Model for the Solid–Liquid Interfacial Free Energy at High Pressures

Abstract

The free energy involved in the formation of an interface between two phases (e.g., a solid−liquid interface) is referred to as the interfacial free energy. For the case of solidification, the interfacial free energy dictates the height of the energy barrier required to nucleate stable clusters of the newly forming solid phase and is essential for producing an accurate solidification kinetics model using classical nucleation theory (CNT)-based methods. While various methods have been proposed for modeling the interfacial free energy for solid−liquid interfaces in prior literature, many of these formulations involve making restrictive assumptions or approximations, such as the system being at or near equilibrium (i.e., the system temperature is approximately equal to the melt temperature) or that the system is at pressures close to atmospheric. However, these approximations and assumptions may break down in highly non-equilibrium situations, such as in dynamic-compression experiments where metastable liquids that are undercooled by hundreds of kelvin or overpressurized by several gigapascals or more are formed before eventually solidifying. We derive a solid−liquid interfacial free-energy model for such high-pressure conditions by considering the enthalpies of interactions between pairs of atoms or molecules. We also consider the contribution of interface roughness (disordering) by incorporating a multilayer interface model known as the Temkin n-layer model. Our formulation is applicable to a diverse variety of materials, and we demonstrate it by developing models specifically for two different materials: water and gallium. We apply our interfacial free-energy formulation to CNT-based kinetics simulations of several suites of dynamic-compression experiments that cause liquid water to solidify to the high-pressure solid polymorph ice VII and have found good agreement to the observed kinetics with only minor empirical fitting.

Interfacial Effects during Phase Change in Multiple Levitated Tetrahydrofuran Hydrate Droplets

“…When ice impacts the local water film, it acts as a template for the hydrate structure and provides energy for hydrate nucleation . At the ice–water interface, hydrogen bonding between ice and liquid water could lower the potential energy of interfacial water molecules that are part of the local solution phase, causing a transition layer of “mediator cages” or cage-like structural fluctuations to develop. , The transition layer has a lower surface free energy than the ice–liquid interface, promoting the formation of amorphous nuclei that grow and evolve into complete THF hydrate cages. − This initial clathrate coating at the new ice-THF hydrate interface then grows perpendicular to that interface into the droplet . Note that this does not mean that a significant portion of the droplet (i.e., what is visible in the nucleation frames of Figure ) is made of ice.…”

“…35,36 The transition layer has a lower surface free energy than the ice-liquid interface, promoting the formation of amorphous nuclei that grow and evolve into complete THF hydrate cages. [35][36][37] This initial clathrate coating at the new ice-THF hydrate interface then grows perpendicular to that interface into the droplet. 35 Note that this does not mean that a significant portion of the droplet (i.e., what is visible in the nucleation frames of Figure 2) is made of ice.…”

Real-time latent heat emission during dynamic-compression freezing of water

“…That transition is characterized by contraction in particle-velocity measurements [4][5][6][7] , loss of optical transparency 8 , and x-ray diffraction patterns consistent with the ice VII phase 9 . Dynamic compression experiments allow both the metastable liquid and kinetic behavior to be investigated, which has huge implications for our general understanding of phase transitions and the classical nucleation theory (CNT) used to model transformations in extreme conditions [10][11][12][13] .…”

“…Temperatures below that threshold are said to be hypercooled because latent heat emission does not bring the liquid back to the melt line and solid nuclei can grow without the need for latent heat to diffuse away from the solid-liquid interface. Hypercooling has been used to describe extremely fast growth rates measured in dynamic compression experiments on water over the past decade 2,7 , and incorporated into a dualtemperature CNT-based kinetic model used to describe phase changes in both water and gallium in extreme conditions [10][11][12][13] .…”