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Increased Compressibility of Pseudobrookite-Type MgTi2O5 Caused by Cation Disorder

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Science  26 Sep 1997:
Vol. 277, Issue 5334, pp. 1965-1967
DOI: 10.1126/science.277.5334.1965

Abstract

Compressibilities were determined for four pseudobrookite-type magnesium titanate (MgTi2O5) samples with different degrees of Mg-Ti disorder. Compressibilities ofa and c axes in disordered MgTi2O5 were 10% and 7% greater, respectively, than those of a relatively ordered sample. The estimated bulk moduli for fully ordered and disordered MgTi2O5 are 167 ± 1 and 158 ± 1 gigapascals, respectively. This difference is an order of magnitude greater than that predicted by bulk modulus–volume systematics. Cation order, in addition to composition and structure information, is thus important when documenting the elasticity of crystalline phases. Elastic constants of mantle silicates that are subject to pressure-induced cation ordering must be reevaluated.

Pressure-volume equations of state (EOS) of crystalline solids impose important constraints on models of interatomic bonding, and they provide an essential foundation for interpreting seismic data from Earth's deep interior. Conventional wisdom suggests that EOS are principally dependent on only two variables: structure and composition. Summaries of mineral EOS parameters (1), for example, are tabulated according to these two variables. Details on the state of order-disorder—which may be important in characterizing the thermochemistry and transport properties of minerals as well as those of alloys, ceramics, and other crystalline phases—are usually omitted in discussions of EOS. Recent studies demonstrate that order-disorder phenomena may be affected by pressure in phases that display a nonzero volume of disordering ΔV dis = V disorderedV ordered (2). Silicate minerals commonly display ΔV dis up to 0.5% (3,4), and values exceeding 1% have been observed in oxides and sulfides (5). However, the extent to which differing states of order affect the physical properties of phases at high pressure is not known.

The comparative compressibility technique, in which several crystals are mounted in the same diamond-anvil cell experiment, can be used to discern subtle differences in EOS. This method has been used, for example, to document otherwise unresolvable differences in the bulk moduli of wüstites with different degrees of oxygen deficiency (6), nonstoichiometric omphacitic pyroxenes (7), Fe-Mg wadsleyites (8), silicate spinels (9), and majoritic garnets (10). Here, we examined EOS of pseudobrookite-type MgTi2O5(karrooite), a dense oxide that displays a wide range of ordered states (11).

Four synthetic MgTi2O5 crystals were annealed at 600°, 700°, 1000°, and 1400°C. Single-crystal x-ray diffraction techniques were used to characterize the orthorhombic (space group Bbmm) unit-cell parameters and to determine the crystal structure and ordered state of each sample (Table1). Ambient-pressure unit-cell parameters for the most ordered crystal of this study are a= 9.712 Å, b = 10.019 Å, c = 3.736 Å, volume = 363.52 Å3; those for the most disordered crystal are a = 9.760 Å, b = 9.979 Å,c = 3.748 Å, volume = 365.00 Å3. The ordered form of MgTi2O5 is denser than the disordered form—a commonly observed situation for close-packed oxide and silicate phases (2). These observed unit-cell parameters can be used to estimate ambient-pressure unit-cell volumes for fully ordered and fully disordered MgTi2O5(Table 1). Estimated volumes for ordered and disordered end members are 363.2 and 365.3 Å3, respectively—a 0.6% difference. Bulk modulus–volume systematics (12), which document an inverse relation between unit-cell volume and bulk modulus (K) of isostructural compounds, thus predict that disordered MgTi2O5 should be about 0.6% more compressible than the ordered variant.

Table 1

Observed ambient-pressure unit-cell parameters, refined octahedral cation occupancies, and isothermal bulk moduli (assuming K′ = 4) for four samples of MgTi2O5, and estimated values for fully ordered and disordered end members. Ideal values are extrapolated from observed unit-cell parameters and bulk moduli in this table. Numbers in parentheses are estimated errors in terms of last significant digits.

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Pseudobrookite has two nonequivalent, octahedrally coordinated cation sites, denoted M1 and M2; each formula unit has one M1 and two M2 sites. In fully disordered MgTi2O5 the average compositions of both M1 and M2 are (Mg0.33Ti0.67). Our most disordered crystal, which was rapidly quenched from 1400°C after annealing for 5 hours, has the formula (Mg0.515Ti0.485)(Ti0.758Mg0.242)2O5. In our most ordered crystal, annealed at 600°C for 35 days, the composition is (Mg0.93Ti0.07) (Ti0.965Mg0.035)2O5. The four crystals (Table 1) thus represent a wide range of Mg-Ti ordered states. These four ordered variants were mounted in one diamond-anvil cell (9). Unit-cell parameters for all four crystals were determined at 13 pressures, and x-ray intensity data were collected for the most ordered and disordered samples at seven pressures to 7.51 GPa (13).

