Elastic properties of sodium‐rich majorite garnet

Abstract

The adiabatic elastic moduli of a high‐pressure sodium‐rich majorite garnet have been measured at ambient conditions using Brillouin spectroscopy. This garnet has the composition, Na1.87Mg1.18Si4.94O12, with sodium and magnesium in eight‐fold coordination and silicon in octahedral and tetrahedral coordination. While the adiabatic bulk modulus, Ks = 173.5 GPa, falls within the range of common garnets, the shear modulus, μ = 114.7 GPa, is unusually large; sodium garnet is elastically similar to the low‐pressure garnet grossular. The variation of elastic properties for garnets of differing composition within the cubic garnet structure can be expressed as a linear function of the ratio of average cation radii in the eight‐fold versus the six‐fold site. The cations in the AO8 polyhedra apparently brace the structure by controlling rotational freedom within corner‐linked chains of alternating tetrahedra and octahedra.

Crystal structure and Raman spectrum of a high-pressure Li-rich majoritic garnet, (Li2Mg)Si2(SiO4)3

“…Using these equations and the effective ionic radii from Shannon (1976) (5). Surprisingly, the estimated a dimension of 11.533 Å for NaMGt is substantially greater than the value of 11.408(2) Å measured by Pacalo et al (1992) or 11.410(1) Å by Hazen et al (1994b). The reason for this is unclear.…”

“…Zhang et al (1998) further pointed out that the ϕ angle in silicate garnets is probably restrained if the Y site is occupied by cations of high valence state, leading to a relatively stiff framework. The high bulk modulus (174)(175)(176)(177)(178)(179)(180)(181)(182)(183)(184)(185)(186)(187)(188)(189)(190)(191)(192) of NaMGt (Pacalo et al 1992;Hazen et al 1994b) appears to support this mechanism for garnet compression. Then, providing that silicate garnets obey Bridgman's law, which correlates bulk modulus inversely with ambient unit-cell volume for isostructural materials (Anderson and Anderson 1970;Hazen et al 1994b), LiMGt, which has the smallest unit-cell volume of all known silicate garnets, should have a bulk modulus that is significantly greater than that for NaMGt.…”

“…Intriguingly, a Na-rich majoritic garnet (NaMGt), (Na 2 Mg)Si 2 (SiO 4 ) 3 , has been synthesized above 15 GPa and 1600 °C (Gasparik 1989;Pacalo et al 1992;Bobrov et al 2008). The discovery of NaMGt not only confirms the mechanism of Na incorporation into majoritic garnet through the pressure-dependent exchange reaction Na + + Si 4+ ↔ M 2+ + Al 3+ (Ringwood and Major 1971), but also suggests that Na concentrations may be used to estimate the formation pressure/ depth of Na-bearing garnets.…”

Thermal equation of state of majoritic knorringite and its significance for continental upper mantle

“… Assumed. 1—[ Gwanmesia et al ., ]; 2—[ Sinogeikin and Bass , ]; 3—[ Wang et al ., ]; 4—[ Stixrude and Lithgow‐Bertelloni , and references there in]; 5—[ Fan et al ., ]; 6—[ Gréaux et al ., ]; 7—[ Gwanmesia et al ., ]; 8—[ Dymshits et al ., ]; 9—[ Pacalo et al ., ]; 10—this study; 11—same as majorite, more explanations in the text. Densities of all phases were calculated from the volume.…”

Majoritic garnet: A new approach to pressure estimation of shock events in meteorites and the encapsulation of sub-lithospheric inclusions in diamond

“…In the latter instance, the substitution of sodium into the structure is intimately tied to both Ti and/or Si substitution into the octahedral site: therefore, this component incorporates a coupling between the classic majorite substitution and sodium/alkali substitution into garnets. Indeed, while the majorite substitution is typically formulated as M 3 Al 2À2x M x Si x (Si 3 O 12 ) where M represents divalent cations and x is the mole fraction of majorite, garnets that have the formula A 2 1+ MSi 2 (Si 3 O 12 ) have been observed, where A is an alkali element (e.g., Pacalo et al, 1992;Bobrov et al, 2008;Yang et al, 2009). The resultant garnet can be termed hypersilicic and, as described below, we find the incorporation of a sodium/alkali component to be more compatible with the compositional patterns that we observe within suites of natural majoritic garnets.…”