Pressure dependence of T in Silicate Glasses from...

Pressure dependence of Tg in Sil icate Glasses from

Electrical Impedance Measurements

NIKOLAI S. BAGDASSAROV , JÉRÔME MAUMUS, BRENT POE§ , ANATOLY B. SLUTSKIY* , AND VADIM

K. BULATOV*

Institut für Meteorologie und Geophysik, Universität Frankfurt, Feldbergstraße 47, D-60323Frankfurt/Main, Germany

§Bayerisches Geoinstitut, Universität Bayreuth, Universitätsstraße 30, D-95447 Bayreuth, Germany

*Vernadsky Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences, Kosyguine str. 19,GSP-1, 117975 Moscow, Russia

Abstract

The effect of pressure as an external control parameter has been estimated on dielectric relaxation in alkaline (albite),

alkaline earth (anorthite) silicates and silica glasses having differing fragility index. The pressure dependence of the

glass transition temperature (Tg) in silicate glasses correlates with a pressure dependence of the shear viscosity, and,

thus, the measurements of pressure dependence of Tg provide an indirect information of the melt rheology under

pressure. Below Tg activation energy of electrical conductivity is less than that at T> Tg. The intersection point of two

Arrhenius dependencies of electrical conductivity as function of 1/T defines Tg. The electrical impedance

measurements has been performed in atmospheric furnace and in 3 types of high-pressure apparatus: piston-cylinder,

belt and multi-anvil presses. The measurements were conducted in the frequency range 100 kHz - 0.01 Hz using

parallel plate and concentric cylinder geometry of a cell . The measured glass transition temperature in anorthite varies

with pressure P (in GPa): Tg= 850°C + 5°/GPa ·P, in albite glass the pressure dependence on Tg = 685°C - 8°/GPa·P, in

HPG8 Tg = 777°C - 45°/GPa· P, and in sili ca glass Tg =1050°C + 17°/GPa·P. The slope of dTg/dP decreasing with the

pressure increase and the contrast between activation energies of the electrical conductivity below and above Tg is

smeared out. Dielectric relaxation times calculated from the imaginary component of the dielectric modulus are three

orders of magnitude smaller than structural relaxation times at Tg and becomes slower with pressure increase. The

activation energy of dielectric relaxation for sili ca glass above Tg is equal to the activation energy of the structural

relaxation. In albite glass this activation energy corresponds to the activation energy of the Na tracer diffusion. In

sodium bearing glasses Tg estimated from electrical conductivity is a “sodium ion mobilit y” Tg, corresponding to a

overlapped α and β-relaxation processes and therefore, shifted to lower temperatures. With the pressure increase the

activation energy of dielectric relaxation in anorthite increases having the activation volume of ca. 10±5cm³/mol, in

albite glass the activation volume is smaller and negative –2±1 cm³/mol.

Key word: glass transition, pressure, impedance spectroscopy, sili ca, albite, anorthite,

haplogranite

Bagdassarov et al. „Pressure dependence of Tg “ submitted to „Physics and Chemistry of Glasses“

2

Introdu ction: Glass transition and Viscosity vs. Pressure

The glass transition temperature Tg of silicates is a homologue temperature at which melts believed

to possess a viscosity c. 1012-13 Pa s and a relaxation time of shear stress c. 100 s [1]. Knowledge of

the glass transition temperature at high pressures provides an indirect information about the

pressure dependent rheology and effect of pressure on relaxation processes. This is of a special

interest in geosciences and in silicate melt physics, where the viscosity measurements at high

pressures and temperatures are technically difficult to carry out: in-situ rheological measurements

need in an implementation of X-ray radiography and synchrotron radiation technique [2].

The question of the pressure dependence of sil icate melt viscosity at high pressures plays a

key role in a prediction of magma accent to the Earth’s surface [3]. For decades earth scientists

have sought a general equation to model viscosity of magmatic sil icate melts as a function of

temperature, pressure and composition (e.g. [4-8]). In early viscosity models [4, 5] the Arrhenian

temperature dependence of viscosity

RT

EA a

T +=ηlog (1)

was suggested, where Ea is the activation energy of viscous flow, A is pre-exponential factor. Eq 1

exploits two parameters both of which depend on melt composition. Recent experimental results

demonstrate that Eq 1 is not adequate for most silicate melts over a wide temperature range [6, 7].

In recent years some new models of viscosity have been applied to silicate melts by the use of VFT

(Vogel-Fulcher-Tammann) equation instead of the Arrhenius type

oT TT

BA

−+=ηlog (2)

[7, 8] or on the basis of the WLF (Will iams-Landel-Ferry) equation

g

gTT TTB

TTAg −+

−−+=

)(loglog ηη (3),

[6]. In Eqs 1-3 ηT is the viscosity at temperature T, A, B, To are the empirical constants, Ea is the

apparent activation energy for viscous flow, ηTg is the viscosity at the glass transition temperature

Tg, and R = 8.314 J mol-1 K-1 is the universal gas constant. In contrast to the temperature


3

dependence, the pressure dependence of magmatic melt viscosity is poorly constrained. There have

been only a few attempts to generalise the viscosity dependence on pressure: (1) either by

introducing a pressure dependent activation energy in Eq 1 [5], or (2) by applying a WLF-type

equation and „correcting“ the glass transition temperature Tg for pressure

)(

)]([loglog ,1, PTTB

PTTA

g

gTTP g −+

−−+= ηη (4),

[6]. One unclear point in the latter approach concerns the type of glass transition temperature to be

used in Eq 3-4: rheological, calorimetric, dilatometric etc.?

A second unclear point is the dependence of Tg on cooling rate q, which has to be taken into

account by measurung Tg from different probing methods. What method of Tg estimation is relevant

to be used, cooling-heating temperature scans in a time domain or dynamic measurements in a

frequency domain? The general dependence of Tg as a function of cooling rate is as follows

2

ln

gTg RT

G

dT

qd ∆= (5),

where ∆G is the activation energy of a physical property used for detecting Tg [9, 10]. Thus, for

samples with differing thermal histories one may expect differing unrelaxed states of supercooled

melt at Tg and, thus, the uncertainty in viscosity estimations by applying Eq 3-4 may be large. In

any case, the essential part of the systematics between viscosity and pressure may be experimental

or theoretical estimations of a glass transition temperature as a function of pressure for samples

having the same q.

A general way to describe the pressure dependence of Tg(P) is to modify Eq 5 by correcting ∆G at

normal pressure for some pressure-volume effect

∆∆+⋅=

11 1)(

G

VPTPT gg

or

11

G

VT

dP

dTg

g

∆∆⋅= (6),


4

where ∆V is the activation volume of a physical property used to determine Tg and index 1 refers to

the normal pressure [11].

A different approach was suggested by considering the glass transition as a kind of second-order

phase transition. In this case, a Clayperon slope of Tg with pressure must obey

p

Tg

dP

dT

αβ

∆∆= (7),

and

P

pg

C

VT

dP

dT

∆∆⋅⋅

=α

(8),

where ∆βT is the jump of the isothermal compressibil ity, ∆αp stands for contrast of isobaric

expansivities, and ∆Cp is the difference in the isobaric heat capacity between liquid and glass [12-

15]. Combination of Eqs 7 and 8 (two Ehrenfest equations) provides a so-called Prigogine-Defay

ratio Π

12

=∆⋅⋅∆⋅∆

=Πpg

Tp

VT

C

αβ

(9).

A number of experimental works have been done on polymers, low temperature glass-formers,

silicates, etc. to test the validity of Eq 7-8 [12, 16-19]. Usually, the value of the PD-ratio is greater

than 1 (Π~ 2÷5). This violation has been explained due to a non-equili brium nature of the glass

transition [20] when one ‘ordering parameter’ does not adequately describe a phase transformation.

