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LA-UR-76-1399

TITLE: STIStfOVtTE: A COMPARISON OF SHOCK COMPRESSION DATA

WITH STATIC COHFRESSION AND ULTRASONIC DATA

AUTHOR(S): ~rt W. ()][nger

SU13M1’1TED TO: U. s. - Japan Saminar “High Pressure

Research Applications in Geophysics’

BY acwptmwe of thk ●mkb for publloatlon, thepublkher~nlza Uta(Jovamrnmt’@ (Ibcanma)rightmInanycopyrlghtmid theQovsmmantaad ksauthorizadro~nti IIvesIwva un~lrktad Anht to r9pduce Inwhole or In part dd ●rtlala under aay copyrightsecured bythepublkhar.

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Stishovite: A Comparison of Shock Compression Oata with

Static Compression and Ultrasonic Data

Bert Olinger

Los Alams Scientific Laboratory

Los Alamos, New Mexico 87545

ABSTRACT

The ultrasonic and static canpression data for stlshovite

were transformed to shock and particle velocities and compared with

the higher pressure shock compression data for u-quartz. Using

the transformation schama described In the text, good agreement is

found between the shock data and stislmvite rero pressure moduli

ranging from KQ - 300 GPa, K~=3 to K = 250 GPa, K&-6.o

J

There is interest in the equation of state of stishovite, the

stable solid phase of S102 at screw pressure above 8 GPa (8o kilobars),

because there is substantial evidence stmlng that silicates decompose

to oxide states at conditions inside the earth; a major constituent

of these oxides 1s S102.

interior conditions using

[Altshuleret al., 1965],

Oata has been gathered on stlshovite at earth-

shock compression techniques, [Uackerle, 1962],

[Trunin et al., 1970], [Trunir, et a~., 1971],

but the results are complicated by having to start with materials, such

as a-quartz or glass, from which the stishovite phase Is obtained under

shock compression only after undergoing a phase transformation Involving

large energy and volume changes.

More recently there has been substantial work on the thermodynamic

properties of pure stishovite. The heat capacities and enthalples of

transformation were determined by Helm et al. [1967] for glass, a-quartz,

and stlshovIte. Also, there have been two determinations of the volume

thermal expansion [Weaver et al., 1973], [Ito et al., 1974]. And finally,

determinations of the zero pressure bulk modulus (Vo~P/3V)F - ~) have been

made using ultraso~ic techniques [HIzutanl et al., 1972], [Chung, 1974],

[Llebermann et al., private communication 1976] and using high pressure

x-ray diffraction techniques [Bassett and Barnett, 1970]0 [Llu et al.,

1974], [Ollnaer, 1976a]. Here the bulk modulus determinations wI1l be

compared to the shock compression data using the heat capacity, trans-

formation enthalpy, and thermal expansion data.

l’he Isothermal compression Is first described In terms of the

linear shock-particle velocity equation analog Introduced by

and Halleck [1975]. The analog relations are

uSt

-Ct+s ut pt’

4

(1)

u ‘-St (Pvo/(bv/vo) ) “2, (2)

upt - (fwo (l-v/vo))“*. (3)

v/v. - (u~t-upt)/u~t, (4)

p = u~tlJpt/vo, (5)

where V. Is the specific volume at ambient conditions and V Is the specific

volumeat pressure P. The compatible units to use In equation (1) through (5)

are P In GPa, V in cm3/g, and Ust, U in km/s. For those more accustomedpt

to the familiar Hurnaghan and Birch-Murnaghan

zero pressure bulk modulus from Eq. (1) Is

and

For

the

K - c:/vooOt

Its pressure derivative Is

K’ - 4 s -19Ot t

P-V equations, the isothermal

(6)

(7) ,

the pressure range

three equations of

covered here for stlshovlte, 200 GPa or 2 megabars,

state are nearly Interchangeable. The P,V conditions

alGng the shock compression locus are descrlbad by equations Identical

to Eqs.(!] throwh (5) ~cept that u~t becomesUsr the S*Ck veloc~ty~ and

uPt becomes Up, the mass or particle velocity. AISO in Eqs. (6) and (7)0

the expressions are equated to adiabatic nmdull instead of isothermal

moduli.

