Crystallization of Hydrous Magmas: Calculation of Associated Thermal
Effects, Volatile Fluxes, and Isotopic ~lteration'
Yuri Y. F'odladchikov2 and Stephen M. W i c k ham
Department of t h e Geophysical Sciences and Enrico Fermi Institute, University of Chicago, Chicago, IL 60637
ABSTRACT
The metamorphism and accompanying isotopic alteration of country rock in contact with an instantaneously emplaced sheet-like body of hydrous magma has been studied using a one-dimensional analytical solution and numerical
modeling. The model includes a consideration of the complete crystallization and degassing history of the magma,
coupled with conductive and convective heat flow and mass transfer in the porous country rock, and in the magma
layer itself. The dynamics of cooling of the magma determine the velocity with which the solidus point (solidification
front) moves downward, and this in turn give's (by conservation of fluid mass) the magnitude of the flux of aqueous
magmatic fluid that is released to flaw upward through the country rock: ~ b ' fluid
e
flux is therefore variable because
it depends upon the temperature evolution of the magma, and this allows +us.to make several new statements about
the P-T-XHZopaths of rocks undergoing contact metamorphism as a function of distance from the contact and the
temperature, composition, and water content of the intruded magma. In previous studies of metamorphic fluid flow,
the fluid flux has usually been assumed constant, or only the integrated effects of the fluid flux were studied. The
parameterization of T-X,,, phase diagrams of hydrous magmas at fixed pressure is discussed in detail and a simple
scheme is developed. For a given magmatic water content, we suggest a description of the variation of the melt
fraction with temperature that includes only one dimensionless parameter, M,,,, which represents the fraction of
melt generated close to the solidus temperature during melting. This parameterization allows us to calculate the
evolution of temperature and volatile flux during magma crystallization. The results of the numerical calculations
are shown to depend upon M,,,and two other dimensionless parameters: the Stefan number (Ste)and the solidus
temperature (Tiol)of the magma. Polynomials are given that describe the numerically calculated contact temperature,
the contact temperature gradient, the timing of fluid release and the crystallization time as a function of these three
parameters. We discuss the application of the results to natural situations and use them to classify the temporal
evolution of metamorphic and isotopic zonation in contact metamorphic aureoles. Three types of time-temperaturefluid infiltration trajectory are recognized within the aureole, and these define a series of zones, following in a specific
sequence moving away from the contact. Identification of such zones in metamorphic terranes allows assessment of
the ~lausibilityof magmas as the principal fluid sources, and documentation of their relative width provides a means
to quantify various aspects of the crystallization history. We demonstrate that the maximum width of an oxygen
isotope alteration zone caused by magmatic volatiles is unlikely to exceed 1 km, and most natural situations will
involve much smaller alteration zones (e.g., tens to hundreds of meters). Because we are able tospredict the thermal
and isotopic effects exclusively due to outward directed flow of magmatic fluids, we can use our results to distinguish
such situations from others which involve inward directed flow of externally derived fluids. Because systems dominated by magmatic fluids are likely to be more common at greater depth in the crust, our model may be particularly
appropriate for metamorphism in the deep crust, adjacent to underplated magmas. Such volatile fluxes will exert an
important influence on deep crustal melting processes.
Introduction
All magmas contain dissolved volatile constituents (predominantly H20 and COz), a large fraction of which are released during crystallization.
Manuscript received September 30, 1992; accepted AUgust 11, 1993.
~nstituteof Experimental Mineralogy of the Russian Academy of Sciences 142432, Chernogolovka, Moscow district, Russia. Present address: Department of Sedimentary Geology, Vrije
Universiteit, De Boelelaan 1085, 1081 WV Amsterdam, The
Netherlands.
Magma emplacement a t depth i n the crust therefore causes both heating of adjacent country rock
(contact aureole formation) and fluxing of these
same roclts with exsolved magmatic volatiles. The
magnitude of t h e volatile flux, and the chemical
and isotopic effect it will have o n the country rock,
depends upon the size and composition of the
magma body, its volatile content and isotopic cornposition, and the kinematics of
flow.
In this paper w e present the results of some cab
[The Journal of Geology, 1994, volume 102, p. 25-45] O 1994 by The University of Chicago. All rights reserved. 0022-1376/94/10201-006$1.00
26
Y . Y . P O D L A D C H I K O V A N D S . M . WICKHAM
culations that document the temporal evolution of
temperature, fluid flux, and isotopic composition
in the rocks adjacent to crystallizing magmas of
different compositions with variable water contents. By characterizing the thermal effects and
volatile fluxes due to magma crystallization, we
seek to identify natural examples of chemical and
isotopic alteration that are exclusively due to magmatic volatiles and to distinguish these from alteration involving external fluids. We compare our
results with some natural examples of metamorphic and isotopic alteration that may be explained
in this way.
Mathematical Model. Consider a crystallizing,
sheet-like body of magma (figure 1) which may i n
part be convecting (Worster et al. 1990; Marsh
1989). The magma cools by conduction of heat
through overlying country rock. The country rock
is porous and permits flow of aqueous pore fluid,
which in our model is exclusively derived from t h e
degassing magma. As discussed in many other
studies (e.g., Jaeger 1964; Irvine 1970; Bickle and
McKenzie 1987; Furlong et al. 1991), these processes may be described by the following system
of equations (see table 1 and figure 1 for notation):
Heat transfer equation:
Model for Conjugate Crystallization and
Degassing of Hydrous Magma, and
Metamorphism and Fluid Flow
in Adjacent Country Rock
In our model, the magma chamber is taken to be
a horizontal layer, thickness Lo; we focus on the
crystallization which occurs from the top down.
All volatiles dissolved in the magma are considered
to be pure H20. Initially the magma is at some
specified temperature, Torn,with melt fraction M,,
but as soon as it is emplaced against cooler overlying country rocks it begins to lose heat through its
roof, causing internal crystallization. The magma
soon evolves into three zones: (1) an overlying
zone, 100% solid; (2) an intermediate, partially
molten mushy zone (Marsh 1989; Worster et al.
1990) within which the crystal fraction ranges
from 100% at the top to 50% at the bottom; and
(3)a body of magma containing - 6 0 % suspended
crystals which may or may not convect (see figure
1).The boundary between Zones (2) and (3)is the
point the magma ceases to take part i n any convective flow and becomes part of the static, high crystal-fraction mushy zone (Marsh 1989). The value
50% is chosen as an approximation (see Bergantz
1991 for discussion) and could be easily varied to
suit any particular situation. The boundary between Zones (1)and ( 2 )corresponds to the solidus
temperature of the magma and is termed the solidification front. Both boundaries move downward
with time as the magma cools and crystallizes.
