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Elasticity of the ilmenite - perovskite phase transformation in CdTiO3
326
Earth and Planetary Science Letters, 29 (1976) 326-332 Q Elsevier Scientific Publishing Company, Amsterdam Printed in The Netherlands [51
ELASTICITY OF THE ILMENITE - PEROVSKITE PHASE TRANSFORMATION IN CdTiO3
ROBERT C. LIEBERMANN Research School of Earth Sciences, Australian National University, Canberra, A. C. T. (Australia) Revised version received December 11, 1975
Ultrasonic data for the velocities of the ilmenite and perovskite polymorphs of CdTiO 3 have been determined as a function of pressure to 7.5 kbar at room temperature for polycrystalline specimens hot-pressed at pressures up to 25 kbar. This transition is characterized by the following velocity (v) density (p) relationships: (1) the changes in compressional (Vp) and bulk sound (v~) velocities are comparable in percentage magnitude to the density jump, while the shear (Vs) velocity jump is three times greater than that for p; (2) (Vp/Vs) decreases across the transition from the low- to high-pressure phase; and (3) low slopes (linear or logarithmic) on v-p diagrams. The (Vp/Vs) behaviour for the ilmenite -perovskite transformation is unusual for the transitions studied in our laboratory. The observed relationships (1) and (2) are typical of the elasticity behaviour across phase transformations which involve increases in cationanion co-ordination and in nearest-neighbour interatomic distances, such as those exhibited by CdTiO 3 in transforming from the ilmenite to the perovskite phase. Elasticity systematics for isostructural sequences are used to estimate the bulk moduli of the perovskite polymorphs of CaSiO3 (2.7 Mbar) and MgSiO3 (2.8 Mbar).
1. Introduction
Pyroxenes with ABO3 stoichiometry are the secondmost abundant mineral constituent of the upper mantle, after olivine. Static experiments (see Ringwood [1 ] for a review) have indicated several possible highpressure crystal structures for silicate pyroxenes in the earth's mantle, including garnet, ilmenite and perovskite. Recently, it has been demonstrated that (Mg,Fe)SiO3 pyroxenes do transform to the ilmenite and subsequently to the perovskite structure at pressures between 300 and 500 kbar [ 2 - 4 ] . Mineralogical models based on these experimental studies suggest that there may be a region of the earth's mantle in which the (Mg,Fe)SiO3 component transforms from the ilmenite to the perovskite structure [1,5]. The ilmenite-perovskite phase transformation was first demonstrated experimentally in CdTiO3 at atmospheric pressure by Posnjak and Barth [6] and has subsequently been observed in CdSnO3 [7], MnVO3 [8] and (Fe,Mg)TiO3 [9]. The transformation in CdTiO3 is characterized by an 8% increase in density as the coordination changes from V I c d V I T i l V o 3 to
X l I c d V I T i V I o 3 ([6], and see later discussion). The P T relations for the ilmenite-perovskite transition in CdTiO3 have been studied by Liebertz and Rooymans [ 10]. The transition occurs with a negative slope dP/dT = 49 bars/°C (Fig. 1) which implies a positive entropy change; this has been verified by direct enthalpy measurements [ 11 ]. The occurrence of such a phase transformation in (Mg,Fe)SiO3 in the earth's interior with an analogous negative slope could have important implications for mantle dynamics (e.g. [1, chapter 15]). The purpose of this paper is to report new elasticity data for the ilmenite and perovskite polymorphs of CdTiO3 and to discuss the importance of these data for v e l o c i t y - d e n s i t y systematics proposed by previous investigators. This study is an outgrowth o f our program to fabricate polycrystalline aggregates of the low- and high-pressure phases of compounds undergoing polymorphic phase transformations in the laboratory and to measure the elastic properties of these phases by ultrasonic techniques [ 12 17]. This paper augments and supplements the brief reports and discussions of these data which we have presented earlier [14,15,18].
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Fig. 1. Phase diagram for the ilmenite-perovskite transformation in CdTiOa (after Liebertz and Rooymans [10]). Circles represent raw experimental data using CdTiOa-ilmenite as the starting material: open circles, no perovskite phase detected; closed circles, perovskite phase observed in quench product [10]. The solid line indicates the phase boundary P (kbar) = 40.7-0.049 T (°C) for T > 500°C where it is well-determined by the experimental data. This slope is quite consistent with the measured enthalpy of the respective phases [ 11 ] which implies that AS = 3.25 cal/deg/mole and thus d P / d T = zaS/,~,V = - 4 9 bar/°C for AV = -2.79 cm3/mole. The X's represent the hot-pressing conditions for the polycrystalline ilmenite and perovskite samples used in the present study.
