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Earth and Planetary Science Le

Viscosity of peridotite liquid

D.B. Dingwell*, P. Courtial, D. Giordano, A.R.L. Nichols

Earth and Environmental Sciences, University of Munich, Theresienstr. 41/III, 80333 Munich, Germany

Received 28 October 2003; received in revised form 28 February 2004; accepted 20 July 2004

Editor: B. Wood

Abstract

The Newtonian viscosity of molten peridotite has been determined experimentally at superliquidus and supercooled

conditions. The high-temperature determinations were obtained using a concentric cylinder technique employing constant high-

speed deformation. The low-temperature determinations have been obtained from the analysis of the glass transition in scanning

calorimetric traces and conversion via published shift factors into viscosity data. These latter measurements were made possible

by the experimental synthesis of peridotite glass using a splat-quenching device.

Despite having an extremely low viscosity near its liquidus temperature (10�1 Pa s), peridotite exhibits a very high glass

transition temperature, 1006 to 1018 K (depending on scanning rates), at which viscosities of 1010.13 to 1010.73Pa s were

calculated. These data show that the viscosity of molten peridotite has an extremely non-Arrhenian temperature dependence and

allow its viscosity to be predicted at the even higher temperatures expected to exist where molten peridotite is or was present in

the mantle.

D 2004 Elsevier B.V. All rights reserved.

Keywords: peridotite; glass transition; viscosity; calorimetry; mantle

1. Introduction

The existence of molten peridotite in the early

history of the Earth has long been the subject of debate

and conjecture. The observation of extrusive Archaean

peridotitic komatiites [1,2] led to the experimental

investigation of such lavas yielding estimates of the

0012-821X/$ - see front matter D 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.epsl.2004.07.017

* Corresponding author. Tel.: +49 89 2180 4250; fax: +49 89

2180 4176.

E-mail address: Dingwell@lmu.de (D.B. Dingwell).

extrusion temperature of 1650 (F20) 8C [3]. Interest in

the physical properties stems from a number of sources

but was refocussed in the wake of the proposal for the

existence of a bmagma oceanQ in the evolution of the

moon, the Earth and other terrestrial planets (see

review in [4]).

The debate surrounding the Earth’s evolution

accompanied by a largely molten magma is increas-

ingly reliant on the results of models for physico–

chemical processes in such a scenario. The applica-

tion of phase equilibrium, buoyancy, thermodynamic

and fluid dynamic constraints on the behavior of

tters 226 (2004) 127–138

D.B. Dingwell et al. / Earth and Planetary Science Letters 226 (2004) 127–138128

molten mantle all rely on adequate characterisation of

the properties of molten peridotite (e.g., [5–7]). To

date, the primary emphasis in the physical character-

isation of molten peridotite has been the determi-

nation of a PVT equation of state with contributions

from shock-wave and buoyancy studies (e.g., [8–

11]). Determinations of other melt properties are

largely lacking to date, although data for analogue

liquids, such as forsterite exist (e.g., [12,13]). The

viscosity, in particular, has received too little atten-

tion. Techniques of high-pressure in situ falling

sphere viscometry (see review in [14]), as well as

the inversion of self-diffusivity data for Si and O

[15,16], are being applied increasingly to basic to

ultrabasic liquids, and it can be expected that results

will be available for molten peridotite in the near

future. It is hoped that those studies may also benefit

from the constraining of the activation energy of

viscous flow provided here.

Normally, in situ high-pressure falling sphere

viscometry contains the natural advantage that the

extrapolation of the results is not required. However,

for peridotite, such measurements are faced with the

challenge of obtaining accurate estimation of the

temperature dependence of viscosity, where the

temperature dependence at the very high temper-

atures of the in situ experiments is very low, and the

range of viscosity investigated very small. The low-

pressure experiments here are a useful complement

to high-pressure studies for the purpose of determin-

ing the absolute pressure dependence of the melt

viscosity and for the determination of the temper-

ature dependence of the viscosity. The synthesis of

peridotite glass in this study, the first of which we

are aware, allows the incorporation of viscosity

determinations at very low temperatures. Those data,

together with determinations near the liquidus,

deliver very precise constraints on the 1-atm temper-

ature dependence of the viscosity of a molten

peridotite facilitating extrapolation to much higher

temperatures.

