2006) High-temperature viscosity measurements of hydrous albite liquid using in-situ
812 falling-sphere viscometry at 2.5 GPa. *Chemical Geology*, 229, 2-9.

813 Pommier, A., and Le-Trong, E. (2011) "SIGMELTS": A web portal for electrical conductivity
814 calculations in geosciences. *Computers & Geosciences*, 37, 9, 1450-1459.

815 Sakamaki, T., Suzuki, A., Ohtani, E., Terasaki, H., Urakawa, S., Katayama, Y., ... and Ballmer,
816 M. D. (2013) Ponded melt at the boundary between the lithosphere and asthenosphere. *Nature*
817 *Geoscience*, 6, 1041-1044.

818 Schulze, F., Behrens, H., Holtz, F., Roux, J., and Johannes, W. (1996) The influence of H₂O on
819 the viscosity of a haplogranitic melt. *American Mineralogist*, 81, 1155-1165.

820 Schulze, M., and Spiekermann, G. (2023) Fivefold-Coordinated Silicon in MgSiO₃ Melt
821 Accommodates Viscous Flow up to Transition Zone Pressures. *Geophysical Research
822 Letters*, 50, e2023GL105750.

823 Shimada, M. (1972). Melting of Albite at High Pressures Under Conditions. *Journal of Physical
824 Earth*, 20, 59-70.

825 Skjerlie, K.P., and Johnston, A.D. (1993). Fluid-Absent Melting Behavior of an F-Rich Tonalitic
826 Gneiss at Mid-Crustal Pressures: Implications for the Generation of Anorogenic Granites.
827 *Journal of Petrology*, 34, 785-815.

828 Spice, H., Sanloup, C., Cochain, B., De Grouchy, C., and Kono, Y. (2015). Viscosity of liquid
829 fayalite up to 9 GPa. *Geochimica et Cosmochimica Acta*, 148, 219-227.
830 Stern, R.J. (2002). Subduction zones. Reviews of Geophysics, 40, 1012.

831 Stewart, D. B. and Limbach, D. (1967). Thermal expansion of low and high albite. *American
Mineralogist*, 52, 389–413.

833 Stolper, E., Walker, D., Hager, B.H., and Hays, J.F. (1981) Melt segregation from partially molten
source regions: the importance of melt density and source region size. *Journal of Geophysical
Research*, 86, 6261–6271.

836 Sutterby, J.L. (1973) Falling Sphere Viscometry - 1. Wall and Inertial Corrections to Stokes' Law
in Long Tubes. *Transactions of the Society of Rheology*, 17, 559–573.

838 Suzuki, A., Ohtani, E., Terasaki, H., Nishida, K., Hayashi, H., Sakamaki, T., Shibazaki, Y. and
839 Kikegawa, T. (2011). Pressure and temperature dependence of the viscosity of a NaAlSi₂O₆
840 melt. *Physics and Chemistry of Minerals*, 38, 59-64.

841 Syracuse, E.M., van Keken, P.E., and Abers, G.A. (2010) The global range of subduction zone
thermal models. *Physics of the Earth and Planetary Interiors*, 183, 73–90.

843 Tange, Y., Nishihara, Y., and Tsuchiya, T. (2009) Unified analyses for P-V-T equation of state of
844 MgO: A solution for pressure-scale problems in high P-T experiments. *Journal of
Geophysical Research: Solid Earth*, 114, 1–16.

846 Tenner, T.J., Lange, R.A., and Downs, R.T. (2007) The albite fusion curve re-examined: New
847 experiments and the high-pressure density and compressibility of high albite and NaAlSi₃O₈
848 liquid. *American Mineralogist*, 92, 1573–1585.

849 Tinker, D., Lesher, C.E., Baxter, G.M., Uchida, T., and Wang, Y. (2004) High-pressure viscometry
850 of polymerized silicate melts and limitations of the Eyring equation. *American Mineralogist*,
851 89, 1701–1708.
852 Urbain, G., Bottinga, Y., and Richet, P. (1982) Viscosity of liquid silica, silicates and aluminosilicates. *Geochimica et Cosmochimica Acta*, 46, 1061–1072.

854 Wang, Y., Rivers, M., Sutton, S., Nishiyama, N., Uchida, T., and Sanehira, T. (2009) The large-volume high-pressure facility at GSECARS: A “Swiss-army-knife” approach to synchrotron-based experimental studies. *Physics of the Earth and Planetary Interiors*, 174, 270–281.

857 Wang, Y., Sakamaki, T., Skinner, L.B., Jing, Z., Yu, T., Kono, Y., Park, C., Shen, G., Rivers, M.L. and Sutton, S.R. (2014) Atomistic insight into viscosity and density of silicate melts under pressure. *Nature Communications*, 5, 3241.

860 White, L.T., Rawlinson, N., Lister, G.S., Waldhauser, F., Hejrani, B., Thompson, D.A., Tanner, D., Macpherson, C.G., Tkalčić, H., and Morgan, J.P. (2019) Earth’s deepest earthquake swarms track fluid ascent beneath nascent arc volcanoes. *Earth and Planetary Science Letters*, 521, 25–36.

864 Williams, D. W. and Kennedy, G. C. (1970). The melting of jadeite to 60 kilobars. *American Journal of Science*, 269, 481–488.

866 Xie, L., Yoneda, A., Yamazaki, D., Manthilake, G., Higo, Y., Tange, Y., Guignot, N., King, A., Scheel, M., and Andrault, D. (2020) Formation of bridgmanite-enriched layer at the top lower-mantle during magma ocean solidification. *Nature Communications*, 11, 1–10.

869 Xie, L., Yoneda, A., Katsura, T., Andrault, D., Tange, Y., and Higo, Y. (2021) Direct Viscosity Measurement of Peridotite Melt to Lower-Mantle Conditions: A Further Support for a Fractional Magma-Ocean Solidification at the Top of the Lower Mantle. *Geophysical Research Letters*, 48.

873 Yang, L., Karandikar, A. and Boehler, R. (2012) Flash heating in the diamond cell: Melting curve of rhenium. *Review of Scientific Instruments*, 83, 2–7.
875 Zhou, W. Y., Hao, M., Hrubiak, R., Kenney-Benson, C., and Zhang, J. S. (2024) Migration and
876 accumulation of hydrous mantle incipient melt in the Earth's asthenosphere: Constraints from
877 in-situ falling sphere viscometry measurements. *Earth and Planetary Science Letters*, 641,
878 118833.
<figure><img src="image_2.png" /></figure>

<figure><img src="image_3.png" /></figure>
<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /></figure>
<figure><img src="image_9.png" /></figure>
<figure><img src="image_10.png" /><figcaption>Pressure (GPa)</figcaption></figure>

<caption>Temperature (K)</caption>

P Pas

P(η<sub>min</sub>) (GPa)

(b)

(c)
<figure><img src="image_11.png" /></figure>