This paper is the third in a series published in this journal during 2017-2018. These three papers present various stages in the development of the PeTa model for phenomena of the same physical nature: cavitational luminescence (CL), multi-bubble sonoluminescence (MBSL), single-bubble sonoluminescence (SBSL), and laser-induced bubble luminescence (LIBL). The basis of this model is the PeTa (Perel’man-Tatartchenko) effect—a nonequilibrium characteristic radiation under first-order phase transitions, for instance, vapour condensation. The third iteration of this model “Vapour bubble luminescence” (VBL) is presented in this paper. The essence of this model is as follows: with a local decrease of pressure or an increase of temperature in a tiny volume of the liquid, one or several bubbles filled with vapour will appear. Subsequently, a very rapid increase in pressure or a decrease in temperature of the bubble leads to super-saturation of the vapour inside the bubble, followed by its instantaneous condensation with the emission of condensation energy (this is the PeTa effect). A sharp decrease in pressure causes the collapse of the bubble accompanied by a shock wave in the liquid. VBL model is conveniently represented on the solid-liquid-vapour phase diagram. A better understanding of the physical nature of the phenomena under consideration could help to find their useful applications. To develop this idea further, we propose a design of a cavity-free pulsed laser on the basis of CL/MBSL/SBSL. An analysis of LIBL in cryogenic liquids is also given in this paper.
This is the third paper in a series presenting different steps in the development of the PeTa model of similar physical phenomena: cavitational luminescence (CL), multi-bubble sonoluminescence (MBSL), single-bubble sonoluminescence (SBSL), and laser-induced bubble luminescence (LIBL). The previous two papers were published in this journal during 2017 [
In this paper, we interpret the spectra of the LIBL in cryogenic liquids. In addition, we continue to improve our model. We show that all of the similar physical effects under consideration, CL/MBSL/SBSL/LIBL, can be generalized as the phenomenon that we call “Vapour bubble luminescence” (VBL). The essence of the model is as follows: when there is a local decrease in pressure or an increase of temperature in a tiny volume of the liquid, one or several bubbles filled with vapour will appear. Subsequently, very rapid increase in pressure or a decrease in temperature in the same volume of liquid leads to supersaturation of the vapour inside the bubble. The instantaneous condensation of the vapour with the emission of condensation energy (this is the PeTa effect) results in a sharp decrease in pressure and collapse of the bubble due to the pressure drop accompanied by a shock wave in a liquid. The VBL model explains all experimental data concerning CL/MBSL/SBSL/LIBL phenomena.
We also propose to design a cavity-free pulsed laser on the basis of CL/MBSL/SBSL.
The emission spectra of CL/MBSL/SBSL/LIBL in water, acids and aqueous solutions of various substances do not differ much in any way [
explain the banded spectrum by the emission of excited chromium atoms, which are trapped in the liquid because of cavitations. Surprisingly, the authors did not verify this hypothesis of cavitation by repeating the same experiment in another liquid medium. In addition, they did not compare spectra of LIBL in liquid argon and nitrogen. But in any case, we have to be grateful for the publication of their interesting experimental results.
Experimental parameters: temperature T = 66 K, external pressure Pe = 580 kPa. Inside the bubble, the Laplace pressure PL = 2 σ/R is added to the external pressure. Here σ is the surface tension of the liquid nitrogen, and R is the radius of a bubble. Let us calculate PL for the initial and final dimensions of the bubble at a little higher temperature 77 K for which σ = 8.5 × 10−3 N/m. At point 1: R1 = 0.75 mm and PL1 = 2σ/R1≈ 23 Pa. At point 2: R2 = 0.1 mm and PL2 = 2σ/R2 ≈ 170 Pa. It means that a full pressure P at point 1: P1 ≈ 580.023 кPa, and at point 2: P2 ≈ 580.170 кPa. In fact, the temperature can be higher or below than 77 K. So, the actual pressure PL can be more or can be less than the calculated one. But in any case, the Laplace pressure PL is a small addition to the pressure P in our system, and like analysis in our previous paper [
As given in paper [
As we have shown in our paper [
We proceed from the assumption that chromium has nothing to do with the spectrum, and the spectrum (
As usual, in the PeTa model, each band is attributed to the radiation of the specified clusters. In accordance with Formula (5) from paper [
λ n ( M ) = 120 n / M ( Λ − Γ M ) (1)
Here, the energy of the phase transition for one atom/molecule is denoted Λ, and the bound energy of the atoms/molecules in clusters is ΓM.
