Nancy L. Ross

Ab initio study of MgSiO3 and CaSiO3 perovskites at lower-mantle pressures

We have used a newly developed ab initio constant-pressure molecular dynamics technique to investigate the zero-temperature behaviour of MgSiO3 and CaSiO3 perovskites up to pressures which exceed the highest values reached within the Earths mantle. Despite the similarities between these solids, we demonstrate that their behaviours at 150 GPa differ: whereas CaSiO3 prefers the cubic perovskite phase, MgSiO3 remains in the orthorhombically distorted perovskite (Pbnm) phase. Our theoretical strategy, besides in principle allowing finite-temperature simulations of solids under isotropic pressure, permits efficient and accurate determination of structural behaviour under arbitrary external pressures and/or stresses. This enabled us to offer reliable predictions for the elastic constants and shear modulus of MgSiO3 perovskite, and to provide an estimate of the bulk modulus and its pressure derivative for CaSiO3. Our calculations show that a Ca-enriched lower mantle would have a similar compressibility to a Ca-poor one.

Stabilities and equations of state of dense hydrous magnesium silicates

Abstract The thermodynamic stability of high-pressure phases in the ternary system MgO–SiO2–H2O is reviewed with special emphasis on hydrated phases including the “alphabet phases”. On the basis of recent experimental data, a stability diagram for these phases along a geotherm appropriate for a subducting slab is constructed. This suggests that at realistic water contents, the breakdown of antigorite will produce olivine plus phase A in the upper mantle, but that the ability of wadsleyite to accommodate wt.% levels of water means that phases E and D are unlikely to occur in the upper portion of the transition zone. For the lower part of the transition zone in which ringwoodite becomes stable, the coexisting hydrous phase would be superhydrous phase B, provided ringwoodite is not able to accommodate significant amounts of water. At the top of the lower mantle, phase D is stable but only at temperatures below 1300°C. As the maximum solubility of H2O in magnesium silicate perovskite is also quite low slabs may dehydrate somewhat as they enter the lower mantle. The available thermodynamic data for these phases is also reviewed. From the most recent measurements of equations of state, it is concluded that the elasticity of the phases in the MgO–SiO2–H2O ternary system is primarily dependent upon the density and not upon the water content. It is, therefore, concluded that the presence of even significant amounts of hydrated phases in subducting slabs could not be unequivocally identified from seismological observations.

Compression of CaTiO 3 and CaGeO 3 perovskites

Abstract High-pressure single-crystal X-ray diffraction measurements of CaTiO3 and CaGeO3 perovskite have been carried out to 9.7 and 8.6 GPa, respectively, at room temperature. Fitting a third-order Birch-Murnaghan equation-of-state to the P-V data yields values of V0 = 223.764 ± 0.017 Å3, KT,0 = 170.9 ± 1.4 GPa, and K′ = ∂K/∂P = 6.6 ± 0.3 for CaTiO3 and V0 = 206.490 ± 0.017 Å3, KT,0 = 194.0 ± 2.1 GPa, and K′ = 6.1 ± 0.5 for CaGeO3. A similar analysis of the axial compressibilities shows that the degree of anisotropic compression in both perovskites is less than 10%. In CaTiO3 the a and b axes have similar compressibilities (Ka= 168.7 ±2.1 GPa, Kb= 168.3 ±1.9 GPa) whereas the c axis is the least compressible (Kc = 175.3 ±1.5 GPa). In CaGeO3, the b axis (Kb = 188 ± 4 GPa) and the a axis (Ka = 195 ± 5 GPa) are more compressible than the c axis (Kc = 204 ± 3 GPa). The variations with pressure of all axes show significant curvature with increasing pressure and have K′ values ranging from 5.7 ± 0.5 to 7.0 ± 0.4 in CaTiO3 and 5.0 ± 0.9 to 6.9 ± 1.2 in CaGeO3. No phase transition was detected. There is evidence, however, that in CaGeO3 the tetragonal to orthorhombic spontaneous strain decreases slightly with pressure which may indicate that a phase transition occurs at a pressure above 10 GPa. Elasticity trends of Ca-perovskites relating bulk modulus and molar volume are independent of both the degree of distortion from cubic symmetry and the symmetry of the structure.