In some works this problem was solved by introducing an additional ‘ordering parameter’ to

generalise Ehrenfest equations for the case of the glass transition (e.g. [20; 21]).

In many works on glass transitions it has been demonstrated that the first Ehrenfest equation (Eq 7-

8) may be satisfied automatically by a proper calculation procedure of volume derivatives in

respect to pressure and temperature [13, 14]. In the derivation of the second Eherenfest equation the

free energy must be corrected to the effect of the configurational entropy - Te x Sconf , where Te >T

an effective temperature at which processes related to the configurational entropy are “thermalized”

[14]. In this way the corrected PD-ratio may be very close to 1 for some glass-formers.

Alternatively to the thermodynamic approach mentioned above, there is an attempt to describe the


5

pressure dependence of the glass transition by use of the VFT relation (Eq 2) and replacing

temperature by a pressure variable. If τ is the shear stress relaxation time, which relates to the

relaxed shear viscosity as τ ~ η/G (G is unrelaxed shear modulus), then

−

⋅=PP

B

oo expττ at T= const (10),

derived from a free-volume model (e.g. [22]). By analogy with temperature glass transition, the

glass transition pressure characterised by a pressure Pg, at which the relaxation time is 10² s and Po

is an ideal glass transition pressure at which the viscosity exponentially diverges. In some

isothermal experiments this behaviour of viscosity was observed [23-24]. On the basis of the

isothermal dielectric relaxation time measurements on supercooled strong liquids another

expression was suggested

−⋅⋅=

PP

PC

o

po exp,ττ at T= const (11),

[22]. In Eqs 10-11 Po is the pressure of an ideal glass transition (by analogy with To in Eq 2), τo,p

denotes the relaxation time at normal pressure 0.1 MPa. The general expression of relaxation time

(or viscosity) can be considered in this case in the form

−⋅+−

−⋅+⋅=)]([

)(exp

10

1

PPaTT

PPbBoττ (12),

where P1 is atmospheric pressure [25-26]. Eq 12 was derived from Eq 2 by introducing constants B

and To , which linearly depend on pressure. Eq 12 has been tested on specific heat spectroscopic

measurements (enthalpy relaxation) with unsatisfactory results for fragile glass-formers [25]. The

fail of the universal pressure-temperature superposition principle is explained by the fact that the

glass transition is sometimes considered as a simple volume-activated process ( ln τ ~1/Vf and Vf is

free volume). The free volume in this approach is believed to depend on pressure and temperature

in the same way through constant compressibility and thermal expansion coeff icient. This is not

true for many classes of glass-forming materials like organic glass-formers, polymers etc. Contrary

results were obtained for dielectric relaxation in epoxy resin, where relaxation times are suitably

described by the extended VFT-equation, Eq 12 [22]. Finally, to construct an expression for

viscosity of magmatic silicate melts according to Eq 12 we would require 5 fitting parameters


6

obtained from a large number of relaxation experiments at different pressures and temperatures.

According to Eq 4 we need only 3 fitting parameters and independent data on Tg(P).

Another important material parameter needed for characterisation of glass-formers is a fragil ity

index, which represents the extent of the liquid’s deviation from Arrhenian behaviour and can be

defined as follows

g

g

TT

gTTg

T

Td

d

TTd

dm

=

=

=

⋅=

)log(

)/(

ln

10ln

1 ητ(13),

(e.g. [27, 28]). From Eq 2 and 13 it follows that the fragil ity index m depends on Tg as

2)(10ln

1

og

g

TT

ATm

−⋅

⋅= (14),

where To <Tg. If Eq 3 is used for the viscosity model, then

B

TAm

g⋅⋅=

10ln

1(14‘).

The behavior of m under pressure is unknown. According to Eq 14 the positive dependence of Tg on

pressure will result in decreasing m (denominator is a stronger function of Tg than nominator), and,

therefore, a liquid under pressure becomes stronger, which was observed in dielectric relaxation

experiments with epoxy resin [22]. If dTg/dP is negative, then m increases with pressure and a

liquid is more fragile. Contrary to conclusions obtained by using Eq 14, the viscosity model

described by Eq 3, predicts an increase or decrease of the fragil ity index m directly proportional to

the pressure dependence of Tg. This simply means, that Eq 3 and 14’ may only be applicable, if the

fragil ity parameter m is small , i.e. for almost strong liquids (Tg>> To).

The relaxation model of Avramov [29] based on the entropy description of the glass

transition predicts viscosity and structural relaxations as a function of pressure and temperature [30,

31]. The model assumes a Poisson distribution of the energy barrier energies of jump frequencies at

temperature of the glass transformation. The temperature and pressure dependence of relaxation

time and fragility index m in the frame of this phenomenological theory is as follows


7

î

+⋅

⋅⋅=

ba

g

P

P

T

T*0 1exp εττ (15),

where ε∼ 30.5 is the dimensionless activation energy at Tg, a=2⋅Cp/ (Z⋅R) plays a role of a fragile

parameter, Cp is the heat capacity, R is the gas constant, Z is the co-ordination number of the liquid

lattice, b= 2⋅κ0⋅Vm⋅P*/(Z⋅R) is the dimensionless constant, κo is a thermal expansion coeff icient, Vm

is the molar volume, P* is pressure constant estimated from an empirical relationship of the

thermal expansion coefficient upon pressure 1

*0 1−

+⋅=

P

Pκκ [31]. By introducing a pressure

dependence of the co-ordination number Z, Eq 15 demonstrates a good agreement with

experimental results on some polymers glass formers [32]. After substitution of Eq 15 in Eq 13 and

neglecting the pressure dependence of a, b and Cp, the fragility index m depends on pressure as

follows

⋅

+⋅

−⋅

+⋅

== gTT

g

b

dT

dP

PP

Tba

P

P

m)(10ln

1

*

*ε

(16).

Thus, depending on the sign of pressure dependence of the glass transition temperature, the

fragil ity index m may increase or decrease with pressure.

Fig. 1. Angell plot of samples used in the electrical conductivity study. The fragility index varies from 17 for SiO2 to 42 for anorthite[33]. Viscosity data for HPG8 glass are from [34].


8

The main purpose of this paper is to demonstrate possibilities and limitations of Tg and the pressure

derivative dTg/dP measurements obtained from dielectric spectroscopy at high pressures on sil icate

glasses having differing fragility index m.

Experiments

Description of Glass Samples

Compositions of sil icate glass samples that were used in impedance spectroscopy experiments are

listed in Table 1. In the present study we have compared the pressure dependence of 4 different

glasses. Their fragil ity index m calculated according to Eq 13 is shown in Fig. 1. Besides the

differing fragil ity index m and plots of viscosity vs. Tg/T in a spirit of the Angell classification (e. g.

[33], these glasses have very different structures and mechanisms of the electrical conductivity.

They can be classified as “ loose” (albite and haplo-granitic glasses), “tight” and “fragile”

(anorthite), and “tight” and “strong” (SiO2) conducting glasses [35], accordingly. The relationship

between dispersion, polarisation, glass transition and “mobile ion Tg“ of these glasses will be

discussed below.

