Water incorporation in synthetic and natural MgAl2O4 spinel

The solubility and incorporation mechanisms of water in synthetic and natural MgAl₂O₄ spinel have been investigated in a series of high-pressure/temperature annealing experiments. In contrast to most other nominally anhydrous minerals, natural spinel appears to be completely anhydrous. On the other hand, non-stoichiometric Al-rich synthetic (defect) spinel can accommodate several hundred ppm water in the form of structurally-incorporated hydrogen. Infrared (IR) spectra of hydrated defect spinel contain one main O-H stretching band at 3343-3352 cm⁻¹ and a doublet consisting of two distinct O-H bands at 3505-3517 cm⁻¹ and 3557-3566 cm⁻¹. IR spectra and structural refinements based on single-crystal X-ray data are consistent with hydrogen incorporation in defect spinel onto both octahedral and tetrahedral O-O edges. Fine structure of O-H bands in IR spectra can be explained by partial coupling of interstitial hydrogen with cation vacancies, or by the effects of Mg-Al disorder on the tetrahedral site. The concentration of cation vacancies in defect spinel is a major control on hydrogen affinity. The commercial availability of large single crystals of defect spinel coupled with high water solubility and similarities in water incorporation mechanisms between hydrous defect spinel and hydrous ringwoodite (Mg₂SiO₄) suggests that synthetic defect spinel may be a useful low-pressure analogue material for investigating the causes and consequences of water incorporation in the lower part of Earth’s mantle transition zone.     

Low-temperature heat capacities,entropies and enthalpies of Mg<Subscript>2</Subscript>SiO<Subscript>4</Subscript> polymorphs,and α−β−γ and post-spinel phase relations at high pressure

The low-temperature isobaric heat capacities (C _p) of β- and γ-Mg₂SiO₄ were measured at the range of 1.8–304.7 K with a thermal relaxation method using the Physical Property Measurement System. The obtained standard entropies (S°₂₉₈) of β- and γ-Mg₂SiO₄ are 86.4 ± 0.4 and 82.7 ± 0.5 J/mol K, respectively. Enthalpies of transitions among α-, β- and γ-Mg₂SiO₄ were measured by high-temperature drop-solution calorimetry with gas-bubbling technique. The enthalpies of the α−β and β−γ transitions at 298 K (ΔH°₂₉₈) in Mg₂SiO₄ are 27.2 ± 3.6 and 12.9 ± 3.3 kJ/mol, respectively. Calculated α−β and β−γ transition boundaries were generally consistent with those determined by high-pressure experiments within the errors. Combining the measured ΔH°₂₉₈ and ΔS°₂₉₈ with selected data of in situ X-ray diffraction experiments at high pressure, the ΔH°₂₉₈ and ΔS°₂₉₈ of the α−β and β−γ transitions were optimized. Calculation using the optimized data tightly constrained the α−β and β−γ transition boundaries in the P, T space. The slope of α−β transition boundary is 3.1 MPa/K at 13.4 GPa and 1,400 K, and that of β−γ boundary 5.2 MPa/K at 18.7 GPa and 1,600 K. The post-spinel transition boundary of γ-Mg₂SiO₄ to MgSiO₃ perovskite plus MgO was also calculated, using the optimized data on γ-Mg₂SiO₄ and available enthalpy and entropy data on MgSiO₃ perovskite and MgO. The calculated post-spinel boundary with a Clapeyron slope of −2.6 ± 0.2 MPa/K is located at pressure consistent with the 660 km discontinuity, considering the error of the thermodynamic data.     

The rheology of olivine and spinel magnesium germanate (Mg2GeO4): TEM study of the defect microstructures

Synthetic polycrystals of α-Mg₂GeO₄ (with the olivine structure) and γ-Mg₂GeO₄ (with the spinel structure) deformed at high temperature and pressure in their respective stability fields were investigated by analytical transmission electron microscopy. Specimens with a mean grain size of 20–30 µm deform by dislocation glide and/or climb. The predominance of glide versus climb depends on stress and grain orientation. The defect microstructures of both polymorphs are very similar to those observed in their respective silicate analogues, α- and γ-(Mg,Fe)₂SiO₄, and, in the case of the spinel phase, very similar to those observed in magnesium aluminate spinels. These observations suggest that Mg₂GeO₄ is a good rheological analogue for the Earth’s upper mantle. A spinel specimen deformed under the same conditions of temperature and strain rate as an olivine specimen was approximately three times stronger than olivine. In specimens of both phases deformed at or above 1400 K, a thin amorphous film composed of Mg, Ge, and O was detected along some grain boundaries. Grains ≤10 µm diameter surrounded by a film of amorphous phase (>10 nm thick) exhibited low dislocation densities, and deformation appeared to have occurred by grain boundary sliding.     

