Elasticity of stishovite at high pressure

ELSEVIER Physics of the Earth and Planetary Interiors 96 (1996) 113-127

PHYSICS OFTHE EARTH

ANDPLANETARY INTERIORS

Elasticity of stishovite at high pressure

Baosheng Li a, *, Sally M. Rigden b, Robert C. Liebermann a

a Center for High Pressure Research ; and Department of Earth and Space Sciences. State University of New York at Stony Brook, Stony Brook, NY 11794, USA

b Research School of Earth Sciences, Australia National University, Canberra, A.C.T. 0200, Australia

Received 12 May 1995; revised 18 August 1995; accepted 25 October 1995

Abstract

The elastic-wave velocities of stishovite, the rutile-structured polymorph of SiO:, were measured to 3 GPa at room temperature in a piston cylinder apparatus using ultrasonic interferometry on polycrystalline samples. These polycrystalline samples (2-3mm in length and diameter) were hot-pressed at 14GPa and 1050°C in a 2000ton uniaxial split-sphere apparatus (USSA-2000) using fused silica rods as starting material. They were characterized as low porosity (less than 1%), single phase, fine grained, free of cracks and preferred orientation, and acoustically isotropic by using density measurement, X-ray diffraction, scanning electron microscopy, and bench-top velocity measurements. On the basis of subsequent in situ X-ray diffraction study at high P and T on peak broadening on similar specimens, it is evident that the single crystal grains within these polycrystalline aggregates are well equilibrated and that these specimens are free of residual strain. P- and S-wave velocities measured at I arm are within 1.5% of the Hashin-Shtrikman bounds calculated from single-crystal elastic moduli. Measured pressure derivatives of the bulk and shear moduli, K~ = 5.3 + 0.1 and G~ ~ !.8 ___ 0.1, are not unusual compared with values measured for other transition zone phases such as silicate spinel and majorite garnet. Isothermal compression curves calculated with the measured values of K o and K~ agree well with experimental P - V data to 16 GPa. The experimental value of d G / d P is in excellent agreement with predictions based on elasticity systematics. Theoretical models are not yet able to replicate the measured values of K~ and G~.

1. I n t r o d u c t i o n

Birch (1952) first predicted that silica could exist as a phase with the rutile structure in the Earth's mantle. This phase of silica was later synthesized by Stishov and Popova (1961) and then a nature example was discovered by Chao et al. (1962) in the coesite-bearing Coconino sandstone of Meteor Crater, Arizona. Crystal chemistry studies showed that stishovite has a tetragonal structure with space group

* Corresponding author. i An NSF Science and Technology Center.

P 4 / m n m and unit cell parameters of a = 4.1790A, C = 2.6649A, (Chao et al., 1962; Sinclair and Ring- wood, 1978). The silicon atom in this polymorph of SiO 2 is coordinated by six oxygens rather than four in the low-pressure phases, and these edge-sharing SiO 6 octahedrals form an infinite chain along the c-axis. Stishovite has a density of 4 .287gcm -3, which is much higher than that of the low-pressure phases of a-quartz (by 60%) and coesite (by 46%).

In situ studies by Yagi and Akimoto (1976) demonstrated that stishovite is the stable phase of SiO 2 above 9GPa at 1000°C although recent work shows that at much higher pressure (approximately 45GPa), stishovite transforms to a CaC12-structure

0031-9201/96/$15.00 Copyright © 1996 Elsevier Science B.V. All fights reserved. PII S0031-9201(96)03144-5

114 B. Li et al. / Physics of the Earth and Planetary Interiors 96 (1996) 113-127

phase (Tsuchida and Yagi, 1989; Cohen, 1992; Kingma et al., 1995). From high-pressure studies of the phase diagram for MgSiO 3 to 20GPa and temperatures of 2000°C (see Sawamoto, 1987; Gasparik, 1990), we know that stishovite (SiO2-mtile) coexists with the beta and spinel phases of Mg2SiO 4 at pressures in excess of 15GPa at 1200°C. Hence stishovite may be a significant mineral constituent of the mantle in the transition zone of the Earth, and thus it is important to know its elastic properties as a function of pressure and temperature. Some previous workers have suggested that the high velocity of P and S waves of stishovite could be invoked to ex- plain the high velocity gradient in the transition zone (e.g. Liebermann et al., 1976; Weidner et al., 1982).

Brillouin spectroscopy data for the single crystal elastic moduli of stishovite reflected the extreme elastic anisotropy of this rutile-structured mineral (31% for P wave and 60% for S wave--see also Fig. 8 below) and the high values of its adiabatic bulk

and shear moduli at ambient pressure, K 0 = 316GPa and G0=220GPa , respectively. Even with this well-constrained value of K 0, analyses of static compression data have resulted in estimates of (OK/OP) r (referred to as K 0) from 0.7 to 6.0 for the pressure derivative of the isothermal bulk modulus (see Bassett and Barnett (1970), Sato (1977), Sugiyama et al. (1987) and Ross et al. (1990), and discussion by Bass et al. (1981)). There are no previous data for the pressure derivative (OG/OP)v (G~) of the shear modulus. Estimates of the pressure derivatives from elasticity systematics include K~ = 4.0 and G~ = 1.8 from Duffy and Anderson (1989) (see also Bina and Wood (1987)).