Table 1. Composition of glass samples (in wt. %)

CaAl2Si2O8 NaAlSi3O8Oxide

Startingcomposition

Afterexperiment

Startingcomposition

Afterexperiment

HPG8

SiO2 42.63 42.62 67.76 67.53 77.9

Al2O3 36.86 37.14 19.58 21.37 11.89

Na2O 12.09 10.39 4.53

K2O 0.21 0.27 4.17

CaO 20.13 19.89 0.18 0.21

Sum: 99.62 99.65 99.82 99.77 98.48

Cooling rate, K/h 20 20 300

Microprobe analysis JEOL JXA – 8900RL, 20 kV, sample current 20nA, average of 3-5 points

The samples of anorthite and albite glass were taken from the collection of silicate glasses used by

Prof. M. Rosenhauer (Göttingen), the sample of HPG8 was given by Prof. D. Dingwell (München),


9

and the sample of SiO2 glass is a commercial glass Suprasil 300Ò (Heraeus, Germany), containing

< 1 ppm of OH-. The synthetic haplo-granitic composition (HPG8) corresponds to the eutectic

composition of SiO2-NaAlSi3O8-KAlSi3O8 at 0.1 GPa PH2O and models well a calcium-free granite

system. The interest of using the HPG8 sample in the present experiments is that many physical

properties of this glass have been measured in recent years [36]. The difference in physical

properties of this glass and albite may be explained as a mix-alkaline effect.

Estimation o f Tg

The electrical conductivity was used as a probing tool to detect Tg at high pressures. The impedance

measurements were performed on glass samples of anorthite (CaAl2Si2O8), albite (NaAlSi3O8),

SiO2, a haplo-granite (HPG8) composition and SiO2. To estimate a glass transition temperature at

pressure we have used a method of defining the activation energy of bulk electrical impedance (or

conductivity) in the glass transition temperature range. Despite a “decoupling” of the macroscopic

viscosity and its relaxation time from electrical conductivity relaxation, the kink in a slope of the

bulk electrical conductivity plotted as function of 1/T can be used as an indicator of Tg [37]. The

experiments have been done on silica, albite, anorthite and haplogranite glasses in an atmospheric

furnace at 0.1 MPa, in a piston-cylinder apparatus at pressures from 0.3 to 1 GPa, in a belt-

apparatus between 3 - 4.5 GPa, and in a multi-anvil press at 6 GPa.

Electrical impedance measurements were carried out using a Solartron 1260 Phase-Gain-

Analyser interfaced with a PC. The device permits a single sine drive and analysis of a system

under test over the frequency range 10µHz to 32 MHz. In the high-pressure experiments we applied

a 1 V sine signal over the frequency range 0.01 Hz to 100 kHz. Typically, the frequency scan

utilised logarithmic steps of 0.2 - 0.5. Signals at higher frequencies were affected by cable

impedance, and at lower frequency signals became too noisy. The estimation of the “bulk”

electrical conductivity from frequency scans provide a “true” dc conductivity data, and, therefore,

the artefact due to a mismatch of the probe frequency and material relaxation times is solved [37].

Measurements at 0.1 MPa

For measurements in the atmospheric furnace (Fig. 2), glass samples (diameter D = 6 mm, 8 mm

for silica glass) were drilled out of blocks of glass and cut in discs with thickness L = 1 - 1.5 mm.


10

Flat surfaces were polished with 0.05µ alumina powder under water up to optical quality of the

surface. The sample of sil ica glass was polished down to 0.5 mm thickness. Pt electrodes (thickness

= 5µ) were sputtered onto both flat surfaces of the glass discs (spot diameter 4.85 mm). On the

silica sample the electrodes were sputtered with a spot of 8 mm in diameter. The samples were

mounted in the inductive furnace (Heraeus , Hanau, Germany) with the heating element made of

Pt-wire. During the measurements samples were fixed between alumina rods (Frialit-Degussit

with flat electrodes made from Pt-foil. The elongation of the sample was measured with a

micrometer gauge having a precision of 0.001 mm. Electrical contact between Pt-foil and sputtered

electrodes was provided by a light flat spring acting axially through one of the alumina rods. The

heating rate of the furnace was approximately 20°/h. A type S thermocouple (Pt-PtRh10) touched

the Pt-foil which was in direct contact with the sample. Electrical impedance measurements were

done only once on each sample during heating cycle. The geometric factor of samples G= πD²/4L,

for albite, anorthite and HPG8 ranged from 1 to 1.3 cm, and for silica glass was approximately 10

cm. Temperature was measured and controlled using a Eurotherm 818P.

Fig. 2. Scheme of the electrical conductivity experiments at 0.1 MPa: 1 – Pt-wire furnace ROR Heraeus , 2 – Al2O3

ceramic rods AL23 Frialit-Degussit , 3 – insulating casting body; 4 – inlet for inert gas (Ar), 5 – flat spring, 6 –electrode contact of Pt-wire, 7 –thermocouple S-type Pt-PtRh, 8 – sample of glass, 9 – sputtered area of sample, 10 –tephlon guiding plug, 11 – Pt-folio cemented to the surface of Al2O3 rods, 12 – inner Al2O3 tube, 13 – elongationgauge.


11

Measurements in piston cylinder apparatus

For the moderate pressure experiments (0.3-1 GPa) we used a conventional piston-cylinder

apparatus with an end load. The measurements of the electrical impedance were performed at

pressures up to 1 GPa and temperatures up to 1200°C. The press (max. load ca. 220 tonnes)

consists of 2 independent hydraulic cylinders: the first provides an end-load and the second moves

the piston at the sample assembly. The diameter of the high-pressure autoclave is ½” (Danfoss ,

Denmark). The inner part of a high-pressure cell is shown in Fig. 3. The pressure calibration of the

cell was determined using some standard point materials: at room temperature the transformations

Bi I-II- III at 2.56 GPa and 2.7 GPa [38] were used; at high temperature, melting curves of NaCl

and CsCl [39] and the α−β transition in LiNaSO4 [40] were used as standard points. Melting points

of NaCl and CsCl as a function of pressure up to 2.5 GPa has been determined in-situ by electrical

conductivity measurements. At a melting point the observed drop in the electrical impedance at 1

kHz was ca. 2 orders of magnitude. The pressure calibration is believed to be within an accuracy of

± 0.03 GPa. The temperature gradient in the cell has been estimated on dummy samples of pressed

Al2O3 powder by monitoring three separate thermocouples. We estimate a radial temperature

gradient of ca. 1°/mm, and a vertical temperature gradient of ca. 2°/mm in the temperature range up

to 900°C.

A cell for electrical impedance measurements in the piston cylinder utilised a coaxial cylindrical

capacitor with a geometric factor of 7-8 cm filled with the sample under test. The exact geometric

factor of the cell was evaluated independently from calibration measurements on NaCl solutions

(0.01M - 3 M) at 22°C and atmospheric pressure. For these purposes, a cylindrical gap between

two Pt-electrodes (made of two Pt-tube 0.1 mm in thickness with outer diameters 2.2 and 4 mm)

has been filled with a NaCl-solution of a known molar concentration. The measured conductivity of

NaCl-solutions was compared with table values [41]. The difference between the calculated

geometric factor of a cylindrical capacitor

=

d

D

LG

ln2π (17),

and the measured geometric factor was about 25%, where D is the diameter of an outer electrode, d


12

is the diameter of an inner electrode, L is the length of the cylinder. Measurements of the geometric

factor of the cell after high-pressure experiments revealed that due to the cell deformation under

pressure L increases by ~3-4%, D increases by 1-2%, and d remains constant. Overall , these

variations of the cell dimensions did not affect the results of Tg or dielectric relaxation

measurements.

