High-temperature behaviour of the elastic moduli of LiF and NaF: Comparison with MgO and CaO

The elastic moduli of single-crystal LiF and NaF have been determined by the ultrasonic pulse superposition technique as a function of temperature from T = 298–650° K. These new data are consistent with low-temperature (T < 298° K) data obtained by other ultrasonic pulse techniques and are superior to previous high-temperature data from resonance experiments. The elastic moduli (c) are represented by quadratic functions in T over the experimental temperature range although the curvature is not in the same sense for all modes. For LiF, NaF, MgO and CaO, evaluation of the temperature derivatives of the elastic moduli at constant volume (V) indicates that the elastic moduli are only weakly dependent on T at constant volume. The fluoride—oxide analogue pair LiFMgO both exhibit high-temperature elastic behaviour at approximately the same absolute temperature. Mitskevich's theory and observed K_S-V systematics imply that (?c/?T)_P should be a function of the nearest neighbour distance for rocksalt fluorides and oxides; this result lends further support to a fluorideoxide modelling scheme based on similar ionic radii.     

Elasticity of (Mg0.83,Fe0.17)O ferropericlase at high pressure: ultrasonic measurements in conjunction with X-radiation techniques

The elasticity of ferropericlase with a potential mantle composition of (Mg_0.83,Fe_0.17)O is determined using ultrasonic interferometry in conjunction with in situ X-radiation techniques (X-ray diffraction and X-radiography) in a DIA-type cubic anvil high-pressure apparatus to pressures of 9 GPa (NaCl pressure scale) at room temperature. In this study, we demonstrate that it is possible to directly monitor the specimen length using an X-ray image technique and show that these lengths are consistent with those derived from X-ray diffraction data when no plastic deformation of the specimen occurs during the experiment. By combining the ultrasonic and X-ray diffraction data, the adiabatic elastic bulk (K_S) and shear (G) moduli and specimen volume can be measured simultaneously. This enables pressure scale-free measurements of the equation of state of the specimen using a parameterization such as the Birch-Murnaghan equation of state. The elastic moduli determined for (Mg_0.83,Fe_0.17)O are K_S0=165.5(12) GPa, G₀=112.4(4) GPa, and their pressure derivatives are K_S0′=4.17(20) and G₀′=1.89(6). If these results are compared with those for MgO, they demonstrate that K_S0 and K_S0′ are insensitive to the addition of 17 mol% FeO, but G₀ and G₀′ are reduced by 14% and 24%, respectively. We calculate that the P and S wave velocities of a perovskite plus ferropericlase phase assemblage with a pyrolite composition at the top of the lower mantle (660 km depth) are lowered by 0.8 and 2.3%, respectively, when compared with those calculated using the elastic properties of end-member MgO. Consequently, the magnitudes of the calculated wave velocity jumps across the 660 km discontinuity are reduced by about 11% for P wave and 20% for S wave, if this discontinuity is considered as a phase transformation boundary only (ringwoodite→perovskite+ferropericlase).     

In situ measurements of sound velocities and densities across the orthopyroxene → high-pressure clinopyroxene transition in MgSiO3 at high pressure

Using acoustic measurement interfaced with a large volume multi-anvil apparatus in conjunction with in situ X-radiation techniques, we are able to measure the density and elastic wave velocities (V_P and V_S) for both ortho- and high-pressure clino-MgSiO₃ polymorphs in the same experimental run. The elastic bulk and shear moduli of the unquenchable high-pressure clinoenstatite phase were measured within its stability field for the first time. The measured density contrast associated with the phase transition OEN → HP-CEN is 2.6-2.9% in the pressure of 7-9 GPa, and the corresponding velocity jumps are 3-4% for P waves and 5-6% for S waves. The elastic moduli of the HP-CEN phase are K_S=156.7(8) GPa, G = 98.5(4) GPa and their pressure derivatives are K_S′=5.5(3) and G′ = 1.5(1) at a pressure of 6.5 GPa, room temperature. In addition, we observed anomalous elastic behavior in orthoenstatite at pressure above 9 GPa at room temperature. Both elastic wave velocities exhibited softening between 9 and 13-14 GPa, which we suggest is associated with a transition to a metastable phase intermediate between OEN and HP-CEN.     

