Kostya Trachenko

1. The phonon theory of liquid thermodynamics
One of the triumphs of physics has been the theory of solid state developed at the beginning of the last century. This provided a fundamental understanding of the basic properties of solid matter such as the ability to absorb and transfer heat. Solid state theory was preceded by the theory of gases, which was equally successful in many respects. But when we turn to the third main phase of matter, the liquid phase, physics and modern textbooks remain silent about the most basic liquid properties such as heat capacity. Paradoxical though it may seem in this age of scientific and technological advancement, we still do not understand the most basic aspects of liquid behaviour. The combination of strong interactions with large atomic rearrangements has proved to be the ultimate obstacle to developing a theory of liquids. This was famously summarized by L. Landau as "liquids do not have a small parameter". Landau&Lifshitz textbook states that liquid energy and heat capacity can not be calculated in general form because interactions in a liquid are strong and system-specific ("Statistical Physics", Moskva, Nauka, 1964, first paragraph in Chapter 66, "Quantum liquid. Bose spectrum" and in Chapter 74, "Van der Waals formula"). This has become an accepted view. I have proposed that contrary to this statement and view, liquid energy and heat capacity can be calculated in more general form than previously thought.

L&L argument concerns the approach to liquids in which the interaction energy is calculated in addition to the gas kinetic energy, as an integral over interatomic potentials and correlations functions. This general approach formed the basis for previous theories of liquids. Apart from the problem of being system-specific as discussed by L&L, there are other important disadvantages of this approach: (a) interatomic potentials and correlations functions are not generally available, consequently, apart from very simple and exotic liquids such as those composed of nobel elements, it has not been possible to calculate liquid energy and heat capacity; (b) calculations become difficult beyond simple cases and approximations difficult to control; (c) it is not easy to see how the results are consistent with large experimental decrease of liquid heat capacity over a wide temperature range. On the other hand, in my solid-like phonon approach to liquids (a) the liquid energy does not depend on system-specific interatomic interactions and correlation functions but on viscosity only, and liquid viscosity is readily available however complex the liquid is in terms of structure and interactions. Importantly, in the context of L&L argument above, this result is more universal in a sense that liquids that are very different in terms of interatomic interactions and correlation functions can have the same viscosity at some temperature, and therefore the same energy in my approach; (b) the resulting equations are simple: the energy of a harmonic liquid is no more complicated than the energy of a harmonic solid; (c) the equations show good agreement with experimental results over a wide temperature range with no fitting parameters.

2. A new line on a phase diagram: the Frenkel line
According to current understanding, no differences can be made between a gas and a liquid above the critical point, an abrupt terminus of the liquid-gas coexisting line. Recently, we have discovered that this is not the case, and that the phase diagram of matter should be modified. We have proposed that a new line ("Frenkel line") exists on the phase diagram above the critical point at arbitrarily high pressure and temperature, and which separates two physically distinct states of matter. Crossing the line corresponds to qualitative changes of the key physical properties of the system, including viscosity, diffusion, thermal conductivity and speed of sound.

3. The problem of glass transition

The problem of glass transition is considered as one of the deepest and most interesting challenges in physics. The problem consists of two parts, dynamic and thermodynamic. The thermodynamic part of the problem of glass transition is related to two widely observed experimental facts: (a) heat capacity changes with a jump at the glass transition temperature Tg, and (b) no distinct solid glass phase has been identified experimentally or suggested theoretically. Therefore, the problem is to explain the jump of heat capacity without asserting the existence of a distinct solid glass phase.  This problem is also common to other disordered systems, including spin glasses. I have proposed that if, as is the case, Tg is defined as the temperature at which the liquid stops relaxing at the experimental time scale, the jump of heat capacity at Tg follows as a necessary consequence due to the change of system's elastic, vibrational and thermal properties. The resulting equations have no fitting parameters, and compare well with experimental results. This theory explains widely observed time-dependent effects of glass transition, including logarithmic increase of Tg with the quench rate, and identifies three distinct regimes of relaxation.

The dynamic part of the problem of glass transition is to explain the physical origin of several famous relaxation laws and dynamic effects that liquids show in the glass transformation range: the Vogel-Fulcher-Tammann law, stretched-exponential relaxation, dynamic crossovers etc. These phenomena are universal and are seen in other systems as well (e.g. spin glasses), yet their physical origin is not understood. I have proposed a solution to this problem based on elastic interactions in a liquid. The solution is based on a non-trivial way in which high-frequency elastic waves propagate in a liquid. Crucially, the propagation range of these waves increases with liquid viscosity. This is in contrast to frequently discussed hydrodynamic waves, whose propagation range decreases with viscosity.

4. Pressure response of amorphous materials

Pressure-induced transformations in crystals are well-known and well-understood phenomena. On the contrary, pressure effects in amorphous solids present us with new, often unexpected, features, and are not understood well. These include gradual coordination changes, long tails of transformations, slow logarithmic relaxation and permanent densification on pressure release. I have used computer simulations to study pressure response of B₂O₃ glass, and discovered novel high-pressure structures that included unusual coordination states. In another study, I elucidated pressure response of amorphous zircon, ZrSiO₄, damaged by radiation. These simulations showed unusual softening under pressure, and helped explain the origin of logarithmic relaxation.

5. Radiation damage

Radiation damage is a large and important area in science and technology, and has far-reaching consequences for materials performance in a wide range of applications, including immobilization of nuclear waste and future fusion reactors. This performance crucially depends on whether a material is amorphizable by radiation damage or is able to recover back to crystal. The phenomenon of resistance to amorphization by radiation damage remains largely not understood from theoretical standpoint. I elucidated the phenomenon of resistance to amorphization by radiation damage using large-scale classical molecular dynamics simulations. This was supported by quantum-mechanical calculations of electronic structure.