Melting of the silica isotypes SiO 2, BeF 2 and GeO 2 at elevated pressures

218

Physics of the Earth and Planetary Interiors, 13 (1976) 218—231 © Elsevier Scientific Publishing Company, Amsterdam — Printed in The Netherlands

MELTING OF THE SILICA ISOTYPES SiO2, BeF2 AND Ge02 AT ELEVATED PRESSURES lAN JACKSON’ Research School of Earth Sciences, A ustralian National University, Canberra, A. C. T. (A ustralia) (Received May 21, 1976; revised and accepted August 23, 1976)

Jackson, 1., 1976. Melting of the silica isotypes Si02, Bet’2 and Ge02 ‘at elevated pressures. Phys. Earth Planet. Inter., 13: 218—231. The melting curves of the structural analogues Si02, BeE2 and Gc02 have been studied at pressures ~40 kbar in a piston-cylinder apparatus. The initial slopes dTm/dP of the ~-quartz-liquid boundaries for Si02 and BeF2 are kbar while the slope of the rutile—liquid boundary for Ge02 is approximately 32°C/kbar.These large values of dT/ dP retied the unusually low entropies of fusion for these compounds in which strong structural similarities exist between the crystalline phases and the melt. Implications for the extended phase diagram of silica are discussed and it is concluded that either: (1) a maximum exists on the coesite melting curve, or (2) estimates of the melting temperature of stishovite need to be revised upwards.

4”, Pb4~)for silicon. In this sense 1. Introduction lt has long been recognized that the crystal structure appropriate for a given binary ionic compound under prescribed conditions of temperature and pressure is determined primarily by the ionic radius ratio rc/ra, where r~and ra are the radii of cation and anion, respectively. The effect of increased pressure on such a compound is to increase rc/ra very often to such an extent that a more close-packed crystal structure results (see e.g., Ringwood, 1975, p. 355). Geophysical interest in such phase transformations has tended to precede the development of technology capable of generating the necessary pressures and for this reason much attention has been devoted to the study ~f analogue compounds. For example the effect of pressure on the crystal structure of a silicate mineral can be deduced by studying the structures exhibited by related cornpounds in which rc/ra is increased by substitution of a larger, equally charged cation (e.g. Ge4~Ti4+ Present address: Seismological Laboratory, California Institute of Technology, Pasadena, Calif. 91125, U.S.A.

Sn

*

Ge0 2 can be

regarded as a model for the high-pressure phase behaviour of Si02. The use of the germanates as models for silicates at high pressures is well documented (see e.g., Ringwood, 1975, pp. 356—364). Another interesting set of analogue compounds (Goldschmidt, 1927; Roy et a!., 1950) for oxides and silicates is obtained via the following scheme: (1) Replace the 02— anions of oxides and silicates by F— which is similar in ionic size but only singly charged.

*

Since Si—O and Ge—O bonds are approximately 50% ionic in character, the covalency of Si and Ge must also be conhybridisasidered in any. discussion of pressure-induced3d2 phase transfor. mations. It suffices to state here that the sp tion of atomic orbitals necessary for octahedral coordination of Si or Ge by 0 is more readily achieved in Ge where orbitals of the fourth “shell” (cf. third “shell” in Si) are involved. Combination of the larger cation—anion radius ratio and the smaller hybridisation energy explains the comparative (relative to Si) willingness of Ge to occupy octahedrally coordinated lattice sites. A more complete discussion of

partial covalency and its implications for pressure-induced transformations will be presented in a later paper.

219 (2) Similarly replace all cations (which must carry an even charge) by others of approximately tile same

size and half the charge. Thus Si4+ is replaced by Be2~’,Mg2’~’or Zn2~by Li~,Ca2~by Na~,etc. Tins transformation tends to preserve crystal structure because of tile maintenance of ionic radius ratios. The halving of charge, however, results in a very considerable weakening of the interatomic bonding which is manifested in substantially reduced melting temperature, hardness, elastic moduli and refractive indices and increased water solubility and chemical reactivity. The fidelity with which BeF2 follows the complicated polymorphism of silica (Everest, 1964, p.40) is a measure of the reliability of such model systems. The room-pressure phase behaviour of fluoride and fluoroberyhlate systems has been extensively studied [see Everest (1964, pp. 45—48) for a review] and tile

using the usual quench techniques as applied to the study of phase equilibria in a conventional piston-cylin-

der device. The equipment and techniques used in this study are essentially those of Green et al. (1966) although two minor modifications are worthy of note: (1) For the melting studies on Si0 2, the boron nitride sleeve in the talc—-boron nitride—-graphite— pyrophylhite ceramic assembly of Green et al. (1966) was replaced by pyrex glass. Calibration of this modified assembly against the Si02 (quartz) Si02 (coesite) transformation requires the application of a —10% correction to nominal “piston-in” pressures. The uncertainty in corrected pressure is estimated to be ±5%for pressures in excess of 10 kbar. (2) Temperatures measured by Pt—Pt90Rh10 tilermocouples (BeF2, Ge02) have been corrected for the

striking similarities between these and the correspond-

effect of pressure on thermocouple ernf using the data of Getting and Kennedy (1970). Allowing for

ing oxide and silicate phase diagrams have been

the uncertainty in pressure-seal’ temperatures inferred

noted. This study of the melting of Si02, BeF2 and Ge02 at elevated pressures is a natural extension of this earlier work to the high-pressure regime and represents part of a wider investigation of phase equilibna in silicate analogue systems. The long range objective of this work is to explore the possibility that important melting parameters:

from measurements of Akella and Kennedy (1971), the correction at 30 kbar and 1 ,000°Camounts to +(7 ±4)°C.Corrected temperatures are believed to be accurate to within ±10°C.