During impedance measurements in the piston-cylinder, the mass of press was isolated from the

ground of the Solartron 1260. Wires from the Pt-thermocouple and the mass of the high-pressure

autoclave were used to connect the measuring device and the cell electrodes. Before doing the

high-pressure experiments a measuring cell was calibrated for short-circuit and open-circuit

impedances over the frequency range 1 MHz - 0.01 Hz. A typical AC-resistance of the cell to a

short connection was 0.4 Ω. These calibrations have been taken into account in the final

calculations of the electrical impedance as a function of frequency. At high pressure and

temperature the measurements of the electrical impedance were conducted without an automatic

temperature control in order to reduce the electrical noise produced from the heater regulation.

During electrical conductivity measurements, the Eurotherm 818P controller was switched off,

and the temperature was regulated manually through a variable transformer.


13

Fig. 3. Principal scheme of a piston-cylinder cell used for electrical impedance measurements [40]: 1 - inner cylindricalPt-electrode; 2 - outer cylindrical Pt-electrode; 3 - sample; 4 - thermocouple S-type; 5 - Al2O3 -ceramic Alsint-99.7; 6 -graphite heater; 7 - CaF2 pressure transmitting medium; 8 - bornitride; 9 – boron nitride ceramic; 10 - hard metal core;11 - hard metal piston; 12 - plug of stainless steel; 13 - unfired pyrophyllit e; 14 - copper-ring; 15 - ground.

Experiments in belt apparatus and multianvil press

A detailed description of the belt-apparatus can be found elsewhere [42]. The construction of the

experimental cells for belt- (Fig. 4) and multi-anvil apparatus (Fig. 5) has the same principle used

by Xu et al. [43]. The geometry of the cell was a parallel-plate capacitor with a geometric factor

approximately 0.3 cm. Metallic electrodes were made from Mo-foil . The cell is protected from

electrical noise of the graphite (belt-apparatus) or LaCrO3 (multi-anvil press) heater by a grounded

shield of Mo-foil. During the electrical impedance measurements in both apparatus the automatic

temperature control was switched off . The temperature was regulated manually through a power


14

thyristor.

Fig. 4. Principal scheme of the electrical impedance measurement in belt apparatus (height 16 mm [42]). 1 – sample(diameter 2.1 mm, thickness 1 mm); 2 – electrical shield from Pt-foil; 3 – electrodes from Pt-foil ; 4 – Al2O3 ceramics;5 - thermocouple; 6 – pyrophyllit e 7 - graphite heater; 8 – boron nitride.

On each sample the electrical conductivity was measured only during a single heating cycle. In

both configurations, one of the thermocouple wires was connected to one electrode of the cell with

the AC-bridge. During the frequency scan the temperature indicator was disconnected from the

thermocouple in order to avoid coupling of the two devices at low frequencies.


15

Fig. 5. A. Principal scheme of electrical conductivity measurements in multi-anvil press [43]; B. The cross-section ofthe cell with anorthite glass sample after experiment. Thickness of the sample is 1 mm, diameter 2.1 mm.

For each glass sample, we measured the impedance over the frequency range 0.01 to 105 Hz. A

bulk electrical conductivity of glasses has been estimated from Argand plots generated from these

measurements or by fitting procedure of impedance spectra discussed below. Fig. 6 ill ustrate the

Argand plots measure for SiO2 at 0.5 GPa. The intersection of the arc with the Re(Z) axes defines

the bulk resistance of the sample. In some cases we compared these electrical conductivity

measurements with an electrical conductivity measured at a constant frequency 10³ Hz. Arrhenius

plots of the electrical measurements of the bulk resistance were measured covering a temperature

range both below and above the glass transition. The plots indicate a change in slope of the


16

conductivity curve at the glass temperature Tg. Measurements from the two methods (bulk

conductivity measurement from Argand plot and isofrequency measurement) provide the same Tg

for both albite and haplogranite glasses but result in significantly differing Tg values for both

anorthite and silica glasses. The reason for the difference between fixed frequency measurements

from a dc conductivity curve and systematically lower values of activation energies obtained from

this method has been discussed in [37].

Fig. 6. Argand diagram of Suprasil 300 sili ca glass. The bulk resistance is estimated from intersection Im(Z)-plot withthe Re(Z)-axes. The impedance arc represents a perfect semicircle. Thus, sili ca glass belongs to a class of “ tight” andstrong glassy conductors [35].

Results

Results of 0.1 MPa experiments

The results of electrical conductivity measurements at 0.1 MPa on albite, haplo-granitic, anorthite

and sil ica glasses are presented in Fig. 7. The bulk conductivity σdc has been estimated from

Argand-plots as an intersection of –Im(Z) graph with Re(Z)-axes [48]. On an Arrhenius type of

diagram the σdc data show two distinct slopes with differing activation energies:


17

−⋅=

RT

Eadcdc exp,0σσ (18).

The kink-point on plots ln(σdc) vs 1/T may be used as a characteristic temperature point to

discriminate glassy and liquid states (e.g. [44, 49]).

Electrical conductivities of Na-bearing glasses (haplogranite, albite) are 104 to 105 times higher

than those of anorthite and SiO2 glasses at comparable temperatures. This difference is attributed to

the easy dipole polarisation of sodium bearing glasses. High conductivity in these glasses

associated with mobil ity of Na+ ions which diffusivity is higher than other species. Above Tg the

rotation and translation movement of Na-cations around non-bridging oxygen atoms contribute to

the electrical conductivity of Na+-bearing glasses at high frequencies (> 10² Hz). The observed

kink of the slope in an Arrhenius plot ln|Z| vs. 1/T (where Z is the bulk impedance and T is the

absolute temperature) measured at high pressure for Na-bearing glasses is significantly lower (>

50°C) than Tg estimated from calorimetric and rheological measurements at 0.1 MPa [47, 50]. For

anorthite and silica glasses the observed kink in the slope is slightly lower than the calorimetric Tg

[51].

For glasses with alkalis, like Na+ in albite and haplo-granitic glass, the activation energy of σdc

depends on the mobil ity of Na+ in the structure. On cooling, at a certain temperature the mobility of

a translation motion of alkali ions is not correlated with the thermal structural modifications. In the

melt phase, structural elements may always be arranged in an energetically favourable network,

leaving minimum space for mobile charged species like Na+. Thus, the activation energy of σdc

above the glass transition temperature may be higher than below. Thus, for alkali -bearing systems

the temperature at which the kink point is observed in electrical conductivity measurementsis

different from the glass transition temperature estimated from rheological, heat capacity, or

dilatometric data (see Table 2). The measured activation energies of σdc for albite differs strongly at

T < 683°C (Ea= 55 kJ/mol), and at T > 683°C (Ea = 90 kJ/mol). For HPG8 at T < 774°C, Ea = 90

kJ/mol, whereas at T > 774°C, Ea= 120 kJ/mol. For anorthite at T < 844°C, Ea= 42 kJ/mol, and at T

> 744°C Ea= 80 kJ/mol. For silica glass at T < 1050°C, Ea = 100 kJ/mol, and at T > 1050°C Ea=

260 kJ/mol. In previous estimations of Ea from electrical measurements above and below Tg the

reported Ea values are significantly different: for albite Ea is ~57 and ~60 kJ/mol below and above

Tg, respectively [44]; for anorthite at 10 kHz Ea is 118 and 9.3 kJ/mol [49].


18

For silica glass containing OH-impurities the reported value of Ea for σdc at T < Tg is ~ 97 kJ/mol

[46]. Measurements on silica glass films at temperatures well below Tg (20-300°C) indicate a

much smaller activation energy for σdc ~39 kJ/mol [61] identified as being the hole-like polaron

hopping energy.

