Compression Studies of Single-Crystal Sn02 and Pb02 in a Diamond Cell

Compression behaviors of two single-crystal rutile-structure dioxides, Sn02 (cassiterite) and Pb02 (plattnerite), were studied in a Merrill-Bassett type diamond cell at room temperature. The samples were compressed in a mixture of 4: 1 methanol­ ethenol solution with pressure measurements by the ruby scale. A four-circle diffractometer was used to obtain the diffraction patterns of these crystals at high pressures. Compression results on Sn02 did not show significant lattice distortion, with a slight increase inc/a up to 35 kbar. The compression data are in excellent agreement with Hazen and Finger (1981) and in reasonable agreement with Ming and Manghnani (1982). Fitting these data to the Birch-Mumaghan equation gives a bulk modulus (K0) of 2.24 ± 0.08 Mbar with K0'= 6.3. On the other hand, the rutile-type Pb02 was found to transform from a tetragonal to an orthorhombic phase above 5 kbar. The cell parameters a, b and c of this phase have different linear compressibility. This phase is different from the reported orthorhombic phases of lead dioxides (a-Pb02). It could represent an intermediate distorted phase which occurs during the transformation from the J3-Pb02 to the a-Pb02 phase. The bulk modulus of Pb02 was determined to be 1.34 ± 0.06 Mbar by fitting the data to the Birch-Mumaghan equation. A linear relationship was found to exist between the bulk sound velocity and mean atomic weight of the rutile-type diox­ ides.


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Our knowledge of the p lanet Earth is limited by the fact that the Earth's interior is inaccessible. An indirect a pp roach must be adopted in order to understand the chemical compositions and physical conditions of the Earth's interior. For instance, an equation of state (EOS) of a mineral can be determined by high-pressure, high-tem p erature a pp arati. The EOS, cou p led with seismic observations, can thus provide constraints on the elastic p ro p erties of the constituting p hases of the Earth's interior.
In order to yield detailed information on the structure and precise measurements on the lattice parameters of a phase, one has to rely on single-crystal com p ression data. The Institute of Earth Sciences, Academia Sinica 2 Dept. Earth Sciences, National Cheng Kung University single-crystal type diamond cell was first invented by Merrill and Bassett (1974) to study the compression behavior of some important geological materials. The cell was later modifi ed by Hazen et al. (1981) to carry out experiments at pressures exceeding 200 kbar. The dev�lopmental history, operating procedure and applications of the single crystal diamond cell have been fully described by Hazen and Finger (1982). The tech nique utilizes the four-circle X-ray diffractometer which has yielded valuable data on the structural details of the crystals (Hazen,198 5).
Si02 is one of the most abundant coumpounds on Earth. Because the high-pressure polymorphic transitions in Si02 might place significant constraints on the evolution of the interior of the Earth and of the other terrestrial planets, its P-T (temperature-pressure) phase diagram and the physical properties of the various polymorphs have been widely invesij ���ed (see Liu and Bassett, 1986 for a detailed description). Similarly, the nature of the pb;�)� behavior of several analogous dioxides at high pressures has also been exten sivelyJrstu _ died (Liu, 1982;Ming and Manghnani, 1982). Studies of dioxides at high pressdges in general are of great interest to physicists, chemists, and material scientists investigati!lg the phase transformations and elastic properties of these materials. rli��i;fes form a variety of crystal structures depending on the size of the cations.
There have been relatively few static compression data on single-crystal dioxides except for some rutile-type , and some Si02 polymorphs (Levien et al., 1980;Levien and Prewitt, 1981 ). Normally, the cell parameters of single-crystals can be determined very accurately (within± 0.001 A) by this method. Thus compression sti.itiY·1&F'Yingt�1ef.Ystal dioxides is important not only in detecting subtle structural changes bf)tcrutdnpmwiN:ltiring compression but also crucial in determining the mechansim of a bJ;.a!leilfrWl §ifilOn .. 5Jw.
.i: m w �1-i a"Ue1b1rrWetf out a systematic compression study of the dioxides in a single-crystal BJb<e>f�l iruRoWd 2dgff1Tu this report, we will describe briefly the technique of the single crystal compression in a diamond cell using f o ur-circle goniometer X-ray diffraction. This f�elfrli�ifie'YWfl l3tfien�ibe used to study the compression behaviors of some dioxides. 1!tltotfgflh:lf�sie�le1S? we are looking for a systematic trend in the compression behaviors of cation polyhedra in various structural types of dioxides. The phase relationships and the mechanism of post-rutile transformation are also briefly discussed.