— Tm(P~0)

~ (drm)

2Tm\ (d._.~._)

3. Si02 The details of quenching experiments on Si0

P0

for a series of isostructurai compounds may be systematically related. Such systematics might eventually be of use in the estimation of melting temperatures

in the earth’s interior. High-pressure melting studies Ilave not previously been performed on any of the silica isotypes Si02, BeF2 and Ge02 except for the hydrothermal studies of Kennedy et al. (1961) and Hill and Chang (1968) on the systems Si02—H20 and Ge02—H20, respectively. The main goals of the present study are to

compare the melting curves of Si02 and BeF2 and to observe the effect of the quartz rutile phase transformation on the melting curve of Ge02. ‘-~

2. Experimental details

Since all three compounds 5i02, BeF2 and Ge02 are glass-formers, melting curves could be established

listed in Table I. For runs of long duration (>152mm are at temperatures in excess of 1,700°C) it was found that replacement of high-temperature ceramic inserts by alumina greatly extended the useful life of the

W97Re3—W75Re25 thermocouples. After quenching and removal from the piston-cylinder device, the phases present were determined by optical examination and X-ray diffraction. No reaction of silica with the graphite reaction capsules was detected and the melting temperature of Si02 at each pressure was successfully bracketed (Fig. 1 and

Table II). These raw data (Table II) have not been corrected for the effect of pressure on thermocouple emf since the relevant correction is only poorly determined for temperatures between 1,500 and 1,800°C and unknown for temperatures in excess of 1,800°C (Williams and Kennedy, 1969). In the absence of a reliable functional form for melting curves Tm(P) of ionic compounds, the data pertinent to the quartz—liquid boundary (Table II)

220

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222 I

2200

when the statistical

I

-

-

significance of tile next term falls

below the 95%-confidence Tile coefficients tile resulting polynomial (alevel. quadratic, in this case)ofare

shown in Fig. 1 where the quadratic is superimposed on the raw data. Several features of this phase diagram should be 2000

noted:

L’ 1800

/

‘s

-

-

T (P)~6956 • 35’48(P-61- 0’3766(P-6~

m

-

the implications of these results for the phase diagram of Si02 are also discussed.

/

Cr

(1) The very steep slope (dT~/dP)p=6 kbar= 35.5°C/kharof thesteep ~-quartz—-1iquidboundary. The significance of this slope is considered in terms of available thermodynamic data in Section 6 where

(2) Melting temperatures determined in this study

‘‘‘

224 TABLEIV I

BeE2 melting data

I

2

T(P)o 513•9’3793P- 0-4407 P /

1200-

(kbar) raw

corrected

-

-

/

•

~

0 Pressure 5 10 15 20 25 30 35

Melting temperature (°C) 688±12 689±12 850 ±10 853 ± 10 980±10 984±10 1,090 ±10 1,095 ±10 1,180 ±20 1,186 ±20 1,240 ±20 1,247 ±20 1,300 ±20 1,308 ±20

Coefficients of best fitting statistically significant polynomials:

iooo-

Co •

D

800

600

-

/

•

-

Be~

~~Cr?

-

i=2

Tm(P)

=

~ a,~P’

i=0

10

20

30

40

P RESSURE 1 KB

Coefficient

Augmented

Depleted

lig. 2. Melting curve for Bel-’

dataset

dataset

2 to 35 kbar. Run products: glass (open circles), quartz (filled circles) and coesite (squares). The stability fields for the quartz (Q),

*2

________

_________________

a0 a1 a2 *1

*2 *3

*3

552.4 33.64 —0.3403

513.9 37.93 —0.4407

Thoma et al. (unpublished—see HoIm and Kleppa, 1969). More recently, Tamura et al. (1975) have reported a discontinuity in the enthalpy of BeE2 in the temperature range 550—560°C.An uncertainty of ±2°C was rather arbitrarily placed on the value of 555°Cused in the curvefitting procedure. Including (P = OC T = 555°C). Excluding the atmospheric pressure data point.

imposed on

the •

corrected

data. Also shown in Fig. 2 L

~

•

~

coesite (Co) and liquid (I~)phases are indicated. Cr denotes a possible wedge of cristobalite stability, and D is used to distinguish runs from a study by Dachille and Roy (1959).

Si02. This important correspondence will be discussed in Section 6. (3) There is absolutely no evidence in tile present study for the persistence of crystalline phases to tern-

peratones of the order of 800°Cat low pressures. Melting temperatures for the ct-cnistobalite modification of 797 and 800°Cderiving from some earlier studies (e.g. see Everest, 1964, p. 41) are therefore CCnnojdprpd

Prrnnpn,,s in the lieht of this new data.

223

bly, the phases present were determined by optical

and temperatures were corrected for the effect of pres-

examination and X-ray diffraction. Definitive runs are described in Table Ill. There was no X-ray evidence for hydrolysis of BeF 2 by adsorbed water to yield

sure on thermocouple emfin the manner described in Section 2. Polynomials were fitted to the corrected

a problem encountered in some earlier studies of BeF2 the glasses produced in this study were genBeO

—

erally clear whereas trace quantities

den the

fluoride

of

the oxide ren-

glass turbid (Everest, 1964, p. 49).