Ultrasonic techniques would yield accurate results if single crystals of sufficient size (1-10mm) were available. Unfortunately, it is impossible to synthe- size such samples of stishovite and other mantle minerals in the laboratory using current techniques. Consequently, since the 1970s, many efforts have

• Graphite heater [ ] Mo (TZM)

[ ] NaCI [ ] Taplate

[ ] Pt capsule 2mm

Fig. 1. The 14/7.5 cell assembly used for hot-pressing polycrystals of high-pressure phases (modified from Gwanmesia et al. (1990a)).

B. Li et al. / Physics of the Earth and Planetary Interiors 96 (1996) 113-127 115

been made to produce large, very dense polycrystals for ultrasonic measurements as a function of pressure (e.g. Mizutani et al., 1972; Liebermann et al., 1976; Liebermann and Ringwood, 1977). However, cracks and pores in the early hot-pressed specimens and a limited pressure range (less than 1.0GPa) made it impossible to determine reliable pressure derivatives of the elastic-wave velocities.

Two recent technological advances have made it possible to conduct more precise studies of the elasticity of stishovite at high pressures: (1) the development of techniques to fabricate well-characterized polycrystalline specimens of high-pressure phases in multi-anvil apparatus at Stony Brook (Gwanmesia and Liebermann, 1992; Gwanmesia et al., 1993); (2) the development of precise techniques to study mil- limeter-size polycrystalline aggregates using ultrasonic interferometry at the Australian National Uni- versity (Niesler and Jackson, 1989; Rigden et al., 1992). We have adopted these techniques to revisit the topic of stishovite elasticity (see preliminary reports of these experiments by Li et al. (1992, 1994), Li (1993) and Rigden et al. (1994)).

The purpose of this paper is to describe the synthesis and characterization of hot-pressed polycrystals of stishovite, to report new ultrasonic data to 3GPa, and to compare these new data with the elastic properties of other rutile-structure oxides from experimental data and theoretical calculations.

telescopic furnace design and the tantalum plates which cap the cylindrical graphite furnace. Pressures are determined from calibration curves based on known phase transformations at high temperature (e.g. garnet to perovskite in CaGeO 3, coesite to stishovite in SiO 2 , olivine to beta phase and spinel in Mg2SiO4), and temperatures are calculated from prior calibration experiments which provide the relationship between sample temperature and electrical power. The reproducibility in temperature is within 1% for the same power (Gwanmesia and Lieber- mann, 1992).

In attempting to hot-press fully dense, isotropic polycrystalline specimens of stishovite, we faced two difficulties not encountered in our previous syntheses of the beta and spinel phases of Mg2SiO 4 (Gwan- mesia et al., 1990a; Rigden et al., 1992) and a pyrope-majorite garnet (Rigden et al., 1994). First, stishovite is much denser (4.287gcm -3) than its low-pressure polymorphs a-quartz (62%) or coesite (45%) and amorphous or fused silica (95%); as a consequence of these large volume redlactions, the hot-pressed specimens are likely to be smaller in dimension. Second, stishovite is extremely anisotropic in its elastic-wave velocities (31% for P waves and 60% for S waves); thus, even a small degree of preferred orientation within the polycrys-

1200

2. Specimen fabrication

All of the stishovite specimens used in this study were synthesized in the 2000 ton uniaxial split-sphere apparatus (USSA-2000) at the Stony Brook High Pressure Laboratory (Liebermann and Wang, 1992) using the specialized cell assembly developed for hot-pressing polycrystalline specimens at pressures up to 20GPa and temperatures up to 1700°C (see details given by Gwanmesia and Liebermann (1992) and Gwanmesia et al. (1993)) (Fig. 1). Key features of this cell assembly for our purposes are: (1) the large sample volume (25mm3); (2) the low deviatoric stress (less than 10 MPa) imposed by the NaCl immediately surrounding the encapsulated sample; (3) the low axial temperature gradient along the sample axis (less than 15°Cmm - l) owing to the

~oooi

800 ~

P soo

i ~. 4oo

200

0 0 16

Qtz Coes~te /

TI

2 4 6 8 10 12 14

Pressure, GPa

Fig. 2. Comparison o f the P - T - t paths explored in the stishovite hot-pressing experiments.


talline specimen would produce a directional dependence of its velocities and their pressure dependence.

For the hot-pressing experiments, we utilized sev- eral P - T - t paths (Fig. 2). In all cases, the cell pressure is first increased slowly (over 3 - 4 h up to the target pressure, after which the temperature is increased to the desired value (T 0) over a period of 10-20min. After maintaining the sample under the peak P - T conditions for a suitable time interval (15-60min), the pressure is decreased slowly over periods extending to 36h at rates monitored by a computer-controlled system. The cell temperature follows one of three paths: (1) Path Q-- the sample is quenched to room temperature in a few seconds and the pressure then decreased at about 1 GPa h- ~; (2) Path R--decompression and cooling occur simultaneously in the stability field of stishovite to room temperature before final decompression to ambient conditions; (3) Path S l - - t h e pressure and temperature initially decrease simultaneously in the stability field of stishovite, at 400°C the temperature is kept approximately constant and the pressure is released slowly at a rate of about 0.5GPah -~ (annealing period) to about 4 GPa, then the pressure and temperature are again decreased simultaneously to ambient conditions at 1.0GPah-~ and 50°Ch -

The annealing temperature in Path S 1 is important to preserve the high-pressure phase and to release the intergranular stresses. High annealing temperatures will result in transforming back to the low-pressure phase. For example, when Run 1481 was simultaneously decompressed and cooled from P = 11 GPa and T = 1100°C, the recovered product was found to

be coesite with trace of stishovite; this is because the run conditions entered the coesite stability field at relatively high temperature (above 550°C).

