JOURNAL OF PETROLOGY
VOLUME 51
NUMBER 7
PAGES 1541^1569
2010
doi:10.1093/petrology/egq028
Crystallization Dynamics of Granite Magma
Chambers in the Absence of Regional Stress:
Multiphysics Modeling with Natural Examples
F. BEA*
DEPARTMENT OF MINERALOGY AND PETROLOGY, CAMPUS FUENTENUEVA, UNIVERSITY OF GRANADA,
18002 GRANADA, SPAIN
RECEIVED SEPTEMBER 6, 2009; ACCEPTED MAY 5, 2010
ADVANCE ACCESS PUBLICATION JUNE 8, 2010
Numerical models built linking an internally consistent rheological
dataset for a cooling granite magma with equations of heat transfer
and fluid motion for geometrically different magma chambers cooling
at various crustal depths reveal that granite magmas first undergo a
short period of chaotic convection, during which wall-rock contamination and magma mixing are possible, followed by a long period of
no convective cooling, during which melt segregation occurs.
Convection is driven by the negative density gradient generated in
the upper cooling zone by melt-to-solid phase transformation.
Convection breaks the upper mushy zone and drags the fragments
downwards with descending Rayleigh^Taylor fingers. Such fragments can be preserved as microgranular enclaves. The descending
Rayleigh^Taylor fingers split low aspect-ratio (sill-like) magma
chambers into nearly isolated convection cells. If the magma is initially heterogeneous, this effect divides the chamber into contiguous
homogeneous zones with distinct trace element and isotope ratios,
and finally results in a pluton with marked lateral compositional
variations, easily misinterpreted as different intrusive batches.
Convective heat-loss quickly leads most of the magma chamber to
critical crystallinity, independently of the vertical coordinate, so that
a chamber-wide three-dimensional skeleton of crystals with uniform
initial porosity c. 0·4^0·5 is formed. This configuration is gravitationally unstable; therefore, it spontaneously compacts towards an
equilibrium vertical variation of porosity approaching Atty’s Law.
In the absence of regional stress, the upwards migration of the
inter-crystalline melts, as a result of compaction, is the most effective
way of melt^solid segregation and causes vertically zoned plutons
with an upper layer of felsic segregates. Granite magma chambers
fractionated by these mechanisms will produce short-range
*Corresponding author. E-mail: [email protected]
differentiation series, from a composition slightly less silicic than
the initial magma to high-silica segregates. In the presence of regional stress, tectonic squeezing and shearing during the post-convective
stage can expel residual fluid more efficiently and lead to wide-range
granite differentiation series, from rocks notably less silicic than the
initial magma to high-silica leucogranites.
crystallization dynamics; magma convection; granite;
autolith; Central Iberia
KEY WORDS:
I N T RO D U C T I O N
Despite more that a century of active research (see reviews
by Wilson, 1993; Young, 2003) the mechanisms of magma
differentiation, especially for intermediate and acid compositions, are not yet properly understood. Since the beginning of the twentieth century most igneous petrologists
have believed that solid^liquid systems are far more
fractionation-efficient on a geological timescale than
vapor^liquid or liquid^liquid systems, and have considered
that the segregation of melt and solids within cooling
magma chambers was the main source of the chemical diversity of igneous rocks. This vision, however, has been
radically challenged by Marsh (1996, 2006), who, based on
consideration of magma crystallization and cooling dynamics, proposed the concept of a magma chamber
‘encased in marginal solidification fronts within which all
crystallization occurs’ (sic.) as an alternative to the classical
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JOURNAL OF PETROLOGY
VOLUME 51
concept of a magma chamber ‘where the crystals nucleate,
grow, and settle from the interior to chemically fractionate
the residual melt’ (sic.) In Marsh’s model the in situ differentiation of an initially crystal-free cooling magma is confined to processes occurring within the solidification front,
which simply produces small interdigitating zones in
which residual magmas are collected, in other words, an
undifferentiated nearly homogeneous pluton. However, if
the in situ differentiated magma initially carries a significant amounts of phenocrysts, what happens is what
Marsh (2006) called ‘punctuated differentiation’, that is, a
differentiation array that progresses to a point and suddenly stops. The differentiation array consists of cumulates
formed by the discharge of phenocrysts, and the stop-point
represents the composition of the initial melt phase,
which, once free from phenocrysts, crystallizes in the
solidification fronts.
Marsh’s model is based on convincing physical and
chemical arguments and supported by evidence derived
from mafic sills (however, see Latypov, 2009). Nonetheless,
it neither fits with observations in well-exposed granitic
sills nor leaves much room for understanding the enormous compositional variability found in many granite
bodies. If granite magmas are initially crystal-free, the
formation of multiphase solidification fronts would
block mechanisms of chemically driven compositional
convection and its derivatives, believed by some workers to be the main engine of differentiation (e.g. Clarke,
1992, p. 88, and references therein). If, on the other hand,
granite magmas are initially crystal-laden, they would
behave as highly viscous, thixotropic fluids from which
the discharge of suspended crystals before being captured
by the inward-growing solidification fronts is unlikely.
The conclusion is that a granite magma chamber crystallizing according to the solidification front model, independent of the initial crystallinity, would produce a
nearly homogeneous undifferentiated granite rock except,
perhaps, for some minor aplopegmatitic segregates.
The corollary is that compositionally complex granite
plutons cannot be generated by closed-system fractionation of a single magma, but can only result from
open-system processesçimplying two, or more, different
end-members.
Nonetheless, there is compelling evidence that granite
bodies of all ages and from a variety of tectonic settings
have undergone ‘in situ’ processes of magmatic differentiation (e.g. Michael, 1984; Sawka et al., 1990; Wark &
Miller, 1993; Bea et al., 1994; Rao et al., 1995; Nishimura &
Yanagi, 2000). These processes are not limited to forming
a few felsic segregates, but rather form a large variety of
rocks that, in some cases, range from gabbro or diorite to
high-silica granite, the whole series featuring identical initial 87Sr/86Sr and 143Nd/144Nd, compositionally almost
homogeneous ferromagnesian minerals, and excellent
NUMBER 7
JULY 2010
linear negative correlations of the most compatible elements with any differentiation index. Well-studied examples
are the Wilmington Complex of the Appalachians (Srogi
& Lutz, 1996) and the Stepninsk pluton of the Urals (Bea
et al., 2005).
The existence of large-scale differentiation processes
in granite magma chambers is, therefore, undeniable.
Understanding how these processes occur requires us first
to ascertain the physical mechanisms capable of segregating the melt phase from a crystallizing magma mush,
a formidable multidisciplinary problem that must be
primarily tackled by combining the three main
fields involved in the process: fluid dynamics, heat-transfer
and the rheology of partially crystallized magmas
(e.g. Sparks et al., 1984; Jaupart & Tait, 1995; Marsh, 1996;
and references therein). The complexity of the problem
is such that it does not admit a general solution, but requires instead multiple numerical simulations accounting
for differences in magma composition, variations in
the shape and size of the magma chamber, and changes
in the crustal depth and thermal regime where the chamber is located.
Here we aim to study the crystallization dynamics of
granite magmas stored in crustal reservoirs. First, to calculate the melt fraction and the rheological and thermal
properties of the melt phase and the magma (melt þ suspended crystals) as a function of decreasing temperature
at different crustal pressures, we ran the MELTS software
(Ghiorso & Sack, 1995) on a common granodioritic composition, the average of the Stepninsk Uralian massif granitoid body (STB magma; see next section). Second, using
TM
COMSOL , a commercial finite-element software code
that permits linking a specific geometry with multiple partial differential equations, we made two-dimensional (2D)
simulations of low aspect-ratio (sills) and high aspect-ratio
(vertical plutons) magma chambers filled with the STB
magma at different initial temperatures. These geometries
were placed at different depths within crust with a somewhat elevated geotherm (equivalent to the pressures at
which MELTS was run) and linked to the heat transfer
(conduction and convection) and the Navier^Stokes equations for studying the dynamics of the cooling magma
before the suspended crystals form a 3D framework,
making convection no longer possible. Then, we linked
the geometry to Darcy’s Law and used the poroelasticity
model to approximate the segregation by gravity compaction of residual melts trapped within the crystalline
framework.
The predictions of the numerical model are then compared with the geometry and the spatial variation in elements and isotopes of an exceptionally well exposed sill-like,
high-silica granite intrusion, and used to discuss the
origin of dark microgranular enclaves in the peraluminous
granodiorites and adamellites of Central Iberia.
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CRYSTALLIZATION DYNAMICS OF GRANITE MAGMAS
M E LT S M O D E L I N G A N D
E S T I M AT I O N O F T H E P H Y S I C A L
P RO P E RT I E S O F T H E M AG M A
A N D H O S T C RU S T
This section discusses the granite composition used for
MELTS modeling, and the most important rheological
parameters and physical properties input into the numerical models. Examples of these models are available from
TM
the author upon request (COMSOL commercial software required).
Starting composition
As the starting composition we have chosen the average
of the Main Series of the Stepninsk massif, which represents a highly fractionated granite body (Bea et al., 2005).
This composition, hereafter called the STB magma,
corresponds to a high-K granodiorite (Table 1) with a 3%
initial water content. We ran MELTS for this composition
using the ADIABAT_1pH front-end (Smith & Asimow,
2005) set for isobaric cooling at pressures of 8, 6, 4, 2 and
1 kbar, the fayalite^magnetite oxygen buffer with an offset of ^5, and clinopyroxene, biotite, feldspars, quartz,
titanite and Fe^Ti oxide as fractionating phases. MELTS
outputs are given in full in Electronic Appendix I (available for downloading at http://www.petrology.oxfordjour
nals.org/).
MELTS does not include solution models for biotite and
amphibole. Therefore, the chemical composition of the liquids fractionated from the STB magma differs somewhat
from the most fractionated rocks of Stepninsk (Table 1).
Fortunately, these differences have little or no effect on the
physical properties, so that the calculated viscosities,
heat-capacities, and densities of the MELTS residual liquids closely match those of the Stepninsk leucogranites
(Table 1). Accordingly, we assumed that the thermal and
rheological properties calculated from MELTS are realistic and may accurately represent a crystallizing granite
magma. A more silicic starting composition was not
chosen because we found that MELTS algorithms often
fail to converge.
Melt fraction
The melt fraction of the crystallizing magma is directly
output by MELTS. In the runs at 8 and 6 kbar the melt
fraction decreases smoothly with decreasing T (Fig. 1), so
Table 1: Compositions used in the modeling
STB mean
STB
MELTS
STB
MELTS
leucogranites
1054 K liquid
leucogranites
1054 K liquid
anhydrous
anhydrous
hydrated
hydrated
73·76
SiO2
61·93
76·69
77·80
72·71
TiO2
0·85
0·19
0·31
0·18
0·29
Al2O3
16·28
13·26
12·67
12·57
12·01
FeOtot
4·74
1·14
0·93
1·08
0·88
MgO
1·95
0·18
0·07
0·18
0·07
CaO
3·99
0·70
1·89
0·66
1·79
Na2O
3·50
3·51
2·28
3·33
2·16
K2O
3·70
4·33
4·06
4·11
3·85
H2O
3·00
5·19
5·19
Zr ppm
132
TZr (K)
1054
Log viscosity (Pa s)*
4·82
4·98
Heat cap. (J/kg per K)y
1495
1495
Density (kg/m3)
2287
2321
*Calculated with the Holtz el al. (1999) model for a T of 1059 K.
yCalculated according to Stebbins et al. (1984).
STB-mean is the average of the Stepninsk granitoids (Bea et al., 1994) used as starting composition for MELTS modeling.
STB-leucogranites is the average of the Stepninsk leucogranites, which represent the most fractionated liquid. Despite
small differences in chemical composition, the physical properties relevant for physical modeling are almost identical for a
magma with the same composition as the STB leucogranites and the liquid predicted by MELTS at 6 kbar and a 1054 K;
that is, a T equal to the zircon saturation temperature of the STB leucogranites.
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NUMBER 7
JULY 2010
which causes a smooth step transition in the intervals
975 10 K and 980 10 K, respectively. The fraction of
solids, hereafter called crystallinity (j), is calculated
simply as j ¼1 ^ y.
Melt viscosity
Fig. 1. Melt fraction as a function of temperature at 6 kbar (almost
identical to 8 kbar) and 2 kbar (almost identical to 4 kbar). The thick
grey lines represent MELTS output. The thinner black
lines represent
TM
equations (2) and (4) as implemented in COMSOL . The discontinuity in the 2 kbar plot should be noted.
that in numerical models it can be approached by a simple
polynomial function:
y 8 kbar ¼ 5599 þ 00088233T 292e06 T 2
y 6 kbar ¼ 469 þ 0007195T
2046e06 T 2 1196e10 T 3
ð1Þ
ð2Þ
where y is the melt fraction (by volume) and T is the
absolute temperature.