Tile melting temperature was bracketed at 5-kbar pressure intervals between S and 35 kbar inclusive,

data (Table IV) with and without the inclusion of the data point (P 1 bar, T 555°C)due to Hoim and

Kleppa (1969). In

each case the inclusion of a quadratic term was statistically significant at the 95%

confidence level. The coefficients of each of these polynomials are presented in Table IV. In Fig. 2, the second of these polynomials is super-

TABLE III BeE2 quenching experiments

Pressure

Run

Temperature

Duration

Phases

(kbar)

No.

(°C)

(h)

present

Comments *‘

5 5 5 5

5953 5965 5961 5955

700 675 650 600

6 16 4 6

GI Qz Qz Qz

10 10 10 10

5947 5949 5944 5936

900 870 850 800

6 5 7 11

GI GI + Qz Qz + GI Qz

clear glass, few crystals crystals + abundant glass shards

15 15 15 15

5461 5468 5474 5476

1,060 1,020 980 940

2/3 1 1 1

GI GI Qz + Gl Qz

no crystals no crystals ragged, poorly crystallised Qz poorly crystallised, no glass

20 20 20

5987 5206 5975

1,120 1,100 1,080

6 1 7

Gl + trace Qz Gl Qz

almost entirely glass, few crystals

25 25 25 25

5414 5982 5410 5406

1,200 1,180 1,160 1,120

1/2 8 1 1

Gl • Gl + Qz Qz Qz

no crystals abundant glass, rounded crystals

30 30 30 30 30 30

5989 5507 5423 5505 5216 5218

1,280 1,240 1,220 1,200 980 900

5 1 1/2 1 1 1

GI + trace Qz Qz + GI Gl + trace Qz Qz Qz Co

almost entirely glass ragged Qz few ragged Qz crystals

35 35 35 35

5990 5980 5440 5430

1,320 1,280 1,240 1,180

7 4 3/4 3/4

Gl + trace Qz Qz Qz + Gl Qz + trace Co

40 40

5501 5497

1,260 1,200

1/2 2/3

Qz Co

*i *2

*2

*2 *2

Co = coesite; GI = glass; Qz = quartz. Graphite capsules and glass starting material. For all other runs platinum

+

very well crystallised

well crystalhised

no glass ragged crystals no glass

trace Co

capsules and BeF2

coesite starting material were

used.

224 TABLEIV

I

I

2 melting data Pressure

-

Melting temperature (°C)

200

689

± 12

1,095 1,186 1,247 1,308

± 10

/~

~

-

corrected

555± 2*1 688 ±12

/

-

0~ i000

• .)/

-

,,/5

Q

1,090 1,180 1,240 1,300

± 10 ± 20 ± 20 ± 20

800

/

Co

/ /

0/

±20

/

•

j,/.

20 25 30 35

7 I

—

T(P)o 513-9’37-93P- 0-4407 P

raw 0 5

~

I 2

BeE

-

±20 ±20

Coefficients of best fitting statistically significant polynomials: 600-f

2

•

Tm(P)= LJa 1P’

I 10

i=0

Coefficient

Augmented dataset *2

Depleted dataset

________

a0 ai a2

*3

_____________

552.4 33.64 —0.3403

513.9 37.93 —0.4407

Thoma et al. (unpublished — see Hoim and Kleppa, 1969). More recently, Tamura et al. (1975) have reported a discontinuity in the enthalpy of BeF2 in the temperature range 550—560°C.An uncertainty of ±2°C was rather arbitrarily placed on the value of 555°Cused in the curvefitting procedure. *2 Including (P = 0, T= 555°C). . *3 Excluding the atmospheric pressure data point.

I 20 30 P RESSUREI K B .1

I 40

Melting curve for BeE2 to 35 kbar. Run products: glass (open circles), quartz (filled circles) and coesite (squares). The stability fields for the quartz (Q), Fig. 2.

coesite (Co) and liquid (L) phases are indicated. Cr denotes a possible wedge of cristobaliie stability, and D is used to distinguish runs from a study by Dachille and Roy (1959).

~‘

.

.

Si02. in

This

.

important correspondence

will be discussed

Section 6.

(3) There is absolutely no evidence in tile present study for tile persistence of crystalline phases to ternperatures of the order of 800°C at low pressures. .•

.

.

Melting temperatures for the ct-cristobalite modification of 797 and 800°Cderiving from some earlier imposed on the corrected data. Also shown in Fig. 2 are the results of several runs which pertain to the location of the quartz-—coesite boundary. Several fea-

studies (e.g. see Everest, 1964, p. 41) are therefore considered erroneous in the light of this new data. (4) The few data pertinent to the quartz—coesite

tures of the diagram are worthy of note:

boundary are generally consistent with the earlier re-

(1) The failure of the quadratic fit to the highpressure data to intersect the room-pressure melting

suits of Dachille and Roy (1959).

point of 5 55°Cis, by analogy with Si02, very suggestive of the existence of a narrow region of stability for the reported cristobalite phase (Roy et al., 1950) extending to pressures of 1 —3 kbar. (2) Whether or not a wedge of cristobalite stability is included the quartz—liquid boundary rises steeply

5. GeO~ Germania (germanium dioxide) exists in two crys-

talhine modifications: the tetragonal rutile and Ilex-

with pressure with a slope identical of about to 36the ±2°C/kbar (Table IV). This is almost initial slope

agonal quartz forms whose densities under standard 3, respectively. conditions 6.277equilibrium and 4.278 has g/cmbeen studied at Tile quartz arerutiie