At some point during crystallization, depending
on the initial water content, the magma will become water-saturated due to crystallization of anhydrous phases. From this point onward, bubbles
of H20 will coexist with liquid and crystals. In our
model, we consider there to be no net movement
between melt and exsolved vapor, so that bubbles
remain fixed within Zone (2)until the solidification f ~ o nmoves
t
past, and they are released to flow
upward through the overlying rocks.
for x > -xs
a2T
- -- k" 2
for -xs> x > -xf
at
(lb)
Isotopic evolution of the fluid:
where, for oxygen,
The Stefan condition at the lower boundary of the
mushy zone (x = -xi):
Simple mass balance for H 2 0 at the solidus t e m perature (x = -x,):
Journal of Geology
CRYSTALLIZATION O F MAGMAS
ZONE 3
T=T,
(convecting[?] magma)
IIIIIIIIIIIII~X=-X~~~~I.(J~=
J
0) m I -
I
-4-final
solidification point
upward
crystallizing
region
(basal heat flux)
bottom of
X=-X b ' m a g m a layer
I
Figure 1. Model for a cooling layer of hydrous magma. The original top and bottom of the layer are indicated by
the bold horizontal lines (x = 0 and x = -xb).The system rapidly evolves into three zones: Zone (1)(heavystipple)
represents rock below the solidus temperature, containing aqueous pore fluid; Zone (2)(light stipple) an intermediate,
partially molten, mushy zone, containing between 0 and 50% silicate liquid; and Zone (3)a body of magma containing
50 to 100% liquid, which may or may not convect. As the magma layer crystallizes, magmatic volatiles are released
to flow upward through Zone 1, causing chemical and isotopic alteration. The position of an alteration front associ, shown. Part of the magma
ated with this volatile flux, x = x,, and its associated diffusive broadening, w ~are
crystallizes from the bottom up, but in this paper we are primarily concerned with modeling the thermal and
degassing history of the upper part of the layer, above x = -xw where the last drop of silicate liquid crystallizes.
Boundary conditions:
Thermal, Ib = 0 a t x = -xfSpand
T = To,at x >> xfV
Compositional, = ,6 at x = -x,and
6,= 6, at x >> xfsp
(5)
Equations (1)and (2)have been discussed by many
authors (see for example Bickle and McKenzie
1987; Sharapov and Avyerkin 1990; various chapters in Kerrick 1991).Note that equation (2)may
be written for any fluid component (e.g., H, C), al-
though in this paper we will primarily be concerned with the transport of oxygen. Equation (3)
is the Stefan condition (Carslaw and Jaeger 1959;
Kerr et al. 1990; Worster et al. 1990) applied with
the assumption that the 50% crystallinity isopleth
divides the convective and conductive part of the
system. This equation represents the balance of
conductive heat transfer through the non-convective region (above the moving T,, isotherm)
with convective heat transfer out of the underlying
melt (including the heat released as the melt temperature falls to T,,).
Accordingly, the last term
in equation (3) denotes the heat flux out of the
28
Y. Y. P O D L A D C H I K O V A N D S. M . W I C K H A M
Table 1. Definitions of Symbols Used i n This Paper
Table 1. (Continued)
Symbol
Symbol
Definition
Temperature transport efficiency
6180 transport efficiency
Heat capacity of fluid
Heat capacity of solid
Effective heat capacity of magma
Effective heat capacity of magma without crystals
Average heat capacity of fluid and rock
Diffusivity of oxygen in water
Effective diffusivity of oxygen in porous
country rock
Constant of proportionality for xi vs.
2
Ste
T
T'
T50
Tm
Tom
Tsat
t
t'
tin
a
Acceleration due to gravity
Enthalpy of crystallization
Heat exchange coefficient for convecting
magma
Heat flux through base of convecting
magma layer
Average thermal diffusivity of fluid and
rock
Average thermal diffusivity of magma
Thickness of intruded magma body
Thickness of convecting magma
Initial melt fraction of magma
Melt fraction of magma
Melt fraction at the temperature of
water saturation
Oxygen concentration in solid
Oxygen concentration in fluid
Oxygen mass ratio
Thermal Peclet number
Compositional Peclet number
Fraction of altered rock within aureole
Constant of proportionality for position
of any isotherm
Stefan number
Temperature
Dimensionless temperature
Temperature of 50% crystallinity isopleth
Contact temperature
Maximum temperature at any point in
the aureole
Maximum contact temperature
Gradient of the maximum temperature
(T,,,) array at the contact (x = 0)
Temperature of convecting magma
Initial temperature of magma
Temperature at which cooling magma
becomes water saturated
Wet solidus temperature
Initial overheating above convective
liquidus
Initial temperature of country rock at intrusion point
Dimensionless wet solidus temperature
Temperature of any isotherm in country
rock
Time
Dimensionless time
Time when fluid enters country rock
tout
Definition
Time when fluid leaves country rock
Fluid velocity
Weight fraction of H,O
Weight fraction of HzO in water saturated magma
Vertical coordinate
Thickness of alteration zone
Maximum thickness of alteration zone
Distance to 50% solidification isopleth
Distance to the magmatic fluid front
Distance to final solidification point
Distance to water saturated solidus
Distance to lower boundary of the convecting magma
Width of alteration front
Coefficient of thermal expansion of
magma
Initial 6180 of solid
6180 of fluid
Dimensionless 6180 of fluid
6180 of magma
Effective thickness of country rock
heated during convective interval
Porosity
pi, 3.142
Thermal conductivity of solid
Thermal conductivity of fluid
Thermal conductivity of magma
Fluid viscosity (kinematic)
Magma effective viscosity (kinematic)
Average density of fluid and rock
Solid density
Fluid density
Magma density
Similarity variable, x/2*
convecting magma. The heat exchange coefficient,
h, is given by
(Huppert and Sparks 1988).
Equation (4)gives the fluid velocity only at t h e
crystallization front (x = -xs).In order to predict
the fluid velocity in the whole cross section, w e
must consider equations for the conservation of
mass of fluid within Zone I (figure 1).For negligible
or quasi-stationary (e.g., Litvinovsky et al. 1990)
variation of pf along the &otherma1 gradient these
can be reduced to the form (alax)(+pfvf)= 0 (constant flux). This implies that equation (4)also expresses the fluid flux for the whole cross section.
In the model, a number of assumptions h a v e
been made that simplify the mathematical treatment. We consider the fluid phase to be pure H,O
Journal of Geology
CRYSTALLIZATION OF MAGMAS
and to contain no other volatile species. The model
is one-dimensional (i.e., the fluid is not channeled
as it is liberated from the retreating crystallization
front, but flows pervasively through the country
rock which is assumed to have a uniform porosity).
On the other hand, the same equations could be
used to describe a medium with variable properties
using averaged, effective parameters. Values of cf,
pi, c,, p,, hf. and A, are taken to be constant, and
any differential flow of melt and fluid in the threephase mushy zone is neglected. Melt fraction is
assumed to be proportional t o latent heat released.
Given these assumptions, the equations give us
a complete description of the evolution of temperature, and of the distribution and isotopic composition of pore fluid above the magma layer. This
allows us to study the effect of advective and conductive heat transfer and the simultaneous isotopic and chemical alteration of country rock by exsolved fluid during crystallization of the magma
body. Although each of the components of the
model and the relevant transport equations are
well known, they have not previously been rigorously coupled in this form. In particular, because
we require that the fluid flux be derived exclusively from magmatic volatiles that are only released as the magma crystallizes, we are able to
predict a specific history of fluid release (and isotopic alteration) directly coupled to the thermal history of the magma-aureole system.
Convection. There has been much recent discussion of the importance of convection in crystallizing magma chambers ( e.g ., Hupp ert and
Turner 1991 Marsh 1991).In general, convection
will be most important during the early stages of
crystallization, w h c h we call the convective inter val. However, convection may continue much
longer without having a significant influence on
the thermal history, due to the small magnitude
of the thermal flux out of the convective layer in
comparison with other terms in equation (3)
(Turner et al. 1986; Kerr et al. 1990j Worster et al.
1990).In this study, we make a simple estimation
of the duration of this convective interval because
we are most concerned with the later stages of
crystallization, when most of the volatiles are released, and when cooling will be ~ r i m a r i l yby conduction. Using simple heat balance constraints we
obtain the following expression for the effective
thickness of country rock heated during the convective interval :
29
(When the initial melt fraction, Mo 5 0.5, E = 0
because there is no convection and cooling is
purely conductive.)
