Supplementary data for Ellis et al. (2015) Groundmass
crystallisation and cooling rates of ignimbrites: the Grey’s Landing
ignimbrite, southern Idaho, USA
XRD calibration curve
The calibration curve was constructed from mixtures of powdered granite (assumed to be
completely crystalline) and powdered glass in known proportions (0, 5, 10, 15, 20, 25, 40, 65,
75, 80, 90, 95 and 100% glass) following methodology of Rowe et al. (2012) and Wall et al.
(2014).
Figure S1: Calibration curve derived for the XRD measurement, x-axis represents the percent
crystalline material / the sum of the crystalline and amorphous components.
Further tests to investigate the reproducibility of the methodology indicate that uniform
powdering of samples using a WC ringmill produces a highly reproducible crystallinity result
(<3% RSD) compared to crystallinities from hand-crushed mortar and pestle powders (7-10%
RSD). From crystallinity measurements, the proportion of phenocrysts can also be determined
simply as the difference between the calculated whole rock and groundmass crystallinity.
Numerical models
The numerical model is a cooling 1D, finite difference model with transient crystallisation
(parameters in table S1, below). For this study we tested a crystal size/temperature controlled
growth models as described by Castro et al. (2008).
GR   6.7 1038 RT 10.52
(0)
Where GR is the crystal growth rate [m s-1], R the crystal size [m] and T the temperature [K].
 is an acceleration factor allowing us to span a variability range of growth rates and test the
possible differences due to the crystallization of quartz compared to plagioclases. For   1 , the
simulation reproduces the model of Castro (2008),   1 reproduces slower crystallization with
similar size and temperature dependence and   1 generates faster crystallization.
The numerical simulations are performed by solving the energy equation
C p
T dNm

L  .  T 
t
dt
(1)
Where 𝜌 is the density [kg m-3], 𝐶𝑝 the specific heat [J kg−1 K−1], 𝑇 the temperature [K], m the
mass produced from crystallisation [kg], N the crystal number density [m-3], L the latent heat of
crystallisation of the melt [J kg-1] (Hoskuldsson and Sparks, 1997, Blundy et al., 2006), 𝜅
thermal conductivity [W m-1 K−1], 𝑡 the time [s]. We assess the thermal effects of crystal growth
using simplified model that follows the growth of a uniform spherical population of crystals
within rhyolitic melt. We assume crystals to grow upon pre-existing “seeds” of radius R0 (5E-7
m). The size- and temperature-dependent growth rates of spherulites ( GR ) in rhyolitic melt
given by Castro et al., (2008) are then used to track the growth of spherulites through time. The
rate of crystallisation per unit volume of magma is calculated, giving the latent heat liberated,
which, converted into a temperature increase in the magma via the magma specific heat capacity.
The growth of the particles is limited by their fraction at equilibrium for a given temperature
obtained from the rhyolite-MELTS model (Gualda et al. 2012). Advection of heat through melt
migration, shear heating or bubble nucleation from crystallisation are not considered.
The model is conditioned to not crystallise above liquidus ( Tl =1000 °C) or below the glass
transition temperature of ( Tg =870 °C) Lavallée et al. (2015).
Our model tested Dirichlet (fixed temperature), Neuman (fixed heat flux) or Robin (mixed
conditions) boundary condition types. For this manuscript we set the upper boundary condition
to an infinite convective heat transfert condition (Robin condition). The heat transfer coefficient
(H), an input to the boundary condition, is set to 10, relevant of atmospheric natural heat transfer
conditions (no forced convection induced by wind). The surrounding bulk temperature far away
from the boundary is set to 25 °C. The lower boundary of the lava is connected to a ground
subdomain, 10 times larger than the lava. The heat transfers naturally into the ground and the
bottom is fixed to a temperature of 40 °C (Dirichlet condition). It ensures a natural conduction
and heat loss.
The time step algorithm is defined by the condition dt  min( x 2 / 2, dlc / Gr ) where x is the
mesh resolution (space in between two nodes) and 𝛼 the thermal diffusivity equals to  