In the runs at 4 kbar and 2 kbar, in contrast, the melt
fraction decreases suddenly at low T (Fig. 1), causing a discontinuity that makes the same approach impossible because discontinuous functions usually cause problems for
the equation solver. For that reason we used a Heaviside
TM
function (flc1hs) implemented in COMSOL for the
numerical representation of these steps:
y 4 kbar ¼ 215 þ 00036T94e07 T 2
038flc1hsðT975,10Þ
y 2 kbar ¼ 000172T1654
þ 0404flc1hsðT 980,10Þ
ð3Þ
ð4Þ
MELTS calculates the viscosity of the melt phase using the
Shaw (1972) model, which assumes an Arrhenian dependence of the temperature. This model yields acceptable results for high-temperature intermediate to basic^
ultrabasic magmas but has been questioned for granite
melts by Hess & Dingwell (1996), Holtz et al. (1999) and
Giordano et al. (2006), who have proposed non-Arrhenian
alternatives. The inset in Fig. 2 shows the viscosity of the
6 kbar run liquids calculated with all these models. The following stands out: the Giordano et al. (2006) model yields
unrealistically high values for the water-rich lowtemperature liquids because it was conceived for anhydrous melts and cannot therefore be applied to the present
problem. The Hess & Dingwell (1996) and Holtz et al.
(1999) models yield parallel results, the former at about
one order of magnitude less, and the latter overlapping
with Shaw’s model over the middle temperature range.
Remarkably, the viscosity calculated for the Stepninsk leucogranites (for a T equal to their zircon saturation temperature, and for a water content equal to MELTS output
at that T) fits the Holtz et al. (1999) model (Fig. 2), which
was specifically formulated for high-silica melts and takes
into account the effects of water. Therefore, we consider
that the most realistic estimation of the viscosity of the
melt phase is a ‘composite’ model that combines Holtz
et al. (1999) viscosity for low-temperature (high SiO2)
melts and Shaw (1972) viscosity for higher temperatures
(moderate SiO2) melts, the boundary placed at the
high-temperature intersection between the two models,
where they merge smoothly (Fig. 2). In this way we
ensured the most accurate estimation possible of the melt
viscosity over its whole SiO2 range.
MELTS calculations reveal that, once about 50% of the
magma has crystallized, the viscosity of the residual melt,
regardless of the viscosity model chosen, shows marked differences depending on the pressure of crystallization.
Figure 3 represents the variation of melt viscosity with
crystallinity for the STB melts. In all cases except the
1kbar run, there is a slope change at j 0·5^0·6, which,
remarkably, coincides with the point (hereafter named the
critical crystallinity) at which crystals begin forming a
3D framework. Whereas in the 6 and 8 kbar runs the viscosity of the residual melts decreases about four orders of
magnitude as j increases from 0·55 to 0·9, in the 4 kbar
run it decreases by less than one order of magnitude, and
in the 2 and 1kbar runs it remains nearly constant. These
differences simply reflect the effects of pressure on water
solubility into the melt and, as discussed below, may have
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CRYSTALLIZATION DYNAMICS OF GRANITE MAGMAS
important consequences regarding the extraction of melt at
supercritical crystallinities.
Magma viscosity
The viscosity of a non-degassing magma is a complex
function of the viscosity of the melt phase and the effects
of the solids in suspension. How to quantify these is still a
matter of vigorous debate. Here we followed the approach
of Pinkerton & Stevenson (1992), though slightly simplified. For magmas with j 0·3, that is to say, with little
interaction among suspended solids, we assumed the
liquid was Newtonian and corrected the viscosity with the
Einstein^Roscoe equation using Marsh (1981) parameters:
¼ 0 ð1 167jÞ25
ð5Þ
where is the viscosity of the magma, 0 is the viscosity of
the melt phase, and j is the crystallinity.
For j 40·3 to j ¼ 0·6 we corrected in the same way but
softening the results to a computational form (in the
above formula /0 becomes infinite when y40·60) and
assuming non-Newtonian behavior with a yield strength
that increases linearly from 0 to 13 Pa as j increases from
0·3 to 0·6. The viscosity at j ¼ 0·6 was set at 109 Pa s
increasing to 1011 Pa s at j ¼ 0·7 and then up to 1013 Pa s as
j approaches unity. The 13 Pa yield strength value was arbitrarily chosen to be similar to that calculated by
Pinkerton & Stevenson (1992) for the high-crystallinity
Mount St Helens dacite. Figure 4 shows the variation of
the assumed computational function for calculating the
STB magma viscosity as a function of the temperature at
different pressures.
Magma density and density gradient
The density of the magma is calculated as
r magma ¼ r solidj þ r meltð1jÞ
ð6Þ
where r_solid and r_melt are MELTS output. This function can be easily approximated by polynomials with T as
independent variable; for example, for 6 kbar it is
r magma 6 kbar ¼ 75660049 123429T
þ 001035T 2 2977e06 T 3 :
ð7Þ
Fig. 2. Melt viscosity as a function of the temperature calculated with the Shaw (1972) and Holtz et al. (1999) models. As they merge smoothly
at 1120 K, we have used a composite model consisting of the former for high Tand the latter for low T. It should be noted how the viscosities
calculated for Stepninsk leucogranites from their zircon saturation T, and a water content equal to that predicted by MELTS at that T, fit the
results of Holtz et al. model. The inset represents two additional viscosity models not used in the calculations.
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VOLUME 51
Fig. 3. Variation in melt viscosity with crystallinity at different pressures as calculated with the composite Shaw (1972) and Holtz et al.
(1999) models from the MELTS output. The divergence between
high-P and low-P runs at supercritical crystallinities should be noted.
This is caused by the increased water solubility in silicate melts at
higher pressures effectively lowering the viscosity. The change of
slope coincidental with the critical crystallinity occurs fully within
the Holtz et al. (1999) model.
The variation of density with decreasing temperature is
then calculated taking the derivative with respect to the
temperature:
r gradient 6 kbar ¼12342939 þ 00206994T
ð8Þ
8931e6 T 2 :
The specific heat of the melt phase given by MELTS is
c. 100 J/kg per K higher than that of solids at the same
temperature. For the sake of simplicity, therefore, we
estimated the specific heat of the melt phase at a given
temperature as equal to the specific heat calculated with
equation (9) plus 100 J/g per K. To calculate the effective
specific heat of the crystallizing magma it is also necessary
to account for the effect of crystallizing phases, calculated
as the product of the latent heat of crystallization of silicates ( 400 kJ/kg per K) and the melt-fraction decrement
with decreasing T provided by MELTS. For the runs at
8 and 6 kbar, this can be approached by functions such as
latent heat 8 kbar ¼ 2915 18392T
ð10Þ
latent heat 6 kbar ¼ 2515 1467T:
ð11Þ
JULY 2010
Fig. 4. Computational form of the magma (melt þ crystals) viscosity
used in the calculations, adapted from the Einstein^Roscoe equation.
(See text for explanation.)
For the runs at 4 and 2 kbar more complex functions are
required because of discontinuities in equations (3) and
(4) relating the melt fraction and the temperature:
latent heat 4kbar ¼ 17515 þ 3273T 00145T 2
þ 4600flc1hsðT970,1Þ
4600flc1hsðT950,1Þ
ð12Þ
latent heat 2kbar ¼ 33646 þ 6064T 00265T 2
ð13Þ
7000flc1hsðT990,1Þ
Specific heat
The specific heat of solids (Cp; J/kg per K), both the host
rocks and those crystallized from MELTS, was calculated
using the method of Robinson & Haas (1983). Because silicate minerals have very similar Cp, to account for the variation of the specific heat with the temperature we
assumed a function unique to all solids involved in the
calculations:
Cp solid ¼ 342 þ 1774T 000125T 2
ð9Þ
þ 32e07 T 3 :
NUMBER 7
þ7000flc1hsðT970,1Þ
TM
where flc1hs is a built-in COMSOL Heaviside function
with a continuous first derivative without overshoot.
The effective specific heat of the magma is then calculated as
specific heat magma ¼ Cp solid þ
latent heat þ 100j:
ð14Þ
Thermal conductivity
The thermal conductivity of solids was calculated with expression (3a) of Clauser & Huenges (1995), which expresses
the dependence of T, corrected for the effect of pressure:
thermal cond solids ¼ ½08 þ 705=ð78 þTÞ
ð1 5e 6 YÞ
ð15Þ
where Y represents the vertical coordinate in meters.
Recently Whittington et al. (2009) have estimated the thermal conductivity of the continental crust based on
laser-flash determinations of the thermal diffusivity of key
minerals, and they ascertained a value of 1·9 W/m per
K at 850 K for the average continental crust. As
these values are almost identical to those predicted by
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CRYSTALLIZATION DYNAMICS OF GRANITE MAGMAS
equation (15) (1·8 W/m per K at 850 K and 7·8 kbar),
and equation (15) also accounts for the influence of pressure, we preferred to apply it rather than use a fixed value.
The thermal conductivity of silicate melts increases as
the temperature decreases, with values close to 1·3 W/m
per K at 1350 K for basaltic melts (Bu«ttner et al., 2000). To
the author’s knowledge there are no similar data for silicic
magmas, although we can assume that they should be
slightly less conductive because of the lower molar fraction
of FeO. The thermal conductivity at the solidus of the
STB composition is close to 1·7 W/m per K, which agrees
well with the result of Vosteen & Schellschmidt (2003).
Therefore, we calculated the thermal conductivity of the
STB magma as a linear function from 1·7 W/m per K at
the solidus to 1W/m per K at the liquidus, with the
expression
thermal cond magma ¼ 17 07y:
ð16Þ
Thermal regime of the crust
We assumed a crust with a somewhat elevated stable
geotherm (Chapman & Furlong, 1992) with a surface heat
flow of 0·07 W/m2, a subcrustal heat flow of 0·03 W/m2, a
thermal conductivity such as in equation (15), and a heat
production that decreases with depth according to the
expression
heat production ¼ 3227e 06
þ 836e 11 Y 4554e 15
2
Y 1268e
19
ð17Þ
3
Y :
The initial vertical distribution of temperature in the
crust is estimated by
geotherm ¼ 283 002Y 468e 8 Y 2
þ108e 12 Y 3 :
ð18Þ
R E S U LT S
Crystallization dynamics of granite
magma chambers
First we describe 2D models of the crystallization dynamics of low aspect-ratio (sills) granite magma chambers, the
dimensions of which have been fixed arbitrarily as 5 km
width and 1km thickness. Increasing either the width or
the thickness of the model chamber does not change the results. However, at a thickness below 200 m the magma
chamber does not convect and cools mostly by conduction,
strictly following the solidification front model.
The magma chamber was placed within the crust with
the prior specifications of the thermal properties at depths
equivalent to 8, 6, 4 and 2 kbar pressure, and the model
was run with the heat transfer (conduction and convection) and the Navier^Stokes equations coupled, so that
the x and y velocities provided by the latter are input into
the convection heat-transfer equation. Calculations were
performed for a magma with initial temperatures of 1273,
1253 and 1173 K. The thermal and rheological properties
of the magma were set for each depth specified. To facilitate the convergence of the equation solvers, gravity was
damped to reach its full value 100 years after the beginning
of the process. The results for 8 and 6 kbar, on the one
hand, and for 4 and 2 kbar, on the other hand, are virtually identical. Accordingly, for the sake of simplicity, only
the results for 6 and 2 kbar are shown (Fig. 5; see animations in Electronic Appendix II).
In all cases we found that melt-to-solid transformation of
a significant mass fraction within the upper cooling zone
caused a negative density gradient that initiated
Rayleigh^Taylor instabilities 200 years after the beginning of the process, and 100 years after gravity reached
full value, for magmas with initial j50·3; instabilities
were initiated later for high-j magmas. The instabilities
evolved quickly into fast descending fingers that pierced
the lower half of the chamber (Fig. 5) where the density
gradient is positive, and split the chamber into as many
convective sections as the chamber’s width/height ratio.
Immediately following this, the whole magma chamber
entered into a state of chaotic convection, with vertical
velocities 1 106 m/s and locally even higher (Fig. 6).
This phenomenon was independent of the crystallization
pressure and reached a maximum shortly after emplacement, about 500 and 600 years if the initial T of the
magma was 9008C, but around 700 years and nearer
1000 years if the initial T was 850 and 8008C, respectively.
After 150^200 years of chaotic convection, the magma
movements became ordered into well-defined convection
cells, and the chamber stabilized with an inward-growing
solidification front and a more liquid, slowly convecting,
core (Fig. 5) in which velocities approached zero after
2000 years from the beginning of the process (Fig. 6).
After this point, the chamber cooled by conduction and
its evolution was almost independent of the initial Tof the
magma.
