How large are departures from lithostatic pressure? Constraints from host–inclusion elasticity

Abstract

Minerals trapped as inclusions within other host minerals will develop non-lithostatic pressures during both prograde and retrograde metamorphism because of the differences between the thermo-elastic properties of the host and inclusion phases. There is only a single possible path in P-T space, the entrapment isomeke, along which no residual pressure would be developed in a host/inclusion system; non-lithostatic pressures are developed in inclusions as a result of the external pressure and temperature deviating from the isomeke that passes through the entrapment conditions. With modern equation of state and elasticity data for minerals now available it is possible to perform precise calculations of the isomekes for mineral pairs. These show that isomeke lines are not straight lines in P-T space at metamorphic conditions. We show that silicate inclusions in silicate hosts tend to have flat isomekes, with small values of dP/dT(isomeke), because of the small range of thermal expansion coefficients of silicate minerals. As a consequence, the general behaviour under decompression is for soft silicate inclusions in stiffer hosts to develop excess pressures, whereas a stiff silicate inclusion in a softer matrix will experience lower pressures than lithostatic pressure. The opposite effects occur for compression after entrapment on the prograde path. The excess pressures in inclusions, including allowance for mutual elastic relaxation of the host and inclusion, are most easily calculated by using the isomeke as a basis. Analysis of the simplest possible model of a host-inclusion system indicates that deviations from lithostatic pressure in excess of 1 GPa can be readily produced in quartz inclusions within garnets in metamorphic rocks. For softer host minerals such as feldspars the pressure deviations are smaller, because of greater elastic relaxation of the host. The maximum pressure deviation from lithostatic pressure in the host phase around the inclusion is one-third of the pressure deviation in the inclusion. Routines for performing these calculations have been added to the EosFit7c software package

Toward a Robust Elastic Geobarometry of Kyanite Inclusions in Eclogitic Diamonds

“…The proximity of this garnet to the external surface of the diamond, which would affect the P inc , cannot be invoked as the garnet was located deep within the diamond host. An alternative explanation is that the garnet was entrapped at relatively high temperatures, that is, along an isomeke passing close to P inc = 0 at room conditions (see Figure 3b in Angel, Nimis, et al, ). Some of these possible explanations might also account for some previously reported garnet inclusions in diamonds, for which P inc ranges from zero (Liu et al, ) to values of about 0.3–0.7 GPa (see, e.g., Harris et al, ; Küter et al, ).…”

“…The procedure to calculate the depth of formation using elastic geobarometry is described in detail in a number of publications; the first approaches were detailed in Rosenfeld and Chase () and Adams et al (, ), followed by more recent publications by, for example, Zhang (), Angel, Gonzalez‐Platas, & Alvaro (), Angel, Alvaro, et al (), Angel, Nimis, et al (), and the introduction of software EosFit7c and EosFit‐P inc by Angel, Nimis, et al () and Angel, Alvaro, & Nestola (). All these works are based on the concept of the isomeke.…”

“…Due to the complexity of the calculations, all of the above studies used a number of simplified assumptions, such as spherical inclusion geometry, isotropic elastic properties and, in most cases, hydrostatic conditions and linear elasticity. In fact, practical methods that avoid the assumption of linear elasticity and explicitly take into account geometric effects have only recently been developed (Angel, Gonzalez‐Platas, & Alvaro, ; Angel, Alvaro, et al, ; Angel, Nimis, et al, ; Mazzucchelli et al, ). In particular, Mazzucchelli et al () showed that neglecting the effect of the inclusion shape on P inc (as done in all previous studies) may severely bias the geobarometric results.…”

The effect of type-B carbonate content on the elasticity of fluorapatite

“…This has to be considered when elasticity of apatite is used for pressure determination like apatite-ingarnet barometer used by Ashley et al (2017) because as discussed by Angel et al (2015) the anisotropic behavior of the inclusion can modify the elastic response of the inclusion. In fact, the anisotropy could be treated as a deviatoric effect relative to the isotropic case (Angel et al 2015).…”

Spectroscopic study of inclusions in gem corundum from Mercaderes, Cauca, Colombia

“…Rather, a radial stress and two tangential stresses are developed, even if both inclusion mineral and host mineral are elastically isotropic (Zhang 1998;Angel et al 2015). As a consequence, the pressure (equal to the average of the three normal stresses) in the host can never match the pressure in the inclusion.…”