2. Initial high-temperature synthesis

The sample investigated in this study was obtained

from a hand specimen of peridotite from Balmuccia,

Italy, which was kindly provided by Prof. Hans

Berckhemer. A cylinder was cored from the sample,

and 120 g was placed in a Pt crucible that was loaded

into a 1-atm NaberthermR box furnace operating at

1650 8C in air. At these conditions, the sample was

completely molten. The sample was removed from

the box furnace and quenched by dipping the lower

surface of the crucible into water. This process took

approximately 1–2 min. The quenched products

appeared to be homogeneous and had crystallized

to a very fine-grained matrix. The quenched material

was broken from the synthesis crucible using a

hammer, and the resulting chips were reloaded into

an Pt80Rh20 crucible for use in concentric cylinder

viscometry. This crucible has a height of 50 mm, an

inner diameter of 25 mm and a wall thickness of 1

mm. Prior to concentric cylinder viscometry, this

crucible was filled with molten peridotite by succes-

sive loading and fusion of chips in the box furnace at

1675 8C. This molten sample was then removed from

the box furnace and transferred to a viscometry

furnace held at a temperature of 1600 8C.

3. Concentric cylinder viscometric methods

The super-liquidus viscosity determinations were

performed using a concentric cylinder viscometer

and methods previously described in detail by [17].

Viscosities were obtained from measurements of

torque, which were performed with a Pt80Rh20spindle rotating at 80 rpm and were an average of

the recordings per second over a total time span of

30 s. The first measurement was at 1600 8C, and

further measurements followed at 10 8C intervals

separated by cooling stages at 5 8C/min. The system

was held at each temperature for 1 h prior to the

measurement. The usual temperature steps of 25–50

8C in such measurements were reduced to 10 8C in

anticipation of a relatively high liquidus and resultant

crystallisation. A large increase in the apparent

viscosity at 1570, 1560 and 1550 8C, combined

with very noisy readings, led us to infer that some

crystallisation had occurred at these temperatures. As

a result, these measurements were rejected from

further analysis. Due to the low range torque

readings (b10% full scale) obtained here, we

estimate larger uncertainties (F0.075 log units) than

normal.

Fig. 1. Schematic diagram of the high-temperature vertical tube

furnace and splat quencher (for more details, see text).

D.B. Dingwell et al. / Earth and Planetary Science Letters 226 (2004) 127–138 129

4. Glass synthesis via splat quenching

On conclusion of high-temperature viscometry

measurements, the sample was returned to 1600 8C,enabling the spindle to be removed. Then, the

viscometry crucible containing the molten sample

was transferred from the viscometry furnace to the

box furnace, which was at 1650 8C. After a 30-min

dwell to ensure complete melting, the sample was

removed from the furnace and rapidly poured onto a

steel plate. As already noted by Green [18], this

composition is particularly difficult to quench to a

glass. The resulting patty-shaped sample appeared to

be predominantly composed of fine-grained crystals.

Small 1- to 2-mm chips were broken from the patty

with a hammer and hung in Pt loops suspended

from a long Pt wire. These loops were lowered by

hand into the high-temperature viscometry furnace

until the chip fused into a bead of liquid held in the

loop by surface tension. These samples were then

removed from the viscometry furnace to cool and

were placed aside to be used in the splat-quenching

device.

To obtain data in the supercooled temperature,

range glassy starting materials are often required [19].

To generate glassy peridotite samples, the so-called

bsplat quenchQ technique was employed (Fig. 1). This

involved positioning a high-temperature vertical tube

furnace above a splat-quenching device. The furnace

consists of ZrO2 insulation surrounding Superkanthal

(MoSi2) heating elements. A four-bore alumina rod

was fixed externally above the furnace, with two of

the bores serving to guide a Type B thermocouple and

the other two serving as conduits for a pair of 1-mm Pt

wires. These two wires were used to suspend a thin Pt

wire, an alumina ring and a Pt loop. The sample

resided within the Pt loop as a wetted meniscus, as

described above. This standard geometry prevents the

Pt loop holding the sample from adhering to the

suspending wires during burn-off. The quench was

initiated by burning off the thin Pt wire via the

application of an electrical current to the 1-mm Pt

wires.