The pressure, Pt, associated with a given volume, VL, along the

Isothermal ccnnpresslon curve of stlshovlte Is transformed to the pressure,

‘h’along the shock compression Hugonlot ●ssociated with the same volume

by the following expression [OIIn~er et al., 1975].

5

J‘L

Pt{vLl v/y + “ PtdV - [Ty/V Cv] (“L-”o) . (8)Ph{vLl -

Wi Y - 1/2 (VO-VL)I

where y is the Grtineisen constant

y = avc~2/CP“ (9)

In the above equations T is the ambient temperature (293° K), Cv and

Cp are the specific

c~ Is the adiabatic

heat capacities at constant volme and pressure and

bulk sound speed. Cv and C5 or Ct can be calculated

from Cp and Ct or C5 or vice-versa wing rhe following relatlons,

Cv.c .av2 T Ctz,P

(10)

[c+ 1/2,Ct - Cs Cp (11)

where av is the volume thermal expansion.

ThP integral in Eq. (8) can be determined by several methods.

Here It was done uslag numerical Integration.

‘LL

J zP

Pt d“ =tr - ‘tr-l

“0 r-l 2

where

Vr - V. (ljtr - uptr)’ustr’

and

Ptr = (l/vo) Ustr Uptr.

(“r - “r - ~), (12)

(13)

(14)

in Eq. (8) both (y/V) and Cv are assumed to remain constant [McQueen

et al., 1967].

Once the P,V conditions have been defined along the Hugoniot starting

with crystal density stishovite (from Eq. 8), then new pressure values

can be calculated for stishov

the energy increase resulting

undar shock compression. The

te at the given volume,

from the transformation

transformation equation

‘L 0to account

from a-quartz

was described

for

6

~rlier [HcQueen et al., 1963], [tlcQueen et al,, 1967]

where Vo~ Is the ambient specific VOIW of stishovite, VOQ is the ambient

specific volume of quartz, and AEo is the ambient Internal energy difference

between a-quartz and stlshovite. ‘ V values for stlshovite‘rice ‘k ‘h’ L

have been calculated, they then can be transformed Into Us, Up values

having o-quartz for the starting material,

us - (P; v@/(l-vL/voQ))”*, (16)

Up= (pi voQ(bv/voQ))]’2, (17)

and compared directly to the shock compression data. The three thermo-

dynamic quantities Independent of the ultrasonic and high pressure x-ray

studies are AEO (822.I J/g [Helm et al., 1967]), CP (0.70& J/g KO [Helm

et al., 1967]), and av (13.1 x 10-6/K0 [ito et al., 1974]). The thermal

expansion of ito et al. [i974] was chosen instead of the value from Weaver

et al, [1973] because nmre Information was availabie about the experimental

technique used by the former, and the experiment appeared to be carefully

done.

The U9, Up shock compression data for stishovite transformed from

near crystal density a-quartz are listed in Table i with their sources.

As canbe seen In the table, the data credited to Altshuler et al= [i9651

arc repeated by Trunin ● t al. [1970]. Whet!ler they ere independent data

or the same is not indicated by Trunin et al. [1970].

The resuits of,the comparisons of the various compression data and

ultrasonic data with the shock data are sunsnarized in Fig. i. The data

listed in Table i are plotted there aiang with the calculated Hugoniot

7

of a-quartz based on a hydrostatic canpression study by Olinaer [1976b].

The bulk mdulus, its pressure derivative, and the Grfineisen constant

used for each calculated curve are listed in Table 2. Curves ~, ~,

and ~ are

Host confl

0.0008, P

SO K“ = 60

taken from the data of Olinger [1967a] plotted in Fig. 2.

dence was placed on a selected, average datun, V/U. = 0.9674 *

= 10.58 t 0.14 GPa. For curve ~the U~,Up slope was adJusted

and yet the curve wouid pass through the averaged datun. The

value of 6 was chosen for the zero pressure, pressure derivative of the

bulk modulus because that was the avera~e value of the derivative of the

nmdulus for similarly structured solids, Ti02, Sn02, and Ge02. The

resultlng bulk nmdulus Is 288 GPa. As shwn in Fig. 1, curve ~~sses

through the lower Us ,Up data but misses the high pressure (200 GPa or

2 megabar) data of Altshuler et al. [1965] and Trunin et al. [1970].

TW other fits to the data of Olinger [1976a] were therefore tried.