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Fig. 2. Compressional and shear velocities vs. pressure at room temperature for polycrystalline CdTiO3-ilmenite using the pulse superposition technique. Precision of individual velocity determinations is 0.02%. imens are less than 3.5% porous and have a grain size generally less than 50 pm. Similar attempts to hotpress CdSnOa-ilmenite at P = 8 kbar, T = 6 0 0 ° C were unsuccessful (the perovskite starting powder was un-
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2. Experimental procedure and data A powder sample of CdTiOs was synthesized by intimately mixing stoichiometric a m o u n t s o f CdO and TiO2 and sintering at 1200°C in air for six hours. Optical examination and X-ray diffraction photographs confirmed that the resultant powder was a single-phase c o m p o u n d with the perovskite structure. Polycrystalline specimens of the ilmenite and perovskite phases were then hot-pressed in a piston-cylinder apparatus [17] under conditions inside their respective stability fields (Fig. 1): CdTiO3-ilmenite, P = 8 kbar, T = 600°C, t = 1½ hours; CdTiOa-perovskite, P = 25 kbar, T = 800°C, t = 1½ hours. The crystallographic structures of the specimens recovered at room conditions were confirmed by comparison of X-ray diffraction photographs with patterns from the literature (Table 1). Bulk densities determined by the Archimedes m e t h o d and singlecrystal X-ray densities are given in Table 1 ; these spec-
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328 TABLE 1 Crystallographic and elastic data for the ilmenite and perovskite polymorphs of CdTiO3 * Property
Symbol
CdTiO3-ilmenite
CdTiO3-perovskite
Crystal structure Lattice parameters [ 31,371, A
a b c Z Vm M t14
hexagonal 5.248 14.906 6 35.69 208.30 41.66 VIcdVITilVo3
orthorhombic 5.301 7.606 5.419 4 32.90 208.30 41.66 (a) XII,~aVITNIc, ~u H '-'3 or (b) VIIlcdVITiVo21Vo
Molecules/unit cell Molar volume, cm3/mole Molecular weight, g Mean atomic weight, g Coordination [10,36] Interatomic distances, A observed [6] calculated ** [44]
Density, g/cm 3 X-ray bulk % X-ray
Cd O Ti-O Cd-O
2.24 1.89 2.33
Ti-O
1.99
2.26 1.88 (a) 2.71 (b) 2.46 (a) 2.01 (b) 2.OO
P 5.836 5.76 98.7
6.331 6.11 96.5
Vp vs v0 Vp/V s
6.49 3.23 5.31 2.01
7.36 3.94 5.79 1.87
Elastic moduli, Mbar bulk modulus shear modulus
KS //
1.65 0.61
2.12 0.98
Poisson's ratio
oS
0.335
0.299
Velocity, km/sec compressional shear bulk sound
* These data supersede preliminary reports given in [14,15,18]. ** Based on sum of ionic radii of cations and anions in respective coordinations [44].
transformed), perhaps due to the u n c e r t a i n t y in the position of the i l m e n i t e - p e r o v s k i t e phase b o u n d a r y [7,10]. " The compressional (Vp) and shear (Vs) wave velocities in our recovered specimens were measured by the ultrasonic pulse superposition m e t h o d [19] m o d i f i e d for our small specimens [13,17] as a f u n c t i o n of hydrostatic pressure to P = 7.5 kbar at r o o m temperature. The cylindrical specimens (diameter = 3 mm, length = 2 - 3 m m ) were j a c k e t e d f r o m the pressure fluid by the metal capsules in which they were fabricated. The velocity vs. pressure data (corrected for length change
u p o n compression) are illustrated in Figs. 2 and 3 ; both Vp and Vs increase systematically with increasing pressure and these changes are c o m p l e t e l y reversible on release o f pressure. The velocities have been measured only along the cylindrical axis o f hot-pressing, but specimens fabricated in such a m a n n e r have b e e n shown to be elastically isotropic [ 12,13,17,20]. We assume that the velocity data at P -- 7.5 kbar are free of the effects of cracks and pores and are representative o f those o f the zero-porosity, elastically isotropic polycrystalline aggregate. On this basis, we adopt the X-ray density and calculate the adiabatic
329 elastic moduli and Poisson's ratio from the equations for an isotropic elastic medium (Table 1). While the inherent precision o f the pulse superposition data in Figs. 2 and 3 is 0.02%, other experimental uncertainties imply a precision of 0.1% for the velocities given in Table 1 (or 0.2% for the elastic moduli).
3. Discussion
The major goal of our experimental program is to determine the elastic properties of the low-pressure and high-pressure polymorphs for a wide variety of crystallographic phase transformations thought to be relevant to discussions of the earth's interior. It is important to attempt to discern characteristics which relate the elasticity and crystallographic data for these polymorphs because, if such relationships do exist, they could provide the basis for predicting the elasticity of phases whose properties cannot or have not yet been measured. Our new elasticity data for the ilmenite and perovskite phases of CdTi03 enable us to compare the density and velocity jumps across this polymorphic transition: A p / p = 8%, Z~p/Vp = 13%, Avs/V s = 22%, A v ¢ / v ¢ = 9%. Thus the jumps in Vp and.re are comparable to or slightly higher than that for/9, while the shear velocity jump is roughly three times the density change. This behaviour for the ilmenite-perovskite transition contrasts with that observed for the pyroxene-garnet, p y r o x e n e - i l m e n i t e , olivine-spinel and o l i v i n e - b e t a phase transformations [15,16], for all of which the Vs jumps are less than or equal to those for Vp and v¢~. As a consequence, the Vp/V s ratio (and thus Poisson's ratio) decreases across the ilmenite perovskite transition, whereas it remains constant or increases for all of the other phase transformations we have studied [ 15,16,21]. Such differences in the elasticity across phase transformations offer the potential of enabling us to distinguish which velocity and density discontinuities in the earth's mantle are related to which crystallographic phase transformations. It is also interesting to test the applicability of various empirical laws describing v e l o c i t y - d e n s i t y systematics proposed by previous investigators to the data for the ilmenite-perovskite phase transformation (Table 2). For the linearized forms of Birch's law: Vp = a + bp [22] and v¢ = A + B p [23], the values
TABLE 2 Elasticity density (volume) systematies across theilmenite perovskite phase transformation in CdTiO3 Parameter of systematics
Ilmenite-perovskite
b = AVp/AO Xp = (3 In Vp/O In p) B = /',Vc~/,',O X0 = (~ In v~]_a In p) n = [~ In (o/M)/~ In ,~] = (2X0)-l X = (~ In KS/a In V) = 2X~ + 1
1.8 1.5 1.0 1.1 0.47 3.1
b = 3.0 3.3 and B = 2 . 4 - 2 . 6 are presumed to represent minerals of common mean atomic w e i g h t . ~ and isothermal compression or isobaric expansion of a homogeneous material [22,23] and the curves for = 2 0 - 2 1 are plotted in Fig. 4. The ilmenite perovskit~ transition in CdTiOa exhibits much low b and B values even when allowance is made for the tendency of both b and B to decrease with increasing/~ [24,13 15];
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Fig. 4. Birch diagram for compressional (Vp) and bulk sound (vg) velocity. Solid and dashed lines with equations represent empirical trends for minerals with ~-t = 20-21 [22,23]. Data for flmenite-perovskite transformation in CdTiO3 indicate substantially smaller slopes than predicted by the empirical trends as evidenced by the divergence of the arrows (predictions) and the measured data (connected circles).