(35.5°C/kbar) for the quartz—liquid boundary in

modest pressures (P< 1 kbar) in hydrothermal (Hill

225

and Chang, 1968) and gas (Majumdar and Roy, 1965)

1,170 and 1,190°C,respectively, the extent of reduc-

apparati. Melting studies at pressures greater than

tion is indicated by CO

1 bar are limited to tile data of Hill and Chang on tile

2 vesicles at tile outer glassy rim and distribution throughout the charge of highly

system Ge02—H20.

reflective grains of metallic Ge. The glass, while re-

The germanium dioxide used in this study was of laboratory reagent grade. The commercially available

hexagonal form of Ge02 is not, as we shall see, in equilibrium with the melt at pressures in excess of some 3 kbar. Consequently, it was desirabic to use tetragona! germania wilich was produced by exposure of the hexagonal form to 1 5-kbar pressure and 1,000°Cfor 2 h. X-ray diffraction indicated complete transformation to the tetragonal phase. Using tetragonal Ge02 as starting material, melting relations for Ge02 were studied at pressures of 5—20 kbar and temperatures of 1,100—1,700°Cusing quench techniques a standardreducing piston-cylinder device. The inextremely conditions prevailing within the internal grapllite furnace and the tendency of Ge

to form low-melting-point alloys with conventional metallic capsule materials posed special problems of sample containment and interpretation of melting

relations. Most of the experimental runs were conducted in graphite reaction capsules which overcame the containment problem but introduced further difficulties associated with reduction of Ge02 to metallic

duced is relatively homogeneous. At somewhat higher pressures (and temperatures)

the sequence of events is as above except that the central crystalline region is better crystallised and the glassy rim no longer quenches to a homogeneous glass (Fig. 3d Run 4836). Presumably the liquid has reached a composition corresponding to the “twoliquid” region of the room-pressure Ge—Ge02 phase diagram in which case the “metallic liquid” yields the quench Ge crystals while the “oxidic” liquid quenches to form the glass. At even higher temperatures andofgreater concen4~ions the viscosity the melt is subtrations of Ge stantially reduced due to the break-up of the Ge0~ or GeO~ network allowing quench crystals of both Ge and Ge0 2 to form on rapid cooling from the melt (Fig. 3e Run 4771). Were the central crystalline —

-

--

regions of Fig. 3a, b and d quite unreduced it would be reasonable to define the melting point of pure

Ge02 as that temperature at which the central crystalline region melts. We have seen evidence that this is not the case. It is clear, however, that reduction of

germanium and oxides of carbon. Tile nature of the

run times at a given pressure will result in less severe

problem is best assessed by reference to the Ge—GeO,

reduction of the GeO2 and presumably higher “apparent melting temperatures”. In Table V itis seen that reduction of run times from 30 to 10 mm in-

phase diagram at atmospheric pressure (Trumbore et al., 1956; see also I.evin eta!., 1969): (1) Progressive addition of iiietaliic Ge to pure Ge02 lowers the liquidus temperature from 1,116°C towards a eutectic temperature of “-910°Cat “88

Ge02 in the binary Ge—Ge02 mixture. (2) At temperatures in excess of 940°C,mixtures containing less than “86 moie% Ge02 exist as two immiscible liquids one metallic and tile other mole%

—

creased the apparent melting temperature at 5 kbar from 1,145 ±5 to 1,180 ±10°Cbut that no further increase resulted when run duration was further reduced to 5 mm. This is good evidence that the actual

melting temperature under these conditions is close to 1,180°C.However, the use of 20-, 10- and 5-mm runs to locate melting temperatures at 10, 15 and 20

“oxidic”. The first of these phenomena is clearly responsible

kbar, respectively, may seriously underestimate actual melting temperatures. These data are plotted in Fig. 4

Ru + Gi + Me of many of the experimental runs listed in Table V. Reduction of Ge02 is most severe at the contact with the graphite capsule so that it is here that the first melting takes place (Fig. 3a Run 5525). As the temperature is increased tile solid—liquid boundary propagates inwards (Fig. 3b Run 5577) until finally the central crystalline region is entirely molten (Fig. 3c Run

and define a straight line whose slope (dT/dP) = 21°C! kbar represents a lower bound for the intial slope (dTmIdP) of the rutile-Ge02 melting curve. At a late stage in this investigation is was realised that the use of A1203 reaction capsules might provide a means for the determination of more reliable melting data for GeO2. Several such runs were performed (Table VI) indicating corrected melting temperatures of 1,313 ±10 and 1,670 ±15°Cat pressures of 10

for tile multipllase assemblages

—

—

—

5786). in these 5-kbar runs at temperatures of 1,140,

226

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~

(a

CCCC~d

C,C,

~

.,50LOr

~

I

(a

A,,,’.,

-a

C

C)

9~~~g~000

8CC, C

(aL)

COCOCO><

.0Q~

~

‘a’~~’~~°°OrOrE 2aaCaCCCOC.EC

5)a.(a

o~a’a~’a.CCCC’0’...C

Ca

~:, —

.0

E

C.)

CO (a N •

ECO

N

cCc~

a~•~ C.)

(a

+

+

2a.