In this formula the initial temperature of the
magma, T,, in excess of T,, plays an important
role. However, during intrusion over significant
distances (several times the dimension of the
magma body), this initial overheating will be rapidly lost (Griffiths 1986; Mahon and Harrison
1988; Paterson and Tobisch 1992). Furthermore,
many thermal models of shallow level aureoles
have successfully replicated the observed contact
aureole metamorphic zonation using purely conductive cooling calculations and do not appear to
require a long convective cooling interval (Furlong
et al. 1991).We therefore Consider that the convective interval may often be neglected, especially for
more silica-rich magmas or for magmas intruded
at middle or upper crustal levels.
Accordingly, in order to obtain an analytical solution, we neglect the convective interval and assume conductive cooling throughout. However, we
do include a convective interval in our more general numerical solutions (see below). In this case,
the variation of temperature within the convecting
magma (T,) may be calculated using a simple heat
balance equation (cf. Huppert and Sparks 1988):
where L, = Lo - xv
We have chosen to simplify this equation by setting Tb (the heat flux out of the base of the magma
layer) to 0, because it is likely that most of the
heat lost by a convecting layer will be from the
upper boundary, particularly if the country-rock
temperature below the layer is fairly high and if a
stagnation layer forms at the lower boundary
(Brandeis and Jaupart 1986).
After convection has ceased, cooling will continue by conduction alone, and temperature below
the magma layer is significant. The T, isotherms
(solidification fronts) will continue to move toward the center of the magma layer from the top
and bottom boundaries and eventually will meet
at some level within the layer which we call the
final solidification point, x = -xf, (at which the
last drop of liquid will disappear, see figure 1).Because several processes are unconstrained below
the magma layer, the basal heat flux, I,, is unknown and xf, cannot be determined. However,
we can say that the temperature gradient at this
point will probably be close to zero. We therefore
30
Y . Y . PODLADCHIKOV A N D S. M . WICKHAM
restrict our calculation to the region above x =
-xfSp,applying a constant boundary condition of
= 8Tlax = 0 at this point during the entire conductive cooling interval. In this way we decouple
the crystallization processes we are trying to
model in the upper part of the magma chamber
from the many unconstrained processes at its base.
To conclude this section we would like to emphasize the difference in our treatment of the Zone
2IZone 3 boundary and the convective layer from
that used by Kerr et al. (1990) and Worster et al.
(1990).These authors used the concept of marginal
equilibrium (Worster 1986) as an additional boundary condition at the Zone 2/Zone 3 boundary,
which in fact defines the temperature of this
boundary. According to this concept, the temperature of the Zone Z/Zone 3 boundary will initially
be very slightly less than the liquidus temperature
(due to kinetic effects), and therefore Zone 3 will
initially be almost free of crystals. However, in the
original paper (Worster 1986), the concept of marginal
equilibrium was derived for a static (nonconvecting)system and may not therefore be applicable to the Zone 21Zone 3 boundary. In this paper
we are using T,,, the temperature of critical crystallinity (Marsh 1989),to define the Zone 2lZone 3
boundary, which roughly corresponds to a magma
with 50% crystals and separates an upper layer
that is too rigid to participate in convection (Zone
2) from a lower layer that may convect (Zone 3).
Parameterization of Phase Diagram. In order to
apply our model to the crystallization of natural
hydrous magmas, we need to parameterize the appropriate temperature-XHIo diagrams (see for example Whitney 1975, 1988))including the waterundersaturated crystallization behavior. This is
a difficult task for a natural multicomponent
magma, because there have been very few experimental studies of the variation of melt fraction (M)
with temperature in undersaturated systems, and
because theoretical predictions are as yet only applicable to simple (i.e.,haplogranitic) systems (e.g.,
Nekvasil 1988).
In fact this parameterization is not an insurmountable problem because (1)M can be easily calculated for any point along the water saturation
boundary (line AB in figure 2)j (2) along the line
H,O = O%, M must vary from 0% at the dry solidus to 100% at the dry liquidus, and for many
systems these temperatures are reasonably well
known; (3) for a few systems the variation of M
with temperature at low water content (vapor absent melting conditions) has been experimentally
determined, and the appropriate parameterization
can be made to fit these data (Marsh 1981; Conrad
Figure 2. Topology of a T-X,,, phase diagram at fixed
pressure, indicating the five main fields common to all
such diagrams. The letters A through E denote special
points on the field boundaries that have been used in the
parameterization of these diagrams (seetext).
et al. 1988; Rutter and Wyllie 198d; Vielzeuf and
Holloway 1988; Patiiio-Douce and Johnston 1991;
Beard and Lofgren 1991; Rushmer 1991; for thermodynamic models see Clemens and Vielzeuf
1987 and Rushmer 1991) and (4)the parameterization can be checked against theoretical predictions
in simpler water-bearing systems ( e.g., Nekvasil
1988) and various other experimental data on systems with added water (Holloway and Burnham
1972; Helz 1976; Wyllie 1977; Huang and Wyllie
1986; Conrad et al. 1988; Whitney 1988; Beard and
Lofgren 1991 Holtz and Johannes 1991).
We can describe the topology of a typical
T-X,, diagram in terms of the five main fields
labeled in figure 2 (cf. Wyllie 1977; Huang and
Wyllie 1986; Whitney 1988). These fields are
termed L (liquid only), L + V (liquid plus vapor),
L + V + S (liquid plus vapor plus solid), L + S
(liquid plus solid), and S + V (solid plus vapor). If
the positions of the lines separating these fields
are known from experiments or from theoretical
considerations, the percentage of crystals and liquid can be easily deduced for all fields except L +
S. This is because we are dealing with crystallization at constant pressure, and we can therefore assume that there is no variation in the water content of the saturated liquid over the crystallization
temperature interval. It is thus possible to determine the water content of the water-saturated liquid from point B (100% liquid), and then calculate
the range of melt fraction from 0-100% melt along
the line AB (assuming that a negligible fraction of
Journal of Geology
CRYSTALLIZATION OF MAGMAS
the total water content is contained in hydrous
minerals). These values can then be extrapolated
into the L + V
S field along lines of constant
temperature.
The chief difficulty in parameterizing melt fraction concerns the vapor undersaturated region (L
+ S). In cases in which there is no or little data,
we can interpolate between the known values
along the line AB,and the dry solidus and liquidus
temperatures at E and C respectively. Along AB,
the most important point is D, at which there is a
sharp change in slope (particularly noticeable in
data for silicic systems) marking the beginning of
eutectic crystallization. Inasmuch as the line segment AD represents almost isothermal crystallization or melting, we connect all the isopleths of
equal M along AD to the dry solidus point (E).The
rest of the isopleths of M starting from line segment DB have been connected with the dry melting line EC, ensuring the same proportional relationship along DB and EC. The form of these
isopleths within the region BCED takes the form
of a simple polynomial for T versus X,,, with the
shape constrained by the shape of the bounding
curve BC. The same format is also used for the
triangular segment EAD.The order of the polynomials for each isopleth of M can be independently
varied and are chosen to give the best match to any
experimental or theoretical data.
