Mattia Luca Mazzucchelli

Geobarometry from host-inclusion systems: The role of elastic relaxation

Abstract Minerals trapped as inclusions within other host minerals can develop residual stresses on exhumation as a result of the differences between the thermo-elastic properties of the host and inclusion phases. The determination of possible entrapment pressures and temperatures from this residual stress requires the mutual elastic relaxation of the host and inclusion to be determined. Previous estimates of this relaxation have relied on the assumption of linear elasticity theory. We present a new formulation of the problem that avoids this assumption. We show that for soft inclusions such as quartz in relatively stiff host materials such as garnet, the previous analysis yields entrapment pressures in error by the order of 0.1 GPa. The error is larger for hosts that have smaller shear moduli than garnet.

EosFit-Pinc: A simple GUI for host-inclusion elastic thermobarometry

Abstract Elastic geothermobarometry is a method of determining metamorphic conditions from the excess pressures exhibited by mineral inclusions trapped inside host minerals. An exact solution to the problem of combining non-linear Equations of State (EoS) with the elastic relaxation problem for elastically isotropic spherical host-inclusion systems without any approximations of linear elasticity is presented. The solution is encoded into a Windows GUI program EosFit-Pinc. The program performs host-inclusion calculations for spherical inclusions in elastically isotropic systems with full P-V-T EoS for both phases, with a wide variety of EoS types. The EoS values of any minerals can be loaded into the program for calculations. EosFit-Pinc calculates the isomeke of possible entrapment conditions from the pressure of an inclusion measured when the host is at any external pressure and temperature (including room conditions), and it can calculate final inclusion pressures from known entrapment conditions. It also calculates isomekes and isochors of the two phases.

Thermal expansion behaviour of orthopyroxenes: the role of the Fe-Mn substitution

Abstract Two Pbca orthopyroxene samples, donpeacorite (DP N.1) and enstatite (B22 N.60) with chemical formulae Mn0.54Ca0.03Mg1.43Si2O6 (XMn = 0.27) and Fe0.54Ca0.03Mg1.43Si2O6 (XFe = 0.27), respectively, were investigated by single-crystal X-ray diffraction at high-temperature conditions. The nearly identical XFe and XMn make the two samples the perfect candidates to investigate the effect of the compositional change at the M2 site (i.e. Fe-Mn substitution) on the thermal expansion behaviour of orthopyroxenes. Therefore, the unit-cell parameter thermal expansion behaviour of both samples has been investigated in the temperature range between room T and 1073 K. No evidence for phase transitions was found over that range. The two samples have been previously disordered with an ex situ annealing at ~1273 K. The unit-cell parameters and volume thermal expansion data, collected on the disordered samples, have been fitted to a Fei Equation of State (EoS) and the following coefficients obtained: V0 = 853.35(4) Å3, αV,303K = 2.31(24) × 10-5 K-1 and V0 = 845.40(6) Å3, aV,303K = 2.51(25) × 10-5 K-1 for DP N.1 and B22 N.60, respectively. While there is no difference in the volume thermal expansion coefficient as a function of composition and the expansion along the b direction is nearly identical for both samples, slight differences have been found along a and c lattice directions. The thermal expansion along the a direction is counterbalanced by that along c being responsible for the changes in lattice expansion scheme from αb > αc > αa at room T, to αc > αb > αa at high T. Therefore, as a result of the different behaviour along a and c, the unit-cell volume thermal expansion for both samples is identical within estimated standard deviations. The negligible effect of the Fe-Mn substitution on the bulk thermal expansion can be applied when dealing with geothermobarometry based on the elastic host-inclusion approach (e.g. Nestola et al., 2011; Howell et al., 2010; Angel et al., 2014a,b, 2015). In fact, though the compressibility effect is still not known, the nearly identical thermal expansion coefficients will not affect the entrapment pressure (Pe).

A new micro-furnace for in situ high-temperature single-crystal X-ray diffraction measurements

A new micro-furnace equipped with an H-shaped resistance heater has been developed to conduct in situ single-crystal X-ray diffraction experiments at high temperature. The compact design of the furnace does not restrict access to reciprocal space out to 2θ = 60°. Therefore, unit-cell parameters and intensity data can be determined to a resolution of 0.71 A with Mo radiation. The combined use of mineral phases with well characterized lattice expansion (e.g. pure Si and SiO2 quartz) and a small-diameter (0.025 mm) K-type thermocouple allowed accurate temperature calibration from room temperature to about 1273 K and consequent evaluation of thermal gradients and stability. The new furnace design allows temperatures up to about 1273 K to be reached with a thermal stability better than ±5 K even at the highest temperatures. Measurements of the lattice thermal expansion of pure silicon (Si), pure synthetic grossular garnet (Ca3Al2Si3O12) and quartz (SiO2) are presented to demonstrate the performance of the device. Its main advantages and limitations and important considerations for using it to perform high-temperature diffraction measurements are discussed.