330 compare the trends of the arrows and the measured data in Fig. 4. Also given in Table 2 are the parameters of the ilmenite-perovskite phase transformation for the seismic equation of state [25]: p/M -- A(M)qbn where • = KS~ p is the seismic parameter; the law of corresponding state [26]: KS = A V o - x where V0 is volume; and the powder law formulations of Birch's law [27, 29]: vi = c(M)pXi. Since all of these semi-empirical laws are really equivalent representations of the relationship of bulk modulus to volume for materials of common M [30], a discussion of X¢ will suffice for all. For the seismic equation of state (n = 1/3) and the law of corresponding states (X = 4), X0 ~ 1.5 from empirical observations. For materials with 3~r _~ 20.2, the powder law gives )to = 1.25 [29]. We note in Table 2 that )~4 = 1.1 for the ilmenite-perovskite phase transformation, or somewhat smaller than implied by the empirical laws. Similar values of ~O have been observed for the coesite-rutile, pyroxene-ilmenite, and pyroxene-garnet phase transformations [14,15], while values of )'O ~ 2 characterize the quartz-coesite, olivine spinel, and olivine-beta transitions [14,16]. We have demonstrated elsewhere that relatively high slopes (linear or logarithmic) on v - p diagrams are characteristic of phase transformations which involve no change in cation-anion co-ordination and nearestneighbour interatomic distances [ 14,16 ]; e.g. quartzcoesite, olivine-spinel and olivine-beta. By contrast, the coesite-rutile, pyroxene-ilmenite and pyroxenegarnet transitions exhibit low v - p slopes and involve major increases in cation co-ordination and cationanion distance [14,15]. The ilmenite perovskite transformation fits into the latter category as it is accompanied by an increase in the co-ordination of Cd2+and in the C d - O distance (Table 1), and it is represented by relatively low slopes on v - p diagrams. The co-ordination and interatomic distances in the polymorphs of CdTiO3 are somewhat uncertain because the crystal structures have not been refined by precise X-ray work. For the ilmenite phase, the VIcdVITilVo3 co-ordination is correct, but the interatomic distances are only approximate since the positional parameters are not known. Posnjak and Barth [6] used reflections from small crystallographic faces to estimate the position of the metal atoms; on the assumption that the oxygen-oxygen distances are between 2.5 and 2.6 A and that the T i - O distance is 1.89 A, they found that
the largest possible C d - O distance was 2.24 A. These distances are slightly smaller than those calculated from the ionic radii of Cd2*and Ti4÷in 6-fold co-ordination (Table 1) and observed for the rocksalt (Cd-O = 2.35 A [310, rutile ( T i - O = 1.96 A [32])and ilmenite ( T i - O = 1.92-2.13 A in FeTiO3 [33,34]). For the perovskite phase, the situation is somewhat more ambiguous, largely due to the uncertainty in the co-ordination of Cd2÷(see discussion in Marezio [35]). If the structure of CdTiO3-perovskite were undistorted, namely cubic, the Cd2+ions would have co-ordination number 12 and the 02- ions co-ordination number 6; it is this co-ordination that was given by Liebertz and Rooymans ([10], see also [36]) and is listed in Table 1. In the orthorhombic perovskite structure, the oxygens are displaced from their ideal cubic positions so that the 12-oxygen polyhedra around the divalent cation are quite distorted [35]. As a consequence, the 12 M - O distances may vary over a large range and in some cases it is more accurate to distinguish between 8 first nearest-neighbour oxygens around the divalent cation and 4 second nearest-neighbours. CdTiO3-perovskite does have orthorhombic symmetry [37,38] and may be characterized by VIIIcdVITiVo21Vo coordination rather than that given in Table 1. In either case, the observed interatomic distances [6] may be compared with those calculated from the unit cell edge of the equivalent cubic cell [39]: C d - O = 2.68 A, T i - O = 1.90 A or from the ionic radii (Table 1), and those observed in CaTiO3-perovskite (Ca-O = 2.70 A, T i - O = 1.91 A [40]). We conclude from this discussion of the detailed crystallography of the polymorphs of CdTiO3 that the ilmenite-perovskite phase transformation is characterized by an increase in Cd2÷co-ordination from 6-fold to 8- or 12-fold and that the C d - O interatomic distance increases from 2.24-2.35 to 2.46-2.68 A. Such structural details are critical in determining elasticity variations across polymorphic phase transitions [15, 16,21,41]. One interesting and useful application of our studies of the elasticity of low- and high-pressure polymorphs of silicate analogue compounds (e.g. germanates, titanates and stannates) is to use such data to predict the elastic properties of the silicates themselves. Previously, we have employed various elasticity systematics in isomorphic series to estimate the properties of MgSiO3 in the garnet and ilmenite phases [ 15] and of Mg2SiO4
331 in the spinel phase [16]. Following similar procedures with the perovskite data for CdTiO3 and CdSnOa [18], the KS V 0 = c o n s t a n t law [42] and v~,~t 1/2 = constant law [27,28] b o t h lead to estimates o f KS = 2.8 Mbar and v~ = 8.3 km/sec for M g S i O r p e r o v s k i t e (Vm = 24.59 cm3/mole, p = 4.083 g / c m a [4]) and K s = 2.7 Mbar and ve = 7.7 km/sec for C a S i O r p e r o v s k i t e (Vm = 25.49 cma/mole, 19 = 4.557 g/cm a a t P = 160 kbar [43]). The latter value of K S is considerably larger than that inferred by Liu and R i n g w o o d [43] from a comparison o f their observed in-situ lattice parameter with values predicted for P = 1 bar. Alternatively, we may estimate the velocities o f MgSiO3-perovskite from the power law parameters ( ~ and ~p) in Table 2 and our earlier predictions for MgSiO3-ilmenite (v¢ = 7 . 5 - 7 . 7 km/sec and Vp = 9.8 km/sec [15]); such an a p p r o a c h predicts v~ = 8 . 1 - 8 . 3 km/sec and Vp = 10.9 km/sec for MgSiO3perovskite. These predictions must be regarded as tentative, especially because we do n o t if the elastic properties o f perovskite are sensitive to the specific coordination; however, t h e y may prove useful until direct determinations are available.
