# Physical Mechanism of Selective Healing of Nanopores in Condensed Matter under the Influence of Laser Irradiation and Plasma

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{−10}to 10

^{−6}m [7,8,9]. Optical breakdown is initiated in micro- and nanoscale defective areas due to irradiation by laser impulse. As a result, the mechanical damage/destruction of the sample takes place. In such cases, the integral exploitation characteristics of the sample are determined by processes in inhomogeneous/defective areas with micro- and nanoscale dimensions.

## 2. Materials and Methods

^{2}. Laser exposure to the metal surface is an intricate process. In accordance with articles [35,36], an impulse with energy of 75 mJ induces a gas–plasma cloud. As a result of the influence of the gas–plasma cloud on the material, a shock wave is initiated. Ultrafast heating of the local region takes place. The temperature of the gas–plasma cloud can exceed 3000 K, thereby leading to the melting of the sample surface. Under these conditions, heating and cooling rates can reach 10

^{−6}–10

^{−7}K/s [36].

## 3. Results

#### 3.1. Experimental Results

#### 3.2. Theoretical Results

^{3}), C

_{p}is the heat capacity (J/(kg·K)), Q is the heat source term (W/m

^{3}), u is a vector-valued convective velocity field (m/s), and k is the solid thermal conductivity (W/(m·K)). The k value describes the relationship between the heat flux vector $\overrightarrow{q}$ and the temperature gradient $\overrightarrow{\nabla}$T; it is defined according to Fourier’s law of heat conduction, which for a two-dimensional model can be written in the form of Equation (2):

## 4. Discussion

_{1}in the material adjacent to the upper point of the pore (e.g., point 1) and the temperature T

_{2}at the lower point of the pore (e.g., point 2) were numerically determined. The temperature increment for each pore was determined by the difference between the higher and lower values: ${T}_{1}={T}_{1}-{T}_{2}$. Similarly, the temperature increments at these points were calculated for the case of the defect-free material: ${T}_{1}^{/}={T}_{1}^{/}-{T}_{2}^{/}$.

^{10}Pa [2,35,36] (these are the standard calculations based on the technical characteristics of the LS-2136 Table 1), conditions were created for the movement of heated material in the direction of the shock wave propagation. The efficiency of the material movement depends on the duration of the laser impulse (laser plasma), the characteristics of the heated material (rheological parameters of the continuous medium), and several other factors. For all the pores shown in Figure 7, the direction of propagation of the compression pulse was vertically downward (perpendicular to the base AC of the triangle ABC). Consequently, plastic movement of the heated material toward the pore can be expected. Additionally, due to the temperature gradient above and below the pore, deformation and filling with a more heated substance may occur. Considering the proposed model (no gases in the pore), complete healing of the pore is possible, thereby filling the entire space with easily movable components of a metal alloy.

_{1}significantly depend on the location of the pores and the distance to the surface of the sample. It is evident from our modeling that the more elevated the temperature of the material and the value of ΔT

