Journal of Petrology Advance Access originally published online on August 31, 2005
Journal of Petrology 2006 47(2):231-254; doi:10.1093/petrology/egi073
© The Author 2005. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org
Dissolution of Quartz, Albite, and Orthoclase in H2O-Saturated Haplogranitic Melt at 800°C and 200 MPa: Diffusive Transport Properties of Granitic Melts at Crustal Anatectic Conditions
ANTONIO ACOSTA-VIGIL*,
DAVID LONDON,
GEORGE B. MORGAN, VI and
THOMAS A. DEWERS
SCHOOL OF GEOLOGY AND GEOPHYSICS, UNIVERSITY OF OKLAHOMA, NORMAN, OK 73019, USA
RECEIVED
DECEMBER 26, 2003;
ACCEPTED
JULY 19, 2005
 |
ABSTRACT
|
|---|
We have conducted experiments on dissolution of quartz, albite,
orthoclase, and corundum into H
2O-saturated haplogranite melt
at 800°C and 200 MPa over a duration of 120–1488 h
with the aim of ascertaining the diffusive transport properties
of granitic melts at crustal anatectic temperatures. Cylinders
of anhydrous starting glass and a single mineral phase (quartz
or feldspar) were juxtaposed along flat and polished surfaces
inside gold or platinum capsules with
10 wt % added H
2O. Concentration
profiles in glass (quenched melt) perpendicular to the mineral–glass
interfaces and comparison with relevant phase diagrams suggest
that melts at the interface are saturated in the dissolving
phases after 384 h, and with longer durations the concentration
profiles are controlled only by diffusion of components in the
melt. The evolution of the concentration profiles with time
indicates that uncoupled diffusion in the melt takes place along
the following four linearly independent directions in oxide
composition space: SiO
2, Na
2O, and K
2O axes (Si-, Na-, and K-eigenvectors,
respectively), and a direction between the Al
2O
3, Na
2O, and
K
2O axes (Al-eigenvector), such that the Al/Na molar ratio is
equal to that of the bulk melt and the Al/(Na + K) molar ratio
is equal to the equilibrium ASI (= mol. Al
2O
3/[Na
2O + K
2O])
of the melt. Experiments in which a glass cylinder was sandwiched
between two mineral cylinders—quartz and albite, quartz
and K-feldspar, or albite and corundum—tested the validity
of the inferred directions of uncoupled diffusion and explored
long-range chemical communication in the melt via chemical potential
gradients. The application of available solutions to the diffusion
equations for the experimental quartz and feldspar dissolution
data provides diffusivities along the directions of the Si-eigenvector
and Al-eigenvector of
(2·0–2·8)
x 10
–15 m
2/s and
(0·6–2·4)
x 10
–14 m
2/s, respectively.
Minimum diffusivities of alkalis [
(3–9)
x 10
–11 m
2/s] are orders of magnitude greater than the tetrahedral components
of the melt. The information provided here determines the rate
at which crustal anatexis can occur when sufficient heat is
supplied and diffusion is the only mass transport (mixing) process
in the melt. The calculated diffusivities imply that a quartzo-feldspathic
source rock with initial grain size of 2–3 mm undergoing
hydrostatic, H
2O-saturated melting at 800°C (infinite heat
supply) could produce 20–30 vol. % of homogeneous melt
in less than 1–10 years. Slower diffusion in H
2O-undersaturated
melts will increase this time frame.
KEY WORDS: chemical diffusion; haplogranite; mineral dissolution experiments; crustal anatexis
|
INTRODUCTION
|
|---|
Mechanical mixing during melt segregation and transport (Wickham,
1987
a
, 1987
b; Brown
et al., 1995
) may play a role in homogenizing
granitic magmas, but diffusion in the melt ultimately controls
the attainment of chemical equilibrium (e.g. Lesher, 1994
; Shaw,
2004
). Understanding the diffusive transport properties of silicate
melts helps to constrain the time frames of some igneous processes
that entail the production or homogenization of silicate liquids
(e.g. Watson, 1982
, 1996
; Baker, 1990
, 1991
; Sawyer, 1991
; Lesher,
1994
; Barbero
et al., 1995
; Harris
et al., 2000
; Acosta-Vigil
et al., 2002
). Knowledge of the diffusive transport properties
of granitic melts can shed light on speciation in the melt that
can be tested or augmented by spectroscopic studies [e.g. compare
Wolf & London (1994)
with Mysen
et al. (1981
, 1999
), Gan
& Hess (1992)
and Toplis & Schaller (1998)
]. Accurate
information on liquid speciation is essential for constructing
rigorous thermodynamic models. The diffusion coefficient matrix
(
D) is a product of the Onsager kinetic matrix (
L) and a matrix
of thermodynamic chemical potentials (
µ); thermodynamic
properties of the melts can be retrieved through a knowledge
of
D (e.g. Chakraborty, 1995
).
