# Interaction of a Low-Power Laser Radiation with Nanoparticles Formed over the Copper Melt in Rarefied Argon Atmosphere

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Laboratory Set-Up and Experimental Procedure

## 3. The Decrease in Reflectance of Molten Copper

## 4. Surface Patterns on Samples of Solid Copper Samples after the Experiments

## 5. Theoretical Model for Interaction of Laser Radiation with a Cloud of Copper Nanoparticles

#### 5.1. Optical Properties of Single Nanoparticles of Copper

#### 5.2. Light Pressure of Probe Laser Beam on a Copper Nanoparticle

^{2}is the average incident radiative flux and ${c}_{0}=3\times {10}^{8}$ m/s is the speed of light. As the above calculations for single particles in Section 5.1, Equation (2) can be used only in the case of the so-called independent scattering when each particle absorbs and scatters the light in exactly the same manner as if other particles do not exist. In addition, this approach is applicable when there is no systematic phase relation between partial waves scattered by individual particles during the observation time interval, so that the intensities of the partial waves can be added without regard to phase. In the case of independent scattering, each particle is in the far-field zones of all other particles and scattering by individual particles is incoherent. The hypothesis of independent scattering is usually true when the distance between randomly positioned particles is greater than both the particle size and the wavelength [44,45,46,47,48,49]. It is highly likely that the last of these conditions is not satisfied during the main part of the melting period of copper samples.

^{3}is the density of copper melt, and $g=9.81$ m/s

^{2}is the acceleration of gravity. The Mie theory calculations show the maximum value of the ratio of ${Q}_{tr}/a=41.8{\mathsf{\mu}\mathrm{m}}^{-1}$ at $a=97\mathrm{nm}$ (see Figure 7). The corresponding maximum value of ${\overline{F}}_{\mathrm{rad}}$ is about $1.9\times {10}^{-3}$. This result is in obvious contradiction with the laboratory observations of the effect of laser light on deposition of particles on the sample surface. This is one more argument to take into account the effect of dependent scattering which is expected to be significant.

#### 5.3. The Model of Dependent Scattering and Explanation of the Observed Decrease in Reflectance

_{v}≈ 0.44 indicates that copper nanoparticles are polydisperse. The calculated value of f

_{v}confirms that there is an increase in the volume fraction of copper nanoparticles above the sample in the period of $570<t<640\mathrm{s}$ in the experiment with 30 kPa argon pressure.

#### 5.4. Possible Explanation of Considerable Contribution of Light Pressue to the Deposition of Particles

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The schematic of the laboratory set-up: 1—vacuum chamber, 2—optical window, 3—electric heater, 4—thermal insulation, 5—thermocouple, 6—copper sample, 7—nickel substrate, 8—probe laser, 9 and 10—semi-transparent mirrors, 11 and 12—sensors, 13—interference filter, 14—flat screen, 15—digital camcorder, and 16—electrical connector. Reprinted with permission from Reference [1]. Copyright 2020 Elsevier.

**Figure 3.**Time variation of (

**a**) thermo-emf of thermocouple and (

**b**) relative normal reflectance in the experiments with different pressures of argon.

**Figure 4.**Photographs of the surface of solid copper samples (

**a**) before the experiments and (

**b**–

**e**) after the experiments: (

**b**,

**c**)—$p=10\mathrm{kPa}$, (

**d**,

**e**)—$p=30\mathrm{kPa},$ (

**b**,

**d**)—the probe laser was on, (

**c**,

**e**)—the probe laser was off during the experiment.

**Figure 5.**Temperature of the copper sample as a function of electric power in the experiments with different values of argon pressure when the probe laser is (1) turned on or (2) turned off during the experiment.

**Figure 6.**Optical properties of spherical copper particles at wavelength $\lambda =660$ nm: (

**a**)—the efficiency factor of absorption and transport efficiency factor of scattering, (

**b**)—the scattering phase function of single scattering. Solid lines—the Mie theory, dashed lines—the Rayleigh theory. The angle of scattering is measured from the direction of incident light.

**Figure 7.**The calculated ratio of transport efficiency factor of extinction to the radius of copper particle at wavelength $\lambda =660$ nm.

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**MDPI and ACS Style**

Dombrovsky, L.A.; Mendeleyev, V.Y.
Interaction of a Low-Power Laser Radiation with Nanoparticles Formed over the Copper Melt in Rarefied Argon Atmosphere. *Thermo* **2021**, *1*, 1-14.
https://doi.org/10.3390/thermo1010001

**AMA Style**

Dombrovsky LA, Mendeleyev VY.
Interaction of a Low-Power Laser Radiation with Nanoparticles Formed over the Copper Melt in Rarefied Argon Atmosphere. *Thermo*. 2021; 1(1):1-14.
https://doi.org/10.3390/thermo1010001

**Chicago/Turabian Style**

Dombrovsky, Leonid A., and Vladimir Ya. Mendeleyev.
2021. "Interaction of a Low-Power Laser Radiation with Nanoparticles Formed over the Copper Melt in Rarefied Argon Atmosphere" *Thermo* 1, no. 1: 1-14.
https://doi.org/10.3390/thermo1010001