Zero-pressure Thermal Expansion Research Articles

Thermal equation of state of post-aragonite CaCO3-Pmmn

AbstractCalcium carbonate (CaCO3) is one of the most abundant carbonates on Earth's surface and transports carbon to Earth's interior via subduction. Although some petrological observations support the preservation of CaCO3 in cold slabs to lower mantle depths, the geophysical properties and stability of CaCO3 at these depths are not known, due in part to complicated polymorphic phase transitions and lack of constraints on thermodynamic properties. Here we measured thermal equation of state of CaCO3-Pmmn, the stable polymorph of CaCO3 through much of the lower mantle, using synchrotron X-ray diffraction in a laser-heated diamond-anvil cell up to 75 GPa and 2200 K. The room-temperature compression data for CaCO3-Pmmn are fit with third-order Birch-Murnaghan equation of state, yielding KT0 = 146.7 (±1.9) GPa and K′0 = 3.4(±0.1) with V0 fixed to the value determined by ab initio calculation, 97.76 Å3. High-temperature compression data are consistent with zero-pressure thermal expansion αT = a0 + a1T with a0 = 4.3(±0.3)×10-5 K-1, a1 = 0.8(±0.2)×10-8 K-2, temperature derivative of the bulk modulus (∂KT/∂T)P = –0.021(±0.001) GPa/K; the Grüneisen parameter γ0 = 1.94(±0.02), and the volume independent constant q = 1.9(±0.3) at a fixed Debye temperature θ0 = 631 K predicted via ab initio calculation. Using these newly determined thermodynamic parameters, the density and bulk sound velocity of CaCO3-Pmmn and (Ca,Mg)-carbonate-bearing eclogite are quantitatively modeled from 30 to 80 GPa along a cold slab geotherm. With the assumption that carbonates are homogeneously mixed into the slab, the results indicate the presence of carbonates in the subducted slab is unlikely to be detected by seismic observations, and the buoyancy provided by carbonates has a negligible effect on slab dynamics.

P-V-T equation of state of CaCO3 aragonite to 29 GPa and 1673 K: In situ X-ray diffraction study

Pressure–volume–temperature relations have been measured to 29GPa and 1673K for CaCO3 aragonite using synchrotron X-ray diffraction with a multianvil apparatus at the ‘SPring-8’ facility. A least-squares fit of the room-temperature compression data to the Vinet-Rydberg equation of state (EOS) yielded KT0=65.7±0.8GPa and KT'=5.1±0.1, with fixed V0=227.11Å3. Further analysis of the high-temperature compression data led to the temperature derivative of the bulk modulus (∂KT/∂T)P=−0.016±0.001GPa/K and zero-pressure thermal expansion α=a0+a1T with a0=4.98 (22)×10−5K−1 and a1=2.81(38)×10−8K−2. The Mie-Gruneisen-Debye approach revealed the Gruneisen parameter γ0=1.39 at a fixed Debye temperature θ0=516K and the parameter q=1. Analysis of axial compressibility and thermal expansion indicates that the c-axis is two times more compressible than the b-axis and four times more compressible than the a-axis, whereas zero-pressure thermal expansion of the a-axis (a0a=2.6×10−5K−1 and a1a=2.3×10−8K−2) is weaker than that of the b-axis axis (a0b=6.3×10−5K−1 and a1b=0.1×10−8K−2) and c-axis axis (a0c=5.2×10−5K−1 and a1c=9.5×10−8K−2). A full set of thermodynamic parameters (including heat capacity, enthalpy and free energy) for aragonite and updated equations of state for magnesite and siderite was obtained using the Kunc-Einstein approach. The new EOS parameters were used for thermodynamic calculations for aragonite decarbonation reactions. The present thermal EOS provides accurate calculations of aragonite density to deep mantle. Decarbonation of subducting oceanic crust containing 2wt% aragonite would result in a 0.5% density reduction at 30GPa and 1273K. Aragonite becomes denser than magnesite at pressures about 16GPa along the 1500K isotherm and at 9GPa along the 298K isotherm.