Let us write out the coordinates of all the bands from
For Argon, Λ = 6.27 kJ/mole, and roughly, for big M, ΓM can be assumed ≈ 0.75 Λ ≈ 4.7 kJ/mole [
Under this assumption and for n = 1, from Formula (1) we obtain the number of argon atoms in each cluster responsible for the corresponding bands: M1 = 99, M2 = 132, M3 = 144, M4 = 174, M5 = 207, M6 = 212, M7 = 239, M8 = 255, M9 = 264, M10 = 273, M11 = 294. Because we used a very rough approximation for ГM, these figures can be considered purely approximate.
Based on direct experiments and calculations [
A feature of the cluster structure of argon inside the bubble formed by the laser is the possibility of the existence of both ordinary clusters and cluster ions, because the high energy of the laser beam leads to ionization of the argon atoms. We have already discussed the effect of cluster ions on the LIBL spectrum in water [
The binding energy of particles in clusters is usually very small (not exceeding several eV), therefore large clusters can exist for a considerable time only at sufficiently low temperatures. Clusters are formed in the gas as a result of triple collisions of particles. Therefore, to create clusters, a sufficiently high pressure of the gas is necessary. Let us note that both of these requirements are met in our case.
We have already described the existence of a big magic number M = 21 for protonated water vapour [
The structure of a large cluster is determined primarily by the interaction of the nearest neighbours. Proceeding from these positions, we see that the case of the interaction of atoms with a closed electron the shell (atoms of an inert gas) has the greatest stability structure with a dense packing of atoms. With regard to binding energy ΓM, it should be noted that while the Ar dimer has a binding energy 12 meV, bulk argon has a sublimation energy of 80 meV and magic number clusters M = 13 and M = 19 have intermediate sublimation energies of approximately 60 meV.
The system under consideration is complicated by the possibility of formation of multiple charged cluster ions. If the cluster ion contains a small number of atoms in its composition, then such formation is unstable and, due to the Coulomb repulsion of the fragments, breaks up into parts. Therefore, there is a critical number Mc of atoms or molecules in a cluster ion, in which the multiply-charged cluster ions are stable. The critical number of Mc atoms in a doubly-charged and multiply-charged cluster ion can be determined from the considerations that at this value of the number of atoms the binding energy of a single ion coincides with the energy of the Coulomb interaction with other simple ions in the cluster. For instance, in argon, if the number of atoms corresponding to the existence of a singly charged ion is 91, for a doubly charged ion it is equal to 225.
Thus, our very brief review of the literature data on the existence of various clusters in inert gases shows that the set of clusters responsible for the LIBL spectrum obtained in our calculations is reasonable. Moreover, if we could know exactly the binding energy of atoms in clusters, LIBL would be a useful tool for cluster structures study.
In this section, we present all the investigated processes CL/MBSL/SBSL/LIBL on the solid-liquid-vapour phase diagram. This concept allows us to clearly understand the unified physical nature of these processes.
more condensed phase to the less condensed one or vice versa), the phase transition rate and the phase transition conditions (amount of matter, the presence of new phase nuclei, etc.). In
Then the description of the VBL phenomenon follows: Let us consider a very small volume of liquid at temperature T0 and pressure P0 which correspond to the figurative point A in the phase diagram (
Let under the action of a local short-term heat source in the small volume around figurative point A, the temperature rise sharply. Such heat sources are, for example, a concentrated laser beam which leads to the LIBL or electric arc discharge that gives the similar effect. The thermodynamic state of the volume under consideration will then correspond to the horizontal movement of the figurative point to the right. When the figurative point reaches position C, a vapour bubble should appear in this volume of the liquid. The appearance of a bubble under a boiling of liquid is a rather complex physical process. In particular, this is due to pressure. Indeed, the horizontal motion of the figurative point corresponds to the isobaric process. In our previous paper [
At an elevated pressure, in supersaturated vapour (figurative point B), three processes occur: First, the vapour molecules are predisposed to form clusters, and most likely this occurs. Second, molecules/clusters become excited compared to the bulk liquid molecules. Third, the density of molecules/clusters in the vapour increases, and in conformity with Dicke [
Let under the action of a stretching mechanical wave propagating in a liquid, the pressure in the small volume around figurative point A decreases rapidly. Such mechanical wave can be, for example, an ultrasonic wave, which leads to the SL effect. At a constant temperature, the thermodynamic state of the volume under consideration will then correspond to the vertical downward movement of the figurative point. When the figurative point reaches position F, vapor bubbles should appear in this volume of the liquid. The further behaviour of the bubbles corresponds to the vertical motion of the figurative point and completely repeats the previous case if the rise and fall of temperature we replace, respectively, with the decrease and increase in pressure. The position of the figurative point G will be equivalent to the position of D, of point F―to point C, of point E―to point B. Thus, the main event―a flash with the release of condensation energy will occur at the figurative point E.