The examination of the streamline plot (Fig. 6) and the
simulation of particle trajectories calculated by
TM
COMSOL (Fig. 7a) indicates that there is little material
interchange between the vertical sections separated by the
Rayleigh^Taylor fingers, so that every convective section
tends to behave as a nearly isolated cell. If the magma
was initially heterogeneous, this may have a strong influence on the spatial distribution of trace element and isotope ratios in the resulting igneous body, especially when
the average composition of each convecting cell is different. In this case, convection would tend to homogenize
each cell almost independently, thus dividing the chamber
into contiguous vertical zones with different trace element
signatures and initial isotope compositions (Fig. 7b), a spatial distribution that may easily be misinterpreted as the
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Fig. 5. A 2D simulation of the crystallization dynamics of low aspect-ratio granodioritic magma chambers (5 km 1km) placed at a depth
equivalent to 6 kbar pressure with different initial temperatures. The left column of numbers indicate the time (years) after emplacement,
except for the three central figures for initial T ¼ 8008C. Convection occurs even when the initial T is 8008C, equivalent to a 0·5 fraction of
solids. It should be noted how Rayleigh^Taylor fingers drag fragments of the upper solidification front downward; these will remain as autoliths.
This effect is more important at higher initial T. It should be noted also how 1000 years after emplacement the evolution of the chambers is
independent of the initial magma T.
result of different intrusive batches caused by the incremental growth of the pluton. An example of this phenomenon
is discussed below.
The model also predicts that highly crystalline clots and
fragments of the mushy upper cooling zone would be
dragged downwards in the descending fingers (Fig. 5; see
animations in Electronic Appendix II). Such fragments
would probably not dissolve in the hot interior of the
magma but instead would recrystallize, being preserved
as autolithic enclaves that are common in many granitic
rocks. This phenomenon would be more pronounced in
magmas with a larger crystallization temperature interval;
that is, higher initial Tand lower initial SiO2 content.
The result of modeling the crystallization of chambers
with a high aspect ratio (Fig. 8; see animations in
Electronic Appendix II) revealed similar features: the collapse of the upper solidification front through the hot interior to establish one or two vertically oriented convection
cells. As before, downward-dragged clots and fragments of
the upper cooling zone would form autolithic enclaves.
The main difference from chambers with low aspect ratio
is that the convecting sections easily interchange material,
so that the whole chamber may become fully homogenized
before massive crystallization.
Evolution after reaching critical
crystallinity
As discussed above, the separation of major minerals from
granitic melts at low crystallinities is hardly possible.
Once the magma reaches the critical crystallinity, the segregation of melt from the network of crystals becomes
easier. This mainly happens by gravity-driven compaction
or tectonic squeezing. In either case, the limiting factor is
the migration velocity of the residual melt throughout the
crystal skeleton, which can be approximated using Darcy’s
Law.
One of the most important predictions of the above
simulations is that most of the chamber will simultaneously reach a crystallinity between 0·5 and 0·6 (Figs 5
and 8), when a 3D skeleton with initial uniform porosity
of 0·4^0·5 begins to form. This configuration is gravitationally unstable, so the skeleton will spontaneously compact towards an equilibrium distribution of porosity that
decreases with depth, in much the same way as
1548
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CRYSTALLIZATION DYNAMICS OF GRANITE MAGMAS
Fig. 6. Streamlines (uniform density), velocity field, and arrow plots of a low aspect-ratio chamber filled with granodioritic
magma at 9008C
TM
initial T. At 650 years after emplacement the convection is so chaotic that no streamlines can be plotted by COMSOL ; 100 years later, convection is in well-ordered cells. Convective velocities tend to zero 2000 years after emplacement, when the fraction of solids is near the critical
crystallinity.
unconsolidated sediments do (Atty, 1930). By analogy with
sediments, therefore, the equilibrium porosity of a compacting magma mush can be approached using Atty’s Law:
Y ¼ 0 e Y
ð19Þ
where p is the porosity and is the Atty’s constant.
The driving force expelling the interstitial fluid upwards
is proportional to the difference between the actual
and the Atty’s equilibrium porosity at each point of
the mushy column. It must be considered, however,
that quantitative modeling of this phenomenon is notably more difficult in a mushy magma than in a sedimentary pile, because the crystallization of the
percolating melt in the former may cause dramatic
1549
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JULY 2010
(a)
(b)
TM
Fig. 7. (a) COMSOL simulation of the trajectories of five particles released at regular intervals (stars) corresponding approximately to the
middle points of the convection cells, separated by the Rayleigh^Taylor fingers (vertical gray arrows). It should be noted that the trajectories
are mainly confined to one cell, suggesting that the interchange of matter between cells is minimal. (b) Simulation of the effect of convection
on the spatial distribution of a heterogeneously distributed trace element or isotope. The irregular pre-convection concentration profile is homogenized within each convection cell, but each cell has a different concentration, resulting in discrete changes in contiguous zones. The same
applies to isotope ratios. (See examples in Figs 12 and 13.) This distribution can easily be misinterpreted as being due to incremental growth of
the pluton from slightly different magma pulses.
changes of porosity as a response to small fluctuations of
temperature.
To assess the melt-segregation rates involved and the influence of different parameters, we undertook unidimensional modeling by linking Darcy’s Law to the variation
of melt fraction as a function of the temperature, and also
to the thermal evolution of the magma chamber after convection. Darcy’s Law can be expressed in a way analogous
to Fourier’s Law:
q ¼ K=mrP
ð20Þ
where q is the flux vector, K is the hydraulic conductivity,
and rP is the pressure gradient. K is given by
K¼ ðrg=mÞ
ð21Þ
where is the permeability, r is the density, g is the acceleration due to gravity, and m is the dynamic viscosity. To
calculate the permeability, we used Bear’s expression
[given by Turcotte & Ahern (1978)]:
¼ 3 b2 =12
ð22Þ
where p is the porosity and b is the mean grain
diameter. rP is the pressure gradient caused by the compaction of the crystalline skeleton towards a vertical porosity distribution identical to that calculated with
Atty’s expression [equation (19)] for a given value of the
constant .
All calculations made for reasonable values of Atty’s
constant () reveal that a layer of fractionated, residual
melt may form on top of the compacting magma column
shortly after the critical crystallinity is reached. The efficiency of the process depends on the average grain size
when the critical crystallinity is reached, the specific
value of the critical crystallinity, the melt viscosity, the
Atty’s constant, and the thickness of the magma chamber.
The effect of these factors is summarized in Fig. 9. The
average grain size () mainly affects the rate of the
process (Fig. 9a). For ¼ 2 mm the segregation of
the top part of the body occurs in the first 200 years
after convection ceases, with this value increasing to
2000^2500 years when decreases to 0·5 mm. The fraction of solids at which the critical crystallinity is reached
mainly affects the thickness of the segregated upper layer,
which is thinner at a higher fraction of solid (Fig. 9b).
At P45 kbar a higher crystallinity may also enhance the
efficiency of the process caused by the lower viscosity of
the residual melt (Fig. 3). At low P, on the other hand, the
separation of a vapor phase may provide an additional
driving force for the segregation of the residual melt (e.g.
Sisson & Bacon, 1999). Increasing Atty’s constant and the
thickness of the magma column also results in a thicker
segregated upper layer (Fig. 9c).
A granite sill fractionated in this way will show a vertical zonation consisting of a (relatively) low-SiO2 lower
zone that becomes gradually more silicic upwards as a
result of the increasing fraction of trapped residual liquid,
until it changes abruptly to an upper aplopegmatitic complex that represent the fractionated felsic liquid free of
early crystals. An example of a granite pluton apparently
formed in this way is described below.
1550
Fig. 8. A 2D simulation of the crystallization dynamics of a high aspect-ratio granodioritic magma chamber (1km 2 km) at a depth equivalent to 6 kbar pressure with initial temperature of
9008C. The lower row represents the crystallinity. The upper row represents the field velocity with streamlines (uniform density) and velocity arrows. As in low aspect-ratio chambers (Fig. 6),
the roof of the chamber collapses shortly after emplacement, producing convection, first chaotic and then more ordered, which homogenizes the whole magma chamber. Convective velocities
tend to zero 3000 years after emplacement.
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NUMBER 7
(b)
JULY 2010
(c)
Fig. 9. Results of applying Darcy’s Law to a compacting magma chamber. Variation of the maximum thickness of the segregated upper layer in
a 1000 m thick mushy magma column (crystallinity ¼ 0·55) as a function of (a) the time for different average crystal grain diameters (Atty’s
constant ¼ 0·0015), and (b) as a function of the specific value of critical crystallinity ( ¼ 2 mm). (c) Percentage variation of the thickness of
the upper layer as a function of the mushy column thickness for different values of Atty’s constant (crystallinity ¼ 0·55, ¼ 2 mm); the star
represent the Pedrobernardo granite sill of Central Iberia, of which both the top and base are exposed (Fig. 10).
S U B S TA N T I AT I O N W I T H
N AT U R A L E X A M P L E S
The Pedrobernardo pluton
Granite sills are common within the Variscan batholiths of
Central Iberia (Bea et al., 1999, 2003). One of the most impressive examples is the late-tectonic 295 Ma
Pedrobernardo pluton (408150 N, 48580 W) of the Avila
batholith (Bea et al., 2004; Fig. 10). This is a 900 m thick,
subhorizontal sheet-like granite body accessible for observation and sampling throughout its entire vertical section
as a result of the great topographic relief of the Sierra de
Gredos. Wall-rocks at both the lower and the upper contact
consist of 310^320 Ma porphyritic, peraluminous,
cordierite-bearing granodiorites and granites. Both contacts are razor-sharp, flat, and subhorizontal, truncating
veins and structures within the host granodiorites.
Pedrobernardo granites (SiO2 71^76%, Table 2) are
notably homogeneous at a mesoscopic scale; the pluton,
however, shows a marked asymmetrical vertical zonation
so that it can be considered to be formed of three zones,
one on top of another. The lower zone (400^500 m thick)
consists of biotite-dominant porphyritic monzogranite.
The middle zone (300^350 m thick) consists of
muscovite-dominant porphyritic or equigranular syenogranite. The upper zone (30^70 m thick) consists of equigranular muscovite leucogranites and aplites that, when
massive, show spectacular rhythmic zoning between thick
aplitic and narrow pegmatitic layers. Whereas the transition from the lower to middle zone is gradual, the change
to the upper zone is abrupt, occurring through a 10 m
thick transition layer (Bea et al., 1994). Magmatic
fractionation parameters, such as Zr/Hf (Fig. 11), show a
smooth vertical variation indicating increased differentiation upwards (Bea et al., 1994).
A remarkable feature of the Pedrobernardo pluton is the
occurrence of subtle lateral variations in some trace elements and radiogenic isotopes, which become evident only
by comparing samples collected along different vertical
sections; for example, those labelled A and B in Fig. 10.
Analytical data are given in Table 2. Despite the mineral
mode and most absolute elemental abundances being indistinguishable from one section to another (e.g. Fig. 11), a
few element pairs such as V^Ti, U^Th, Sn^Li and Ga^Al
revealed consistent differences (Fig. 12). Of special significance is the Rb^Sr isotope system (Fig. 13); seven samples
from each section yield excellently fitted isochrons:
295·1 2·8 Ma with initial 87Sr/86Sr ¼ 0·713226 0·000409
and MSWD ¼ 0·17 for section A, and 295·6 2·7 Ma with
initial 87Sr/86Sr ¼ 0·712215 0·000377 and MSWD ¼ 0·17
for section B; exactly the same age, but different initial
ratios. Not surprisingly, therefore, the isochron goodness
of fit worsens when the 14 samples are plotted together, so
that the MSWD increases to four, and the error on the
age to 14 Ma (Fig. 13). It seems, therefore, that whereas
the samples from each section were derived from a perfectly homogeneous batch of magma, the two sections were
derived from magma batches that maintained slightly different initial 87Sr/86Sr (and trace element ratios; see
Fig. 12) through the entire crystallization history of the
pluton. As the field relationships, rock compositions and
geochronology leave no doubt that the Pedrobernardo
pluton originated from a single magmatic chamber, the
above-described lateral isotope heterogeneity, despite
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Fig. 10. Geological sketch of the Pedrobernardo pluton of Central Iberia (Bea et al., 1994). The location of the two vertical sections, A and B,
sampled for studying lateral compositional variations, is indicated. SPZ, OMZ, CIZ, WALZ and CZ are the zones of the Iberian Massif:
South Portuguese, Ossa Morena, Central Iberia, Western Asturian^Leonian and Cantabric, respectively.
perfect vertical homogeneity, can hardly be understood in
terms other than the splitting of an initially heterogeneous
magma into nearly isolated convection cells that were
subsequently separately homogenized.
The origin of microgranular enclaves in
the Hoyos granodiorites
As is the case for most of the high-silica granites of Central
Iberia, the Pedrobernardo granites contain few or no enclaves; therefore, they are unsuitable for checking the
model prediction about the formation of autholiths. In contrast, the neighboring Hoyos granodiorites and adamellites
(SiO2 63^70%, Bea et al., 1999; Table 3; 207Pb/206Pb
zircon age 313 6 Ma; Montero et al., 2004), which also
form sill-like bodies albeit unexposed from top to bottom,
contain numerous enclaves. These belong to three main
types: (1) xenoliths of mafic rocks, mostly concentrated
around coeval small gabbro^dioritic bodies; (2) xenoliths
of metamorphic rocks, mostly migmatites, more abundant
near the contact with anatectic complexes; (3) globular
dark microgranular enclaves of no obvious origin, which
are the most abundant and occur ubiquitously.