This study complements that of Acosta-Vigil et al. (2002, 2005) in the investigation of diffusivities and directions of uncoupled chemical diffusion in composition space (e.g. Chakraborty, 1995) in H2O-saturated haplogranitic melts at typical crustal anatectic temperatures. To obtain this information we conducted experiments on dissolution of quartz, albite, orthoclase, and corundum into metaluminous haplogranitic melt at 800°C and 200 MPa H2O. The starting haplogranite melt had the composition of the 200 MPa H2O minimum (Tuttle & Bowen, 1958), and the 115°C interval between eutectic and experimental temperature ensured mineral dissolution and the development of oxide concentration gradients in the melt. Concentration profiles of the oxide components in the glass (quenched melt) were measured perpendicular to the mineral–glass interfaces. Published solutions to the diffusion equations were used, together with constraints provided from the evolution of concentration profiles with time, to determine part of the diffusion matrix of the system by inversion of the concentration profiles. The results confirm the distinctly different behavior of Na and K in relation to Al gradients in the melt (Acosta-Vigil et al., 2002), and can be used to estimate the rate at which melting and melt homogenization can occur during crustal anatexis in an end-member case of infinite (transitory) heat supply and diffusion in the melt as the only mixing mechanism.
|
MATERIALS AND METHODS
|
|---|
Starting materials and experimental methods
The starting materials used in this study include hydrothermal
quartz (McCurtain County, Oklahoma, USA), albite (Copelinha,
albite I, and Urucum, albite II, both from pegmatite mines in
Minas Gerais, Brazil), orthoclase (Little Three pegmatite, California,
USA), corundum (source unknown), and synthetic anhydrous metaluminous
haplogranite glass (Corning Lab Services, New York, USA) with
the nominal composition of the haplogranite eutectic at 200
MPa H
2O (Tuttle & Bowen, 1958
).
Table 1 shows mean electron
microprobe analyses of minerals and starting anhydrous glass
and some experimental glasses.
Mineral and glass cylinders
1·7 or
2·5 mm in diameter
and 2–4 mm in length were prepared by drilling the starting
materials with diamond coring bits. Mineral and glass cylinder
surfaces to be in contact during the experiment were polished
flat to a 0·3 µm alumina grit finish. Cores were
cleaned with de-ionized, ultra-filtered (DIUF) water in an ultrasonic
bath. Mineral and glass cores were loaded inside platinum or
gold capsules (
1·8 or
2·6 mm i.d.) with enough
DIUF water (
10 wt %) to ensure saturation of the melt. Capsules
were sealed by d.c. argon plasma arc welding while keeping the
capsule frozen to prevent volatilization of added water. To
ensure no leakage, capsules were placed overnight in an oven
at
130°C and then reweighed.
Experiments were conducted in water-pressurized NIMONIC 105® cold-seal pressure vessels inclined 15° from the horizontal. Capsules were placed with their long axes parallel to the vessels, such that the mineral–melt interfaces remained near vertical during the experiment. Target temperature and pressure were 800°C and 200 MPa, respectively; variations in these target values during the experiments were 2°C and 1 MPa. Temperature was monitored with an internal chromel–alumel thermocouple, and pressure was monitored with a factory-calibrated Heise bourdon tube gauge; uncertainties in temperature and pressure are <10°C and <10 MPa, respectively. The samples were first pressurized cold, and then the temperature was raised to the target value at a rate of 40°C/min. Oxygen fugacity was controlled indirectly by the composition of the reaction vessels at 0·5 log units below the Ni–NiO buffer, based on the fO2 dependence of tin solubility in H2O-saturated haplogranite melts [measured by Wolf et al. (1994) and compared with Taylor & Wall (1992) and Linnen et al. (1996)]. Experiments were quenched isobarically at a rate of 75°C/min using a jet of air and water. After quench, capsules were weighed, punctured, placed in a desiccator overnight, and then reweighed to check for the loss of free water (indicating H2O saturation at run conditions and providing an estimate of water dissolved into the melt). Products were mounted in Buehler Transoptic® thermal plastic, ground to the center of the cylinders, and polished to a final grit size of 0·3 µm for microprobe analysis.
Two series of experiments were conducted (Table 2): (1) those in which a core of quartz, albite, or orthoclase was juxtaposed against a core of haplogranitic glass (single-mineral dissolution experiments); (2) experiments in which a cylinder of glass was sandwiched between cores of quartz and albite, quartz and orthoclase, or albite and corundum (‘sandwiched glass’ experiments). The single-mineral dissolution experiments were conducted to obtain concentration gradients of the different oxide components in the liquid resulting from diffusion along different directions in composition space (defined by mineral–glass vectors). The sandwiched glass experiments were conducted to test the validity of the inferred directions of uncoupled diffusion in the melt (see below), to explore the long-range chemical communication in melt via chemical potential gradients (e.g. see the results of the albite–glass–corundum sandwich experiment), and to understand the generation of granite liquids in nature throughout intermediate steps between ‘simple’ single-mineral dissolution experiments and complex natural rock melting experiments (e.g. Mehnert et al., 1973; Büsch et al., 1974; Arzi, 1978; Acosta-Vigil et al., 2004, and unpublished work in review).
Analytical methods
Starting materials and experimental products were analyzed with
a Cameca SX-50 electron microprobe at the University of Oklahoma.
Matrix reduction used the PAP correction algorithm (Pouchou
& Pichoir, 1985
). Mineral phases were analyzed using an
accelerating voltage of 20 kV, a beam current of 10 nA, and
a 3 µm spot size. Counting times for all elements except
Ca, Ba, Sr and Fe were 30 s on peak, 45 s for Ca, Ba and Sr,
and 60 s for Fe. Calculated 3
minimum detection limits (in wt
%) were 0·06 for SiO
2, 0·03 for Al
2O
3 and Na
2O,
0·01 for CaO and K
2O, 0·02 for Fe
2O
3, 0·05
for P
2O
5, 0·09 for BaO, and 0·07 for SrO. The
glasses were analyzed using an accelerating voltage of 20 kV,
a beam current of 2 nA, and a 20 µm defocused spot. Sodium,
potassium, and aluminum were concurrently analyzed first to
minimize alkali volatilization and attendant changes in elemental
ratios. Counting times were 30 s on peak for all elements, yielding
calculated 3
minimum detection limits of
0·02 wt % for
Na
2O, K
2O and Al
2O
3, and
0·05 wt % for SiO
2. Based on
counting statistics, analytical uncertainties relative to their
reported concentrations in glass are in the range of
0·5–1·0
% for SiO
2 and Al
2O
3, and
1·5–3·0 % for
Na
2O and K
2O. Using these methods, the loss of sodium and grow-in
of aluminum and silicon intensities during analysis are negligible
and comparable with or less than the analytical uncertainties,
so that no corrections to the data are needed (Morgan &
London, 1996
). H
2O concentrations in glass are calculated by
difference of the electron microprobe analyses totals from 100%.