Temperature dependence of the elastic moduli of ringwoodite

The elastic moduli of polycrystalline ringwoodite, (Mg_0.91Fe_0.09)₂SiO₄, were measured up to 470 K by means of the resonant sphere technique. The adiabatic bulk (K_S) and shear (μ) moduli were found to be 185.1(2) and 118.22(6) GPa at room temperature, and the average slopes of dK_S/dT and dμ/dT in the temperature range of the study were determined to be −0.0193(9) and −0.0148(3) GPa/K, respectively. Using these results, we estimate seismic wave velocity jumps for a pure olivine mantle model at 520 km depth. We find that the jump for the S-wave velocity is about 1.5 times larger than that for the P-wave velocity at this depth. This suggests that velocity jumps at the 520 km discontinuity are easier to detect using S-waves than P-waves.     

Capillary pressure for the sand–CO2–water system under various pressure conditions. Application to CO2 sequestration

Accurate modeling of storage of carbon dioxide (CO₂) in heterogeneous aquifers requires experiments of the capillary pressure as function of temperature and pressure. We present a method with which static drainage and imbibition capillary pressures can be measured continuously as a function of saturation at various temperature (T) and pressure (P) conditions. The measurements are carried out at (T, P) conditions of practical interest. Static conditions can be assumed as small injection rates are applied. The capillary pressure curves are obtained for the unconsolidated sand–distilled water–CO₂ system. The experimental results show a decrease of drainage and imbibition capillary pressure for increasing CO₂ pressures and pronounced dissolution rate effects for gaseous CO₂. Significant capillary pressure fluctuations and negative values during imbibition are observed at near critical conditions. The measurement procedure is validated by a numerical model that simulates the experiments.     

Phase relations in the system LiFMgF2 at elevated pressures: Implications for the proposed mixed-oxide zone of the earth's mantle

Solvi and liquidi for various LiFMgF₂ mixtures have been determined at pressures up to 40 kbar by differential-thermal-analysis in a piston-cylinder high-pressure device. The melting curves of pure LiF and MgF₂ were also studied and the initial slopes (dT_m/dP)_{P = 0} were found to be 11.2 and 8.3°C/kbar, respectively. The eutectic composition (LiF)_0.64(MgF₂)_0.36 is independent of pressure to 35 kbar and the eutectic temperature rises approximately 6.3°C per kbar. Initial slopes of 11°C/kbar and 35°C/kbar are inferred for the melting curves of MgO and SiO₂ (stishovite) respectively, on the basis of data for their structural analogue compounds. The observed solid solution of LiF in MgF₂ and other evidence suggest the possibility of solid solution in the system (Mg,Fe)OSiO₂ (stishovite) under mantle conditions which may have important consequences for the elastic properties of a “mixed-oxide” zone of the earth's mantle.     

Melting of the silica isotypes SiO 2, BeF 2 and GeO 2 at elevated pressures

The melting curves of the structural analogues SiO ₂, BeF ₂ and GeO ₂ have been studied at pressures ?40 kbar in a piston-cylinder apparatus. The initial slopes dT_m/dP of the β-quartz-liquid boundaries for SiO ₂ and BeF ₂ are ～35° while the slope of the rutile-liquid boundary for GeO ₂ is approximately 32°C/kbar. These large values of dT/dP reflect the unusually low entropies of fusion for these compounds in which strong structural similarities exist between the crystalline phases and the melt. Implications for the extended phase diagram of silica are discussed and it is concluded that either: (1) a maximum exists on the coesite melting curve, or (2) estimates of the melting temperature of stishovite need to be revised upwards.     

Melting of some alkaline-earth and transition-metal fluorides and alkali fluoroberyllates at elevated pressures: A search for melting systematics

The melting curves of the fluorides ZnF₂ and NiF₂ (rutile structure), CaF₂, SrF₂ and BaF₂ (fluorite structure), and of the fluoroberyllates Na₂BeF₄ and Li₂BeF₄ have been studied at pressures ? 40 kbar by differential thermal analysis in a piston-cylinder high-pressure device. The initial slopes (dT_m/dP)₀ of these melting curves are respectively 7.2, 5.8, 16.7, 15.2, 15.7, 15.1 and <0°C/kbar. A new Li₂BeF₄ polymorph, apparently of the olivine structure type, is stable at pressures > 10 kbar and its melting curve has an average slope of ～6.7°C/kbar. These new data and those for SiO₂, BeF₂, GeO₂, LiF and MgF₂, recently studied by Jackson, are combined with existing data for elements, ionic compounds and silicates to assess the influence of crystal structure, molar volume and the nature of interatomic bonding on the initial slopes of melting curves. It is found that the entropy of fusion (ΔS_m) is primarily a function of crystal structure while the volume change on fusion (ΔV_m) is controlled by crystal molar volume within each isostructural series. Such systematics have recently facilitated estimation of the initial slopes of the melting curves of periclase and stishovite. New and existing melting data for silicates and their analogues have been analysed and a systematic dependence of (dT_m/dP)₀ on SiO₂ concentration has been demonstrated. Possible implications of this trend for partial melting of upper-mantle garnet lherzolite are illustrated. Finally, the use of the traditional silicate-germanate and oxide-fluoride modelling schemes is reviewed in the light of information from this present study.     