The splat quencher consists of a set of copper

cylinders. They rest in their retracted state with their

active cylindrical opposing ends separated by a few

millimeters. This forms a space through which bodies

as small as the samples on Pt loops may pass. The

copper cylinders are housed within coils of wire that

act as electromagnets when a current is applied. The

sphere of liquid falls through the space between the

retracted copper cylinders. The role of the copper

cylinders is to accelerate towards each other in a

reproducible manner to catch the liquid. Their

acceleration is generated by the electromagnetic wire

coils, whose electromagnetism is triggered by a

photoelectric device located above the cylinders,

below the furnace and aimed in the line of the falling

body. The timing of the entire device is tuned on the

basis of a trial-and-error calibration using falling

bodies.

The rapid collision of the two copper cylinders

traps the spherical bead and deforms it into a disk-like

plate whose thickness and diameter are essentially

Table 1

Mean composition, from 10 analyses, of the glass synthesised using

the splat quench technique (Fig. 2). The glass is peridotitic in

composition and homogenous. This is used to calculate the

compositional parameters shown and in the calculations that depend

on composition

(wt.%) r Normalised

(wt.%)

(mol%)

SiO2 45.83 0.70 46.85 41.54

TiO2 0.18 0.03 0.18 0.12

Al2O3 4.87 0.08 4.98 2.60

Cr2O3 0.36 0.05

FeO 8.63 0.30 8.81 6.53

MgO 31.63 0.50 32.33 42.74

CaO 6.37 0.16 6.52 6.19

K2O 0.00 0.00 0.00 0.00

Na2O 0.32 0.02 0.33 0.28

Total 98.18 100.00 100.00

SM (mol%) 52.47

Excess oxides (mol%) 46.48

NBO/T 2.27

Measurements were performed on a Camebax SX50 microprobe a

the Department of Earth and Environmental Sciences, University of

Munich, with an accelerating voltage of 15 kV and a beam curren

of 15 nA. Synthetic oxides and natural minerals were used as

standards, and a matrix correction was performed, using the PAP

procedure (Pouchou and Pichoir 1984). The reproducibility for each

element was b1%. Cr2O3 is not considered in the calculation of the

D.B. Dingwell et al. / Earth and Planetary Science Letters 226 (2004) 127–138130

defined by the Pt loop. High cooling rates (estimated

to be on the order of 104 K/s [20]) can be achieved

using this device. This is because of the high

conductivity of the copper, its large and intimate

contact surface with the sample and the deformation

of the sample to obtain a relatively high surface-to-

volume ratio of the sample.

The quenched peridotite samples obtained in this

study were investigated by optical microscopy and

electron microprobe. The samples are dominated by

an isotropic green glass, which is accompanied by

occasional opaque crystals in its interior and an

enhanced crystallinity along the contact between the

loop and the sample (Fig. 2). It is important to note

here, that although the samples have clearly suffered

some crystallisation during the quench, the crystal-

lisation is no more than a few percent by volume and

appears to be locally isochemical, in the sense that the

volume of preexisting melt has transformed locally

and isochemically into a finely crystalline aggregate

(see below).

Before characterising the melt properties, it is

essential that we confirm that the glassy fraction of the

quench products is homogeneous peridotite in com-

Fig. 2. Backscattered electron image of a typical product of splat

quenching. Microcrystalline clots are surrounded by homogeneous

glass. The mean composition of the glass (shown in Table 1) is

peridotitic and forms the basis of the compositional evaluation of

the results. Scale bar in bottom left of the image represents 200 Am.

compositional parameters.

t

t

position. To do this, loop samples were prepared as

polished mounts for electron microprobe analysis.

Analyses were performed along traverses, which ran

from the interior of the glassy portion of the quenched

samples up to the edge of the glassy region abutting

onto the microcrystalline regions (Fig. 2). The

analyses show that the glass is peridotitic in compo-

sition and is homogeneous (Table 1). There is no

detectable zonation of glass composition whatsoever.