The microgranular enclaves range from 10 to 50 cm in
diameter. Petrographically they are fine-grained tonalites
to granodiorites composed of quartz, andesine and biotite,
with rare K-feldspar and scarce amphibole, always partially transformed to biotite. As accessories they contain abundant needle-like apatite and zircon, ilmenite, rare
magnetite, Fe^Cu sulfides and Th-rich monazite, exactly
the same assemblage as the host Hoyos granodiorites.
Their chemical composition (Table 4) corresponds to
intermediate to acid peraluminous granitoids, with
SiO2 59·2^69·2%, FeO 3·9^6·8%, MgO 1·3^3·4%,
CaO 2·7^4·6%, Na2O 2·1^4·1%, K2O 2·1^3·6%
and aluminium saturation index (ASI) 1·05^1·27.
Contrary to popular belief, therefore, they do not represent quenched globules of mafic magma. In Harker plots,
the enclaves overlap with the less silicic samples of the
host Hoyos granodiorites (Fig. 14).
U^Pb ion microprobe dating of zircons separated from
two large enclaves yielded the same age, 314·1 1·6 Ma,
identical to that of the zircons separated from the host
Hoyos granodiorite, 314·4 1·8 Ma (Fig. 15; Table 5).
The initial Sr and Nd isotope composition of the
enclaves is markedly crustal (87Sr/86Sr314Ma 0·7082;
"Nd314Ma 4·4; Time of Crustal Residence 1·5) and
matches almost exactly the initial Sr and Nd isotope composition of the host Hoyos granodiorites (Fig. 16; Tables 3
and 4), thus indicating that they shared the same source.
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Table 2: Major and trace element, and Sr isotope composition of the Pedrobernardo granites
Sample no.: A1
SiO2
TiO2
Al2O3
A2
A3
A4
A5
74·66 74·98 71·601 75·41 72·71
0·03
0·04
0·34
0·04
0·26
13·96 14·12 14·206 13·54 14·65
A6
A7
73·01
72·75
0·28
0·23
14·445
13·79
A8
A9
72·78 72·26
0·29
0·29
14·32 13·95
A10
A11
71·32 71·98
0·26
0·29
14·78 14·25
A12
A13
72·44 72·67
0·25
A14
A15
71·89
71·35
0·21
0·33
0·34
14·46 13·77
14·66
14·78
FeOtot.
0·70
0·75
1·59
0·64
1·63
1·84
2·09
1·79
2·10
1·87
2·39
1·68
1·53
2·32
2·48
MgO
0·11
0·12
0·46
0·07
0·45
0·53
0·59
0·54
0·57
0·55
0·69
0·47
0·37
0·63
0·72
MnO
0·02
0·03
0·02
0·02
0·02
0·02
0·02
0·03
0·03
0·02
0·03
0·02
0·01
0·02
0·03
CaO
0·32
0·41
0·78
0·31
0·86
1·00
0·82
0·93
0·87
0·88
0·91
0·89
0·56
0·98
1·05
Na2O
3·84
3·87
3·10
4·12
3·38
3·37
3·12
3·11
3·09
3·37
3·25
3·40
3·67
3·21
3·14
K2O
4·29
4·35
5·71
4·40
5·48
5·20
5·13
4·94
5·27
5·26
4·83
5·12
4·84
5·42
5·66
P2O5
0·55
0·49
0·25
0·34
0·26
0·26
0·32
0·28
0·21
0·27
0·287
0·27
0·33
0·23
0·23
Li
246
188
77
130
88
93
114
86
91
98
102
104
107
79
80
Rb
443
403
294
357
325
316
312
327
304
312
313
326
313
300
295
Cs
23
20
6
11
9
9
13
9
9
11
11
11
10
7
6
Sr
5
13
93
14
78
74
69
81
84
76
73
70
77
90
117
Ba
10
27
445
5
355
363
297
342
378
367
307
306
299
428
463
Sc
1
1·2
V
4
4
21
4
16
19
15
19
19
18
20
16
13
20
21
Ga
26
26
24
30
23
25
27
25
26
25
26
24
26
23
23
Y
3
3
13
3
14
14
15
13
17
15
18
16
13
14
15
Nb
9
11
10
13
12
15
13
12
15
14
17
14
14
12
10
Ta
1
Zr
17
Hf
Sn
0·9
15
1·5
22
1
13
2·6
2·4
1·1
159
4·3
4
1·6
23
0·9
10
1·5
132
3·9
1·8
136
3·3
2·7
1·8
1·5
130
144
3·3
1·6
158
3·7
1·7
143
3·7
2
137
2·6
1·8
129
2·7
1·7
92
4
4·3
1·4
1
155
176
4
3·9
4·3
4·1
4·7
4·5
4·3
4
3
4·3
4·8
5
6
7
6
5
6
7
7
8
4
4
2·8
Pb
7
U
1·41
1·94
6·89
5·99
5·17
6·61
6·3
Th
1·87
2·43 24·58
0·84 21·09
23·56
26·46
22·54 25·72
27·79 28·51
20·07 19·18
23·51
25·61
30
5·77
2·5
2·6
Tl
12
1·9
0·9
8
3·45
2
33
5·9
2·1
30
2·4
2·2
30
25
5·03
2·1
30
6·23
2·1
31
6·87
2·1
26
7·19
2·3
27
4·6
2·4
27
1·8
1·8
33
35
La
1·71
1·71 30·6
1
27·5
29·6
35·8
27·9
33
31·3
34·7
25·9
25·8
28·6
32·1
Ce
3·2
3·49 68·3
1·95 61·1
66·1
80·6
61·7
73·1
68·8
77·6
57·4
58·7
63·2
70·6
Pr
0·4
0·38
0·25
7·6
8·3
10·2
7·9
9·4
8·5
9·9
7·1
7·2
8·3
9
Nd
1·76
1·43 33·1
1·06 28·8
31·6
35·5
30·3
35·6
36·5
26·9
25·3
30·3
34·2
Sm
0·47
0·39
7
0·37
6·6
7·1
7·9
6·8
7·9
7·4
8·6
6·1
4·9
6·8
6·8
Eu
0·03
0·03
0·64
0·02
0·69
0·56
0·71
0·49
0·6
0·64
0·53
0·48
0·51
0·64
0·85
Gd
0·5
0·46
4·93
0·4
4·7
5·19
5·96
4·53
5·72
5·48
6·31
4·75
4·32
5·2
5·55
Tb
0·08
0·08
0·59
0·06
0·63
0·69
0·78
0·64
0·75
0·68
0·79
0·63
0·54
0·66
0·71
Dy
0·46
0·45
2·94
0·36
3·09
3·22
3·41
2·89
3·6
3·43
3·82
3·17
2·7
2·99
3·47
Ho
0·08
0·09
0·43
0·06
0·49
0·51
0·53
0·45
0·59
0·56
0·66
0·53
0·39
0·47
0·56
Er
0·22
0·27
1·02
0·18
1·16
1·33
1·22
1
1·44
1·26
1·42
1·34
0·99
1·17
1·27
Tm
0·03
0·04
0·14
0·04
0·17
0·2
0·18
0·15
0·19
0·18
0·21
0·2
0·15
0·17
0·17
Yb
0·21
0·24
0·78
0·26
1·15
1·23
1·02
0·95
1·27
1·15
1·31
1·27
0·86
0·99
1·11
Lu
0·03
0·04
0·12
0·04
0·16
0·16
0·15
0·14
0·19
0·17
0·19
0·2
0·13
0·15
0·17
12·162
12·536
13·205
11·891
9·635
7·356
0·753762
0·744123
87
Rb/86Sr
87
Sr/86Sr
8·8
0·764474
0·765756
35
10·502
0·768741
0·757247
0·763036
(continued)
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CRYSTALLIZATION DYNAMICS OF GRANITE MAGMAS
Table 2: Continued
Sample no. B1
B2
B3
B4
B5
B6
B7
B8
B9
73·4
B10
72·8
B11
B12
B13
SiO2
75·32
73·89
72·69
74·29
76·01
75·24
72·91
73·36
71·62
71·48
TiO2
0·06
0·09
0·28
0·06
0·04
0·04
0·27
0·23
0·28
0·33
0·34
0·37
72·36
0·33
Al2O3
13·87
14·11
13·88
14·08
13·35
13·66
13·65
13·71
13·52
14·04
14·22
14·39
14·36
FeOtot.
0·89
1·43
1·98
0·76
0·61
0·68
1·70
1·34
1·67
1·72
2·04
2·02
1·96
MgO
0·16
0·35
0·41
0·12
0·07
0·10
0·44
0·36
0·47
0·51
0·57
0·59
0·56
MnO
0·02
0·03
0·03
0·03
0·02
0·01
0·03
0·02
0·02
0·02
0·02
0·02
0·02
CaO
0·37
0·57
0·74
0·29
0·14
0·16
0·72
0·64
0·72
0·77
0·96
1·01
0·93
Na2O
3·90
3·70
3·12
4·04
4·03
4·22
3·24
3·29
3·20
3·10
3·11
3·13
3·06
K2O
4·26
4·47
4·95
4·03
3·68
3·60
5·03
5·35
4·98
5·28
5·14
5·19
5·12
P2O5
0·42
0·43
0·39
0·64
0·51
0·42
0·40
0·32
0·26
0·36
0·29
0·32
0·28
Li
109
125
93
256
144
164
72
75
81
65
63
68
56
Rb
361
354
329
558
537
485
331
323
307
278
297
270
256
Cs
15
15
10
29
20
17
10
8
10
11
10
8
7
Be
6·4
5·9
4·6
4
4·5
6·2
3·9
5·2
5·7
4·5
4·8
6·2
3·5
Sr
28
26
67
7
3
6
70
72
71
78
96
93
96
Ba
55
73
271
7
10
6
367
351
334
378
449
405
476
Sc
1·9
3·3
V
3
4
3·2
16
1·5
1·9
1·3
3
0
3
3·7
15
2·6
13
2·8
17
2·7
18
5·5
17
3·6
21
2·3
20
Cu
5
5
4
2
8
3
7
11
3
7
7
6
8
Zn
61
68
82
64
74
49
94
49
79
68
97
66
86
Ga
24
24
24
31
31
30
26
25
26
24
25
24
23
Y
13
12
17
3
4
3
15
14
15
14
16
18
15
Nb
12
13
14
15
10
11
13
13
14
13
11
14
12
Ta
Zr
Hf
Sn
Tl
Pb
1·6
71
2·8
11
2·5
13
1·4
82
3·5
11
2·6
16
4·6
8
2·3
26
1·1
13
3·6
9
1·4
24
1·3
11
3·1
12
1·3
20
0·8
13
3·2
6
1·6
129
1·6
104
1·6
140
1·4
107
1·4
136
1·8
172
1·7
174
4·2
3·3
4·3
3·1
3·9
4·7
4·7
6
7
7
6
5
5
3
1·8
28
2·2
28
1·4
1·7
0·88
7·5
1·46
1·5
0·8
20·6
16·2
20·4
22·7
26·2
28·4
24·9
La
5·5
21·8
26·9
1·5
1·3
1·2
27·3
21·7
27·6
30·3
35·3
37·6
32·9
Ce
13·2
49·8
58·9
2·97
2·72
2·3
57·4
46·3
58·6
66·5
79·2
82·7
72·3
Pr
1·9
6·2
7·4
0·36
0·37
0·32
7·4
5·8
7·6
8·5
9·5
10·3
9·1
Nd
7·5
22·6
28·5
1·37
1·34
1·21
28·3
22·3
28·8
31·5
37·4
39·8
34·3
Sm
2·20
4·90
6·39
0·51
0·49
0·48
5·90
5·20
6·50
7·10
8·00
8·50
7·21
Eu
0·19
0·18
0·46
0·03
0·03
0·03
0·53
0·55
0·49
0·56
0·67
0·63
0·7
Gd
2·52
3·53
4·96
0·47
0·59
0·48
4·71
3·94
4·71
5·83
5·62
6·35
5·61
Tb
0·39
0·51
0·66
0·08
0·10
0·08
0·67
0·54
0·63
0·69
0·76
0·86
0·72
Dy
2·15
2·67
3·23
0·50
0·66
0·51
2·97
2·78
3·18
3·28
3·38
3·93
3·38
Ho
0·44
0·41
0·57
0·10
0·14
0·11
0·54
0·45
0·48
0·49
0·58
0·6
0·59
Er
1·03
1·03
1·50
0·29
0·36
0·25
1·24
1·12
1·21
1·16
1·22
1·47
1·23
Tm
0·16
0·15
0·21
0·05
0·06
0·04
0·17
0·15
0·2
0·17
0·16
0·24
0·16
Yb
0·95
0·91
1·27
0·26
0·43
0·25
1·16
0·91
1·21
1·02
1·1
1·36
1·11
Lu
0·14
0·14
0·2
0·04
0·06
0·04
0·17
0·14
0·17
0·14
0·16
0·18
0·17
13·754
13·018
12·675
10·363
8·976
8·403
7·705
0·749823
0·747624
0·744675
0·765456
0·755810
9·29
1·5
32
20·2
0·766878
8·3
1·9
29
16·7
0·770195
8·03
1·6
35
5·23
Sr/86Sr
6·33
1·9
29
1·32
87
5·14
2·1
27
Th
Rb/86Sr
5·83
1·9
22
U
87
4·52
1·8
139
8·8
Major elements are in wt %, trace elements in ppm. Samples prefixed A and B correspond to sections A and B,
respectively (see text).
