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Shock-wave compression of vitreous and rutile-type GeO2: A comparative study
60
Physics of the Earth and Planetary Interiors, 20 (1979) 60—70 © Elsevier Scientific Publishing Company, Amsterdam — Printed in The Netherlands
SHOCK-WAVE COMPRESSION OF VITREOUS AND RUTILE-TYPE Ge02: A COMPARATIVE STUDY1 IAN JACKSON2 and THOMAS J. AHRENS Seismological Laboratory, California Institute of Technology, Pasadena, CA 91125 (U.S.A.)
(Received January 25, 1979; revised and accepted May 2, 1979)
Jackson, I. and Ahrens, T.J., 1979. Shock-wave compression of vitreous and rutile-type Ge0 2: a comparative study. Phys. Earth Planet. Inter., 20: 60—70. The dynamic compression of both vitreous and rutile-type Ge02 has been studied throughout the pressure range 0—160 GPa (1.6 Mbar). At sufficiently high pressures (respectively >35 GPa and >70 GPa) both materials attain densities greater than those expected for the rutile phase at the same pressure. These results may be explained in terms of transformation of both vitreous and rutile-type Ge02 to a common high-pressure phase or state with a zeropressure density —~5%greater than that of the rutile polymorph. The vastly different thermal regimes associated with the two Hugoniots allow important deductions to be made concerning the elasticand thermodynamic properties of shocked germanium 3. Inconsistency dioxide. between In particular, this valueanand effective those calculated Grüneisenfrom parameter the Vashchenko—Zubarev of 1.24 ±0.1 is required model at asuggests density of 7.4 g/cm that the latter may not provide an adequate description of the thermal properties of close-packed germanates and
silicates.
1. Introduction The reliability of germanates as models (Goldschmidt, 1931) for the high-pressure phase behaviour of corresponding silicates has now been conclusively demonstrated (Ringwood, 1975; Liu, 1976). Thus, germanates, by virtue of their inclination to crystallize in close-packed structures at modest pressures, afford an opportunity for indirect study of the physical and chemical properties of corresponding silicate high-pressure phases, otherwise beyond the capabilities of current high-pressure, high-temperature technology. For example, ultrasonic studies (Liebermann, 1974, 1975; Liebermann et al., 1977) of germanate and
1
Contribution No: 3256, Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA
2 Present address: Research School of Earth Sciences, Austrahan National University, P.O. Box 4, Canberra, A.C.T. 2600, Australia.
other analogue compounds have yielded estimates of the bulk moduli of ‘y-Mg 2SiO4, and the ilmenite- and perovskite-structured polymorphs of MgSiO3. In the present context, we take advantage of the accessibility of quartz * rutile polymorphism in Ge02, and consequent availability of large single crystals of the rutile phase, to perform a comparative study of the shock compression of vitreous and rutilestructured GeO2. The motivation for such a study [See also Ringwood (1972, p. 89) and Wang and Simmons (1973, p. 1271)] is manifold: (1) Shock compression of high- and low-density phases of the same material provides a test of the hypothesis that low-density phases suffer shockinduced phase changes to equilibrium high-pressure phases. No such test of this hypothesis has yet been performed on oxide compounds, although the unpublished Hugoniot data of McQueen and Marsh (1977) for graphite and a diamond-graphite mixture provide some support for the hypothesis. 3), (2) The high zero-pressure density (6.277 g/cm
61
and incompressibility (I(~~ = 259 GPa, K’ 05 = 6.16; Wang and Simmons, 1973) of the rutile polymorph guarantee relatively low temperatures along the Hugoniot. will As abeconsequence, derived isentropes and isotherms relatively insensitive to the assumptions concerning the thermal part of the equation-ofstate. (3) Assuming that vitreous Ge0 2 suffers a shockinduced phase change to the rutile polymorph, and that vast the difference latter survives the passage of (respectively the shock-wave, the in initial densities 3.654 and 6.277 g/cm3) and the considerable metastability of the glass even at atmospheric pressure [ETR (glass rutile) = —0.353 kJ/g; Navrotsky, 19711 will displace the glass Hugoniot to much higher pressure at any given density. The magnitude of this thermal pressure offset, along with knowledge of the relevant elastic and thermodynamic parameters might provide important information concerning the thermal part of the equation-of-state, by constraining the volume dependence of the Grüneisen parameter y(V). (4) Finally, these studies may serve to clarify the position regarding possible post-rutile polymorphism in GeO 2 and SiO2. Recent static high-pressure studies by Liu et al. (1978) suggest that the rutile polymorphs of both Ge02 and SiO2 become unstable at pressures in excess of 300 kbar. Shock-wave data for GeO2 should provide an estimate of the density change associated with any post-rutile polymorphism. In particular, the possibility of an (eight-coordinated) fluorite-related high-pressure phase could be assessed, -+
2. Experimental details and data reduction 3) crystals of rutile-type GeO Two large (—1 cm 2, grown by Goodrum (1970), and similar in morphology and quality to that described by Wang and Simmons (1973), were cut to yield crystallographically oriented slabs approximately 2—3 mm thick. Slab normals were shown to be within 2°of the desired crystallographic direction (either 001 or 110) by Laue methods. Cylindrical discs (10 mm in diameter, 2—3 mm thick) of bubble-free vitreous GeO2 were purchased from A. Vas of Monash University, Melbourne. The glass was prepared by maintaining Ge02 (encapsulated in platinum tubing) at 1400°Cfor 72 hours, followed by quenching and subsequent annealing at
500°C.Density determinations by the usual (toluene) immersion technique on eight such discs used in the present study yielded densities in the range 3.652— 3 with a mean of 3.655 (standard devia3.66 0.003). 1 g/cm This value, which is used throughout this tion paper as the zero-pressure density of vitreous Ge0 2, 3) of reported lies within the range (3 .628—3 .667 g/cm values. Densities similarly measured on six slabs of rutile-type GeO2 were indistinguishable the 3 which has from therefore X-rayused density of 6.277 g/cm been throughout. All samples were polished to within ±0.003mm of uniform thickness and then mounted with an appropriate array of mirror surfaces on aluminium, tantalum or tungsten driver plates which were exposed to highvelocity impact by projectiles bearing similar metal flyer plates. Impact velocities in the range 1.0—2.5 km/sec were achieved through use of a 40 mm bore single-stage propellant gun previously described in detail by Ahrens et al. (1971). The procedure adopted for the.present low velocity shots (No. 418— No. 427) differs from that described by Ahrens et al. (1971) in only two important respects. Firstly, accurate measurement of both the shock arrival time at the silvered free surface of the rather small sample and of the subsequent motion of the free surface was facilitated by use of a double slit in the optical system. In this way, the flat driver arrival mirrors and the silvered sample free surface, illuminated by an intense Xenon flash lamp (Goto et al., 1977), were viewed through one of two parallel slits by a Beckman and Whitley (model 339B) rotating-mirror streak camera. The second slit allowed light reflected frbm an inclined mirror mounted elsewhere on the sample to be monitored. The use of two slits thus produces two superimposed streak records and thereby increases the quality of data obtained from samples of limited cross-sectional area. Secondly, use of the rotatingmirror streak camera necessitated careful preliminary calibration of the (geometrical) relationship between mirror rotation rate and writing rate on the film (typically —‘7 mm/psec). This calibration was performed using a Pockel-cell modulated (20 MHz) Arion laser beam which provided time markers with a 50 nsec spacing. For impact velocities in excess of 2.5 km/sec it was necessary to use the Caltech two-stage light-gasgun whose operation has previously been described
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63 (Jeanloz and Ahrens, 1977). Light-gas-gun impact velocities were determined by the usual flash X-ray technique while the sample-mirror assembly was viewed through a single slit with an image-converter streak camera. The measured impact velocities and shock velocities combined with the known equations-of-state of the flyer-driver materials (McQueen et al., 1970) yield the pressure-particle velocity state behind the shock front by use of the Rankine—Hugoniot equations and
sample from the free surface, have been proposed (e.g. Wackerle, 1962; Ahrens et al., 1968) but none is totally satisfactory. Fortunately, uncertainties in the correction to the apparent second shock velocity are impOrtant only when the second shock is weak. This is not the regime of principal interest in the present study. The measured impact, shock (corrected where appropriate as described above), and free surface velocities for shock experiments on rutile-type Ge02 3) are displayed in Table I along (Pa = the 6.277 g/cm uncertainties and the calculated with associated particle velocities, pressures and densities. Similar data for vitreous Ge0 2 are presented in Table II. It is evident from these tabulations that propellant gun impact velocities are generally known to within ±1% but that the uncertainties are somewhat larger at higher velocities. Velocities determined by laser intervalometry (Ahrens et al., 1971) over two contiguous paths have not been extrapolated over the remaining distance to the target, because of uncertainties in the uniformity of any observed acceleration. Rather, the velocities associated with the second of the two paths have been assumed to represent impact velocities while the magnitude of the observed acceleration provides an estimate of the likely uncertainty introduced by this assumption. Light-gas-gun impact velocities
the well known impedance matching (see, e.g. Jackson andprocess Ahrens,of1979 for details). For shots where two distinct shock fronts (travelling with different velocities) were detected, the usual free surface approximation was made. Thus, the particle velocity u~1associated with the first shock was assumed to be given by one half of the corresponding (measured) free surface velocity. The pressure-density-internal energy state behind the first shock may then be calculated from the Rankine-Hugoniot equations. Finally, the state behind the second shock is calculated as above by impedance matching, after correction of the second shock velocity U~2for the change in sample length arising from the first shock (Fowles, 1967). Various alternative corrections, which seek to describe the interaction of the second shock with the rarefaction propagating back into the
TABLE II Hugoniot data for vitreous Ge02 (p0 Shot Flyer! Impact driver velocities
=
3) 3.655 g/cm Shock velocities
Free surface velocities
Particle velocities
Pressures P 1. P2 (GPa)
Densities p 1’ P23) (g/cm
composition
(km/sec) Vimp
(km/sec) U~1,U~
(km/sec) f/f51, Uf52
(km/sec) U~,1,U~,2
419
W
1.18
± 0.01
3.53 2.89
± 0.04 *1 ± 0.03 *2
0.63 1.47
± 0.03 ± 0.06
0.32 1.04
± 0.01
4.1 ±0.01 11.6 ±0.1
4.01 5.58
±0.05 ± 0.04
418
W
1.55
± 0.02
3.25
± 0.02
2.43
± 0.10
1.35
± 0.02
16.1
± 0.2
6.26
± 0.07
421
W
2.02 ±0.02
3.90
± 0.03
2.98
±
W
2.52 ±0.03
4.53
± 0.04
3.94
±
0.24 0.24
1.73
422 LGGO32
Al-2024
5.15 ±0.02
LGGO39
Ta
4.36±0.02
6.71
LGGO5O
Ta
5.88
±0.02
LGGO33
Ta
6.06 ±0.02
*
0.07
± 0.02
24.6
± 0.3
6.56
±
2.12 ±0.03
35.0
± 0.5
6.86
± 0.09
—
2.74
± 0.03
57.6
± 1.1
6.96
±
—
3.32±0.02
81.3
± 1.3
7.22±0.17
8.63 ± 0.09
—
4.33
± 0.02
136.5
± 1.2
7.33
± 0.10
8.74 ± 0.17
—
4.46
± 0.02
142.4
± 2.2
7.46
± 0.18
5.76 ± 0.17 ± 0.13
0.26
1 Hugoniot elastic state; *2 Corrected for path length change arising from first wave but not for wave interaction (see text).