The mean composition, shown in Table 1, is used in

the compositionally dependent calculations that fol-

low. The composition is similar to the primary mantle

estimate of McDonough and Sun [21], except for a

lower MgO content compensated by a higher CaO

content. The influences of Ca and Mg on silicate melt

viscosity are similar [22]. Thus, the glass is compa-

rable with the primitive mantle composition of [21].

The composition measured here is also very similar to

that of the Mt. Burges peridotite, for which phase

equilibrium data exist [18]. These provide a liquidus

temperature of 1605 8C, which is in excellent agree-

ment with that estimated (1603 8C) using the olivine-

Table 2

Viscosity and calorimetric determinations and calculations

T

(K)

Measured high-T

viscosity

(log Pa s)

Cooling /heating rates

(K/min)

Calorimetric

Tg values

(K)

Calculated low-T

viscositya

(log Pa s)

G&D 2003b

(log Pa s)

1006 5 1006 10.73 8.31

1013 8 1013 10.52 8.04

1013 10 1013 10.43 8.04

1017 15 1017 10.25 7.89

1018 20 1018 10.13 7.85

1866.94 �0.967 �1.15

1857.10 �0.943 �1.11

1847.25 �0.900 �1.06

a Viscosity data calculated using Eqs. (1) and (2) [33].b Data calculated using the Giordano and Dingwell [29] viscosity model.

D.B. Dingwell et al. / Earth and Planetary Science Letters 226 (2004) 127–138 131

melt partitioning method of Ford et al. [23] for this

composition. At the temperature conditions of the

high-temperature concentric cylinder viscometry in

this study, the peridotite might be slightly subliquidus.

From the experimental study of the Mt. Burges

samples, however, it is apparent that a maximum of

5–7 vol.% of olivine crystals would be present at the

lowest experimental temperature used here (Green,

personal communication). This amount of potential

crystallinity, for which we have no direct evidence

from the viscometry, would be expected to have a

very minor influence on the melt viscosity. This is

entirely consistent with our observations in this study.

Fig. 3. Viscosity of molten Balmuccia peridotite obtained using

concentric cylinder viscometry (lower left, main diagram) and

scanning calorimetric relaxation equivalence (upper right, main

diagram). The strongly non-Arrhenian behavior of this melt is

evident, but it can be fitted using the VFT equation (solid line, see

text for details). Viscosities range from 10�1 to 1011 Pa s. Insets

viscosity data shown in more detail.

5. Calorimetric methods

The initial investigation of the peridotite loop

samples indicated that, although the crystalline

regions were not likely to be an obstacle to micro-

penetration viscometry, the dimensions of the samples

would be. Instead, we used differential scanning

calorimetry to obtain glass transition temperatures

[24–27], for which we were able to derive the (low

temperature) viscosity (Eq. (1)) of the peridotite. A

series of calorimetric measurements were performed

on slices of splat-quenched glass using a differential

scanning calorimeter (Netzsch DSC 404 C Pegasus).

These followed the procedure in [28], except that the

peridotite was initially heated at 20 K/min, into the

supercooled liquid field, and then at rates of 20, 15,

10, 8 and 5 K/min after cooling at rates that matched

the subsequent heating rate.

6. Results and discussion

The results of the high-temperature concentric

cylinder viscometry are presented in Table 2 and Fig.

3 (lower right inset). The viscosity ranges from 0.108 to

0.126 Pa s in the restricted temperature range of 1873–

1853 K investigated here. These viscosities and the

temperature dependence of viscosity are both ex-

tremely low for silicate melts (see summary in [29,66]).

