## Abstract

Ultrasonic interferometric measurements of the shear elastic properties of MgSiO_{3} perovskite were conducted on three polycrystalline specimens at conditions up to pressures of 8 gigapascals and temperatures of 800 kelvin. The acoustic measurements produced the pressure (*P*) and temperature (*T*) derivatives of the shear modulus (*G*), namely (∂*G/∂P*)_{T} = 1.8 ± 0.4 and (∂*G/∂T*)_{P} = −2.9 ± 0.3 × 10^{−2} gigapascals per kelvin. Combining these derivatives with the derivatives that were measured for the bulk modulus and thermal expansion of MgSiO_{3} perovskite provided data that suggest lower mantle compositions between pyrolite and C1 carbonaceous chondrite and a lower mantle potential temperature of 1500 ± 200 kelvin.

Experimental and theoretical efforts have focused on determining the elastic behavior of (Mg,Fe)SiO_{3} perovskite, the most abundant mineral in Earth's lower mantle, because its physical properties constrain the chemical composition and rheology of the lower mantle (1–4). Experimental and theoretical studies of the ambient elastic moduli indicate that MgSiO_{3} perovskite has an anomalously high shear modulus *G*, which requires a large temperature derivative of *G* to satisfy seismic velocities in the lower mantle with reasonable petrological models (5,6).

In the absence of sufficiently large specimens for acoustic techniques, static compression studies have been employed to determine the isothermal bulk modulus *K*
_{T}, the pressure and temperature derivatives of *K*
_{T}, and thermal expansion α for silicate perovskite. Discrepancies in α and (∂*K*
_{T}/∂*T*)_{P}resulted in different lower mantle bulk compositions. The lower values of α and ∣(∂*K*
_{T}/∂*T*)_{P}∣ (7) favor a chemically uniform mantle with a composition similar to pyrolite (8) [Si/(Mg + Fe) = 0.69], whereas analyses based on the higher values of α and ∣(∂*K*
_{T}/∂*T*)_{P}∣ (9) favor a hotter, heterogeneous lower mantle that is enriched in silica [Si/(Mg + Fe) ∼ 1]. To determine which model might be more realistic, we measured the pressure and temperature dependence of *G* of MgSiO_{3} perovskite, which allows us to constrain the possible temperature and chemical composition of the lower mantle more precisely.

Polycrystalline samples of MgSiO_{3} perovskite were synthesized in a uniaxial split-sphere apparatus at pressures above 24 GPa and at temperatures around 1700 K, for run durations between 0.5 and 3 hours. By modifying the existing 10-mm octahedral cell assembly (10) to maximize the sample volume and to produce minimal temperature gradients, we were able to recover cylindrical specimens that were ∼1.5 mm in diameter and thickness, suitable for ultrasonic experiments with bulk densities within 2% of the single-crystal x-ray values (Table 1).

Monochromatic x-ray diffraction spectra from the polished tops and bottoms of the cylinders contained only perovskite peaks (11). Each sample was thoroughly examined from the ends and sides of the cylinders with microfocus Raman spectroscopy (12), and the best three samples of structurally pure, polycrystalline perovskites were chosen for subsequent high-pressure acoustic experiments. After polishing the cylinders under liquid nitrogen cooling, we performed acoustic tests at high pressures to confirm that the propagation of 20- to 70-MHz signals was possible through the samples.

With a recently developed technique (13), ultrasonic interferometric measurements of the shear elastic properties of the three samples were performed over a range of pressure and temperature (Fig. 1). The experimental paths consisted of initial compression at room temperature followed by a series of heating and cooling cycles as pressure was slowly decreased. The in situ acoustic and x-ray diffraction measurements were performed simultaneously at high pressure and at high temperature.

At each pressure and temperature for which travel times (14) were measured, energy-dispersive x-ray diffraction patterns from the sample and from the NaCl-confining media were collected. The sample patterns provided structural information complementary to the information obtained from the microfocus Raman studies, and the NaCl patterns provided the pressure standard. The temperature was measured with two thermocouples (W/Re26%-W/Re5%) inserted opposite to each other into a salt layer adjacent to the sample.

Because the travel time measurements were made outside the thermodynamic stability field of the MgSiO_{3} perovskite samples, the maximum temperature was limited to 800 K at the highest attained pressure to avoid retrogressive transformation. After recovery, all samples were examined with a combination of x-ray diffraction, Raman spectroscopy, density, and length measurements. In the first sample (2997) recovered from 800 K, a small amount (<10%) of orthoenstatite was detected by microfocus Raman spectroscopy. In the subsequent two experiments with samples 3020 and 3081, the maximum temperature was kept below 600 K, and no irreversible changes were detected for these samples.

Assuming hydrostatic compression, the travel times were converted to shear velocities and moduli with the equation-of-state coefficients from Wang *et al*. (15), who performed a static compression study of MgSiO_{3} perovskite in the SAM-85 apparatus over a comparable pressure and temperature range (16). The calculated specimen lengths at high pressure and high temperature were compatible with the specimen lengths that were determined from the in situ x-ray diffraction observed in our study. The *G* values that we calculated (Fig. 2) as a function of pressure at temperatures from 300 to 800 K were fit as linear functions of pressure and temperature, which resulted in the values of *G* and the derivatives of *G* (Table 1). By averaging the parameters for the three experiments, we obtained the pressure and temperature derivatives of *G*: (∂*G*/∂*P*)_{T} = 1.8(4) and (∂*G*/∂*T*)_{P} = −0.9(3) × 10^{−2} GPa/K. (Numbers in parentheses are uncertainties in measured parameters.)