+ C)C’a

~

~L1~-~e)

~ .0 0~

— *

C)_

CC

+ (a~(a(aC)

a~ ++

‘a+ C)(aC)C)

~

~

+++++ ++++++ ._.aa...,aaa._..-.a ~

++++

‘a~—

~e’ ~

~

++ aa.-.a ~

0000

88

aCa

‘a

.0

zsroz~~

++ ‘a’a

Ci)

‘aCa

‘a’a’a~~Ca

~

+++

a0

a. ~

++4-+++ ~

~s;

+++++++++++

a_....~_.aaa

CON

~II —

a.

C

~

.~

C

.E

-a.-

aE

(a

2 a.

a ~

CO 05

8.

-

CCCCCCIICr)CCCCr)Cl)Cr) ~C~CCI

CCCCCCC

CCC

CCCCCr)Cr)Cr)Cr)Cr)Cr)Cr)

CCCCCCCCCCCCC

CCr)CCCCC

CCC

CCCCCCCCCCC

CCC-’..0Cr)C00CCCCINNC-CNNC.--C

c~COr-. CCICCI

Cr)a~Cr)’.oCICa~00r—~-

C

‘C’.0’.0’.0’.0NN

-~

E’’ ~L) ~.,9,,

~CCICr)~

CIC0~CC-CCI—’O~

NN~ —_

~

~

~

a

Ca

~

a. Or

C a ~Z

.

