Efficiency of compaction and compositional convection during mafic crystal
mush solidification: the Sept Iles layered intrusion, Canada
To be submitted to Contributions to Mineralogy and Petrology
Olivier Namur1,2*, Bernard Charlier3
1. Département de Géologie, Université de Liège, Belgium
2. Department of Earth Sciences, University of Cambridge, Cambridge, UK
3. Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of
Technology, Cambridge, USA
*Corresponding author: obn21@cam.ac.uk
Analytical methods
Whole rock analyses
All the samples were carefully cleaned prior to crushing. They were manually crushed
with a hammer and milled in agate mortars. Whole-rock compositions were presented in
Namur et al. (2010). Here, we present newly acquired accurate analyses of whole-rock trace
elements (P, Zr, Cr and V). Measurements were performed by XRF using an ARL 9400XP
spectrometer at the University of Liège on pressed powder pellets. Eight successive
measurements were realized for each sample and the values reported here correspond to the
average of the 8 measurements. Data were corrected for matrix effects by Compton peak
monitoring. The spectrometer was calibrated for phosphorous analyses using 40 international
standards ranging from 0.01 to 5 wt.% P2O5. Repeated measurements (n=17) of 15
international standards (0.01-1.39 wt.% P2O5), some of them being not included in the
calibration curve, indicate an accuracy relative to the reference values in the range between
0.3 and 10.5 %, with an average of 3.1 %. For other trace elements, the spectrometer was
calibrated using 64 international standards and analytical errors are estimated to be lower than
10 % in most samples.
Mineral analyses
One or two thin sections for each sample were carefully examined under the
microscope to select samples for electron microprobe analyses of plagioclase. Plagioclase
compositions from 38 samples were obtained with a Cameca SX100 electron probe microanalyzer (EPMA) at the University of Clermont-Ferrand (France). Analytical conditions were
15 kV for the accelerating voltage and 15 nA for the beam current. A focused beam was used
for the analyses. The following standards were used for K X-ray lines calibration:
wollastonite for Si and Ca; albite for Na; forsterite for Mg, fayalite for Fe, orthoclase for K,
synthetic Al2O3 for Al and synthetic TiMnO3 for Ti. Standard ZAF corrections have been
made on all analyses.
In situ mineral analyses of trace elements were performed by LA-ICP-MS at the
Research School of Earth Sciences (RSES; the Australian National University, Australia). A
pulsed 193 nm ArF Excimer laser with 100 mJ energy at a repetition rate of 5 Hz coupled
with an Agilent HP7500 quadrupole ICP-MS system was used for ablation (Eggins et al.,
1998). Laser sampling was performed in a He-Ar atmosphere with a beam diameter of 150
µm. Analyses were calibrated using 29Si and 47Ti as internal standard isotopes based on SiO2
and TiO2 concentrations measured by EPMA and XRF. During time resolved analyses of
minerals, possible contamination from inclusions and fractures was detected by monitoring
several elements and only the “clean” part of the signals was integrated. The glasses NIST612 (Pearce et al., 1997) and BCR-2G (Norman et al., 1998) were employed as external and
secondary standards, respectively. The reproducibility of trace element results for the BCR
glasses using the RSES analytical protocols are between 0.5 % and 4 % relative (1 sigma) for
the majority of elements (Eggins, 2003).
Bulk rock densities
Bulk-rock densities (g/cm3) were determined by weighing the samples (5-15 cm in
length and 4.6 cm diameter) in air and then in water. Replicate measurements (n=15) for 5
samples indicated an uncertainty between 0.001 and 0.012 g/cm3, with an average value of
0.007 g/cm3. Density of the high-temperature crystal matrix was also calculated at the
liquidus temperature using mineral mode and mineral compositions given in Namur et al.
(2010) and thermal expansion coefficients of Niu and Batiza (1991). Liquidus temperatures
were estimated using the linear relationship between temperature and the An-content of
plagioclase experimentally observed by Toplis and Carroll (1995).
Compaction and compositional convection: Theoretical formulations
Compaction of the crystal mush


In a crystal mush that accumulates at the floor of a magma chamber, the lower part is
represented by a compacting layer, while the upper part is not compacted (Fig. A1). The
porosity decrease in the compacting layer results from the expulsion of the intercumulus melt
and its progressive crystallization. With time, the front of compaction moves upwards through
the crystal mush. Original equations for the compaction process have been formulated by
McKenzie (1984; 1985) and Sparks et al. (1985) and assume textural equilibrium between the
crystals and the liquid in the crystal mush, i.e. there is no occlusion of the pores when the
residual porosity becomes low (Hunter, 1987; Mathez et al., 1997). The theoretical thickness
of the compacting layer is given by the compaction length scale parameter,  c (m) i.e. the
height over which the compaction rate decreases by a factor e (2.718), that can range from as
much as km to as little as a few cm, depending on the values of the relevant physical
parameters of the crystal mush and the liquid:
1/ 2

