Copper has been considered as a common pressure calibrant and equation of state (EOS) and shock wave (SW) standard, because of the abundance of its highly accurate EOS and SW data, and the assumption that Cu is a simple one-phase material that does not exhibit high pressure (P) or high temperature (T) polymorphism. However, in 2014, Bolesta and Fomin detected another solid phase in molecular dynamics simulations of the shock compression of Cu, and in 2017 published the phase diagram of Cu having two solid phases, the ambient face-centered cubic (fcc) and the high-$PT$ body-centered cubic (bcc) ones. Very recently, bcc-Cu has been detected in SW experiments, and a more sophisticated phase diagram of Cu with the two solid phases was published by Smirnov. In this work, using a suite of ab initio quantum molecular dynamics (QMD) simulations based on the Z methodology, which combines both direct Z method for the simulation of melting curves and inverse Z method for the calculation of solid–solid phase boundaries, we refine the phase diagram of Smirnov. We calculate the melting curves of both fcc-Cu and bcc-Cu and obtain an equation for the fcc-bcc solid–solid phase transition boundary. We also obtain the thermal EOS of Cu, which is in agreement with experimental data and QMD simulations. We argue that, despite being a polymorphic rather than a simple one-phase material, copper remains a reliable pressure calibrant and EOS and SW standard.

We demonstrate the topological equivalence of the phase diagrams of molybdenum (Mo) and tungsten (W), Group 6B partners in the periodic table. The phase digram of Mo to 800 GPa from our earlier work is now extended to 2000 GPa. The phase diagram of W to 2500 GPa is obtained using a comprehensive ab initio approach that includes (i) the calculation of the $T=0$ free energies (enthalpies) of different solid structures, (ii) the quantum molecular dynamics simulation of the melting curves of different solid structures, (iii) the derivation of the analytic form for the solid–solid phase transition boundary, and (iv) the simulations of the solidification of liquid W into the final solid states on both sides of the solid–solid phase transition boundary in order to confirm the corresponding analytic form. For both Mo and W, there are two solid structures confirmed to be present on their phase diagrams, the ambient body-centered cubic (bcc) and the high-pressure double hexagonal close-packed (dhcp), such that at $T=0$ the bcc–dhcp transition occurs at 660 GPa in Mo and 1060 GPa in W. In either case, the transition boundary has a positive slope $dT/dP.$

Silver has been considered as one of the simple one-phase materials that do not exhibit high pressure or high temperature polymorphism. The solid phase of Ag at ambient conditions is face-centered cubic (fcc) one. However, very recently another solid phase of silver, body-centered cubic (bcc) one, was detected in shock-wave (SW) experiments, and a more sophisticated phase diagram of Ag with the two solid phases was published by Smirnov. In this work, using a suite of ab initio quantum molecular dynamics (QMD) simulations based on the Z methodology which combines both direct Z method for the simulation of melting curves and inverse Z method for the calculation of solid–solid phase boundaries, we refine the phase diagram of Smirnov. We calculate the melting curves of both fcc-Ag and bcc-Ag and obtain an equation for the fcc–bcc solid–solid phase transition boundary. We also obtain the thermal equation of state of Ag which is in agreement with experimental data and QMD simulations. We argue that, despite being a polymorphic rather than a simple one-phase material, silver can be considered as an SW standard.

