 Springer-Verlag 1997
Contrib Mineral Petrol (1997) 126: 377 – 385
Harald Behrens · Marcus Nowak
The mechanisms of water diffusion in polymerized silicate melts
Received: 26 March 1996 / Accepted: 23 August 1996
Abstract Diffusion of water was experimentally investigated for melts of albitic (Ab) and quartz-orthoclasic
(Qz29Or71, in wt %) compositions with water contents in
the range of 0 to 8.5 wt % at temperatures of 1100 to
1200 °C and at pressures of 1.0 and 5.0 kbar. Apparent
chemical diffusion coefficients of water (Dwater) were
determined from concentration-distance profiles measured by FTIR microspectroscopy. Under the same P-T
condition and water content the diffusivity of water in
albitic, quartz-orthoclasic and haplogranitic (Qz28Ab38
Or34, Nowak and Behrens, this issue) melts is identical
within experimental error. Comparison to data published in literature indicates that anhydrous composition
only has little influence on the mobility of water in
polymerized melts but that the degree of polymerization
has a large effect. For instance, Dwater is almost identical
for haplogranitic and rhyolitic melts with 0.5–3.5 wt %
water at 850 °C but it is two orders of magnitude higher
in basaltic than in haplogranitic melts with 0.2–0.5 wt %
water at 1300 °C. Based on the new water diffusivity
data, recently published in situ near-infrared spectroscopic data (Nowak 1995; Nowak and Behrens 1995),
and viscosity data (Schulze et al. 1996) for hydrous
haplogranitic melts current models for water diffusion in
silicate melts are critically reviewed. The NIR spectroscopy has indicated isolated OH groups, pairs of OH
groups and H2O molecules as hydrous species in polymerized silicate melts. A significant contribution of isolated OH groups to the transport of water is excluded
for water contents above 10 ppm by comparison of
viscosity and water diffusion data and by inspection of
concentration profiles from trace water diffusion. Spec-
H. Behrens (&) · M. Nowak1
Institut für Mineralogie, Universität Hannover, Welfengarten 1,
D-30167 Hannover, Germany
1
Present address:
Bayerisches Geoinstitut, Universität Bayreuth,
D-95440 Bayreuth, Germany
Editorial responsibility: J. Hoefs
troscopic measurements have indicated that the interconversion of H2O molecules and OH pairs is relatively
fast in silicate glasses and melts even at low temperature
and it is inferred that this reaction is an active step for
migration of water. However, direct jumps of H2O
molecules from one cavity within the silicate network to
another one can not be excluded. Thus, we favour a
model in which water migrates by the interconversion
reaction and, possibly, small sequences of direct jumps
of H2O molecules. In this model, immobilization of
water results from dissociation of the OH pairs. Assuming that the frequency of the interconversion reaction is faster than that of diffusive jumps, OH pairs and
water molecules can be treated as a single diffusing
species having an effective diffusion coefficient
DOHpair;H2 O . The shape of curves of Dwater versus water
content implies that DOHpair;H2 O increases with water
content. The change from linear to exponential dependence of Dwater between 2 and 3 wt % water is attributed
to the influence of the dissociation reaction at low water
content and to the modification of the melt structure by
incorporation of OH groups.
Introduction
Diffusion of water in silicate glasses and melts becomes
increasingly important in geosciences, e.g. for understanding and modelling of processes during volcanic
eruptions. In the past twenty years several experimental
and theoretical attempts were made to quantify the
transport of water and to clarify the mechanisms of
water diffusion. A comprehensive review of the experimental techniques and basic results is given by Watson
(1994), and models for diffusion of water are summarized by Zhang et al. (1991a).
Zhang et al. (1991a) have demonstrated that combination of water speciation data and water diffusion data
can give new insights to the mechanisms of water diffusion. As shown recently, water species of the melt are
not quenchable and, thus, its concentrations cannot be
378
determined by measurements on glasses at room temperature but only by direct measurements on the melt at
high temperature and pressure (Nowak 1995; Nowak
and Behrens 1995; Shen and Keppler 1995). For the
haplogranite composition used to study water diffusion
(Nowak and Behrens, this issue) quantitative measurements of water species in the melt are available from in
situ near-infrared spectroscopy at temperatures up to
800 °C and pressure up to 3 kbar (Nowak 1995; Nowak
and Behrens 1995). Furthermore, the influence of water
on melt viscosity was investigated for the same haplogranitic composition by Schulze et al. (1996). Thus, in
the present paper we firstly can combine water diffusivity
data, water speciation data and viscosity data determined for the same melt composition to elucidate the
mechanisms of water diffusion. The possible application
of the results to other melt compositions (e.g. rhyolitic)
is tested by studying the effect of anhydrous composition
on water diffusivity in the haplogranite system and by
comparison to literature data. Models for water diffusion in polymerized melts are critically reviewed on the
basis of the new data and a preferred model for water
diffusion is presented.