64
determined from flash X-ray shadowgraphs are generally reliable within ±0.3%.Uncertainties in shock velocities are generally less than ±1%for samples of 2—3 mm thickness. The larger uncertainties in the vitreous GeO2 shock velocities for shots LGGO32, 033 and 039 result from the use of thinner (‘—-1 mm) samples as driver arrival mirrors. Uncertainties in free surface velocities vary considerably with details of inclined mirror and streak record geometry. The analysis of error propagation has been performed in the manner described by Jackson and Ahrens (1979) suitably extended to deal with the double shock cornplication.
3. Discussion The data of Tables I and II are presented in particle velocity—shock velocity (un, U~)space in Fig. I and I
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-
shock velocity and the appropriate zero-pressure compressional wave velocity, indicates that the shocked state behind the first front is the result of elastic cornpression of material below its dynamic yield point. (2) The offset in the u~,—U~ trend for rutile-type GeO2 at u~, 1.0—1.4 km/sec and U~ 8.0 km/sec is strongly suggestive of shock-induced transformation of rutile-type Ge02 to an intrinsically denser state. (3) The well defined linear u~,—U5trend displayed by the five highest velocity vitreous GeO2 data suggest an absence of major structural changes throughout this high-pressure regime. In order to assess the Ge02 Hugoniot data more quantitatively, theoretical Hugoniots for both the glass and rutile-type GeO2 have been constructed after the manner of McQueen
I
/
9~
8
/
again in density—pressure (p, F) space in Fig. 2. Several features of Fig. 1 are noteworthy: (1) In those cases where two distinct shock fronts are observed, the correspondence between the first
/
5-
I\
I
-
0
0~
“—U~’O63+I84u~ -
0 40
-
•iio
//
40,
HELS
I
~
-
3 Fig. 1. Hugoniot data Particle for vitreous and rutile-type velocity ,km/sec Ge0 2 in particle velocity-shock velocity space. Shock propagation directions 001 and 110 for rutile Ge02 are distinguished. Plotting symbols on the particle velocity = 0 axis correspond to the appropriate compressional and bulk sound (V~,)velocities as reported by Wang and Simmons (1973) and Soga (1969).
Density
,
g/cm
Fig. 2. Hugoniot data for vitreous and rutile-type Ge02 in density-pressure space. The curves labelled G and R are respectively glass-(G) and rutile-(R) based Hugoniots for rutile-type Ge02. Unless indicated otherwise, density and pressure uncertainties are smaller than the plotting symbols. The Hugoniot elastic limits (HEL’s) for vitreous Ge02 and both propagation directions in the rutile phase are indicated.
65
et al. (1963). The Hugoniot pressure,PH, at a given
TABLE IH
density, p, may be related to the appropriate principal
Parameters used in construction ofisentropes and Hugoniots
P5(p), through the Mie-Gruneisen descripof the thermal equation-of-state.
isentrope tion
~Ps ypQ.~U1+ETR)}/{1 —
—
(7/2)(p/p’0
—
l)}(1)
for various Ge02 phases. Ge02 (glass) E~~(gl-+ ru)
=
P0 E~~(gl —~ hpp) *~
=
—0.353 kJ/g 3[Navrotsky (1971)1 3.655 g/cm —0.253 kJ/g
Ge0 2 (rutile) In the density above, p~, ‘y, and ETR are respectively the initial of the shocked material, the Grüneisen
K
parameter and the energy change at zero pressure associated with any shock-induced phase transformation. The density dependence of the Grüneisen para-
~
05 *2
meter was assumed to be of the form: 7
=
(2)
~ is the internal energy change along the principal isentrope between the zero-pressure density Po and
the given density: =
5
Pa
F~dp/p2
(3)
F
7”3— =
ETR(ru—~hpp)*
1
Po *3 K 05 K~5
6.59 g/cm
=
324GPa 5.8 1.24 (n = 0)
=
1.5 (n
213— 1]
}
=
1.5)
2with ETR(ru —~hpp) was estimated as —PTR~VTR/ ~TR 60 GPa and ~VTR 0.0037 cm3/g (see Fig. 2); *2 Voigt-Reuss-Hil averages of single-crystal moduli and their pressure derivatives; * ~ see text for details of the deriva*1
tion of this and other high-pressure “phase” (hpp) parameters.
(plpo)5/3}
(3K05!2)~(p/po)
3
=
OR ~‘o
Principal isentropes are assumed to be of the thirdorder Eulerian (Birch-Murnaghan) form:
5(p)
*2
i’o
Ge02 (high-pressure “phase”)
7~(p~/p)’~
p
3 6.277 g/cm = 259 GPa = 6.16 [Wangand Simmons = 1.16 (1973)] = 1.0 — +0.1 kJ/g =
P~(p/p’ (4)
X {l + 3/4[K~5 _4] [(p/Po)
0— l)/2p) and thus guarantees a very rapid increase in temperature along the Hugoniot. It is clear from Fig. 2 that the rutile-type Ge0
2 where K0~and K’o~ are respectively the isentropic
data below 60 GPa (600 kbar) are consistent with the
incompressibility and its first pressure derivative, Theoretical Hugoniots, based on the data of Table III have been calculated for each of the two Ge02 starting materials and are compared with the Hugoniot data in Fig. 2. These calculated Hugoniots are based
compression of the rutile crystal structure. The relatively high dynamic yield points (Hugoniot elastic limits, or HEL’s) of 12.7—16.8 GPa and 8.7—10.1 GPa respectively, for shock propagation parallel to 001 and 110, are consistent with the known hard-
on the assumption that vitreous Ge02 suffers a shock induced transformation to the rutile modification and that the latter yields, but otherwise survives the shock loading. Thus the calculated curves labelled “R” and “G” in Fig. 2 indicate the expected high-pressure behaviour of the same phase (rutile-type Ge02) under two very different thermal regimes. As explained in
ness and incompressibility of rutile-type Ge02, and quite similar to those reported for single-crystal sap-
the introduction, very modest increases in internal energy (and thus temperature) are expected in rutiletype Ge02 owing to the high initial density and incompressibility. For the shocked glass, however, the enormous compression results in large changes in internal energy L~EHacross the shock front (AEH =
phire (Graham and Brooks, 1971) which approach the theoretical strength of defect-free A1203. At pressures above the HEL but less than 60 GPa, the usual collapse toward the hydrostat (e.g. Graham and Brooks, 1971) is evident. At still greater pressures, shocked rutile-type Ge02 exhibits densities too large to be consistent with the continued survival of the rutile crystal structure in accord with the previously mentioned offset in the u~—U5trajectory. Ge02 glass, on the other hand, when shocked above its HEL (—-‘4 GPa) displays a dramatic increase —
66 in density at pressures below 40 GPa so much so that its density at 35 GPa is clearly in excess of that expected in the event of shock induced transformation to the rutile phase. It is worth emphasising that this conclusion is independent of the theoretical calculations. The identical densities attained in shocked rutile-type Ge02 and shocked glass near 35 GPa —
despite the very much higher temperatures expected in the latter, demand an intrinsically more close packed structure (than rutile) for the shocked glass. At higher pressures the shocked glass displays con-
I
I
I
I R S
G 60
/
/j
-
134
124 114
20
-
80
-
40
-
0
On
Hugoniots. The principal question clearly siderably greater outstanding incompressibility thanisthe calculated whether the very high densities attained by glass shocked to pressures above 25 GPa and by rutile-type Ge02 above 60 GPa are consistent with the hypothesis of shock induced transformation of both vitreous and rutile-type Ge02 to the same high pressure phase or state, order to test thisdensity, hypothesis we seek first to findInthe zero-pressure incompressibility, ~
-
/ I
65
I
70
75
I
803
85
Density, Fig. 3. A comparison of the highest g/cm pressure Hugoniot data
K 05, and its first pressure derivative, K’05 which characterise the high-pressure phase or state attained by rutile-type Ge02 shocked to pressures in excess of 60 GPa. The relevant high-pressure data have been replotted with an expanded scale in Fig. 3. Taking advantage of the small difference in internal energy between the Hugoniot and isentrope, we shall, initially, neglect the distinction between Flugoniot and isentrope. Furthermore, since the density excess over that expected for the rutile modification (Fig. 2) is nowhere greater than 3%, we can safely assume that no change of primary cation coordination from 6—8 or 9 is involved [For discussion the density changes associated with rutile * of fluorite * a-PbC1 2 phase transformations see Liu (1975) and Jamieson (1977)]. In the absence of changes in primary coordination number, relative changes in bulk sound velocity, V~,and density, p, across phase transformations in silicates and germanates are related by the expression: = ~‘.%~/3/f~ (5) with X~--’2 (Liebermann, 1974, 1975; Davies, 1974, 1976). Since V~,~ eq. 5 may be rewritten in terms of the incompressibility K, as: LIK/K
(1
+ 2X~,)(~p/p)
(6)
from Fig. 2 with the inferred isentrope (5) and calculated glass-(G) rutile-(R) based Hugoniots for the Ge02 high-pressure “phase”. The glass-based Hugoniots (G), are labelled
according the Gruneisen parameter which they were to calculated. The number 1.24models refers,with for example, to the model (see Table III) ‘y,, = 1.24, n = 0 while V denotes the volume dependent model ~ = 1.5, n = 1.5. The arrow indicates the zero-pressure density of the rutile modification.