Thermodynamic properties of calcium ferrite-type MgAl2O4: A first principles study

The diamond anvil cell experiments have revealed that the calcium ferrite (CF)-type aluminous phase is probably an important component of subducted mid-oceanic ridge basalt (MORB) in the lower mantle. In this study, we have performed first principles lattice dynamics calculations for the MgAl2O4 end-member of the aluminous phase based on density functional perturbation theory using two functionals within the local density approximation (LDA) and generalized gradient approximation (GGA) for bracketing the calculated properties at their lower and upper limits, respectively. A simple empirical pressure correction at zero temperature has been applied to both LDA and GGA. The results of room-temperature equation of state (EOS) and zero-pressure thermal expansion calculated by GGA with pressure correction have shown the best agreement with available experimental data. The high-pressure and temperature thermodynamic properties have been obtained using the GGA with correction method. The pressure-volume relations are fitted with a third-order high-temperature Birch-Murnaghan EOS. The isobaric heat capacity, the coefficient of thermal expansion and isothermal bulk modulus are fitted with polynomials and their coefficients are reported in the range of 0–40 GPa and 300–2000 K. The density profile of MORB estimated using the computational thermo-elastic constants supports the hypothesis that the subducted oceanic slabs could gain enough downwelling forces into the lower mantle.

P–V–T equation of state of siderite to 33 GPa and 1673 K

Pressure–volume–temperature relations have been measured to 33GPa and 1673K for natural siderite (Fe0.95Mn0.05CO3) using synchrotron X-ray diffraction with a multianvil apparatus at the ‘SPring-8’ facility. A least-squares fit of the room-temperature compression data to a third-order Birch–Murnaghan equation of state (EOS) yielded K0=120±1GPa and K′=3.57±0.09, with fixed V0=293.4±0.1Å3. Further analysis of the high-temperature compression data yielded the temperature derivative of the bulk modulus (∂KT/∂T)P=−0.015±0.001GPa/K and zero-pressure thermal expansion α=a0+a1T with a0=3.57(9)×10−5K−1 and a1=0.06(14)×10−8K−2. The analysis of axial compressibility indicates that the c-axis is more compressible (KTc=59±1GPa at K′=2.7±0.1) than the a-axis (KTa=166±2GPa at K′=14.0±0.8). The present thermal EOS enables accurate calculation the density and thermodynamic properties of siderite to the deep mantle conditions.

Pressure-temperature stability studies of FeOOH using X-ray diffraction

The Mie-Grüneisen formalism is used to fit a Birch-Murnaghan equation of state to high-temperature (T), high-pressure (P) X-ray diffraction unit-cell volume (V) measurements on synthetic goethite (α-FeOOH) to combined conditions of T = 23-250 °C and P = 0-29.4 GPa. We find the zero-pressure thermal expansion coefficient of goethite to be α0 = 2.3 (±0.6) × 10-5 K-1 over this temperature range. Our data yield zero-pressure compressional parameters: V0 = 138.75 (±0.02) Å3, bulk modulus K0 = 140.3 (±3.7) GPa, pressure derivative K0′ = 4.6 (±0.4), Grüneisen parameter γ0 = 0.91 (±0.07), and Debye temperature Θ0 = 740 (±5) K. We identify decomposition conditions for 2α-FeOOH → α-Fe2O3 + H2O at 1-8 GPa and 100-400 °C, and the polymorphic transition from α-FeOOH (Pbnm) to ε-FeOOH (P21mn). The non-quenchable, high-pressure ε-FeOOH phase P-V data are fitted to a second-order (Birch) equation of state yielding, K0 = 158 (±5) GPa and V0 = 66.3 (±0.5) Å3.