Experimental methods
Experiments were performed using the diffusion couple technique
as described in detail by Nowak and Behrens (this issue). Starting
materials were dry and hydrous glasses of Ab (albite) and
Qz(quartz)29Or(orthoclase)71 (in wt %) anhydrous compositions.
Dry glasses were synthesized by Schott company in Mainz, Germany (Ab) and by F. Holtz in Orléans, France (Qz29Or71). Electron
microprobe analyses are given in Table 1. The same Ab composition [denoted as glass (I) in previous studies] was used for investigation of water solubility in melts (Behrens 1995) and of water
speciation in glasses (Behrens et al. 1996).
Hydrous glasses were prepared in internally heated pressure
vessels (IHPV) using Ar as pressure medium. In the diffusion experiments two cylinders with different water contents were encapsulated in a platinum tube with the contact area marked by
some grains of platinum powder. Runs were performed in a horizontally working IHPV. After the runs NIR (near-infrared) spectra
were measured along the diffusion direction of water using an IR
microscope. Concentration-distance profiles were calculated from
the spectra using for Ab the linear molar extinction coefficients and the density/water content relation published by Behrens et al.
(1996). For Qz29Or71 the values were determined experimentally
using five hydrous glasses with known water content ( =
Table 1 Electron microprobe analyses of dry glasses normalized to
100 wt %
Na2O
K2O
Al2O3
SiO2
Ab
Qz29Or71
11.96
–
18.83
69.19
–
17.76
19.23
63.02
1.69 l · mol)1 · cm)1 for the band at 4500 cm)1 due to OH groups
and = 1.89 l · mol)1 · cm)1 for the band at 5200 cm)1 due to H2O
molecules). Densities of hydrous Qz29Or71 glasses were calculated
with a precision better than 2 % relative using the density equation
for Qz28Ab38Or34 glasses given by Nowak and Behrens (this issue).
Effective diffusion coefficients of water (Dwater) were determined
from total water versus distance profiles using a modified Boltzmann-Matano analysis. The maximum uncertainty of the obtained
diffusion coefficients is estimated to be 25 % relative for both Ab
and Qz29Or71 samples.
Results
Experimental parameters and diffusion coefficients for
selected water contents are given in Table 2. Because of
the small temperature range in which experiments could
be performed without crystallization no attempt was
made to determine the temperature dependence and,
hence, the activation energy of water diffusion for these
melts.
The Dwater determined for albitic and quartz-orthoclasic compositions agree within experimental error with
corresponding values for haplogranitic compositions
(Fig. 1). An influence of the type of alkali, Na or K, on
water diffusion was not found. As observed for haplogranitic compositions, the dependence of Dwater on total
water content (Cwater) changes from linear to exponential between 2 and 3 wt % water.
Experiments with Ab melts at 1 and 5 kbar show the
same trend as observed for haplogranitic melts. At
higher pressure the diffusivity of water seems to be
slightly lower than at low pressure at least for high water
contents (Fig. 2). However, the small pressure range and
the number of experiments can not give unequivocal
proof of a pressure effect.
Table 2 Parameters and results of water diffusion experiments with Ab and Qz29Or71 melts. (Cwater water contents of both parts of the
starting diffusion couple, tn nominal run duration, te effective run duration considering heating and cooling time, MI Matano-interface)
No.
Cwater
[wt %]
T
[ °C]
P
tn
[kbar] [min]
te
[min]
Shift of Dwater [10–7cm2/s]
MI [mm]
0.5 wt % 1 wt % 1.5 wt % 2 wt % 3 wt % 4 wt % 5 wt % 6 wt %
AbD07
AbD06
AbD05
AbD10
AbD08
8.43/1.28
4.02/0.05
4.16/0.02
6.28/0.04
6.25/0.03
1100
1150
1150
1150
1200
5.0
1.0
5.0
5.0
5.0
30
30
30
60
30
33.7
33.7
33.7
63.7
33.7
0.156
0.026
0.081
0.172
0.168
–
0.57
0.37
0.76
0.61
–
1.19
0.61
1.12
1.07
–
1.74
0.89
1.60
1.46
0.95
2.47
1.26
2.01
1.88
1.57
4.56
3.05
3.36
3.00
2.38
–
–
5.82
5.22
3.73
–
–
12.63
11.20
6.43
–
–
–
–
Qz29Or71D01 6.89/0.26 1200
5.0
60
66.9
0.214
0.73
1.31
1.75
2.20
3.31
5.39
9.24
17.52
379
Fig. 1 Comparison of water diffusivity in haplogranitic (Qz28
Ab38Or34, labelled AOQ), albitic (Ab) and quartz-orthoclasic (Qz71
Or29) melts. Data for AOQ are from Nowak and Behrens (this issue).