Curve &was chosen because it gave a good flt to the shock compression

data and passed through

Curve ~was based on a

Ollnqer [1976a] (K. = 3’

the Iwer pressure Us,UP

the selected datm (K. = 304 GPa, K: = 3 GPa).

Inear least squares fIt to all the data from

4 GPa, K: = -0.4). Again, the curve passes through

data but misses the high pressure data. These

three curves, =, ~, and ~, can equally well represent the results of

Bassett and Barnett [1970] and Chun~

found to be approximately 300 GPa.

Both MizutanI et al. [1972] and

modulus of stishovlte to be 345 G?a.

[1974] where the bulk mdul us was

Liu et al. [1974] determined the bulk

Curves ~and ~ represent stishovite

having a modull of 350 GPa and

and 3 respectively. Obviously

Finally, Liebermann et al. [pr

a pressure derivative of the nmdulus of 6

the curves miss the UsBUp data entirely.

vate communication 19762 determined a

8

bulk ~dulus of 250 GPa for st

derivative of 6 as others have

shovite and selected the pressure

done. Curve ~ represents his results

and that curve agrees as well with the U U data as does curve ~.SP

(Both curve band f ar- shown hereas one curve.) In sumnary, based

on the calculation scheme used here, and mre imprtant, based on the

assumption the very high pressure U .U data is correct (in the 200 GPaSP

region), the presently available U ,U data is consistent with aSP

spectrun of experimental static data for pure stishovite ranging from

Ko= 300 GPa, K:= 3 to Ko= 250, K:= 6. Should it turn out that the

three highest pressure shock data considered here are for Si02 In the

llquid state, a possibility discussed by Trunln [1970], the metastable

stishovite In the Up range of 6.2 km/s would have higher Us values than

the 12.01 to 12.12 Iun/s listed for the data in Table 1. This wuld,

in turn, alter the conclusions here by suggesting that the pressure

differential of the bulk modulus would be greater than 3 for a nmdulus

of 300 GPa.

I wish to than~once again, Joseph Fritz * aided ma in understanding

tlw concepts and assumptions incorporated in this paper. This -rk was

supported by the U.S. Energy Research and Development Administration.

This paper was presented at the U.S.-Japan Saninar “High Pressure Research ,

Application in Geophysics” July 6-9, 1976, Honolulu, Hawaii, which was

sponsored by the National Science Foundation,

10

BIBLIOGRAPHY

Altshuler, L. V., and R. F. Trunin, ard G. V. Slmakov, Shock canpressionof periclase and quartz and the coaqmsition of the Iovmr mantie.Izv. Acad. Sci. USSR, Phys. Solid Earth, ~ Engl. Transl., 657~660,1965.

Bassett, W. A. and J. D. Barnatt, isothermal c~ression of stishovite andcoasite up to 8S kilobars at room temperature by x-ray diffraction,Phys. Earth Planet. interiors, ~, 54-60, 1970.

Chung, D. H.. General relationship amng sound speeds, Phys. Earth Planet.inter., ~, 113-120, 1974.

Hoim, J. L., O. J. Kleppa, and E. F. Westrum, Jr., Thermodynamics ofpolynmphic transformations in silica. Thermai properties from 5 to1070 K and pressure-temperature stability fields for coesite andstishovite, Geochim. Cosrmchim. Acts ~, 2289-23o7, 1967.

ito, H., K. Kaweda, and S. i. Akinmto, Thermal expansion of stishovltePhys. Earth Planet. interiors, ~ 2?7-281, 1974.

Liu, L., W. A. Bassett, and T. Takehashi, Effect of pressure on the latticeparameters of stlshovite, J. Geophys. Res., 74, 4317-4328, i969.

MeQueen, R. G., J. N. Fritz, and S. P. Marsh, On the equation of state ofstishovite. ~. Geophys. Res., ~ 2319-2322t 1963.

flcQueen, R. G., S. P. Harsh, and J. N. Fritz, Hugoniot equation of state oftwelve rocks, J. Geophys. Re~., 72, 4999-5036, 1967.

Mitzutanl, H., Y. Iiamano, and S. Akimoto, Elastic-wave velocities of poly-crystalline stiskvlte, J. Geophys. Res., ~, 3744-3749, 1972.

Olinger, B., The compression of stishovite, submitted to J. Geophys. Res.,1976a.