With K05 related to Po through eq. 6, Pa and K’05 were varied to yield the third-order Eulerian isentrope (eq. 4) which best fits the three high-pressure 3, Hugoniot data. These values are Po = 6.59 g/cm K05 = 324 GPa and K’05 = 6.5. An uncertainty of ±0.3 in the3, value of X,~, results ininuncertainties of ±0.06 ±20GPa and ±0.3 p g/cm 0. K05 and K’c,s respectively. An effective temperature-independent GrUneisen parameter was then calculated for each of the vitreous Ge02 Hugoniot data (Fig. 3) from eq. 1 rearranged to give: 7 = (1/p)(F~ P5)/ L&EH (ETR + i~U5)} (7) where ~.EH PH(P/P~ l)/2p is, as before, the internal energy change across the shock front, and —
—
—
ETR
is the zero-pressure energy difference between
67
vitreous Ge02 and the high pressure phase (see Table III). The resulting values of 7 at densities of 6.86, 6.96, 7.22, 7.33 and 7.46 were respectively 1.21, 1 .34, 1.05, 1.29, 1 .14. In the absence of any systematic variation with density, a weighted average of 1 .22 was obtained using the reciprocal squares of the density uncertainties as weights. Having thus established a volume-independent ~ of 1.22 as appropriate, Hugoniot densities for shocked rutile-type Ge02 were calculated from eqs. 1—4, K’05 being revised downward from to 5.8 to obtain best fit (abetween consequence of the6.5 earlier neglect of thethe distinction Hugoniot and isentrope). A further iteration resulted in a small change of 7 from 1.22 to 1.24. The final estimates of all elastic and thermodynamic parameters used in the calculations and derived from them are displayed in Table III. The principal isentrope and the derived glass- and rutilebased Hugoniots for the high-pressure phase are cornpared with the data in Fig. 3. The calculated Hugoniots clearly provide an adequate description of the experimental data. The apparent constancy of 7 is perhaps the most startling conclusion and as a consequence, the ability of the data to resolve any possible volume dependence of y and to constrain a volumeindependent 7 was tested by construction of glassbased Hugoniots for a range of alternative 7 models. Hugoniots calculated on the basis of a range of volume independent 7 values serve, in fact, to define a grid from which the volume dependence of 7, permitted by the data, may be assessed. In this way, it is evident from the spacing of the constant 7 Hugoniots that for a given density uncertainty, the highest pressure data have far more resolving power than those at lower pressure. Thus, while 7 is constrained to lie within the approximate range 1.2—1.4 at 136 GPa, the 35 GPa datum (Fig. 3) clearly permits a much wider range. As a consequence, a wide range of volume dependences of 7 are permitted, if not required, by the data. As an example, a volume dependence defined by 7~= n = 1 .5 (see eq. 2) allows consistency within the stated uncertainties, It is thus clear that use of the Mie-Grüneisen description of the thermal equation-of-state allows explanation of the high-pressure data for both vitreous and rutile-Ge02 in terms of a common high-pressure phase or state without resort to unreasonable 7(p) models (see e.g. Davies and Gaffney, 1973, p. 169).
Further insight into the nature of this possible cornmon high-pressure state and the significance of the derivedy(p) models is provided by estimation of Hugoniot temperatures using the expression: 1~TH
[~~.EH— (ETR + L~U5)]/C~
(8)
where ~TH is the difference between Hugoniot and initial temperatures and C~,is the average specific heat which, for this purpose, may be approximated 1 K~m,R andMbeing the by gas con9R/M” gm stant and0.7, the Jmolecular weight, respectively. For pressures of 40, 80, 120 and 160 GPa on the rutilebased Hugoniot, the estimated temperature increases are respectively 240, 640, 1230 and 1860 K. (These are probably underestimates as a result of the madequacy of the assumption that C~,= 9R/M at low temperatures). Corresponding estimates for the glass-based Hugoniot are respectively 4000, 7700, 11 600 and 15 700 K. The latter temperature estimates probably exceed the melting point of Ge0 2 throughout most of the 40—160 GPa pressure range (for relevant melting data see Jackson, 1976) but do not guarantee the existence of the equilibrium melt phase on the restricted timescale of the shock-wave experiment. Equally, the (sub-solidus) state obtained by shocked rutile may be one of short-range-order only. Thus, while shocked rutile (F> 70 GPa) and shocked Ge02 glass (F> 35 GPa) may represent a common (probably short-range-order only) phase or state at vastly different temperatures, the possibility of different shock-induced high-pressure phases cannot be discounted. Nevertheless, the fact that ~‘~‘H is very much greater than both ETR and ~U5means that uncertainties in the latter arising from possible phase differences between the two Hugoniots contribute negligibly to the uncertainty in the calculated “effective” 7 (see eq. 7). Furthermore, it should be noted that the plausibility of the above temperature estimates may be assessed by calculating the average thermal expansion coefficient ~(F) required to reconcile the observed density contrast, PR/PG, at pressure F with the estimated temperature difference, I~THG ~TH,R, between the two Hugoniots: —
—
ct(P)
~PR(F)/PG(F)
~4TH,G(P)
—
—
I }/
~TH,R(F)}
(9)
68 ~ values for F = 80, 120 and 160 GPa are 1.19 X l0~K1, 0.95 X i0~K’ and 0.81 X l0~K1, respectively. That such reasonable thermal expansion parameters are implied by such calculations tends to lend support to the temperature estimates presented above, For each such 7(p) model, isentrope temperatures may be calculated from the expression:
tural changes in the glass than in rutile is suggestive of enhanced reaction kinetics in the former associated with much higher temperatures. (2) The modest internal energy changes associated with the shock loading of the rutile modification along with empirical observations of elasticity changes accompanying phase transformationshave facilitated construction of a third-order Eulerian principal isentrope (p 3, K 0 = 6.59 g/cm 05 = 324 GPa,
T5(p)
K~5’~ 5.8) for the high-pressure phase or state attained by shocked rutile. (3) If the existence of a common shock-induced
=
T0 exp{,f 7(p) dp/p}
(10)
0
Temperature along the isentrope 3 toincreases p = 7.5 g/cm3 do not exceedfrom ‘-‘50 Po K. = 6.59 g/cm Under these circumstances, one may neglect the distinction between the isentrope and the 0 K isotherm and calculate the Vashchenko-Zubarev 7 (Vashchenko and Zubarev, 1963; Irvine and Stacey, 1975): 7uz = /1 dK K~)/~‘.l 4p\ (11) 5 + 92P\II —
—
~-_)
from the Birch-Murnaghan isentrope. 7~is found to decrease from 2.07 at p = 6.59 g/cm3 (P = 0) to 1.91 at p 7.5 g/cm3, and is thus clearly inconsistent with the measured value of 1.24 ±0.1 at ‘~7.4g/cm3. Rigorous application of eq. 11 by construction of the 0 K isotherm will result in a somewhat lower value of 7vz (principally by decreasing dK/dP) but will not eliminate the wide discrepancy between the observed and calculated values a discrepancy which may reflect the inadequacy of the central-force-approximation in the derivation of eq. 11 (see Irvine and Stacey, 1975, for further discussion of the centralforce-approximation). —
4. Conclusions Analysis of these new data for vitreous and rutiletype Ge02 has thus addressed the questions outlined in the introduction and the principal conclusions are as follows: (1) There is strong evidence that vitreous and rutile-type Ge0 2 both suffer shock-induced structural changes to phases or states intrinsically more closepacked than the rutile crystal structure. The fact that lower pressures are required to produce these struc-
high-pressure for bothpressure Hugoniots assumed, comparison ofstate the highest dataisfor vitreous Ge0 2 with this isentrope yields estimates of the Grüneisen parameter of the high-pressure phase at a series of densities, via the Mie-GrUneisen prescription. The data serve to constrain 7 best at the highest pressures attained in the present study with a value of 3.The data are equally well satisfied, however, by a volume order 1.24±0.1requirednearp7.4g/cm independent 7 of 1.24 ±0.1 and an alternative model, 7 = 1.5 (po/p)LS, with a substantial volume dependence. In the absence of a common shock-induced high pressure phase or state, the value of the calculated 7 is only negligibly altered, although its physical significance is somewhat different. The considerable discrepancy between the observed 7’s and those calculated from the Vashchenko-Zubarev model may reflect the inadequacy of the central-force assumption in the description of inter-atomic bonding in close-packed germanates (and, by analogy, silicates). (4) The zero-pressure density increase associated with the shock-induced structural changes is quite well constrained at 5 ±1%, referred to the density of the rutile phase. The magnitude of this density increase is strongly suggestive of structural changes which do not involve any increase in the primary cation coordination number of six. Thus there would appear to be no likelihood of Ge0 2 polymorphism involving fluorite or a-PbCl2 modifications in the pressure range 0—160 GPa (1.6 Mbar). As4~ a and consequence the that relative “ionic” of Ge Si41’ it isofclear increases insizes Si44’ coordination by oxygen in Si02 beyond six at mantle pressures (e.g. Fujisawa, 1968), are also excluded. The attainment of densities significantly greater than those expected for the rutile polymorph by the shocked
69 glass at pressures as low as 35 GPa would appear to
call into question the existence of a high-pressure
—
high-temperature stability field for the NiAs-related Ge02 polymorph recently discovered by Liu et al. (1978) in samples quenched from ‘-‘lOOO°Cat 25— 30 GPa and subsequently recovered at atmospheric pressure.