Calculations for AOQ use Eq. (9) of Nowak and Behrens (this issue)
Fig. 2 Effect of pressure on water diffusivity in Ab melts
The effect of anhydrous composition on water diffusion
The experimental results on Ab, Qz29Or71 and Qz28Ab38
Or34 compositions suggest that water diffusivity in
haplogranitic melts is independent of anhydrous composition at least for feldspar-rich compositions. Furthermore, the good agreement of data for haplogranitic
(Nowak and Behrens, this issue) and for rhyolitic melts
(Shaw 1974; Karsten et al. 1982; Lapham et al. 1984)
implies that the results for the haplogranite system can
directly be applied to other polymerized silicate melt
systems (Fig. 3). Differences of the shape of Dwater versus. Cwater of the various data sets are attributed to the
Fig. 3 Comparison of water diffusion data for haplogranitic and
rhyolitic melts. The water diffusivity in rhyolitic melt with low water
content given by Jambon et al. (1992) is related to the average of
initial and equilibrium water content of the sample used in the
dehydration experiments. All other data refer to the water contents for
which the diffusion coefficients are calculated. Preliminary data from
hydration of obsidian by Jambon (1979) are in good agreement to the
data of Shaw (1974) but are not included in the plot because they can
not be related directly to the water content. Data for AOQ are from
Nowak and Behrens (this issue)
precision of the analytical techniques and to the evaluation procedure. It is worth noting that the curve of
Shaw (1974) was not based on concentration profiling
but on time dependent sorption of water in cylinders.
Nevertheless, this curve gives a good approximation to
the data obtained from diffusion profiles. Reinvestigation of the diffusion samples of Shaw (1974) by ion
probe profiling and iterative determination of diffusion
coefficients by Delaney and Karsten (1981) basically
confirm the results of Shaw (1974). The only significant
difference is that Shaw (1974) chose a linear function and
Delaney and Karsten (1981) an exponential one to describe the dependence of diffusivity on water content.
A direct comparison to results of Zhang et al. (1991a)
for rhyolitic glasses is not possible because these authors
evaluated individual diffusion coefficients of hydrous
species (OH and H2O) from profiles produced by dehydration experiments below the glass transition temperature. We have determined graphically chemical
diffusion coefficients of water from a concentration-distance profile (Run KS-D3, their Fig. 3) given by Zhang
et al. (1991a). The obtained value of Dwater is for 0.5 wt %
water 0.7 log units below the value calculated for haplogranitic composition using Eq. (7) of Nowak and
Behrens (this issue) (Fig. 4). As shown by Cockram et al.
(1969) and Haider and Roberts (1970) for several silicate
and aluminosilicate glasses with low water contents the
activation energy for water diffusion typically is higher
below than above the glass transition (note the change in
380
mechanisms do not fundamentally change from polymerized (e.g. rhyolitic) to weakly depolymerized (e.g.
andesitic) melt structures. However, in strongly depolymerized (e.g. basaltic) melts the diffusivity of water is
considerably higher than in polymerized melts and a
different diffusion mechanism seems to be operative. In
basaltic melts with 0.2 wt % water Dwater is two orders of
magnitude higher at 1300–1500 °C and 10 kbar (Zhang
and Stolper 1991) than extrapolated values for haplogranitic melts (Nowak and Behrens, this issue). Furthermore, it is worth noting that trace water diffusion in
simple silicate melts also strongly increases with depolymerization of the melt (e.g. Scholze and Mulfinger
1959; Moulson and Roberts 1961; Haider and Roberts
1970). For instance, at 1200–1300 °C the diffusivity is
three orders of magnitude higher for Na2Si3O7 melts
(Scholze and Mulfinger 1959) than for SiO2 supercooled
melts (Moulson and Roberts 1961) (see Fig. 4).