The approach used in this parameterization is
appropriate for a system without hydrous minerals, but we can adapt it to include these phases
using the following simple rules. At temperatures
below where major dehydration melting of hydrous phases begins, we assume the water held in
these hydrous phases is subtracted from the total
water content of the system, and the variation of
M is calculated as in the previous example. Over
the temperature range during which major dehydration melting is occurring, we assume a linear
decomposition of the hydrous mineral with increasing temperature (Patifio-Douce and Johnston
1991). Over the dehydration melting interval we
continuously add water to the system proportional
to the fraction of hydrous mineral that has been
decomposed. An example is our parameterized
T-XHZodiagram for tonalite containing biotite and
hornblende (figure 3). This diagram may be compared with the experimental results of Rutter and
Wyllie (1988),who measured the variation of melt
fraction with temperature for hydrous tonalite at a
fixed water content of 0.8%, containing 9% modal
hornblende and 12.5% modal biotite.
We have modeled crystallization of four magma
types: (1) adamellite without hydrous minerals
+
Tonalite 101, 10 kbar
'\
'.
..--..------ Melt fraction
---------__-__
~_____-_____-__--__--------------------------------.
1
I
I
I
I
Water content, wt.%
Figure 3. An example of the parameterization of a
phase diagram (tonalite 101 at 10 kb), using the scheme
adopted in this paper.
(corresponding to the synthetic adamellite of Whitney 1975)j(2)tonalite containing the hydrous minerals biotite and hornblende (corresponding to
tonalite 101 of Piwinski [1968],Huang and Wyllie
[1986], and Rutter and Wyllie [1988]); (3)hydrous
gabbro, corresponding to gabbro DW1 of Huang
and Wyllie (1986); (4) muscovite granite corresponding to sample L26 of Wyllie (1977).The values necessary to parameterize M on T-X,,, diagrams for three of these magmas at various
different pressures are given in table 2. The variation of these values in silicate melts over a wide
range of Si02 contents is summarized by Huang
and Wyllie (1986, their figure 4, 15 kbar) and Wyllie (1977, his figures 12 and 13, 10 kbar). These
diagrams indicate that the temperature corresponding to point A stays almost constant with
composition while the temperature corresponding
to point B decreases with increasing SiO,.
A cross-section of a T-XH, diagram at fixed total
water content may be simplified further. Generally, in magmas with a significant water content,
there is a strong linear variation of melt fraction
with temperature within the three-phase (L + V
+ S) interval (from the water-saturated solidus
temperature to the temperature at which the melt
becomes water-undersaturated], and there is also a
close-to-linear dependence (with lower slope) in
the water-undersaturated region (between T,,, and
T , , the temperature of critical ~rystallinity)~
see
figure 4a and b. This means that within the coordinate frame, T' = ( T - TS)/(TN- T,), M = melt
fraction, the variation of melt fraction depends on
only two free parameters because of two default
relationships: melt fraction M is equal to 0 at T'
= 0 and to 0.5 at T' = 1. These two free parame-
32
Y . Y. P O D L A D C H I K O V A N D S. M. WICKHAM
Table 2. Reference Points Used in the Parameterization
of T-Xfio Phase Diagrams for Three Common Magma
Types
Reference point
in figure 3
Tonalite, 8 kbar, no hydrous mineralsa
B
11.1
E
A
C
0
0
0
D
9.8
Adamellite, 8 kbar, no hydrous mineralsafb
B
11.1
E
A
C
D
0
0
0
7.4
Tonalite 101, 10 kbarctdje
B
E
A
C
D
11.1
0
0
0
7.4
Tonalite 101, 15 kbard
B
E
A
C
18.0
0
B
E
A
C
D
15.O
0
0
0
B
22.0
0
0
D
12
Muscovite granite L26, 10 kbarc
5.4
Muscovite granite L26, 15 kbarc
a
Whitney 1975.
Nekvasil 1988.
Wyllie 1977
Huang and Wyllie 1986.
Rutter and Wyllie 1988.
ters may be fixed as: TLat = (T,,, - Ts)/(T5,- T,),
the dimensionless temperature of water saturation,
and M,,,, the melt fraction at the temperature of
water saturation (see figure 5).
Fortunately, Tiat may be set to zero for most
problems under consideration. This is because the
water saturation interval is very narrow for granitic magmas, and furthermore, a high percentage
of melt usually appears near the solidus (figure 4).
For basic and intermediate magmas Ti,, becomes
greater, but the variation within both intervals is
similar so that a simple linear dependence may be
used for the whole melting interval by setting
Ti,, = 0 and M,,,= 0. Under the assumption t h a t
T;,, = 0, in our model we will have quasi-eutectic
melting between the solidus temperature and t h e
Msatmelt fraction, and a linear increase of M w i t h
temperature from this point to the convective liquidus (T50)Note that M,,, corresponds to a point
on line AB in figure 2, and can therefore also b e
expressed by the ratio X,,/Xgi0
(total water content/magrnatic water solubility),providing an easy
way to estimate this parameter. As shown in figure
4, M,,,increases with increasing water and silica
content of the magma (seealso McMillan and Holloway 1987 for discussion).
Dimensionless Parameters of the Model. Analysis
of equations (1-6) and the results of our parameterization of the phase diagram yield the following
dimensionless parameters :
Ste-the
Stefan number, given by:
Ste =
MoAH
c,P,(T,,
- Tosl
Tiol-the dimensionless temperature of the watersaturated solidus, given by:
TIsol
=
(Ts - To,)
(Tom - Tos 1
Msat-the melt fraction at the temperature of water
initial overheating of t h e
saturation; TA,the
magma above the temperature of critical crystallinity TS0,given by:
TL, = (Tom - T50)
(Torn - Tos 1
Parameters related to advective heat and m a s s
transfer :
characteristic length scale, xh; characteristic time
scale, x k l k ; temperature, (T,, - TOsJi
magma density,. ,P
Mass Balance Relationships
Two useful kinematic constraints on fluid flow exist based solely on mass conservation laws and d o
not depend on the specific dynamics of fluid flow.
One of these is the thickness of isotopic alteration,
x, as a function of the solidus position, x, (i.e.,
Westerly Granite
2 kb confining pressure
7D0
720
740
760
780
800
T deg C
A
I
..................i..................... .....-............c.;......*........... ...........
/
*
*island
arc tholeiite, 8kb, vapor absen
,+alkali
basalt, 8 kb, vapor-absent
- - x- - tonalite, 10 kb, vapor-absent
-*
gabbro, 1 5kb, 5% water added
d -synthetic adamellite,2kb,2.8~t.~/~water
- @ -synthetic
adamellite,8kb,2.8~t.~/~water
A
600
B
700
800
900 1000 1100 1200 1300
T deg C
Figure 4. Melt fraction as a function of temperature for various rock compositions, containing different water
contents and at various different pressures: (a)Westerly granite (Whitney 1988); (b) island arc tholeiite and alkali
basalt (Rushmer 1991)) tonalite (Rutter and Wyllie 1988)) gabbro (Huang and Wyllie 1986))basalt (Helz 1976),
synthetic adamellite (Nekvasil 1988))peraluminous quartzo-feldspathic gneiss (Holtz and Johannes 1991). These
diagrams illustrate the approximately linear relationship between temperature and melt fraction in the regon beand
tween the solidus and the temperature at which the melt becomes water-undersaturated (melt fraction = M,,,),
also in the region between Ms., and the convective liquidus (M = 0.5).