The accuracy of water by difference, using the current analytical
methods, is equal to or better than ±10% relative (Morgan
& London, 1996
; Acosta-Vigil
et al., 2003
). The maximum
uncertainty for the reported ASI values is ±0·035
(ASI = mol. Al
2O
3/[CaO + Na
2O + K
2O]), calculated by the propagation
of errors. To ensure (1) that diffusion in the melt occurred
only in the direction perpendicular to the mineral–melt
interface, and (2) statistical accuracy at critical points in
the diffusion profile, we conducted several analytical transverses
throughout the experimental glasses: three transverses perpendicular
to the mineral–melt interface for each experiment—one
at the center of the cylinder and two more at
100–200
µm from each of the cylinder sides—plus two additional
transverses parallel to the interface at distances of
30 and
100 µm from the interface.
|
RESULTS
|
|---|
Run products and dissolution rates
The experiments involved dissolution of the starting mineral
phase(s) into the melt, with no significant new mineral growth
in the silicate liquid or at the mineral–melt interface.
Mineral–melt interfaces for quartz and corundum remained
flat during dissolution, but these became irregular at the 10–100
µm scale during feldspar dissolution (
Fig. 1). Back-scattered
electron imaging shows no recrystallization or alteration of
quartz, orthoclase, or corundum during the experiments. Albite,
however, shows minor recrystallization to a binary feldspar
solid solution, mostly along fractures connected to the interface
(
Fig. 1,
Table 3). With this exception, relict feldspars close
to the interface melt show no change in composition with respect
to the starting feldspars (
Table 3).
View larger version (57K):
[in this window]
[in a new window]
|
Fig. 1. Back-scattered electron images of mineral–glass interfaces in experiments Acasi 229 (albite dissolution) and Acasi 232 (orthoclase dissolution). Light gray domains in Acasi 229 correspond to a binary feldspar recrystallized after the starting albite. Mineral symbols are taken from Kretz (1983); gl, glass.
|
|
Dissolution rates were calculated by mass balance using starting
and final SiO
2 and Al
2O
3 concentration profiles in the glass,
together with quartz, albite, and orthoclase compositions. This
method indicates a retreat of the interfaces proportional to
the square root of time after
120–384 h (
Fig. 2), suggesting
that dissolution is interface reaction-controlled up to 120–384
h and becomes diffusion-controlled afterwards (e.g. Cooper &
Kingery, 1964).
View larger version (22K):
[in this window]
[in a new window]
|
Fig. 2. Retreat of the quartz–, albite–, and orthoclase–melt interfaces (dissolution distance) vs the square root of time, calculated by mass balance based on starting and final silica and alumina concentration profiles in the glasses.
|
|
Chemical composition of the glasses
All experimental glass columns are characterized by (1) a reaction–diffusion
zone adjacent to the mineral–glass interfaces, hereafter
referred as the ‘boundary layer’, in which gradients
in the concentration profiles of the oxide components are present,
and (2) a zone beyond the boundary layer in which the concentration
profiles are flat.
Single-mineral dissolution experiments
After 384 h, the compositions of glasses within the boundary layer at 20 µm from mineral–melt interfaces lie very close to the liquidus surfaces for the respective minerals in the H2O-saturated quartz–albite–orthoclase system at the experimental conditions (5–10 normative wt % off the 800°C liquidus isotherms as taken from Tuttle & Bowen, 1958) (Fig. 3). Feldspars and interface melts are not strictly in equilibrium because the feldspars should be binary and not end-members (see Tuttle & Bowen, 1958). Albite shows signs of very local equilibration with the interface melt in the timeframe of the experiments; orthoclase does not. The location of the interface melts very close to the liquidus surfaces after 384 h of run duration, however, strongly suggests that they are saturated in the dissolving mineral phases.
The dissolution of quartz vs feldspars produced contrasting
concentration profiles in the melt. Quartz dissolution involved
mainly addition of silica and dilution of alumina and alkalis
in the boundary layer. Beyond the boundary layer, the concentrations
of silica, alumina, and alkalis are similar to those in the
starting hydrated glass (
Table 4,
Fig. 4). The molar ratios
Al/Na, Al/K, and Na/K remained nearly constant throughout the
entire melt column and equal to the values in the starting hydrous
glass (
Fig. 4, see insets). These facts indicate that diffusion
of silicon occurs only within the boundary layer and does not
involve coupling with any other component in melt.
View larger version (47K):
[in this window]
[in a new window]
|
Fig. 4. Composition of glasses in the quartz dissolution experiments as a function of experimental time and distance to the quartz–glass interface. In this and subsequent figures, each concentration profile represents the mean values of three analytical transverses perpendicular to the interface; the compositions are shown as obtained from the electron microprobe; the dashed lines refer to concentrations or molar ratios in the starting H2O-saturated metaluminous melt; analytical uncertainties (error bars) are shown within rectangles (analytical uncertainties are equal to or smaller than the symbols when not shown).
|
|
View this table:
[in this window]
[in a new window]
|
Table 4: Oxide concentrations (in wt %) and molar ratios in the glasses of the single mineral dissolution and sandwiched glass experiments, along analytical transverses perpendicular to the mineral–glass interfaces
|
|
Upon dissolution of albite, the concentrations of alumina, sodium,
and potassium in the glass increase monotonically within the
boundary layer toward the mineral–glass interface, whereas
silica decreases (
Table 4,
Fig. 5). Beyond the boundary layer,
the concentrations of alumina and silica and the Al/Si molar
ratios are similar to those in the starting hydrated glass,
whereas alkali concentrations and Na/Si and K/Si molar ratios
change significantly with respect to the starting glass (
Table 4).
