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In this work, the Common Model of Multi-phase Strength and Equation of State (CMMP) model was applied to tin. Specifically, calibrations of the strength-specific elements of the CMMP foundation were developed with a combination of experiments and theory, and then the model was validated experimentally. The first element of the foundation is a multi-phase analytic treatment of the melt temperature and the shear modulus for the solid phases. These models were parameterized for each phase based on ab initio calculations using the software VASP (Vienna Ab initio Simulations Package) based on density functional theory. The shear modulus model for the ambient β phase was validated with ultrasonic sound speed measurements as a function of pressure and temperature. The second element of the foundation is a viscoplastic strength model for the β phase, upon which strength for inaccessible higher-pressure phases can be scaled as necessary. The stress–strain response of tin was measured at strain rates of 10 − 3 to 3 × 10 3 s − 1 and temperatures ranging from 87 to 373 K. The Preston–Tonks–Wallace (PTW) strength model was fit to that data using Bayesian model calibration. For validation, six forward and two reverse Taylor impact experiments were performed at different velocities to measure large plastic deformation of tin at strain rates up to 10 5 s − 1 . The PTW model accurately predicted the deformed shapes of the cylinders, with modest discrepancies attributed to the inability of PTW to capture the effects of twinning and dynamic recrystallization. Some material in the simulations of higher velocity Taylor cylinders reached the melting temperature, thus testing the multiphase model because of the presence of a second phase, the liquid. In simulations using a traditional modeling approach, the abrupt reduction of strength upon melt resulted in poor predictions of the deformed shape and non-physical temperatures. With CMMP, the most deformed material points evolved gradually to a mixed solid–liquid but never a fully liquid state, never fully lost strength, stayed at the melt temperature as the latent heat of fusion was absorbed, and predicted the deformed shape well. [ABSTRACT FROM AUTHOR]

Control of oxygen fugacity during high-temperature phase equilibrium experiments is required to simulate the conditions that exist in natural systems. At high pressures, oxygen fugacity may be imposed using solid buffer equilibria via the classic "double capsule" technique. This design becomes untenable, however, at temperatures above the melting points of commonly used noble metal capsule materials and/or where buffer assemblages may alloy with the capsule or contaminate the sample. Here we introduce and test a modified double capsule approach that includes a solid metal-oxide buffer in close proximity to but separate from the sample of interest. Buffers used include (in order of most oxidized to reduced) Ni-NiO, Co-CoO, W-WO3, Fe-FeO, Mo-MoO2, Cr-Cr2O3, V-V2O3, Ta-Ta2O5, and Nb-NbO. At a fixed temperature, these buffers span a wide range—up to 10 log fO2 units. To demonstrate the buffering capacity of this double capsule approach, secondary redox equilibria and V-doped CaO-MgO-Al2O3-SiO2 system glasses were studied in experiments using the double capsule geometry. The secondary equilibria provide an independent verification of the oxygen fugacity established in the double capsule environment. The glasses proved difficult to interpret, and our results provide guidance to future efforts to utilize the glass oxybarometer at reducing conditions. Application of this modified double capsule technique to studies of V valence in MgAl2O4 spinels led to the recognition of several factors that will affect V valence in this system: temperature of equilibration, duration of experiment, and spinel bulk composition. We have synthesized V-bearing MgAl2O4 spinel at the reduced conditions of the Cr-Cr2O3, (IW-3.51), Ta-Ta2O5, (IW-5.37), and Nb-NbO buffers (IW-5.44). This spinel exhibits a very small V3+ pre-edge peak consistent with its reduced nature. The absence of evidence for V2+ suggests that MgAl2O4 spinel excludes V2+ due to the preference of V for octahedral sites. This finding is supported by DFT calculations for spinels of variable composition, and in agreement with some other indirect evidence for preference for V3+ in aluminous spinels (Bosi et al. 2016,; Paque et al. 2013,). [ABSTRACT FROM AUTHOR]