High-pressure X-ray diffraction studies on β- and γ-Mg2SiO4

Pressure effects on the lattice parameters of β- and γ-Mg₂SiO₄ have been measured at room temperature and at pressures up to 100 kbar using a multi-anvil high-pressure X-ray diffraction apparatus. The volume changes (ΔV/V₀) at 90 kbar are 5.4 · 10^?2 and 4.2 · 10^?2 for β- and γ-Mg₂SiO₄, respectively. Isothermal bulk moduli at zero pressure have been calculated from least-square fits of the data to straight lines. They turn out to be 1.66 ± 0.4 and 2.13 ± 0.1 Mbar for β- and γ-Mg₂SiO₄, respectively. The α → γ transition obeys Wang's linear V_φ?ρ relation but the α → β transition does not.     

Elastic properties of polycrystalline diopside (CaMgSi2O6)

A polycrystalline specimen of clinopyroxene diopside has been hot-pressed at P = 15 kbar and T = 850°C in a piston-cylinder apparatus. Compressional (ν_P) and shear (ν_S) velocities are determined as a function of pressure to 7.5 kbar at room temperature by an ultrasonic pulse transmission technique. The velocities at 7.5 kbar are ν_P = 8.06 km/sec and ν_S = 4.77 km/sec. These data are consistent with velocity-density trends for orthopyroxenes due to the compensating effects of the monoclinic structure (positive) and Ca content (negative). With the addition of the new data for diopside, it is possible to calculate directly the velocities of various upper-mantle mineral assemblages.     

Spinel disproportionation at high pressure: calorimetric determination of enthalpy of formation of Mg2SnO4 and Co2SnO4 and some implications for silicates

The enthalpies of formation from the oxides of Mg₂SnO₄ and Co₂SnO₄ were found by oxide melt solution calorimetry to be +1.13 ± 0.48 kcal/mol and ?2.31 ± 0.28 kcal/mol, respectively. Using these data, the slopes, ?P/?T, for disproportionation of these spinels to the component oxides at high pressure were calculated to be +30.4 ± 4.2 bar/K for Mg₂SnO₄ and ?10.3 ± 2.4 bar/K for Co₂SnO₄, in general agreement with the data of Jackson et al. (1974a,b). Using thermochemical data for the formation of olivines, for olivine-spinel transitions and for the transformation of quartz to stishovite, we calculate pressures for the disproportionation of silicate spinels to be in the range 150–200 kbar. Calculated slopes ?P/?T for the disproportionation reactions are ?10.7, ?24.9, ?11.2, and +7.6 bar/K for Mg₂SiO₄, Fe₂SiO₄, Co₂SiO₄, and Ni₂SiO₄. The large negative slope calculated for Fe₂SiO₄ results from a surprisingly large positive slope reported for the olivine-spinel transition in that compound (Akimoto et al., 1969). Further consideration of the systematic trends in the thermodynamics of spinel formation from the oxides suggests that the silicate spinels should have entropies of formation close to zero, resulting in values of ?P/?T which are zero or at most only slightly negative. This confirms the conclusion of Jackson, Liebermann, and Ringwood that values of ?P/?T for spinel disproportionation are unlikely to be more negative than ?10 bar/K and may well be slightly positive. Reaction of spinels to form other post-spinel phases, particularly ilmenite and perovskite, are discussed in terms of available thermochemical data.     