Fig. 7. Results of the bulk electrical resistance σdc measurements at 0.1 MPa. The kink in the slope of the Arreniusdependence of the bulk electrical conductivity indicates the glass transition temperature for mobile charge carriers(cations) in the structure of Ab, HPG and An glasses. In SiO2 glass the charge carriers are impurities, li ke OH-speciesand alkalis.

Structure of glasses and electrical cond uctivity at 0.1 MPa

The significant difference in electrical conductivity of sil ica and feldspar glasses might be

understood from their differing structures. The structure of feldspar and silica glasses has been

determined by X-ray radial distribution analysis [62]. Silica glass has a trydimite-like bonding

topology based on stuffed six-membered rings of SiO4 tetrahedra. Albite glass has the same

structure as silica with aluminium substituting for silicon in some of the tetrahedral sites. In order


19

to accommodate sodium cations such a structure has more „void spaces and interstices“ between

rings than SiO2 [62]. In anorthite the glass structure is based on four-membered rings of SiO4 and

AlO4 tetrahedra.

The mechanism of electrical conductivity in feldspar and silica glasses may be described as a

hopping of alkali-ion (Na+ in albite; Na+ and K+ in HPG8) or Ca2+ (in anorthite) from one non-

bridging oxygen site (NBO) to another. In sili ca glass the electrical conductivity mechanism is a

hopping process of OH- and alkalis impurities between defect [AlO4-M]0 tetrahedra (AlO4-alkalie

metal centres), as well as interconversion of charged NBO sites by hopping of polarons and

electrons [47, 63]. The relative effectiveness of a charge transport mechanism in glasses will

depend on average distance and value of energetic barriers between neighbouring NBO-sites or

defected SiO4-tetraedra (hopping activation energy). It will depend also on the concentration of

NBO-sites and impurities, and on the relative size of hopping electric charge carriers (Na+, K+, Ca2+

or OH-). The highest electrical conductivity was observed in albite glass rather than in HPG8. In

HPG8 glass Na-ions are partially substituted by larger K-ions, and the concentration of alkali i ons

is also smaller than in albite (Table 1). The least conductive of the feldspar glasses is anorthite. In

anorthite glass the structure is less open compared to albite. Average interatomic distances, which

might be correlated to hopping distances, are 1.63 and 1.66 Å for T-O, and 3.12 and 3.15 Å for T-T

for albite and anorthite, respectively [62]. In anorthite Al and Si are the most ordered in comparison

with other feldspar glasses, i.e. substitution of Al to Si is less random than in alkali

aluminosil icates. Sili ca glass, Suprasil 300, used in this study possesses the lowest electrical

conductivity due to much smaller concentration of defects, OH-groups and [AlO4-M]0 tetrahedra.

The lower values of σdc for SiO2 and anorthite glasses in comparison with albite and haplo-granitic

glasses is due to the greater distances between NBO sites and other Si+ and O- defects in the glass

structure. Effectively, the longer distance for hopping electrical carriers results in fewer percolation

paths for conduction [63].


20

Table 2 . Glass transition temperature Tg (° C) at 0.1 MPa obtained by different

methods

Glass Cooling

rate, K/h

Viscosity Calorimetry &

DTA

Volume expansion Electrical

conductivity

Light

scattering

SiO2 slow(?)

slow(?)

100

1150 [54] 1180 [52]

1090 [55]

1100 [53] 1050 [t. s.] 1100 [18]

1050 [56]

CaAl2Si2O6 20

20

slow (?)

12

40

600

845 [57]

878 [59]

875 [59]

836 [48]

813 [58]

820 [49]

844 [t. s.]

NaAlSi3O8 20

slow(?)

20

12

40

765 [57]

763 [58]

737 [59]

734 [59]

678-687 [49]

683 [t. s.]

HPG8 300 864 [H96] 856 [34]

800 [60]

774 [t. s.]

[t. s.] – this study

Experiments in p iston-cylinder

For high pressure experiments in piston-cylinder samples of glasses were ground into powder and

pressed into the gap between two coaxial electrodes (see Fig. 3). The bulk electrical conductivity

was measured with a temperature step ca. 10°, and plotted on an Argand diagram. The electrical

impedance data were collected in a scan with 0.17 log step of frequency between 105 and 10-1 Hz.

Imaginary component of Z for anorthite glass in the glass transition temperature range is shown in

Fig. 8. The data of bulk resistance of anorthite presented on an Arrhenius plot demonstrate a

significant change of the activation energy of Ζdc of anorthite glass below and above Tg (see Fig.9)

allowing the determination of Tg with an accuracy ±5°. In albite and HPG8 samples there is a

noticeable frequency dependence of Z at low frequencies (Fig. 10). Plotted in double log co-


21

ordinates, the frequency dependence of Z allows estimation of a maximum frequency, F, at which

the polarisation is observed at each temperature. The temperature dependence of the occurrence of

this frequency F differs above and below Tg, providing an alternative way to estimate the glass

transition temperature, as shown in Fig. 11. The albite glass possesses a rather high electrical

conductivity, and, therefore, may be classified as a “ loose” conductor. This class of conducting

glasses has also high polarisation (polarisation exponent is <<1) and a broad dispersion range of

dielectric properties [35]. The estimation of Tg in albite at 0.5 and 1 GPa are shown in Fig. 12.

Sili ca glass is probably a strong and “tight” glass having low electrical conductivity and

polarisation exponent close to 1. In the Argand diagram the bulk properties of SiO2 glass are

marked by a perfect semi-circle (Fig. 5). Estimation of Tg at 0.6 GPa in Suprasil 300 is shown in

Fig. 13. The difference in activation energies of σdc for SiO2 and albite are very small resulting in

an error of Tg ±10°C (Fig.12-13).

Dielectr ic Relaxation Peak in Anorthite at 0.3 GPa

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05

f, Hz

Z"p

, ohm

s

1013°C exp. 1013°C fitting (n =0.90)994°C 994°C (0.93)960°C 960°C (0.94)926°C 926°C (0.95)900°C 900°C (0.97)856°C 856°C (0.99)833°C 833°C (1)814°C 814°C (1)800°C 800°C (1)

dielectr ic relaxation peak

Fig. 8. The imaginary component of electrical impedance of anorthite at 0.3 GPa. The frequency scans have been fittedto Eq 19 for each temperature. With the temperature increase the dielectric relaxation peak shifts toward highfrequencies as indicated by the arrow. Numbers in brackets are estimated values of n. At T>Tg n becomes less than 1.

For albite, similar to the behavior of viscosity vs. pressure, Tg also decreases with increasing


22

pressure. The same effect of pressure is observed for the haplogranitic glass. For anorthite and

silica glasses Tg is an increasing function of pressure, as may be the viscosity of these melts.

The data of electrical impedance Im(Zp), where Zp = Zp’ – j·Z’’ p. for anorthite glass at 0.3 GPa are

shown in Fig. 8. The data can be fitted to a sum of two relaxation functions:

nld

ppe

pj

R

j

RZ

)(1)(1 ..

2

..

1

τωτω ⋅⋅++

⋅⋅+= (19),

where the first term corresponds to the electrode polarisation process and the second term stands

for dielectric losses in the sample [44]. The results of fitting are shown in Fig. 8. The temperature

dependence of d.l. determines the activation energy of the dielectric loss peak c.110 kJ/mol. The

parameter n in Eq 19 characterises the broadness of the dielectric loss peak in comparison with a

Debye peak (n=1). As it follows from Fig. 8 by crossing the glass transition temperature m

becomes less than 1 (n ~0.95). Thus, the anorthite is fragile and “tight” glassy conductor [35].