Thermal equation of state of magnesite to 32 GPa and 2073 K

Pressure–volume–temperature relations have been measured to 32 GPa and 2073 K for natural magnesite (Mg 0.975Fe 0.015Mn 0.006Ca 0.004CO 3) using synchrotron X-ray diffraction with a multianvil apparatus at the SPring-8 facility. A least-squares fit of the room-temperature compression data to a third-order Birch–Murnaghan equation of state (EOS) yielded K 0 = 97.1 ± 0.5 GPa and K′ = 5.44 ± 0.07, with fixed V 0 = 279.55 ± 0.02 Å 3. Further analysis of the high-temperature compression data yielded the temperature derivative of the bulk modulus (∂ K T /∂ T) P = −0.013 ± 0.001 GPa/K and zero-pressure thermal expansion α = a 0 + a 1 T with a 0 = 4.03 (7) × 10 −5 K −1 and a 1 = 0.49 (10) × 10 −8 K −2. The Anderson–Grüneisen parameter is estimated to be δ T = 3.3. The analysis of axial compressibility and thermal expansivity indicates that the c-axis is over three times more compressible ( K Tc = 47 ± 1 GPa) than the a-axis ( K Tc = 157 ± 1 GPa), whereas the thermal expansion of the c-axis ( a 0 = 6.8 (2) × 10 −5 K −1 and a 1 = 2.2 (4) × 10 −8 K −2) is greater than that of the a-axis ( a 0 = 2.7 (4) × 10 −5 K −1 and a 1 = −0.2 (2) × 10 −8 K −2). The present thermal EOS enables us to accurately calculate the density of magnesite to the deep mantle conditions. Decarbonation of a subducting oceanic crust containing 2 wt.% magnesite would result in a 0.6% density reduction at 30 GPa and 1273 K. Using the new EOS parameters we performed thermodynamic calculations for magnesite decarbonation reactions at pressures to 20 GPa. We also estimated stability of magnesite-bearing assemblages in the lower mantle.

Thermal equation of state of superhydrous phase B to 27 GPa and 1373 K

Pressure–volume–temperature relations have been measured to 27 GPa and 1373 K for superhydrous phase B (Mg 10Si 3O 14(OH) 4) using synchrotron X-ray diffraction with a multi-anvil apparatus at the SPring-8 facility. The analysis of room-temperature data fitted to a third-order Birch–Murnaghan equation of state (EOS) yields V 0 = 623.38 ± 0.39 Å 3; K 0 = 138.7 ± 3.0 GPa and K′ = 4.9 ± 0.3, when pressure was calibrated using the Au EOS of Anderson et al. [Anderson, O.L., Issak, D.G., Yamamoto, S., 1989. Anharmonicity and the equation of state for gold. J. Appl. Phys. 65, 1534–1543]. These values are consistent with subsequent thermal EOS analysis and previous estimations for superhydrous phase B. A fit of P– V– T data to high-temperature Birch–Murnaghan EOS yields V 0 = 623.47 ± 0.37 Å 3; K 0 = 135.8 ± 2.6 GPa; K′ = 5.3 ± 0.2; (∂ K T /∂ T) P = −0.026 ± 0.003 GPa/K and zero-pressure thermal expansion α = a 0 + a 1 T with a 0 = 3.2 (1) × 10 −5 K −1 and a 1 = 1.2 (4) × 10 −8 K −1. The Anderson–Grüneisen parameter is estimated to be δ T = 5.4. A fit to the thermal pressure EOS gives V 0 = 623.50 ± 0.36 Å 3; K 0 = 135.3 ± 2.3 GPa; K′ = 5.3 ± 0.2; (∂ K T /∂ T) V = −0.002 (2) GPa/K and α 0 = 3.8 (2) × 10 −5 K −1. The lattice dynamical approach using a Mie–Grüneisen–Debye EOS yields Grüneisen parameter γ 0 = 1.33 ± 0.05 and q = 2.03 ± 0.35, if the Debye temperature θ 0 is fixed at 860 K, as calculated from sound velocities. The analysis of axial compressibility and thermal expansivity indicates that the a-axis is more compressible ( K Ta = 126 ± 3 GPa) than the b-axis ( K Tb = 137 ± 1 GPa) and c-axis ( K Tc = 143 ± 1 GPa). The temperature dependence of K T is stronger for the b-axis, (∂ K T /∂ T) Pb = −0.033 (3) GPa/K, than for the a-axis (∂ K T /∂ T) Pa = −0.028 (7) GPa/K and c-axis (∂ K T /∂ T) Pc = −0.017 (3) GPa/K. The present EOS enables us to accurately estimate the density of superhydrous phase B in a pyrolitic composition under deep mantle conditions. The density reduction of hydrated subducting slab (∼1 wt.% H 2O) at the top of the lower mantle due to the presence of ∼18% of superhydrous phase B would be 1.9–2.1%. Accordingly, a model slab that is homogeneously hydrated may be buoyant relative to the surrounding mantle rocks and would not penetrate to the deep lower mantle.