Y. Y. P O D L A D C H I K O V A N D S . M . W f C K H A M
Analytical Solution for Simple
Conductive Cooling
For the case in which (i)the initial condition at the
interface between the magma and country rock is
a step function for temperature and isotopic composition; (ii)the country rock forms an infinite half
space; (iii)TA, < 1or T,, < T,, (i.e.,no conve~tion)~
and (iv) Tid = 1 (i.e., the magma is emplaced water-saturated), the system of equations (1))( 2 ) )(4)
and boundary conditions (5)has the following analytical solutions (cf. Carslaw and Jaeger 1959):
T = To, + (Tom-
TT
T'= >
+
k(l +
T,-*s
Figure 5. Simplified diagram of the relationship be-
(c
1 - erf - FA,)
1 erf [F(l + A,)] (11)
ti1 = So
Omr) (t;
- FA,)
+ (Sm- So)
tween melt fraction and dimensionless temperature according to the scheme adopted in this paper, highlighting
the definition of Ti,,and M,,,
(see text for further explanation).
(12)
where
degree of crystallization of the magma). For oxygen
isotopes this is given by:
Similarly, the position of the magmatic fluid front
as it moves out away from the crystallizing magma
body is given by
erf (x)=
1,
2 "
e-Pd[
the error function.
As the crystallization front moves downward, its
distance from the contact is given by
This demonstrates that, inasmuch as rock porosity is usually very small, in general, any exsolved magmatic fluid will occupy the whole contact aureole very soon after the magma begins to
degas, and the crystallization front (x,)starts to
move downward, at dimensionless time ti, (see
below).
As far as these relationships are purely kinematic, they are independent of vertical variations
in permeability. However, equations ( 9 ) and (10)
are not valid if lateral permeability variation leads
to significant perturbation of one dimensional flow
(i.e., channelling of fluid).
and the value of F may be obtained from the following equation:
Ste =
P~,(T,, - To,) *HMO
expi - [4
I + AT)2])
~ { lerf[F(l + A,)]}
+
This relationship between F and the Stefan
number is illustrated in figure 6. Similarly, the po-
CRYSTALLIZATION OF MAGMAS
Journal of Geology
35
sition of any isotherm (T = T * )will be given by
x = - 2 ~ * , where S may be obtained from the
equation
The contact temperature (which does not
change during the whole crystallization interval)
may be obtained by setting x = 0 in equation (11):
1 + erf (FA,)
Tc = To, + (Torn - T o s ) 1 + erf [fll + A,)]
0.5
1.O
1.5
Ste number
2.0
Temperature profiles
2.5
The solidification time (whichis identical to the
time when the fluid will leave the system) may be
obtained by substituting xf, into (16):
b
-
-
-
The gradient of the array of maximum temperature (T,,) points, taken at the contact (x = O),
may be obtained from (11)by taking the partial
derivative with respect to x and by substituting t
= to,, from the previous formula:
-
-----...-...-
The t, time is equal to zero for this solution,
i.e., fluid pervades the system immediately afer intrusion of the magma. These analytical solutions
are illustrated in figures G and 7.
Neglection of Adjective Heat Transfer by Fluid.
One of the important results of the analytical solu-
&
Similarity variable,
X
4= 2*
Concentration profile
Similarity variable,
5=
C
X
-
2J-F
Figure 6. Analytical solution: some relationships between the various dimensionless variables (see text, Appendix, and table 1 for definitions). ( a ) F value (from
equation 17), dimensionless contact temperature (from
equation 19),dimensionless gradient of maximum temperature (T,,,)array at the contact (from equation 21))
and dimensionless crystallization time (from equation
20) versus Stefan number. (b) Dimensionless temperature (from equation 11) versus similarity variable 6
(where 6 = x / ( 2 f i ) ,i.e., scaled distance from the contact)for different Stefan numbers. (c)Dimensionless concentration of a tracer such as 6180 (from equation 12)
versus similarity variable 6 for different transport efficiencies, A, whereeffective diffusivities,
D , where D, = V ~ / [ k (+l Om,)].
Note the broadening
of the profiles at higher values of Dr.
36
Y. Y. P O D L A D C H I K O V A N D S . M. W I C K H A M
Figure 7. Schematic representation
of the distribution of temperature
and isotopic composition (shown
here for oxygen isotopes) after time,
t, in the region adjacent to a cooling,
hydrous magma body. Analytical solutions for the position of the crystallization front (equation 16), the
isotopic alteration front (equation
22) and the diffusive broadening of
the alteration front (equation24) are
given, (comparewith figure 1).
mT
I
I
I
I
xfz- 2 ~ ( k t Y
IIt
I
I
I
I
1
I
tion is that for AT < 1, advective heat transport
by the fluid is negligible, no matter what values
any of the other parameters take (see [Ill, [13],and
[17]).Therefore, according to equation (13),for any
magma containing -10% H,O or less, the magmatic volatile flux released on crystallization will
have negligble effect on the thermal structure (cf.
Thompson and Connolly 1992).
Isotopic Alteration of Country Rock at High Pe,.
From the analytical solution (12)we can derive the
effective thickness of the isotopically altered zone
(x,,
see figure 7) due to the flus of magmatic fluids
(with magmatic isotopic composition) into the adjacent country rock. For oxygen, the thickness of
this zone is given by:
For a magma with re1ativi:ly low water content
(XHIO
< 0.05) the thickness of the zone of isotopic
alteration (x,) will be much less than the total
thickness of magma crystallized (xi) (compare
equations (16)and (22)).Also, the range of temperature throughout the alteration zone will be very
small at any particular instant throughout the crystallization history.
The maximum thickness of the isotopic alteration will be x,, which occurs when the distance
to the crystallization front, xp equals xfsp(the distance to the final solidification point). Therefore,
using (16),we can substitute for xf in (22)to obtain
This last relationship is i n agreement with simple
mass balance and could be obtained from timeintegrated flux calculations for the isothermal case
(e.g., Ferry 1991 Ferry and Dipple 1992). This
equation is therefore valid for all numerical solutions presented in the next section.
An interesting consequence of the model is that
the progressive flux generated by crystallization
from the top down does not constitute all the magmatic water initially present in the layer. Below
the point x = -xfspin the lower part of the magma
layer, any volatiles released will be trapped beneath the layer of melt + crystals that continually
grows smaller due to the advance of the solidification fronts from top and bottom (see figure 1).It is
difficult to predict the behavior of this water, and
it may be expelled from the system laterally or be
released at the very end of crystallization, perhaps
by more strongly channelized two-dimensional
flow. It is possible that this fluid may contribute
additional minor alteration above the magma
layer, but we would expect it to be more heterogeneous and associated with obviously retrograde
features.
The isotopic alteration front at x = x, will be
broadened due to diffusive and dispersive processes
(e.g., Lassey and Blattner 198gj Bickle 1992). Here
we obtain the solution for diffusive broadening and
in this case the width of the front, w,, is given by:
Journal of Geology
37
CRYSTALLIZATION OF MAGMAS
-
-
c
The final width of the front will be w,,,for which
we can substitute for to,, to give
0.6
c
.2
.I.r
0.4
m
or substituting for xfspfrom (23),we obtain
This last relationship is based on mass balance for
magmatic fluid and therefore is valid for the numerical solutions as well. This demonstrates that
for any magmatic water content and normal diffusivities, wDm,will be very small i n comparison
with x,,,.
Numerical Solutions; Systematic Investigations
For other cases in which the simple conditions required for the analytical solution do not apply, the
main equations have been solved using a numerical implicit finite difference scheme. The simple
parameterization of the crystallization behavior of
the magma at constant X
,, (as described above)
was retained. The melt fraction, M, first increases
from 0 to Msa, at the saturation temperature, T =
T,,,; it then increases linearly with temperature up
to M, at Torn,the magma intrusion temperature.