~

~ ~CIN~-”100CCr~00CO00 sososo~~soso~r”~—r--r--

.-C.l~\0CCIC’.0~-

~

.l~~~-CO-C!)Cr)

~~~~Cl)Cr)

—r--v~,r~

CC-N0~ ~‘r)’O~

r~r~

Cr)Cr)Cr)

00~Nr—r-’.0—CCO’.0CC-Cr ~ -r--r--r--r-r--CC-CO0000CC~

0

>8

,,~ ~0

C.)

I-’ C.~

~II

2 CO

05(0

2 a’~

~II

~‘

0......-

r)Cf)Cl)Cr)Cl)Cr)Cr)Cr)Cr)Cr)

CCCCCCC -

Cr)Cl)Cr) .—..

CCCCCCCCCCC

.00)

NNNNNNNNNNN

*

*

(a)

Cc)

(b)

~d) Fig. 3. Reflected light photomicrographs of polished sections of the charges from runs 5525 (a), 5577 (b), 5786 Ic), 4836 Id) and 4771 (e). The symbols Ru, GI and V denote rutile—Ge0 2, glass and CO2 vesicles. respectively. The highly reflective grains Isee especially (d)l are metallic germanium.

TABLE VI Ge02 quenching experiments

—

Al203 reaction capsules *1

Pressure (kbar)

Run No.

Temperature (°C)

Duration (mm)

Phases present *2

Comments

10 10 10 10 10

5979 5981 6061 6121 5983

1,380 1,350 1,350 1,320 1,300

10 5 15 10 5

GI Gl Gl Gl Ru

clear glass clear glass clear glass clearglass abundant Ru + clear glass

20

5971

1,680

5

Gl

20 20 20

5976 5986 5985

1,650 1,620 1,570

5 5 5

Ru Ru Ru

+ + + + +

Gl Ru

+

Me Me Me

Me

abundant glass (refractive index quench crystals of Ru very well crystallised Ru very well crystallised Ru very well crystallised Ru

=

1.715

±0.01),

Crushable A1203 capsules were used in the lO-kbar runs — otherwise the assembly was unchanged from that of Table V except for the replacement of boron nitride by pyrex glass and the use of alumina inserts (in place of high-temperature ceramic) in runs 5971 and 5976. *2 GI = glass, Me = metallic germanium, Ru = rutile. *1

228 I

60

I

I

spectively] for the observed melting curves. Since tile I

-

-

/

-

—j~

-

~)I40-

dTfl

1/dP=~Vf/z~.Sf

slope it is natural is giventoby seek theanClapeyron explanation relation: of these high slopes in terms of uniformly high values of ~Vf and/or uniforrniy low values of ~Sf. (z~ Vf and ~Sf are tile molar

Ca

~2O Ca = Ca

-

-

L

.10

V

‘~°

Ge02

00 I 5

10 PRESSURE (KB.)

I 15

I 20

volume and entropy changes values associated fusion.) In the ofmeaningful reliable of ~ with V~-it of is tile not possible toabsence perform calculations slope (~ Vf/~f). It is of interest, however, to note that ~ values for tile quartz phases of Si02, BeF2 and GeO2 and the cristobalite pilase of Si02 are consistently low when compared to corresponding values for materials which form simple ionic melts (Table Vii).

l-’ig. 4. Phase diagram for germania (Ge02). Open and filled circles denote runs performed in graphite capsules which were judged to be respectively above and below the melting curve (see text). Open and tilled diamonds have

Scherer et ai. (1970) claim that the low values of ~Sf for the quartz and cristobalite polymorphs of silica

similar significance with respect to runs performed in alumina capsules. The stability fields for quartz (Q), rutile (R) and liquid (L) are indicated. The solid line labelled 32°C/KB. iS the melting curve while that labelled M is a determination of the quarta—rutile boundary by Majumdar and Roy (1965).

polyhedra and their arrangement in the liquid and crystal modifications”. Tilis undoubtedly explains the uniformly high melting slopes observed in this suite of close structural analogues. A more detailed discus-

reflect “the known similarity of the coordination

sion of melting—-crystal-structure systematics will be and 20 kbar, respectively. As can be seen froni Fig. 4 these two data points and the earlier 5-khar determination define an almost linear trend with slope dT/ dP = 32°C/kbar.This is regarded as a reasonable estimate of tile slope of tile Ge02 melting curve although

TABLE VII Entropies of fusion of the silica isotypes and some ionic

materials Material

~Sf

there is clearly scope for further work with this awkward systeill. The quartz-—rutile—liquid triple point was not di rectly observed in this study although its approximate location (2 kbar, 1,100°C)may be inferred from tile intersection of the quartz—rutile (Majumdar and Roy, 1965) and rutile—liquid boundaries (see Fig. 4). It is also apparent that the quartz—liquid phase boundary must ilave a near-zero slope wllich is in accord with similar data for some of the alkali halides at tileir Bi —

SiO2 (quartz) Si02 (cristobalite) Bel2 (Qz) Ge02 (Qz) MgF2 FeF2 CaF2 LiF NaF

9.05 9.03 (estimated) 4.20 ~ 5.78 6.28

B2—hiquid triple points(e.g., Kl: Pistorius, 1965).

KU

5.75

KCI

6.02

6. Systematics in melting data for Si02, BeF2 and Ge02 Tile most obvious feature of the melting data for SiO2, BeF2 and GeO2 is the uniformly high initial slope [(dTm/dP~0 = 35.5, 36 ±2 and 32°C/kbar,re-

(cal. °C~niole~) ___________

NaCl

•

~—

________

1.3 ±0.1~ 1.2 ±0.1 ‘5~ 1.37 2.76

*2, *4

1.35 ~

6.27

~ Schereretal. (1970). *3

HoIm and Kleppa (1969). Tamura et al. (1975)

*4

Navrotsky (1971).

*2

~ Robie and Waldbauni (1968). All data without superscripts are from JANAF Thermochemical Tables (1971).

229 presented in a later paper wllen data are available for a wide range of fluoride compounds currently under study in this laboratory (Jackson, 1977).

I

I

—.

~__~

/

6.1. Implicationsfor the Si02 phase diagram Tile phase diagram of silica has long been of interest to chemists and mineralogists because of tile multiplicity of polymorpils exhibited (Sosman, 1965) and the importance of SiO 2 as tile dominant chemical constituent of tile eartil’s crust and mantle. More recently