The b-axis compressibility (Fig.1) is about 0.0024 GPa–1 for all four ordered variants, but the compressibilities of thea and c axes in disordered MgTi2O5 are 10% and 7% greater, respectively, than corresponding values for the ordered phase. Axial compression ratios thus vary from 1.58:2.02:1.00 for the most ordered crystal to 1.63:1.85:1.00 for the most disordered crystal. Resulting K values for these two MgTi2O5 crystals (assuming the pressure derivative of K, K′ = 4) are 166.8 ± 0.9 and 160.2 ± 0.7 GPa, respectively—a 4% difference (Fig.2). Intermediate Mg-Ti ordered states display intermediate K (Table 1 and Fig.3). We extrapolate K for fully ordered and fully disordered MgTi2O5 to be 167.3 ± 1.0 and 157.6 ± 1.0 GPa—a 6% difference, which is an order of magnitude greater than that predicted byK-V systematics. This unexpected 6% change is greater than the variations in K observed for the entire compositional range of Mg-Fe solid solution in many oxides and silicates (2).

Figure 1

Variations of unit-cell dimensions for four ordered variants of MgTi2O5. The baxis displays similar compressibility (that is, the four lines ofb versus pressure are essentially parallel). This behavior contrasts with that of the a and c axes; axes of the disordered end member are more compressible by 10% and 7%, respectively, relative to the more ordered variant. The almost fully ordered specimen P600 was annealed at 600°C for 35 days, the relatively disordered specimen P1400 was quenched rapidly from 1400°C, and specimens P700 and P1000 with intermediate states of order were annealed at 700° and 1000°C, respectively.

Figure 2

Relative volume (V/V 0) for MgTi2O5 crystals versus pressure. The partially disordered specimen P1400 is about 5% more compressible than the almost fully ordered specimen P600.

Figure 3

Observed isothermal bulk modulus K(assuming K′ = 4) for four MgTi2O5crystals versus disorder parameter X. Extrapolated bulk moduli for fully ordered (X = 0) and fully disordered (X = 0.67) MgTi2O5 are 167.3 ± 1.0 and 157.6 ± 1.0 GPa, respectively.

The observed dependence of K on Mg-Ti ordering is a consequence of the differential compressibilities of weaker Mg2+–O and stronger Ti4+–O bonds. The structure parallel to the b axis features an alternating sequence of one M1 and two M2 octahedra. Compressibility along this direction, therefore, is always the average of one Mg-O and two Ti-O bonds, regardless of the state of Mg-Ti order. Compression along thea and c axes, by contrast, is dictated primarily by M2 octahedra, which form a continuous edge-sharing octahedral linkage in the (010) plane. In ordered MgTi2O5, the M1 (Mg) octahedron is relatively compressible with an octahedralK of 172 ± 4 GPa, whereas the M2 (Ti) octahedron is relatively rigid with an octahedral K of 250 ± 7 GPa. In disordered MgTi2O5, M1 and M2 octahedra display the same compressibilities, with an average K of 225 GPa. Crystal compression of this disordered variant is less constrained along the a and c axes, and is thus more isotropic.

High pressure has been observed to induce ordering in many silicates (3, 14), including most of the major phases postulated for Earth's mantle (15). This pressure-induced ordering will affect EOS in two ways. First, the typically negative volume of ordering (2) will reduce room-pressure unit-cell volume,V 0, of mantle phases equilibrated at high pressure; indeed, this negative ΔV dis is the driving force for pressure-induced ordering. Second, ordering will itself affect elastic constants by subtle alteration of compression mechanisms, especially in cases of mixed-valence cation ordering, such as MgTi2O5. We conclude that phases with significant ΔV dis greater than 0.1%, including olivines, spinels, pyroxenes, carbonates, and feldspars (2), may also display EOS that are order-dependent.

EOS for geophysically relevant materials are usually made assuming rapid and reversible pressure-temperature-volume systematics. This assumption is invalid for phases that display order-disorder, because V 0, compressibility, and presumably thermal expansivity are functions of the state of order. Given this situation, seismic velocities alone may be insufficient to resolve compositional effects from those of ordering in some minerals. Determination of EOS of minerals relevant to mantle conditions must thus be performed in situ, on crystals that have ordered states equilibrated with respect to both temperature and pressure.

  • * To whom correspondence should be addressed. E-mail: hazen{at}gl.ciw.edu

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