Fig. 4 Water diffusion in selected melt compositions with low water
contents. Wt % in the plot are estimated averages of initial and
equilibrium water contents for Na2O · 3SiO2 (Scholze and Mulfinger
1959), SiO2 (Moulson and Roberts 1961), Ab (Haider and Roberts
1970) and rhyolite A (Jambon et al. 1992). For other compositions
(basalt, Zhang and Stolper 1991; haplogranite, Nowak and Behrens,
this issue; rhyolite B, recalculated from Zhang et al. 1991a) wt % refer
to the water content for which the diffusion coefficients are
determined. Data for the haplogranite composition (AOQ) with 0.2
and 0.02 wt % water were extrapolated from experimental data using
the linear relationship of diffusivity on water content. Note that
diffusivities are higher in depolymerized melts (Na2O · 3SiO2, basalt)
than in polymerized melts (haplogranite, rhyolite, SiO2, Ab) for given
water contents
slope for Ab at 690 °C in Fig. 4). Therefore, the deviation is attributed mainly to the extrapolation of our data
to low temperature, because Zhang et al. (1991a) performed the experiments below the glass transition.
For comparison to trace water diffusion (the term
‘‘trace water diffusion’’ is used for water contents up to
several hundred ppm by weight which are typically for
sorption and desorption experiments with glasses and
melts at ambient pressure) in other polymerized melts we
have linearly extrapolated the data of haplogranitic
melts down to very low water contents of 0.02 wt %. The
extrapolated values for the haplogranitic composition
are in good agreement with experimental data for
rhyolite (Jambon et al. 1992, revised data from Jambon
1979), Ab (Haider and Roberts 1970) and SiO2 (Moulson and Roberts 1961) considering that only average
diffusion coefficients were determined in the latter studies (Fig. 4). The insensibility of Dwater to anhydrous
composition implies that the bond strength of tetrahedral cations (Al or Si) to oxygen and the distribution
of sizes of tetrahedral rings in the melt structure have
little influence on water diffusion and that the diffusion
mechanisms are the same for various polymerized melts.
Stanton et al. (1988) noted that the diffusivity of
water is similar in melts ranging from rhyolitic to andesitic compositions. This implies that the diffusion
Mechanisms of water diffusion in polymerized melts
At least five different diffusion mechanisms may contribute to the transport of water in silicate melts: (1) coupling of fluxes of H+ and OH); (2) parallel diffusion of
OH) and alkali cations or interdiffusion of H+ (or
H3O+) and alkali cations; (3) diffusion of OH groups
bound to tetrahedral cations; (4) direct jumps of water
molecules from one site into a neighbouring site without
interaction with the silicate framework; (5) reaction of
water molecules with bridging oxygens by formation of
OH group pairs. After recombination water molecules
may be expelled on different sites adjacent to the reformed oxygen bridge.
These five possible mechanisms are discussed in the
following sections.
1. Mechanisms involving diffusion of H+ and OH)
Coupled motion of H+ and OH) has been inferred as a
predominant mechanism for diffusion of water in silicate
glasses and aluminosilicate glasses with alkali/Al » 1
(Scholze and Mulfinger 1959; Haider and Roberts 1970).
The depolymerized glasses have high concentrations of
singly bonded oxygens which can react with diffusing
protons to form OH groups. This leads to a local charge
imbalance which facilitates the attack of a diffusing OH)
on one of the associated (Al, Si)-O-(Al, Si) bonds
(Haider and Roberts 1970). Because the transport of the
chemical component water always is determined by the
slowest step of the diffusion and reaction process this
mechanism implies that diffusion is controlled by
movement of OH) or breaking of (Al, Si)-O-(Al, Si)
bonds whereas protons can migrate rapidly within the
silicate structure.
Based on high temperature IR spectroscopy Keppler
and Bagdassarov (1993) suggested a highly mobile type
of proton at 1300 °C in a rhyolitic melt containing about
381
300 ppm water. For haplogranitc melts at 800 °C we
found identical diffusion coefficients of protons (measured by H/D interdiffusion) and water (measured by
chemical diffusion) (Nowak and Behrens, this issue).
This implies that self diffusion of protons in haplogranitic melts is limited by the diffusion of water under
these conditions. Thus, if protons really have high mobility their movement must locally be restricted or in
other words rapid jumps of the protons occur only
within cavities of the structure and not between cavities.
It is emphasized that the field strength of a bare proton
prohibits it existing in a condensed phase (Ernsberger
1980) and, therefore, a rapid motion of protons only is
expected in the presence of singly bonded oxygens.
Consequently, it is inferred that a mechanism involving
H+ and OH) is less important for polymerized (e.g.
rhyolitic) melts but could be more important for basaltic
melts.
2. Mechanisms involving alkali diffusion
Interdiffusion of alkali and protons or H3O+ is known to
be a fundamental process during reaction of water with
glasses (see, e.g. Doremus 1979; Scholze 1988, 1989).