Effect of incorporation of iron and aluminum on the thermoelastic properties of magnesium silicate perovskite

In situ X-ray diffraction measurements of Fe- and Al-bearing MgSiO3-rich perovskite (FeAl-Pv), which was synthesized from a natural orthopyroxene, were performed at pressures of 19–32 GPa and temperatures of 300–1,500 K using a combination of a Kawai-type apparatus with eight sintered-diamond anvils and synchrotron radiation. Two runs were performed using a high-pressure cell with two sample chambers, and both MgSiO3 perovskite (Mg-Pv) and FeAl-Pv were synthesized simultaneously in the same cell. Thus we were able to measure specific volumes (V/V0) of Mg-Pv and FeAl-Pv at the same P−T conditions. At all the measurement conditions, values of the specific volume of FeAl-Pv are consistent with those of Mg-Pv within 2 Standard Deviation, strongly suggesting that effect of incorporation of iron and aluminum on the thermoelastic properties of magnesium silicate perovskite is undetectable in this composition, pressure, and temperature range. Two additional runs were performed using a high-pressure cell that has one sample chamber and unit-cell volumes of FeAl-Pv were measured at pressures and temperatures up to 32 GPa and 1,500 K, respectively. All the unit-cell volume data of FeAl-Pv perovskite were fitted to the high temperature Birch–Murnaghan equation of state and a complete set of thermoelastic parameters of this perovskite was determined with an assumption of K′300,0 = 4. The determined parameters are K300,0 = 243(3) GPa, (∂KT,0/∂T)P = −0.030(8) GPa/K, a0 = 2.78(18) × 10−5 K−1, and b0 = 0.88(28) × 10−8 K−2, where a0 and b0 are the coefficients of the following expression describing the zero-pressure thermal expansion: αT,0 = a0 + b0T. The equation-of-state parameters of FeAl-Pv are in good agreement with those of MgSiO3 perovskite at the conditions corresponding to the uppermost part of the lower mantle.

Stability and P–V–T equation of state of KAlSi3O8-hollandite determined by in situ X-ray observations and implications for dynamics of subducted continental crust material

In situ X-ray diffraction measurements of KAlSi3O8-hollandite (K-hollandite) were performed at pressures of 15–27 GPa and temperatures of 300–1,800 K using a Kawai-type apparatus. Unit-cell volumes obtained at various pressure and temperature conditions in a series of measurements were fitted to the high-temperature Birch-Murnaghan equation of state and a complete set of thermoelastic parameters was obtained with an assumed K′300,0=4. The determined parameters are V300,0=237.6(2) A3, K300,0=183(3) GPa, (∂KT,0/∂T)P=−0.033(2) GPa K−1, a0=3.32(5)×10−5 K−1, and b0=1.09(1)×10−8 K−2, where a0 and b0 are coefficients describing the zero-pressure thermal expansion: αT,0 = a0 + b0T. We observed broadening and splitting of diffraction peaks of K-hollandite at pressures of 20–23 GPa and temperatures of 300–1,000 K. We attribute this to the phase transitions from hollandite to hollandite II that is an unquenchable high-pressure phase recently found. We determined the phase boundary to be P (GPa)=16.6 + 0.007 T (K). Using the equation of state parameters of K-hollandite determined in the present study, we calculated a density profile of a hypothetical continental crust (HCC), which consists only of K-hollandite, majorite garnet, and stishovite with 1:1:1 ratio in volume. Density of HCC is higher than the surrounding mantle by about 0.2 g cm−3 in the mantle transition zone while this relation is reversed below 660-km depth and HCC becomes less dense than the surrounding mantle by about 0.15 g cm−3 in the uppermost lower mantle. Thus the 660-km seismic discontinuity can be a barrier to prevent the transportation of subducted continental crust materials to the lower mantle and the subducted continental crust may reside at the bottom of the mantle transition zone.