1555
JOURNAL OF PETROLOGY
VOLUME 51
Fig. 11. Variation of Zr/Hf ratio in the Pedrobernardo granites as a
function of the altitude above sea level (that is, roughly above the
lower contact). This indicates progressive magmatic differentiation
from bottom to top of a single magma batch (see Bea et al., 2006).
It should be noted that there are no differences between samples
collected along sections A and B (Fig. 10).
All these features suggest that the microgranular enclaves are early crystallization products from the Hoyos
magma representing either settled cumulates or fragments
of quickly cooled zones. Because neither textural evidence
nor crystallization dynamics supports the first alternative,
we favor the second; that is, the microgranular enclaves
represents clots or fragments of the upper cooling zone
dragged downwards and randomly distributed in the
magma chamber during the chaotic convection stage
predicted by the numerical models.
DISCUSSION
The above model for the evolution of granite magma
chambers relies heavily on the assumption that the driving
force for magma convection is the increased density of the
upper zone caused by the new crystals forming there as
the magma cools. For this to be true, we must be sure that
crystallization occurs within the magma rather than in
the boundary layer between the melt and the
inward-progressing solidification front, and that the crystallization products reside within the upper cooling zone
long enough to generate the required density gradient.
Homogeneous versus heterogeneous
nucleation
Heterogeneous nucleation is kinetically more favorable
than homogeneous nucleation and it is probably the main
process for slightly undercooled superliquidus magmas.
When it occurs in the boundary layer between the melt
NUMBER 7
JULY 2010
and the inward-progressing solidification fronts, it causes
what is often called congelation crystallization (e.g.
Hughes, 1982, pp. 225^229), in which a magma chamber
with no suspended crystals solidifies progressively by
crystallization over the walls.
Notwithstanding demonstration of this mechanism of
crystallization in mafic magmas, it can hardly be invoked
in granitic magmas. First, granitic magma temperatures
are typically well below the liquidus, thus making homogeneous nucleation more likely. Second, granitic magmas
often contain suspended crystals around which heterogeneous nucleation will also occur, thus increasing the
magma density in the same way as homogeneous crystallization does. Third, the internal structure resulting from
congelation crystallization is totally different from what is
found in granite sills. Congelation crystallization leads to
differentiated magma bodies with the most leucocratic
facies located in the centre (see Hughes, 1982, pp. 225^229,
and references therein). In contrast, the markedly asymmetric vertical zoning and the chemical structure of granite sills such as Pedrobernardo suggests a single magma
pulse that evolved following the low aspect-ratio magmachamber evolution model described in the previous section; that is, nearly simultaneous crystallization within
the whole magma chamber during the convective stage,
followed by upwards migration of the intercrystalline
fluid caused by gravity-driven compaction.
Residence of the newly formed crystals in
the upper cooling zone
If crystals growing in the upper cooling zone sink rapidly
and accumulate in the chamber’s lower zone, they will
create a positive density gradient that can compensate for
the thermal expansion of the melt phase and contribute to
stabilizing the magma chamber in a static, non-convective
state. If, on the other hand, the crystals sink very slowly,
the upper cooling zone will become progressively denser
than the underlying less-crystalline magma, resulting in a
marked negative density gradient that eventually leads to
Rayleigh^Taylor instabilities and convection. Whether this
happens or not depends on the balance between the time
required to initiate Rayleigh^Taylor instabilities, the maximum crystal sinking velocity, and the inward growth velocity of the solidification front.
To understand how these factors interact, we must first
consider that crystal settling in granitic magmas most
probably occurs at j50·3. Above this value, the exponential increase of viscosity [see equation (5)], and the concomitant beginning of thixotropic behavior in the melt
(see Pinkerton & Stevenson, 1992) almost totally prevent
crystal settling. These considerations led Marsh (1996,
2006) to conclude that newly formed crystals are never displaced from their crystallization zone. This, however,
1556
BEA
CRYSTALLIZATION DYNAMICS OF GRANITE MAGMAS
Fig. 12. Variation of selected element pairs in the two sampled vertical sections of the Pedrobernardo pluton revealing that lateral heterogeneity
of the initial magma composition was preserved during crystallization (see also Fig. 13).
cannot be taken for granted in all cases, as revealed by the
following calculations.
Equation (26) of Marsh (1998) for predicting crystal size
distribution is
ln½nðxÞ=n0 ¼ lnð1 jc Þf ðx,a,bÞ þ ða bÞx
ð23Þ
where jc is the crystallinity, x is the dimensionless time,
n(x) is the number of crystals at time x, n0 is the number
of crystals when x ¼ 0, a is a constant that defines the exponentiality of the nucleation rate (a ¼ 0 means constant), b
is a constant that defines the exponentiality of the growth
rate (b ¼ 0 means constant), and f(x,a,b) is a function
describing the Avrami (1939, 1940) integral.
Marsh (1998) concluded that the nucleation rate (i.e. the
a constant) exerts the maximum influence on the temporal
evolution of the crystallinity, whereas the growth rate (i.e.
the b constant) has only a minor influence. Marsh also realized that theoretical crystal size distribution models obtained with equation (23) only approach those of natural
igneous rocks when a ^ b 8. Therefore, we solved the
above equation for a magma with the STB composition,
jc ¼ 0·3 (the most favorable combination of large crystal
size and low viscosity), Newtonian behavior, a ^ b ¼ 8,
and maximum final radius of 0·5, 1, 2 and 4 mm.
Considering that the crystal size of slowly cooled igneous
rocks such as granites is the result of extensive annealing
and modification of the earlier crystal size distribution
(Simakin & Bindeman, 2008), this grain size range seems
adequate for representing medium- to coarse-grained
granitoids. The results of these calculations, expressed as
1557
JOURNAL OF PETROLOGY
VOLUME 51
NUMBER 7
JULY 2010
After a given time since the process began, the bulk mass
of crystals tends to disperse within a vertical column of
magma, the height of which depends on the maximum
sinking velocities (the minimum is always close to zero).
To determine whether the velocities calculated with equation (23) are sufficiently fast to prevent the establishment
of a negative vertical density gradient, we must compare
TM
them with the results of COMSOL models for magmas
with initial j 5 0·3. In these, the thickness of the upper
layer initiating Rayleigh^Taylor instabilities is 50 m,
and convection begins about 100 years after applying full
gravity. Therefore, the vertical dispersion of a significant
mass-fraction of crystals for more than 50 m in the first
100 years would seriously limit the chances of convection.
This places a limit of 0·5 m/a, that is, 1·6 108 m/s, on
the maximum settling velocity of crystals. Comparing
this value with the results of equation (23) (Fig. 17), it follows that 100% of the bulk crystalline mass in the models
with final crystal radius of 0·5 mm and 1mm, and 85%
and 45% in the models with a final radius of 2 mm and
4 mm, do not reach that value and will remain, therefore,
in the upper cooling zone. From this perspective convection seems inevitable in the first three models, and probable in the last one.
Convection can also be prevented if the inward displacement of the upper solidification front is faster than
required to initiate Rayleigh^Taylor instabilities, that is to
say, if at any given altitude in the magma chamber the
mushy zone freezes totally before it can induce convection.
TM
COMSOL calculations reveal that this is possible only
if the thickness of the magma chamber does not exceed
0·2 km. Thicker granite sills (0·2^1km) placed at crustal
depths equivalent to 1^8 kbar pressure, cooling solely by
conduction. always have a 50^100 m thick mushy zone beneath the upper solidification front; this moves inward at
velocities from 5 109 to 4 1010 m/s; that is, slower
than required to induce convection.
Implications for the differentiation of
granite magma chambers
Fig. 13. Rb^Sr isochrons for the Pedrobernardo granites. It should be
noted how the excellent goodness-of-fit of each vertical section isochron worsens when they are combined in a single isochron. This reveals that whereas initial Sr isotope compositions were almost
perfectly homogenized in each vertical section, the magma retained
lateral heterogeneity, as predicted by the numerical model.
the mass fraction of crystals of a given size against the terminal Stokes’ velocity for that size, show that sinking velocities range from almost zero for the smallest crystals, to
about 3 107 m/s for the largest crystals (Fig. 17). Their influence on establishing convection can be assessed as
follows.
Numerical simulations indicate that convection in granite
magma chambers is the rule rather than the exception,
and that convecting velocities (Fig. 6) are about one order
of magnitude larger than the largest terminal Stokes’ velocities (Fig. 17). These conditions lead to crystal settling
being unlikely as a feasible mechanism for granite magma
differentiation (Bartlett, 1969), and make melt^crystal segregation very difficult until the chamber reaches critical
crystallinity and convection stops. It might be argued that
convecting velocities larger than terminal Stokes’ velocities
do not automatically imply that crystal cannot sink. For example, Sparks et al. (1993) found that there is a critical concentration of phenocrysts in mafic magmas above which
convection is unable to keep them suspended. The situation, however, is different for felsic magmas because their
1558
BEA
CRYSTALLIZATION DYNAMICS OF GRANITE MAGMAS
Table 3: Major and trace element, and Sr^Nd isotope composition of microgranular enclaves in Hoyos granodiorites
Sample no.:
EH1
EH2
EH3
EH4
EH5
EH6
EH7
EH8
62·7
EH9
63·2
EH10
EH11
EH12
SiO2
65·76
62·97
63·73
63·18
66·79
65·58
63·54
62·63
65·17
TiO2
0·76
0·98
0·73
1·08
0·68
0·86
1·25
0·92
1·00
1·03
1·04
Al2O3
15·85
15·89
15·64
16·38
16·03
16·14
16·37
16·48
17·09
16·68
16·2
64·39
0·83
15·97
FeOtot.