This process as well as the coupled motion of alkali and
OH) should produce gradients of alkali along the diffusion profile. Such gradients are not observed for
haplogranitic (Nowak and Behrens, this issue) and
rhyolitic (e.g. Lapham et al. 1984; Zhang et al. 1991a)
melts and thus we conclude that these mechanisms do
not significantly contribute to the transport of water in
polymerized silicate melts under the conditions studied.
Mechanisms involving alkali diffusion may be important
for magma/fluid interaction if alkalis are dissolved in the
fluid or for magma mixing if water diffusion is coupled
to chemical exchange fluxes.
3. Mechanisms involving OH diffusion
Experimental data on the diffusivity of OH groups
bonded to tetrahedral cations (DOH) are not available.
As a raw approximation we have estimated DOH from
viscosity measurements using the Eyring equation:
D
ˆ
kT
gk
1
… †
where k is the Boltzmann constant, T the absolute temperature, g the viscosity and k the diffusive jump distance,
Fig. 5 Scheme of diffusion of
OH groups in silica glass
for which the average distance of the tetrahedral cations
(3.6 Å) in haplogranitic melts is used. The approximate
validity of the Eyring equation has been demonstrated
for oxygen diffusion in a polymerized (jadeite) melt
(Shimizu and Kushiro 1984). Watson and Baker (1991)
noted for several melt compositions that the Eyring
equation can predict the diffusivities of non-alkalies
during interdiffusion in the range 10)11–10)7 cm2/s within
a factor of 3. The application of the Eyring equation is
probably limited to polymerized melts, because data for
more depolymerized melts such as diopside are not well
reproduced by Eq. (1) (Shimizu and Kushiro 1984). This
implies that the breaking of Si-O and Al-O bonds is a
fundamental feature of viscous flow, and diffusion of
oxygen and network formers in polymerized melts as
noted by Rubie et al. (1993).
Diffusion of isolated OH groups in polymerized melts
is assumed to be similar to that of bridging oxygens. A
possible mechanism relating both viscous flow and OH
diffusion is the exchange of bonds between adjacent
tetrahedra. This process is illustrated in Fig. 5 for hydrous silica glass. The movement of an OH group results
in formation of new ring connections and, thus, in local
displacement of the tetrahedra in the melt.
The OH diffusivities estimated by the Eyring relation
from viscosity data for AOQ (albite-orthoclase-quartz)
melts at 800 °C given by Schulze et al. (1996) are 4
orders of magnitude below the measured water diffusivities (Fig. 6). This strongly supports that OH groups
do not contribute to the transport of water under the
conditions of our experiments. From the diffusivity and
viscosity data for haplogranitic melts we can exclude a
significant contribution of OH to the effective diffusion
of water down to 1 wt % water (DOH = 3.6 · 10)11 cm2/s;
Dwater = 1.26 · 10)7 cm2/s, both for 1 wt % water at
1200 °C and 5 kbar). The good agreement of extrapolated diffusivities for haplogranitic melts with experimental data for other polymerized melts (Fig. 4) implies
that the diffusion mechanism does not change at least for
water contents down to several hundred ppm. Trace
water diffusion studies show that this is probably also
the case for much lower water contents. Concentrationdistance profiles from sorption of tritiated water in silica
glass (Drury et al. 1962; Roberts and Roberts 1964;
Burn and Roberts 1970) and aluminosilicate glass
(Haider and Roberts 1970) slightly deviate from error
function shape indicating that in the range of water
contents covered by the experiments Dwater is slightly
increasing with water content. This conclusion is sup-
382
Fig. 6 Comparison of water diffusion (Nowak and Behrens, this
issue) and chemical diffusion in hydrous haplogranitic melts. Chemical
diffusivities of haplogranite melts are calculated from viscosity data of
Schulze et al. (1996) using the Eyring equation. Dotted lines are
extrapolations from the experimental range. Note the same slope of
both curves
ported by higher diffusion coefficients determined for
removal of water from silica glass compared to entry of
water (Moulson and Roberts 1961). Doremus (1995)
noted that the diffusion profiles in silica glass measured
by Roberts and coworkers can be fitted well by a diffusion coefficient varying linearly with water content.
Combining the trace water diffusion data with our results it is inferred that a linear relationship between
Dwater and Cwater exists over a large range of water
contents from about 10 ppm to ca. 3 wt % in polymerized melts. We conclude that a contribution of isolated OH groups to the transport of the chemical
component water only is expected for water contents
below 10 ppm. This is in contrast to the assumption of
Chekhmir et al. (1988) that OH is the dominant diffusing
species below 0.4 wt % water.