:

D.B. Dingwell et al. / Earth and Planetary Science Letters 226 (2004) 127–138132

The calorimetric scans of the quenched peridotite

glass are presented graphically in Fig. 4. They clearly

exhibit the typical features of all silicate glasses upon

heating in a scanning calorimeter (for review, see

[26]). The temperature-dependent segment of the

trace, at a low temperature, corresponds to the value

of the heat capacity of the peridotite glass. The peak in

the trace at a high temperature is a reflection of the

glass transition, where the exponentially falling value

of the melt viscosity with increasing temperature

results in melt relaxation at a temperature where the

intrinsic time scale of relaxation corresponding to the

heating rate approaches that of the viscous relaxation

time scale [14,27,30]. Above the peak, the heat

capacity falls to a value that corresponds to the

equilibrium value of the heat capacity for the liquid at

that temperature, in the supercooled state. In these

measurements, the time spent in the supercooled

liquid state has been kept to a minimum to preserve

and protect the supercooled peridotite liquid from

crystallisation in the relaxed state above the glass

transition. Nevertheless, an indication of the liquid

heat capacity value can be gained from Fig. 4. The

reproducibility of the heat capacity curves obtained is

a clear indication that no significant degradation of the

samples occurred. Such sample degradation is typi-

cally evident as noisy data traces, irreproducible heat

capacity values and drift of the peak temperature due

to the composition dependence of the glass transition

temperature. The bglassyQ heat capacity data for

peridotite do not correspond to pure glassy samples

due to the presence of a few percent of microcrystal-

Fig. 4. Calorimetric (DSC) scans of the quenched peridotite glass.

The heat capacity of the glass is evident at low temperatures. The

position of the glass transition peak is clear. The peak shifts

systematically with heating/cooling rate, as is expected from glass

transition theory. The heat capacity data for the glass agree well with

the model of [31].

line clots, as noted above (Fig. 2). Nevertheless, the

impact of such small microcrystalline clots on the

value of the bulk heat capacity of the sample is likely

to be relatively small. This is due to the similar heat

capacities to be expected for crystalline and glassy

materials of such low silica contents. In fact, interest-

ingly, the predicted value of the heat capacity of

peridotite glass, according to the model of Richet [31],

ranges from 0.991 to 1.006 J/g K at 500 K and 1.162

to 1.195 J/g K at 900 K, depending on the oxidation

state of iron (the lower values at each temperature are

calculated assuming that all the iron is Fe3+, gfw

59.009; the higher values are calculated assuming that

all the iron is Fe2+, gfw 53.271). These values are in

excellent agreement with the values determined in this

study, implying that the glass heat capacity model of

[31] can be extrapolated to ultrabasic compositions.

Using the peak in heat capacity in the glass

transition to define the glass transition temperature,

scanning rates from 5 to 20 K/min yield glass

transition temperatures from 1006 to 1018 K (Table

2). This is quite similar to the glass transition temper-

ature for forsterite obtained by Richet et al. [13] of

990F10 K. Knowledge of the scanning rate permits

the viscosity to be estimated at each glass transition

temperature [28,30,32,33]:

logg ¼ K � logjqj ð1Þ

where g is the viscosity (Pa s) at the glass transition

temperature, q is the heating or cooling rate (in K/s)

and K is a constant relating the two. The approxima-

tion of K as a constant has been examined in detail in

two separate studies [32,33] where ranges of glass

composition were compared. The most recent study

[33] investigated a wide range of melt compositions,

from basanite to rhyolite, and proposed a functional

dependence of the K factor on the mol% of the excess

oxides, a sort of depolymerisation index:

K ¼ 10:321� 0:175lnx ð2Þ

where x is the mol% of excess oxides (the value for

our peridotite composition is given in Table 1). We

obtain a K factor of 9.65 for the peridotite glass using

this equation. Fig. 5 illustrates the extrapolated

location of the K factor for the Balmuccia peridotite

with respect to the compositions investigated in [33].

Using this K factor in Eq. (1), the viscosities range

from 1010.13 to 1010.73 Pa s at the measured glass

Fig. 5. Derivation of the shift factor for the application of scanning

calorimetry to viscosity data. The line of best fit is calculated using

Eq. (2) [33]. The line has been extrapolated to the peridotite

composition (5), allowing its K factor (9.65) to be determined.

D.B. Dingwell et al. / Earth and Planetary Science Letters 226 (2004) 127–138 133

transition temperatures (Table 2 and Fig. 3, upper left

inset). The much greater dependence on temperature of

these viscosity data is reflected in their much higher

activation energy. The viscosities are 11.6 log units

higher than the values obtained in the super-liquidus

region.