Acknowledgements I thank A.E. R i n g w o o d for his c o n t i n u e d advice and e n c o u r a g e m e n t in this collaborative program, L.G. Liu and M. Marezio for helpful discussions, L.G. Liu and A.E. R i n g w o o d for preprints o f their papers, and D.J. Mayson for technical assistance.
References 1 A.E. Ringwood, Composition and Petrology of the Earth's Mantle (McGraw-HiU, New York, N.Y., 1975) 618 pp. 2 N. Kawai, M. Tachimori and E. lto, A high-pressure hexagonal form of MgSiO 3, Proc. Japan Acad. 50 (1974) 378-38O. 3 L.C. Ming and W.A. Bassett, High-pressure phase transformations in the system of MgSiOa-FeSiO 3, Earth Planet. Sci. Lett. 27 (1975) 85-89. 4 L.G. Liu, Post-oxide phases of forsterite and enstatite, Geophys. Res. Lett. 2 (1975) October issue. 5 L.G. Liu, Post-oxide phases of olivine and pyroxene and mineralogy of the mantle, Nature (1975) in press. 6 E. Posnjak and T.F.W. Barth, Notes on some structures of the ilmenite type, Z. Kristallogr. 88 (1934) 271-280. 7 I. Morgenstern-Badarau, P. Poix and A. Michel, Mise en
~vidence d'une nouvelle phase dans le syst~me SnO2-CdO, C.R. Acad. Sci. Paris 256 (1963) 692-693. 8 Y. Syono, S.I. Akimoto and Y. Endoh, High-pressure synthesis of ilmenite and perovskite type MnVO3 and their magnetic properties, J. Phys. Chem. Solids 32 (1971) 243-249. 9 L.G. Liu, High-pressure phase transformations and compressions of ilmenite and ruffle, 1. Experimental results, Phys. Earth Planet. Inter. 10 (1975) 167-176. 10 1. Liebertz and C.J.M. Rooymans, Die Ilmenit/PerowskitPhasenumwandlung yon CdTiO3 unter hohem Druck, Z. Phys. Chem. Neue Folge 44S (1965) 242-249. 11 J.M. Neil, A. Navrotsky and O.J. Kleppa, The enthalpy of ilmenite-perovskite transformation in cadmium titanate, Inorg. Chem. 10 (1971) 2076-2077. 12 R.C. Liebermann, Compressional velocities of polycrystalline olivine, spinel, and rutile minerals, Earth Planet. Sci. Lett. 17 (1972) 263-268. 13 R.C. Liebermann, Elastic properties of polycrystalline SnO 2 and GeO2: comparison with stishovite and rutile data, Phys. Earth Planet. Inter. 7 (1973) 461-465. 14 R.C. Liebermann and A.E. Ringwood, Birch's law and polymorphic phase transformations, J. Geophys. Res. 78 (1973) 6926-6932. 15 R.C. Liebermann, Elasticity of pyroxene--garnet and pyroxene-ilmenite phase transformations in germanates, Phys. Earth Hanet. Inter. 8 (1974) 361-374. 16 R.C. Liebermann, Elasticity of olivine (tx), beta (/3) and spinel (3') polymorphs of germanates and silicates, Geophys. J.R. Astron. Soc. 42 (1975) 899-929. 17 R.C. Liebermann, A.E. Ringwood, D.J. Mayson and A. Major, Hot-pressing of polycrystalline aggregates at very high pressure for ultrasonic measurements, in: Proc. 4th Int. Conf. High Pressure, Kyoto 1974 (Physico-Chemical Society of Japan, 1975) 495-502. 18 L.E.A. Jones and R.C. Liebermann, Elastic and thermal properties of fluoride and oxide analogues in the rocksalt, fluorite, rutile and perovskite structures, Phys. Earth Planet. Inter. 9 (1974) 101-107. 19 H.J. McSkimin, Pulse superposition method for measuring ultrasonic wave velocities in solids, J. Acoust. Soc. Am. 33 (1961) 12-16. 20 R.C. Liebermann and A.E. Ringwood, Elastic properties of anorthite and the nature of the lunar crust, Earth Planet. Sci. Lett., submitted for publication. 21 R.C. Liebermann and A.E. Ringwood, Elasticity systematics across polymorphic phase transformations, in preparation. 22 F. Birch, The velocity of compressional waves in rocks to 10 kilobars, 2, J. Geophys. Res. 66 (1961) 2199 2224. 23 C.Y. Wang, Constitution of the lower mantle as evidenced from shock-wave data for some rocks, J. Geophys. Res. 73 (1968) 6459-6476. 24 N. Soga, Sound velocity of some germanate compounds and its relation to the law of corresponding states, J. Geophys. Res. 76 (1971) 3983-3989. 25 D.L. Anderson, A seismic equation of state, Geophys. J. R. Astron. Soc. 13 (1967) 9-30.