4, 5. Mechanism involving diffusion of H2O molecules
Diffusion of H2O molecules has been inferred as the
fundamental process for the transport of water in silicate
glasses and melts by several authors (e.g. Drury et al.
1962; Roberts and Roberts 1966; Doremus 1969, 1995;
Tomozawa 1985; Wasserburg 1988; Zhang et al. 1991
a,b). The basic difference of the discussed models is the
role of the reaction of H2O molecules with bridging
oxygen. Mechanism 4 denoted as the diffusion-reaction
mechanism by Doremus (1969, 1995) assumes that H2O
molecules move through the silicate network by direct
jumps from one cavity to another one without reaction
with oxygen of the silicate network. The H2O molecules
that are occasionally trapped as hydroxyl groups are
considered as immobile. This model is favoured for in-
stance by Wasserburg (1988) and Zhang et al. (1991a,b).
In contrast, mechanism 5 further denoted as the interconversion-diffusion mechanism assumes that the reaction
of H2O molecules with bridging oxygen is an active step
during movement of water. After re-formation of the
oxygen bridge the H2O molecule can be expelled on a
site different from the starting site and, thus, an effective
jump of the H2O molecule occurs. Such a mechanism is
preferred for instance by Roberts and Roberts (1966)
and Tomozawa (1985).
The diffusion-reaction mechanism was examined
from a theoretical point of view by Wasserburg (1988),
Zhang et al. (1991b) and Doremus (1995). At temperatures above the glass transition structural relaxation of
the melt is assumed to be fast enough to establish local
equilibrium of water species during diffusion. Assuming
that the reaction of H2O molecules with bridging oxygens results in an immobilization it follows that for low
water contents the effective diffusion coefficient is proportional to the concentration of water. As noted above,
such a dependence was experimentally found for trace
water diffusion in silica glass and for diffusion of water
up to 3 wt % in haplogranitic and quartz-feldspathic
melts. At temperatures far below the glass transition
structural relaxation is too slow to achieve equilibrium
of hydrous species. A model for diffusion of water under
such non-equilibrium condition was developed and
successfully tested for silica glass by Doremus (1995).
Zhang et al. (1991a) analysed dehydration experiments on rhyolite glasses by considering the diffusion of
both H2O molecules and OH groups and the reaction
between them. From fits of water diffusion profiles by a
two species model Zhang et al. (1991a) concluded that
DOH is negligible for the transport of water. In the
context of their model Dwater simply is determined by the
diffusivity of water molecules DH2 O and by the ratio of
H2O/OH. The authors concluded that DH2 O is independent of total water concentration in the range 0.2
to 1.7 wt %. However, a basic assumption for the evaluation of the experiments by Zhang et al. (1991a) is that
the water speciation is not modified during quench
which may not strictly be valid according to recent in
situ near-infrared spectroscopic measurements (Nowak
1995; Nowak and Behrens 1995; Shen and Keppler
1995). In order to test the applicability of the model of
Zhang et al. (1991a,b) for our diffusion conditions we
calculated Dwater for 850 °C and compared the calculated data with our experimental data (Fig. 7). For the
same temperature Zhang et al. (1991a) found a good fit
for their model to the data from diffusion couple experiments of Lapham et al. (1984). Assuming local
equilibrium of OH and H2O effective diffusion coefficients of water can be calculated from the model using
Dwater
ˆ
DH2 O
dXH2 O
dXwater
2
… †
where XH2 O and Xwater are the mole fractions of water
molecules and total water calculated on a one-oxygen
basis. Assuming an ideal mixture of H2O, OH and O and
383
dence of Dwater on total water that DH2 O depends on
water content and, hence, on the structure of the melt. It
is inferred that the model of Zhang et al. (1991a) may be
useful to analyse water diffusion below the glass transition but can not be extrapolated to higher temperatures
and water concentrations.