Thermal equation of state of akimotoite MgSiO3 and effects of the akimotoite?garnet transformation on seismic structure near the 660 km discontinuity

Pressure (P)–volume (V)–temperature (T) relations of akimotoite (ilmenite structured MgSiO3) have been measured up to 19 GPa and 1373 K in a T-Cup multi-anvil apparatus. Polycrystalline specimens synthesized at 21 GPa and 1723 K were loaded in a specially designed cell assembly, together with Au or NaCl pressure standard, for synchrotron X-ray diffraction studies. Two runs were carried out with multiple temperature excursions at various pressures both inside and outside the akimotoite stability field. At conditions outside the stability field, temperature was kept below 873 K, as previous test runs indicated that akimotoite back-transformed to enstatite at about 900 K. In order to minimize effects of non-hydrostatic stress on volume and pressure determination, P–V–T data were collected on cooling cycles from the peak temperature. A total of 134 volume measurements were obtained. Adopting an ambient isothermal bulk modulus (210 GPa) obtained previously using the Brillouin scattering technique, analysis using the third-order Birch–Murnaghan equation of state yielded pressure derivative KT0′=5.6(8), with zero-pressure volume of 263.9(2) Å3 for MgSiO3 akimotoite. The high-temperature data were fit to several thermal equations of state to cross-examine consistency among the thermoelastic parameters obtained. Using the data with NaCl as the pressure standard combined with previous zero-pressure thermal expansion data of [Phys. Chem. Min. 16 (1988) 239], we obtained (∂KT/∂T)P=−0.040(1) GPa K−1, with a zero-pressure thermal expansion α0=2.41(19)×10−5 K−1. The results were applied to model seismic profiles of the transition zone, in order to examine the effects of akimotoite-forming transitions on lateral velocity variations. In depths where no phase transformations and chemical heterogeneities are present, hotter and colder areas relative to a reference geotherm are characterized by similar dlnVS/dlnVP and dlnρ/dlnVS ratios, which are material properties. The akimotoite–garnet phase transformation, however, skews the ratios because akimotoite has much higher acoustic velocities than garnet. Thus if the mantle geotherm is close to the transition temperature, anomalous apparent dlnVS/dlnVP and dlnρ/dlnVS ratios may be observed, which are no longer material properties. Aluminum content plays an important role in defining the akimotoite–garnet phase boundary relative to the geotherm and lateral Al variations may cause the transition boundary to fluctuate with depth. Therefore one must be cautious in interpreting seismic tomography observations in the transition zone.

Thermal equation of state of akimotoite MgSiO 3 and effects of the akimotoite–garnet transformation on seismic structure near the 660 km discontinuity

Pressure ( P)–volume ( V)–temperature ( T) relations of akimotoite (ilmenite structured MgSiO 3) have been measured up to 19 GPa and 1373 K in a T-Cup multi-anvil apparatus. Polycrystalline specimens synthesized at 21 GPa and 1723 K were loaded in a specially designed cell assembly, together with Au or NaCl pressure standard, for synchrotron X-ray diffraction studies. Two runs were carried out with multiple temperature excursions at various pressures both inside and outside the akimotoite stability field. At conditions outside the stability field, temperature was kept below 873 K, as previous test runs indicated that akimotoite back-transformed to enstatite at about 900 K. In order to minimize effects of non-hydrostatic stress on volume and pressure determination, P– V– T data were collected on cooling cycles from the peak temperature. A total of 134 volume measurements were obtained. Adopting an ambient isothermal bulk modulus (210 GPa) obtained previously using the Brillouin scattering technique, analysis using the third-order Birch–Murnaghan equation of state yielded pressure derivative K T0 ′=5.6(8), with zero-pressure volume of 263.9(2) Å 3 for MgSiO 3 akimotoite. The high-temperature data were fit to several thermal equations of state to cross-examine consistency among the thermoelastic parameters obtained. Using the data with NaCl as the pressure standard combined with previous zero-pressure thermal expansion data of [Phys. Chem. Min. 16 (1988) 239], we obtained ( ∂K T / ∂T) P =−0.040(1) GPa K −1, with a zero-pressure thermal expansion α 0=2.41(19)×10 −5 K −1. The results were applied to model seismic profiles of the transition zone, in order to examine the effects of akimotoite-forming transitions on lateral velocity variations. In depths where no phase transformations and chemical heterogeneities are present, hotter and colder areas relative to a reference geotherm are characterized by similar dln V S /dln V P and dln ρ/dln V S ratios, which are material properties. The akimotoite–garnet phase transformation, however, skews the ratios because akimotoite has much higher acoustic velocities than garnet. Thus if the mantle geotherm is close to the transition temperature, anomalous apparent dln V S /dln V P and dln ρ/dln V S ratios may be observed, which are no longer material properties. Aluminum content plays an important role in defining the akimotoite–garnet phase boundary relative to the geotherm and lateral Al variations may cause the transition boundary to fluctuate with depth. Therefore one must be cautious in interpreting seismic tomography observations in the transition zone.

