The phase boundary between spinel (gamma phase) and MgSiO3 perovskite + MgO periclase in Mg2SiO4 was determined by in situ x-ray measurements by a combination of the synchrotron radiation source (SPring-8) and a large multianvil high-pressure apparatus. The boundary was determined at temperatures between 1400 degrees to 1800 degreesC, demonstrating that the postspinel phase boundary has a negative Clapeyron slope as estimated by quench experiments and thermodynamic analyses. The boundary was located at 21.1 (+/-0.2) gigapascals, at 1600 degreesC, which is approximately 2 gigapascals lower than earlier estimates based on other high-pressure studies.

Using multi-anvil high-pressure devices and synchrotron radiation, X-ray in situ observations of HfO 2 under high pressure and high temperature have been performed to investigate its phase relations and compression behavior. An orthorhombic phase (orthoI) is stable from 4 to 14.5 GPa below 1250°-1400°C and transforms to a tetragonal phase, which is one of the high-temperature forms of HfO 2 , above these temperatures. Another orthorhombic phase (orthoII) with a cotunnitetype structure appears above 14.5 GPa. OrthoII is stable up to 1800°C at 21 GPa. OrthoII is quenchable to ambient conditions. The orthoI-to-orthoII transition is accompanied by ϳ8 vol% decrease. The bulk moduli of orthoI and orthoII at room temperature are 220 and 312 GPa, respectively. This low compressibility of orthoII indicates that it is a potential candidate for very hard materials.

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We generalize the notion of "ground states" in the Pirogov-Sinai theory of first order phase transitions at low temperatures, applicable to lattice systems with a finite number of periodic ground states to that of "restricted ensembles" with equal free energies. A restricted ensemble is a Gibbs ensemble, i.e. equilibrium probability measure, on a restricted set of configurations in the phase space of the system. When a restricted ensemble contains only one configuration it coincides with a ground state. In the more general case the entropy is also important.An example of a system we can treat by our methods is the g-state Potts model where we prove that for q sufficiently large there exists a temperature at which the system coexists in q + \ phases; ^-ordered phases are small modifications of the q perfectly ordered ground states and one disordered phase which is a modification of the restricted ensemble consisting of all "perfectly disordered" (neighboring sites must have different spins) configurations. The free energy thus consists entirely of energy in the first ^-restricted ensembles and of entropy in the last one.Our main motivation for this work is to develop a rigorous theory for phase transitions in continuum fluids in which there is no symmetry between the phases, e.g. the liquid-vapour phase transition. The present work goes a certain way in that direction.

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Molecular dynamics simulations of single water, water-methanol, or water-IPA (isopropyl-alcohol) mixture droplets on a solid surface were performed with various mixture ratios. An increase in alcohol fraction generally gave an increase in droplet wettability. Both methanol and IPA molecules showed a strong preference to gather at various interfaces, with methanol molecules also showing a tendency to diffuse into the droplet bulk. Specific interfacial tensions were investigated using quasi-one-dimensional simulation systems, and liquid-vapor and solid-liquid interfacial tensions were found to decrease greatly due to the presence of interfacial alcohol, while solid-vapor interfacial tensions were proved to have little influence on wettability. Young's relation was found to hold quantitatively well for both water-methanol and water-IPA droplets. The validity of using Bakker's equation on solid-liquid interfaces was also investigated, and it was shown that for tightly spaced crystal surfaces, the introduced uncertainly is small.