This indicates that diffusion of aluminum and silicon takes
place only within the boundary layer, whereas alkalis diffuse
throughout the entire (
2000–4000 µm long) melt column.
This further reveals (1) that alkalis can diffuse much faster
than silicon and aluminum, and (2) that aluminum and sodium
decouple upon entering the melt during the dissolution of albite.
By ‘decouple’ we mean that although a certain amount
of sodium or potassium diffuses together with aluminum (the
concentration profiles of alkalis match exactly those of alumina
in all the runs), the rest diffuses further beyond the boundary
layer and therefore diffuses independently of aluminum. Although
the shapes of the concentration profiles for both alkalis are
similar in albite dissolution runs, the direction of diffusion
for sodium is opposite to that for diffusion of potassium: sodium
diffuses downhill away from the interface, producing an increase
in its concentration throughout the melt column with respect
to the starting glass, and potassium diffuses uphill toward
the interface, with an overall decrease in its concentration
(
Fig. 5). These changes in concentration are above analytical
uncertainties.
View larger version (53K):
[in this window]
[in a new window]
|
Fig. 5. Composition of glasses in the albite dissolution experiments as a function of experimental time and distance to the albite–glass interface.
|
|
Orthoclase dissolution experiments yield observations comparable
with those for albite (
Fig. 6). The migration of aluminum and
silicon takes place only within the boundary layer, whereas
alkalis diffuse throughout the entire melt reservoir. Upon entering
the melt, aluminum and potassium (from orthoclase) become decoupled.
Potassium diffuses down its concentration gradient away from
the interface, increasing its concentration throughout the melt,
whereas sodium diffuses uphill toward the interface, decreasing
its concentration in the melt beyond the boundary layer.
View larger version (52K):
[in this window]
[in a new window]
|
Fig. 6. Composition of glasses in the orthoclase dissolution experiments as a function of experimental time and distance to the orthoclase–glass interface.
|
|
We note that in all the feldspar dissolution experiments, the
Al/Na molar ratio is constant at any time throughout the entire
melt (
Table 4,
Figs 5 and
6). As the Al/Na ratio in the starting
glass (
1·75) is different from that in albite (
1) and
orthoclase (>>1·75), and diffusion of aluminum
occurs only within the boundary layer, these observations require
that sodium diffuses throughout the entire melt column to erase
any gradient in the Al/Na molar ratio. Despite the large fluxes
of alkalis in opposite directions, the ASI throughout the entire
melt column at any experimental time remains constant within
analytical uncertainty, and equal to the ASI of melt at equilibrium,
ASI
1·025 ± 0·035.
Sandwiched glass experiments
Metaluminous haplogranite system. The experiments in which glass was sandwiched between quartz and feldspars produced results comparable with those of the single-mineral dissolution experiments (Table 4, Fig. 7). Silica concentration in the glass increases toward quartz and decreases toward feldspars. Alumina and alkali concentrations increase toward feldspars and decrease toward quartz. The Al/Na molar ratio is constant throughout the glass. The Al/K molar ratio is constant except within the boundary layer close to feldspars, where it increases toward the interface. The ASI is constant throughout the glass except in the boundary layers close to feldspars, where it increases slightly toward the interfaces, although it remains constant within analytical uncertainty.
View larger version (50K):
[in this window]
[in a new window]
|
Fig. 7. Composition of glasses sandwiched between two mineral phases, as a function of distance to one of the interfaces. The nature and disposition of the mineral phases with respect to the glass are indicated at the top of the figure; for instance ‘Quartz–Glass–Albite’ means quartz to the left and albite to the right of the compositional profiles.
|
|
Peraluminous haplogranite system. The only significant differences
between the sandwich experiment in the peraluminous system (corundum–glass–albite)
and those in the metaluminous system are the greater ASI values
throughout the entire glass and the notable increase in ASI
within the boundary layers toward corundum and, importantly,
toward albite as well (
Table 4,
Fig. 7).
Effects of glass hydration–melting and an H2O fluid phase
The starting glass cores are anhydrous. For the correct interpretation of results, it is important to determine if hydration–melting of the glass cores is complete prior to mineral dissolution. A study of H2O diffusion (Acosta-Vigil et al., 2005) showed that cylinders of the starting dry haplogranite glass 3·5 mm in diameter and 4–6 mm long (larger than in the current study) are completely hydrated and compositionally homogeneous after 48–60 h at the current run conditions. After 69 h of reaction in orthoclase dissolution experiment Acasi 286 (Table 2), glass farther than 30–50 µm from the mineral–melt interface is homogeneous (concentration profiles are flat) and compositionally identical to the starting hydrated glass CG 1 (Tables 1 and 2, Fig. 8a). This demonstrates that dissolution of orthoclase was just beginning after about 69 h, an experimental duration longer than that required for complete hydration–melting of the glass cylinders. Therefore, mineral dissolution in the current experiments is initiated in homogeneous, hydrous liquid.