In the body of Fig. 3, the high- and low-temper-

ature viscosity data are plotted together in an

Arrhenian diagram. The extreme deviation from

Arrhenian viscosity-temperature dependence is evi-

dent. This is one of the most non-Arrhenian temper-

ature dependencies of the viscosity of a silicate melt

observed to date. Nevertheless, the high- and low-

temperature viscosity data can be fitted to a single and

continuous temperature-dependent viscosity relation-

ship via the use of the Vogel–Fulcher–Tammann

(VFT; [34–37]) equation:

logg ¼ Aþ B

T � Cð3Þ

where A , B and C are constants, termed the

preexponential factor, the pseudoactivation energy

and the VFT temperature, respectively, and T is

temperature (K). This combined fit is also capable

of reproducing, within error, the activation energy

values obtained from taking the high- and low-

temperature data separately. Russell et al. [38]

postulated that the high-temperature viscosities of

silicate melts, represented by the preexponential factor

in Eq. (3), converge to a common value of �4.31

(F0.74). In Fig. 3, we report the best-fit curve (solid

line) obtained by using such a constraint (obtaining

B=3703; C=761.7). By extrapolating this equation to

even higher temperatures (above 2000 K), we fit the

forsterite viscosity data of Urbain [12] remarkably

well.

The chemical composition of the molten peridotite

investigated here places it outside the compositional

range of the calibration of all previous multicompo-

nent models of melt viscosity. Nevertheless, it is

interesting to compare the results with predictions of

preexisting models for the viscosity of multicompo-

nent silicate melts. The extremely non-Arrhenian

temperature dependence of the viscosity of molten

peridotite essentially precludes a reasonable compar-

ison with the earlier Arrhenian models of Bottinga and

Weill [39] and Shaw [40]. Fortunately, the situation

has changed recently with the development of new

non-Arrhenian models [29,41]. The Giordano and

Dingwell model [29] involves a fully multicomponent

non-Arrhenian approach. It has been calibrated with

melts as basic as basanite. The prediction of viscosity

temperature relationships using this model is based on

the casting of the composition into network formers

and network modifiers. Fig. 6 illustrates the log

viscosity versus the reciprocal temperature trend for

peridotite with respect to the multicomponent liquids

investigated in [29]. The inserts in Fig. 6 show the

isothermal viscosity calculated at three different

temperatures (800, 1100 and 1600 8C) using the (a)

SM and (b) NBO/T parameters of [29]. A comparison

between the relationship predicted by the model for

peridotite and the experimental data is presented in

Fig. 7. The comparison requires two extrapolations.

The first involves the shift factor, as described above.

The second involves the chemical composition, as the

peridotite investigated here lies well outside the

compositional range calibrated in the multicomponent

model of [29]. Fig. 7 shows that in the range 900 to

1600 8C, the viscosity calculated according to [29] is

very similar to those measured or calculated according

to Eq. (3), if A=�4.31, whereas at temperatures lower

than 900 8C, the discrepancy becomes significant.

Despite the enormous range of viscosity exhibited,

and the very large temperature range accessed, to

model the dynamics and petrogenesis of a largely

Fig. 7. Comparison of the measured and predicted (using the mode

of Giordano and Dingwell [29]) values of viscosity for molten

peridotite. This comparison represents a compositional extrapola-

tion of the derivation of the shift factor for scanning calorimetry and

an extrapolation outside the multicomponent space of the model

Nevertheless, the prediction of the model is acceptable in the

temperature range of 1600 to 900 8C [10,000/T(K) ~8.5]. Below

this temperature, it underestimates the viscosity significantly.

Fig. 6. Comparison of the measured viscosities of peridotite melt

with those of other multicomponent silicate melts. At the highest

temperatures, these are the lowest viscosities we have measured for

silicate melts to date. At the lowest temperatures, these are some of

the highest viscosities we have observed. Insets: calculated

isothermal viscosity at three different temperatures [800 8C (solid

line); 1100 8C (dotted line); 1600 8C (dashed line)] versus the SM

(top left) and the NBO/T parameters (bottom right), comparing the

Balmuccia peridotite (5) with the complete data sets investigated

from [29].