Our initial runs used amorphous silica powder as the starting material (cold-pressed into the Pt capsule) and followed Path R. These specimens (Table 1) were fully transformed in 1 h at 1050°C, and well sintered with high bulk densities (greater than 99% of theoretical), but were irregular in shape and rather small owing to the large volume reduction (49%) on conversion to stishovite and the initial porosity of the powder silica. In addition, the P-wave velocities were low and exhibited a tendency to decrease with time, suggesting that microcracks within the specimen were gradually opening up (see Run 1422 in Table 1). In an attempt to minimize the volume loss, small amounts of stishovite (20% estimated from X-ray diffraction) and coesite (5%) were mixed with quartz (75%) and run at relatively higher P and T conditions to ensure conversion of the coesite to stishovite. However, even these specimens were not sintered as well as those using amorphous silica as the starting material.

To solve the problem of densely packing the starting material, a solid fused quartz rod (3 mm diameter) was sanded to just fit inside the capsule; the starting rod usually weighs about 50 mg, which is about 15 mg more than that for the amorphous silica powder. The recovered specimens were about 2.5 mm long and 2.5 mm in diameter, and most importantly, the specimens exhibited good cylindrical shape with flat ends. Specimens 1500 and 1502 were produced by quenching from peak temperature; X-ray spectra

Table 1

Hot-pressed stishovite samples

Run no. Starting material P (GPa) T (°C) P - T path Sample length ( m m ) Density (g c l n - 3 ) P-wave velocity

v~ v, v, 1411 ASP 10 1050 R 1.27 4.29 - -

1422 ASP 10 1050 R 1.71 4.26 10.1 10.2

1481 SCQ 11 1100 S1 - 2.90 - -

1500 FSR 14 1050 Q 2.41 4.29 - -

1502 FSR 14 1050 Q 2.23 4.25 - -

1520 FSR 14 950 R 2.54 4.05 - -

1533 FSR 14 1050 SI 2.54 4.27 - -

1581 FSR 14 950 SI 2.54 4.18 - 11.4

1639 FSR 14 1050 Q - 4.03 - -

9.0 10.3 a

11.4 l l.4 10.2 I 1.6 I 1.4

a Vz = 1 0 . 8 k m s - i measured 2months earlier. ASP, amorphous silica powder; SCQ, mixture of stishovite, coesite and quartz; FSR, fused silica rod.

B. Li et a l . / Physics of the Earth and Planetary Interiors 96 (1996) 113-127 117

demonstrate that they are fully transformed to stishovite within 30min at 1050°C; it should be noted that this was not true for specimens 1520 (950°C, 25min) and 1639 (1050°C, 15min), both of which contained some coesite. The optimum polycrystalline specimens were produced from the fused silica starting material and runs along Path S1 (1533 and 1581), as we shall demonstrate below.

3. Specimen characterization

Acoustic properties are very sensitive to the quality of the hot-pressed polycrystalline specimens (e.g. Spetzler et al., 1972). In the previous studies of stishovite by Liebermann et al. (1976) and Mizutani et al. (1972), the polycrystalline aggregates had large porosity (up to 5%) and exhibited some diametrical cracks; also, little information is available about the characterization of grain distribution and preferred orientation in their samples. In our study, a detailed characterization combining X-ray diffraction spectra, density measurements, optical and scanning electron microscopy and acoustic velocity measurements at room conditions was made to check the quality of the recovered polycrystalline aggregates of the hot- pressed stishovite.

For the preliminary experiments, the run products were ground in a mortar and the powders mounted onto a microscope slide. X-ray diffraction spectra were taken on a Scintag diffractometer (Scintag, Inc., Sunnyvale, CA) at 1600W (45kV and 35mA) using a copper K-alpha target. Comparison of the observed spectrum from 20 to 70 ° in 2 0 with JCPDS spectra of stishovite (Card 150026) demonstrates that all the observed diffraction peaks match those of stishovite (Fig. 3(a) and Fig. 3(b)). For those specimens hot-pressed along Path SI and which were eventually used for acoustic measurements, a non- destructive technique was used to obtain diffraction spectra from the end of the specimen. The spectrum taken from Specimen 1533 using this technique is shown in Fig. 3(c). It is evident that the spectra from the powder and the end of the hot-pressed specimen are identical even though much lower sample diffraction intensities and relatively high glass background (from the microscope slide on which the sample was mounted) are observed in the spectrum taken from

n

_=

(C) #1533 End Surface

.• (B) #1411 Powder

= _ , L _ , L . J ....

(A) JCPDS Card File (Stishovite)

25 30 35 40 45 50 55 60 65 70

20 (o)

Fig. 3. Comparison of the X-ray diffraction spectra from (a) JCPDS card of stishovite, (b) powder sample, and (c) end surface of a cylindrical sample.

the end of the specimen (Fig. 3(b) and Fig. 3(c)). In some cases, spectra were taken from both ends of the specimens to check its homogeneity. When this was done, very similar spectra were observed.