During initial cold pressurization of capsules, the gold or
platinum tubes collapse around the length of the cores, squeezing
almost all of the added water to strain shadows at the ends
of the capsule. After hydration–melting of the glass cores,
there is about 4–5 wt % free H
2O fluid inside the capsule
in contact with the mineral and melt cylinders. To verify that
oxide concentration profiles in glass were produced only by
dissolution of the mineral phase into melt at the interface
and transport of components through the liquid, and was not
influenced by lateral diffusion from the sides of the melt column
via an aqueous vapor film, we conducted a 384 h orthoclase dissolution
experiment using a glass core previously hydrated at the experimental
conditions (Acasi 292,
Table 2). An additional 1 wt % water
was added to the capsule to keep the melt just at H
2O saturation.
Concentration profiles produced in this experiment are functionally
identical to those in a 384 h orthoclase dissolution experiment
starting with an anhydrous glass core. Small differences in
K
2O and Al/K profiles (
Fig. 8b) are explained by the different
lengths of starting glass cores (the starting anhydrous core
being slightly shorter, implying a smaller volume for K diffusion
as compared with the pre-hydrated core). Otherwise the behavior
in both experiments is exactly the same, with aluminum diffusing
about 250 µm away from the interface, sodium diffusing
toward the interface throughout the entire melt reservoir to
maintain a constant Al/Na ratio, and K diffusing away from the
interface to maintain a constant ASI throughout the melt column.
No irregular concentration profiles corresponding to sidewall
diffusion from the melt–capsule interface were found in
the current experiments [compare with
fig. 2 of Acosta-Vigil
et al. (2002)
and relevant discussion]. These observations confirm
that neither an excess H
2O fluid phase in the capsule nor starting
with anhydrous glass cylinders has any effect on the resultant
concentration profiles in experimental glasses.
|
ORIGIN OF THE CONCENTRATION PROFILES IN EXPERIMENTAL GLASSES
|
|---|
There are three main processes that potentially can govern the
concentration profiles of melt components during the dissolution
of a mineral phase into the melt: (1) the interface reaction
or process by which mineral components detach from the mineral
surface to enter the melt; (2) the diffusion of components through
the melt; (3) convection in the melt (e.g. Donaldson, 1985
;
Zhang
et al., 1989
). Convection did not occur or was not significant
in these experiments because: (1) the concentrations of the
oxide components in the glasses vary monotonically with the
distance from the mineral–melt interface (compare with
Shaw, 2000
); (2) with increasing time the width of the melt
boundary layer increases whereas the mineral dissolution rate
decreases [
Table 2 and
Fig. 2; compare with Watson (1982)
].
There are three conditions to be fulfilled for the profiles
to be solely controlled by diffusion in the melt: (1) the composition
of the interface melt is at the liquidus of the dissolving mineral
phase at the conditions of the experiments; (2) the retreat
of the mineral–melt interface is proportional to the square
root of time; (3) the concentration profiles overlap when plotted
against distance normalized to the square root of time (e.g.
Crank, 1975
; Zhang
et al., 1989
; Liang, 1999
). Regarding condition
(1),
Fig. 3 shows that after 384 h the interface melts are located
very close to the liquidus surfaces of quartz and feldspars.
Figure 2 shows that condition (2) is reasonably satisfied after
384 h of experimental time.
Figure 9 shows that condition (3)
also seems to hold after 384 h. However, we call attention to
the observation that concentration profiles in albite and orthoclase
dissolution experiments cannot rigorously overlap when plotted
against distance normalized to time, because of the uphill diffusion
of melt components throughout the entire melt column and the
finite nature of the melt reservoir. Condition (3) seems to
hold only for the case of semi-infinite melt reservoirs (see
Acosta-Vigil
et al., 2002
). We conclude that concentration profiles
in the current experiments are controlled both by the kinetics
of the interface reaction and diffusion in melt during an initial
period of
240–384 h, but solely by diffusion of components
in melt afterwards. Therefore, concentration profiles in experiments
with durations
384 h can be reasonably described mathematically
in terms of chemical diffusion in a multicomponent system.
View larger version (42K):
[in this window]
[in a new window]
|
Fig. 9. Concentration of oxide components as a function of time and distance to the mineral–glass interface normalized to the square root of time, in glasses of the quartz, albite, and orthoclase dissolution experiments.
|
|
|
MULTICOMPONENT DIFFUSION MODELING
|
|---|
General approach
A background on multicomponent chemical diffusion can be found
elsewhere (e.g. Trial & Spera, 1994
; Chakraborty, 1995
).
The current modeling aims to elucidate all or part of the diffusion
matrix,
D. The matrix
D contains information about the directions
in composition space along which diffusion is uncoupled (eigenvectors
of
D,
i), and the diffusivities along these directions (eigenvalues
of
D,
i) at the given
P–
T–
X conditions (e.g. Chakraborty,
1995
). Our approach to gain information about the eigenvectors
is different from previous ones. Previous studies have used
results from diffusion couple experiments (or isothermal interdiffusion
experiments; Trial & Spera, 1994
) for determining the entire
diffusion matrix in silicate liquids (e.g. Kress & Ghiorso,
1993
; Chakraborty
et al., 1995
a; Liang
et al., 1996
; Mungall
et al., 1998
). Rather than diffusion couples, we began with
dissolution experiments utilizing phases that contain only a
single oxide component: corundum (Acosta-Vigil
et al., 2002
),
quartz (this work), and H
2O (Acosta-Vigil
et al., 2005
). This
approach produces relatively simple concentration profiles in
the melt because diffusion occurs mainly along the single uncoupled
direction that is responsible for the diffusive transport of
the oxide component (SiO
2, Al
2O
3, H
2O) added to the interface
melt. Therefore, information about individual directions of
uncoupled diffusion in the system can be obtained directly from
the study of experimental concentration profiles. Diffusion
data along additional directions of uncoupled diffusion in compositional
space are then derived by dissolution of more complex mineral
phases (e.g. feldspars: this work), each of which adds only
one new component (e.g. K or Na) to the previously defined system.