Goodrum, J.W., 1970. Top-seeded flux growth of tetragonal Ge0
2. J. Cryst. Growth, 7: 254—256.
Goto, T., Rossman, G.R. and Ahrens, 1977. Absorption spectroscopy in solids under shock T.J., compression. High
Pressure Science and Technology: Proc. AIRAPT mt. High-Pressure Conf., 6th, 2: 895—904. Graham, R.A. and Brooks, W.P., 1971. Shock-wave compression of sapphire from 15 to 420 kbar. The effects of large anisotropic compressions. J, Phys. Chem. Solids, 32:
23 11—2330.
Acknowledgements
Irvine, R.D. and Stacey, F.D., 1975. Pressure dependence of the thermal Grüneisen parameter, with application to the Earth’s lower mantle and outer core. Phys. Earth Planet.
We thank C.S. Sahagian of the Solid State Sciences Hanscom Air Force Base, Massachusetts and J.S. White of the Division of Mineralogy,National Museum of Natural History, Smithsonian Institution, Washington for making available the crystals of rutile-
Inter., 11: 157—165. Jackson, I., 1976. Melting of the silica isotypes Si02, BeF2 and Ge02 at elevated pressures. Phys. Earth Planet. Inter., 13: 218—231. Jackson, I. and Ahrens, T.J., 1979. Shock-wave compression of single-crystal forsterite. J. Geophys. Res., 84: 3039—
Laboratory,
type Ge02 without which this work would not have been possible. H, Richeson, E. Gelle and R. Smith are thanked for their assistance in conducting the experi-
ments. Much fruitful discussion with R, Jeanloz, L. Liu, A.E. Ringwood, L. Thomsen and D.J. Weidner is also acknowledged. The manuscript was improved as a result of thoughtful comments by an anonymous reviewer. Financial support was provided by the U.S. National Science Foundation (Grant EAR-7515 006A0 1).
References Ahrens, T.J., Gust, W.H. and Royce, E.B., 1968. Material strength effect and the shock compression of alumina. J. AppI. Phys., 39: 4610—4616. Ahrens, T.J., Lower, J.H. and Lagus, P.L., 1971. Equation of state of forsterite. J, Geophys. Res., 76: 518—528. Davies, G.F., 1974. Elasticity, crystal structures and phase transitions. Earth Planet, Sci. Lett., 22: 339—346. Davies, G.F., 1976. The estimation of elastic properties from analogue compounds. Geophys. J.R. Astron. Soc., 44: 625 —647. Davies, G.F. and Gaffney, E., 1973. Identification of highpressure phases of rocks and minerals from Hugoniot data. Geophys. J.R. Astron. Soc., 33: 165—183. Fowles, G.R., 1967. Dynamic compression of quartz. J. Geo-
phys. Res., 72: 5729—5742. Fujisawa, H., 1968. Temperature and discontinuities in the
transition layer in the Earth’s mantle: geophysical application of the olivine—spinel transition in the Mg2SiO4— Fe2SiO4 system. J. Geophys. Res., 73: 3281—3294.
Goldschmidt, V.M., 1931. Zur Kristallchemie des Germaniums. Nachr. Ges. Wiss. Gottingen, Math. Phys., 52: 184—190.
3048.
Jamieson, J.C., 1977. Phase transitions in rutile-type structures. In: M.H. Manghnani and S. Akimoto (Editors), High-pressure research: applications to geophysics, Academic Press, New York, pp. 209—218. Jeanloz, R. and Ahrens, T.J., 1977. Pyroxenes and olivines: structural implications of shock-wave data for high pressure phases. In: M.H. Manghnani and S. Akimoto (Editors), High pressure research: applications to geophysics. Academic Press, New York, pp. 439—461. Liebermann, R.C,, 1974. Elasticity of pyroxene—garnet and pyroxene—ilmenite phase transformations in germanates. Phys. Earth Planet. Inter., 8: 36 1—374. Liebermann, R.C., 1975. Elasticity of olivine (o),beta (a) and spinel (y) polymorphs of germanates and silicates. Geophys. J.R. Astron. Soc., 42: 899—930. Liebermann, R.C., Jones, L.E.A. and Ringwood, A.E., 1977. Elasticity of aluminate, titanate, stannate and germanate compounds with the perovskite structure. Phys. Earth Planet. Inter,, 14: 165—178. Liu, L., 1975. High-pressure phase transformations and compressions of ilmenite and rutile. II. Geophysical Implications, Phys. Earth Planet, Inter., 10: 344—347. Liu, L, 1976. High-pressure phases of Co2GeO4, Ni2GeO4, Mn2GeO4 and MnGeO3: implications for the germanatesilicate modelling scheme and the Earth’s mantle. Earth Planet. Sci. Lett., 31: 393—396. Liu, L., Bassett, W.A. and Sharry, J., 1978, New high pressure modifications of Ge02 and Si02. J. Geophys. Res., 83: 2301—2305. McQueen, R.G. and Marsh, S.P., 1977. Unpublished data, In:
M. Van Thiel, (Editor), Compendium of shock-wave data UCRL-50108. Univ. of Calif., Livermore, Calif.,
754 pp. McQueen, R.G., Fritz, J.N. and Marsh, S.P., 1963. On the equation of state of stishovite. J. Geophys. Res., 68:
2319—2322. McQueen, R.G., Marsh, S.P., Taylor, J.W., Fritz, J.N. and Carter, W.J., 1970. The equation of state of solids from
70 shoch-wave studies. In: R. Kinslow (Editor), HighVelocity Impact Phenomena. Academic Press, New York, pp. 293— 417. Navrotsky, A., 1971. Enthalpies of transformation among the tetragonal hexagonal and glassy modifications of Ge0 2. J. Inorg. Nuci. Chem., 33: 1119—1124. Ringwood, A.E., 1972. Mineralogy of the deep mantle: current status and future developments. In: E.C. Robertson (Editor), The Nature 67—92. of the Solid Earth. McGraw-Hill, Ringwood, A,E., New York, pp.1975. Composition and Petrology of the Earth’s Mantle. McGraw Hill, New York, 618 pp.
Soga, N., 1969. Pressure derivatives of the elastic constants of vitreous germania at 25°,—78.5°and —195.8°C.J. Appl. Phys., 40: 3382—3385. Vashchenko, V.Y. and Zubarev, V.N., 1963. Concerning the Grilneisen constant. Sov. Phys. Solid. State, 5: 65 3—655. Wackerle, J., 1962. Shock-wave compression of quartz. J. Appl. Phys,, 33: 922—937. Wang, H. and Simmons, G., 1973. Elasticity of some mantle crystal 78: 1262—127 structures. 3. II. Rutile Ge02. J. Geophys. Res,,
Physics of the Earth and Planetary Interiors, 20 (1979) 60—70 © Elsevier Scientific Publishing Company, Amsterdam — Printed in The Netherlands
SHOCK-WAVE COMPRESSION OF VITREOUS AND RUTILE-TYPE Ge02: A COMPARATIVE STUDY1 IAN JACKSON2 and THOMAS J. AHRENS Seismological Laboratory, California Institute of Technology, Pasadena, CA 91125 (U.S.A.)