Bulk densities of the specimens were determined using the Archimedes immersion method and carbon tetrachloride as the weighing fluid (see results in Table 1); tests with MgO single crystals of compara- ble mass indicate that the precision of these measurements is + 0.3%. All of the fully transformed specimens have bulk densities within 1% of the theoretical X-ray density for stishovite (4.287 gcm- 3), including Specimen 1533 (4.274 gcm- 3) used for subsequent ultrasonic studies at high pressure.

Scanning electron microscopy (SEM) enables us to characterize the grain sizes and their distributions in the synthesized stishovite specimens and provides insight into the possibility of shape anisotropy. Spec- imens examined by SEM were broken along directions perpendicular and parallel to the axial direction and these pieces were mounted onto the flat surfaces of aluminum cylinders; then they were coated with an ultra-thin layer of gold. The experiments were conducted on a JSM-25 Scanning Electron Micro- scope at 15 kV with a working distance of 10mm.


The scanning electrom micrographs shown in Fig. 4 were taken from the broken surfaces along the axial direction in Run 1502. Most grains are less than 71xm, have excellent crystal faces and some exhibit triple junction boundaries (Fig. 4(b)). Two major populations of grain sizes around 5 I~m and 2 ixm are distributed randomly over the entire broken surfaces. No significant variation in grain size was observed from the center to the boundaries of the specimen. A photograph of a 2001~m× 150p.m window (Fig. 5) located near the central region along the axial direction of 1502 demonstrates random

A.

lOlun

B.

10 iJxn Fig. 4. Scanning electron micrographs of Specimen 1502. (a) Random distribution of grains; (b) triple junctions.

distribution of the elongated crystals. The textural homogeneity of these specimens suggests that both the temperature and pressure gradients in the sample chamber are small.

Internal residual strain may affect the elastic-wave velocity measurements for polycrystalline samples as noted by Spetzler et al. (1972). Recently, Weidner et al. (1994) have developed a new technique based on the peak width of the X-ray diffraction peaks to determine the microscopic yield strength using synchrotron radiation in conjunction with a DIA-type cubic anvil apparatus (SAM 85) installed in the superconducting wiggler beamline (X17B1) of the National Synchrotron Light Source at the Brookhaven National Laboratory. We have used this new technique to study powder and polycrystalline specimens of stishovite (Figs. 6 and 7). The two specimens were simultaneously compressed (in different parts of the same sample chamber) up to P = 12 GPa and then heated to T = 1030°C and monitored with in situ X-ray diffraction. Both the powder and polycrystalline samples were surrounded by BN as the pressure transmitting medium with NaC1 as the pressure standard. As the powder sample is compressed at room temperature, the individual diffraction peaks broaden as a consequence of the compacting process (Fig. 6(a)), indicating an increase in microscopic deviatoric stress. When heated under high pressure, these peaks sharpen above 400°C and approach their initial widths. In contrast, as the polycrystalline specimen is compressed to 12GPa and subsequently heated to 1030°C (Fig. 6(b)), the diffraction peaks exhibit no broadening or sharpening. These data indicate that the microscopic deviatoric stress experi- enced by the individual grains in the polycrystal under high pressure and temperature is extremely low. Consequently, we conclude that the single- crystal grains within this polycrystalline aggregate are well equilibrated (at least at 10GPa and 1000°C) and the hot-pressed specimen is free of residual strain.

To assess the acoustic quality of our stishovite specimens, P-wave velocities are measured using the pulse transmission technique (e.g. Liebermann et al., 1975). The cylindrical specimens were polished using Glennel Diamond Compound (Dunnington Co., Chester Springs, PA) with a final polishing grade of 3 Ixm. Piezoelectric transducers (PZT-5)(Valpey

B. Li et a l . / Physics of the Earth and Planetary Interiors 96 (1996) 113-127 l 19

Fisher Corp., Hopkinton, MA) of frequency 5 MHz were used to generate and detect the acoustic signals; after corrections for system delays, the measured travel times are precise within + 2%.

Preliminary P-wave velocities in both axial and radial directions were measured to see whether preferred orientation in the specimens produced velocity anisotropy. Fig. 8 is a schematic diagram showing polished surfaces and measuring directions; the measured P-wave velocities are listed in Table 1. For both Specimens 1422 and 1581, the velocities observed in the axial and radial directions are identical within the experimental uncertainty. Stishovite is so anisotropic (31% for P and 60% for S waves) that even a minor amount of preferred orientation should produce velocity anisotropy. The results of prelimi-

nary P-wave velocity measurements for Specimens 1422 and 1581 indicate that the possibility of having preferred orientation in these specimens is extremely low.

Velocity measurements using an ultrasonic inter- ferometer were conducted at the Australian National University at ambient pressure and temperature conditions; the experimental equipment and its operation have been described in detail by Rigden et al. (1992). The measured acoustic velocities for Specimen 1533 are Vp = 11.78 + 0.11 km s-~, ~ = 7.12 ± 0.07 km s ~ (Table 2); these results agree within the nmtual uncertainty with the Hashin-Shtrikman average of the single crystal data of stishovite from Brillouin spectroscopy (Weidner et al., 1982).

In summary, the application of these high-pres-

m 101ma

Fig. 5. Scanning electron micrograph of a 200mm × 150mm window near the central region along the axial direction of Specimen 1502.