In this manner, diffusion data for all of the principal components
in the granitic system can be derived from a succession of glass
hydration–melting and single-mineral dissolution experiments.
These results can be tested and verified afterward via additional
complex mineral dissolution experiments (e.g. Acosta-Vigil
et al., 2002
) or with sandwiched glass experiments (this work).
In a system with
N components,
D is an
N – 1 by
N –
1 matrix, and the number of linearly independent eigenvectors
is
N – 1, each of them with an associated eigenvalue.
The eigenvectors represent a new set of chemical components
whose fluxes are independent of each other (e.g. Chakraborty,
1995
). Each eigenvector is related to any other set of chemical
components (e.g. oxide components) by
N – 1 coefficients,
which specify the proportions of the old components (oxides)
in that particular eigenvector.
P is an
N – 1 by
N –
1 matrix made of the eigenvector coefficients arranged in columns.
For instance,
Pij is a coefficient of
P that refers to the proportion
of the old component
i in the eigenvector
j. As eigenvectors
represent directions of uncoupled diffusion, these coefficients
refer to the relative amounts of old components migrating at
the same time and speed (see also Mungall
et al., 1998
). We
rely on this observation to gain information on the eigenvectors
(matrix
P) from the analysis of the oxide concentration profiles.
Finally, to elucidate the eigenvalues of
D we inverted the concentration
profiles in melt produced by diffusion along three directions
in composition space: quartz–, albite–, and orthoclase–water-saturated
metaluminous haplogranite (
Fig. 10). The procedure has been
used previously (e.g. Trial & Spera, 1994
; Mungall
et al.,
1998
; Acosta-Vigil
et al., 2002
) and the reader is referred
to these publications for a detailed explanation. During inversion
of concentration profiles we used the information gained on
the eigenvectors as additional constraints.
View larger version (10K):
[in this window]
[in a new window]
|
Fig. 10. Location in composition space (wt %) of the starting melt (Gl) and mineral phases used in the current experiments, projected from (a) H2O and Al2O3, (b) H2O and Na2O, or (c) H2O and K2O. Mineral symbols are taken from Kretz (1983).
|
|
Eigenvectors of D: constraints from compositional profiles
Quartz dissolution experiments show that neither aluminum nor
alkalis are coupled with the diffusion of silica, because incorporation
of silica into the melt produces proportionate dilution of the
other components (compare with Sato, 1975
; Watson, 1982
; Chekhmir
& Epel'baum, 1991
; Shaw, 2000
; Acosta-Vigil
et al., 2002
).
The collinearity of starting hydrous melt, quartz, and melt
compositions from the boundary layers of all the quartz dissolution
experiments demonstrates this conclusion (
Fig. 11). In contrast,
moderate coupling of CaO with SiO
2 in the system CaO–Al
2O
3–SiO
2 at 1500°C and 1 GPa produces compositions of bulk and boundary
layer melts that are not collinear with quartz (Liang, 1999
,
fig. 5). Therefore, the coefficients of
P associated with
Si (the direction in composition space along which silica migrates
to erase its concentration gradients), referenced to a six-oxygen
oxide component stoichiometry, are
PAlSi 0,
PNaSi 0,
PKSi 0, and
PSiSi = 1 (
Table 5).
View larger version (16K):
[in this window]
[in a new window]
|
Fig. 11. Composition of starting hydrated melt and all analyses of glass (wt %) in the boundary layers of quartz dissolution experiments, projected from (a) H2O and K2O, or (b) H2O and Na2O. (See text for details.)
|
|
View this table:
[in this window]
[in a new window]
|
Table 5: Eigenvectors coefficients (P matrix) deduced from analysis of the concentration profiles and referred to six-oxygen oxide components with H12O6 as solvent
|
|
Feldspar dissolution experiments show that the migration of
alkalis through melt does not require concomitant migration
of silicon or aluminum; hence, neither silicon nor aluminum
is coupled with the diffusion of alkalis. Although Na and K
diffuse in the same direction during the dissolution of corundum
and andalusite (Acosta-Vigil
et al., 2002
), these components
diffuse in opposite directions in the current feldspar dissolution
experiments at the same
P–
T–
X conditions, suggesting
that Na and K can diffuse independently of each other. The coefficients
for
K are
PAlK 0,
PNaK 0,
PKK 1 and
PSiK 0, and those for
Na are
PAlNa 0,
PNaNa 1,
PKNa 0 and
PSiNa 0 (
Table 5).
Feldspar dissolution experiments also show that the migration of aluminum through melt requires concomitant migration of alkalis and, therefore, sodium and potassium are coupled with the diffusion of aluminum. The constant Al/Na molar ratio throughout the entire melt column at any experimental time implies that sodium is coupled with aluminum during diffusion along Al, and that the relative molar amounts of Al and Na diffusing together are equal to the molar Al/Na ratio in the bulk melt (boundary layer + rest of melt cylinder). The constant ASI throughout the entire melt reservoir, equal to the ASI of melt at equilibrium, implies that potassium is also coupled with aluminum, and that the amount and direction of potassium diffusing with aluminum (and sodium) is such that the molar ratio Al/(Na + K) of this diffusing component is equal to the ASI of melt at equilibrium (see Fig. 12a). Following the previous observations we derive the following coefficients for Al (always referenced to the six-oxygen oxide component stoichiometry): PAlAl 1, PNaAl 0·184, PKAl 0·142 and PSiAl 0 (Table 5).