Comparison of the raman microprobe spectra of (Mg,Fe)2SiO4 and Mg2GeO4 with olivine and spinel structures

Raman microprobe (RMP) spectra were produced for each of the olivine and spinel structured phases of Mg₂GeO₄ and (Mg, Fe)₂SiO₄. The assembled data show that bands due to the tetrahedra in silicate and germanate olivines shift in a way that indicates a dominant mass effect. This correspondence is difficult to make in spinels due to differences in structural type. Differences in Fe/Mg content of olivine shift the tetrahedral vibration bands only slightly, but their linear shifts could be used to indicate the composition of the phase.     

Heat capacity of γ-Fe2SiO4 between 5 and 303 K and derived thermodynamic properties

A multi-anvil device was used to synthesize 24 mg of pure γ-Fe₂SiO₄ crystals at 8.5 GPa and 1,273 K. The low-temperature heat capacity (C _p) of γ-Fe₂SiO₄ was measured between 5 and 303 K using the heat capacity option of a physical properties measurement system. The measured heat capacity data show a broad λ-transition at 11.8 K. The difference in the C _p between fayalite and γ-Fe₂SiO₄ is reduced as the temperature increases in the range of 50–300 K. The gap in C _p data between 300 and 350 K of γ-Fe₂SiO₄ is an impediment to calculation of a precise C _p equation above 298 K that can be used for phase equilibrium calculations at high temperatures and high pressures. The C _p and entropy of γ-Fe₂SiO₄ at standard temperature and pressure (S°₂₉₈) are 131.1 ± 0.6 and 140.2 ± 0.4 J mol⁻¹ K⁻¹, respectively. The Gibbs free energy at standard pressure and temperature (ΔG° _f,298) is calculated to be −1,369.3 ± 2.7 J mol⁻¹ based on the new entropy data. The phase boundary for the fayalite–γ-Fe₂SiO₄ transition at 298 K based on current thermodynamic data is located at 2.4 ± 0.6 GPa with a slope of 25.4 bars/K, consistent with extrapolated results of previous experimental studies.     

Synthetic MgGa2O4-Mg2GeO4 spinel solid solution and β-Mg3Ga2GeO8: chemistry, crystal structures, cation ordering, and comparison to Mg2GeO4 olivine