this interest has been reinforced by the suggestion (e.g., Birch, 1952; Ringwood, 1962; Anderson, 1967; Liu, 1975) that silica (as stishovite) might be an important mineral in the “post-spinel” region of the earth s mantle. Published phase diagrams for silica (see, e.g. Boyd and England, 1960; Lindsley, 1966; Ostrovsky, 1967; Davies, 1972) are necessarily rather vague in their treatment of melting relations. However, several inferences are made: (1) The steep slope (dT/dP~for the cristobalite— /3-quartz boundary and the location of the cristobalite —tridynlite—/3-quartz triple point (1.43 kbar, 1,190°C) require a cristobalite—liquid—/3-quartz triple point at a pressure of the order of a few (3—6) kilobars and a teniperature not far in excess of the atmospheric-pressure melting point of cristobalite (1,723°C). (2) The ~3-quartzmelting curye, with an average slope of about I 0°C/kbar,intersects the quartz—coesite boundary (slope 1 33°C/kbar,Bdhler and Arndt, 1974) to produce a further triple point (~3.quartz-coesite—liquid) at 40—45 kbar and 2,100—2,200°C. (3) Davies (1972), in a thorough analysis of the available high-pressure (static and shock-wave cornpression) and thermochemical data, suggests that stishovite and a coesite-like liquid coexist along a boundary of slope (“-17°C/kbar)which terminates in the coesite—stishovite—liquid triple point at approximately 125 kbar and 2,230°C. The data presented in way: this paper qualify these inferences in the following

• (1) The location of the Qz—Cr—Liq triple point ±3 kbar, 1,720 ±20°C)is confirmed (Fig. 5). (2) The slope of the /3-Qz—iiquid boundary is very much steeper than has been thought, with the result that our extrapolated melting curve (Table II) inter-

I

-‘

7 260C

-

L

~

/,Il

ii

“~

/j

//

~22OO

~I8OO

/ / / / /

-

-

—/Cr

-

I6~KB~ \\

Co

/ i / / / St /

/

//

jj

II i I

/

BE! ~

II

11 AS

I

/ 1 40

-

I

II

I I

/

/D

/ /

/ /fD

/ / PRESSURE (KB)

i 120

Fig. 5. Hypothetical phase diagram for silica to 150 kbar. Curves and BA extrapolations the data and EnglandBE(1960) andare Böhler and Arndtof(1974) for ot theBoyd quartz coesite transformation. Curve AS is a similar extrapolation of the coesite stishovitc boundary from Akiinoto and Syono (1969). Curves Dare from Davies (1972). The stability fields for quartz (Q), cristobalite (Cr), coesite (Co), stishovite (St) and liquid (L) are indicated. The region In which partial octahedral coordination of Si by 0 may be inlportant in

the liquid is denoted LVI. The upward revision of the temperature of the Co-St- 1 triple point (required if a negative

slope of the coesite melting curve is to be avoided) is indicated by the arrow.

boundary (e.g., Boyd and England, 1960; Böhler and Arndt, 1974) at approximately 2,530°C and 50 kbar —

some 300-—400°Chigher than earlier estimates

(Fig. 5). (3) The slope of tile coesite melting curve at the Qz—Co--L triple point may be estimated as follows: (a) From the data of Table VIII and the Murnaghan equation ~ (Co —* Qz) is found to be approx3. Available thermal expansion data imately 0.8and cm coesite (Skinner, 1966) suggest that for quartz

~V(Co

—~

Qz) might increase marginally with tema value of ~ (Co -~ Qz) = 1.0 cm3

(6

perature

sects the projection of the observed /3-quartz—coesite

seems reasonable. Now, ~S~jijit~ (Co Qz) can be calculated from the Clapeyron relation using the known slope (133°C/kbarfor the Qz—Co boundary, yielding 0.18 cal. °C mole—1.

—

-+

230 TABLE VIII Data used in estimation of

the initial

slope of

o kbar V29S0K 3)

the coesite melting curve

,

K 0 (kbar)

K0

50 kbar V298°K (calculated) (cm3)

~ *2 1,110 *3

6.4 *2 *3

20.601 19.815

(cm 22.688 *1 20.641 ~

Quartz Coesite

50 kbar V2800°K (calculated) (cm3) *4 20.211 *4

• 21.219

~ Robie and Waldbaum (1968). Anderson et al. (1968). *3 R.C. Liebermann (personal communication, 1975). *4 Estimates based on the data of Skinner (1966), see text. *2

(h) ~Sf and ~Vf generally decrease as the pressure increases (e.g. Clark, safe to assume that ~ 1963, 1.3 cal. °C~illole1

—

p. (Qz 14) andLiq) it isistherefore less than —~

the corresponding value under

Zn 2SiO4 (Taylor et al.,2+1971) appears to be four associated coordination from in with an increase ofthe Zn melt. Recently, Waff (1975) willernite to six in has suggested that pressure-induced coordination

standard conditions. The slope of the quartz melting

changes (~‘Al3~ VIA13+) are likely to occur at

curve at the Qz—Co—•Liq triple point is likely to be positive but snlali in magnitude implying that

quite modest pressures (<35 kbar) in tholeiitic and andesitic melts.

~

(Qz

-÷

Liq) ~ 0.

More recently, Kushiro (1977) has obtained direct

(c) The estimates of (a) and (b) when combined, yield:

(Co

L~VO~O~j

I

(Co

—~

-~

Liq)

~‘

1.0 cm3

.

experimental evidence for pressure-induced changes (IV -* VI) in the coordination of M3~and Si4~in silicate liquids at pressures in the 0—70-kbar range.

The alternative to the above is to assume that z~Vf remains positive. If this is the case, Davies’ (1972) location of the coesite—stishovite—liquid triple point

Liq) <1.5 cal. °C~mole~

-

_*

.

and tilus by application of the Clapeyron equation:

must be low by at least 300—500°C and the Hugoniot data may need to be reinterpreted.

(dT/dP)~ 0~//~ (Co

-~

Liq) ~ 1 5.9°C/kbar

The combination of a Qz—Co—-Liq triple point at about 50 kbar and 2,530°Cand a substantial positive initial slope (~16°C/kbar)for the coesite melting curve requires the existence of a maximum on the coesite melting curve, if Davies’ (1972) location of the

Acknowledgements

coesite—stishovite—liquid triple point is correct (see Fig. 5). At this maximum melting temperature z~Vf= 0, and beyond it, coesite to octalledral a more dense liquid 4+ inmelts partial coordinawhich may feature Si tion. In this connection, it is interesting to note that the

manuscript; the advice of Dr. J.F. Gettrust on curvefitting procedures was much appreciated. Financial support from thePost-Graduate Australian taxpayer through Commonwealth Research Awarda is

high refractive index (1.715 ±0.01, cf. 1.695—1.735 for the quartz polymorph) of GeO 2 glass quenched from the melt at 20 kbar (Table VI) may be explained by partial conversion of GeO~ tetrahedra to GeO~ octahedra. Equally, the negative melting slope for