332 26 O.L. Anderson and J.E. Nafe, The bulk modulus-volume relationship for oxide compounds are related geophysical problems, J. Geophys. Res. 70 (1965) 3951-3963. 27 T.J. Shankland, Velocity-density systematics: derivation from Debye theory and the effect of ionic size, J. Geophys. Res. 77 (1972) 3750-3758. 28 D.H. Chung, Birch's law: why is it so good?, Science 177 (1972) 261 263. 29 T.J. Shankland and D.H. Chung, General relationships among sound speeds, II. Theory and discussion, Phys. Earth Planet. Inter. 8 (1974) 121-129. 30 O.L. Anderson, Comments on the power-law representation of "Bitch's law", J. Geophys. Res. 78 ( 1 9 7 3 ) 4 9 0 1 4914. 31 R.A. Robie, P.M. Bethke, M.S. Toulmin and J.L. Edwards, X-ray crystallographic data, densities, and molar volumes of minerals, in: Handbook of Physical Constants, Revised Edition, cd. S.P. Clark, Jr., Geol. Soc. Am. Mere. 97 (1966) 27 73, revised ed., section 5. 32 W.lt. Baur and A.A. Khan, Rutile-type compounds, IV. SiO2, GeO2 and a comparison of other rutile-type structures, Acta Crystallogr. B27 (1971) 2133-2139. 33 R.W.G. Wyckoff, Crystal Structures, Vol. 2 (John Wiley, New York, N.Y., 1964). 34 L.G. Liu, Isothermal compression of minerals pertinent to the Earth's mantle, Ph.D. Thesis, Univ. of Rochester, Rochester, N.Y. (1970).
35 M. Marezio, Oxides at high pressure, Trans. Am. Crystallogr. Assoc. 5 (1969) 29-36. 36 R.D. Shannon and C.T. Prewitt, Coordination and volume changes accompanying high-pressure phase transformations of oxides, Mat. Res. Bull. 4 (1969) 57-62. 37 R.S. Roth, Classification of perovskite and other ABO3type compounds. J. Res. Natl. Bur. Standards, U.S. 58, No. 2 (1957) 75-88. 38 H.D. Megaw, Crystal structure of double oxides of the perovskite type, Proc. Phys. Soc. 58 (1946) 133--152. 39 F.S. Galasso, Structure, Properties and Preparation of Perovskite-Type Compounds (Pergamon Press, Oxford, 1969). 40 L. Bragg, G.F. Claringbull and W.H. Taylor, The Crystalline State, IV. Crystal Structure of Minerals (Cornell Univ. Press, Ithaca, N.Y., 1965) 409 pp. 41 R.C. Liebermann and A.E. Ringwood, Elasticity and crystallography of phase transformations (abstract), EOS 56 (1974) 1188. 42 D.L. Anderson and O.L. Anderson, Bulk modulus-volume relationship for oxides, J. Geophys. Res. 75 (1970) 34943500. 43 L.G. Liu and A.E. Ringwood, Synthesis of a perovskitetype polymorph of CaSiO3, Earth Planet. Sci. Lett. 28 (1975) 209-211. 44 R.D. Shannon and C.T. Prewitt, Effective ionic radii in oxides and fluorides, Acta Crystallogr. B25 (1969) 9 2 5 945.
Earth and Planetary Science Letters, 29 (1976) 326-332 Q Elsevier Scientific Publishing Company, Amsterdam Printed in The Netherlands [51
ELASTICITY OF THE ILMENITE - PEROVSKITE PHASE TRANSFORMATION IN CdTiO3
ROBERT C. LIEBERMANN Research School of Earth Sciences, Australian National University, Canberra, A. C. T. (Australia) Revised version received December 11, 1975
Ultrasonic data for the velocities of the ilmenite and perovskite polymorphs of CdTiO 3 have been determined as a function of pressure to 7.5 kbar at room temperature for polycrystalline specimens hot-pressed at pressures up to 25 kbar. This transition is characterized by the following velocity (v) density (p) relationships: (1) the changes in compressional (Vp) and bulk sound (v~) velocities are comparable in percentage magnitude to the density jump, while the shear (Vs) velocity jump is three times greater than that for p; (2) (Vp/Vs) decreases across the transition from the low- to high-pressure phase; and (3) low slopes (linear or logarithmic) on v-p diagrams. The (Vp/Vs) behaviour for the ilmenite -perovskite transformation is unusual for the transitions studied in our laboratory. The observed relationships (1) and (2) are typical of the elasticity behaviour across phase transformations which involve increases in cationanion co-ordination and in nearest-neighbour interatomic distances, such as those exhibited by CdTiO 3 in transforming from the ilmenite to the perovskite phase. Elasticity systematics for isostructural sequences are used to estimate the bulk moduli of the perovskite polymorphs of CaSiO3 (2.7 Mbar) and MgSiO3 (2.8 Mbar).