Effect of pressure on the thermal expansion of MgO up to 8.2 GPa

Isobaric volume measurements for MgO were carried out at 2.6, 5.4, and 8.2 GPa in the temperature range 300–1073 K using a DIA-type, large-volume apparatus in conjunction with synchrotron X-ray powder diffraction. Linear fit of the thermal expansion data over the experimental pressure range yields the pressure derivative, (∂α/∂P) T , of −1.04(8) × 10−6 GPa−1 K−1 and the mean zero-pressure thermal expansion α0, T = 4.09(6) × 10−5 K−1. The α0, T value is in good agreement with results of Suzuki (1975) and Utsumi et al. (1998) over the same temperature range, whereas (∂α/∂P) T is determined for the first time on MgO by direct measurements. The cross-derivative (∂α2/∂P∂T) cannot be resolved because of large uncertainties associated with the temperature derivative of α at all pressures. The temperature derivative of the bulk modulus, (∂K T/∂T) P , of −0.025(3) GPa K−1, obtained from the measured (∂α/∂P) T value, is in accord with previous findings.

P-V-T equation of state of MgSiO 3 perovskite

A pressure-volume-temperature data set has been obtained for MgSiO 3 perovskite, using synchrotron X-ray diffraction with a laser-heated diamond-anvil cell. The unit cell parameters of the silicate perovskite were measured by angle dispersive X-ray diffraction using imaging plates up to pressures of 57 GPa and temperature in excess of 2500 K. These measurements are in good agreement with the previously reported data of Funamori et al. [Funamori, N., Yagi, T., Utsumi, W., Kondo, T., Uchida, T., Funamori, M., 1996. J. Geophys. Res. 101 (B4), 8257–8269] at lower pressure and yield ( ∂K ∂T ) P = −0.027 GPa K −1 for a fixed value K′ 0 of 4 and a zero-pressure thermal expansion parameter α = 1.55 × 10 −5 K −1 at 300 K. Assuming that the thermoelastic parameters of MgSiO 3 perovskite are applicable to perovskites with moderate iron content, the comparison of the density and K T profiles calculated for a mixture of perovskite and magnesiowüstite and for PREM model indicates that a pure perovskite lower mantle is very unlikely. On the other hand, we obtain a very good match with PREM density and K T profiles for a mixture of 83 vol % (Mg 0.93Fe 0.07)SiO 3 perovskite and 17 vol % (Mg 0.79Fe 0.21)O magnesiowüstite, compatible with a pyrolytic lower mantle.