Previous models for water diffusion in silicate glasses
and melts only consider one type of OH group and one
type of H2O molecule (e.g. Chekhmir et al. 1988; Zhang
et al. 1991a,b; Doremus 1995). However, near-infrared
spectroscopy indicates at least two different types of OH
groups in silicate glasses (e.g. Langer and Flörke 1979;
Zhang et al. 1995; Nowak and Behrens 1995). For a
more detailed view on the mechanism of water diffusion
it is useful to specify the reaction between water molecule and bridging oxygen and to distinguish OH singletons and OH pairs. In the first step of the reaction a
pair of OH groups is formed:
Fig. 7 Comparison of experimental water diffusion data for
haplogranitic melts (run AOQD002 of Nowak and Behrens, this
issue) with calculations using the model of Zhang et al. (1991a). Note
the different shape of experimental and calculated curves
a concentration independent equilibrium constant K1 for
the reaction (H2O + O = 2 OH) XH2 O can be calculated
from Eq. (5.2) of Silver and Stolper (1985)
XH2 O
ˆ
Xwater
ÿ
K1
K1 ÿ 4
"
2
1
1
ÿ
2
4
ÿ
K1 ÿ 4 ÿ
Xwater
K1
ÿ
2
Xwater
1
1=2 #
3
… †
Combining the derivative of Eq. (3) with Eq. (2) gives
2
Dwater
ˆ
ÿ1
6
DH2 O 41 ÿ h
1
4
ÿ
K1 ÿ 4
K1
2
ÿ
ÿ
Xwater
Xwater
3
1
ÿ
2
Xwater
7
1i1=2 5
4
… †
In the calculation we use DH2 O = 7.47 · 10)8 cm2/s extrapolated from data for rhyolite melts of Zhang et al.
(1991a) and K1 = 0.986 extrapolated from in situ NIR
spectroscopic measurements on haplogranitic melts of
Nowak and Behrens (1995). The Dwater values calculated
by the model of Zhang et al. (1991a) are significantly
lower than experimental ones, especially at high water
content (Fig. 7). This can simply be explained by lower
contents of molecular H2O in the melts at 850 °C than in
glasses investigated at room temperature because the
DH2 O values of Zhang et al. (1991a) are based on NIR
measurements at room temperature. However, it is obvious that the shapes of the experimental and calculated
curves are different. The second derivative is positive for
the experimental data but it is negative for the calculated
curve. This fundamental difference can be explained
neither by possible different DH2 O for rhyolitic or haplogranitic melts (compare Fig. 4) nor by the use of in situ
measured speciation data instead of speciation data of
quenched glasses. Thus, assuming OH and H2O to be
the only hydrous species we conclude from the depen-
H2 O
‡
O
OH 1 1 1 HOŠ
ˆ ‰
5
… †
The notation [OH···HO] implies an interaction of both
OH groups and a thermodynamic stability of the associate. In the second step the pair can dissociate to
form OH singletons:
‰
OH 1 1 1 HOŠ
ˆ
2 OH
6
… †
The dissociation of OH pairs is very slow because it is
controlled by diffusion of OH singletons. The time scale
of this reaction is several minutes or more at 400–600 °C
for rhyolitic glasses with 0.5–2.3 wt % water as inferred
by kinetic experiments of Zhang et al. (1995).
The time sale of interconversion of water species is
much smaller than that of dissociation of OH pairs as
indicated by several experimental observations. The
NIR and MIR heating stage experiments on hydrous
silicate glasses of various anhydrous compositions performed at 1 atmosphere (Nowak 1995; Schmidt et al.
1995, 1996) show that the water speciation can not be
frozen even with cooling rates of 300 K/s. Rapid and
reversible changes in water speciation are already observed at temperatures of several hundred degrees below
the glass transition. A rapid interconversion of water
species also is inferred by NMR experiments on D2O–
containing rhyolite by Eckert et al. (1987). They suggest
that protons might be exchanging between H2O molecules and OH groups on a time scale faster than 10)6 s
above 100 °C. Condensation of SiOH groups and hydrolysis of Si-O-Si bonds are well known to take place
during corrosion of glass at temperatures below 100 °C
(Scholze 1989). Direct evidence for a condensation reaction at 55 °C during corrosion of potassium-calciumsilicate glass is given by 29Si-MAS-NMR (Böhm et al.
1995). These examples demonstrate that interconversion
of water species can be highly dynamic even at very low
temperature. On the other hand, no exchange of oxygen
between diffusing H218O and the network was observed
in short time sorption experiments with silica glass at
temperatures between 100 and 200 °C (Helmich and
Rauch 1993). However, this is not necessarily in con-
384
tradiction with the assumption of rapid interconversion
reaction. An exchange of oxygen only can be expected if
the formed OH groups are equivalent for the condensation reaction. Due to the rigidity of the network in
the glass at low temperature this is probably not the case
and the same oxygen preferentially re-forms the bridge
between the tetrahedral cations.