The mathematical treatment of this behavior requires introduction of a Stefan-like discontinuity
at T = TSat(cf. Bergantz 1992). One hundred numerical calculations were made to investigate the
influence of varying the values of the principal dimensionless parameters. The following parameters
were chosen:
Ste = 0.5, 1.0, 1.5,2.0, Tiol = 0.5,0.6,0.7,0.8,0.9,
Msa, = 0,0.25,0.5,0.75, 1.0
Selected results are presented in figure 8, and
the combined results are summarized in an Appendix that may be obtained, together with reprints,
from the authors, or (the Appendix only) from
the Journal of Geology, or is available by e-mail
(podl@geo.vu.nlor smwx@midway.uchicago.edu).
They indicate that the crystallization time and the
contact temperature are strongly dependent on
the Stefan number and moderately dependent on
Dimensionless time,
k t / ( ~ , ~ ~ ) ~
Figure 8. Selected results of numerical calculations. Dimensionless position of solidification front (the ratio of
its present distance (x,)and its maximum distance (xi,)
from the contact)versus dimensionless time (kt/xfsp)
for
different sets of the three dimensionless parametersStefan number, TioI,and M,,,.
the two other parameters. ti,, the time when the
solidus isotherm starts to move downward through
the magma body, strongly depends upon all three
parameters. If two parameters are fixed and one
is varied, we obtain the following relationships:
(1) increasing Ste drastically increases the crystallization time, tin, and the contact temperaturej
(2) increasing TLoI decreases the crystallization
time, tin,and the contact temperature; (3)increasing M,,,increases the crystallization time, decreases tin and the contact temperature. The same
series of calculations using various sets of convective parameters did not show any noticeable deviation from numerical solutions to the conductive
models and are not discussed further.
Calculation of T-X,,o-d80 Paths. Some numerical solutions (figure 9) plot the evolution of dimensionless temperature [(T - ToS)/(Tom
- To,)]as a
function of dimensionless time (ktlxf,) and difor two different valmensionless distance (x/xf,)
ues of M,,, (0, 0.5; see figure caption). The Stefan
number and Tio1are assumed to equal 2 and 0.5,
respectively. These parameters were chosen because these cases cannot be accurately approximated by our analytical solution (for which Tsol
= I), or by the well-known analytical solution for
conductive cooling of a slab-shaped intrusion (see,
for example, Barton et al. 1991),in which Ste = 0.
The sets of parameters in figure 9 correspond to
granitic magma with an initial temperature of
-800°C and various different water contents,
Y. Y. PODLADCHIKOV A N D S . M. W I C K H A M
38
0
-1
1
3
5
7
9
11
Intruded magma
Zone 111
15
13
Dimensionless distance f r o m t h e contact
x/x,~
Zone I1
Zone I
b)
Dimensionless distance f r o m the c o n t a c t
x/xfSp
Figure 7. Time-space diagrams for the evolution of
temperature and fluid flux throughout the contact aureole. These diagrams are both for Ste = 2 and correspond
to M,,,= 0.5 (a)and M,,,= 0 (b).Magma only becomes
water saturated at the solidus temperature. Note the occurrence in both diagrams of Zones I, 11, and 111 in the
same regular sequence approaching the contact. In figure
(b)"fluid in" and "fluid out" occur very close together in
time because all degassing occurs at the magma solidus
temperature. See text for further details.
placed in contact with country rocks with a temperature of 600°C.
We can subdivide each diagram into a prograde
and retrograde field; we also show the evolution of
magmatic fluid at the same scale (cf.Barton e t al.
1991). he 0.5 contour represents the position of
the solidus within the magma body (in the region
above the final solidification point, where x/xh <
0). The "fluid in" line is defined as the time at
which magmatic fluid arrives at a particular point
in the system and is approximately an isochron
line, t = t,. This corresponds to the time when the
solidus isotherm starts to move downward through
the intrusion (or when the 0.5 contour crosses the
edge of the intrusion), and also may be approximated by the arrival of a fast-moving tracer. The
fluid is assumed to leave the whole system simultaneously when xs = xi, (or the 0.5 contour
reaches the point x/xh = - l),where the last drop
of degassing melt disappears. Thus fluid out is also
an isochron line, t = t,,,. Note that because the
topology changes dramatically with increasing
MSa,an analysis of natural situations may provide
a further possible way to check the value of this
parameteiand could, for example, be used to estimate the initial water content of the magma.
In the first diagram (figure 9a, M,,, = 0.5), all
the magmatic fluid will be released over a moderate range of the total crystallization time. The
region close to the intrusion will experience a
retrograde fluid flux, while further away, fluid infiltration will be under prograde conditions. In
figure 9b (M,,, = 0), fluid will be released very late
in the crystallization history, over a very short
time interval. At distances far from the intrusion,
however, infiltration will again be under exclusively prograde conditions, while the region close
to the intrusion will experience a retrograde flux.
Zoning in Contact Aureole. A systematic series
of zones can be defined, based on the position of
the "fluid in" and "fluid out" isopleths in relation
to the prograde-retrograde boundary. The systematics of fluid infiltration are illustrated in figure
10, where we define three separate regimes based
on the timing of fluid flow relative to the temperature maximum at any point i n the aureole. These
correspond to situations i n which the fluid arrives
and leaves before the maximum temperature is
reached (Zone I), after the maximum temperature
is reached (Zone 111),and an intermediate situation
in which the fluid arrives before the maximum
temperature is reached, but disappears from the
system after the temperature maximum (Zone 11).
These three zones may not all be present but can
only occur in the sequence: contact -+ Zone 111-,
C R Y S T A L L I Z A T I O N OF M A G M A S
Journal of Geology
TEMPERATURE AND FLUID FLOW HISTORY IN CONTACT
AUREOLE
ZONE 1
FLUID OUT
C,
time
(a)
time
39
In our analytical solution (Tsol= 1)only Path A
and Zone I are present. Increasing the parameters
M,,,and the water content of the crystallizing
magma and decreasing TSoItends to increase the
width of all other zones, which always follow in
the same order mentioned above. Since it is not
necessary to reach the maximum temperature to
produce a clockwise path in T-Xmo space, there is
no strong correlation between paths and zones. We
can only specify that the boundary between Paths
A and B lies somewhere within Zones I or I1 and
that Zone I11 definitely corresponds to Path B (retrograde metamorphism produces an anti-clockwise
path).
Applications of the Model
decreasing X
"20
-
Figure 10. Sketch to show the general relationships be-
tween temperature, fluid flow and time in contact aureole rocks. Diagram (a) shows the classification of the
aureole into three zones corresponding to fluid arriving
and leaving a point in the system before, during and after
the thermal maximum (ZonesI, I1 and III respectivelycompare with figure 9). The three zones may not all be
present in certain situations, but they must all occur in
the order contact -+ Zone 111 -+ Zone I1 + Zone I. Diagram (b)plots temperature against the water content of
the local fluid phase. The two possible scenarios are denoted Paths A and B and can only occur in the sequence
contact 4 Path B + Path A.
Zone I1+ Zone I, as illustrated in figure 1On. Thus,
for example, in figure 9b, Zones I and I1 are present
at distances >-GI whereas at distances less than
this only Zone 111 is present.
These contrasting histories can also be distinguished i n terms of a schematic T-X,,, diagram
(figure lob). Here we can subdivide the systematics
into two categories: Path A-clockwise path (first
water infiltrates, then temperature increases); Path
B-anti-clockwise
path (first temperature increases, then water infiltrates). These paths can
also only occur in the sequence: contact + Path B
+ Path A.