View larger version (48K):
[in this window]
[in a new window]
|
Fig. 12. (a) Schematic representation of an albite dissolution experiment showing starting and final oxide concentration profiles in the melt, and direction and distance of diffusion of the different oxide components. The melt column can be divided into two reservoirs: the volume within the boundary layer (BL) and the volume beyond the boundary layer (BBL). After an experimental time t, 2n moles of aluminum coming from albite have entered the BL melt reservoir. An equal molar amount of sodium has entered the melt too: a fraction of sodium atoms 2(n – x) remain in the BL and diffuse together with aluminum, whereas the rest (2x) decouple with respect to aluminum and migrate into the BBL reservoir in order to maintain a constant Al/Na molar ratio throughout the melt. Simultaneously, potassium diffuses uphill toward the interface: 2y moles of potassium leave the BBL reservoir and enter the BL reservoir to follow aluminum during its diffusion away from the interface. Because the ASI is roughly constant throughout the entire melt, the amount of sodium leaving BL and entering BBL, 2x, is equal to the amount of potassium leaving BBL and entering BL, y. Therefore, the Al–Na–K diffusing component has an ASI 1 and its Al/Na molar ratio is that of the bulk system. (b) Schematic representation of the albite–glass–corundum sandwich experiment showing starting and final oxide concentration profiles in the melt, and direction and distance of diffusion of the different melt oxide components. The increase in ASI (Fig. 7) within the boundary layer next to the albite–glass interface (BL1) implies that the amount of sodium that decouples from aluminum and diffuses out of BL1 is greater than the amount of potassium migrating into BL1 to couple with aluminum. This means that the Al–Na–K diffusing component is peraluminous with an ASI of 1·15 or higher.
|
|
The orientations of the eigenvectors are invariant properties
of the system at fixed
P–
T–
X conditions and, therefore,
are independent of the compositional direction along which diffusion
takes place (e.g. Chakraborty, 1995
). Together with Acosta-Vigil
et al. (2002)
, the directions of uncoupled diffusion described
above have been derived from diffusion concentration profiles
along four different directions that intersect at the starting
glass composition, three of them at high angle (
Fig. 10). In
addition, melt concentration profiles in the metaluminous quartz–feldspar
sandwiched glass experiments are comparable with those in the
single-mineral experiments. This supports the validity of the
inferred directions of uncoupled diffusion. The addition of
corundum in the albite–corundum sandwiched glass experiment
makes the system peraluminous, and consequently
Al has a slightly
different stoichiometry with respect to the metaluminous system
(
Fig. 12b; see also Acosta-Vigil
et al., 2002
).
Eigenvalues of D: inversion of concentration profiles
The single-mineral dissolution experiments have been modeled using the solutions to the diffusion equations provided by Smith et al. (1955) [as described by Acosta-Vigil et al. (2002)] and Liang (1999). These solutions are appropriate for diffusive mineral dissolution into a semi-infinite melt reservoir, with the mineral–melt interface retreating at a constant velocity (Smith et al., 1955) or proportionally through the dissolution parameter 
to the square root of both time and the diffusivity of the slowest component in melt (Liang, 1999). These solutions are convenient to model the quartz dissolution experiments, but not entirely appropriate to model the feldspar experiments because melt in the latter constitutes a finite reservoir. Their application to the feldspar experiments, however, can provide a good estimate of the diffusivity along the Al-eigenvector (see Acosta-Vigil et al., 2002). These solutions assume that diffusion takes place only in one direction in space, that D is constant for the range in compositions of the melt, and that the changes in melt density with composition are negligible. We chose a six-oxygen stoichiometry for the oxide components, and H12O6 as the solvent. The six-oxygen basis permits comparison with previous sources of similar data (e.g. Mungall et al., 1998), but is otherwise an arbitrary choice. The following modeling strategy was observed: (1) we inverted simultaneously all the concentration profiles in glass obtained by dissolution of a single mineral at different run times; (2) the eigenvector directions were fixed according to the observations regarding the evolution of concentration profiles with time (Table 5); (3) Si was calculated by applying the solutions to the quartz dissolutions runs with durations of 384 h; (4) Al was calculated by inverting the concentration profiles from the albite and orthoclase dissolution experiments with durations of 384 h.
The model results are presented in Table 6. Comparison between theoretical (Smith et al., 1955) and experimental profiles for quartz, albite, and orthoclase dissolution experiments are shown in Fig. 13. Results for Al are similar to those obtained by Acosta-Vigil et al. (2002) using corundum dissolution experiments in the H2O-saturated peraluminous haplogranite system at the same P–T conditions. Although diffusivities for the alkalis were not obtained directly by the method described above, application of the equation x2 = Dt (e.g. Chakraborty, 1995) to data from Acosta-Vigil et al. (2002, 2005; this work) provides minimum chemical diffusivities of (3–9) x 10–11 m2/s for sodium and potassium.