(Received January 25, 1979; revised and accepted May 2, 1979)
Jackson, I. and Ahrens, T.J., 1979. Shock-wave compression of vitreous and rutile-type Ge0 2: a comparative study. Phys. Earth Planet. Inter., 20: 60—70. The dynamic compression of both vitreous and rutile-type Ge02 has been studied throughout the pressure range 0—160 GPa (1.6 Mbar). At sufficiently high pressures (respectively >35 GPa and >70 GPa) both materials attain densities greater than those expected for the rutile phase at the same pressure. These results may be explained in terms of transformation of both vitreous and rutile-type Ge02 to a common high-pressure phase or state with a zeropressure density —~5%greater than that of the rutile polymorph. The vastly different thermal regimes associated with the two Hugoniots allow important deductions to be made concerning the elasticand thermodynamic properties of shocked germanium 3. Inconsistency dioxide. between In particular, this valueanand effective those calculated Grüneisenfrom parameter the Vashchenko—Zubarev of 1.24 ±0.1 is required model at asuggests density of 7.4 g/cm that the latter may not provide an adequate description of the thermal properties of close-packed germanates and
silicates.
1. Introduction The reliability of germanates as models (Goldschmidt, 1931) for the high-pressure phase behaviour of corresponding silicates has now been conclusively demonstrated (Ringwood, 1975; Liu, 1976). Thus, germanates, by virtue of their inclination to crystallize in close-packed structures at modest pressures, afford an opportunity for indirect study of the physical and chemical properties of corresponding silicate high-pressure phases, otherwise beyond the capabilities of current high-pressure, high-temperature technology. For example, ultrasonic studies (Liebermann, 1974, 1975; Liebermann et al., 1977) of germanate and
1
Contribution No: 3256, Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA
2 Present address: Research School of Earth Sciences, Austrahan National University, P.O. Box 4, Canberra, A.C.T. 2600, Australia.
other analogue compounds have yielded estimates of the bulk moduli of ‘y-Mg 2SiO4, and the ilmenite- and perovskite-structured polymorphs of MgSiO3. In the present context, we take advantage of the accessibility of quartz * rutile polymorphism in Ge02, and consequent availability of large single crystals of the rutile phase, to perform a comparative study of the shock compression of vitreous and rutilestructured GeO2. The motivation for such a study [See also Ringwood (1972, p. 89) and Wang and Simmons (1973, p. 1271)] is manifold: (1) Shock compression of high- and low-density phases of the same material provides a test of the hypothesis that low-density phases suffer shockinduced phase changes to equilibrium high-pressure phases. No such test of this hypothesis has yet been performed on oxide compounds, although the unpublished Hugoniot data of McQueen and Marsh (1977) for graphite and a diamond-graphite mixture provide some support for the hypothesis. 3), (2) The high zero-pressure density (6.277 g/cm
61
and incompressibility (I(~~ = 259 GPa, K’ 05 = 6.16; Wang and Simmons, 1973) of the rutile polymorph guarantee relatively low temperatures along the Hugoniot. will As abeconsequence, derived isentropes and isotherms relatively insensitive to the assumptions concerning the thermal part of the equation-ofstate. (3) Assuming that vitreous Ge0 2 suffers a shockinduced phase change to the rutile polymorph, and that vast the difference latter survives the passage of (respectively the shock-wave, the in initial densities 3.654 and 6.277 g/cm3) and the considerable metastability of the glass even at atmospheric pressure [ETR (glass rutile) = —0.353 kJ/g; Navrotsky, 19711 will displace the glass Hugoniot to much higher pressure at any given density. The magnitude of this thermal pressure offset, along with knowledge of the relevant elastic and thermodynamic parameters might provide important information concerning the thermal part of the equation-of-state, by constraining the volume dependence of the Grüneisen parameter y(V). (4) Finally, these studies may serve to clarify the position regarding possible post-rutile polymorphism in GeO 2 and SiO2. Recent static high-pressure studies by Liu et al. (1978) suggest that the rutile polymorphs of both Ge02 and SiO2 become unstable at pressures in excess of 300 kbar. Shock-wave data for GeO2 should provide an estimate of the density change associated with any post-rutile polymorphism. In particular, the possibility of an (eight-coordinated) fluorite-related high-pressure phase could be assessed, -+
2. Experimental details and data reduction 3) crystals of rutile-type GeO Two large (—1 cm 2, grown by Goodrum (1970), and similar in morphology and quality to that described by Wang and Simmons (1973), were cut to yield crystallographically oriented slabs approximately 2—3 mm thick. Slab normals were shown to be within 2°of the desired crystallographic direction (either 001 or 110) by Laue methods. Cylindrical discs (10 mm in diameter, 2—3 mm thick) of bubble-free vitreous GeO2 were purchased from A. Vas of Monash University, Melbourne. The glass was prepared by maintaining Ge02 (encapsulated in platinum tubing) at 1400°Cfor 72 hours, followed by quenching and subsequent annealing at
500°C.Density determinations by the usual (toluene) immersion technique on eight such discs used in the present study yielded densities in the range 3.652— 3 with a mean of 3.655 (standard devia3.66 0.003). 1 g/cm This value, which is used throughout this tion paper as the zero-pressure density of vitreous Ge0 2, 3) of reported lies within the range (3 .628—3 .667 g/cm values. Densities similarly measured on six slabs of rutile-type GeO2 were indistinguishable the 3 which has from therefore X-rayused density of 6.277 g/cm been throughout. All samples were polished to within ±0.003mm of uniform thickness and then mounted with an appropriate array of mirror surfaces on aluminium, tantalum or tungsten driver plates which were exposed to highvelocity impact by projectiles bearing similar metal flyer plates. Impact velocities in the range 1.0—2.5 km/sec were achieved through use of a 40 mm bore single-stage propellant gun previously described in detail by Ahrens et al. (1971). The procedure adopted for the.present low velocity shots (No. 418— No. 427) differs from that described by Ahrens et al. (1971) in only two important respects. Firstly, accurate measurement of both the shock arrival time at the silvered free surface of the rather small sample and of the subsequent motion of the free surface was facilitated by use of a double slit in the optical system. In this way, the flat driver arrival mirrors and the silvered sample free surface, illuminated by an intense Xenon flash lamp (Goto et al., 1977), were viewed through one of two parallel slits by a Beckman and Whitley (model 339B) rotating-mirror streak camera. The second slit allowed light reflected frbm an inclined mirror mounted elsewhere on the sample to be monitored. The use of two slits thus produces two superimposed streak records and thereby increases the quality of data obtained from samples of limited cross-sectional area. Secondly, use of the rotatingmirror streak camera necessitated careful preliminary calibration of the (geometrical) relationship between mirror rotation rate and writing rate on the film (typically —‘7 mm/psec). This calibration was performed using a Pockel-cell modulated (20 MHz) Arion laser beam which provided time markers with a 50 nsec spacing. For impact velocities in excess of 2.5 km/sec it was necessary to use the Caltech two-stage light-gasgun whose operation has previously been described
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63 (Jeanloz and Ahrens, 1977). Light-gas-gun impact velocities were determined by the usual flash X-ray technique while the sample-mirror assembly was viewed through a single slit with an image-converter streak camera. The measured impact velocities and shock velocities combined with the known equations-of-state of the flyer-driver materials (McQueen et al., 1970) yield the pressure-particle velocity state behind the shock front by use of the Rankine—Hugoniot equations and
sample from the free surface, have been proposed (e.g. Wackerle, 1962; Ahrens et al., 1968) but none is totally satisfactory. Fortunately, uncertainties in the correction to the apparent second shock velocity are impOrtant only when the second shock is weak. This is not the regime of principal interest in the present study. The measured impact, shock (corrected where appropriate as described above), and free surface velocities for shock experiments on rutile-type Ge02 3) are displayed in Table I along (Pa = the 6.277 g/cm uncertainties and the calculated with associated particle velocities, pressures and densities. Similar data for vitreous Ge0 2 are presented in Table II. It is evident from these tabulations that propellant gun impact velocities are generally known to within ±1% but that the uncertainties are somewhat larger at higher velocities. Velocities determined by laser intervalometry (Ahrens et al., 1971) over two contiguous paths have not been extrapolated over the remaining distance to the target, because of uncertainties in the uniformity of any observed acceleration. Rather, the velocities associated with the second of the two paths have been assumed to represent impact velocities while the magnitude of the observed acceleration provides an estimate of the likely uncertainty introduced by this assumption. Light-gas-gun impact velocities
the well known impedance matching (see, e.g. Jackson andprocess Ahrens,of1979 for details). For shots where two distinct shock fronts (travelling with different velocities) were detected, the usual free surface approximation was made. Thus, the particle velocity u~1associated with the first shock was assumed to be given by one half of the corresponding (measured) free surface velocity. The pressure-density-internal energy state behind the first shock may then be calculated from the Rankine-Hugoniot equations. Finally, the state behind the second shock is calculated as above by impedance matching, after correction of the second shock velocity U~2for the change in sample length arising from the first shock (Fowles, 1967). Various alternative corrections, which seek to describe the interaction of the second shock with the rarefaction propagating back into the
TABLE II Hugoniot data for vitreous Ge02 (p0 Shot Flyer! Impact driver velocities
=
3) 3.655 g/cm Shock velocities
Free surface velocities
Particle velocities
Pressures P 1. P2 (GPa)
Densities p 1’ P23) (g/cm
composition
(km/sec) Vimp
(km/sec) U~1,U~
(km/sec) f/f51, Uf52
(km/sec) U~,1,U~,2
419
W
1.18
± 0.01
3.53 2.89
± 0.04 *1 ± 0.03 *2
0.63 1.47
± 0.03 ± 0.06
0.32 1.04
± 0.01
4.1 ±0.01 11.6 ±0.1
4.01 5.58
±0.05 ± 0.04
418
W
1.55
± 0.02
3.25
± 0.02
2.43
± 0.10
1.35
± 0.02
16.1
± 0.2
6.26
± 0.07
421
W
2.02 ±0.02
3.90
± 0.03
2.98
±
W
2.52 ±0.03
4.53
± 0.04
3.94
±
0.24 0.24
1.73
422 LGGO32
Al-2024
5.15 ±0.02
LGGO39
Ta
4.36±0.02
6.71
LGGO5O
Ta
5.88
±0.02
LGGO33
Ta
6.06 ±0.02
*
0.07
± 0.02
24.6
± 0.3
6.56
±
2.12 ±0.03
35.0
± 0.5
6.86
± 0.09
—
2.74
± 0.03
57.6
± 1.1
6.96
±
—
3.32±0.02
81.3
± 1.3
7.22±0.17
8.63 ± 0.09
—
4.33
± 0.02
136.5
± 1.2
7.33
± 0.10
8.74 ± 0.17
—
4.46
± 0.02
142.4
± 2.2
7.46
± 0.18
5.76 ± 0.17 ± 0.13
0.26
1 Hugoniot elastic state; *2 Corrected for path length change arising from first wave but not for wave interaction (see text).