 Structural parameters and cation ordering are determined for four compositions in the synthetic MgGa₂O₄-Mg₂GeO₄ spinel solid solution (0, 8, 15 and 23 mol% Mg₂GeO₄; 1400 °C, 1 bar) and for spinelloid β-Mg₃Ga₂GeO₈ (1350 °C, 1 bar), by Rietveld refinement of room-temperature neutron diffraction data. Sample chemistry is determined by XRF and EPMA. Addition of Mg₂GeO₄ causes the cation distribution of the MgGa₂O₄ component to change from a disordered inverse distribution in end member MgGa₂O₄, ^[4]Ga = x = 0.88(3), through the random distribution, toward a normal cation distribution, x = 0.37(3), at 23 mol% Mg₂GeO₄. An increase in a_o with increasing Mg₂GeO₄ component is correlated with an increase in the amount of Mg on the tetrahedral site, through substitution of 2 Ga³⁺⇄ Mg²⁺+Ge⁴⁺. The spinel exhibits high configurational entropy, reaching 20.2 J mol⁻¹ (four oxygen basis) near the compositional upper limit of the solid solution. This stabilizes the spinel in spite of positive enthalpy of disordering over the solid solution, where ΔH _D  = αx + βx ², α = 22(3), β = −21(3) kJ mol⁻¹. This model for the cation distribution across the join suggests that the empirically determined limit of the spinel solid solution is correlated with the limit of tetrahedral ordering of Mg, after which local charge-balanced substitution is no longer maintained. Spinelloid β-Mg₃Ga₂GeO₈ has cation distribution ^M1[Mg_0.50(2)Ga_0.50(2)] ^M2[Mg_0.96(2)Ga_0.04(2)] ^M3[Mg_0.77(2) Ga_0.23(2)]₂ (Ge_0.5Ga_0.5)₂O₈ (tetrahedral site occupancies are assumed). Octahedral site size is correlated to Mg distribution, where site volume, site distortion, and Mg content follow the relation M1<M3<M2. The disordered cation distribution provides local electrical neutrality in the structure, and stabilization through increased configurational entropy (27.6 J mol⁻¹; eight oxygen basis). Comparison of the crystal structures of Mg_{1+ N} Ga_{2−2 N} Ge _N O₄ spinel, β-Mg₃Ga₂GeO₈, and Mg₂GeO₄ olivine reveals β-Mg₃Ga₂GeO₈ to be a true structural intermediate. Phase transitions across the pseudobinary are necessary to accommodate an increasing divergence of cation size and valence, with addition of Mg₂GeO₄ component. Octahedral volume increases while tetrahedral volume decreases from spinel to β-Mg₃Ga₂GeO₈ to olivine, with addition of Mg and Ge, respectively. Furthermore, M-M distances increase regularly across the join, suggesting that changes in topology reduce cation-cation repulsion. Received: 9 November 1998 / Revised, accepted: 3 August 1999     

Spinelloid phases in the system MgGa2O4-Mg2GeO4

Spinelloid phases have been observed and characterized by powder X-ray diffraction and high-resolution electron microscopy. Mg₃Ga₂GeO₃(III), with a narrow composition range of approximately 3 mole percent Mg₂GeO₄, is stable at atmospheric pressure up to about 1,420° C, and is isostructural with β-Mg₂SiO₄ and the spinelloid Phase III of the NiAl₂O₄-Ni₂SiO₄ system. This represents the first occurrence of a β-phase structure stable at 1 atm pressure. Above 1,420° C (1 atm) Mg₃Ga₂GeO₈ (III) decomposes reversibly into a mixture of spinel and olivine. At high pressure (around 30 kbar at 1,100° C) it transforms into another spinelloid phase, Mg₃Ga₂GeO₈ (IV), isostructural with Phase IV of the NiAl₂O₄-Ni₂SiO₄ system. In terms of crystal structures and phase relations therefore there exists a close analogy between the magnesium gallo-germanate and nickel alumino-silicate systems, the former being a lower-pressure analogue of the latter. Our investigation of a number of other pseudo-binary spinel-olivine oxide systems suggests that the formation of spinelloid phases can be associated with the inverse character of the spinel component.     

Thermochemistry of phases in the system MgGa2O4-Mg2GeO4

The enthalpies of solution in molten 2PbO · B₂O₃ of phases synthesized at one atmosphere in the system MgGa₂O₄-Mg₂GeO₄ have been measured. A spinel solid solution, which is stable at 1400 °C from the MgGa₂O₄ end-member to 27 mole percent Mg₂GeO₄, shows endothermic heats of mixing of up to 10 kJ/mole at the solubility limit. The spinelloid phase, Mg₃Ga₂GeO₈, is energetically less stable than a mixture of terminal spinel solid solutions (0.73 MgGa₂O₄·0.27 Mg₂GeO₄(sp)+Mg₂GeO₄(sp)), by 3.63±3.64 kJ/mole. This indicates that the spinelloid is a high-entropy phase.The volume of the spinel solid solution, MgGa₂O₄-Mg₂GeO₄, shows a positive deviation from Vegard's Law. Modeling of the cation distribution in the solid solution indicates that this V is due to a change in the spinel type from inverse towards normal as the Mg₂GeO₄ content increases.     