The three ultrasonic experiments on MgSiO_{3} perovskite produced results for *G* and the derivatives of *G*that were consistent with previous measurements or predictions (Table 1). The experimental *G* values are consistent with those obtained by averaging the single-crystal elastic moduli that were measured by Brillouin scattering. The (∂*G/∂P*)_{T} and (∂*G/∂T*)_{P} values agree with elasticity systematics estimates (1). Our (∂*G/∂P*)_{T} value is similar to the recent measurement for ScAIO_{3} perovskite, which is sometimes regarded as the most similar analog for MgSiO_{3} perovskite because of the similarities in the ionic radii of the cations (17); however, our value of (∂*G*/∂*P*)_{T} is higher than the high-temperature (∂*G/∂P*)_{T} that is inferred for the lower mantle by Stacey (18).

The measured *G* of MgSiO_{3} perovskite at ambient conditions is higher than the *G* that was modeled for a hot, adiabatically decompressed lower mantle (4, 5). To reconcile the high measured value of *G* with the value of *G*for a lower mantle of pyrolite (8) at a potential temperature of 1600 K at the foot of the mantle adiabat, Jackson (4) found the average ∣(∂*G*/∂*T*)_{P}∣ value of 2 × 10^{−2} to 2.5 × 10^{−2} GPa/K. From the radial and lateral variations of the seismic wave velocities in the lower mantle, Wang and Weidner (5) deduced the temperature-averaged value of ∣(∂*G*/∂*T*)_{P}∣ to be 2 × 10^{−2} to 3.5 × 10^{−2} GPa/K, which is consistent with a pyrolite compositional model; compositions that are more silicic require a larger ∣(∂*G*/∂*T*)_{P}∣ value of ∼5.5 × 10^{−2} GPa/K. In contrast, Zhao and Anderson (19) found that a ∣(∂*G*/∂*T*)_{P}∣ value of 3.5 × 10^{−2} GPa/K was compatible with a wide range of perovskite-rich compositions. An indirect constraint on the value of ∣(∂*G*/∂*T*)_{P}∣ comes from seismic tomography studies, which have shown a significant correlation (20) between heterogeneity in compressional wave (*V*
_{p}) and shear wave (*V*
_{s}) speeds. Karato (21) argued that anelastic effects are required to explain the large values of [(∂ ln *V*
_{s})/(∂ ln*V*
_{P})]_{P} observed in the lower mantle. However, Wang and Weidner (5) showed that lateral variations in *V*
_{p} and*V*
_{s} can be explained as being solely due to temperature fluctuations that give the temperature-averaged ∣(∂*G*/∂*T*)_{P}∣ value of about 3 × 10^{−2} to 4.3 × 10^{−2}GPa/K for a pyrolite mantle. Our measured value of ∣(∂*G*/∂*T*)_{P}∣ is 2.9 × 10^{−2} GPa/K at high frequency (10^{7}Hz) and supports the conclusion that anharmonic processes are sufficient to account for the [(∂ ln*V*
_{s})/(∂ ln*V*
_{p})]_{P} value that was observed at seismic frequencies (on the order of 1 Hz), without invoking anelastic processes.

We have calculated the bulk modulus *K*
_{s} and*G* at high temperatures and ambient pressure for a suite of compositional models and compared them with the values inferred for the hot, adiabatically decompressed lower mantle (4, 5) [*K*
_{0}(*T*) = 213(10) and*G*
_{0}(*T*) = 130(5) GPa] as a function of the Si/(Mg + Fe) ratio and the potential temperature. Our model lower mantle consisted of a mixture of silicate perovskite and magnesiowüstite [(Mg,Fe)O]; the total iron content was fixed at Fe/(Mg + Fe) = 0.12 (3, 5), and appropriate corrections were applied to the densities of perovskite and magnesiowüstite and elastic properties of magnesiowüstite (6, 15).

The possible mantle models demonstrate the tradeoff between the Si/(Mg + Fe) ratio and the potential temperature (Fig. 3). Higher temperatures are associated with higher Si/(Mg + Fe) ratios. For the lower values of α and (∂*K/∂T*)_{P}, which were determined in multianvil and diamond-anvil cell experiments on MgSiO_{3}perovskite (7), the solutions for the bulk and shear moduli (bands *K*
_{1} and *G* in Fig. 3) of the lower mantle intersect at a potential temperature *T* ≈ 1500 K and Si/(Mg + Fe) ≈ 0.78, a value between the values for pyrolite (8) and Cl carbonaceous chondritic meteorites (22). Within the model uncertainties, pyrolitic and chondritic models are permissible, but pure enstatite (perovskite with no magnesiowüstite) models are not. For the higher values of α and (∂*K/∂T*)_{P} that were determined in diamond-anvil experiments on (Mg,Fe)SiO_{3} perovskite (9), there were no allowable (no intersection of the*K*
_{2} and *G* bands) solutions in the compositional range between pure olivine and pure enstatite models and the potential temperature range between 600 and 2100 K. The uncertainty of 10% in the measured value of (∂*G/∂T*)_{P}results in variations of ±0.02 in the Si/(Mg + Fe) ratio and variations of ±100 K in temperature. Adding Fe of 10 mole percent (mol%) to the perovskite phase in the model calculations (23) decreases *G* (by 8%), thus leading to lower potential temperatures and to compositions that are more olivine-rich.