Our ability to determine the density (specific volume) as a function of pressure and temperature has drastically improved in the last several decades, with the combination of synchrotron X-ray diffraction and high-pressure techniques such as laser-heated diamond-anvil cell and large-volume multi-anvil press. The improvements are in both pressure–temperature range and data quality, and obtaining high-resolution 2D angle-dispersive diffraction data at over a megabar pressure and above 2,500 K is now routine. In parallel, dynamic compression techniques, such as laser-driven shock wave and magnetically accelerated flyer plate-impact experiments, have provided new ways to measure density at extreme conditions. The combination of static and dynamic compression data allows us to examine internal consistency in pressure determination and establish reliable pressure scales. Internally consistent pressure scales for several pressure standards are emerging through extensive comparison of compression data over a large pressure range and simultaneous measurements of elasticity and density. A concerted effort is needed to further expand and improve measurements under simultaneous high pressure and temperature, particularly at temperatures above 2,500 K, in order to accurately model the thermal pressure. To decipher the compositions of the Earth’s interior based on density observations from seismology requires high accuracy in measuring the subtle compositional effects on the density of mantle and core materials. For a universal understanding of the thermal equations of state of solids, the emphasis should be on reconciling the static and dynamic data of well-studied materials that have substantial overlap in pressure–temperature ranges.

Multi-anvil press (MAP) is a major type of apparatus for phase equilibrium, material synthesis, and property investigations at up to 120 GPa of static compression. Here I summarize the fundamental aspects of the MAP techniques, highlighting uncertainties in pressure and temperature in experiments using tungsten carbide (WC) anvils with 3 mm and 5 mm truncation edge lengths (TEL). To illustrate the application of the MAP for synthesizing millimeter-sized single crystals of deep mantle silicates, I review the theory of crystal growth and compile relevant phase diagrams. The theory informs synthesis methods such as slow cooling of a fluid solution and growing crystals in a thermal gradient. The updated phase diagrams involve Mg2SiO4, MgSiO3, and H2O at pressures up to 27 GPa and touch upon iron-bearing compositions. Also reviewed briefly are techniques to characterize the compositions and structures of synthesis products.

The combination of double-sided laser heating in the diamond anvil cell and detailed chemical analysis of the recovered samples is a promising approach to explore the chemistry of the Earth’s deep interior from the lower mantle to the core. Routine recovery of laser-heated samples coupled with chemical and textural characterization at the submicron scale is the key to expand knowledge of chemical interactions and melting at extreme conditions, particularly in complex systems. Recent technical developments have allowed us to investigate element partitioning and melting relations at pressures approaching the Earth’s inner-core boundary. In this chapter, we review the techniques used for recovering tiny laser-heated samples and analyzing their chemical compositions and quenched textures, while highlighting key experiments that address silicate–metal element partitioning during mantle–core differentiation, silicate melting relations with applications to early magma ocean crystallization and deep mantle melting, and melting relations in iron-alloy systems relevant to the core. The results have drastically expanded our understanding of element redistribution at deep chemical boundaries and the chemical evolution of the deep mantle and the inner core. Finally, we emphasize the need for standardized protocols to obtain consistent, reproducible results and streamlined procedures to promote good practice and increase productivity. A broad collaboration with a systematic approach would further advance the field of high-pressure geochemistry.

Multi-anvil press (MAP) is a major type of apparatus for phase equilibrium, material synthesis, and property investigations at up to 120 GPa of static compression. Here I summarize the fundamental aspects of the MAP techniques, highlighting uncertainties in pressure and temperature in experiments using tungsten carbide (WC) anvils with 3 mm and 5 mm truncation edge lengths (TEL). To illustrate the application of the MAP for synthesizing millimeter-sized single crystals of deep mantle silicates, I review the theory of crystal growth and compile relevant phase diagrams. The theory informs synthesis methods such as slow cooling of a fluid solution and growing crystals in a thermal gradient. The updated phase diagrams involve Mg2SiO4, MgSiO3, and H2O at pressures up to 27 GPa and touch upon iron-bearing compositions. Also reviewed briefly are techniques to characterize the compositions and structures of synthesis products.

Fundamental data on planetary materials under extreme conditions are required to establish physics-based models of planetary interiors and impact events. Dynamic compression experiments provide a means of studying material properties under the conditions of planetary interiors. Experimental shock wave studies also present a unique capability to study impact phenomena in real time, providing insight into hypervelocity collisions relevant to planetary formation and evolution. Recent experimental developments have extended the types of measurements that are possible during the nanosecond to microsecond duration of shock experiments – opening entirely new lines of inquiry. New facilities that couple dynamic compression platforms with high-flux X-ray sources have allowed for in situ X-ray diffraction under dynamic loading. Such experiments can address a range of longstanding questions, including the following: What crystallographic phases are stable under what conditions? What is their thermoelastic behavior? When do they melt or vaporize? And what phases will form on release? Answers to these questions and others will provide input for next-generation models of the structure, dynamics, and evolution of planetary interiors as well and natural impact processes.

In honor of H. K. (David) Mao and our interactions over half a century, this chapter focuses on the techniques and application of calorimetry to high-pressure research. The chapter reviews thermodynamic concepts and calorimetric methodology. It summarizes a large body of work over many years, with emphasis on mantle mineralogy, and also discusses recent developments in a broader context, including calorimetric studies of hydrous phases, nonoxides, and nanophase materials.

This chapter reviews the tremendous progress over the past several decades in experimental research of molecular solids at high pressures. The interatomic interactions in these materials are greatly modified under pressure and generally strengthen intermolecular and weaken intramolecular bonds. This leads to the formation of structurally complex crystals and inclusion compounds at moderate pressures, where a variety of intermolecular bonds can exist. Pressing on, a great majority of molecular solids demonstrate transformations to extended (e.g., polymeric) states, which vary drastically in bonding and electronic properties. The most prominent example of such behavior is the symmetrization of hydrogen bonds in ionic ice X and metallization of hydrogen in monatomic solid. Dave Mao’s legacy in this research has been remarkable ranging from discovering and establishing the structure and properties of hydrogen clathrate hydrates at 200 MPa to investigating the structure of a mixed atomic-molecular phase IV of hydrogen at 260 GPa. New generations of scientists continue to use and build upon his technical developments, which have enabled multimegabar investigations of molecular solids, including diamond anvil cell (DAC) design, the DAC gas-loading system, and a variety of optical, electric, magnetic, and X-ray DAC probes.