Fig. 9. Results of electrical resistance measurements in anorthite glass at 0.3 and 0.6 GPa. At 0.3 GPa measurements ata fixed frequency 10³ Hz are compared with bulk resistance obtained from Argand plots. Bulk resistance measurementsprovide higher values of Tg (solid arrows) in comparison with measurements at fixed frequency (dotted arrows).


23

Fig. 10. Method of estimation of the polarisation frequency F. The intersection point of two derivativesdlog(Z’ )/dlog(f) calculated at f>>1 Hz and f<<1 Hz, corresponds to “mobile Na-ion Tgs” .

Fig. 11. Estimations of glass transition temperature from electrical conductivity measurements in HPG8 glass at 0.3(solid arrow) and 0.6 GPa (dotted arrow) and fixed frequency 10³ Hz. At 0.6 GPa the data of polarisation frequency F(Hz) are plotted as a function of 1/T,K. The kink in the slope on the F-graph corresponds to the kink in the slope on theelectrical impedance curve.


24

Fig. 12. Glass transition temperature in albite glass under pressure 0.5 and 1 GPa. Arrows indicate Tg, the temperature

point at which the activation energy starts to increase.

Table 3. Results of Tg (° C) from electrical conductivity data

Pressure, GPa Albite Anorthite HPG8 Suprasil 300

0.1 MPa 683±2 844±3 774±3 1050±5

0.3 GPa 850±3 769±2

0.5 690±3

0.6 863±3 747±3 1060±5

1 675±5

3 662±5 863±5

4.5 871±3

6 635±10 880±10


25

Fig. 13. Estimation of the glass transition temperature in Suprasil 300 at 0.6 GPa from the change in the activation energy of thebulk resistance from impedance frequency scans and at fixed frequency 10³ Hz. The Argand plots are shown in Fig. 6.

Fig. 14. Results of Tg measurements in the belt apparatus on anorthite and albite glasses.


26

Experiments in Belt-Apparatus and Multi-Anvil Press

The results of electrical conductivity measurements carried out in the belt apparatus are shown in

Fig. 14. The change in the slope of the bulk conductivity below and above Tg is very small for

anorthite as a result of increasing pressure and pressure-dependent compressibil ity of the glass. In

albite glass the difference in the activation energy below and above Tg is significant. In reality, the

kink of the slope in the dependence log(σ) vs. 1/T,K for albite glass corresponds to “mobile Na+

Tgs” because of the presence of “ loose” species Na+ in the structure [35]. Data [64] for albite glass

at T<Tg and pressures 3-4 GPa are in a good agreement with this study. With the pressure increase

the free volume becomes so small that above and below Tg the difference of activation energy of

hopping process of electrically charged defects or defect-sites becomes rather small [64, 65].

Fig. 15. Estimation of glass transition temperature under 6 GPa in multi-anvil press in albite (A) and anorthite (B).

Only two experiments were done in the multi-anvil press on anorthite and albite glasses. Tg in both

samples was very hard to detect, but likely corresponds to a maximum decrease of the bulk

resistance on the Arhhenius plot (Fig 15).


27

Discussion of Results

Fig. 16 represents a pressure dependence of measured Tg from electrical impedance measurements

in four type of experimental facil ities: atmospheric furnace, piston-cylinder, belt- and multi-anvil

presses. Table 3 summarises the glass transition temperature estimated from electrical conductivity

measurements in this study. The absolute value of the derivative dTg/dP decreases with the pressure

increase, however, as noted above, Tg is diff icult to estimate at high pressures due to the pressure

dependent compressibility. To detect a correct change in glass temperature with pressure at P = 0.1

MPa perhaps only a short pressure interval is necessary (< 0.1 GPa). Theoretically, the distribution

of relaxation times will broaden at high pressure [66] and the transition occurs over a wider

temperature range. This would make it impossible to detect Tg at some critical pressure. In the

method which was used in this study, this happens when the activation energies of electrical

conductivity below and above Tg become equal.

Table 4 lists previous estimations of the pressure dependence of Tg. Only one experimental work

[67] reports results of in-situ high pressure dilatometric measurements of Tg on glass samples

having very fast cooling rates. dTg/dP measured for diopside glass is in a good agreement with

calculated glass transition slope from the second Ehrenfest equation [47, 68] and viscosity

measurements [6]. The direct measurements of dTg/dP on other glass formers indicate that the

pressure dependence of Tg may vary from 200- 150 K/GPa for B2O3 or lead [69] to 3.6 K/GPa for

metallic glasses [19].

Table 4. Pressure Dependence of Glass Transition Temperature of Some Sili cate

Glasses dTg/dP (K/GPa)

Cooling rate Diopside Albite Anorthite

[67] 22-28 °C/min 37±3 -25±10

[6] calculated from

viscosity

34±14 -70±8 -4±17

[68] 49±3 108±40

Calculated from Eq 6 and ∆V* and Ea ofdielectric relaxation in this study

20°/h -20±100 100±100

from electrical conductivity of this study 20°/h -8±3 +5±5


28

1 DTA measurements at pressures up to 0.7 GPa, ² indirect estimations using WLF-equation at 0.1 MPa and the

viscosity data at pressures up to 1.5 GPa (no cooling rate are reported), 3 calculated from thermodynamic data and Eq 8,

not cooling rate reported. In the original paper this result is swapped with the result of [67].

The rheological measurements of albite melt has been studied under pressure up to 7 [2, 3]. It was

established that the decrease of albite melt viscosity is about 0.38 log[Pa s]/GPa. Using temperature

dependence of viscosity of albite melt, the estimation of the glass transition temperature in albite

glass is c. 58 K/GPa.

The glass transition temperature in sil ica glass is the most poorly constrained. Tg may vary from

>1200°C according rheological data [70] and calorimetry [52]) to 1100-1050°C according to high-

temperature light scattering experiments [18, 56] depending on cooling rate, content of OH-, and

annealing temperature. The Prigogin-Defay ratio for SiO2 glass Π ~ 2·105 (!) is unexpectedly high,

indicating that a single relaxation parameter to describe a glassy state is not [18].

Fig. 16. Pressure dependence of the glass transition temperature from electrical impedance measurements. The slope ofthe pressure dependence of Tg at low pressures is higher than in the whole pressure range.

In order to estimate a dielectric relaxation time from measured electrical impedance data (Z* ) the

expressions for the complex modulus as follows were used [44]:


29

GZiMiM 0* εω=′′−′ (20),

where G is a geometric factor, ε0 is the dielectric constant of a free space, ω is angular frequency.

The dielectric relaxation times were calculated from frequency corresponding to a peak of M“

1)2( −= peakfπτ (21).

The alternative method to estimate a dielectric relaxation time is to make a fitting of the electrical

impedance spectrum to an equivalent electric circuit, for example Eq 19. As a result of fitting of the n, polarisation exponent [65].

Both methods Eqs 19 and 21 must give the same result, if the impedance data only in the frequency

band around dielectric relaxation peak are used. The activation energy of ! DC may depend on" # $ % # & ' " ( & # ) * " + # , ' $ # ' , - .

RC , where R resistivity and C capacity at a peak frequency, only

when R and C have a same activation energies. The tracer diffusion coeff icient is inversely/ 0 1 / 1 0 2 3 1 4 5 6 2 1 2 7 8 7 1 / / 3 4 9 2 3 : 8 ; < = > ? > @ A B C @ D ? ? E @ F D B G > H H > = > @ A I J D K H J A F L I J M L I A F D N > A F > I D M >D @ A C N D A C < K > K > B G E D I A F > H C > ? > @ A B C @ B > ? D O D A C < K P Q R S T U V T W X S Y X Z Z S Y [ V Z \ S T ] ^ [ V W \ S \ _ W ` W T Y ] \ aEinstein equation the activation energy of the ion trace diffusion ED and Ea of b c d DC must have the

same values.