5·01
5·59
5·81
6·06
4·01
4·76
6·28
5·14
5·42
5·99
5·07
5·14
MgO
1·87
2·74
3·11
1·76
1·55
1·75
1·87
2·83
1·83
2·57
1·92
2·73
MnO
0·06
0·08
0·10
0·09
0·07
0·08
0·08
0·07
0·08
0·10
0·06
0·09
CaO
2·68
3·79
3·44
3·88
3·41
3·47
4·25
3·16
3·90
4·49
3·55
3·11
Na2O
3·16
3·28
2·48
3·59
3·41
3·48
2·64
3·44
3·58
2·52
3·35
2·88
K2O
2·23
2·70
3·03
2·11
2·62
2·15
2·40
2·81
2·37
2·62
2·26
2·70
P2O5
0·28
0·32
0·18
0·27
0·21
0·21
0·34
0·34
0·27
0·26
0·31
0·18
Li
87
56
108
78
77
93
58
256
95
101
114
116
Rb
87
115
232
145
158
167
263
338
182
200
244
237
Cs
6·4
5
Be
8·5
2·8
11·1
2·8
9·8
9·4
12·9
15·1
23·5
7·3
9
4
3·7
5·4
2·6
2·5
3·8
3·2
15·2
9·7
0·9
3·2
Sr
144
258
158
178
164
140
190
137
157
190
188
116
Ba
162
623
248
266
250
196
451
118
214
409
240
176
Sc
11·3
13·1
V
72
84
Cr
313
Co
10
Ni
18·1
11·2
13·5
18·2
14·6
15·4
106
65
60
74
91
89
74
254
69
95
28
18
6
38
15
88
13
98
89
61
65
67
64
20
20
9
7
3
Cu
11
5
13
11
11
7
Zn
84
98
105
94
69
Ga
23
21
21
24
Y
20
21
25
32
Nb
13
13
10
14
Ta
1·1
Zr
210
1
219
17·7
1·2
193
1·2
272
13·7
14·1
112
65
79
14
35
13
104
95
79
76
77
14
6
11
7
23
15
4
7
21
10
6
97
112
137
108
99
107
106
23
24
23
23
24
22
25
22
22
26
39
24
33
34
30
22
12
15
15
9
14
11
16
12
1·4
199
1·9
218
1·5
253
0·9
254
1·5
283
18·5
1·4
215
1·4
1·4
327
183
Hf
5·8
5·9
5·3
7
5·5
5·6
6·8
6·6
7·3
5·6
8·5
5·1
Mo
12·7
11·5
0·7
0·7
1
0·7
1·5
0·1
0·8
1
1·3
0·2
Sn
2·3
3·5
4·1
4·7
5·1
6·9
5·1
5·6
5
2·7
3·8
3·5
Tl
0·6
0·7
1·3
0·9
0·9
1
1·8
2
1·1
1·2
1·6
1·4
Pb
U
14
3·27
13
12
14
19
1·97
3·94
1·67
3·34
9·55
11·84
11·69
13·6
15
3·59
9
11
17
8
12
11
4·31
5·94
2·65
5·4
3·24
3·24
13·3
13·26
27·49
18·98
12·91
20·72
14·95
Th
14·3
La
32·4
37·9
28·2
42·5
32·4
32·1
39·1
44·9
41·6
33·7
48·2
32·4
Ce
72·4
79·9
60·1
89·9
68·5
67·4
84·1
104·7
91·7
72·5
106·1
68·1
Pr
8·7
9·4
7·2
10·9
8·1
8·0
10·2
12·9
10·6
8·7
12·5
8·0
Nd
34·0
36·5
27·6
42·1
30·8
30·4
40·6
50·2
41·1
33·5
48·3
30·3
Sm
6·7
6·8
5·8
8·8
6·2
6·4
8·8
9·4
8·6
7·0
9·7
6·0
Eu
0·98
1·44
0·92
1·29
1·05
0·91
1·41
0·73
1·06
1·17
1·20
0·73
Gd
5·57
5·17
4·92
7·91
5·08
5·37
7·66
6·27
7·31
6·06
7·63
4·84
Tb
0·80
0·66
0·77
1·19
0·75
0·83
1·22
0·85
1·12
0·99
1·12
0·72
Dy
4·10
3·49
4·39
6·1
4·05
4·71
6·94
4·44
6·18
5·88
6·00
3·95
Ho
0·70
0·62
0·88
1·26
0·80
0·92
1·40
0·84
1·19
1·23
1·11
0·78
Er
1·69
1·44
2·3
3·12
2·07
2·39
3·55
2·09
2·92
3·25
2·66
2·07
Tm
0·23
0·22
0·34
0·41
0·30
0·36
0·53
0·31
0·40
0·50
0·37
0·29
Yb
1·37
1·33
2·08
2·22
1·85
2·08
3·32
1·89
2·32
3·22
2·07
1·76
Lu
0·19
0·20
0·32
0·33
0·27
0·29
0·49
0·28
0·34
0·49
0·28
0·26
87
4·26
2·801
3·457
4·004
3·363
3·752
87
Rb/86Sr
0·726899
0·720628
0·723152
0·724994
0·723117
0·725819
Sr/86Sr
147
0·126
0·121
0·126
0·131
0·126
0·122
143
Sm/144Nd
0·512249
0·512272
0·51224
0·51234
0·512317
0·512251
Nd/144Nd
(continued)
1559
JOURNAL OF PETROLOGY
VOLUME 51
NUMBER 7
JULY 2010
Table 3: Continued
Sample no.:
EH13
EH14
EH15
EH16
66·8
61·4
EH17
64·53
EH18
66·9
EH19
EH20
EH21
EH22
EH23
SiO2
63·95
59·16
60·29
63·68
63·49
66·09
TiO2
0·77
1·16
0·73
1·10
0·74
0·70
1·42
1·03
0·91
0·71
64·05
0·94
Al2O3
15·96
17·87
16·06
16·82
16·19
15·61
16·50
16·44
17·00
15·95
16·62
FeOtot.
4·98
5·76
4·37
6·38
5·52
3·88
6·78
5·49
4·91
4·44
5·27
MgO
3·10
3·38
1·39
2·75
2·29
1·80
3·05
2·12
2·63
1·32
1·87
MnO
0·08
0·08
0·08
0·11
0·09
0·07
0·09
0·08
0·08
0·07
0·09
CaO
3·93
4·37
3·26
4·58
3·18
2·97
3·71
3·48
3·88
2·82
3·56
Na2O
2·80
3·20
4·09
2·12
3·27
2·98
3·41
2·93
3·00
3·89
3·58
K2O
2·64
2·75
2·33
2·87
2·66
3·52
2·70
2·48
2·73
3·21
2·33
P2O5
0·22
0·37
0·21
0·26
0·18
0·22
0·38
0·3
0·22
0·26
0·25
Li
119
55
111
133
183
82
58
66
95
90
105
Rb
203
123
198
210
216
176
168
119
200
207
205
Cs
11·8
4·5
21·9
14·2
Be
3·1
2·6
5·8
3·2
10·8
3.4
7·3
6·5
6·2
8
3·3
2·8
2·2
3·4
12·4
3·3
13·5
3·9
Sr
180
312
112
193
150
158
195
228
190
145
158
Ba
324
965
239
348
83
399
410
606
260
429
144
Sc
15
19·7
12·9
V
89
89
54
117
113
57
Cr
88
242
82
26
202
Co
71
16
10
78
12
Ni
26
93
10
7
Cu
6
21
5
Zn
98
117
Ga
21
Y
27
Nb
10
Ta
1·1
Zr
229
15·7
15·4
12·7
112
90
81
61
104
37
137
209
47
187
10
91
17
14
89
9
76
20
11
31
33
8
30
6
11
11
5
17
14
6
14
8
76
96
106
73
114
97
86
77
109
23
25
22
23
22
28
22
21
23
26
26
40
32
22
22
38
27
27
29
28
21
15
11
13
12
19
13
11
14
15
0·9
333
2·4
273
20·5
1·3
213
16·8
1·3
243
11
1·5
192
20·6
1·2
381
1·3
217
1·3
211
1·3
215
16
1·7
207
Hf
6·1
8·6
7·2
5·7
6·5
5·3
9·9
5·7
5·7
5·5
5·7
Mo
0·1
17·6
0·7
0·7
4·2
0·8
7·5
7·6
0·8
8·6
0·8
Sn
3·1
9·6
14·7
2·9
8·2
5
3·8
2·1
2·7
8·2
6·1
Tl
1·1
0·7
1·1
1·3
1·3
1
1
0·8
1·1
1·2
Pb
5
22
17
77
19
8
15
19
12
23
1·2
16
U
3·66
2·13
5·68
3·97
3·91
3·53
2·89
3·18
4·31
9·05
6·04
Th
16·02
12·76
16·18
9·16
12·63
15·31
19·55
10·54
15·05
17·37
12·26
La
37·8
56·5
40·3
26·8
28·3
32·2
51·6
32·4
35·9
36·2
31·5
Ce
80·2
116·8
84·4
58·8
58·7
71·6
110·7
68·9
77·1
75·1
68
Pr
9·6
14·2
9·9
7·2
7·2
8·8
13·0
8·7
9·2
9·3
Nd
36·9
54·5
37·2
26·8
33·8
50·4
35·3
35·1
35·3
Sm
7·3
9·9
8·0
6·4
5·9
6·9
10·8
7·6
7·2
7·4
6·8
Eu
1·07
1·82
0·83
1·19
0·71
0·98
1·32
1·39
1·13
1·05
0·99
Gd
5·76
7·32
7·39
5·74
5·00
5·38
9·24
6·34
5·76
6·31
5·84
Tb
0·86
1·07
1·16
0·93
0·76
0·80
1·34
0·96
0·86
0·98
0·90
Dy
4·76
5·34
6·55
5·5
4·07
4·28
6·88
5·24
4·83
5·3
5·15
Ho
0·95
0·94
1·35
1·14
0·79
0·81
1·33
1·03
0·97
1·07
2·72
Er
2·51
2·31
3·66
2·98
1·89
1·96
3·24
2·61
2·5
2·7
1·02
Tm
0·38
0·3
0·57
0·46
0·26
0·28
0·46
0·38
0·39
0·42
0·41
Yb
2·4
1·77
3·46
2·85
1·63
1·71
2·41
2·30
2·37
2·52
2·60
Lu
0·36
0·23
0·53
0·44
0·25
0·26
0·37
0·35
0·34
0·37
0·39
87
3·257
5·134
3·155
3·221
3·044
0·721654
Rb/86Sr
87
Sr/86Sr
29
0·722342
0·734006
0·721732
0·722538
147
0·120
0·130
0·132
0·124
0·123
143
0·512236
0·512211
0·512364
0·512236
0·512226
Sm/144Nd
Nd/144Nd
Major elements are in wt %, trace elements in ppm.
1560
8·2
32
BEA
CRYSTALLIZATION DYNAMICS OF GRANITE MAGMAS
Table 4: Major and trace element, and Sr^Nd isotope composition of Hoyos granodiorites
Sample no.: HO1
HO2
HO3
SiO2
65·42
TiO2
0·73
Al2O3
15·91
FeOtot.
4·33
4·36
4·87
MgO
1·37
1·39
1·85
MnO
0·07
0·07
CaO
3·03
2·75
HO4
65·83 65·43 66·05
HO5
HO6
HO7
HO8
HO10 HO11
64·76
68·44
0·72
0·64
0·46
16·11 15·99 16·16
17·00
15·84
4·24
3·37
2·75
4·01
3·96
4·69
4·42
1·63
1·56
0·97
1·96
1·54
1·68
1·67
0·07
0·08
0·06
0·05
0·06
0·06
0·08
3·18
2·16
3·45
1·51
1·90
2·90
3·24
0·73
0·82
66·13 65·42
HO9
0·77
0·66
16·02 16·15
63·78 66·06 64·98
HO12
HO13
HO14 HO15
66·81
65·19
0·71
0·74
0·74
16·91 16·21 16·19
15·79
16·02
4·22
4·49
4·51
3·42
3·90
1·66
1·83
1·74
1·15
1·48
0·07
0·07
0·07
0·07
0·06
0·06
2·43
2·65
2·74
2·48
2·78
3·23
0·79
0·76
67·3
0·56
65·02
0·66
15·98 16·7
Na2O
3·35
3·52
3·46
3·31
3·38
3·06
2·96
3·55
3·39
3·23
3·67
2·93
3·19
3·56
3·11
K2O
3·89
3·79
3·60
3·46
4·64
5·06
3·74
4·23
3·67
3·62
4·12
3·65
3·73
3·66
3·90
P2O5
0·25
0·38
0·29
0·27
0·31
0·45
0·23
0·25
0·31
0·23
0·29
0·18
0·37
0·29
0·31
Li
73
118
47
75
50
44
83
53
98
94
102
82
121
85
80
Rb
182
189
192
166
147
208
146
172
203
132
209
149
240
139
183
Cs
11·4
13·8
5·6
5·7
9·3
7·7
7·9 9.2
Be
3·8
3
2·3
4·1
3·6
4·9
3·8
3
12·8
14·2
11·7
13·5
21·6
16·1
4·1
4·5
2·9
3·8
6·5
4
8·7
3·4
Sr
172
143
190
176
247
261
181
192
186
142
176
153
160
188
212
Ba
658
445
674
486
1166
695
742
793
460
601
666
505
717
676
737
Sc
13·1
11·8
13·1
12·2
V
58
58
69
62
54
35
53
51
64
59
56
61
62
43
52
Cr
133
180
145
164
26
36
65
21
30
95
26
132
443
160
21
Co
10
9
11
9
55
5
9
40
74
9
39
10
9
7
67
Ni
23
21
21
40
8
16
15
6
11
15
7
27
22
7
9
Cu
11
15
13
8
4
13
9
9
13
11
9
10
10
5
11
Zn
70
89
93
67
60
75
93
65
100
98
87
82
101
90
79
Ga
23
25
24
23
21
23
19
32
26
20
32
20
23
21
23
Y
27
35
28
36
15
20
25
27
29
26
29
24
14
21
22
Nb
13
18
15
12
10
13
13
13
16
14
15
14
18
13
13
Ta
1·4
1·5
1·3
1·4
1·3
1·2
2·5
2·3
1·9
2·8
7·6
6·6
5·6
5·3
5·7
7
5·4
5·5
5·7
3·5
1
0·5
0·6
0·3
0·4
1
0·6
0·7
1·3
Sn
9·3
7·2
1·4
9·5
8·8
10·8
2·9
3·2
8·5
4·1
4
3·1
1
37
0·5
27
3·3
3·43
1·1
22
5·67
1·3
24
4·2
0·7
27
1·2
23
6·2
48
8·1
1·8
19
3·2
206
5·5
15·3
1·3
209
5·3
1·4
0·5
7·6
3·6
1·3
27
5·15
1
22
6·52
3·34
3·74
4·13
5·78
12·81
13·71
17·31 17·15 18·05
20·49
17·6
17·31 18·33
16·35 16·84 13·85
16·71
5·4
La
33
38·5
40·6
41·4
55·6
34·7
33·3
45·5
41·3
29·1
40·3
33·7
21·3
34·1
35·9
Ce
70·5
84·8
90·5
90·4
114·3
77·2
73·5
90·2
83·7
68
83
76·9
45·4
75·9
73·6
Pr
8·2
10·1
10·4
10·9
12·1
9·2
8·6
10·3
10·3
8·3
9·7
9·2
5·6
8·9
8·9
Nd
31·7
38·7
40·3
42·6
41·4
35·8
34·8
41
38·9
32·5
38·8
36·1
23·1
33·7
33·3
Sm
6·9
8·3
8·0
9·2
6·2
6·9
7·2
8
8
6·9
8·0
7·1
4·9
6·9
6·4
Eu
1·26
1·00
1·19
1·18
1·39
1·04
1·37
1·35
1·24
1·22
1·25
1·34
1·43
1·35
1·36
Gd
5·99
7·26
7·43
7·67
4·93
6·17
6·14
6·44
6·55
5·52
6·37
5·87
3·92
5·72
5·39
Tb
0·87
1·14
1·07
1·12
0·65
0·89
1·00
0·94
1·00
0·83
0·91
0·84
0·51
0·93
0·77
Dy
4·51
6·4
5·76
5·79
3·18
4·18
5·26
4·68
5·34
4·89
4·79
4·7
2·95
4·69
4·04
Ho
0·89
1·22
1·08
1·19
0·61
0·73
1·05
0·85
2·69
0·99
0·92
0·91
0·5
0·96
0·74
Er
2·38
3·11
2·44
3·18
1·54
1·73
2·74
2·34
1·04
2·72
2·57
2·27
1·14
2·35
1·84
Tm
0·36
0·46
0·29
0·46
0·24
0·24
0·43
0·35
0·41
0·41
0·44
0·31
0·13
0·37
0·26
Yb
2·19
2·81
1·66
2·91
1·58
1·32
2·45
2·14
2·51
2·51
3·10
1·80
0·67
1·71
1·49
Lu
0·35
0·41
0·25
0·42
0·26
0·20
0·37
0·29
0·37
0·38
0·47
0·27
0·09
0·22
0·20
87
3·057
1·72
2·309
2·597
3·331
2·931
4·343
2·497
87
0·720931
0·714961
0·718684
0·7198
0·723534
0·722404
0·727598
0·718408
Sm/144Nd
4·59
1·3
25
4·7
245
8·7
Th
Sr/86Sr
2·62
0·9
31
211
14·3
U
Rb/86Sr
5·14
1
205
2·9
7·7
21
212
3·3
4·8
1·1
259
9·2
6·8
26
218
11·9
1·7
1·2
200
8·1
6
23
221
14
Mo
1
249
9·4
Hf
24
283
8·5
221
Pb
290
7·6
Zr
Tl
256
7·7
3·22
17·86 13·52
147
0·132
0·091
0·117
0·117
0·124
0·119
0·128
0·116
143
0·512291
0·512205
0·512247
0·512312
0·512299
0·512241
0·51231
0·512237
Nd/144Nd
(continued)
1561
JOURNAL OF PETROLOGY
VOLUME 51
NUMBER 7
JULY 2010
Table 4: Continued
Sample no.: HO16
HO17
HO18
HO19
HO20
HO21
HO22
SiO2
65·45
68·08
67·65
66·05
66·24
65·97
TiO2
0·98
0·52
0·46
0·73
0·57
0·69
Al2O3
15·98
15·89
15·79
15·91
16·45
16·4
68·4
HO23
HO24
HO25
67·6
66·93
67·8
0·51
0·65
0·6
0·48
15·16
15·52
15·52
15·57
HO26
65·52
0·85
15·8
HO27
66·6
0·73
16·1
HO28
HO29
HO30
68·66
69·21
0·55
0·82
65·89
0·71
15·21
14·49
15·97
FeOtot.