It is quite obvious from the phase diagram (
It can be concluded that the term VBL, proposed by us, fully corresponds to the described mechanism of CL/SBSL/MBSL/LIBL.
In
With a relatively rapid crystallization of the molten substances, the PeTa effect is observed if these substances are transparent to PeTa radiation. In the phase diagram of
We have already described this phenomenon: in the process of formation of hail in the clouds, small drops of water in the clouds can be super-cooled up to 40˚C. In our experiments, when crystallizing sapphire with the emission of PeTa radiation, super-cooling temperature reached 65˚C. Our experiments on the observation of the PeTa effect during the crystallization of sapphire and 7 alkali-halide crystals are described in papers [
Fortunately, crystal and melt of STSP are rather transparent in the range near 5.1 μm―expected maximum of the PeTa radiation. The substances were melted in a cylindrical aluminium cuvette of 27 mm diameter with thin walls. A volume of every specimen was 8 cm3. Thus, the thickness of a melt layer was 14 mm. Crystallization began from the bottom of the cuvettes that was touching water kept at regulated temperature.
To clarify a shape of the infrared peak, differential measurements were carried out. For this, two identical cuvettes with STSP substances were used, but a surface of the specimen in one of the cuvettes was covered with a thin blackened copper foil. Both specimens were melted and crystallized in the same regime identical to the curve B (
to note that the shape of the radiation peak (
At equilibrium pressure, the vapour is in dynamic equilibrium with the surface of the solid. If the vapour pressure is above equilibrium, the vapour will be deposited on the surface of the solid. Under small supersaturation, the process passes slowly and the liberated heat of deposition is removed by thermal conductivity (figurative point M on
PeTa model states that in the processes considered here, SL/MBSL/SBSL/LIBLE, the vapor is in the supercooled state inside the bubble before the flash. All atoms/molecules and clusters are united in a single system by the electromagnetic field of interaction. During the flash, the excitation energy of all particles of the cloud is instantaneously released. We described in detail all these processes in our previous paper [
Imagine a system of SL/MBSL/SBSL in which only molecules/atoms of vapour are contained, and there are no clusters. In fact, such a system will be a natural cavity-free laser. For all possible liquids, this radiation will be in a relatively far IR region and, consequently, will be absorbed by the liquid. But it is possible to form bubbles near walls of the vessel that is transparent for this range of radiation, or make an ultrasonic horn from a transparent material and, thus, to obtain a working laser. Furthermore, the SL in molten metals was observed through the transparent horn [
It is obvious that in all considered cases of PeTa radiation―melt crystallization and vapour deposition, the recorded IR radiation peaks consist of a set of pulses similar to CL/SBSL/MBSL/LIBL.
In this paper, we continue the development of the PeTa model for CL/SBSL/MBSL/LIBL:
1) Based on this model, LIBL in cryogenic liquids is analysed. For each of the bands of the LIBL spectrum in liquid argon, a cluster responsible for its emission is calculated.
2) All the investigated processes CL/MBSL/SBSL/LIBL are presented on the solid-liquid-vapour phase diagram. This concept―VBL (vapour bubble luminescence) allows us to clearly understand the unified physical nature of these processes.
3) Other 2 cases of PeTa radiation (under the crystallization of melts and under vapour deposition) are also presented in this phase diagram. This allows us to clearly understand the place of CL/MBSL/SBSL/LIBL in the general picture of PeTa radiation.
4) We show that in many respects the systems under investigations, CL/MBSL/SBSL/LIBL, are similar to cavity-free pulsed lasers. The difference lies in the fact that the radiation is nonmonochromatic and incoherent. But the aggregate of homogeneous particles emits monochromatic and coherent radiation. If we exclude the formation of clusters in the system, we will get a natural cavity-free pulsed laser.
5) The design of such a laser is proposed.
Tatartchenko, V.A. (2018) Sonoluminescence as the PeTa Radiation, Part Three. Optics and Photonics Journal, 8, 187-200. https://doi.org/10.4236/opj.2018.86017