View this table:
[in this window]
[in a new window]
|
Table 6: Eigenvalues calculated for the Si- and Al-eigenvectors with the solutions provided by Smith et al. (1955) and Liang (1999)
|
|
|
DISCUSSION
|
|---|
Comparison with previous diffusion studies
Several studies of major element diffusion in granitic liquids
(Watson, 1982
; Baker, 1990
, 1991
; van der Laan & Wyllie,
1993
) have provided effective binary diffusion coefficients
(EBDC; Cooper, 1968
) that are applicable to problems involving
diffusion along the same directions of the diffusion couples
in these experiments. They are not directly comparable with
our diffusion coefficients, which are thought to represent diffusivities
along chemical directions of uncoupled diffusion. Chakraborty
et al. (1995
b)
found that in peralkaline and peraluminous portions
of the system K
2O–Al
2O
3–SiO
2 at 1100–1600°C
and 1 atm, diffusion of aluminum is coupled with a certain amount
of potassium in the same direction, whereas diffusion of potassium
does not involve migration of aluminum. These eigenvectors are
in agreement with those obtained in the current study. Mungall
et al. (1998)
conducted diffusion couple experiments along several
directions in composition space of the metaluminous H
2O-saturated
haplogranite system at 1300–1600°C and 1 GPa, and
also derived values for
Al and
Al comparable with our results
(see also Acosta-Vigil
et al., 2002
). Freda & Baker (1998)
investigated the diffusion of Na and K between albite and orthoclase
melts at 1200–1500°C, 1 GPa, and dry conditions. They
observed that in the alkali feldspar system, alkalis interdiffuse
independently of the other components. This is in accord with
our observations in the H
2O-saturated haplogranite system, though
we have also found that simultaneous migration of both alkalis
can occur in either the same or opposite directions (Acosta-Vigil
et al., 2002
). The diffusive transport properties of haplogranite
melts do not vary from metaluminous to peraluminous systems
(compare with Acosta-Vigil
et al., 2002
). These similarities
in the diffusion properties of a system at different pressure
and temperature, or among systems with slightly different composition,
are consistent with previous observations in the ternary K
2O–Al
2O
3–SiO
2 and CaO–Al
2O
3–SiO
2 systems, which showed only a
small dependence of the eigenvector directions on pressure and
temperature (Chakraborty
et al., 1995
a, 1995
b; Liang
et al.,
1996
, and references therein) or composition (peralkaline to
peraluminous, Chakraborty
et al., 1995
a, 1995
b). However, the
stoichiometry of eigenvectors can be appreciably different in
systems of very different composition. For instance, several
workers (Sato, 1975
; Watson, 1982
; Donaldson, 1985
; Chekhmir
& Epel'baum, 1991
; Shaw, 2000
) have found that potassium
and sodium diffuse toward SiO
2-rich environments (e.g. as a
result of dissolution of quartz) in basaltic systems, which
we did not observe in our experiments. Such differences from
the current study probably reflect significant changes in the
coordination environments of elements and, hence, structure
of the melt.
Interaction between H2O and haplogranite components
Experimental data presented in this paper and by Acosta-Vigil et al. (2002, 2003, 2005) indicate that H2O in haplogranitic melts interacts preferentially with sodium and aluminum rather than with silicon and potassium. The concentration of H2O in melt seems to increase toward the mineral–melt interfaces in the corundum and several albite dissolution experiments, whereas it remains approximately constant in quartz and orthoclase dissolution experiments (Fig. 14a and b). This is in accordance with the observation by Holtz et al. (1992a, 1995), Behrens (1995), and Romano et al. (1996) that H2O solubility increases with the Na/K ratio of the melt, and with a growing body of experimental evidence pointing to an association of excess aluminum and H2O or its dissociated components in granitic melts. For instance, various experimental studies have revealed that the capacity of granitic melts to dissolve H2O increases with their excess alumina concentration (Dingwell et al., 1984, 1997; Holtz et al., 1992b; Linnen et al., 1996; Behrens & Jantos, 2001; Acosta-Vigil et al., 2002). Mungall et al. (1998) deduced a slight coupling of hydrogen to aluminum during diffusion in H2O-saturated haplogranite melt. Acosta-Vigil et al. (2003) have shown that H2O plays an essential role in dissolving excess alumina in granitic melts (see also Clemens & Wall, 1981; Patiño Douce, 1992; Dingwell et al., 1997). Hence, excess aluminum and sodium seem to decrease the activity of H2O in granitic melt, suggesting that H2O or its dissociated components interact preferentially with these elements compared with silica and potassium. These observations can be relevant to the mechanisms of H2O dissolution in granitic melts (e.g. Schmidt et al., 2000; Zeng et al., 2000).
Diffusion of group IA cations
In accordance with previous studies on diffusion in silicate
(basaltic to granitic) melts at higher temperatures and variable
pressures (1200–1600°C, 0·001–10 kbar:
Watson, 1982
; Baker, 1990
; Mungall
et al., 1998
), we find that
chemical diffusion of alkalis is much faster (at least
3–4
orders of magnitude) than diffusion of the tetrahedral components
of melt. There is a difference, however, in the behaviour of
group IA cations during tracer vs chemical diffusion. Tracer
diffusivities for group IA cations generally decrease with increasing
atomic number, and hence with increasing ionic radius and mass;
this occurs at a variety of dry glass and melt compositions,
temperatures, and pressures (Jambon & Carron, 1973
, 1976
;
Jambon, 1982
; Lowry
et al., 1982
; Henderson
et al., 1985
). Our
diffusion studies in wet haplogranite liquids at 800°C (Acosta-Vigil
et al., 2002
, 2005
; this work) show, however, that chemical
diffusivities for sodium and potassium are comparable with,
and at least of the same magnitude as those for hydrogen (
10
–11–10
–10 m
2/s). In agreement with this, Mungall
et al. (1998)
have found
that calculated eigenvalues for
TOP
ABSTRACT
INTRODUCTION
), albite (
), and orthoclase (
) dissolution experiments. Each point represents the mean value of three analyses along the interface. Numbers close to the points refer to run duration in hours. The curved lines correspond to the projections of the liquidus surfaces of quartz and feldspar in the haplogranite system at the experimental conditions (from Tuttle & Bowen, 1958