EXPERIMENTAL METHOD
Sn02 and Pb02 single-crystals were requested from the Smithsonian Museum, Wash ington, D. C. Electron microprobe examination indicated that ·the crystals used in this experiment consisted mostly of Sn and Pb, respectively. Prior to the experiments, the crystals were examined with a four-circle diffractometer to determine their structures and lattice parameters. The crystals were then carefully chopped to small chips with dimen sions of lOOx 100x50 µm for the experiment. A Merrill and Bassett type diamond cell ( Figure 1) was used to generate pressure. A T301 stainless steel gasket (250 µm thick) was indented by the diamonds and a hole (200 µm) was drilled in the center of the indentation. The crystal was mounted in the gasket hc:ile with ruby chips (15 µm in size) for pressure measurements Huang, 1992). Pressure was measured each time before and after the diffrcation signal was collected. Several ruby chips were measured in order to test the hydrostaticity of the run. A mixture of 4: 1 methenol-ethenol solution was used as a pressure medium. After the sample was loaded, the orientation of the sample in the diamond cell was determined preliminarily by a precession camera. The cell wa5 then mounted on the four-circle diffractometer to determine the structure and lattice parameters. A sophisticated and specified program was needed to drive the four circle diffractometer and to collect and analyze the diffraction signals. It took 1 to 2 days for the data acquisition of each pressure increment. A flow chart shows the experimental procedure is outlined in Figure 2. The experiments were carried out at the Geophysical Laboratory, Carnegie fustitute. A detailed description of the principle, the methods and procedure of the experiment was reported by Li (1992).

RESULTS
In single-crystal compression experiments, error in the calculation of lattice param . eters is of the order of 0.1 %, which results in an uncertainty of 0.3 % in molar volume determination. Uncertainty in pressure estimation by the ruby fluorescence is less than 0.5 kbar.
Compression <;>f the single-crystal Sn02 remains rutile structure up to 30 kbar. The experiment ended with further compression to 36 kbar where the crystal was found to be in contact with both of the diamond anvils. Results of the cell parameters, a, c, c!a, and molar volume, V, of Sn02 at various pressures are listed in Table 1 and the variations of a, c, and V/V0 with pressure are shown in Figure 3.
In Pb02, the cell parameter a splits into two cell parameters a and b above 5 kbar.
The compression results of Pb02 up to 21.2 kbar are listed in Table 2. The variations of cell parameters. a and b, and relative change of cell parameters with pressure are shown in Figure 4. Cell parameters, a and c , decrease with pressure while the new cell param eter, b, increases slightly up to 18 kbar and then decreases with pressure ( Figure 4b). The molar volume shows a slightly higher compressibility at about 5 kbar ( Figure 6). The change from tetragonal to orthorhombic phase in Pb02 above 5 kbar has never been reported.

Compressibility of Sn02
From Figure 3, it is obvious that the linear compressibility of a is higher than that of c in Sn02• This results in an increase of c/a ratio with pressure. Results on the variation of c/a in Sn02 with pressure observed in our study are consistent with that obtained by Hazen and Finger (1981). This implies that the lattice of cassiterite, despite being some what distorted, still remains its rutile-type structure during the compression. Lattice distor tion of this type is best observed by the single-crystal lattice refinement method in the single-crystal experiment which is greatly superior to the powder method.
Our compression data are in excellent agreement with those obtained in single-crystal measurements by Hazen and Finger (1981 ). These results are combined and fit to the Birch-Mumaghan equation: where P is the pressure in Mbar, K0 and K01 are isothermal bulk modulus (in Mbar) and its derivative, respectively. The bulk modulus thus obtained is 2.24±0. 08 Mbar assuming that K01 is 4. These data are not sufficient to further constrain the value of K01 • Ming and Manghnani (1982) have reported the compression data of powdered Sn02 up to 330 kbar.
Their data are in reasonable agreement with the Birch-Mumaghan equation of state using     the above values (K0=2.24, K01=4). However, when the compression data of Sn02 ob tained by the single-crystal method (including this study and Hazen and Finger, 1981) and by the powder method (Ming and Manghnani, 1982) are combined, a K0 of 2.24 Mbar and K01=6.3 fit best for the Birch•Murnaghan equation (Figure 5). The K0 is 10% higher than that reported by Liebermann (1973) determined by the ultrasonic method. The dis crepancy may be due to the porosity and anisotropy of the sample in ultrasonic measure ment. Clendenen and Drickamer (1966) have studied the compression behaviors of some rutile-type dioxides powder by the Bridgman anvil. The compression data of Sn02 re ported by them are not suitable for fi tting the Birch-Mumaghan equation. They have reported a convex-upward compression curve for Sn02, which is in contrast with the normal concave-upward compression curve. The discrepancy can be attributed to the nonhydrostatic condition in their experiments. They have used LiF, Ag and Al as pressure calibrants which are much more compressible than Sn02• This has resulted in the pressure inhomogeneity (J ameison and Olinger, 1971) where soft materials respond to uniaxial compression sooner than hard materials. As a consequence, the sample is less compressed while the pressure calibrants are highly compressed at low pressures. At sufficiently high pressures, the sample and pressure calibrants are compressed more uniformly due to the relaxation of the uniaxial loading (Huang and Bassett, 1984). Hence, at low pressures, the sample behaves very incompressibly while at high pressures it shows normal compressibility (see Figure 6, Ming and Manghnani, 1982). Similar abnormal compres sion curve ofMn02 reported by Clendenen and Drickamer (1966) may also be due to this effect.