Fig. 17. Temperature dependencies of dielectric vs. structural relaxation time for sili cate glasses. Dielectric relaxation


30

time has been estimated from impedance measurements by using Eq. 21. The structural relaxation time has beencalculated from shear viscosity data at 0.1 MPa by using the Maxwell relationship τ (s) = η (Pa s) /25 GPa. For SiO2

(solid bold line) the data are from [46]; for anorthite (solid thin line) the shear viscosity data are from [47, 71, 72]; foralbite (dashed line): 1 – shear viscosity from [71, 73], 2 – from [47, 68, 74]; for haplo-granitic glass HPG8 (dotted line)the viscosity data are from [34, 75].

The results of dielectric relaxation measurements for silicate glasses are presented in Fig. 17, and

the calculated activation energies of dielectric relaxation are listed in table 4 and compared with the

tracer diffusion activation energies. The values of dielectric relaxation times are much smaller than

structural or shear stress relaxation for about 4 orders of magnitude.

For SiO2 the activation energy of dielectric relaxation below Tg corresponds to tracer diffusion of Si

ca. 220 kJ/mol and secondary relaxation. Above the glass transition Ea of dielectric relaxation is

close to Ea of O-trace diffusion or structural relaxation ~515 kJ/mol [46].

For anorthite, the reported activation energies are for chemical diffusion ~ 230-460 kJ/mol and

significantly larger than measured Ea of dielectric relaxation 75 – 125 kJ/mol. The compiled data

on tracer diffusion in the CaO-Al2O3-SiO2 (40-20-40 wt. %) system indicate that in the glass (600-

900°C) Ea ~ 245 (for 18O) and ~ 255 (for 30Si) kJ/mol [76]. In the melt (1550-1350°C) Ea ~ 230 (for26Al), 290 (for 31Si) and ~ 380 (for 18O). In the supercooled liquid regime at temperatures just

above Tg the activation energy for 18O tracer diffusion may even be 900 kJ/mol. Smaller activation

energies for tracer diffusion of Ca, Al, Si, and O were obtained from molecular dynamic

simulations (MD), for anorthite glass (~ 110 kJ/mol), for melt (~ 180 kJ/mol) [77]. The activation

energy of dielectric relaxation in albite correlates well with the tracer diffusion of Na and differs

from those of Si, Al, and O. From MD simulations, the tracer diffusion coeff icients in [78] have

activation energies ~80 kJ/mol for Na, ~280 kJ/mol for Si, ~ 290 KJ/mol for O, and ~270 kJ/mol

for Al. In general, Ca2+ and Al3+ in sil icate melts have rather low mobilities and their presence in

the alkaline aluminosilicates may even impede the motion of alkali ions [79]. Thus, the estimated

Tg in albite glass from electrical impedance measurements characterises only a hopping and charge

separation relaxation process of sodium and not related to the structural relaxation. The same is

probably true for HPG8. The small scale hopping and charge separation in the electric field is an

effective mechanism of the electrical conductivity in sodium aluminosil icates [80]. The hopping of

sodium ions between positions adjacent to NBO- and Al-tetrahedra sites may explain the high

electrical conductivity of these glasses. The lower values of Tg estimated for albite and HPG8 from

electrical impedance measurements in comparison with calorimetric and dilatometric data are


31

indicators of the beginning of a “loose” mobil ity of Na+ in the structure at temperatures below

rheological or calorimetric Tg (Table 2). The idea of a “decoupling” character of dielectric

relaxation from mechanical spectroscopy relaxation in sodium-bearing glasses was discussed in

[81] and, subsequently, was compiled and adapted for geologists in [82]. Activation energies of

dielectric relaxation measured in this study are listed in Table 5 and compared with diffusion

activation energy of cations.

Table 5. Activation energy of diffusion and d ielectric relaxation D.R. (in kJ /mol)

Ions SiO2 CalAl2Si2O8 NaAlSi3O8 KAlSi3O8

OH- 83 (1100-500°C)1

Si 237 (1200-800)2

579 (1410-1113) 3

230 (845-765) 6 337 (1500-1100°C)8

O 48 (250°C)4

516 (2500-1250°C)5

247 (760-760) 6

Ca 327(1600-1350)7

Al 462 (1600-1350)7 425 (1500-1100°C)8

Na 56 (800-350)9 79 (800-350) 9

K 99.5 (1000-350) 9 63 (1000-350)9

D.R.10

this

study.

Eε

222 (0.1 MPa, <Tg)

515 (0.1 MPa >Tg)

226 (0.6 MPa)

74 (0.1 MPa)

111 (0.3 GPa)

138 (4.5 GPa)

43 (0.1 MPa, <Tg)

66 (0.1 MPa, >Tg)

65 (1 GPa)

64 (0.1 MPa)11

98 (0.1 MPa, HPG8)

40 (0.1MPa) 11

1 effective OH diffusion [83], 2 effective SiOSi diffusion [83], 3 tracer diffusion 30Si [84], 4 18O diffusion in sili ca glass

[85], 5 estimated from viscosity measurements and Eyring equation [86], 6 tracer diffusion of 18O and 30Si in CaAlSiO4.5

[84], 7 chemical diffusion of CaO/MgO and Al2O3 between diopside-anorthite compositions [87], 8 self-diffusion of Si

and tracer diffusion Al /Ga [88], 9 tracer diffusion of 24Na and 42K [89], 10Eε is the activation energy of dielectric

relaxation (D.R.) measured in this study, 11 calculated from electrical impedance data [49].


32

Fig. 18. Dielectric relaxation time of anorthite glass as a function of pressure. ∆V* is the activation volume calculatedat 800°C according to Eq 22.

The pressure increase results in slowing dielectric relaxation time. This may best be explained by a

continuous diminishment of open paths and mobili ty of alkaline ions, increasing the time for defect

diffusion. The pressure dependence of dielectric relaxation in anorthite is plotted in Fig. 18.The

activation volume of τ for anorthite glass, calculated as follows,

P

EV a

∂∂

=∆ * (22),

is about 10 ± 5 cm³/mol. For albite glass the estimated activation volume is about 0 (-2 ± 1

cm³/mol, Table 5). For comparison, MD simulations [78] of the tracer diffusion in albite provides

for Na an activation volume ~3 cm³/mol, ~ -4.5 cm³/mol for Al, ~ -6 cm³/mol for Si, and ~ -5

cm³/mol for O. From the negative pressure dependence of viscosity the calculated activation

volume of the shear viscosity in albite melt at 1900-2000 K and in pressure range 2.6-5.3 GPa is -

5.4 cm³ mol-1 [2]. It should be noted here that the experimental error of the data in Fig. 18 is rather

large, the data were collected in three different apparatus (atmospheric pressure furnace, piston-

cylinder and belt apparatus), each with different sample geometries.