Thermal equation of state of magnesiowüstite (Mg0.6Fe0.4)O

Volume measurements for magnesiowüstite (Mg_0.6Fe_0.4)O, were carried out up to pressures of 10.1 GPa in the temperature range 300–1273 K, using energy-dispersive synchrotron X-ray diffraction. These data allow reliable determination of the temperature dependence of the bulk modulus and good constraint on the thermal expansitivity at ambient pressure which was previously not known for magnesiowüstite. From these data, thermal and elastic parameters were derived from various approaches based on the Birch–Murnaghan equation of state (EOS) and on the relevant thermodynamic relations. The results from three different equations of state are remarkably consistent. With (∂K_T/∂P)_T fixed at 4, we obtained K₀=158(2) GPa, (∂K_T/∂T)_P=−0.029(3) GPa K⁻¹, (∂K_T/∂T)_V=−3.9(±2.3)×10⁻³ GPa K⁻¹, and α_T=3.45(18)×10⁻⁵+1.14(28)×10⁻⁸T. The K₀, (∂K_T/∂T)_P, and (∂K_T/∂T)_V values are in agreement with those of Fei et al. (1992) and are similar to previously determined values for MgO. The zero pressure thermal expansitivity of (Mg_0.6Fe_0.4)O is found to be similar to that for MgO (Suzuki, 1975). These results indicate that, for the compositional range x=0–0.4 in (Mg_1−xFe_x)O, the thermal and elastic properties of magnesiowüstite exhibit a dependence on the iron content that is negligibly small, within uncertainties of the experiments. They are consequently insensitive to the Fe–Mg partitioning between (Mg, Fe)SiO₃ perovskite and magnesiowüstite when applied to compositional models of the lower mantle. With the assumption that (Mg_0.6Fe_0.4)O is a Debye-like solid, a modified equation of heat capacity at constant pressure is proposed and thermodynamic properties of geophysically importance are calculated and tabulated at high temperatures.     

Pyroxene-garnet solid-solution equilibria in the systems Mg4Si4O12Mg3Al2Si3O12 and Fe4Si4O12Fe3Al2Si3O12 at high pressures and temperatures

Pyroxene-garnet solid-solution equilibria have been studied in the pressure range 41–200 kbar and over the temperature range 850–1,450°C for the system Mg₄Si₄O₁₂Mg₃Al₂Si₃O₁₂, and in the pressure range 30–105 kbar and over the temperature range 1,000–1,300°C for the system Fe₄Si₄O₁₂Fe₃Al₂Si₃O₁₂. At 1,000°C, the solid solubility of enstatite (MgSiO₃) in pyrope (Mg₃Al₂Si₃O₁₂) increases gradually to 140 kbar and then increases suddenly in the pressure range 140–175 kbar, resulting in the formation of a homogeneous garnet with composition Mg₃(Al_0.8Mg_0.6Si_0.6)Si₃O₁₂. In the MgSiO₃-rich field, the three-phase assemblage of β- or γ-Mg₂SiO₄, stishovite and a garnet solid solution is stable at pressures above 175 kbar at 1,000°C. The system Fe₄Si₄O₁₂Fe₃Al₂Si₃O₁₂ shows a similar trend of high-pressure transformations: the maximum solubility of ferrosilite (FeSiO₃) in almandine (Fe₃Al₂Si₃O₁₂) forming a homogeneous garnet solid solution is 40 mol% at 93 kbar and 1,000°C.If a pyrolite mantle is assumed, from the present results, the following transformation scheme is suggested for the pyroxene-garnet assemblage in the mantle. Pyroxenes begin to react with the already present pyrope-rich garnet at depths around 150 km. Although the pyroxene-garnet transformation is spread over more than 400 km in depth, the most effective transition to a complex garnet solid solution takes place at depths between 450 and 540 km. The complex garnet solid solution is expected to be stable at depths between 540 and 590 km. At greater depths, it will decompose to a mixture of modified spinel or spinel, stishovite and garnet solid solutions with smaller amounts of a pyroxene component in solution.     

Compression and phase behavior of solid CO2 to half a megabar

CO₂ has been investigated up to 514 kbar at23 ± 2°C by both optical and in situ X-ray diffraction studies using a diamond-anvil pressure cell. CO₂ solidifies in an unknown structure in the pressure range 5 to 23 kbar, and transforms to ordinary dry-ice structure above 23 kbar at room temperature. Isothermal compression data for dry ice have been obtained above about 24 kbar. These appear to be the first data at room temperature known in the literature. The data fitted to the Birch equation of state yieldK₀ = 29.3 ± 1.0kbar andK₀^′ = 7.8 assuming the volume of the hypothetical dry ice at zero-pressure and room temperature is 31.4 ± 0.2 cm³/mole. The isothermal bulk modulus(K₀) thus derived is consistent with the compression data and compressibilities for dry ice obtained at low temperatures using dilatometry and ultrasonic techniques, respectively, reported in the literature. By comparing shock-wave data for relevant materials, it is suggested that CO₂ is not likely to transform to one of the crystalline forms of SiO₂ which is otherwise expected from empirical grounds, but may instead decompose into C (diamond) + O₂, at high pressures.     