Compressibility of Pb02
In Pb02, the tetragonal ciystal (rutile structure, or the P-Pb02 phase) is observed to transform into an orthorhombic phase by the splitting of a0-parameter to a and b above 5 kbar (Figure 4 ). Refinement on the cell parameters of this phase yields three orthorgonal axes with a-b >c. The splitting of tt to a and b becomes more prominent with pressure ( Figure 4a). The compressibility of the cell parameters increases in the following order: b<c<<a (Figure 4b). High-pressure studies on Pb02 in past years have concentrated on the phase transition and relatively few compression results have been reported. This distortion of the tetragonal phase to the orthorhombic phase has never been reported to occur at such low pressure (see next section). Though distorted, the molar volume of Pb02 does not show a discontinuity with pressure. The compression data can be fit to the Birch-Murnghan equation to yield a bulk modulus of 1.34±0. 0 6 Mbar. Again, our data are not suffi cient to further constrain the value of K0'. In studying the phase transitions of Pb02, Liu (1980) also reported several compression data of the P-Pb02 phase up to 100 kbar. A reasonable fit can be obtained by combining our data with those of Liu (1980) for K0=1.34 Mbar and K01=0.5. A value of K01 =0.5 is abnormally low compared with other rutile-type dioxides (cf K01=6.8 for Ti02 by Manghnani (1969)

Phase transformation in Pb02
In Pb02, the orthorhombic phase which occurs above 5 kbar is different in lattice parameters and molar volume from the previous reported orthorhombic phase (a-Pb02) (Rueschi and Chana, 1975;Dachille and Roy, 1960;White et al., 1961;Liu, 1980;Yagi and Akimoto, 1980;Ming and Manghnani, 1982). A comparison of cell parameters and molar volume between this phase and the a-Pb02 phase was described by Li (1992).
Phase transition between J3-Pb02 and a-Pb02 was reported to occur at ca. I 0 kbar in the previous studies (Ruetschi and Cahan, 1957;Dachil1e and Roy, I 960;and White et al. 1961 ). However, detailed experimental methods were not reported and pressure measure ments were ambiguous in the studies of Ruetschi and Cahan (1957) and Dachille and Roy (1960). The transition pressure (10 kbar, at room temperature) reported by White et al (1961) was an extrapolated value from their high-temperature and high-pressure results. It is likely that the transition from the J3-Pb02 to the a-Pb02 phase at room temperature may be affected by the kinetic effect. The a-Pb02 phase (i.e. reported by White et al., 1961) was not found in this experiment up to 22 kbar. In a separate run, the phase transition to a Pb02 was optically observed to take place at about 47 kbar.
Though structure varys at 5 kbar, the volume changes nearly continuously with the pressure in Pb02 (Figure 6), indicating a possible second order phase transformation. It is likely that the lattice was distorted during the compression which results in the splitting of the a-parameter. On the basis of the hard-sphere model, phase transition in ionic crystals is governed by Pauling's rule, i.e. the relative size of the cations and anions. Prewitt (1982) has argued that the contribution of cations to the structural change is much more significant than the anions in ionic bonding compounds. Ida (1976), on the other hand, proposed that anions are more compressible than cations and the phase transition may thus depend on the compressibility of the anions. However, detailed calculations based •:11>nH he hard-sphere model indicate that neither of the models can account for the ve, ry small amount of change in the c-parameter ( � 10-3 A) of Pb02. Hazen and Fingef (1981) proposed that violating· the p-olylredral · bulkmodo1us-volurrr1;f relat1onsh.ip-(Hazetr"ari'd · f' in ger, 1979) ant:l1tnverse rela�fonship in ili�\utile-type ui· oxides ma)Pbe due to thd ) fact that these compounds have higher covalent:!y!.Hence, the hard-sphere model may not be appli �P.:'?l�H�U fuj §1 f,�t::tf J ,Q t ��r:l�i;rtprA 1;)1-!Cl h . :W?1 ifu�rPi9llSRh�rjo,W �eJ�cµ;9n.(pq_ rxfi g µr;�1l!p».>5'. :Pf jQI),$�\ metaJ<:-met� .. hinter:aotions" fua.y: a1s0'!play ran1 :import<il}t rnleoin :th@ lattide1 di s:t 0vtid#1@Baur and Khan, 1971). The distortion of the tetragonal to orthorhombic phase obs. erved in this study may also involve an intimately twinned array of domains, similar to thatreported by Hara and Nicol (1979). Detailed description of the mechanism of the phase transition in Pb02 will be reported elsewhere (Li et cz/., in prep).