_{1}are, the more intensive the process of pore healing is. In addition, for the upper pore, the direction of propagation of the isotherms coincides with the direction of the impact of the compression force. The isotherms are symmetrical with respect to this direction.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Aronin, A.; Abrosimova, G. Specific features of structure transformation and properties of amorphous-nanocrystalline alloys. Metals
**2020**, 10, 358. [Google Scholar] [CrossRef] - Ushakov, I.V.; Safronov, I.S. Directed changing properties of amorphous and nanostructured metal alloys with help of nanosecond laser impulses. CIS Iron Steel Rev.
**2021**, 22, 77–81. [Google Scholar] [CrossRef] - Savin, A.V.; Kosevich, Y.A.; Cantarero, A. Semiquantummolecular dynamics simulation of thermal properties and heattransport in low-dimensional nanostructures. Phys. Review. B Condens. Matter
**2012**, 86, 064305. [Google Scholar] [CrossRef] - Shelyakov, A.; Sitnikov, N.; Zaletova, I.; Borodako, K.; Tabachkova, N. Study of structure and phase transformations in rejuvenated rapidly quenched TiNiCu alloys. Metals
**2023**, 13, 1175. [Google Scholar] [CrossRef] - Wang, Z.; Ummethala, R.; Singh, N.; Tang, S.; Suryanarayana, C.; Eckert, J.; Prashanth, K.G. Selective laser melting of aluminum and its alloys. Materials
**2020**, 13, 4564. [Google Scholar] [CrossRef] - DebRoy, T.; Wei, H.L.; Zuback, J.S.; Mukherjee, T.; Elmer, J.W.; Milewski, J.O.; Beese, A.M.; Wilson-Heid, A.; De, A.; Zhang, W. Additive manufacturing of metallic components—Process, structure and properties. Prog. Mater. Sci.
**2018**, 92, 112–224. [Google Scholar] [CrossRef] - Ushakov, I.V. How a crack and the defect material in its neighborhood affect the radiation strength of transparent materials. J. Opt. Technol.
**2008**, 75, 128–131. [Google Scholar] [CrossRef] - Genin, F.Y.; Michlitsch, K.; Furr, J.; Kozlowski, M.R.; Krulevitch, P. Laser-induced damage of fused silica at 355 and 1064 nm initiated at aluminum contamination particles on the surface. Proc. SPIE. Proc. Int. Soc. Opt. Eng.
**1997**, 2966, 126–138. [Google Scholar] [CrossRef] - Wang, Z.-Y.; Harmer, M.P.; Chou, Y.T. Laser-induced internal cracks in LiF single crystals. J. Mater. Sci.
**1989**, 24, 2756–2760. Available online: https://link.springer.com/article/10.1007/bf02385622 (accessed on 20 November 2020). [CrossRef] - Kaputkina, L.M.; Kaputkin, D.E. Structure and phase transformations under quenching and tempering during heat and thermomechanical treatment of steels. Mater. Sci. Forum
**2003**, 426–432, 1119–1126. [Google Scholar] [CrossRef] - Chichenev, N.A.; Gorbatyuk, S.M.; Naumova, M.G.; Morozova, I.G. Using the similarity theory for description of laser hardening processes. CIS Iron Steel Rev.
**2020**, 19, 44–47. [Google Scholar] [CrossRef] - Li, R.; Chen, H.; Zhu, H.; Wang, M.; Chen, C. Tiechui Yuan Effect of aging treatment on the microstructure and mechanical properties of Al-3.02Mg-0.2Sc-0.1Zr alloy printed by selective laser melting. Mater. Des.
**2019**, 168, 107668. [Google Scholar] [CrossRef] - Safronov, I.S.; Ushakov, A.I. Targeted alternation in properties of solid amorphous-nanocrystalline material in exposing to nanosecond laser radiation. Defect Diffus. Forum
**2021**, 410, 469–474. [Google Scholar] [CrossRef] - Kaputkin, D.E. Application of focused optic irradiation for surface treatment of commercial steels. Mater. Sci. Forum
**2003**, 426–432, 1285–1288. [Google Scholar] [CrossRef] - Vandzura, R.; Simkulet, V.; Gelatko, M.; Michal; Mitalova, Z. Effect of hardening temperature on maraging steel samples prepared by direct metal laser sintering process. Machines
**2023**, 11, 351. [Google Scholar] [CrossRef] - Shinkaryov, A.S.; Ozherelkov, D.Y.; Pelevin, I.A.; Eremin, S.A.; Anikin, V.N.; Burmistrov, M.A.; Chernyshikhin, S.V.; Gromov, A.A.; Nalivaiko, A.Y. Laser fusion of aluminum powder coated with diamond particles via selective laser melting: Powder preparation and synthesis description. Coatings
**2021**, 11, 1219. [Google Scholar] [CrossRef] - Yasa, E.; Kruth, J.