Experimental Investigation and Optimization of Thermodynamic Properties and Phase Diagrams in the Systems CaO-SiO2, MgO-SiO2, CaMgSi2O6-SiO2 and CaMgSi2O6-Mg2SiO4 to 1{middle dot}0 GPa

Using experimental results at 1·0 GPa for the systemsCaO–SiO₂, MgO–SiO₂, CaMgSi₂O₆–SiO₂ and CaMgSi₂O₆–Mg₂SiO₄,and all the currently available phase equilibria and thermodynamicdata at 1 bar, we have optimized the thermodynamic propertiesof the liquid phase at 1·0 GPa. The new optimized thermodynamicparameters indicate that pressure has little effect on the topologyof the CaO–SiO₂, CaMgSi₂O₆–SiO₂, and CaMgSi₂O₆–Mg₂SiO₄systems but a pronounced one on the MgO–SiO₂ binary. Themost striking change concerns passage of the MgSiO₃ phase fromperitectic melting at 1 bar to eutectic melting at 1·0GPa. This transition is estimated to occur at 0·41 GPa.For the CaMgSi₂O₆–SiO₂ and CaMgSi₂O₆–Mg₂SiO₄ pseudo-binaries,the size of the field clinopyroxene + liquid increases withincreasing pressure. This change is related to the shift ofthe piercing points clinopyroxene + silica + liquid (from 0·375mol fraction SiO₂ at 1 bar to 0·414 at 1·0 GPa)and clinopyroxene + olivine + liquid (from 0·191 molfraction SiO₂ at 1 bar to 0·331 at 1·0 GPa) thatbound the clinopyroxene + liquid field in the CaMgSi₂O₆·SiO₂and CaMgSi₂O₆·Mg₂SiO₄ pseudo-binaries, respectively. KEY WORDS: CaO–SiO₂; CaMgSi₂O₆–Mg₂SiO₄; CaMgSi₂O₆–SiO₂; experiments; MgO–SiO₂     

Variation of the oxygen content and point defects in olivines, (Fe x Mg 1−x )2SiO4, 0.2 ≤ x ≤ 1.0

 The variation of the oxygen content in olivines, (Fe _x Mg_{1− x} )₂SiO₄, with 0.2 ≤ x ≤ 1.0, was investigated by thermogravimetric measurements. Mass changes occurring upon oxygen activity changes were measured as a function of oxygen activity and cationic composition at 1130 and 1200 °C. During the measurements the samples were in direct contact with gases containing CO, CO₂ and N₂ and, at a few spots at the bottom of the sample stack, also with SiO₂. By fitting experimental data of mass changes to equations derived using point defect thermodynamics, it was shown for olivines with 0.2 ≤ x ≤ 1.0 at 1130 °C and 0.2 ≤ x ≤ 0.7 at 1200 °C within the oxygen activity ranges investigated that the observed variations in the oxygen contents are compatible with cation vacancies and Fe³⁺ ions on M sites and Fe³⁺ ions on silicon sites as majority defects if it is assumed that only three types of point defects occur as majority defects. Different cases were considered, closed systems, taking into account that ξ=[Si]/([Si]+[Fe]+[Mg]) is not necessarily equal to 1/3, and olivines in equilibrium with SiO₂ or pyroxenes. The oxygen content variations observed in this study are significantly smaller than those reported previously in the literature. It is proposed that these differences are related to the dissolution of Fe into noble metal containers used as sample holders in earlier studies and/or to the presence of secondary phases. Received: 1 November 1995 / Accepted: 15 September 2002 Acknowledgements This work was supported by the Cornell Center for Materials Research (CCMR), a Materials Research Science and Engineering Center of the National Science Foundation (DMR-0079992). The authors thank Mr. Daniel M. DiPasquo and Mr. Jason A. Schick for helping in experimental work.     

