Phase stability of carbon, oxygen and carbon dioxide under extreme P-T conditions, beyond the harmonic approximation

Abstract

Daily, we can observe how pressure and temperature have a profound e ect on matter. For instance, at ambient pressure water transforms into vapor when heated to 100 °C, and becomes ice when cooled to temperatures below 0 °C. Nonetheless, these transformations can also be achieved starting from the liquid state by reducing or increasing pressure to reach the vapor o solid state, respectively. We can study the phase transitions by minimizing the Gibbs free energy: G = U ð€€€ ST + pV (0.1) Where U holds for the internal energy, S for the entropy, and V for the volume of the piece of matter under study. According to this expression, solid phases are favored at low temperatures and/or at high pressures, while at opposite conditions gas phases are favored. Liquids are favored at intermediate regimes. Oxygen is a highly reactive nonmetal and an oxidizing agent that easily forms mixtures with most elements and several other compounds. By mass-fraction, oxygen is the third-most abundant element in the universe, after hydrogen and helium. At ambient conditions, oxygen is a colorless and odorless gas with the molecular formula O2, where two oxygen atoms are chemically bound to each other with a covalent double bond. At atmospheric pressure and low temperature (below 54.36 K), solid oxygen is formed. Solid oxygen is particularly interesting because it is the only simple diatomic molecule to carry a magnetic moment, and it is considered a \spin-controlled" crystal that displays antiferromagnetic order in the low-temperature phases. At high pressure, solid oxygen transforms from an insulating to a metallic state; and at very low temperatures, it even changes into a superconducting state. Referred to as the \king of the elements", carbon is a nonmetallic and tetravalent element, that is also the fourth most abundant element in the universe by mass. Because of the four electrons available to form covalent bonds, the atoms of carbon can bond 1 together in diverse ways, resulting in various allotropes of this element, being the bestknown graphite and diamond. This element has attracted attention because of the system of carbon allotropes spans a range of extremes, i.e., graphite is one of the softest materials known, it is opaque and a good conductor of electricity, while diamond is the hardest naturally occurring substance, it is highly transparent and is an excellent electrical insulator. At elevated temperatures, carbon reacts with oxygen to form oxocarbons or carbon oxides. The simplest and most common oxocarbons are carbon monoxide (CO) and carbon dioxide (CO2). Carbon dioxide consists of a carbon atom covalently double bonded to two oxygen atoms. CO2 is characterized by strong double bonds (C=O distance of 1.16 A ) and rather weak intermolecular interactions, which has made it a very stable system that exhibits several molecular phases before its polymerization. Also at high pressures, another form of solid carbon dioxide is observed: an amorphous glass-like solid named carbonia, that can be produced by supercooling heated CO2 at pressures above 40 GPa. Although this discovery con rmed that carbon dioxide could exist in a glass state similar to other members of its elemental family, like silicon (silica glass) and germanium dioxide, carbonia glass is not stable at normal pressures and reverts to gas when pressure is released. Given their importance for life as we know it, carbon and oxygen have been extensively studied at pressures and temperatures found on the surface of the Earth. Nevertheless, despite their simplicity, they exhibit remarkable properties. Their abundance in the universe justi es the attention of the scienti c community and explains the constant study of these two elements under extreme conditions. In order to study materials at extreme conditions, i.e., those similar at the interior of planets, experimentalists have designed apparatuses that apply force to a small area where the sample is con ned. The diamond anvil cell (DAC) is the most commonly used device and state of the art DACs are able to reach pressures up to 600 GPa, but experiments at these extreme pressures are very challenging. Laser shock-wave experiments are able to reach he terapascal regime for a limited short time. However, along with very high pressures, temperatures of several thousand Kelvin are also achieved, altering the sample's state and making challenging the study of solids at extreme conditions, from the experimental point of view. The technical di culty and high economical cost of high pressure experiments make theoretical approaches specially necessary. Fortunately, theoretical