Cp
,
dlc is a prescribed maximal crystal size increase and Gr is the growth rate [m s-1]. The thermal
conductivity of the lava is fixed to 1 [Wm-1K-1], the ground to 4 [Wm-1K-1].
During the eruptive process (hours to several days) the ash is expected to cool to the initial
temperature ( T0 ). Once emplaced, the magmas will start to exhibit significant crystallisation after
a week. The generated latent heat will meet the equilibrium temperature condition defined by
rhyolite-MELTS and further crystallisation will then be dependent of the thermal cooling of the
lava. For the thick profile (50 m) it results in a long period where the crystal fraction will not
exceed 0.32, allowing rheomorphism. Once the magma starts to display efficient cooling it will
get fully crystallised and rheologically jammed in a short period of time. For the thin profile (12
m), the crystallisation is more continuous as the cooling timescale is much shorter compared to
the crystallisation timescale. Note that the growth rate model and more specifically the choice of
 defining the crystallisation timescale is of primary importance.
References for supplementary materials
Blundy J, Cashman K, Humphreys M (2006) Magma heating by decompression-driven crystallization beneath
andesite volcanoes. Nature 443:76-80
Castro JM, Beck P, Tuffen H, Alexander RL, Dingwell DB, Martin C (2008) Timescales of spherulite crystallization
in obsidian inferred from water concentration profiles. Am Mineral 93:1816-1822.
Gottsmann J, Dingwell DB (2001).The cooling of frontal flow ramps: a calorimetric study on the Rocche Rosse
rhyolite flow, Lipari, Aeolian Islands, Italy. Terra Nova 13:157–164. doi:10.1046/j.13653121.2001.00332.x
Gualda GAR, Ghiorso MS, Lemons RV, Carley TL (2012) Rhyolite-MELTS: A modified calibration of MELTS
optimized for silica-rich, fluid-bearing magmatic systems. J Petrol 53:875-890.
Hardee HC (1983) Heat Transfer Measurements of the 1983 Kilauea Lava Flow. Science 222 (4619):47-48
Hoskuldsson A, Sparks RSJ (1997) Thermodynamics and fluid dynamics of effusive subglacial eruptions. Bull
Volcanol 59:219-230.
Lavallée Y, Wadsworth FB, Vasseur J, Russell JK, Andrews GDM, Hess K-U, von Aulock FW, Kendrick JE,
Tuffen H, Biggin AJ, Dingwell DB (2015) Eruption and emplacement timescales of ignimbrite super-eruptions
from thermo-kinetics of glass shards. Front Earth Sci 3:2. doi:10.3389/feart.2015.00002
Rowe MC, Ellis BS, Lindeberg A (2012) Quantifying crystallization and devitrification of rhyolites via X-ray
diffraction and electron microprobe analysis. Am Mineral 97 (10):1685-1699.
Wall KT, Rowe MC, Ellis BS, Schmidt ME, Eccles JD (2014) Determining volcanic eruption styles on Earth and
Mars from crystallinity measurements. Nat Comm 5:5090
Figure S2: Diagram showing sensitivity of the numerical models to various parameters. The Y
axis compares the thickness of the upper or basal vitrophyres normalized to the thickness
observed for various initial parameters values (X axis). When equal to 1 the numerical model
matches geological observations. Parameters tested are, on top, the heat diffusivity coefficients,
in the centre the growth rate model parameters and in the bottom the initial crystal seed
conditions.
Figure S3: Diagram comparing the cooling model of Gottsmann and Dingwell (2001) to the
model used in this study illustrating the ability of our model to replicate the results of Gottsmann
and Dingwell (2001) in making a glassy lava.
Figure S4: Diagram illustrating the changing effects of various conductivities (α) of the lava (L)
and the ground (G) on the numerical model results. These results are shown with two different
crystal growth rates (δ).
Symbol
N0
R0
 max (T )
h
T0
Tl
Description
Nucleation density site
Default Value
5 1013
Range tested
1011-1014
Dimension
[m-3]
Reference / method
Observations
Initial crystal seeds radii
5 10-7
10-7-10-5
[m-3]
Observations
Maximum/Equilibrium
crystal fraction
Flow height
Initial temperature
0.98
-
[-]
Observations
57
900
1-100
650-1150
[m]
[°C]
Liquidus Temperature
1100
-
[°C]
25
-
[°C]
Field observations
Andrews et al.
(2008)
Rhyolite-MELTS,
Gualda et al. (2012)
Estimated
40
-
[°C]
Estimated
Upper boundary condition
temperature
Lower boundary condition
temperature
Glass transition
temperature
Diffusivity of lava
870
500-870
[°C]
1.67 10-6
2.63 10-7- 2.09 10-6
[m2 s-1]
g
Diffusivity of basal rock
4.18 10-7
2.6310-7-1.67 10-6
[m2 s-1]
Lm
Latent heat of fusion
2.09E5
-
[J Kg-1]
l
Thermal conductivity of
lava
4
0.63-5
[W m-1 K1]
g
Thermal conductivity of
basal rock
1
0.63-4
[W m-1 K1]
l
Density of Lava
2300
-
[Kg m-3]
Lavallée et al.
(2015)
Arbitrary (literature
and calculation for
porosity
Arbitrary (literature
and parametric)
Hoskuldsson and
Sparks (1997)
Estimated (dense
rhyolite at high
temperature)
Estimated (porous
rhyolite at low
temperature)
Estimated (rhyolite)
g
Density of basal rock
2300
-
[Kg m-3]
Estimated (rhyolite)
GR
Growth Rate parameter
δ6.7.10-38 RT10.52
10-14-10-6
[m s-1]
Castro et al. (2008)
0.25
0.1-5
[]
Arbitrary
5 108
10
-
[s]
[W m-2 K1]
Parametric
Set to low wind
conditions. Forced
convection; slow air
flow. Free
convection being 1
and 5 (Hardee 1983)
BCTUp
BCTLow
Tg
l

t
H
Growth Rate acceleration
factor
Simulation time
Heat transfer coefficient
Table S1: Table of parameters used in the numerical models