64
determined from flash X-ray shadowgraphs are generally reliable within ±0.3%.Uncertainties in shock velocities are generally less than ±1%for samples of 2—3 mm thickness. The larger uncertainties in the vitreous GeO2 shock velocities for shots LGGO32, 033 and 039 result from the use of thinner (‘—-1 mm) samples as driver arrival mirrors. Uncertainties in free surface velocities vary considerably with details of inclined mirror and streak record geometry. The analysis of error propagation has been performed in the manner described by Jackson and Ahrens (1979) suitably extended to deal with the double shock cornplication.
3. Discussion The data of Tables I and II are presented in particle velocity—shock velocity (un, U~)space in Fig. I and I
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,Y-U1’523+196,~,/
-
shock velocity and the appropriate zero-pressure compressional wave velocity, indicates that the shocked state behind the first front is the result of elastic cornpression of material below its dynamic yield point. (2) The offset in the u~,—U~ trend for rutile-type GeO2 at u~, 1.0—1.4 km/sec and U~ 8.0 km/sec is strongly suggestive of shock-induced transformation of rutile-type Ge02 to an intrinsically denser state. (3) The well defined linear u~,—U5trend displayed by the five highest velocity vitreous GeO2 data suggest an absence of major structural changes throughout this high-pressure regime. In order to assess the Ge02 Hugoniot data more quantitatively, theoretical Hugoniots for both the glass and rutile-type GeO2 have been constructed after the manner of McQueen
I
/
9~
8
/
again in density—pressure (p, F) space in Fig. 2. Several features of Fig. 1 are noteworthy: (1) In those cases where two distinct shock fronts are observed, the correspondence between the first
/
5-
I\
I
-
0
0~
“—U~’O63+I84u~ -
0 40
-
•iio
//
40,
HELS
I
~
-
3 Fig. 1. Hugoniot data Particle for vitreous and rutile-type velocity ,km/sec Ge0 2 in particle velocity-shock velocity space. Shock propagation directions 001 and 110 for rutile Ge02 are distinguished. Plotting symbols on the particle velocity = 0 axis correspond to the appropriate compressional and bulk sound (V~,)velocities as reported by Wang and Simmons (1973) and Soga (1969).
Density
,
g/cm
Fig. 2. Hugoniot data for vitreous and rutile-type Ge02 in density-pressure space. The curves labelled G and R are respectively glass-(G) and rutile-(R) based Hugoniots for rutile-type Ge02. Unless indicated otherwise, density and pressure uncertainties are smaller than the plotting symbols. The Hugoniot elastic limits (HEL’s) for vitreous Ge02 and both propagation directions in the rutile phase are indicated.
65
et al. (1963). The Hugoniot pressure,PH, at a given
TABLE IH
density, p, may be related to the appropriate principal
Parameters used in construction ofisentropes and Hugoniots
P5(p), through the Mie-Gruneisen descripof the thermal equation-of-state.
isentrope tion
~Ps ypQ.~U1+ETR)}/{1 —
—
(7/2)(p/p’0
—
l)}(1)
for various Ge02 phases. Ge02 (glass) E~~(gl-+ ru)
=
P0 E~~(gl —~ hpp) *~
=
—0.353 kJ/g 3[Navrotsky (1971)1 3.655 g/cm —0.253 kJ/g
Ge0 2 (rutile) In the density above, p~, ‘y, and ETR are respectively the initial of the shocked material, the Grüneisen
K
parameter and the energy change at zero pressure associated with any shock-induced phase transformation. The density dependence of the Grüneisen para-
~
05 *2
meter was assumed to be of the form: 7
=
(2)
~ is the internal energy change along the principal isentrope between the zero-pressure density Po and
the given density: =
5
Pa
F~dp/p2
(3)
F
7”3— =
ETR(ru—~hpp)*
1
Po *3 K 05 K~5
6.59 g/cm
=
324GPa 5.8 1.24 (n = 0)
=
1.5 (n
213— 1]
}
=
1.5)
2with ETR(ru —~hpp) was estimated as —PTR~VTR/ ~TR 60 GPa and ~VTR 0.0037 cm3/g (see Fig. 2); *2 Voigt-Reuss-Hil averages of single-crystal moduli and their pressure derivatives; * ~ see text for details of the deriva*1
tion of this and other high-pressure “phase” (hpp) parameters.
(plpo)5/3}
(3K05!2)~(p/po)
3
=
OR ~‘o
Principal isentropes are assumed to be of the thirdorder Eulerian (Birch-Murnaghan) form:
5(p)
*2
i’o
Ge02 (high-pressure “phase”)
7~(p~/p)’~
p
3 6.277 g/cm = 259 GPa = 6.16 [Wangand Simmons = 1.16 (1973)] = 1.0 — +0.1 kJ/g =
P~(p/p’ (4)
X {l + 3/4[K~5 _4] [(p/Po)
0— l)/2p) and thus guarantees a very rapid increase in temperature along the Hugoniot. It is clear from Fig. 2 that the rutile-type Ge0
2 where K0~and K’o~ are respectively the isentropic
data below 60 GPa (600 kbar) are consistent with the
incompressibility and its first pressure derivative, Theoretical Hugoniots, based on the data of Table III have been calculated for each of the two Ge02 starting materials and are compared with the Hugoniot data in Fig. 2. These calculated Hugoniots are based
compression of the rutile crystal structure. The relatively high dynamic yield points (Hugoniot elastic limits, or HEL’s) of 12.7—16.8 GPa and 8.7—10.1 GPa respectively, for shock propagation parallel to 001 and 110, are consistent with the known hard-
on the assumption that vitreous Ge02 suffers a shock induced transformation to the rutile modification and that the latter yields, but otherwise survives the shock loading. Thus the calculated curves labelled “R” and “G” in Fig. 2 indicate the expected high-pressure behaviour of the same phase (rutile-type Ge02) under two very different thermal regimes. As explained in
ness and incompressibility of rutile-type Ge02, and quite similar to those reported for single-crystal sap-
the introduction, very modest increases in internal energy (and thus temperature) are expected in rutiletype Ge02 owing to the high initial density and incompressibility. For the shocked glass, however, the enormous compression results in large changes in internal energy L~EHacross the shock front (AEH =
phire (Graham and Brooks, 1971) which approach the theoretical strength of defect-free A1203. At pressures above the HEL but less than 60 GPa, the usual collapse toward the hydrostat (e.g. Graham and Brooks, 1971) is evident. At still greater pressures, shocked rutile-type Ge02 exhibits densities too large to be consistent with the continued survival of the rutile crystal structure in accord with the previously mentioned offset in the u~—U5trajectory. Ge02 glass, on the other hand, when shocked above its HEL (—-‘4 GPa) displays a dramatic increase —
66 in density at pressures below 40 GPa so much so that its density at 35 GPa is clearly in excess of that expected in the event of shock induced transformation to the rutile phase. It is worth emphasising that this conclusion is independent of the theoretical calculations. The identical densities attained in shocked rutile-type Ge02 and shocked glass near 35 GPa —
despite the very much higher temperatures expected in the latter, demand an intrinsically more close packed structure (than rutile) for the shocked glass. At higher pressures the shocked glass displays con-
I
I
I
I R S
G 60
/
/j
-
134
124 114
20
-
80
-
40
-
0
On
Hugoniots. The principal question clearly siderably greater outstanding incompressibility thanisthe calculated whether the very high densities attained by glass shocked to pressures above 25 GPa and by rutile-type Ge02 above 60 GPa are consistent with the hypothesis of shock induced transformation of both vitreous and rutile-type Ge02 to the same high pressure phase or state, order to test thisdensity, hypothesis we seek first to findInthe zero-pressure incompressibility, ~
-
/ I
65
I
70
75
I
803
85
Density, Fig. 3. A comparison of the highest g/cm pressure Hugoniot data
K 05, and its first pressure derivative, K’05 which characterise the high-pressure phase or state attained by rutile-type Ge02 shocked to pressures in excess of 60 GPa. The relevant high-pressure data have been replotted with an expanded scale in Fig. 3. Taking advantage of the small difference in internal energy between the Hugoniot and isentrope, we shall, initially, neglect the distinction between Flugoniot and isentrope. Furthermore, since the density excess over that expected for the rutile modification (Fig. 2) is nowhere greater than 3%, we can safely assume that no change of primary cation coordination from 6—8 or 9 is involved [For discussion the density changes associated with rutile * of fluorite * a-PbC1 2 phase transformations see Liu (1975) and Jamieson (1977)]. In the absence of changes in primary coordination number, relative changes in bulk sound velocity, V~,and density, p, across phase transformations in silicates and germanates are related by the expression: = ~‘.%~/3/f~ (5) with X~--’2 (Liebermann, 1974, 1975; Davies, 1974, 1976). Since V~,~ eq. 5 may be rewritten in terms of the incompressibility K, as: LIK/K
(1
+ 2X~,)(~p/p)
(6)
from Fig. 2 with the inferred isentrope (5) and calculated glass-(G) rutile-(R) based Hugoniots for the Ge02 high-pressure “phase”. The glass-based Hugoniots (G), are labelled
according the Gruneisen parameter which they were to calculated. The number 1.24models refers,with for example, to the model (see Table III) ‘y,, = 1.24, n = 0 while V denotes the volume dependent model ~ = 1.5, n = 1.5. The arrow indicates the zero-pressure density of the rutile modification.