4·97
2·79
2·88
4·29
3·73
4·18
3·41
4·05
4·16
3·28
4·39
4·34
3·67
4·35
4·17
MgO
1·72
0·59
1·05
1·72
1·41
1·26
1·23
1·46
1·58
1·27
1·85
1·48
1·41
1·57
1·45
MnO
0·04
0·05
0·06
0·07
0·06
0·06
0·05
0·06
0·06
0·06
0·04
0·06
0·07
0·05
0·09
CaO
1·52
1·25
1·85
2·82
2·93
3·21
2·71
2·42
2·13
2·5
1·41
2·88
1·69
1·47
2·66
Na2O
2·88
3·05
3·54
3·31
3·45
3·41
3·44
2·82
2·74
3·29
2·40
3·44
3·21
3·03
3·43
K2O
4·86
6·40
5·20
3·75
3·61
3·60
4·03
3·67
3·50
4·88
4·14
3·39
3·83
3·2
4·00
P2O5
0·44
0·43
0·22
0·28
0·31
0·25
0·28
0·27
0·20
0·18
0·40
0·26
0·17
0·37
0·30
Li
39
117
74
79
123
70
124
88
76
89
137
94
156
94
90
Rb
139
320
230
135
161
165
231
149
143
211
194
161
222
111
169
Cs
5·5
12·5
13·2
5·5
12·1
11·8
18·1
8·2
7·2
15·7
15·3
12·4
22·6
14·2
Be
1·9
8·6
2·6
2·6
3·7
3·9
3·5
3·2
3·7
3·5
2·5
3·9
7·7
3·8
12·5
4·5
Sr
171
124
134
286
213
190
167
154
183
147
146
156
143
107
129
Ba
1092
492
645
657
658
705
697
627
706
686
623
539
489
387
526
Sc
17·2
5·1
V
84
24
Cr
52
Co
86
Ni
7·5
20·1
10·5
12·6
8
8·3
12·3
10
11·9
9·1
5·9
9·4
38
69
55
55
71
59
21·9
32
110
52
58
43
50
61
84
11
179
23
142
59
102
512
2
96
112
107
47
189
5
42
19
48
10
6
8
10
68
9
10
8
99
10
24
7
3
41
8
20
7
27
229
1
14
18
22
24
64
Cu
21
6
1
12
8
15
11
4
13
5
8
10
19
22
13
Zn
121
67
62
109
85
67
79
84
86
75
115
100
78
117
97
Ga
21
25
29
22
23
24
21
20
22
19
22
23
21
22
17
Y
23
23
26
33
25
25
16
26
26
25
28
27
12
20
23
Nb
15
15
11
13
14
12
11
16
13
11
18
16
13
14
15
Ta
1·1
Zr
205
1·5
210
2·4
178
1
225
1·5
227
1·2
1·9
211
205
2·9
176
1·6
197
1·7
196
3·3
222
3·1
211
3·6
199
1·7
179
2·2
228
Hf
5·5
5·6
4·7
6·1
6
5·7
5·8
4·7
5·3
5·2
6
5·5
5·4
4·9
6·1
Mo
1
2
0
3·3
0·4
1·8
0·8
0·6
1·7
0·1
1
0·7
0·8
1
2
Sn
3·9
8·2
3·1
1·8
9·9
7·1
16·9
3·2
6·3
9·1
4·9
3·5
5·8
7·5
4·4
Tl
0·9
1·8
0·8
0·8
1
0·9
1·4
1·3
1
1·4
1·7
1·4
1·7
1·1
1·3
Pb
U
33
2·85
Th
17·8
La
40·8
Ce
100·6
40
7·26
22·4
33
2·52
12·16
13
4·27
15·9
32
3·86
19·7
22
24
5·25
5·25
12·6
15·7
25
4·74
17·1
23
3·18
13·7
30
3·78
15·1
27
5·06
31·7
24
3·29
16·3
22
5·48
12·9
21
3·63
17·3
9
3·73
20·9
35·2
30·9
29
45·2
39·4
29·5
31·4
34
32·3
43
33·3
22·6
30·8
26·1
80
62·8
67·4
93·4
81·5
69
72·3
73·9
69·4
103·2
74·6
52·9
76
59·3
12·8
Pr
11·4
9·7
7·2
8·5
10·8
9·6
7·4
8·5
9
8·4
Nd
42·8
36·3
30·5
34·7
39·7
35·3
27·5
34·2
33·4
31·3
51
8·9
6·3
9·2
7·1
36·1
24·2
34·8
27·2
Sm
9·1
8·0
6·4
7·9
8·1
7·6
5·4
6·9
6·9
6·8
9·3
7·1
4·7
7·6
5·6
Eu
1·61
0·83
1·05
1·37
1·2
1·41
0·79
1·27
1·12
1·31
1·2
1·39
0·91
0·95
1·04
Gd
7·11
6·44
5·04
7·13
7·02
6·19
4·6
5·78
5·89
5·15
6·94
5·98
3·75
6·00
4·84
Tb
1·01
0·88
0·8
1·09
1·01
0·83
0·65
0·83
0·9
0·81
1·01
0·9
0·50
0·81
0·79
4·35
Dy
5·18
4·23
4·23
5·93
5·13
4·43
3·45
4·71
5·04
4·61
5·33
5·2
2·59
4·47
Ho
0·84
0·72
0·76
1·23
0·97
0·81
0·61
0·93
1·00
0·93
1·07
1·06
0·47
0·75
0·86
Er
2·15
1·77
2·17
3·22
2·52
2·17
1·42
2·24
2·64
2·20
2·71
3·02
1·16
1·97
2·26
Tm
0·31
0·23
0·31
0·48
0·36
0·29
0·19
0·36
0·39
0·37
0·40
0·46
0·17
0·28
0·37
Yb
1·89
1·11
1·99
2·90
2·14
1·77
1·15
2·04
2·46
2·28
2·17
2·90
0·98
1·64
2·03
Lu
0·27
0·14
0·27
0·43
0·32
0·25
0·17
0·31
0·36
0·32
0·32
0·44
0·14
0·24
0·3
7·475
4·992
2·255
3·239
4·521
0·728485
87
Rb/86Sr
87
Sr/86Sr
0·743122
0·730623
0·718474
0·726009
147
0·133
0·126
0·123
0·110
0·119
143
0·512228
0·512327
0·512274
0·51216
0·512286
Sm/144Nd
Nd/144Nd
Major elements are in wt %, trace elements in ppm.
1562
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CRYSTALLIZATION DYNAMICS OF GRANITE MAGMAS
Fig. 14. Harker variation diagrams for Hoyos granodiorites and adamellites and their microgranular enclaves. It should be noted that the
enclaves overlap with the less silicic end of the host granodiorite trend. ASI ¼ mol. Al2O3/(CaO þ Na2O þ K2O).
1563
JOURNAL OF PETROLOGY
VOLUME 51
NUMBER 7
JULY 2010
Fig. 15. Concordia plot of ion-microprobe U^Pb data for zircons separated from two microgranular enclaves and the host Hoyos granodiorite.
The identical crystallization ages, which preclude the enclaves being metamorphic xenoliths, should be noted.
higher viscosity and smaller melt^crystal density contrast.
Numerical experiments by Martin & Nokes (1988, 1989)
have revealed that the residence time of 1mm diameter
plagioclase is about 105 years in a granite magma but less
than 102 years in a basaltic magma before being discharged, which implies that a convecting granite magma
cooling at any geologically reasonable rate can hardly
discharge the crystals growing in it.
Convection prevents fractionation, but enhances
wall-rock contamination. The violent stirring caused by
turbulent convection drags wall-rock xenoliths and blobs
of already contaminated cold marginal magma into the interior of the chamber, and brings uncontaminated hot
magma in contact with the walls. Convection also tends
to homogenize the initial composition of the magma.
In high aspect-ratio chambers homogenization occurs all
over the chamber. In low-aspect ratio chambers, convective homogenization occurs within each convective cell,
which can split the magma into homogeneous sections
with slightly different chemical and isotopic composition
(see above).