Professor A.E. Ringwood and Dr. R.C. Liebermann are thanked for their guidance and encouragement throughout this project and for comments on the

gratefully acknowledged.

References Akella J. and Kennedy, G.C., 1971. Melting of gold, silver and copper — Proposal for a new high-pressure calibration scale. J. Geophys. Res., 76: 4969—4977.

231 Akimoto, S. and Syono, Y., 1969. Coesite stishovite transition. J. Geophys. Res., 74: 1653—1659. Anderson, DL., 1967. Phase changes in the upper mantle. Science, 157: 1165—1173. Anderson, O.L., Schreiber, E., Liebermann, R.C. and Soga, N., 1968. Some elastic constant data on minerals relevant to geophysics. Rev. Geophys., 6:491—524. Bevington, P.R., 1969. Data Reduction and Error Analysis for the Physical Sciences, McGraw-Hill, New York, N.Y., 336 pp. Birch, F., 1952. Elasticity and constitution of the earth’s interior. J. Geophys. Res., 57: 227—286. Böhler, R. and Arndt, J., 1974. Direct determination of the quartz—coesite transition by in situ X-ray measurements, Contrib. Mineral. Petrol,, 48: 149—152. Boyd, FR. and England, J.L., 1960. Quartz—coesite transition. Carnegie Inst. Washington, Yearb., 58: 86. Clark, Jr., S.P., 1963. Variation of density in the earth and • the melting curve in the mantle, In: T.W. Donnelly (Editor), The Earth Sciences: Problems and Progress in Current Research. University of Chicago Press, Chicago, 111., pp. 5—42. Dachille, F. and Roy, R., 1959. High pressure region of the silica isotypes. Z. Kristallogr., 111: 451—461 Davies, G.F., 1972. Equations of state and phase equilibria of stishovite and a coesitelike phase from shock-wave and other data. J. Geophys. Res., 77: 4920—4933. Everest, D.A., 1964. The Chemistry of Beryllium. Elsevier, Amsterdam, 151 pp. Getting, IC. and Kennedy, G.C., 1970. Effect of pressure on the emf of chromel—alumel and platinum—platinum 10% rhodium thermocouples. J. Appl. Phys., 41: 4552—4562. Goldschmidt, V.M., 1927. Geochemische Verteilungsgesetze der Elemente: VIII. Untersuchungen Ober Bau and Eigenschaften von Krystallen. Skr. Nor. Vidensk.-Akad. Oslo, 1, Mat.-Naturv. KI., 8: 1—156. Green, T.H., Ringwood, A.E. and Major, A., 1966. Friction effects and pressure calibration in a piston-cylinder apparatus at high pressure and temperature. J. Geophys. Res., 71: 3589—3594. Hill, V.G. and Chang, L.L.Y., 1968. Hydrothermal investigation of Ge02. Am. Mineral., 53: 1744—1748. Hoim, J.L. and Kleppa, O.J., 1969. Enthalpies of mixing in liquid beryllium fluoride—alkali fluoride mixtures. Inorg. Chem., 8: 207—212. Jackson, I., 1977. Melting of some alkaline-earth and transition-metal fluorides and alkali fluoroberyllates at elevated pressures: A search for melting systematics. Phys. Earth Planet. Inter., 14 (in press). JANAF Thermochemical Tables, 1971, NSRDS—NBS 37, Washington, D.C., 2nd ed. Kennedy, G.C., Wasserburg, G.J., Heard, H.C. and Newton, R.C., 1961. The upper three-phase region in the system Si02—H20. Am. J. Sci., 260: 501—521. Kushiro, I., 1977. Changes in viscosity and structure of silicate melt at high pressures. Proc. U.S.—Jpn. Sem. on

High-Pressure Research Applications in Geophysics, Honolulu, Hawaii, July 6—9 1976 (in press). Levin, E.M., Robbins, CR. and McMurdie, H.F., 1969. Phase Diagrams for Ceranoists, 1969 Supplement. Am. Ceram. Soc. Columbus, Ohio. Lindsley, D.H., 1966. Pressure—temperature relations in the system FeO—Si0 2. Carnegie Inst. Washington, Yearb., 65: 226 --230. Liu, L., 1975. Post-oxide phases of olivine and pyroxene and mineralogy of the mantle. Nature (London), 258: 510— 511. Majumdar, A.J. and Roy, R., 1965. Test of the applicability of the Clapeyron relationslup to a few cases of solid— solid transitions. J. Inorg. NucI. Chem., 25: 1961—1973. Navrotsky, A., 1971. Enthalpies of transformation among the tetragonal, hexagonal and glassy modifications of Ge02. J. Inorg. Nucl. Chern., 33: 1119—1124. Ostrovsky, l.A., 1967. On some sources of errors in phaseequilibria investigations at ultra-high pressure; phase diagram of silica. Geol. J., 5 (Part 2): 32 1—328. Pauling, L., 1960. The Nature of the Chemical Bond. Cornell University Press, Ithaca, N.Y., 3rd. ed., 644 pp. Pistorius, C.W.F.T., 1965. Melting curves of the potassium halides at high pressures. J. Phys. Chem. Solids., 26: 1543—1548. Ringwood, A.E., 1962. Mineralogical constitution of the deep mantle. J. Geophys. Res., 67: 4005—4010. Ringwood, A.E., 1975. Composition and Petrology of the Earth’s Mantle. McGraw-Hill, New York, N.Y., 672 pp. Robie, R.A. and Waldbaum, DR. 1968. Thermodynamic properties of minerals and related substances at 298.l5°K (25.0°C)and one atmosphere (1.013 bars) pressure and at higher temperatures. U.S. Geol. Surv., Bull., 1259. Roy, D.M., Roy, R. and Osborn, E.F., 1950. Phase relations and structural phenomena in the fluoride-model systems LiF—BeF2 and NaF--BeF2. J. Am. Ceram. Soc., 33: 85—90. Scherer, G., Vergano, P.J. and Uhlmann, DR., 1970. A study of quartz melting. Phys. Chem. Glasses, 11: 53—58. Skinner, B.J., 1966. Thermal Expansion In: S.P. Clark, Jr., (Editor), Handbook of Physical Constants, Section 6. Geol. Soc. Am., Mem, 97. Sosman, RB., 1965. The Phases of Silica. Rutgers University Press, 388 pp. Tamura, S., Yokokawa, K. and Niwa, K., 1975. The enthalpy of beryllium fluoride from 456° to 1083°K by transposed temperature drop calorimetry. J. Chem. Thermodyn., 7: 633—643. Taylor, L.A., Bell, P.M. and Muan, A., 1971. The effects of pressure in the Zn2SiO4—Co2SiO4 system. Carnegie Inst. Washington, Yearb., 69: 194—195. Trumbore, F.A., Thurmond, CD. and Kowalchik, M., 1956. Germanium—oxygen system. J. Chem. Phys., 24: 1112. Waff, H.S., 1975. Pressure-induced coordination changes in magmatic liquids. Geophys. Res. Lett., 2: 193—196. Williams, D.W. and Kennedy, G.C., 1969. Melting curve of diopside to 50 kilobars. J. Geophys. Res., 74: 4359—4366.