Elasticity of pyrope and majorite-pyrope solid solutions to high temperatures

Majorite-garnet solid solutions are major mineral phases in the Earth’s upper mantle and transition zone. Here we present the first Brillouin scattering measurements of the elasticity of majorite (Mj, Mg₄Si₄O₁₂)-pyrope (Py, Mg₃Al₂Si₃O₁₂) solid solutions (Mj₅₀Py₅₀ and Mj₈₀Py₂₀) and single-crystal elasticity of pure synthetic pyrope at temperatures up to 800°C. The temperature derivatives of the adiabatic bulk (K_S) and shear (μ) moduli for all compositions along the Mj-Py join are the same within the experimental uncertainties (−∂K_S/∂T=14.0-14.5(20) MPa/K, −∂μ/∂T=8.3-9.2(10) MPa/K). The temperature dependence of the acoustic velocities for Mj-Py solid solutions is about half that of other major transition zone minerals. This implies that temperature variations in the transition zone, inferred from lateral velocity heterogeneity, can be significantly underestimated if the properties of majoritic garnet are not taken into account.     

Calorimetric study of the stability of high pressure phases in the systems CoOSiO2 and “FeO”SiO2, and calculation of phase diagrams in MOSiO2 systems

High temperature calorimetric measurements of the enthalpies of solution in molten if2 PbO · B₂O₃ of α- and γ-Fe₂SiO₄ and α-, β-, and γ-Co₂SiO₄ permit the calculation of phase relations at high pressure and temperature. The reported triple point involving α-, β-, and γ-Co₂SiO₄ is confirmed to represent stable equilibrium. The curvature in the α?β phase boundary in Co₂SiO₄ and of an α?γ boundary in Fe₂SiO₄ at high temperature is explained in part by the effects of compressibility and thermal expansion, but better agreement with the observed phase diagram is obtained when one considers the effect of small amounts of cation disorder in the spinel and/or modified spinel phases. The calculated ΔH⁰ and ΔS⁰ values for the α?β, α?γ, and β?γ transitions show that enthalpy and en changes both vary strongly in the series Mg, Fe, Co, and Ni, and are of equal importance in determining the stability relations. The disproportionation of Fe₂SiO₄ and Co₂SiO₄ spinel to rocksalt plus stishovite is calculated to occur in the 170–190 kbar region; cation disorder and/or changes in wüstite stoichiometry can affect the P?T slope. The calorimetric data for CoSiO₃ and FeSiO₃ are in good agreement with the observed phase boundary for pyroxene formation from olivine and quartz. The decomposition of pyroxene to spinel and stishovite at pressures near the coesite-stishovite transition is predicted in both iron and cobalt systems. The use of calorimetric data, obtained from small samples of high pressure phases, is very useful in predicting equilibrium phase diagrams in the 50–300 kbar range.     

Melting of forsterite Mg2SiO4 up to 15 GPa

The melting curve of forsterite has been studied by static experiment up to a pressure of 15 GPa. Forsterite melts congruently at least up to 12.7 GPa. The congruent melting temperature is expressed by the Kraut-Kennedy equation in the following form: T_m(K)=2163 (1+3.0(V₀ ? V)/V₀), where the volume change with pressure was calculated by the Birch-Managhan equation of state with the isothermal bulk modulus K₀ = 125.4 GPa and its pressure derivative K′ = 5.33. The triple point of forsterite-β-Mg₂SiO₄-liquid will be located at about 2600°C and 20 GPa, assuming that congruent melting persists up to the limit of the stability field of forsterite. The extrapolation of the previous melting data on enstatite and periclase indicates that the eutectic composition of the forsterite-enstatite system should shift toward the forsterite component with increasing pressure, and there is a possibility of incongruent melting of forsterite into periclase and liquid at higher pressure, although no evidence on incongruent melting has been obtained in the present experiment.     