Synchrotron IR study of hydrous ringwoodite (γ-Mg2SiO4) up to 30 GPa

High-pressure synchrotron infrared (IR) absorption spectra were collected between 650 and 4,000 cm⁻¹ at ambient temperature for hydrous Mg-ringwoodite (γ-Mg₂SiO₄) up to 30 GPa. The main feature in the OH⁻ stretching region is an extremely broad band centred at 3,150 cm⁻¹. The hydrogen bond is strong for most protons and the most probable site for protonation is the tetrahedral edge. With increasing pressure, this band shifts downward while decreasing its integrated intensity until disappearance at a pressure of 25 GPa. Only one band at 2,450 cm⁻¹ and an absorption plateau persist with a maximum wavenumber of 3,800 cm⁻¹. This behaviour is reversible upon pressure release. We interpret this as a second-order phase transition occurring in hydrated Mg-ringwoodite at high pressure (beyond ∼ 25 GPa). This result is compatible with the observation by Kleppe et al. (Phys Chem Miner 29:473–476, 2002a) who suggested the presence of Si–O–Si linkages and/or partial increase in the coordination of Si. Beyond the phase transition, the protons are delocalized and their environment on the ringwoodite structure is probably quite different from that at low pressure. Data obtained in situ at high pressures and temperatures are needed to better understand the effect of protonation on the structure and to better constrain this phase transition.     

^29Si,^27Al Magic—Angle—Spinning Nuclear Magnetic Resonance（MAS NMR） Studies of Kaolinite and Its Thermal Transformation Products

²⁷Al,²⁹Si MAS NMR studies of kaolinite and its thermal transformation products show that in the kaolinite-mullite reaction series there is an extensive segregation of Al₂O₃ and SiO₂ and the reaction of Al₂O₃ with SiO₂ to form mullite is the main path of mullite formation. At about 850° C, the peak intensity of A1(V) reaches its maximum and with the further rise of temperature the A1(V) signal completely disappears. At about 950°C, γ-Al₂O₃ accounts for about 71% of the material phases containing Al atoms. In the series there is no obvious presence of Al-Si spinel. The²⁷Al and²⁹Si MAS NMR spectra show that there is an obvious difference between the temperature points for Al-O₂(OH)₄ octahedral sheet collapsing and Si-O₄ tetrahedral sheet breaking down.     

Heat capacity and phase equilibria of wadeite-type K2Si4O9

The low-temperature heat capacity (C _p) of Si-wadeite (K₂Si₄O₉) synthesized with a piston cylinder device was measured over the range of 5–303 K using the heat capacity option of a physical properties measurement system. The entropy of Si-wadeite at standard temperature and pressure calculated from the measured heat capacity data is 253.8 ± 0.6 J mol⁻¹ K⁻¹, which is considerably larger than some of the previous estimated values. The calculated phase transition boundaries in the system K₂O–Al₂O₃–SiO₂ are generally consistent with previous experimental results. Together with our calculated phase boundaries, seven multi-anvil experiments at 1,400 K and 6.0–7.7 GPa suggest that no equilibrium stability field of kalsilite + coesite intervenes between the stability field of sanidine and that of coesite + kyanite + Si-wadeite, in contrast to previous predictions. First-order approximations were undertaken to calculate the phase diagram in the system K₂Si₄O₉ at lower pressure and temperature. Large discrepancies were shown between the calculated diagram compared with previously published versions, suggesting that further experimental or/and calorimetric work is needed to better constrain the low-pressure phase relations of the K₂Si₄O₉ polymorphs. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Raman spectroscopic study of hydrous <Emphasis Type="Italic">γ</Emphasis>-Mg<Subscript>2</Subscript>SiO<Subscript>4</Subscript> to 56.5 GPa

 Raman spectra of a single-crystal fragment of hydrous γ-Mg₂SiO₄, synthesized in a multianvil press, have been measured in a diamond-anvil cell with helium as pressure-transmitting medium to 56.5 GPa at room temperature. All five characteristic spinel Raman modes shift continuously up to the highest pressure, showing no evidence for a major change in the crystal structure despite compression well beyond the stability field of ringwoodite in terms of pressure. At pressures above ∼30 GPa a new mode on the low-frequency site of the two silicate-stretching modes is clearly identifiable, indicating a modification in the spinel structure which is reversible on pressure release. The frequency of the new mode (802 cm⁻¹ extrapolated to 1 bar) suggests the presence of Si–O–Si linkages and/or a partial increase in the coordination of Si. Direct determination of the subtle structural change causing the new Raman mode would require high-pressure, single-crystal synchrotron X-ray diffraction experiments. The Raman modes of hydrous and anhydrous Mg-end-member ringwoodite are nearly identical up to 20 GPa, suggesting that protonation has only minor effect on the lattice dynamics over the entire pressure stability range for ringwoodite in the mantle. Received: 7 December 2001 / Accepted: 16 April 2002     