The equation of state and high-pressure behavior of magnesite

Abstract Unit-cell parameters of magnesite have been measured to high precision between 0 and 7 GPa using single-crystal X-ray diffraction. The isothermal bulk modulus of magnesite determined from fitting a Birch-Mumaghan third-order equation of state to the volume compression data is KT = 117(3) GPa with KʹT = 2.3(7), and KT = 111(1) GPa if KʹT is constrained to a value of 4. Crystal structure parameters have been determined from X-ray intensity data at room pressure, 2.26, 3.09, 4.16, 4.77, and 6.05 GPa. The principal structural change with increasing pressure is compression of the MgO6 octahedra while the CO3 group remains invariant (within the experimental uncertainty) throughout the pressure range studied. The effect of the polyhedral compression is reflected in the anisotropic compression of the unit-cell parameters with the c axis approximately twice as compressible as the a axis. The polyhedral bulk modulus of the MgO6 octahedron is 113 GPa, which is greater than that observed in other rhombohedral carbonates, but significantly smaller than values observed in many oxides and silicates. The distortion of the octahedra, though already small, decreases slightly with pressure. No phase change or change in compression behavior was observed throughout the pressure range studied.

Neutron diffraction at simultaneous high temperatures and pressures, with measurement of temperature by neutron radiography

Abstract The commissioning and operation of apparatus for neutron diffraction at simultaneous high temperatures and pressures is reported. The basic design is based on the Paris-Edinburgh cell using opposed anvils, with internal heating. Temperature is measured using neutron radiography. The apparatus has been shown in both on-line and off-line tests to operate to a pressure of 7 GPa and temperature of 1700°C. The apparatus has been used in a neutron diffraction study of the crystal structure of deuterated brucite, and results for 520°C and 5.15 GPa are presented. The diffraction data that can be obtained from the apparatus are of comparable quality to previous high-pressure studies at ambient temperatures, and are clearly good enough for Rietveld refinement analysis to give structural data of reasonable quality.

The Stability of minerals

Preface. The stability of minerals: an introduction - N L Ross and G D Price Bond topology, bond valence and structure stability - F C Hawthorne Electronic paradoxes in the structures of minerals - J K Burdett Lattice vibration and mineral stability - N L Ross Thermodynamics of phase transitions in minerals: a macroscopic approach - M A Carpenter The stability of modulated structures - J D C McConnell Thermochemistry of tetrahedrite-tennanite fahlores - R O Sack Thermodynamic data for minerals: a critical assessment - M Engi The stability of clays - B Velde

Equation of state of dense hydrous magnesium silicate phase A, Mg7Si2O8(OH)6

Abstract The isothermal equation of state (EoS) of phase A, Mg7Si2O8(OH)6, has been determined using high-pressure single-crystal X-ray diffraction. A third-order Birch-Murnaghan EoS fit to pressurevolume data collected from room pressure and temperature to 7.6 GPa results in V0 = 512.56(3) Å3, K0 = 97.5(4) GPa, and K = 5.97(14). Compression of the hexagonal (P63) structure is anisotropic with the c axis, which is perpendicular to the distorted close-packed planes of anions, approximately 23% less compressible than the a axis: Ka = 90.1(5) GPa with Ka = 5.4(2) and Kc = 116.8(9) GPa with Kc = 7.5(3). The bulk modulus of phase A is intermediate between those of brucite (Br) and forsterite (Fo) and less than those of hydroxylclinohumite and hydroxylchondrodite, in a manner that is entirely consistent with its water content and density in relation to the Fo-Br series of minerals.