Elasticity of single-crystal SmAlO3, GdAlO3 and ScAlO3 perovskites

The adiabatic single-crystal elastic moduli of SmAlO₃, GdAlO₃ and ScAlO₃, all with the orthorhombic perovskite structure, have been measured by Brillouin spectroscopy under ambient conditions. These 3 compounds display various degrees of crystallographic distortion from the ideal cubic perovskite structure. We find that longitudinal moduli in directions parallel to the axes of a pseudocubic subcell are nearly equal and insensitive to distortions of the crystal structure from cubic symmetry, whereas, the moduli C₁₁ and C₂₂, parallel to the orthorhombic axes, display pronounced anisotropy with the exception of ScAlO₃. The shear moduli also correlate with distortion from cubic symmetry, as measured by rotation, or tilt angles, of the AlO₆ octahedra. Our data support the observations of Liebermann et al. that perovskite-structure compounds define consistent elasticity trends relating bulk modulus and molar volume, and sound speed and mean atomic weight. These relationships have been used to estimate bulk and shear moduli for the high-pressure polymorphs of CaSiO₃ and MgSiO₃ with the perovskite structure.     

Thermal regime of the Earth's core

The outer core is assumed to consist of iron and sulfur, with a small amount of potassium that generates heat by radioactive decay of sim||pre|40 K. Two cases are considered, corresponding respectively to a high rate of heat production (Q = 2 · 10¹² cal./sec, about 0.1% K), and to a low rate (Q = 2 · 10¹¹ cal./sec). The temperature at a depth of 2800 km in the mantle is taken to be 3300°K (Wang, 1972). The temperature T_c at the core-mantle boundary depends on whether or not a density gradient in the lowermost layer D″ of the mantle prevents convection in that layer. In the first case, and for high Q, T_c = 4500–5000°K. In the second case, or for low Q, T_c ≈ 3500°K.The heat-conduction equation is used to calculate the temperature T_i at the inner-core boundary in the absence of convection. For high Q, T_i ? T_c ≈ 1600°K; for low Q, T_i ? T_c ≈ 160°K. Corresponding temperature gradients at r = r_c and r = r_i are listed in Table I.The adiabatic gradient at the top of the core is calculated by the method of Stewart (1970). It strongly depends on the parameters (ρ₀, c₀, γ₀, etc.) that characterize core material at low pressure. Stewart has drawn graphs that allow the selection of sets of parameters that are consistent with seismic velocities and a given density distribution in the core. Some acceptable sets of parameters are listed in Table II. Many sets yield temperatures T_c in the range 3500–5000°K; some give an adiabatic gradient steeper than the conductive gradient and are compatible with convection; others do not. Since properties of FeS melts remain unknown, there is at present no way of selecting any set in preference to another.Properties of the FeS system at low pressure suggest the possible appearance of immiscibility at high temperature in liquids of low sulfur content; accordingly, the inner-core boundary is thought to represent equilibrium between a solid (FeNi) inner core and a liquid layer containing only a small amount of sulfur; layer F in turn is in equilibrium with another liquid (forming layer E) containing more sulfur, and slightly less dense, than F. The temperature T_i at the inner-core boundary is about 6000–6500°K for high Q and T_c ≈ 4500–5000°K. It is consistent with Alder's (1966) and Leppaluoto's (1972) estimates of the melting point of iron at 3.3 Mbar, but not with that of Higgins and Kennedy (1971).     

Compressibility of brownmillerite (Ca2Fe2O5): effect of vacancies on the elastic properties of perovskites

The evolution with pressure of the unit-cell parameters brownmillerite (Ca₂Fe₂O₅), a stoichiometric defect perovskite structure, has been determined to a maximum pressure of 9.46 GPa, by single-crystal X-ray diffraction measurements at room temperature. Brownmillerite does not exhibit any phase transitions in this pressure range. A fit of a third-order Birch–Murnaghan equation-of-state to the P–V data yields values of K_T0=127.0(5) GPa and K₀′=5.99(13). Analysis of the unit-cell parameter data shows that the structure compresses anisotropically. Compressional moduli for the axes are K_a0=141(1) GPa, K_b0=118(3) GPa and K_c0=122.2(2) GPa, with K_a0′=8.9(3), K_b0′=6.2(6) and K_c0′=4. The stiffest direction (i.e. along a) coincides with the direction of the FeO₄ tetrahedral chains. Comparison of these data with the elasticity systematics of Ca-perovskites shows that the presence of oxygen vacancies in the brownmillerite structure softens the structure by ∼25% and that the ordering of vacancies in the perovskite structure increases the anisotropy of compression.