(1)
 c  (  (4 /3)) /  ( )1/ 2
where  and  are the bulk and shear viscosities of the crystal mush (Pa.s), ø is the
permeability of the crystal matrix (m2) and  is the melt viscosity (Pa.s). Following Maaloe
and Scheie (1982) and McKenzie (1985), the permeability of the crystal mush can be
calculated as follows:
(2)
  a2 3 /1000
where a is the average grain size (grain radius, m) and  is the porosity, i.e. the fraction of
intercumulus melt by volume unit (ranging from 0 to 1).
In large layered intrusions, the thickness of the cumulate pile where compaction
occurs is generally significantly different than the length scale parameter,  c (Sparks et al.,
1985; Tharp et al., 1998; Mathez et al., 1997). In a partially molten cumulate layer of
thickness h (m), the velocity of the expelled intercumulus melt is zero at the base of the layer
and increases upwards. The relative velocity of the liquid at the top of the compacting layer
(
rate (Sparks et al., 1985) and
; m/s) is considered as the expression of the compaction 
can be calculated as follows:

  W   0 1  (1/cosh( h / c ))
(3)
where (m/s) is the velocity of the expelled liquid, W (m/s) is the velocity of the sinking
crystal matrix and 0 (m/s) is the relative velocity between the melt and the crystal matrix of
initially constant porosity, i.e. when no compaction occurs, and is defined by:
(4)
 0   (1 )( s  l )g / 
3
where s and l are the densities (g/cm ) of the crystal matrix and the liquid, respectively, and
g is the standard acceleration constant.

Fig. A1: Theoretical model for compaction of a crystal mush (crystal matrix + liquid) beneath the liquid of the
main magma body in a magma chamber. a. Density distribution between liquid and crystal matrix necessary for
the onset of compaction. b. Representation of the effect of compaction on the fluid flow, the stratigraphy of the
crystal mush and its porosity. It should be noted that the porosity of the not compacted part of the crystal mush
could be reduced by crystallization of the intercumulus melt c. Physical properties of the liquid and the crystal
mush that enhance the compaction efficiency (rate of compaction). d. Physical properties of the liquid and the
crystal mush that decrease the compaction efficiency.
Compositional convection


Crystallization and fractionation of the intercumulus melt may locally decrease its
density down to values lower than the density of the overlying magma (Fig. 2a). In this case,
the intercumulus melt may be continuously expelled from the crystal mush through
convective separation of the melt from growing crystal, and replaced in the pore space by the
overlying liquid, generally coming from the main magma body. This process called
compositional convection enables the pore melt to maintain a constant composition (Sparks
and Huppert, 1984; Sparks et al., 1984; 1985; Tait et al., 1984). The original mathematical
expression of compositional convection was given by Tait et al. (1984), Sparks et al. (1985)
and Kerr and Tait (1986).
Instability occurs in the porous medium and leads to upwards intercumulus melt
convection when the dimensionless local solutal Rayleigh number (Ra) of the compositional
porous boundary layer ahead of the advancing crystallization front exceeds a critical value
(25-80; Lapwood, 1948; Nield, 1968; Sparks et al., 1985; Tait and Jaupart, 1992; Tait et al.,
1992). Following Tait et al., (1984), Ra can be calculated as follows:
Ra   hg /D
(5)
2
where   is the permeability of the crystal matrix (m ),  is the compositional density
difference across the boundary layer (g/cm3), h is the vertical thickness of the porous medium
(m), g is the standard acceleration constant, D is the melt diffusivity of the chemical species
involved in the convection process (m2/s) and µ is the viscosity of the melt (Pa.s).


Following Sparks et al. (1985), the velocity at which the liquid is expelled from the
pore space (characteristic convective velocity; vc) can be calculated as follows:
v c  a 2 g 4.5 /10
(6)
Liquid expelling trough compositional convection will occur if vc is higher than the rate of
crystal accumulation (Kerr and Tait, 1986). If vc is lower than the rate of crystal accumulation,
convection can occur but will be not efficient because the pore fluid will be frozen before it
can move.
Fig. A2 Theoretical model for compositional convection within a crystal mush. a. Density distribution between
the intercumulus melt and the overlying melt (here the main magma body) necessary for the onset of
compositional convection. b. Representation of the effect of compositional convection on the fluid flow. The
downward decrease of crystal mush porosity is due to the crystallization of the intercumulus melt of uniform
composition. c. Physical properties of the liquid and the crystal mush that enhance the compositional convection
efficiency (rate of compaction). d. Physical properties of the liquid and the crystal mush that decrease the
compositional convection efficiency.
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