Inasmuch as several parameters are involved in the
relationships derived in the previous section, we
first discuss ways in which the solutions might be
applied to natural situations. Some of the parameters may be fixed on the basis of available geological data. For example, in well-studied areas it may
be possible to constrain both the thickness of a
zone of isotopic alteration by magmatic volatiles
(e.g., Wickham and Peters 1990, 1992; Nabelek
et al. 1992) and the diffusive width of the associated infiltration front, and to use these to assess
the nature of the magma source and associated
thermal perturbations. Alternatively, the depth of
emplacement of the magma layer and its thickness
could be estimated and used to predict thermal and
isotopic alteration effects. In either case i t is necessary to estimate porosity, which is difficult to
quantify. Estimates for metamorphic rocks vary
widely, from lo-' to l o m 6(e.g., Ganor et al. 1989;
Bickle and Baker 1990; Nabelek et al. 1992),with
strong contrasts between different lithologies (e.g.,
quartzite and marble, Wickham and Peters 1992).
For examples with heterogeneous porosity, we
would need to take into account the relative proportions of layers of differing porosity and average
them.
A simple averaging procedure can be used to estimate effective fluid/rock partitioning for different tracers. For oxygen and water-rich fluid, the
typical value for (O1/0,)is -2, but in aureoles with
multiple lithologies (e.g., carbonatehilicate) and
heterogeneous alteration, due for example to heterogeneous porosity, this value must be replaced
by Oi/(qO,),where q is the fraction of isotopically
altered rocks in a unit cross-section of the aureole.
This correction will increase the thickness of the
altered zone proportionally to parameter q.
If we are able to estimate x,,, (thickness of iso-
Y . Y. PODLADCHIKOV AND S. M. WICKHAM
40
topic alteration zone), xh (thickness of magma
crystallized), Of/(qOs),and +, then we are able to
make the following series of deductions.
(1)From (23)we can calculate the water content
of the intruded magma body
(2)Knowing the Stefan number for the magma
layer, F may be directly calculated using (17)-see
figure 6a. The chief uncertainty in finding Ste is in
the value of M,, which may not be well constrainedj in this case a range of values may be considered.
(3)Knowing F, the time at which the solidification front reaches xf, may then be estimated from
(20)using the analytical solution or from (A2)using numerical solutions that require estimation of
the parameters Tioland M,,,.
(4)Using the formula for the width of the diffusive front (26)we can check our estimate of porosity for self-consistency by calculating w,,, and
comparing it to the observed width. Note that this
formula can apply to the width of a diffusive profile
observed in any lithology in the whole cross section, but that the appropriate value of must be
used in each case.
and
(5) The estimated values of t,, t,,,, T,,
(dT/~x),, may be used as additional constraints if
these data can be independently estimated from
metamorphc or geochronological studies.
Natural Examples. With the analytical solutions
described above, and the parameterization of the
phase diagrams for various hydrous magma types,
we are now able to predict the evolution with time
of country rock temperatures and the accompanying water flux, during crystallization of some
natural magma types. The simple mass balance relationship of equation (23)tells us that the maximum width of oxygen isotope aiteration caused by
degassed magmatic volatiles that is ever likely to
be observed is a few kilometers (a 1 km zone would
correspond to xfsp = 5 km and a magmatic water
content of 10%) . Most natural situations will involve much smaller values for both xfspand X
,
and the resulting isotopic alteration zone should
be correspondingly smaller. This is well illustrated
in table 3, where we summarize our results for
three common magma types, adamellite, tonalite,
and basalt, having a range of likely water contents
and crystallizing at various different pressures. For
each case we list xb,/xfsp (the ratio of the thick-
+
-
ness of oxygen isotope alteration to the thickness
of magma crystallized, from the top down), kt/x&
(the characteristic cooling time), the convective
cooling interval, and the characteristic diffusively
broadened width of the isotopic alteration front.
x ~ ~ , is/ proportional
x ~ ~ ~
to XHz0of the magma, b u t
even for high water contents, ,x
will never b e
more than -one-ath xfspand more typically w i l l
be about a tenth the thickness of crystallizing
magma. For a kilometer-sized crystallizing layer
thickness, cooling timescales are in t h e range
10,000 to 100,000 yr.
We can immediately note that oxygen i s o t o p e
alteration zones several kilometers across (e.g., a s
observed in the Hercynian prograde metamorphic
sequences in the Pyrenees: Wickham and Taylor
1985) or tens of kilometers across (e.g., the Idaho
Batholith: Criss and Fleck 1987, 1990) are m u c h
too large to be explained by a one-pass flux of magmatic volatiles. The typical length scales of oxygen
isotope alteration due to magmatic volatiles
should be in the meters to hundreds of m e t e r s
range, depending on the water content of the
magma source. Natural examples attributed to this
process include isotopic alteration in the N o t c h
Peak aureole (Nabelek et al. 1984), where fluids
channeled through impure carbonate layers caused
180-depletion effects extending out several hundred meters from the pluton contact. In this c a s e
Nabelek et al. (1992) consider the fluid t o have
been transported in fractures rather than by s i m p l e
pervasive intergranular flow, which results in a
narrower isotopic alteration zone.
At Notch Peak, where significant lateral flow i s
proposed, the country rock lithological layering is
subhorizontal and contains relatively impermeable
pure calcite marble layers, allowing the potential
for substantial subhorizontal channeling of fluid
(Nabelek et al. 1984). Although this geometry is
rather different from our model and the emplacement depth was shallow (1.5 kbar)-meaning that
there was a possibility that external fluids b e c a m e
involved at some point (Ferry 1991)-we can m a k e
comparisons with the thermal and isotopic effects
that our model predicts because both isotopic and
petrological information is available on the a u r e o l e
assemblages (Nabelek et al. 1984, 1992; Labotka
et al. 1988).The Notch Peak pluton is best approximated in table 3 by the adamellite magma w i t h
2% H,O (Nabelek et al. [I9831 estimate 3% H,O)
emplaced at 2 kbar. Our model predicts t h a t for
oxygen isotopes, x8mmlxi, -- 0.04, and this compares favorably with the width of the isotopically
affected zone (-200 m ) and the radius of the p l u t o n
(-4 km) (P. I. Nabelek, pers. comm. 1993). The
Journal of Geology
41
C R Y S T A L L I Z A T I O N OF M A G M A S
Table 3. Model Solutions for Some Common Magma Types, with Various Water Contents, Emplaced at Different
Depths
Composition
of Magma
Adamellit e
(750°C)
Water
Content
(wt % )
Emplacement
Depth (Pressure, kbar)
kt
x,ma/xfspx lo2"
xip
E
Lo
(convective
IntervalJb
Alteration Front Widthc
wo,,
$ .xi, (1 +
2
2
5
5
10
Tonalite
(850°C)
Basalt
(1100°C)
2
2
5
5
1
2
T-X,,, paths deduced for the aureole calc-silicate
assemblages are also consistent with our predicted
pattern of fluid release and thermal history. Nabelek et al. (1984)present evidence that high-grade
rocks near the contact first experienced temperature increase, then water infiltration (Path B in
figure 10)while lower-grade rocks first experienced
water infiltration, then temperature increase (Path
A in figure 10).The sequence contact -,Path B +
Path A is i n accord with our model predictions (see
also figure 9) and is consistent with the interpretation that the Notch Peak aureole systematics could
have been caused by outward flow of magmatic
fluids (Labotka et al. 1988).