Thermal equation of state of CaSiO3 perovskite

A comprehensive pressure‐volume‐temperature data set has been obtained for CaSiO3 perovskite up to 13 GPa and 1600 K, using synchrotron X ray diffraction with a cubic‐anvil, DIA‐6 type apparatus (SAM‐85). For each volume measurement, nonhydrostatic stress is determined from the relative shift in the diffraction lines of NaCl, within which the sample was embedded. Heating to above 973 K greatly reduced the strength of NaCl (to below 0.05 GPa), making the measurements hydrostatic. At room temperature the cubic perovskite structure remains metastable at pressures as low as 1 GPa, below which the sample transforms into an amorphous phase as indicated by a large background, a marked decrease in diffraction signals, and an anomalous volume decrease of the remaining crystalline phase. Because our experimental uncertainties are significantly smaller than those in previous measurements, the new data provide a tighter constraint on the zero pressure bulk modulus for CaSiO3 perovskite. A new set of room temperature equation of state parameters are identified so that both our data and the diamond cell data of Mao et al. [1989] are compatible [KT0 = 232(8) GPa, K′T0 = 4.8(3), and V0 = 45.58(4) Å3]. Volume measurements along several isotherms under both stable and metastable pressure conditions allow isochoric and isobaric interpolations within the range of experimental pressure and temperature conditions. Analyses using various approaches yielded consistent results for (∂KT/∂T)P of −0.033(8) GPa K−1, and (∂α/∂P)T of −6.3 × 10−7 GPa−1 K−1, with a zero‐pressure thermal expansion α0 of 3.0 × 10−5 K−1. The thermal pressure is found to be virtually independent of volume, and thus the Anderson‐Grüneisen parameter δT = K′T0 = 4.8. These results are used to predict the bulk modulus and density of CaSiO3 perovskite under lower mantle conditions. Along an adiabat with the foot temperature of 2000 K, the density of the perovskite agrees with that of the preliminary reference Earth model (PREM) within 1% throughout the lower mantle. The bulk modulus shows a smaller pressure dependence along the adiabat; it matches that of PREM at the top of the lower mantle but is about 10% too low near the core‐mantle boundary.

Thermal expansion of silicate perovskite and stratification of the Earth's mantle

A pressure of 24 GPa and temperatures of about 2,000–3,000 K correspond to the observed 670-km seismic discontinuity which separates the upper and lower mantle. In such conditions the major minerals of the Earth's upper mantle, olivine ((Mg, Fe)2SiO4), pyroxene ((Mg, Fe)SiO3) and garnet ((Mg, Fe, Ca)3Al2Si3O12) transform to a distorted (orthorhombic) perovskite-structured mineral ((Mg, Fe)SiO3), or to a perovskite-dominated assemblage (refs 1–4). Because silicate perovskite is stable to at least 70 GPa, it is thought to be the most abundant mineral in the lower mantle and, possibly, in the entire Earth. Despite its importance, silicate perovskite was only discovered in 1976, and little is known about its physical properties because of the difficulty in achieving the conditions of pressure and temperature required for the synthesis of this phase. For example, the value of the thermal expansion coefficient of perovskite provides an important constraint on possible compositional models for the lower mantle5–7. We have recently produced sufficient amounts of (Mg0.9, Fe0.1)SiO3 perovskite to measure its zero-pressure thermal expansion to 840 K by X-ray diffraction. At high temperatures, the average thermal expansion coefficient is 4×l0−5K−1. Such a large value for the thermal expansion coefficient implies that standard models of upper mantle composition, such as pyrolite or garnet peridotite (Mg value ≍ 0.89), yield zero-pressure densities that are about 2% lower than that of the density of the lower mantle extrapolated to zero pressure conditions. This result suggests that the upper and lower mantle are chemically distinct, in accord with layered models of the thermal and convective state of the mantle.

Evidence for two magnetic phase transitions in CeAl 2: Resolution of high pressure results

Zero-pressure thermal-expansion and specific-heat experiments on CeAl 2 show that two phase transitions having pressure dependences of the transition temperature, t p=T −1 N( dT N dp ) p=0> , of opposite sign occur near T N⋍3.8 K . Comparison with earlier high-pressure neutron-diffraction results reveals an antiferromagnetic nature of both transitions: The one with t p <0 signals an incommensurate sine wave, which is quenched by lattice defects and leaves behind a simple type-II structure, indicated by the transition with t p >0.

An improved self-consistent phonon approximation including four-phonon processes

An improved self-consistent phonon theory (ISC) including three- and four-phonon processes has been used to calculate the zero-pressure lattice parameters and the zero-pressure thermal expansion for Kr. The results indicate that, however limited ISC theory with three-phonon processes may be, trying to supplement this theory with higher-order phonon terms will make the convergence of the theory less satisfactory. In the light of our results we discuss earlier related work as well as a paper by Van Doren and Henkel.

Qualitative Temperature and Volume Dependence of the Thermal Expansion Coefficient of Solids

A thermodynamic expression is derived whereby the measured zero-pressure thermal expansion coefficient may be corrected to a fixed-volume condition for all temperatures. Experimental data so corrected show that the expansion coefficient at fixed volume is nearly constant for temperatures above the Debye temperature. This behavior is in qualitative agreement with the results of lattice-dynamics calculations.