120 B. Li et al . / Physics of the Earth and Planetary Interiors 96 (1996) 113-127

(a) Polycrystalline Sample ]

10GPa 1030 *C 110

101 J

10 0

12GPa 25 °C

~ m Condition

J

I I I I I i I I

400 600 800 1000 1200 1400 1600 1800

Channel Number

I. oorS.m ol 11o

lO GPa 1030 *C

111 211

5 I I

400 600 i I I i I

800 1000 1200 1400 1600

Channel Number

i

1800

25

20

15 u .

lO

25

2o

15 u .

Polycrystal (T=25 °C )

--*-- 220

111 101

10

S . . . . . . . . . .

0 2 4 6 8 10 200 400 600 800 1000

Pressure (GPa) Temperature (°C)

Fig. 7. Variations of the X-ray diffraction peak widths (FWHM) with P and T for powder and polycrystal stishovite samples.

sure techniques to hot-pressed polycrystailine stishovite is successful; the specimens using fused quartz rods as starting material and recovered along P - T Path S1 are homogeneous, fine grained (around 71~m), well crystallized with equilibrium texture, low porosity (less than 1%), free of preferred orientation and in agreement with the Hashin-Shtrikman average of the single crystal velocities for both P and S waves. In the following section, we describe the measurement of the pressure dependence of the elastic-wave velocities.

4. High-pressure ultrasonic interferometry

High-pressure ultrasonic interferometry experiments to measure P- and S-wave travel time as a

Fig. 6. Comparison of X-ray diffraction spectrum at room conditions with those at high P and T for stishovite. (a) Polycrystal sample; (b) powder sample.

B. Li et al. / Physics o f the Earth and Planetary Interiors 96 (1996) 113-127 121

Z

t

i :- X

i: I ....... = : ....... ~'...-

Fig. 8. Schematic diagram for the P-wave velocity measurements in axial (Z) and radial (X and Y) directions.

function of pressure (to 3 GPa) were carried out in a liquid medium piston cylinder apparatus. The details of both the configuration of these experiments and the technique of phase-comparison interferometry employed have been presented in detail elsewhere (e.g. Niesler and Jackson, 1989; Rigden et al., 1992). Important features of the experiment include: utiliza- tion of the top high-pressure seal as a buffer rod to separate the piezoelectric transducer from the high- pressure environment; a liquid pressure medium to provide hydrostatic conditions around the specimen; surrounding the sample free surfaces with highly attenuative lead to avoid the return of any unwanted reflections from beyond the end and from the sides of the sample; a soft copper jacket to isolate any porosity in the sample from the fluid, thereby pre- venting the possibility of fluid-generated fracture; a thin gold bond between the sample and buffer rod whose well-characterized elastic properties allow bond corrections to be made readily over the entire experimental pressure range; use of the lower high- pressure seal as a former for a calibrated minalpha wire resistance pressure gauge allowing measurement of pressure to a precision of better than 10MPa (Niesler et ai., 1989).

Two-way elastic-wave travel times were measured as a function of frequency (20-60 MHz) between atmospheric pressure and 3 GPa. Travel times were averaged from the high-frequency part of the frequency range (40-60MHz) and velocities were

calculated from these travel times. Correction for the change of sample length with pressure was calculated from the pressure dependence of the travel times using the method of Cook (1957). Before averaging, raw travel times were corrected for the effect of the gold bond (Niesler and Jackson, 1989). For P waves this correction is approximately - 3.5 ns and for S waves it is approximately 1.2 ns.

5. H i g h - p r e s s u r e resul ts

Velocities calculated from the high-pressure P- and S-wave travel times are shown in Fig. 9(a) and Fig. 9(b). Also shown are the values for P- and S-wave velocity at zero pressure calculated from the single crystal Brillouin scattering measurements of Weidner et al. (1982). The velocities extrapolated from the high-pressure results to atmospheric pressure for this small specimen are somewhat lower (1.4% for P waves and 0.3% for S waves); however, the velocities again agree within the mutual uncer- tainties of each set of measurements. As in our earlier studies (Rigden and Jackson, 1991), linear trends of velocity as a function of pressure were observed above a threshold pressure of between 1 and 1.5 GPa. At lower pressures, the velocities are compromised by incomplete coupling across the sample-buffer rod interface. This is identified in the raw signals observed on the oscilloscope as a rapid change in the ratio of sample echo to buffer echo at low pressures. At pressures between 1 and 1.5 GPa,

Table 2 Elastic properties of stishovite of Specimen 1533 (length 1.833mm, diameter 2.300mm)

Elastic properties

Properties at P = I bar Density (g cm - 3) 4.274 (99.8%) Vp (km s t) ll.78_+0.11 V s (kms- i) 7.12_+0.07 K o (GPa) 305 +_ 5 Go (GPa) 217 _+ 4 Pressure derivatives OVp/bP (km sGPa- ~ ) 0.056 + 0.002 3V s / ~ P (km sGPa- J) 0.017+0.001 3K / 3 P 5.3 +_ O. I 3 G / 3 P 1.8 + O. I

122 B. Li et al. / Physics o f the Earth and Planetary Interiors 96 (1996) 113-127

(a) 12

.-,, 11.9

E 11.8

11.7 4.l ¢J o 11.6

> 11.5

11.4

.s Bounds

J

1 atm ~ -

• 0•0 °° :]j o P increasing

• 0 • P decreasing :

°° =P waves

0 0.5 1 1.5 2 2.5 3 3.5

P r e s s u r e ( G P a )