Many examples of oxygen isotope alteration in
the contact aureoles of epizonal intrusions (for review, see Nabelek 1991)have detected very limited
effects on the country rock, often extending out
only a few centimeters (e.g., Shieh and Taylor
1969a, 1969b; Hoernes et al. 1991). However,
many of these studies were made in regions where
the contact surface of the intrusion with the country rock was close to vertical, and the roof rocks
that originally overlay the pluton were eroded
away. In such cases it might be expected that most
magmatic volatiles would flux upward through the
roof zone rather than being expelled laterally, and
that lateral alteration would be relatively minor.
One case in which substantial contact aureole isotopic alteration has been observed is in country
rock forming the roof to the Precambrian Johnny
Lyon granodiorite of Arizona. Here, Turi and Taylor (1971)observed a 2 to 3 per mil shift in 8180in
the country rock adjacent to the granodiorite over
a zone -80 m wide. The location of this effect,
and the width of the isotopic alteration zone, are
appropriate to it having been caused by an upward
flux of volatiles released during crystallization of
the Johnny Lyon magma body.
In general, the isotopic effects of magmatic volatile fluxes may be hard to detect adjacent to plutons emplaced within the upper crust even if the
roof rocks above the pluton are available for study.
This is because in addition to magmatic fluids,
other fluids of external origin (e.g., surface waters,
pore waters) may also be available to flow through
contact aureoles, and these may contribute much
more extensive isotopic effects, because of the
much larger volume of fluid potentially available.
Examples include well-documented meteoric hydrothermal effects ( Criss and Taylor 1986),marine
surface waters or formation waters (Wickham and
Taylor 1985) and an alternative interpretation of
the Notch Peak systematics (Ferry and Dipple
1992).At deeper crustal levels, these external fluids will diminish in abundance and the fluid budget will tend to become dominated by strictly magmatic volatiles (Barton et al. 1991).It is therefore
at mid- and deep crustal levels that isotopic alteration due to magma degassing may be most easily
detected.
A possible example is the extreme 180-depletion
to mantle-like 6180 values documented by Wickham and Peters (1990)over a -200 m zone exposed
at deepest structural levels in the East Humboldt
Range, Nevada. Wickham and Peters (1992) proposed that this alteration was caused by degassing
of volatiles released from leucogranite magmas,
42
Y . Y. P O D L A D C H I K O V A N D S . M . WICKHAM
based on the observed correlation between leucogranite abundance and isotopic alteration. They
further suggested that the leucogranite magmas
were carriers of mantle-derived H,O, originally dissolved in basalts, from a deeper level zone of anatexis adjacent to underplated or intruded basaltic
magmas.
Despite the fact that the magmatic volatiles
were delivered by numerous distinct leucogranite
intrusions rather than one large intrusion, we can
use our model to address the integrated effects of
this process. In this case the magma would probably be best approximated in table 3 by the adamellite containing 5% H,O emplaced at 8 kbar pressure (Peters and Wickham [1992] estimate a
magmatic water content of -8% for East Humboldt Range leucogranites and an emplacement
pressure of -6 kbar). In this case x8,,/xf,
0.1,
implying that the -200-m alteration zone could
have been generated by a pluton at least 2 km
thick. Although this is more than the observed
thickness of leucogranite, it certainly represents a
plausible quantity of magma that might underlie
the area.
Peters and Wickham (1992)document reactions
in calc-silicate rocks close to leucogranites that
suggest they were infiltrated by H20-rich magmatic fluids. In T-Xspace, they consider that these
rocks followed an anti-clockwise path (Path B,
figure lo), equilibrating first at higher X,,, and
then being infiltrated by H,O-rich fluid with falling temperature. Such retrograde high-temperature
events are in fact typical of inner aureole rocks
(Bartonet al. 1991)and are consistent with our prediction (figures 9 and 10)that this type of behavior
should be observed in the country rocks closest t o
the intrusion.
-
Conclusions
The model i n this paper describes quantitatively
the thermal effect of the emplacement of a layer
of hydrous magma within the crust, coupled with
the degassing history and associated fluid flux in
the adjacent country rock. This allows us to evaluate the complete, coupled thermal and isotopic alteration history i n the country rock. Although in
some geological environments (notablywithin the
upper crust) these effects will be complicated by
the influx of external fluids not originally dissolved in the magma, we feel that it is important
to separate out the effects that may be related exclusively to the magma itself. This situation may
prevail at mid- or deep crustal levels where t h e
fluid budget is more likely to be dominated by
magmatic volatiles. The following important new
points were developed.
1) The variation of melt fraction with temperature in silicate systems under a fixed water content
may be described by two dimensionless parameters, M,,,,the melt fraction when the magma becomes water saturated, and Tiol, the temperature
of the water-saturated solidus.
2) A systematic numerical investigation of the
complete thermal and degassing history of a layer
of hydrous silicate magma has been fit by polynomials versus the dimensionless parameters, M,,,
Tiol and Ste, the Stefan number.
3) M,,,has a strong influence on the timing of
crystallization and degassing, which i n turn determines the zonation in the aureole. This implies
that previous models that use a linear approximation of the latent heat released between the solidus
and liquidus do not accurately predict the T-X,,
history.
4) Three types of metamorphic zonation may
be distinguished within contact aureoles. Moving
toward the magma body these are: (a)Zone 1: prograde metamorphism. Time sequence: fluid in,
fluid out, T
(b) Zone 2: prograde-retrograde
,,
metamorphism. Time sequence: fluid in, T
fluid out; (c) Zone 3: retrograde metamorphism.
Time sequence: ,T
fluid in, fluid out.
5) These different zones correspond to two difdiagram: Path Aferent paths on a T-X,,
clockwise path (first fluid in, then T increases);
Path B-anti-clockwise path (first T increases,
then fluid in).
6) In our analytical solution in which Tiol = 1,
only Path A and Zone 1 are present. Increasing the
value of M,,,and the water content of the crystallizing magma and decreasing Tid increases the
width of the other zones, but these can only follow
in the same order as stipulated above. An important result of our analytical solution is that for normal magmas, advective heat transport by the magmatic fluid is negligible.
In studies of fluid transport at depth i n the crust,
a major research problem is to identify the fluid
sources and define the pathways of fluid transport,
In the metamorphic environment, it is frequently
a difficult task to distinguish between magmatic
fluids released from crystallizing magmas, fluids
released by metamorphic reactions, or connate
pore fluids. In many cases, fluids from all of these
sources may be present. In our model, we have calculated the thermal effects and fluid fluxes exclusively attributable to crystallizing, degassing
magma bodies. Although there are relatively few
Journal of Geology
CRYSTALLIZATION O F MAGMAS
places where sufficiently detailed isotopic and petrological studies of the contact aureoles adjacent
to major intrusions have been made, we suggest
that such observations be compared with our
model predictions in order to establish whether
deep or mid-crustal fluid flow may be ascribed entirely to magmatic sources, or whether external
fluid sources need to be invoked. This should help
considerably to clarify the interpretation of fluid
flow in high-grade metamorphic rocks.
43
ACKNOWLEDGMENT
This work was partly supported by NSF Grant EAR
90-19256 to S. M. Wickham and a Royal Swedish
Academy of Sciences grant to Yuri Y. Podladchikov. We are grateful to Fred Anderson, Frank Richter, and Mark Peters for discussions and to James
Eason for typing the manuscript. Very helpful and
constructive reviews by Peter Nabelek and George
Bergantz are gratefully acknowledge.
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