Because of the high interconversion rate of OH pairs
and H2O molecules we infer that reaction (5) is a basic
step during movement of water within polymerized silicate melts and glasses. However, a contribution of
direct jumps of water molecules without interaction to
the framework can not completely be ruled out. A distinction of both diffusion mechanisms by considering
the activation volume for water diffusion in haplogranitic melts is not possible. The positive activation
volume can be explained by an expansion of aluminosilicate rings if H2O diffuses as a rigid molecule as well
as by an enlargement of the structure during reaction of
H2O molecules and (Al, Si)-O-(Al, Si) bonds, e.g. by
formation of transient 5-coordinated tetrahedral cations. A critical argument of Doremus (1969) against a
diffusion mechanism which involves breaking of silicon
oxygen bonds is that the activation energy should be at
least as high as the bond energy of about 380 kJ/mol.
However, the activation energy corresponds to the difference in energy of the stable states and the transition
state. It can be considerably lower than the bond energy
if, for instance, the process is catalysed by protons.
In conclusion we favour an interconversion-diffusion
model in which water mainly migrates by the interconversion reaction but small sequences of direct jumps
are possible. In this model the mobile species are water
molecules as well as OH pairs. With the assumption that
the interconversion of both species is faster than the
diffusive jump or, in other words, a water molecule reacts several times with the same oxygen bridge before it
attacks another one, in first approximation both species
can be considered as a single moving species (H2O,OH
pair). Thus, effective diffusion of water in the melt can
be described as the sum of contributions from
(H2O,OHpair) and OH singletons
Dwater
ˆ
DH2 O; OH pair
dXH2 O; OH pair
dXwater
‡
DOH single
dXOH single
dXwater
7
… †
Quantitative modelling of water diffusion by Eq. (7) is
complicated because the concentrations of OH pairs and
OH singletons can not be determined directly from
spectroscopic measurements. From our experimental
results we conclude that the first term of Eq. (7) dominates for water contents > 100 ppm. The second term is
expected to be dominant only at very low water contents
(« 10 ppm). The convex shape of Dwater versus Cwater
implies that DH2 O;OHpair increases with increasing water
content as discussed before for the model of Zhang et al.
(1991a).
The change from linear to exponential dependence of
Dwater on Cwater between 2 and 3 wt % observed for Ab,
Qz29Or71 and Qz28Ab38Or34 compositions can result
from the dissociation reaction (6) and from modification
of the melt structure by incorporation of OH groups.
The OH pairs becomes immobile by splitting into two
OH singletons. With decreasing water content the mean
distance between OH singletons becomes larger and,
therefore, longer times are required for bringing OH
singletons together to form a mobile OH pair. From this
point of view, the change in the dependence of Dwater on
Cwater is related to a critical distance of OH groups for
which the dissociation reaction does not significantly
affect the transport of water. This critical distance is
estimated to be 6 Å assuming 3 wt % of water dissolved
as randomly distributed OH groups.
However, the diffusion-reaction problem is too complicated for a quantitative modelling of the diffusion
data. As shown by Zhang et al. (1995) for the interconversion reaction a solution of this problem only is
possible for relatively simple approaches, for instance,
ignoring different subspecies of OH and H2O and assuming concentration independent mobilities of the
species. Such approaches are not reasonable for the
water diffusion process. The viscosity of haplogranitic
melts changes by several orders of magnitude for water
contents ranging from 0 to 1 wt % (Dingwell et al. 1996;
Schulze et al. 1996) which indicates strong variation of
the melt structure and of the mobility of OH singletons
in this concentration range. Thus, the time in which
water is immobile is not only determined by the distance
of OH singletons but also by the melt structure. Moreover, it is emphasized that the same slope (0.25 log units
per wt % water) is observed for water diffusion and viscous flow in haplogranitic melts at high water contents
although the mechanisms of both processes are different.
This implies that the exponential dependence of Dwater
on water content is at least in part the result of modification of the melt structure by incorporation of OH
groups.
Concluding remarks
On the basis of the water diffusivity data, in situ determination of hydrous species by NIR spectroscopy
and viscosity data we conclude that OH pairs and water
molecules are the hydrous species which control the
transport of water in polymerized melts. It is inferred
that the reversible reaction H2O + O = OH···HO is a
basic step for movement of water but small sequences of
direct jumps of H2O molecules also may contribute to
migration of water. The proposed diffusion mechanism
implies that only a part of the OH groups (OH singletons) is immobile on the time scale of water diffusion but
the other (OH pairs) is directly involved in the transport
of water. From viscosity data and trace water diffusion
data it is estimated that OH singletons only may influence the transport of water at water contents « 10 ppm.
The change in water concentration dependence of Dwater
at about 3 wt % is attributed to the kinetics of dissociation and re-formation of OH pairs and to changes
of the melt structure.
385
Acknowledgment We thank K. Roselieb and M. Carroll for stimulating comments on the manuscript. This work was supported
by the SFB173 of the DFG.
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