(b)

~ ' 7.16

E 7.14

>., 7.12 tO

o

> 7.1

7 . 1 8 ' ~ . . . . . ' . . . . ' r ; ' . . . . 1 . . . . ~ . . . .

i5a3 HS Bounds (7.14.7.22) [ 1533~

611 atrn y 0 o P increasing

• o • P decreasing o

S waves I 7 .08 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

0 0.5 1 1.5 2 2.5 3 3.5

P r e s s u r e ( G P a )

Fig. 9. P- and S-wave velocity of stishovite vs. pressure up to 3GPa as determined by ultrasonic interferometry in a piston cylinder apparatus. (a) P waves; (b) S waves. The HS bounds for P and S waves are calculated from the single-crystal data of Weidner et al. (1982).

this ratio becomes constant, indicating that the interface is behaving like a welded contact. Slight hysteresis is observed in the high-pressure results. For shear waves, the velocities measured as pressure is decreased define a slightly lower slope than those measured as pressure is increased. This amounts to a d i f f e r e n c e in s l o p e o f a p p r o x i m a t e l y 0 .0015kms - 1 G P a - l and is reflected in the quoted errors.

Values of ( ~ K , / ~ P ) r ( K s is adiabatic bulk modulus) and ( a G / ~ P ) r (henceforth referred to as K~ and G~) were calculated in two different ways from our experimental data. First, a simultaneous fit for K s, G, K~ and G~ was made with the measured veloci-

ties and a Birch-Murnaghan equation-of-state (e.g. Gwanmesia et al., 1990b; Rigden et al., 1992, Rig- den et al., 1994). A second approach, which yields essentially identical results for K~ and G o, used the measured velocity derivatives, (SVp/SP) r and (avs /aP) r, in combination with the Hashin-Shtrik- man average from single crystal Brillouin scattering measurements and the theoretical density. The quoted errors in K~ and G~ (Table 2) reflect both hysteresis in the shear-wave velocity measurements and the two methods of calculation. The values of K~ and G~ determined from this study (Table 2) are compared in Table 4 (below) with other experimental measurements and theoretical calculations.

6. Comparison with other experimental data

Mizutani et al. (1972) and Liebermann et al. (1976) both measured the P- and S-wave velocity as a function of pressure to about 1 GPa using ultrasonic pulse transmission techniques on polycrystals of stishovite. Information about the sample quality used in the study of Mizutani et al. (1972) (e.g. the acoustic isotropy, grain size and distribution, and porosity) is not available. The sample used by Liebermann et al. (1976) was characterized as an acoustically isotropic, sintered cylinder with bulk density of 98.4%. Both studies reported similar P- wave velocity but different S-wave velocity in ambient condition measurements, presumably owing to the presence of cracks in the sample used by Mizu- tani et al. (1972) as noted by Liebermann and Ring- wood (1977). Both of these earlier P- and S-wave velocity measurements are lower than the values obtained using ultrasonic interferometry and Bril- louin scattering (Table 3). By comparison of our

Table 3 Elastic-wave velocities of polycrystal stishovite

Vv (kms- ]) Vs (kms -l ) Mizutani et al. (1972) 11.0 5.5 Liebermann et al. (1976) 11.0 (2) 6.9 (3) This study 11.78(11) 7.12(7) Weidner et al. (1982) a 11.93 (5) 7.18 (4)

a Calculated from the single-crystal elastic moduli by the Hashin-Shtrikman average.

B. Li et at./Physics of the Earth and Planetary Interiors 96 (1996) 113-127 123

zero-pressure P- and S-wave velocities with those calculated from single crystal data of Weidner et al. (1982), excellent consistency is obtained within the mutual uncertainty of both techniques (see also Li et al. (1992)). This suggests that the measurements on current polycrystalline specimens are representative of the bulk elastic properties of stishovite. The dis- crepancies between this study and the earlier ultrasonic studies (Mizutani et al., 1972; Liebermann et al., 1976) are probably caused by the quality of the samples used in the earlier measurements, including the porosity, internal residual strain and preferred orientation.

P - V - T compression studies also provide information on bulk modulus and its pressure derivative. However, the non-hydrostaticity of the pressure makes it difficult to determine correct P - V relationship and to constrain the bulk modulus. To avoid this problem, Olinger (1976) and Sato (1977) performed isothermal compression studies on stishovite in a fluid pressure medium, and their results are also listed in Table 4. From a combined analysis of the data of Olinger and Sato, Bass et al. (1981) inferred

! _ _ values of isothermal K 0 = 298 + 8 GPa and K 0 - 3.7 _ 1.6, which are compatible with current results. In recent static studies, using diamond anvil appara-

tus, by Sugiyama et al. (1987) and Ross et al. (1990), P - V data were collected in the pressure range of 0 - 6 G P a and 0-16GPa, respectively. The adiabatic bulk modulus from our measurements is converted to an isothermal value of K 0 = 302 GPa using the same parameters as those of Weidner et al. (1982). In Fig. 10, we compare the isothermal compression data of Ross et al. (1990) with a Birch-Murnaghan equation-of-state using new measurements of K 0 and K 0. Clearly, the calculated curve fits the experimental data well to pressure of 16 GPa.