With K05 related to Po through eq. 6, Pa and K’05 were varied to yield the third-order Eulerian isentrope (eq. 4) which best fits the three high-pressure 3, Hugoniot data. These values are Po = 6.59 g/cm K05 = 324 GPa and K’05 = 6.5. An uncertainty of ±0.3 in the3, value of X,~, results ininuncertainties of ±0.06 ±20GPa and ±0.3 p g/cm 0. K05 and K’c,s respectively. An effective temperature-independent GrUneisen parameter was then calculated for each of the vitreous Ge02 Hugoniot data (Fig. 3) from eq. 1 rearranged to give: 7 = (1/p)(F~ P5)/ L&EH (ETR + i~U5)} (7) where ~.EH PH(P/P~ l)/2p is, as before, the internal energy change across the shock front, and —
—
—
ETR
is the zero-pressure energy difference between
67
vitreous Ge02 and the high pressure phase (see Table III). The resulting values of 7 at densities of 6.86, 6.96, 7.22, 7.33 and 7.46 were respectively 1.21, 1 .34, 1.05, 1.29, 1 .14. In the absence of any systematic variation with density, a weighted average of 1 .22 was obtained using the reciprocal squares of the density uncertainties as weights. Having thus established a volume-independent ~ of 1.22 as appropriate, Hugoniot densities for shocked rutile-type Ge02 were calculated from eqs. 1—4, K’05 being revised downward from to 5.8 to obtain best fit (abetween consequence of the6.5 earlier neglect of thethe distinction Hugoniot and isentrope). A further iteration resulted in a small change of 7 from 1.22 to 1.24. The final estimates of all elastic and thermodynamic parameters used in the calculations and derived from them are displayed in Table III. The principal isentrope and the derived glass- and rutilebased Hugoniots for the high-pressure phase are cornpared with the data in Fig. 3. The calculated Hugoniots clearly provide an adequate description of the experimental data. The apparent constancy of 7 is perhaps the most startling conclusion and as a consequence, the ability of the data to resolve any possible volume dependence of y and to constrain a volumeindependent 7 was tested by construction of glassbased Hugoniots for a range of alternative 7 models. Hugoniots calculated on the basis of a range of volume independent 7 values serve, in fact, to define a grid from which the volume dependence of 7, permitted by the data, may be assessed. In this way, it is evident from the spacing of the constant 7 Hugoniots that for a given density uncertainty, the highest pressure data have far more resolving power than those at lower pressure. Thus, while 7 is constrained to lie within the approximate range 1.2—1.4 at 136 GPa, the 35 GPa datum (Fig. 3) clearly permits a much wider range. As a consequence, a wide range of volume dependences of 7 are permitted, if not required, by the data. As an example, a volume dependence defined by 7~= n = 1 .5 (see eq. 2) allows consistency within the stated uncertainties, It is thus clear that use of the Mie-Grüneisen description of the thermal equation-of-state allows explanation of the high-pressure data for both vitreous and rutile-Ge02 in terms of a common high-pressure phase or state without resort to unreasonable 7(p) models (see e.g. Davies and Gaffney, 1973, p. 169).
Further insight into the nature of this possible cornmon high-pressure state and the significance of the derivedy(p) models is provided by estimation of Hugoniot temperatures using the expression: 1~TH
[~~.EH— (ETR + L~U5)]/C~
(8)
where ~TH is the difference between Hugoniot and initial temperatures and C~,is the average specific heat which, for this purpose, may be approximated 1 K~m,R andMbeing the by gas con9R/M” gm stant and0.7, the Jmolecular weight, respectively. For pressures of 40, 80, 120 and 160 GPa on the rutilebased Hugoniot, the estimated temperature increases are respectively 240, 640, 1230 and 1860 K. (These are probably underestimates as a result of the madequacy of the assumption that C~,= 9R/M at low temperatures). Corresponding estimates for the glass-based Hugoniot are respectively 4000, 7700, 11 600 and 15 700 K. The latter temperature estimates probably exceed the melting point of Ge0 2 throughout most of the 40—160 GPa pressure range (for relevant melting data see Jackson, 1976) but do not guarantee the existence of the equilibrium melt phase on the restricted timescale of the shock-wave experiment. Equally, the (sub-solidus) state obtained by shocked rutile may be one of short-range-order only. Thus, while shocked rutile (F> 70 GPa) and shocked Ge02 glass (F> 35 GPa) may represent a common (probably short-range-order only) phase or state at vastly different temperatures, the possibility of different shock-induced high-pressure phases cannot be discounted. Nevertheless, the fact that ~‘~‘H is very much greater than both ETR and ~U5means that uncertainties in the latter arising from possible phase differences between the two Hugoniots contribute negligibly to the uncertainty in the calculated “effective” 7 (see eq. 7). Furthermore, it should be noted that the plausibility of the above temperature estimates may be assessed by calculating the average thermal expansion coefficient ~(F) required to reconcile the observed density contrast, PR/PG, at pressure F with the estimated temperature difference, I~THG ~TH,R, between the two Hugoniots: —
—
ct(P)
~PR(F)/PG(F)
~4TH,G(P)
—
—
I }/
~TH,R(F)}
(9)
68 ~ values for F = 80, 120 and 160 GPa are 1.19 X l0~K1, 0.95 X i0~K’ and 0.81 X l0~K1, respectively. That such reasonable thermal expansion parameters are implied by such calculations tends to lend support to the temperature estimates presented above, For each such 7(p) model, isentrope temperatures may be calculated from the expression:
tural changes in the glass than in rutile is suggestive of enhanced reaction kinetics in the former associated with much higher temperatures. (2) The modest internal energy changes associated with the shock loading of the rutile modification along with empirical observations of elasticity changes accompanying phase transformationshave facilitated construction of a third-order Eulerian principal isentrope (p 3, K 0 = 6.59 g/cm 05 = 324 GPa,
T5(p)
K~5’~ 5.8) for the high-pressure phase or state attained by shocked rutile. (3) If the existence of a common shock-induced
=
T0 exp{,f 7(p) dp/p}
(10)
0
Temperature along the isentrope 3 toincreases p = 7.5 g/cm3 do not exceedfrom ‘-‘50 Po K. = 6.59 g/cm Under these circumstances, one may neglect the distinction between the isentrope and the 0 K isotherm and calculate the Vashchenko-Zubarev 7 (Vashchenko and Zubarev, 1963; Irvine and Stacey, 1975): 7uz = /1 dK K~)/~‘.l 4p\ (11) 5 + 92P\II —
—
~-_)
from the Birch-Murnaghan isentrope. 7~is found to decrease from 2.07 at p = 6.59 g/cm3 (P = 0) to 1.91 at p 7.5 g/cm3, and is thus clearly inconsistent with the measured value of 1.24 ±0.1 at ‘~7.4g/cm3. Rigorous application of eq. 11 by construction of the 0 K isotherm will result in a somewhat lower value of 7vz (principally by decreasing dK/dP) but will not eliminate the wide discrepancy between the observed and calculated values a discrepancy which may reflect the inadequacy of the central-force-approximation in the derivation of eq. 11 (see Irvine and Stacey, 1975, for further discussion of the centralforce-approximation). —
4. Conclusions Analysis of these new data for vitreous and rutiletype Ge02 has thus addressed the questions outlined in the introduction and the principal conclusions are as follows: (1) There is strong evidence that vitreous and rutile-type Ge0 2 both suffer shock-induced structural changes to phases or states intrinsically more closepacked than the rutile crystal structure. The fact that lower pressures are required to produce these struc-
high-pressure for bothpressure Hugoniots assumed, comparison ofstate the highest dataisfor vitreous Ge0 2 with this isentrope yields estimates of the Grüneisen parameter of the high-pressure phase at a series of densities, via the Mie-GrUneisen prescription. The data serve to constrain 7 best at the highest pressures attained in the present study with a value of 3.The data are equally well satisfied, however, by a volume order 1.24±0.1requirednearp7.4g/cm independent 7 of 1.24 ±0.1 and an alternative model, 7 = 1.5 (po/p)LS, with a substantial volume dependence. In the absence of a common shock-induced high pressure phase or state, the value of the calculated 7 is only negligibly altered, although its physical significance is somewhat different. The considerable discrepancy between the observed 7’s and those calculated from the Vashchenko-Zubarev model may reflect the inadequacy of the central-force assumption in the description of inter-atomic bonding in close-packed germanates (and, by analogy, silicates). (4) The zero-pressure density increase associated with the shock-induced structural changes is quite well constrained at 5 ±1%, referred to the density of the rutile phase. The magnitude of this density increase is strongly suggestive of structural changes which do not involve any increase in the primary cation coordination number of six. Thus there would appear to be no likelihood of Ge0 2 polymorphism involving fluorite or a-PbCl2 modifications in the pressure range 0—160 GPa (1.6 Mbar). As4~ a and consequence the that relative “ionic” of Ge Si41’ it isofclear increases insizes Si44’ coordination by oxygen in Si02 beyond six at mantle pressures (e.g. Fujisawa, 1968), are also excluded. The attainment of densities significantly greater than those expected for the rutile polymorph by the shocked
69 glass at pressures as low as 35 GPa would appear to
call into question the existence of a high-pressure
—
high-temperature stability field for the NiAs-related Ge02 polymorph recently discovered by Liu et al. (1978) in samples quenched from ‘-‘lOOO°Cat 25— 30 GPa and subsequently recovered at atmospheric pressure.