Compression of synthetic hydroxylclinohumite [Mg9Si4O16(OH)2] and hydroxylchondrodite [Mg5Si2O8(OH)2]

Abstract The isothermal equations of state (EoS) of synthetic hydroxylclinohumite, Mg9Si4O16(OH)2, and synthetic hydroxylchondrodite, Mg5Si2O8(OH)2, have been determined using high-pressure singlecrystal X-ray diffraction, carried out in a diamond anvil cell under hydrostatic conditions. Both humites are monoclinic (space group P21/b with a unique): a = 4.7490(3) Å, b = 10.2861(4) Å, c = 13.6991(11) Å and α = 100.649(6)° for hydroxylclinohumite, and a = 4.7449(2) Å, b = 10.3464(2) Å, c = 7.8990(6) Å, and α = 108.681(3)° for hydroxylchondrodite. A third-order Birch-Murnaghan EoS was determined from unit-cell volume data to 8.1 GPa for hydroxylclinohumite: V0 = 657.69(5) Å3, KT = 119.4(7) GPa and K = 4.8(2). A similar analysis of hydroxylchondrodite for data collected to 7.8 GPa resulted in V0 = 367.36(3) Å3, KT = 115.7(8) GPa and K = 4.9(2). Axial compression is anisotropic with the direction perpendicular to the close-packed anion layer, i.e., the a axis, being the least compressible. Axial moduli and their pressure derivatives are: Ka = 162(1) GPa, Ka = 6.7(3), Kb = 97.9(5) GPa, Kb = 4.0(1), Kc = 111.1(7) GPa and Kc = 4.2(2) for hydroxylclinohumite. For hydroxylchondrodite: Ka = 149(1) GPa, Ka = 6.8(3), Kb = 101.3(4) GPa, Kb = 4.3(1), Kc = 102.4(6) GPa, and Kc = 4.1(2). Comparison of the bulk moduli of these phases with other phases along the Mg2SiO4-Mg(OH)2 join shows that the bulk modulus increases systematically with density (ρ) and can be approximated by, KT (GPa) = 97(6) × ρ - 186(17). The bulk modulus also decreases systematically with water content: KT (GPa) = 127.9 (16) - 2.75 (11) × wt% H2O.

Computer simulation of the infrared and Raman activity of pyrope garnet, and assignment of calculated modes to specific atomic motions

Abstract The lattice dynamics computer code PARAPOCS was successfully used to calculate the 240 vibrational frequencies of pyrope garnet, Mg3Al2Si3O12, at ambient conditions. The atomic displacement vectors (eigenvectors) for each frequency were also calculated and their symmetry relations analyzed with the aid of factor group analysis (FGA), to determine the symmetry species of each vibrational mode. Comparison with the experimental IR and Raman data shows excellent agreement, but no LO-TO reversals were identified. Calculation of the frequency shifts due to the isotopic substitution of 26Mg and 30Si, together with a more detailed analysis of the calculated eigenvectors, enabled identification of the dominant site or cation motion contributing to each vibrational mode. Previous assignments of the high-frequency vibrations to pure SiO4 internal modes and the lower-frequency vibrations to mixed cation modes are supported. We conclude that the specific number of site/atom motions predicted by site group analysis (SGA) is not adhered to due to substantial mode mixing, and that FGA and SGA, in which the SiO4 tetrahedra are treated as isolated units, are only applicable at high frequencies. The agreement observed between the calculated and experimental data leads us to conclude that the method of computer modeling used and the interatomic potentials employed in the simulations provide a good description of the lattice dynamical behavior of pyrope garnet.

Equation of state of phase E

Abstract The isothermal equation of state (EoS) of phase E, Mg1.96(7)Fe0.072(5)Si1.04(5)H3.7(8)O6, has been determined using high-pressure single-crystal X-ray diffraction. A third-order Birch Murnaghan EoS fit to pressue-volume data collected from room pressure and temperature to 6.7 GPa reveals that phase E has the lowest bulk modulus, KT = 92.9(7) GPa, and highest pressure derivative of the bulk modulus, K’ = 7.3(2), for any dense hydrous magnesium silicate (DHMS) yet measured. A parameterized third-order Birch-Murnaghan EoS was also fit to the unit-cell parameters which display significant curvature with increasing pressure. This analysis shows that the c-axis (Kc = 89.1(10) GPa) is 6% more compressible than the a-axis (Ka = 94.8(6) GPa), with little of the anisotropy commonly observed in other layered structures. The high K’ is indicative of the similarity to layers of the brucite structure. The introduction of interlayer cation polyhedra to the structure serves to reduce both the anisotropy, by reducing the compressibility perpendicular to the sheets, and the ability to shear, by increasing the coherence between layers.