7. Comparison with theoretical calculations

A number of theoretical calculations using different models (Striefler and Barsch, 1976; Park et al., 1988; Cohen, 1991; Keskar et al., 1991; Sherman, 1993; Jolly et al., 1994) also have been carried out that lead to predictions of elastic properties of stishovite. A selection of the predicted bulk and shear moduli and their pressure derivatives are sum- marized in Table 4. Early studies by Striefler and Barsch (1976), using a modified rigid ionic model, predicted K o = 315 GPa and G o = 203 GPa. These

Table 4

Compar i son o f elastic modul i o f st ishovite with other experimental results and theoretical ca lcula t ions

Method K o (GPa) K~ G O (GPa) G~

Experimental results This study (1995) Ul t rasonic 305 a 5.3 217 1.8

Weidner et al. (1982) Bri l louin scattering 316 ~ - 220 -

Mizutani et al. (1972) Ultrasonic 346 a _

Liebermann et al. (1976) Ultrasonic 250 a _ _ _

Ol inger (1976) Compress ion 298 6

Sato (1977) Compress ion 298 0.7 - -

S u g i y a m a et al. (1987) Compress ion 313 6 - -

Ross et al. (1990) Compress ion 313 1.7 - -

Bass et al. (1981) 295 3.7

Theoretical calculations Keskar et ai. ( 1991 ) Pseudopotent ia l 292 .0 5.86 124 b _

Cohen ( 1991 ) L A P W 324 4 .04 - -

Park et al. (1988) F L A P W 288 3 .14 - -

Sherman (1993) Periodic H a r t r e e - F o c k 328 4.0 - -

Jol ly et al. (1994) Per iodic H a r t r e e - F o c k 327 2.8 - -

S t r i c t e r and Barsch (1976) Rigid ionic model 315 7.0 203 1.13

a Adiabat ic bulk modulus .

b Calcula ted f rom given K and o-.


1.01

1.00

0.99

0.98 >~

0.97 ' " %...%~...

0.96 "'1%-..

~ 0.95 ........... Uncertainty

• Ross et al. (1990)

0 . 9 4 ¢ I i I I I I I

0 2 4 6 8 10 12 14 16 18

Pressure (GPa)

Fig. 10. Isothermal compression of stishovite to 16GPa determined experimentally using in situ X-ray diffraction of single crystals by Ross et al. (1990) and calculated via the Birch- Mumaghan equation-of-state using the values of K o = 302GPa and K~ = 5.3 measured in this study.

calculated results agree very well with the experimentally determined values of K 0 = 305GPa and Go = 217GPa from this study, and K 0 = 316GPa and G O = 220 GPa from single-crystal Brillouin scattering by Weidner et al. (1982). However, in com-

¢ t parison with K 0 = 5.3 and G O = 1.8 measured in this study, their calculated derivatives K~ = 7.0 and G~ = 1.13 are 32% higher and 33% lower, respectively. As noted by Striefler and Barsch (1976), the lack of data for the zero-pressure elastic moduli of stishovite to constrain their calculations may be a potential source of error. Using a pseudopotential method, Keskar et al. (1991) predicted K o = 292GPa and K; = 5.86, in good agreement with current measurements; however, the shear modulus calculated from K and tr given in their study (G O = 124GPa) is much lower than that measured. By comparison, the predictions of K 0 from the linearized augmented plane wave (LAPW) approach by Cohen (1991) ( K 0 = 3 2 4 G P a ) and the periodic Hartree-Fock model by Sherman (1993) (K 0 = 328 GPa) and Jolly et al. (1994) (K o = 327GPa) agree very well with each other, but are slightly (around 5%) higher than the experimental values. The predictions of K', including FLAPW by Park et al. (1988) (K~ = 3.14),

LAPW by Cohen (1991) (K~ = 4.04), Hartree-Fock by Sherman (1993) (K~ = 4.0) and Jolly et al. (1994) (K~ = 2.8), are all lower than the K 0 = 5.3 reported in this study. Clearly, it is still not possible to replicate the measured experimental values of K 0, G o , and their pressure derivatives with theoretical calculations.

8. Elasticity systematics in ruti le-structured oxides

Recently, there has been much interest in the prediction of high-pressure and high-temperature elasticity of phases stable in the Earth's mantle. At present, the bulk and shear moduli at ambient P and T conditions for most of the important deep mantle phases have been determined. However, the information on how these parameters change under conditions relevant to the deep mantle is still lacking. There has been substantial progress in the measurement of the pressure dependence of elastic moduli of mantle minerals, not only through acoustic and im- pulsively stimulated scattering measurements (e.g. Rigden et al., 1992; Zaug et al., 1993) but also through the measurement of acoustic modes by side band fluorescence techniques (Chopelas, 1992). High-quality, X-ray diffraction studies in the diamond cell or cubic anvil apparatus are providing increasingly strong constraints on pressure and temperature derivatives of the bulk modulus (e.g. Wang et al., 1994; Utsumi et al., 1996).

G '

2 .2 . . . , . . . , . . . , . . , , , r

1.7

1 .2

0 SlO=

GeO= o

[ Rutile-structured I TIO= 0.7 [ Oxides I o

o s h e 2

0 . 2 . . . . . . . . . . . . . . . . . . .

1.2 1.4 1.6 1.8 2 2.2

K I G

Fig. l I. G' vs. K / G for futile-structured oxides.