The pressure-induced ringwoodite to Mg-perovskite and periclase post-spinel phase transition: a Bader’s topological analysis of the ab initio electron densities

In order to characterize the pressure-induced decomposition of ringwoodite (γ-Mg₂SiO₄), the topological analysis of the electron density ρ(r), based upon the theory of atoms in molecules (AIM) developed by Bader in the framework of the catastrophe theory, has been performed. Calculations have been carried out by means of the ab initio CRYSTAL09 code at the HF/DFT level, using Hamiltonians based on the Becke- LYP scheme containing hybrid Hartree–Fock/density functional exchange–correlation terms. The equation of state at 0 K has been constructed for the three phases involved in the post-spinel phase transition (ringwoodite → Mg-perovskite + periclase) occurring at the transition zone–lower mantel boundary. The topological results show that the decomposition of the ringwoodite at high pressures is caused by a conflict catastrophe. Furthermore, topological evidences of the central role played by the oxygen atoms to facilitate the pressure-induced ringwoodite decomposition and the subsequent phase transition have been noticed.     

Thermodynamic properties and phase stability of wadsleyite II

The thermodynamical stability of a newly observed wadsleyite II phase in the Mg₂SiO₄ system is studied by the density functional theory. The wadsleyite II equation of state has been derived. The phase boundaries of Mg₂SiO₄ polymorphs: wadsleyite, wadsleyite II and ringwoodite are studied using the quasi-harmonic approximation at high external pressures. Clapeyron slopes determined for wadsleyite II–ringwoodite and wadsleyite–wadsleyite II boundaries are 0.0047 and 0.0058 GPa/K, respectively. It is shown that the wadsleyite II phase is not thermodynamically preferred in the pure Mg₂SiO₄ system and will probably not occur between wadsleyite and ringwoodite phases.     

Characterization of NH4-phlogopite (NH4) (Mg3) [AlSi3O10] (OH)2 and ND4-phlogopite (ND4) (Mg3) [AlSi3O10] (OD)2 using IR spectroscopy and Rietveld refinement of XRD spectra

 A synthesis technique is described which results in >99% pure NH₄-phlogopite (NH₄) (Mg₃) [AlSi₃O₁₀] (OH)₂ and its deuterium analogue ND₄-phlogopite (ND₄) (Mg₃) [AlSi₃O₁₀] (OD)₂. Both phases are characterised using both IR spectroscopy at 298 and 77 K as well as Rietveld refinement of their X-ray powder diffraction pattern. Both NH₄ ⁺ and ND₄ ⁺ are found to occupy the interlayer site in the phlogopite structure. Absorption bands in the IR caused by either NH₄ ⁺ or ND₄ ⁺ can be explained to a good approximation using T_d symmetry as a basis. Rietveld refinement indicates that either phlogopite synthesis contains several mica polytypes. The principle polytype is the one-layer monoclinic polytype (1M), which possesses the space group symmetry C2/m. The next most common polytype is the two-layer polytype (2M ₁ ) with space group symmetry C2/c. Minor amounts of the trigonal polytype 3T with the space group symmetry P3₁12 were found only in the synthesis run for the ND₄-phlogopite. Electron microprobe analyses indicate that NH₄-phlogopite deviates from the ideal phlogopite composition with respect to variable Si/Al and Mg/Al on both the tetrahedral and octahedral sites, respectively, due to the Tschermaks substitution ^VIMg²⁺+^IVSi⁴⁺↔^VIAl³⁺+^IVAl³⁺ and with respect to vacancies on the interlayer site due to the exchange vector ^XII(NH₄)⁺+^IVAl³⁺↔^XII□+^IVSi⁴⁺. Received: 30 August 1999 / Accepted: 2 October 2000     

The nonlinear elasticity and related properties of anhydrous and hydrous γ-Mg2SiO4: a theoretical study