1. Introduction
Pyroxenes with ABO3 stoichiometry are the secondmost abundant mineral constituent of the upper mantle, after olivine. Static experiments (see Ringwood [1 ] for a review) have indicated several possible highpressure crystal structures for silicate pyroxenes in the earth's mantle, including garnet, ilmenite and perovskite. Recently, it has been demonstrated that (Mg,Fe)SiO3 pyroxenes do transform to the ilmenite and subsequently to the perovskite structure at pressures between 300 and 500 kbar [ 2 - 4 ] . Mineralogical models based on these experimental studies suggest that there may be a region of the earth's mantle in which the (Mg,Fe)SiO3 component transforms from the ilmenite to the perovskite structure [1,5]. The ilmenite-perovskite phase transformation was first demonstrated experimentally in CdTiO3 at atmospheric pressure by Posnjak and Barth [6] and has subsequently been observed in CdSnO3 [7], MnVO3 [8] and (Fe,Mg)TiO3 [9]. The transformation in CdTiO3 is characterized by an 8% increase in density as the coordination changes from V I c d V I T i l V o 3 to
X l I c d V I T i V I o 3 ([6], and see later discussion). The P T relations for the ilmenite-perovskite transition in CdTiO3 have been studied by Liebertz and Rooymans [ 10]. The transition occurs with a negative slope dP/dT = 49 bars/°C (Fig. 1) which implies a positive entropy change; this has been verified by direct enthalpy measurements [ 11 ]. The occurrence of such a phase transformation in (Mg,Fe)SiO3 in the earth's interior with an analogous negative slope could have important implications for mantle dynamics (e.g. [1, chapter 15]). The purpose of this paper is to report new elasticity data for the ilmenite and perovskite polymorphs of CdTiO3 and to discuss the importance of these data for v e l o c i t y - d e n s i t y systematics proposed by previous investigators. This study is an outgrowth o f our program to fabricate polycrystalline aggregates of the low- and high-pressure phases of compounds undergoing polymorphic phase transformations in the laboratory and to measure the elastic properties of these phases by ultrasonic techniques [ 12 17]. This paper augments and supplements the brief reports and discussions of these data which we have presented earlier [14,15,18].
327 4O
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Fig. 1. Phase diagram for the ilmenite-perovskite transformation in CdTiOa (after Liebertz and Rooymans [10]). Circles represent raw experimental data using CdTiOa-ilmenite as the starting material: open circles, no perovskite phase detected; closed circles, perovskite phase observed in quench product [10]. The solid line indicates the phase boundary P (kbar) = 40.7-0.049 T (°C) for T > 500°C where it is well-determined by the experimental data. This slope is quite consistent with the measured enthalpy of the respective phases [ 11 ] which implies that AS = 3.25 cal/deg/mole and thus d P / d T = zaS/,~,V = - 4 9 bar/°C for AV = -2.79 cm3/mole. The X's represent the hot-pressing conditions for the polycrystalline ilmenite and perovskite samples used in the present study.
0
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Pressure, kbar
Fig. 2. Compressional and shear velocities vs. pressure at room temperature for polycrystalline CdTiO3-ilmenite using the pulse superposition technique. Precision of individual velocity determinations is 0.02%. imens are less than 3.5% porous and have a grain size generally less than 50 pm. Similar attempts to hotpress CdSnOa-ilmenite at P = 8 kbar, T = 6 0 0 ° C were unsuccessful (the perovskite starting powder was un-
I
2. Experimental procedure and data A powder sample of CdTiOs was synthesized by intimately mixing stoichiometric a m o u n t s o f CdO and TiO2 and sintering at 1200°C in air for six hours. Optical examination and X-ray diffraction photographs confirmed that the resultant powder was a single-phase c o m p o u n d with the perovskite structure. Polycrystalline specimens of the ilmenite and perovskite phases were then hot-pressed in a piston-cylinder apparatus [17] under conditions inside their respective stability fields (Fig. 1): CdTiO3-ilmenite, P = 8 kbar, T = 600°C, t = 1½ hours; CdTiOa-perovskite, P = 25 kbar, T = 800°C, t = 1½ hours. The crystallographic structures of the specimens recovered at room conditions were confirmed by comparison of X-ray diffraction photographs with patterns from the literature (Table 1). Bulk densities determined by the Archimedes m e t h o d and singlecrystal X-ray densities are given in Table 1 ; these spec-
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328 TABLE 1 Crystallographic and elastic data for the ilmenite and perovskite polymorphs of CdTiO3 * Property
Symbol
CdTiO3-ilmenite
CdTiO3-perovskite
Crystal structure Lattice parameters [ 31,371, A
a b c Z Vm M t14
hexagonal 5.248 14.906 6 35.69 208.30 41.66 VIcdVITilVo3
orthorhombic 5.301 7.606 5.419 4 32.90 208.30 41.66 (a) XII,~aVITNIc, ~u H '-'3 or (b) VIIlcdVITiVo21Vo
Molecules/unit cell Molar volume, cm3/mole Molecular weight, g Mean atomic weight, g Coordination [10,36] Interatomic distances, A observed [6] calculated ** [44]
Density, g/cm 3 X-ray bulk % X-ray
Cd O Ti-O Cd-O
2.24 1.89 2.33
Ti-O
1.99
2.26 1.88 (a) 2.71 (b) 2.46 (a) 2.01 (b) 2.OO
P 5.836 5.76 98.7
6.331 6.11 96.5
Vp vs v0 Vp/V s
6.49 3.23 5.31 2.01
7.36 3.94 5.79 1.87
Elastic moduli, Mbar bulk modulus shear modulus
KS //
1.65 0.61
2.12 0.98
Poisson's ratio
oS
0.335
0.299
Velocity, km/sec compressional shear bulk sound
* These data supersede preliminary reports given in [14,15,18]. ** Based on sum of ionic radii of cations and anions in respective coordinations [44].