B. Li et al. / Physics of the Earth and Planetary Interiors 96 (1996) 113-127

Table 5 Elastic properties of oxides with the futile structure

125

SiO 2 Ti02 GeO2 SnO2

Density (g cm - 3) 4.287 4.260 6.277 6.992 Mean atomic weight (g) 20.0 26.6 35.0 50.0

Cation radius (,~) 0.400 0.605 0.530 0.690 Molar v olume (cm 3 ) 14,014 18.820 16.660 21.55 V p ( k n l s - I ) 1 . 7 8 9 . 2 6 8 . 5 5 6 7 . 0 6

V s (kms-~) 7.12 5.14 4.898 3.82 Bulk sound velocity (km s -~ ) 8.43 7.12 6.42 5.51 K o (GPa) 305 216 258.9 212.3 G O (GPa) 217 112 150.9 101.8 (~Ks/3P) T 5.3 6.76 6.15 5.13 (~G/~P)T 1.8 0.78 1.22 0.61 Reference This study Manghnani (1969) Wang and Simmons (1973) Chang and Graham (1975)

Elasticity systematics may allow these parameters to be predicted. This approach was successful in predicting both K~ and G~ for 13- and ~,-Mg2SiO 4 (Duffy and Anderson, 1989). Interestingly, it is G~ that seems to be more reliably predicted from systematics than is K', which should be more amenable to prediction theoretically. A correlation between G~ and K / G which gives linear trends for a given structure was noted by Duffy and Anderson (1989) (see also Anderson (1988)) for a large set of pub- lished data. This correlation was observed to hold at a finer level for spinel-structured oxides with subpar- allel trends for spinels with the same cation in tetrahedral coordination. This allowed a prediction of G~ for Mg2SiO4-spinel to be made; a later experimental study demonstrated that the prediction was within 10% of the measured G~ (Rigden and Jack-

7 . 5 . . . . F . . . . i . . . . i . . . . i . . . . i . . . .

Oxide 7 ~ 0 TIO2

N 6.5 GeO= o K' 6

. . . . i . , _ _ i . . . . i . . . . i , x . . i . . . .

4 0 1 2 3 4 5 6

K(M/p ) 1/3

Fig. 12. K' vs. K ( M / p ) I/3 relationships. Continuous lines represent oxides and non-oxides; O, ruffle-structured oxides (modified from Duffy and Anderson (1989)).

son, 1991). The elastic properties of stishovite are tabulated in Table 5 in combination with other iso- morphic oxides. The rutile-structured oxides, SnO 2, SiO 2, GeO 2, and TiO 2 itself, show a strong linear correlation on such a diagram, reinforcing the coher- ence in elastic properties within a single structure (Fig. 11).

Systematic variation of K~ is less obvious even for this suite of oxides with the same structure. The dependence of K r on the repulsive range parameter in a central force model of interatomic potential that is expected from theoretical considerations (Ander- son and Anderson, 1970) would suggest a linear relationship between K~ and interatomic spacing. This relationship has been observed to hold for simple diatomic ionic compounds for which estima- tion of reliable interatomic spacing is clear (Duffy and Anderson, 1989). An analogous relationship that has been observed to hold empirically is one between K' s and Ks(M/p) 1/3, where (M/p) 1/3 is a measure of interatomic distance (M is the average atomic weight and p is density). Two broad trends of K~ vs. K~(M/p) 1/3 were identified by Duffy and Anderson (1989) for oxide and non-oxide structures. A number of 'anomalous' materials with high K~ were also identified, particularly the rutile-structured oxides GeO 2, SnO 2 and TiO 2. Inclusion of the new data for stishovite indicates a linear trend for GeO 2, SiO 2 and TiO 2 with SnO 2 as an outlier (Fig. 12). It seems clear that something distinctive about the rutile structure is responsible for the high values of K~, at relatively high values of Ks(M/o) 1/3.

126 B. Li et al. / Physics t~f the Earth and Planetary Interiors 96 (1996) 113-127

Acknowledgements

It is a special pleasure for us to contribute this paper to the special issue in memory of A.E. (Ted) Ringwood, in whose laboratory R.C.L. worked as a research associate for 6years. We would like to dedicate this paper to Alan Major, long-time research associate in Ted's laboratory, who helped to develop the techniques of hot-pressing at high pressures and synthesized the specimens studied in our earlier work on the elasticity of stishovite. We thank G.D. Gwan- mesia for his tutelage in hot-pressing experiments, Don Weidner for his encouragement and scientific advice on the experiments of characterization of polycrystalline stishovite using synchrotron X-ray radiation, and Greg Symmes for his assistance in the SEM work. We have also benefited from discussions with Jianzhong Zhang and Ian Jackson, and the technical assistance from Tibor Gasparik, Ken Bald- win, Benedict Vidale and Bill Hibberson. We appre- ciate the constructive reviews of this paper by D.G. Isaak and A. Yoneda. We are grateful to the Re- search School of Earth Science of ANU for a Visit- ing Fellow position at ANU for R.C. Liebermann in 1992. The hot-pressing experiments were conducted in the Stony Brook High Pressure Laboratory, which is jointly supported by the State University of New York and the NSF Science and Technology Center for High Pressure Research (EAR 89-20239). This research was also supported by EAR 93-04502 and the US-Australia Cooperative Research Program (NSF INT 89-13363) and the Australia Department of Industry, Technology and Commerce. This paper is MPI Contribution 150.

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Elasticity of stishovite at high pressure