The second-order elastic constants up to 30 GPa, which encompass the stability field of the spinel forms, their pressure derivatives and the third-order elastic constants of both hydrous and anhydrous -Mg₂SiO₄ have been obtained theoretically. A combination of deformation theory and finite strain elasticity theory has been employed to arrive at the expressions for second-order and third-order elastic constants from the strain energy of the lattice. The strain energy is calculated by taking into account the interactions up to second nearest neighbours in the -Mg₂SiO₄ lattice. This is then compared with the strain-dependent lattice energy from continuum model approximation to obtain the expression of elastic constants. The second-order elastic constants C_ij compare favourably with the measurements in the case of anhydrous as well as hydrous -Mg₂SiO₄ and with other calculations on the anhydrous phase. All the third-order elastic constants of both the compounds are negative. The third-order elastic constant C₁₄₄(–52.41 and –45.07 GPa for anhydrous and hydrous -Mg₂SiO₄, respectively) representing the anisotropy of shear mode has a smaller value than C₁₁₁ (–2443.94 and –2101.25 GPa for anhydrous and hydrous phases, respectively), which corresponds to the longitudinal mode. The pressure-induced variations in the longitudinal elastic constants (i.e.,dC₁₁/dp) are relatively large (4.08 and 4.09 for dry and hydrous ringwoodite, respectively) compared with those for the shear (0.22 and 0.32 for dry and hydrous ringwoodite, respectively) and off-diagonal constants (1.40 and 1.41 for dry and hydrous ringwoodite, respectively). The variation of the shear moduli C_s and anisotropy factor A with pressure have also been studied. The average value of elastic anisotropy is 0.835 in the case of anhydrous -Mg₂SiO₄ and 0.830 in the hydrous phase. The reversal of sign of the Cauchy pressure C₁₂ – C₄₄, which describes the angular character of atomic bonding in metals and other compounds, at around 21 GPa for both the compounds may be a precursor to the phase transition from ringwoodite to periclase and perovskite at an elevated temperature. The aggregate elastic properties like the adiabatic bulk modulus K (175.4 and 150.2 GPa for anhydrous and hydrous phases, respectively), and the isotropic compressional (P) and shear (S) wave velocities were calculated and the mode Grüneisen Parameters (GPs) of the acoustic waves were determined based on the quasi-harmonic approximation. The low temperature limit of both hydrous and anhydrous phases of -Mg₂SiO₄ are positive (1.69 and 1.78, respectively, for hydrous and anhydrous phases) and hence we expect the thermal expansion to be positive down to absolute zero. The Anderson–Grüneisen parameter obtained for hydrous as well as anhydrous phases of -Mg₂SiO₄ from the second-order and third-order elastic constants are 2.30 and 2.29, respectively.     

Single crystal hydrostatic compression of (Mg,Mn,Fe,Co)2SiO4 olivines

Four synthetic endmember olivines (Mg,Mn, Fe,Co)₂SiO₄ with space group Pbnm were loaded together in one diamond cell mount. Their unit-cell parameters were determined by single crystal X-ray diffraction to 10 GPa. The linear compressibilities β_a, β_b, β_c were 1.53, 2.90, 2.32; 1.45, 3.48, 1.98; 1.35, 3.29, 1.76; and 1.25, 2.82, 2.01×10⁻³ GPa⁻¹ for Mg₂SiO₄, Mn₂SiO₄, Fe₂SiO₄ and Co₂SiO₄, respectively. The b axis is the most compressible direction in all crystals studied. Bulk modulus K_T0 and its first pressure derivative were simultaneously determined for Mg₂SiO₄, Fe₂SiO₄ and Co₂SiO₄ crystals respectively by fitting volume data to a third order Birch-Murnaghan equation of state. They are 127(4) and 4.2(8), 136(3) and 4.1(7), and 144(2) and 4.1(5). The K_T0 and could not simultaneously be determined unambiguously for Mn₂SiO₄. Direct comparisons of unit-cell volumes at high pressure among pairs of olivines reveal anomalous compression behavior of the Mg₂SiO₄ crystal regarding the bulk modulus-volume relationship. This behavior, however, could not be observed in the transition metal olivines (Mn,Fe,Co)₂SiO₄. The distinct electronic configurations of Mg²⁺ and the transition metal cations Mn²⁺, Fe²⁺, and Co²⁺ result in the different compression behaviors of Mg₂SiO₄ and (Mn,Fe,Co)₂SiO₄. Received: 14 April 1997 / Revised, accepted: 29 July 1997