transformed), perhaps due to the u n c e r t a i n t y in the position of the i l m e n i t e - p e r o v s k i t e phase b o u n d a r y [7,10]. " The compressional (Vp) and shear (Vs) wave velocities in our recovered specimens were measured by the ultrasonic pulse superposition m e t h o d [19] m o d i f i e d for our small specimens [13,17] as a f u n c t i o n of hydrostatic pressure to P = 7.5 kbar at r o o m temperature. The cylindrical specimens (diameter = 3 mm, length = 2 - 3 m m ) were j a c k e t e d f r o m the pressure fluid by the metal capsules in which they were fabricated. The velocity vs. pressure data (corrected for length change
u p o n compression) are illustrated in Figs. 2 and 3 ; both Vp and Vs increase systematically with increasing pressure and these changes are c o m p l e t e l y reversible on release o f pressure. The velocities have been measured only along the cylindrical axis o f hot-pressing, but specimens fabricated in such a m a n n e r have b e e n shown to be elastically isotropic [ 12,13,17,20]. We assume that the velocity data at P -- 7.5 kbar are free of the effects of cracks and pores and are representative o f those o f the zero-porosity, elastically isotropic polycrystalline aggregate. On this basis, we adopt the X-ray density and calculate the adiabatic
329 elastic moduli and Poisson's ratio from the equations for an isotropic elastic medium (Table 1). While the inherent precision o f the pulse superposition data in Figs. 2 and 3 is 0.02%, other experimental uncertainties imply a precision of 0.1% for the velocities given in Table 1 (or 0.2% for the elastic moduli).
3. Discussion
The major goal of our experimental program is to determine the elastic properties of the low-pressure and high-pressure polymorphs for a wide variety of crystallographic phase transformations thought to be relevant to discussions of the earth's interior. It is important to attempt to discern characteristics which relate the elasticity and crystallographic data for these polymorphs because, if such relationships do exist, they could provide the basis for predicting the elasticity of phases whose properties cannot or have not yet been measured. Our new elasticity data for the ilmenite and perovskite phases of CdTi03 enable us to compare the density and velocity jumps across this polymorphic transition: A p / p = 8%, Z~p/Vp = 13%, Avs/V s = 22%, A v ¢ / v ¢ = 9%. Thus the jumps in Vp and.re are comparable to or slightly higher than that for/9, while the shear velocity jump is roughly three times the density change. This behaviour for the ilmenite-perovskite transition contrasts with that observed for the pyroxene-garnet, p y r o x e n e - i l m e n i t e , olivine-spinel and o l i v i n e - b e t a phase transformations [15,16], for all of which the Vs jumps are less than or equal to those for Vp and v¢~. As a consequence, the Vp/V s ratio (and thus Poisson's ratio) decreases across the ilmenite perovskite transition, whereas it remains constant or increases for all of the other phase transformations we have studied [ 15,16,21]. Such differences in the elasticity across phase transformations offer the potential of enabling us to distinguish which velocity and density discontinuities in the earth's mantle are related to which crystallographic phase transformations. It is also interesting to test the applicability of various empirical laws describing v e l o c i t y - d e n s i t y systematics proposed by previous investigators to the data for the ilmenite-perovskite phase transformation (Table 2). For the linearized forms of Birch's law: Vp = a + bp [22] and v¢ = A + B p [23], the values
TABLE 2 Elasticity density (volume) systematies across theilmenite perovskite phase transformation in CdTiO3 Parameter of systematics
Ilmenite-perovskite
b = AVp/AO Xp = (3 In Vp/O In p) B = /',Vc~/,',O X0 = (~ In v~]_a In p) n = [~ In (o/M)/~ In ,~] = (2X0)-l X = (~ In KS/a In V) = 2X~ + 1
1.8 1.5 1.0 1.1 0.47 3.1
b = 3.0 3.3 and B = 2 . 4 - 2 . 6 are presumed to represent minerals of common mean atomic w e i g h t . ~ and isothermal compression or isobaric expansion of a homogeneous material [22,23] and the curves for = 2 0 - 2 1 are plotted in Fig. 4. The ilmenite perovskit~ transition in CdTiOa exhibits much low b and B values even when allowance is made for the tendency of both b and B to decrease with increasing/~ [24,13 15];
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Fig. 4. Birch diagram for compressional (Vp) and bulk sound (vg) velocity. Solid and dashed lines with equations represent empirical trends for minerals with ~-t = 20-21 [22,23]. Data for flmenite-perovskite transformation in CdTiO3 indicate substantially smaller slopes than predicted by the empirical trends as evidenced by the divergence of the arrows (predictions) and the measured data (connected circles).