Goodrum, J.W., 1970. Top-seeded flux growth of tetragonal Ge0
2. J. Cryst. Growth, 7: 254—256.
Goto, T., Rossman, G.R. and Ahrens, 1977. Absorption spectroscopy in solids under shock T.J., compression. High
Pressure Science and Technology: Proc. AIRAPT mt. High-Pressure Conf., 6th, 2: 895—904. Graham, R.A. and Brooks, W.P., 1971. Shock-wave compression of sapphire from 15 to 420 kbar. The effects of large anisotropic compressions. J, Phys. Chem. Solids, 32:
23 11—2330.
Acknowledgements
Irvine, R.D. and Stacey, F.D., 1975. Pressure dependence of the thermal Grüneisen parameter, with application to the Earth’s lower mantle and outer core. Phys. Earth Planet.
We thank C.S. Sahagian of the Solid State Sciences Hanscom Air Force Base, Massachusetts and J.S. White of the Division of Mineralogy,National Museum of Natural History, Smithsonian Institution, Washington for making available the crystals of rutile-
Inter., 11: 157—165. Jackson, I., 1976. Melting of the silica isotypes Si02, BeF2 and Ge02 at elevated pressures. Phys. Earth Planet. Inter., 13: 218—231. Jackson, I. and Ahrens, T.J., 1979. Shock-wave compression of single-crystal forsterite. J. Geophys. Res., 84: 3039—
Laboratory,
type Ge02 without which this work would not have been possible. H, Richeson, E. Gelle and R. Smith are thanked for their assistance in conducting the experi-
ments. Much fruitful discussion with R, Jeanloz, L. Liu, A.E. Ringwood, L. Thomsen and D.J. Weidner is also acknowledged. The manuscript was improved as a result of thoughtful comments by an anonymous reviewer. Financial support was provided by the U.S. National Science Foundation (Grant EAR-7515 006A0 1).
References Ahrens, T.J., Gust, W.H. and Royce, E.B., 1968. Material strength effect and the shock compression of alumina. J. AppI. Phys., 39: 4610—4616. Ahrens, T.J., Lower, J.H. and Lagus, P.L., 1971. Equation of state of forsterite. J, Geophys. Res., 76: 518—528. Davies, G.F., 1974. Elasticity, crystal structures and phase transitions. Earth Planet, Sci. Lett., 22: 339—346. Davies, G.F., 1976. The estimation of elastic properties from analogue compounds. Geophys. J.R. Astron. Soc., 44: 625 —647. Davies, G.F. and Gaffney, E., 1973. Identification of highpressure phases of rocks and minerals from Hugoniot data. Geophys. J.R. Astron. Soc., 33: 165—183. Fowles, G.R., 1967. Dynamic compression of quartz. J. Geo-
phys. Res., 72: 5729—5742. Fujisawa, H., 1968. Temperature and discontinuities in the
transition layer in the Earth’s mantle: geophysical application of the olivine—spinel transition in the Mg2SiO4— Fe2SiO4 system. J. Geophys. Res., 73: 3281—3294.
Goldschmidt, V.M., 1931. Zur Kristallchemie des Germaniums. Nachr. Ges. Wiss. Gottingen, Math. Phys., 52: 184—190.
3048.
Jamieson, J.C., 1977. Phase transitions in rutile-type structures. In: M.H. Manghnani and S. Akimoto (Editors), High-pressure research: applications to geophysics, Academic Press, New York, pp. 209—218. Jeanloz, R. and Ahrens, T.J., 1977. Pyroxenes and olivines: structural implications of shock-wave data for high pressure phases. In: M.H. Manghnani and S. Akimoto (Editors), High pressure research: applications to geophysics. Academic Press, New York, pp. 439—461. Liebermann, R.C,, 1974. Elasticity of pyroxene—garnet and pyroxene—ilmenite phase transformations in germanates. Phys. Earth Planet. Inter., 8: 36 1—374. Liebermann, R.C., 1975. Elasticity of olivine (o),beta (a) and spinel (y) polymorphs of germanates and silicates. Geophys. J.R. Astron. Soc., 42: 899—930. Liebermann, R.C., Jones, L.E.A. and Ringwood, A.E., 1977. Elasticity of aluminate, titanate, stannate and germanate compounds with the perovskite structure. Phys. Earth Planet. Inter,, 14: 165—178. Liu, L., 1975. High-pressure phase transformations and compressions of ilmenite and rutile. II. Geophysical Implications, Phys. Earth Planet, Inter., 10: 344—347. Liu, L, 1976. High-pressure phases of Co2GeO4, Ni2GeO4, Mn2GeO4 and MnGeO3: implications for the germanatesilicate modelling scheme and the Earth’s mantle. Earth Planet. Sci. Lett., 31: 393—396. Liu, L., Bassett, W.A. and Sharry, J., 1978, New high pressure modifications of Ge02 and Si02. J. Geophys. Res., 83: 2301—2305. McQueen, R.G. and Marsh, S.P., 1977. Unpublished data, In:
M. Van Thiel, (Editor), Compendium of shock-wave data UCRL-50108. Univ. of Calif., Livermore, Calif.,
754 pp. McQueen, R.G., Fritz, J.N. and Marsh, S.P., 1963. On the equation of state of stishovite. J. Geophys. Res., 68:
2319—2322. McQueen, R.G., Marsh, S.P., Taylor, J.W., Fritz, J.N. and Carter, W.J., 1970. The equation of state of solids from
70 shoch-wave studies. In: R. Kinslow (Editor), HighVelocity Impact Phenomena. Academic Press, New York, pp. 293— 417. Navrotsky, A., 1971. Enthalpies of transformation among the tetragonal hexagonal and glassy modifications of Ge0 2. J. Inorg. Nuci. Chem., 33: 1119—1124. Ringwood, A.E., 1972. Mineralogy of the deep mantle: current status and future developments. In: E.C. Robertson (Editor), The Nature 67—92. of the Solid Earth. McGraw-Hill, Ringwood, A,E., New York, pp.1975. Composition and Petrology of the Earth’s Mantle. McGraw Hill, New York, 618 pp.
Soga, N., 1969. Pressure derivatives of the elastic constants of vitreous germania at 25°,—78.5°and —195.8°C.J. Appl. Phys., 40: 3382—3385. Vashchenko, V.Y. and Zubarev, V.N., 1963. Concerning the Grilneisen constant. Sov. Phys. Solid. State, 5: 65 3—655. Wackerle, J., 1962. Shock-wave compression of quartz. J. Appl. Phys,, 33: 922—937. Wang, H. and Simmons, G., 1973. Elasticity of some mantle crystal 78: 1262—127 structures. 3. II. Rutile Ge02. J. Geophys. Res,,