33

Table 6. Prigogine-Defay ratio and pressure dependence of glass transition

temperature.

e f g h i j h k l m g n o oAnorthite SiO2 Albite HPG8 Orthoclase

p q r s t -5 K-1 2.3 [58]

1.9 [47]

3.0 [91]

0.135 [53]

10.3 [90]

1.1 [17]

0.76 [58]

3.3 [91]

1.7 [36] 0.8 [58]

2.4 [92]

u v w10-11 Pa-1 2.5-2 [93]

1.92[95]

5.7 [K86]

6.3 [96]

4-3 [94]

2.12 [95]

3.73 [93]

2.12 [95]

4.5-43 [93]

2.52 [95]x y

p J mol-1 K-1 48 [68]

56.3 [92]

8 [68] 26.7 [68] 8 [60] 21.6 [55]

37 [92]

V z | -6 m3 mol-1 110 [58] 27.4 [K86] 112 [58] 28.2 [36] 1121 [97]

Tg, K 1160 [55]

1109 [48]

1373 [K86]

1460 [68]

1096 [68]

1036 [92]

1129 [H96]

1073 [60]

1221 [55]

1178 [92]

22-1.5 7.6~ 103 – 1.2 135 – 4.2 34-18 200 – 20

p

gg

C

VT

dP

dT

∆∆

=α

,

K GPa-1

185 - 47 470 – 6 150 - 33 70-64 145 – 28

dP

dTg, K GPa-1

[ts]

5

30 (P< 1GPa)

17 -8 -45

1 calculated from [97]; 2 T from [95]; 3 data are

extrapolated from [93], ; [ts] – from electrical conductivity measurements, this study.

Table 6 summarises the literature data on parameters used in calculations of Prigogin-Defay

parameter and the pressure dependence of Tg for studied sil icate glasses. The span of parameter Π

is one order of magnitude and it is much higher than 1 for all sil icate glasses. The extreme high

value of Π= 1.7·104 is calculated for SiO2 by using the thermal expansion coefficient measurements

from [53]. However, if one uses the thermal expansivity data from [90] the value of Π for silica

glass may be even close to 1. In the present work, the upper limit of Π estimated for SiO2 glass by

assuming that ∆α ∼ α from [53]. In reality, the thermal expansion coefficient of sil ica glass is

negative at temperatures up to 100-150° above Tg and, then, above 2000K becomes again positive ~


34

10-4 K-1[53]. In [17] α of SiO2 was erroneously averaged in the wide temperature interval and the

suggested ∆α between silica glass and melt ~ 1.1·10-5 K-1 is tool small . In [17] the estimations of Π

for albite and anorthite (from15 to 3 and from 38 to 7, respectively), the authors used rather

arbitrary values of ∆β (the contrast of isothermal compressibilities in glass and in melt has been

taken from 1 to 5·10-11 Pa-1). In the present estimation of Π, the experimental compressibility of

melt was calculated by using the method of [95] and extrapolated data of [93]. The contrast in

compressibility between melt and glass was assumed 0.5βT of the melt. In reality, ∆βT may cover a

much broader span. For example, in metallic glasses ∆βΤ is about 1% of βΤ [19], in SiO2 ∆β is

about 75% of β . For albite glass, the compressibility from the measurements of glass

density at high pressure were also used [94]. A comparison between calculated and measured

dTg/dP in electrical impedance experiments indicates that only SiO2 and anorthite (if only data at

pressures <1 GPa are taken into account) are in a satisfactory agreement. Otherwise, Tg and dTg/dP

estimated from electrical impedance data for alkaline aluminosil icates are very different from the

structural glass transition. But even for anorthite, for which the present estimations of Tg are close

to the structural glass transition, the Π value is much larger than 1, which does not permit

consideration of the glass transition in anorthite as a second order phase transition, i.e. a relaxation

process with one ordering parameter.

The results of Tg estimation from electrical impedance measurements provide different

results in comparison with rheological, calorimetric or dilatometric measurements. There are few

reasons for that. The question which arises, is it right to compare dynamic methods of Tg

determination using variable frequency and methods using down- and up-scan definitions of Tg [1].

Usually, dynamic or ac methods result in higher values of Tg in comparison of time scanning of

heating-cooling cycles. The observed in the present study small difference of Tg for anorthite and

SiO2 may be attributed to the difference in the definition of Tg: as midpoint of specific heat capacity

rise in a heating temperature scan and as a temperature of the maximum in imaginary part of the

electrical impedance. For alkaline bearing glasses the difference in Tg obtained from electrical

measurements and rheological, calorimetric or dilatometric studies, from other hand, is more

fundamental. Essentially, the difference in the relaxation time of mechanical and electric properties

lies in the differing nature of contributions of these two relaxation and may attain a factor of 101-2

near Tg for some glass formers [37]. To electric relaxation there is a contribution from two

processes, charge separation and charge migration. Thus, it may expected that in glass where


35

charge separation is significant, will behave differently from glasses where charge transport is

mostly due to a charge carrier migration. In sil icate glasses and melt containing in the structure Na+

the effects of charge separation are very important, sodium is highly unharmonic species,

especially, in the aluminosil icate structure. Sodium ions are responsible for a significant

polarisation (n<<1 in Eq. 17). By replacing Si4+ to Al3+ sodium becomes surrounded by several

non-bridging oxygen ions and aluminium tetrahedra which results in an increase of the dielectric

constant and increase of ionic polarasabil ity with the increase of aluminium substitution [80]. The

albite and haplo-granitic glasses due to their high conductivity and polarasabil ity can be classified

as “ loose” glass formers. The Tg measured in these glasses by electrical impedance method is a

temperature above which Na+ ions become sufficiently mobile, and the kink in the slope log(σ) vs.

1/T,K corresponds to “mobile Na-ion Tgs[81].

Judging from the sign of dTg/dP for studied glasses and qualitative behavior of the fragil ity

index m from Eq 14 or 16, it may be concluded that “ loose” conductive glasses (albite and

haplogranite) becomes even more fragile with the pressure increase, and “tight” glasses (anorthite

and SiO2) are getting more stronger under pressure.

Conclusions

1. The use of electrical impedance measurements to determine a glass transition temperature at

high pressures provides results for anorthite and sil ica glasses consistent with previous studies.

According to the structure of these glasses, the transport or diffusion of structural and

electrically charged defects are correlated. Anorthite may be classified as a “tight” fragile glass

former, silica glass is probably a “tight” strong glass. For albite and haplogranitic glasses the

established Tg is not a structural glass transition because of the “decoupling” between alkaline

mobil ity/charge separation and structural relaxation. These glasses belong to a class of “ loose”

glassy conductors.

2. Pressure dependence of Tg estimated from electrical conductivity measurements reflects

viscosity variations with pressure. For albite, the negative slope dTg/dP corresponds to a

decrease of the shear viscosity of albite melt under pressure. The greatest variation of Tg with

pressure occurs at P< 1 GPa. Further decrease of Tg is hindered by a decrease of percolation

paths for conduction. As a result of this, the contrast between electrical conductivity below and

above Tg becomes indistinguishable at pressures above 1 GPa.


36

3. Effect of pressure on dielectric relaxation times and the activation energy dielectric relaxation

may be explained in terms of the activation volume of dielectric relaxation. Positive activation

volume relates to a positive dTg/dP and strong behavior under pressure (SiO2, anorthite).

Negative or 0 activation volume correlates with the negative dTg/dP (sodium-bearing sil icates).

4. The determined dTg/dP values compared with those calculated from the second Ehrenfest

relationship show a significant discrepancy. Combined with the fact that a significant deviation

of the Prigogin-Defay ratio from 1 is observed, this indicates a difference of the glass transition

in sil icates from a second order phase transition.

Acknowledgements

The experimental works has been supported by Deutsche Forschungsgemeinschaft in the frame of

Special Program „Melts in the Earth: structure, formation and properties“ (SPP 1015). The authors

grateful to H. Höfer and T. Stachel for the help with the microprobing. Multi-anvil experiments

were performed at Bayerisches Geoinstitut under the EU “TMR – Large Scale Facil ities“

programme (Contract No. ERBFMGECT980111 to Prof. D. C. Rubie). A. S. and V. B. thank

Exchange Program between DFG and Russian Academy of Sciences for covering their travel and

stay costs at Univ. Frankfurt.

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