Equilibration of energies in a two-dimensional harmonic graphene lattice

Motion of localized disturbances in scalar harmonic lattices

We present analytical and numerical investigations of energy propagation in systems of massive particles that interact via harmonic (linear) forces. The particle motion is described by a scalar displacement, and the particles are arranged in a simple crystal lattice. For the systems under consideration we prove the conservation of the total energy flux analytically. Then, using a sample case of a square lattice, we confirm the analytical results numerically. We create disturbances of a special kind which can move with a predefined velocity with a minor change in their shape. We show that a clot of energy, associated with each disturbance, moves similarly to a free body of matter in classical mechanics. We also numerically study a simultaneous propagation of a number of energy clots as an analogy to the motion of point masses in the conventional mechanics of particles. The obtained results demonstrate that an energy flow in lattices can be described in terms of numerous separated energy bodies, making a step towards a linkage between lattice dynamics and the kinetic theory of heat transfer in solids.

Mechanical Properties of Cubene Crystals

The fullerene family, whose most popular members are the spherical C60 and C70 molecules, has recently added a new member, the cube-shaped carbon molecule C8 called a cubene. A molecular crystal based on fullerenes is called fullerite. In this work, based on relaxational molecular dynamics, two fullerites based on cubenes are described for the first time, one of which belongs to the cubic system, and the other to the triclinic system. Potential energy per atom, elastic constants, and mechanical stress components are calculated as functions of lattice strain. It has been established that the cubic cubene crystal is metastable, while the triclinic crystal is presumably the crystalline phase in the ground state (the potential energies per atom for these two structures are −0.0452 and −0.0480 eV, respectively).The cubic phase has a lower density than the monoclinic one (volumes per cubene are 101 and 97.7 Å3). The elastic constants for the monoclinic phase are approximately 4% higher than those for the cubic phase. The presented results are the first step in studying the physical and mechanical properties of C8 fullerite, which may have potential for hydrogen storage and other applications. In the future, the influence of temperature on the properties of cubenes will be analyzed.

Unsteady two-temperature heat transport in mass-in-mass chains

We investigate the unsteady heat (energy) transport in an infinite mass-in-mass chain with a given initial temperature profile. The chain consists of two sublattices: the β-Fermi-Pasta-Ulam-Tsingou (FPUT) chain and oscillators (of a different mass) connected to each FPUT particle. Initial conditions are such that initial kinetic temperatures of the FPUT particles and the oscillators are equal. Using the harmonic theory, we analytically describe evolution of these two temperatures in the ballistic regime. In particular, we derive a closed-form fundamental solution and solution for a sinusoidal initial temperature profile in the case when the oscillators are significantly lighter than the FPUT particles. The harmonic theory predicts that during the heat transfer the temperatures of sublattices are significantly different, while initially and finally (at large times) they are equal. This may look like an artifact of the harmonic approximation, but we show that it is not the case. Two distinct temperatures are also observed in the anharmonic case, even when the heat transport regime is no longer quasiballistic. We show that the value of the nonlinearity coefficient required to equalize the temperatures strongly depends on the particle mass ratio. If the oscillators are much lighter than the FPUT particles, then a fairly strong nonlinearity is required for the equalization.

Unsteady ballistic heat transport in two-dimensional harmonic graphene lattice

We study the evolution of initial temperature profiles in a two-dimensional isolated harmonic graphene lattice. Two heat transfer problems are solved analytically and numerically. In the first problem, the evolution of a spatially sinusoidal initial temperature profile is considered. This profile is usually generated in real experiments based on the transient thermal grating technique. It is shown that at short times the amplitude of the profile decreases by an order magnitude and then it performs small decaying oscillations. A closed-form solution, describing the decay of the amplitude at short times is derived. It shows that due to symmetry of the lattice, the anisotropy of the ballistic heat transfer is negligible at short times, while at large times it is significant. In the second problem, a uniform spatial distribution of the initial temperature in a circle is specified. The profile is the simplest model of graphene heating by an ultrashort localized laser pulse. The corresponding solution has the symmetry of the lattice and many local maxima. Additionally, we show that each atom has two distinct temperatures corresponding to motions in zigzag and armchair directions. Presented results may serve for proper statement and interpretation of laboratory experiments and molecular dynamics simulations of unsteady heat transfer in graphene.

Transition to thermal equilibrium in a crystal subjected to instantaneous deformation

An adiabatic transition between two equilibrium states corresponding to different stiffnesses in an infinite chain of particles is studied. Initially, the particles have random displacements and random velocities corresponding to uniform initial temperature distributions. An instantaneous change in the parameters of the chain initiates a transitional process. Analytical expressions for the chain temperature as a function of time are obtained from statistical analysis of the dynamic equations. It is shown that the transition process is oscillatory and that the temperature converges non-monotonically to a new equilibrium state, in accordance with what is usually unexpected for thermal processes. The analytical results are supplemented by numerical simulations.

Equilibration of kinetic temperatures in face-centered cubic lattices

We study thermal equilibration in face-centered cubic lattices with harmonic and anharmonic (Lennard-Jones) interactions. Initial conditions are chosen such that the kinetic temperatures, corresponding to three spatial directions, are different. We show that in the anharmonic case the approach to thermal equilibrium has two time scales. The first time scale is the period of atomic vibration. At times of the order of several atomic periods, the approach to equilibrium is accompanied by decaying high frequency oscillations of the temperatures. The oscillations are described analytically using the harmonic approximation. In particular, the characteristic frequencies of the oscillations are calculated. It is shown that the oscillations decay in time more slowly than expected. The second time scale, presented in the anharmonic case only, depends on the initial temperature of the system. Normalizing time by this scale, we obtain numerically a universal curve describing equilibration in the Lennard-Jones crystal over a wide range of temperatures.