Olinger, B., The compression of a-quartz, submitted to J. Geophys. Res.,1976b.

Olinger, B. and P. M. Haileck, Compression and bonding of ice Vii and anempirical linear expression for the Isothermal compression of solids,J. Chem. Phys., 62, 94-99, 1975.

Olinger, B., P. M. Halleck, and H. H. Cady, The isothermal Iinesr and volumecompression of pentaerythritol tetranitrate (PETN) to iO GPa (100 Kbars)and the calculated shock compression, J. Chem. Phys., 62, 4480-4483, 1975.

Trunin, R. F., M. A. Podurets, and G. V. Simakov, Compression of porous quartzby strong shock waves, izv. Acad. Sci. USSR, Phys. Solid Earth, Enql.

Transl. ~, 8-i2, ~970.

Trunin, R. F., G. V. Slmakov, M. A. Podurets, B. N. Moeseyev, and L. V. POPOV,Dynamic compressibility of quartz and auartzite at high pressure, izv.Acad. Sci. USSR, Phys. Solid LarthJ Engi. Transl. ~, 102-106, 1971=.—

11

Wackerle, J., Slwck-wave compression of quartz, J. Applied phys~ ~~ 922-937*1962.

Weaver, J. S., T. Takahashl, W. A. Bassett, Thermal expansion of stlshovite,EOS (Trans. Am. Geophys. Union), ~, 475. 1973.

12

TABLE 1. Stlsiwwite U5,UP Hugoniot Data Between Up = 2.5 to 6.5 ldsCentered on Near Crystal Density a-Quartz at Ambient Conditions

Wackerle [1962]

up(iun/s) u#ln/s)

2.55 6.12

2.70 6.29 ;

2.89 6.66

2.89 6.66

3.03 6.95

3.03 6.95

3.42 7.76

3.49 7.76

3.50 7.63

3.50 7.72

3.52 7.70

3.52 7.75

Altshuleret al. [1965]

up(km/s) u#n/s)

3.13 7.18

3.92 8.54

6.2cJ 12.01

Truninet al. [1970]

2.52 6.27

2.54 6.10

3.13 7.18*

3.91 8.56

3.92 8.54*

6.I8 12.12

6.20 12.01*

‘These data may be the same data published in-Altshuier et al. [1965].

Howaver, Trunin et al. [1970] does not indicate they are from the

former. They are considered here to be from 2 different experiments.

13

TABLE Il. The Bulk Modu!,i, Their Pressure Derivatives, andAssociated Gruneisen Constants Used to Calculatethe Curves in Figure 1.

Curve K. K; Y

(Gpa)

& 288 6 1.26

~ 304 3 1.33

& 314 -.4 1.37

g 35C 6 1.53

~ 350 3 1.53

~ 2S0 6 1.08

FIGURE CAPTIONS

Figure 1, The circles, diamonds, ●nd squares ●re the shock compression

data of S102 with a-quartz as the starting material from

Wackerle [1962], TrunIn et al. [1970], ●nd Altshular et al.

[1965], respective y. The short curveon the left slda Is

the calculated Hugonlot of the a-quartz phase of S102 [Ollngar.,

1976b] . Curves a-f are the calculated Hugoniots of stishovite.-

centered on a-quartz at ambient conditions, The stlshovite

represented by each curve has ● zero pressure bulk modulus, a

medulus pressure dtrivativeo ●nd ● Grtineisen constant associated

with it as listed in Table ii. The datum shown with vertical

error bars is from tho static work of Olinger []976].

Figure 2. The date from Olinger [1976a]. Linear flts~, ~, and ~-are

transformed to Hugoniots centered on a-quartz at ambient con-

ditions shown In Fig. 1. The bulk modulus, its pressure

derivative, and the Gruneisen constant ●ssociated with each

fit are listed in Table il.

12

II

10

9

-8w

D

‘6s

5

4

3

2

I

I I I I I I 1 I 1 I I

— ‘Y 0

—

—

— —

— —

— —

— —

;/

—

-

— —

— —

— —

1 I 1 I 1 I I I I 1 1 II 2 3 4 5 6

Up (km/s)

Figure I

9.5

9.0

8.5

8.0

7.5.

.

0.05 0.[0 0.15 0.20 0.2s 0.30

Upt ( km/s)Figure 2