Palladium is one of the most important technological materials, yet its phase diagram remains poorly understood. At ambient conditions, its solid phase is face-centered cubic (fcc). However, another solid phase of Pd, body-centered cubic (bcc), was very recently predicted in two independent theoretical studies to occur at high pressures and temperatures. In this work, we report an experimental study on the room-temperature equation of state (EOS) of Pd to a pressure of 80 GPa, as well as a theoretical study on the phase diagram of Pd including both fcc-Pd and bcc-Pd. Our theoretical approach consists in ab initio quantum molecular dynamics (QMD) simulations based on the Z methodology which combines both direct Z method for the simulation of melting curves and inverse Z method for the calculation of solid–solid phase transition boundaries. We obtain the melting curves of both fcc-Pd and bcc-Pd and an equation for the fcc–bcc solid–solid phase transition boundary as well as the thermal EOS of Pd which is in agreement with experimental data and QMD simulations. We uncover the presence of another solid phase of Pd on its phase diagram, namely, random hexagonal close-packed (rhcp), and estimate the location of the rhcp-bcc solid–solid phase transition boundary and the rhcp–fcc–bcc triple point. We also discuss the topological similarity of the phase diagrams of palladium and silver, the neighbor of Pd in the periodic table. We argue that Pd is a reliable standard for shock-compression studies and present the analytic model of its principal Hugoniot in a wide pressure range.

Chromium possesses remarkable physical properties such as hardness and corrosion resistance. Chromium is also a very important geophysical material as it is assumed that lighter Cr isotopes were dissolved in the Earth’s molten core during the planet’s formation, which makes Cr one of the main constituents of the Earth’s core. Unfortunately, Cr has remained one of the least studied $3d$ transition metals. In a very recent combined experimental and theoretical study (Anzellini et al., Scientific Reports, 2022), the equation of state and melting curve of chromium were studied to 150 GPa, and it was determined that the ambient body-centered cubic (bcc) phase of crystalline Cr remains stable in the whole pressure range considered. However, the importance of the knowledge of the physical properties of Cr, specifically its phase diagram, necessitates further study of Cr to higher pressure. In this work, using a suite of ab initio quantum molecular dynamics (QMD) simulations based on the Z methodology which combines both direct Z method for the simulation of melting curves and inverse Z method for the calculation of solid–solid phase transition boundaries, we obtain the theoretical phase diagram of Cr to 2.5 TPa. We calculate the melting curves of the two solid phases that are present on its phase diagram, namely, the lower-pressure bcc and the higher-pressure hexagonal close-packed (hcp) ones, and obtain the equation for the bcc-hcp solid–solid phase transition boundary. We also obtain the thermal equations of state of both bcc-Cr and hcp-Cr, which are in excellent agreement with both experimental data and QMD simulations. We argue that 2180 K as the value of the ambient melting point of Cr which is offered by several public web resources (“Wikipedia,” “WebElements,” “It’s Elemental,” etc.) is most likely incorrect and should be replaced with 2135 K, found in most experimental studies as well as in the present theoretical work.

The lockdown policies enacted in the spring of 2020, in response to the growing severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic, have remained a contentious policy tool due to the variability of outcomes they produced for some populations. While ongoing research has illustrated the unequal impact of Coronavirus disease (COVID-19) on minority populations, research in this area has been unable to fully explain the mechanisms that produce these findings. To understand why some groups have been at greater risk of contracting COVID-19, we employ structural inequality theory to better understand how inequality may impact disease transmission in a pandemic. We used a novel approach that enabled us to focus on the microprocesses of structural inequality at the zip code level to study the impact of stay-at-home pandemic policies on COVID-19 positive case rates in an urban setting across three periods of policy implementation. We then analyzed data on traffic volume, income, race, occupation, and instances of COVID-19 positive cases for each zip code in Salt Lake County, Utah (USA) between 17 February 2020 and 12 June 2020. We found that higher income, percent white, and white-collar zip codes had a greater response to the local stay-at-home order and reduced vehicular traffic by nearly 50% during lockdown. The least affluent zip codes only showed a 15% traffic decrease and had COVID-19 rates nearly 10 times higher. At this level of granularity, income and occupation were both associated with COVID-19 outcomes across all three stages of policy implementation, while race was only predictive of outcomes after the lockdown period. Our findings illuminate underlying mechanisms of structural inequality that may have facilitated unequal COVID-19 incidence rates. This study illustrates the need for more granular analyses in policy research and adds to the literature on how structural factors such as income, race, and occupation contribute to disease transmission in a pandemic.