Japanese physicists have modeled the behavior of two-dimensional amorphous two-component bodies for various types of diatomic interaction. They were interested in the origin of the apex of the boson, that is, the excessive vibrational density of conditions inherent in all amorphous bodies. They found that this excess was due to the strong interaction of phonons in seemingly localized one-dimensional ways, but only in the transverse case. Research published in physics of nature.
Solids are interesting because their properties are largely determined not so much by the chemical nature of their constituent atoms as by the way they are arranged together. The situation when atoms are arranged in an ordered arrangement (crystal) differs significantly from their erratic arrangement (amorphous body). The presence of large order and symmetry plays an important role. Crystal theory is largely based on the idea that if the lattice is shifted by an integer number of periods, the equations must not change (translation symmetry). This approach proved to be very fruitful and allowed scientists to link the experimentally observed properties of crystals (thermal conductivity, heat capacity, electrical conductivity, etc.) to the behavior of electrons and the collective vibrations of atoms (phonons).
Amorphous bodies lack metaphorical symmetry, so the understanding of relative physics is inferior to that of crystals. One of the biggest mysteries in this case remains the so-called boson peak, ie an abnormal overcoming of the reduced density of phonon states in low energies. Typically, it is manifested in experiments for measuring thermal capacity and thermal conductivity at low temperatures, as well as in experiments for Raman light scattering and structural analysis of X-rays and neutrons.
The tip of the boson appears in all amorphous bodies and even in some liquids. This means that its cause is the structural disorder and, consequently, the disharmony of the individual vibrations. Despite the great interest of physicists in this phenomenon and the research of almost half a century, there is still no generally accepted interpretation.
The mystery of the boson peak prompted Yuan-Chao Hu and Hajime Tanaka of Tokyo University to understand its nature through numerical simulations with large numbers of people. Applying simulations to three different two-dimensional systems that look like glass, they concluded that the almost localized vibrations in the form of threads or rings are responsible for the appearance of the top of the boson.
The difficulty with amorphous body simulation is that if we simply arrange random atoms interacting in the model and perform the simulation, they can crystallize with some probability without forming a glassy state. Therefore, physicists started at high temperatures and gradually cooled the model liquid, giving it time for structural rearrangement until it glazed.
The specific parameters depend on the peculiarities of the diatomic interactions. The authors examined two-dimensional mixtures of particles of two types, the interaction between which was repulsive, attractive, and dependent on the orientation of the bond. In total, 8192 people were taken into account in the model and the calculation area was a square with periodic boundary conditions. Despite the differences in the type of interaction, the results were the same in all three cases.
By accessing each individual’s condition and the conditions in which they find themselves, the researchers were able to understand how the collective vibrations of the whole body are arranged. At low frequencies, the vibration functions have a spatial coherence and are phonons. At high frequencies, however, the propagation of oscillations through the glass has a random, diffuse character (such modes are often called diffuse). Finally, in the intermediate case, when the oscillation wavelength coincides with the mean free path of the phonon (Ioffe – Regel condition), hybrid oscillations occur, which can occur and attach to certain parts of the body. Under such conditions, as a rule, a boson peak is observed.
To see it in their model, physicists constructed the reduced density of vibration modes using various methods. They separated the longitudinal vibrations from the transverse ones and also constructed dynamic structural factors for each of them, which contain information about the correlations between the particles and their evolution over time.
As a result, scientists have discovered that increasing the density of states in almost localized modes of operation occurs only for transverse vibrations. This means that the appearance of the top of the boson is not related to the measurement of body volume and therefore can easily be observed in dense glasses. The energy of the quasi-localized modes themselves circulates along the filamentous and annular one-dimensional structures.
Despite the universality of the observed processes in relation to the details of diatomic interactions, the authors note that in real systems the nature of the appearance of the boson peak may be of a different nature. As an example, they cited silicon-based glasses, in which the detected modes of operation can correspond to rotational vibrations between adjacent tetrahedra.
We have previously described how a French physicist developed a statistical field theory to describe the behavior of amorphous bodies.