Once the whole magma chamber reaches the fraction of
solids at which crystals begin forming a ubiquitous 3D
framework, then the residual magma can be segregated
far more efficiently than before. This can be accomplished
in different ways. In the absence of regional stress, the
most effective way to expel the residual melt is
gravity-driven compaction, which leads to a body with
asymmetric vertical zoning and an upper layer of felsic
segregates. At low P the separation of a vapor phase may
1564
U
1565
448
z16
114
153
114
205
162
344
125
376
347
96
820
1011
378
89
89
1105
831
621
448
1042
1153
966
489
673
z13
z14
z15
z16
z17
z18
z19
z20
z21
d(%) ¼ 100(1 370
1709
354
z10
z12
418
z9
z11
835
z8
178
z5
593
273
z4
1354
1014
z3
z7
1228
z2
z6
1144
z1
0·3
0·24
0·41
0·44
0·48
0·25
0·25
0·06
0·51
0·10
0·43
0·41
0·22
0·36
0·55
0·29
0·36
0·33
0·16
0·13
0·53
0·25
0·25
0·58
0·60
0·04
0·65
0·04
0·07
0·90
0·39
0·52
0·63
0·88
0·03
0·31
0·32
Th/U
0·17
0·16
0·08
0·06
0·06
0·94
0·09
0·47
0·33
0·01
0·05
0·31
0·00
0·09
0·67
0·08
0·05
0·77
0·05
0·08
0·14
0·22
0·11
0·97
0·21
0·05
0·29
0·83
0·08
0·07
0·05
0·27
0·59
0·11
0·06
0·12
0·60
f206%
Pb/238U
206
1s
207
Pb/235U
1s
0·05196
0·05301
0·05206
0·05298
0·05319
0·05303
0·05278
0·05282
0·05304
0·05334
0·05279
0·05309
0·05257
0·05303
0·05384
0·05323
0·05283
0·05298
0·05439
0·05326
0·05293
0·05303
0·05278
0·05377
0·05273
0·05237
0·05253
0·05297
0·05280
0·05330
0·05388
0·05336
0·05285
0·05356
0·05294
0·05203
0·05244
0·78
1·20
0·98
1·10
1·40
0·94
0·86
0·76
0·72
0·53
1·30
1·14
1·16
0·76
0·70
0·88
1·65
1·33
0·97
0·67
0·66
0·94
0·86
1·74
1·34
0·38
0·97
0·43
0·40
1·27
1·58
0·66
0·63
1·29
0·46
1·43
1·52
0·04950
0·05061
0·04955
0·04967
0·05031
0·04964
0·05101
0·05021
0·04990
0·05047
0·04892
0·04924
0·04915
0·05030
0·04955
0·05107
0·05000
0·05027
0·04946
0·04957
0·05060
0·04964
0·05101
0·04998
0·05033
0·05006
0·05034
0·04955
0·04913
0·04969
0·05005
0·04927
0·04925
0·05092
0·05062
0·05055
0·05029
1·35
1·33
1·37
1·32
1·34
1·34
1·32
1·37
1·34
1·34
1·34
1·34
1·57
1·42
1·34
1·34
1·34
1·34
1·34
1·34
1·34
1·34
1·32
1·23
1·23
1·22
1·22
1·22
1·22
1·22
1·27
1·23
1·22
1·22
1·22
1·24
1·23
0·35463
0·36991
0·35567
0·36284
0·36897
0·36299
0·37122
0·36567
0·36493
0·37119
0·35608
0·36044
0·35626
0·36778
0·36783
0·37482
0·36421
0·36722
0·37092
0·36402
0·36928
0·36299
0·37122
0·37054
0·36592
0·36147
0·36461
0·36189
0·35767
0·36517
0·37182
0·36250
0·35889
0·37604
0·36950
0·36264
0·36362
1·56
1·79
1·68
1·72
1·94
1·64
1·58
1·57
1·52
1·44
1·87
1·76
1·95
1·61
1·51
1·6
2·13
1·89
1·65
1·5
1·49
1·64
1·58
2·13
1·82
1·28
1·56
1·29
1·28
1·76
2·03
1·40
1·37
1·78
1·30
1·89
1·96
311
318
312
313
316
312
321
316
314
317
308
310
309
316
312
321
315
316
311
312
318
312
321
314
317
315
317
312
309
313
315
310
310
320
318
318
316
Pb/238U
206
1s
207
Pb/206Pb
Age (Ma)
Isotope ratio
4
4
4
4
4
4
4
4
4
4
4
4
5
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
1s
Pb/235U
308
320
309
314
319
314
321
316
316
321
309
313
309
318
318
323
315
318
320
315
319
314
321
320
317
313
316
314
311
316
321
314
311
324
319
314
315
207
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
3
3
3
3
3
3
3
4
3
3
3
3
3
3
1s
age/207/235age). Data are uncorrected for common lead. Analytical methods are given in Electronic Appendix III.
35
24
51
59
58
24
32
45
64
94
21
20
19
49
80
35
10
15
55
65
66
24
32
12
21
224
32
182
319
25
14
94
99
29
160
16
16
Pb
206/238
200
117
397
512
496
114
153
46
567
178
158
146
94
304
739
173
64
91
160
162
604
Microgranular enclaves
621
3399
z10
z15
5674
z9
196
386
z8
z14
245
z7
343
1569
z6
z13
1608
z5
527
432
z4
4082
2950
z3
z12
289
z2
z11
286
z1
91
Th
Conc. (ppm)
Hoyos granodiorites
Spot
Table 5: U^Pb ion-microprobe data for analyzed zircon grains
0·97
0·62
0·97
0·32
0·94
0·64
0
0
0·63
1·25
0·32
0·96
0·00
0·63
1·89
0·62
0·00
0·63
2·81
0·95
0·31
0·64
0·00
1·88
0·00
0·64
0·32
0·64
0·64
0·95
1·87
1·27
0·32
1·23
0·31
1·27
0·32
d(%)
312
318
312
312
316
312
321
316
314
317
308
310
309
316
311
321
315
316
311
312
318
312
321
314
317
315
317
312
309
312
314
310
310
320
318
318
316
207-corr
4
4
4
4
5
4
4
4
4
4
4
4
5
5
4
4
5
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
1s
BEA
CRYSTALLIZATION DYNAMICS OF GRANITE MAGMAS
JOURNAL OF PETROLOGY
VOLUME 51
Fig. 16. The initial Sr and Nd composition of microgranular enclaves
and host granodiorites is indistinguishable. This, the identical age,
and the overlapping chemical composition support the idea that the
enclaves represent fragments of the granodiorite upper mushy zone
dragged downwards during convection.
NUMBER 7
JULY 2010
contract because of lithostatic pressure, the contraction of
the magma would create a transient zone of lower pressure
at the top of the chamber to which volatiles and residual liquids would tend to migrate. Granite magma chambers
fractionated by these mechanisms will produce short-range
differentiation series: from a composition slightly less silicic
than the initial magma to high-silica segregates.
If, on the other hand, the magma body crystallizes in the
presence of regional stress, tectonic squeezing and shearing
can expel the residual fluid more efficiently (Rabinowicz
& Vigneresse, 2004; Katz et al., 2006), leading to a
wide-range granite differentiation series, from rocks notably less silicic than the initial magma to high-silica leucogranites (e.g. Bea et al., 2005). Although discussion of
magma segregation by these mechanisms is beyond the
scope of this study, we must emphasize that most of the
life of granite magma chambers is at supercritical crystallinity, so that they have every opportunity to be affected
by shearing and deformation when they crystallize in
tectonically active regions.
CONC LUSIONS
Fig. 17. Mass fraction of crystals vs terminal Stokes’ velocities resulting from equation (23). The vertical coordinate represents the mass
fraction of crystals with a settling velocity higher than the value represented in the corresponding horizontal coordinate in the four
curves that result from equation (23) resolved for maximum final
crystal radius of 0·5, 1, 2 and 4 mm. The vertical line labeled ‘critical
velocity’ represents a settling velocity equivalent to 0·5 m/a. (See text
for explanation.)
provide an additional driving force for the segregation of
the residual melt (Sisson & Bacon, 1999), although in this
case the pluton does not have to be vertically zoned and
felsic segregates would probably occurs in dikes resulting
from hydraulic fracturing caused by volatile overpressure
(e.g. Oliver et al., 2006). Furthermore, in the absence of regional stress, the upwards segregation of the residual melt
will also be facilitated by the volume reduction of the
magma, about 10% from the liquidus to the solidus, a
factor that is seldom accounted for in melt segregation calculations. Despite the fact that the chamber will also
Cooling granite magma chambers do not strictly follow
the Marsh (1996) solidification front model. They can
begin cooling conductively and initiate solidification
fronts, but quickly evolve to chaotic convection because of
the density increase resulting from melt^crystal transformations in the upper cooling region before it reaches critical
crystallinity.
During convection, highly crystalline clots and fragments of the upper mushy zone are dragged downwards
as descending convecting fingers. Such fragments would
probably not dissolve in the hotter interior of the chamber
but would be preserved as autolithic enclaves. As illustrated in the Hoyos granodiorites, these enclaves are recognizable because they have the same age and initial
isotope composition as the host granitoids, and a chemical
composition compatible with being early crystallization
products. The formation of enclaves in this way will be
more pronounced in low-SiO2 magmas of high initial T.
During convection, granite magmas can also be heavily
contaminated either by wall-rock interaction or by mixing
with other magmas. Convection does not permit crystal
settling or any other mechanism of melt^solid segregation,
so that during this stage granite magmas do not tend to
fractionate, but instead tend to homogenize.
Convection splits low aspect-ratio chambers (sills) into
nearly isolated convection cells that become separately
homogenized. If the magma is initially heterogeneous,
this phenomenon may divide the chamber into contiguous
zones with different trace element signatures and initial
isotope compositions, which may be easily misinterpreted
as different intrusive batches. The lateral variations despite
perfect vertical homogeneity, in trace-element and isotope
1566
BEA
CRYSTALLIZATION DYNAMICS OF GRANITE MAGMAS
ratios, found in the Pedrobernardo pluton illustrate this
effect.
Convective heat-loss quickly leads the whole magma
chamber to reach the fraction of solids at which crystals
begin to form a ubiquitous 3D framework; that is, when
massive melt^solid segregation may occur.
In the absence of regional stress, the intercrystalline melt
may be expelled by gravity-driven compaction leading to
a body with asymmetric vertical zoning and an upper
layer of felsic segregates. At low P the separation of a
vapor phase may provide an additional driving force for
the segregation of the residual melt.
Granite magma chambers fractionated by these mechanisms will produce short-range differentiation series,
from a composition slightly less silicic than the initial
magma to high-silica segregates. If, on the other hand,
the magma body crystallizes in the presence of regional
stress, tectonic squeezing and shearing can expel residual
fluid more efficiently and produce wide-range granite differentiation series, from rocks notably less silicic than the
initial magma to high-silica leucogranites.
AC K N O W L E D G E M E N T S
The author is indebted to T. Geryan, M. Wilson, R.
Latypov and two anonymous referees for their valuable
comments and suggestions, which greatly contributed to
improve the manuscript, and to J. H. Scarrow for her
suggestions and assistance with the English.
FUNDING
This work was financially supported by the Spanish
M.E.C. grant CLG2008-02864 and the Andalucian grant
RNM1595.
S U P P L E M E N TA RY DATA
Supplementary data for this paper are available at Journal
of Petrology online.
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A P P E N D I X : A N A LY T I C A L
M ET HODS
Major-element and Zr were determined at the University
of Granada by X-ray fluorescence (XRF) after fusion
with lithium tetraborate. Typical precision was better than
1·5% for an analyte concentration of 10 wt %, and
5% for 100 ppm Zr. Trace elements, except Zr, were
determined at the University of Granada by inductively
coupled plasma mass spectrometry (ICP-MS) after
HNO3 þ HF high-pressure digestion (20 p.s.i.) in a Teflonlined vessel, evaporation to dryness, and subsequent dissolution in 100 ml of 4 vol. % HNO3. Precision was better
than 5% for analyte concentrations of 10 ppm. Hf was
calculated after XRF Zr and ICP-MS Zr/Hf.
Samples for Sr and Nd isotope analysis (0·1000 g) were
digested with HNO3 þ HF in a Teflon-lined vessel at
20 p.s.i. The elements were separated with ion-exchange
resins, and the Sr and Nd isotope ratios were determined
by thermal ionization mass spectrometry (TIMS) with a
Finnigan Mat 262 at the University of Granada. All
reagents were ultra-clean. Normalization values were
86
Sr/88Sr ¼ 0·1194 and 146Nd/Nd ¼ 0·7219. Blanks were 0·6
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BEA
CRYSTALLIZATION DYNAMICS OF GRANITE MAGMAS
and 0·09 ng for Sr and Nd. The external precision (2s),
estimated by analyzing 10 replicates of the standard WS-E
(Govindaraju et al., 1994), was better than 0·003% for
87
Sr/86Sr and 0·0015% for 143Nd/144Nd. 87Rb/86Sr and
147
Sm/144Nd were directly determined by ICP-MS at the
University of Granada following the method developed by
Montero & Bea (1998), with a precision better than
1·2% and 0·9% (2s) respectively.
Zircon was separated using conventional magnetic and
density techniques. Once mounted and polished, zircon
grains were studied by cathodoluminescence imaging and
analyzed for U^Pb using using the sensitive high-resolution ion microprobe (SHRIMP) IIe of Geoscience
Australia, Canberra. Ion microprobe analytical methods
broadly follow those described by Williams & Claesson
(1987). U element concentration was calibrated using the
SL13 reference zircon (U: 238 ppm). U/Pb ratios were calibrated using the TEMORA-1 reference zircon (417 Ma;
Black et al., 2003). Data reduction was carried out first
with the SQUID software (Ludwig, 2002) to obtain the
raw isotope ratios and element concentrations, and the
data were then reprocessed to obtain 207-corrected and
204-corrected ratios and ages with ISOTOOLS, a software
code developed by F. Bea (available upon request) as a
TM
STATA program (ado file) which includes an iterative
204-correction based on the Stacey & Kramers (1975)
model.
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