D.B. Dingwell et al. / Earth and Planetary Science Letters 226 (2004) 127–138134

molten mantle, the data must be extrapolated to the

higher temperatures expected to be relevant in

planetary mantles. Several factors facilitate this. First,

the combination of high- and low-temperature vis-

cosity data provides a better constraint for the

interpolation, and even for the extrapolation, in

temperature of the viscosity of a molten peridotite.

Second, the convergent nature of the Arrhenian

temperature scale at a high temperature [38] results

in the variation of viscosity, with temperature dimin-

ishing with increasing temperature. Finally, the

strongly non-Arrhenian nature of the temperature

dependence of the viscosity of molten peridotite

demonstrated here means that the extrapolation of

viscosity to higher temperatures is far less in

magnitude than even the diminishing variation pre-

dicted by the Arrhenian temperature scale. The

extrapolation of viscosity from our maximum exper-

imental determination at 1873 K to temperatures near

5000 K, anticipated on the basis of extrapolation of

experimental studies of phase stabilities to the core–

mantle boundary [42,43], results in a predicted

decrease to 10�3.5 Pa s. This value is near the

probable theoretical limit of 10�4.3 Pa s [38].

If we ask the following question: What further

factors might wield influences on the viscosity of

ultrabasic melts at the pressures and temperatures of

the core–mantle boundary, we are, with some modest

reasoning, able to rule out the significant influence of

the main candidates: pressure, oxidation state and

volatile content.

The influence of pressure on melt viscosity has

been investigated both at high and low viscosities.

The high-temperature studies were spearheaded in the

1970s by piston-cylinder-based falling sphere deter-

minations at low viscosities (see review in [44,45]).

The trends of pressure dependence with melt compo-

sition indicate that viscosity is provided by the glass

transition temperatures determined for a diopside

liquid by Rosenhauer et al. [46]. These indicate only

a slight increase in viscosity with a moderate pressure

increase. This has been subsequently confirmed in

low- [47] and high-viscosity [48] measurements in the

system albite–diopside. Further analysis of the pres-

sure dependence of viscosity of peridotite is clearly

l

.

D.B. Dingwell et al. / Earth and Planetary Science Letters 226 (2004) 127–138 135

required, and predictions of the viscosity of peridotite

at intermediate mantle temperatures should wait for

those data. Nevertheless, here, we make the predic-

tion that the viscosity of molten mantle at the

temperatures attending core–mantle interactions is

likely to be well described by the present data set.

This is because the theoretical and empirical con-

straints on the preexponential factor will force melts

of higher viscosity to have higher activation energies

and thus low viscosities at temperatures relevant to

the core–mantle boundary, comparable with those

extrapolated here.

The influence of volatiles on the viscosity of an

ultrabasic melt is difficult to quantify. However,

studies from low pressure on melts with a range of

silica contents indicate quite clearly that the effect of

water on melt viscosity decreases with decreasing

silica content, such that the viscosity of basaltic melts

are less sensitive to water content than that of silicic

melts [31,49,50]. It is expected that ultrabasic melts

are even less sensitive to water content than basaltic

melts are, but this should be investigated. A further

consideration is that there is a natural limit to the

amount of water that can actually reduce the viscosity

of ultrabasic melts.

The Balmuccia peridotite contains 8–9 wt.% iron.

In general, iron leads to low viscosities of silicate

melts [51]. We do not have an accurate determination

of the oxidation state. However, the general effects of

melt composition and temperature on the oxidation

state of iron, with iron being reduced by increasing

temperature, decreasing total iron content and low

alkali content, would lead to relatively reduced iron at

the high temperatures of synthesis employed here

[52,53]. The viscosity of iron-bearing silicate melts is,

in general, a function of the oxidation state of the iron

[17,54–57]. Nevertheless, the magnitude of the effect

of oxidation state on the viscosity of low viscosity

melts with moderate iron contents is expected to be

negligible, especially if they are relatively reduced

[58]. In high-viscosity melts, the situation may be

different, with significant variations in viscosity with

oxidation state having been observed [55,57]. This is

clearly a subject worthy of further investigation at low

temperature.