330 compare the trends of the arrows and the measured data in Fig. 4. Also given in Table 2 are the parameters of the ilmenite-perovskite phase transformation for the seismic equation of state [25]: p/M -- A(M)qbn where • = KS~ p is the seismic parameter; the law of corresponding state [26]: KS = A V o - x where V0 is volume; and the powder law formulations of Birch's law [27, 29]: vi = c(M)pXi. Since all of these semi-empirical laws are really equivalent representations of the relationship of bulk modulus to volume for materials of common M [30], a discussion of X¢ will suffice for all. For the seismic equation of state (n = 1/3) and the law of corresponding states (X = 4), X0 ~ 1.5 from empirical observations. For materials with 3~r _~ 20.2, the powder law gives )to = 1.25 [29]. We note in Table 2 that )~4 = 1.1 for the ilmenite-perovskite phase transformation, or somewhat smaller than implied by the empirical laws. Similar values of ~O have been observed for the coesite-rutile, pyroxene-ilmenite, and pyroxene-garnet phase transformations [14,15], while values of )'O ~ 2 characterize the quartz-coesite, olivine spinel, and olivine-beta transitions [14,16]. We have demonstrated elsewhere that relatively high slopes (linear or logarithmic) on v - p diagrams are characteristic of phase transformations which involve no change in cation-anion co-ordination and nearestneighbour interatomic distances [ 14,16 ]; e.g. quartzcoesite, olivine-spinel and olivine-beta. By contrast, the coesite-rutile, pyroxene-ilmenite and pyroxenegarnet transitions exhibit low v - p slopes and involve major increases in cation co-ordination and cationanion distance [14,15]. The ilmenite perovskite transformation fits into the latter category as it is accompanied by an increase in the co-ordination of Cd2+and in the C d - O distance (Table 1), and it is represented by relatively low slopes on v - p diagrams. The co-ordination and interatomic distances in the polymorphs of CdTiO3 are somewhat uncertain because the crystal structures have not been refined by precise X-ray work. For the ilmenite phase, the VIcdVITilVo3 co-ordination is correct, but the interatomic distances are only approximate since the positional parameters are not known. Posnjak and Barth [6] used reflections from small crystallographic faces to estimate the position of the metal atoms; on the assumption that the oxygen-oxygen distances are between 2.5 and 2.6 A and that the T i - O distance is 1.89 A, they found that
the largest possible C d - O distance was 2.24 A. These distances are slightly smaller than those calculated from the ionic radii of Cd2*and Ti4÷in 6-fold co-ordination (Table 1) and observed for the rocksalt (Cd-O = 2.35 A [310, rutile ( T i - O = 1.96 A [32])and ilmenite ( T i - O = 1.92-2.13 A in FeTiO3 [33,34]). For the perovskite phase, the situation is somewhat more ambiguous, largely due to the uncertainty in the co-ordination of Cd2÷(see discussion in Marezio [35]). If the structure of CdTiO3-perovskite were undistorted, namely cubic, the Cd2+ions would have co-ordination number 12 and the 02- ions co-ordination number 6; it is this co-ordination that was given by Liebertz and Rooymans ([10], see also [36]) and is listed in Table 1. In the orthorhombic perovskite structure, the oxygens are displaced from their ideal cubic positions so that the 12-oxygen polyhedra around the divalent cation are quite distorted [35]. As a consequence, the 12 M - O distances may vary over a large range and in some cases it is more accurate to distinguish between 8 first nearest-neighbour oxygens around the divalent cation and 4 second nearest-neighbours. CdTiO3-perovskite does have orthorhombic symmetry [37,38] and may be characterized by VIIIcdVITiVo21Vo coordination rather than that given in Table 1. In either case, the observed interatomic distances [6] may be compared with those calculated from the unit cell edge of the equivalent cubic cell [39]: C d - O = 2.68 A, T i - O = 1.90 A or from the ionic radii (Table 1), and those observed in CaTiO3-perovskite (Ca-O = 2.70 A, T i - O = 1.91 A [40]). We conclude from this discussion of the detailed crystallography of the polymorphs of CdTiO3 that the ilmenite-perovskite phase transformation is characterized by an increase in Cd2÷co-ordination from 6-fold to 8- or 12-fold and that the C d - O interatomic distance increases from 2.24-2.35 to 2.46-2.68 A. Such structural details are critical in determining elasticity variations across polymorphic phase transitions [15, 16,21,41]. One interesting and useful application of our studies of the elasticity of low- and high-pressure polymorphs of silicate analogue compounds (e.g. germanates, titanates and stannates) is to use such data to predict the elastic properties of the silicates themselves. Previously, we have employed various elasticity systematics in isomorphic series to estimate the properties of MgSiO3 in the garnet and ilmenite phases [ 15] and of Mg2SiO4
331 in the spinel phase [16]. Following similar procedures with the perovskite data for CdTiO3 and CdSnOa [18], the KS V 0 = c o n s t a n t law [42] and v~,~t 1/2 = constant law [27,28] b o t h lead to estimates o f KS = 2.8 Mbar and v~ = 8.3 km/sec for M g S i O r p e r o v s k i t e (Vm = 24.59 cm3/mole, p = 4.083 g / c m a [4]) and K s = 2.7 Mbar and ve = 7.7 km/sec for C a S i O r p e r o v s k i t e (Vm = 25.49 cma/mole, 19 = 4.557 g/cm a a t P = 160 kbar [43]). The latter value of K S is considerably larger than that inferred by Liu and R i n g w o o d [43] from a comparison o f their observed in-situ lattice parameter with values predicted for P = 1 bar. Alternatively, we may estimate the velocities o f MgSiO3-perovskite from the power law parameters ( ~ and ~p) in Table 2 and our earlier predictions for MgSiO3-ilmenite (v¢ = 7 . 5 - 7 . 7 km/sec and Vp = 9.8 km/sec [15]); such an a p p r o a c h predicts v~ = 8 . 1 - 8 . 3 km/sec and Vp = 10.9 km/sec for MgSiO3perovskite. These predictions must be regarded as tentative, especially because we do n o t if the elastic properties o f perovskite are sensitive to the specific coordination; however, t h e y may prove useful until direct determinations are available.
Acknowledgements I thank A.E. R i n g w o o d for his c o n t i n u e d advice and e n c o u r a g e m e n t in this collaborative program, L.G. Liu and M. Marezio for helpful discussions, L.G. Liu and A.E. R i n g w o o d for preprints o f their papers, and D.J. Mayson for technical assistance.
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