Limitation of the Single-Crystal Compression
Single-crystal compression studies in a diamond cell suffer from two serious limita tions. Firstly, in a routine experiment, the pressure is limited to less than 70 kbar (Hazen and Finger, 1982) despite the fact that pressure as high as multimegabar can be generated in the diamond · cell (Xu et al., 1986). This is due to. that the single�crystal has to be large enough to give significant diffraction signals and the difficulty in maintaining the hydrostaticity in the diamond cell above 100 kbar . This limitation can be partly overcome by using synchrotron radiation as the X-ray source. In addition, using inert-gas solids as pressure tran � mitting media could provide a hydrostatic environ ment in a diamond cell . Recently, synchrotron radiation has been applied to study the EOS and phase transition of single-crystal He up to 233 kbar (Mao et al., 1990). Although technical difficulties in loading the sample cryogenically (Mao and Bell, 1980) are often encountered, this technique has opened up a feasible way for produc ing an accurate EOS of minerals to a wider P and T regime. Another problem in single crystal compression is that in-situ structural refinement of the highly absorbing materials is always difficµlt. For instance, the structural refinement of Pb0 2 is very difficult because of the absorption of X-rays by Pb. This has sometimes hindered the interpretation of the phase transition. Therefore, improvement in the structural refinement of the single-crystal diffraction and its coulping with synchrotron radiation may be needed to provide us with reliable compression data, to detect phase transitions, and to resolve the mechanism of the transformation.

IMPLICATIONS
In past years, numerous efforts have been made to find systematics in the compres sion behavior of materials, as in the case of Birch's law which relates the bulk sound velocity with the density of minerals (Birch, 1961): and bulk modulus-volume relation for polyhedra (Hazen and Finger, 1979). Some of the empirical formulae such as the seismic equation of state (Anderson, 1967) have also been proposed for application to the elastic behaviors of minerals in the Earth's interior. A typical example is the plot of the bulk sound velocity (ct>) versus mean atomic weight ( M ) of minerals by Liebermann (1973) who discovered the following relationship: in some of the rutile-type dioxides (Si02, Ge02, Ti02 and Sn02) with n= 1/2, in accord- ance with the observation of Shankland (1972). Using the available data (Table 3), we have found a similar relationship exists for the rutile-type dioxides. However, a linear relationship fits better in the bulk sound velocity versus mean-atomic-weight plot as seen in Figure 7. In some of the calculations, we have used isothermal bulk modulus in place of the adiabatic bulk modulus Ks for the determination of bulk sound velocity (Table 3 ). At room temperature, the difference between the two is less than 1 % which is within the eFror of the determination of the bulk modulus itself. The significance of this relation is still unknown. Anderson (1972) has proposed that KV0 = constant holds for alkali halides and fluo rides. A K-v-1 law seems to hold for some rutile-type dioxides such as Ge02 and Sn02 (Liebermann, 1973). Our data do not support that KV0 =constant but favor a linear relationship between molar volume and bulk modulus in rutile-type dioxides. The correla tion is not as good as that between bulk sound velocity and mean atomic weight. The linear relation shown in Figure 7 is: <I> ( km/s) = 9.34 -0.0721 M (g) The theoretical basis for this relationship is not clear. This empirical formula is then used to infer the less well-known bulk p)Odulus of Mn02 to be 2. 75 Mbar since the bulk modulus cannot be obtained from the compression data of Clendenen and Drickamer (1966) due to the effect of pressure inhomogeneity (see 4.1 ). Further research on the compression study of Mn02 is required to justify the validity of the formula proposed above.

SUMMARY
Reliable data obtained from single-crystal compression can reveal subtle change in the cell parameter of the lattice. This report describes results on the compression behaviors of two rutile-type dioxides, Sn02 and Pb02. A slight lattice distortion which is manifested by the increase in the c/a ratio with pressure is observed in Sn02 up to 30 kbar. It Pb02. This phase may be treated as the distortion of the rutile structure of Pb02 during compression. A linear relationship is found to exist between the bulk sound velocity .and mean atomic weight among the rutile-type dioxides as: <I> (km/s) = 9.34 -0.0721 M (g).