It is perhaps of interest to compare the relative

viscosities of a molten peridotite liquid with other

liquids that might be stable under mantle conditions.

Data do exist, some of it for high-pressure con-

ditions, for the viscosities of sulfide [58], carbonate

(e.g., [59]), oxide [54,60,61] and metallic liquids (see

review in [62]). All of these liquids fall into a class

whose viscosity remains lower than that of molten

peridotite at the high temperatures of this study.

However, the viscosity contrast is not of large

magnitude. The minimum viscosity of any liquid is

likely to be substantially higher than 10�4 Pa s due

to both theoretical (as discussed in [63]) and

empirically derived [38] constraints. The data for

nonsilicate liquids noted above lies within the range

of 10�2–10�3 Pa s. Therefore, the viscosity contrast

is no larger than a factor of 10 and probably much

less. This implied similarity in the viscosities of liquids

that potentially are or were coexisting immiscible

phases in the deep mantle or at the core–mantle

boundary means that fluid dynamic mixing of such

phases via forced convection should be very efficient

with a relatively even distribution of strain in both

liquid phases. In this manner, advective mixing of such

melts should serve to greatly enhance the rate of their

chemical exchange. On the other hand, in the absence

of strong convective forces, the separation of both

liquids, in the presence of an unmixing event, should

be facilitated greatly by the low viscosities of both

liquid phases.

Direct studies of the viscosity of ultrabasic melts

under pressure are fraught with experimental difficul-

ties related to the nonquenchability of the samples and

the small dimensions of samples accessible in very

high pressure solid media (multianvil or diamond cell)

experiments [64]. This led some researchers to derive

viscosity data indirectly from self-diffusivity data for

oxygen and silicon in melts, with the use of the

Stokes–Einstein or Eyring formulations [15]. Those

studies are performed at temperatures higher than

those here and provide activation energies for the melt

viscosity, which were calculated to be 267 kJ mol�1

[16].

Extrapolation to low temperatures is impossible

because of the extreme temperature dependence

exhibited by viscosity at these low temperatures.

Fortunately, however, the viscosity of molten peri-

dotite at such low temperatures is not relevant to any

common petrogenetic process. One potential excep-

tion to be provided were evidence to emerge for the

presence of ultramafic glasses of compositions similar

D.B. Dingwell et al. / Earth and Planetary Science Letters 226 (2004) 127–138136

to that investigated here, such as in ultramafic nodules

or in pseudotachylite associated with landslides. We

are not aware of the description of any such para-

genesis in the literature.

This first determination of the viscosity of liquid

peridotite also provides a temperature scaling for

kinetic studies of melt properties, such as diffusivity

measurements on ultrabasic liquids. As described in

detail by Dingwell [65], for melts of such low

viscosity as peridotite, near its liquidus, it is very

probable that the self-diffusivity of virtually all silicate

melt compositions will be subequal to the self-

diffusivity of Si, obtained using the Eyring relation.

For temperatures between 2000 and 5000 K, this

translates into diffusivities of 5�10�9 to 5�10�7 m2/s.

This provides a useful basis for interpreting the

kinetics and quenchability of chemical interactions

of molten peridotite with other phases.

7. Conclusion

The viscosity of molten peridotite is described by a

extremely non-Arrhenian temperature dependence.

Near liquidus temperatures, the viscosity is in the

order of 10�1 Pa s. In the extrapolation of peridotite

viscosity to core–mantle boundary conditions, the

primary uncertainty is likely provided by the temper-

ature dependence. The very low temperature depend-

ence of viscosity at superliquidus conditions obtained

from the fitting here indicates that the viscosity will

decrease two further log units to 10�3.5 Pa s at

putative temperatures of the core–mantle boundary

near 5000 8C.

Acknowledgements

Thanks are due to Kurt Klasinski and Georg

Hermannsdfrfer for the construction of the splat-

quench device and Thomas Fehr for the electron

microprobe analyses. A.N. was supported by EU

Volcano Dynamics Research Training Network

(HPRN-CT-2000-00060) during this work. We thank

Christian Liebske and Brent Poe for discussions, and

Pascal Richet and Kelly Russell for constructive

reviews.

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