-P. Microstructural investigation of selective laser melting 316L stainless steel parts exposed to laser re-melting. Procedia Eng.
**2011**, 19, 389–395. [Google Scholar] [CrossRef] - Kolobov, Y.R.; Manokhin, S.S.; Odintsova, G.V.; Betekhtin, V.I.; Kadomtsev, A.G.; Narykova, M.V. Studying the influence of nanosecond pulsed laser action on the structure of submicrocrystalline titanium. Pisma v Zhurnal Tekhnicheskoi Fiz.
**2021**, 47, 21–25. [Google Scholar] [CrossRef] - Manokhin, S.S.; Tokmacheva-Kolobova, A.Y.; Karlagina, Y.Y.; Betekhtin, V.I. Investigation of changes in the structure of submicrocrystalline titanium of VT1-0 brand under heat treatment and laser processing with nanosecond pulses. J. Surf. Investig. X-ray Synchrotron Neutron Tech.
**2021**, 15, 59–64. [Google Scholar] [CrossRef] - Lu, Y.; Huang, G.; Wang, Y.; Li, H.; Qin, Z.; Lu, X. Crack-free Fe-based amorphous coating synthesized by laser cladding. Mater. Lett.
**2018**, 210, 46–50. [Google Scholar] [CrossRef] - Maharjan, N.; Wu, N.; Zhou, W. Hardening efficiency and microstructural changes during laser surface hardening of 50CrMo4 steel. Metals
**2021**, 11, 2015. [Google Scholar] [CrossRef] - Zhao, Z.-Y.; Li, L.; Bai, P.-K.; Jin, Y.; Wu, L.-Y.; Li, J.; Guan, R.-G.; Qu, H.-Q. The heat treatment influence on the microstructure and hardness of TC4 titanium alloy manufactured via selective laser melting. Materials
**2018**, 11, 1318. [Google Scholar] [CrossRef] [PubMed] - Ushakov, I.; Simonov, Y. Formation of surface properties of VT18u titanium alloy by laser pulse treatment. Mater. Today Proc.
**2019**, 19, 2051–2055. [Google Scholar] [CrossRef] - Duan, X.; Long, T.; Zhu, K.; Li, W. Formation mechanism of pore defects and surface ripples under different process parameters via laser powder bed fusion by numerical simulation and experimental verification. Res. Sq.
**2023**, 2–23. [Google Scholar] [CrossRef] - Betekhtin, V.I.; Kadomtsev, A.G.; Larionova, T.V.; Narykova, M.V. Effect of thermobaric treatment on the nanoporosity and properties of amorphous alloys. Met. Sci. Heat Treat.
**2015**, 56, 555–558. [Google Scholar] [CrossRef] - Betekhtin, V.I.; Veselkov, S.Y.; Dal, Y.M.; Kadomtsev, A.G. Theoretical and experimental investigation of the effect of an applied load on pores in solids. Phys. Solid State
**2003**, 45, 649–655. [Google Scholar] [CrossRef] - Sotov, A.V.; Agapovichev, A.V.; Smelov, V.G.; Kyarimov, R.R. Development algorithm of the technological process of manufacturing gas turbine parts by selective laser melting. IOP Conf. Ser. Mater. Sci. Eng.
**2018**, 302, 012065. [Google Scholar] [CrossRef] - Yap, C.Y.; Chua, C.K.; Dong, Z.L.; Liu, Z.H. Review of selective laser melting: Materials and applications. Appl. Phys. Rev.
**2015**, 2, 041101. [Google Scholar] [CrossRef] - Prashanth, K.G.; Kolla, S.; Eckert, J. Additive manufacturing processes: Selective laser melting, electron beam melting and binder jetting—Selection guidelines. Materials
**2017**, 10, 672. [Google Scholar] [CrossRef] - Deng, J.; Chen, C.; Zhang, W.; Li, Y.; Li, R.; Zhou, K. Densification, microstructure, and mechanical properties of additively manufactured 2124 Al–Cu alloy by selective laser melting. Materials
**2020**, 13, 4423. [Google Scholar] [CrossRef] - Khairallah, S.A.; Anderson, A.T.; Rubenchik, A.; King, W.E. Laser powder-bed fusion additive manufacturing: Physics of complex melt flow and formation mechanisms of pores, spatter, and denudation zones. Acta Mater.
**2016**, 108, 36–45. [Google Scholar] [CrossRef] - Prashanth, K.G.; Scudino, S. Quasicrystallyne composites by additive manufacturing. Key Eng. Mater.
**2019**, 818, 72–76. [Google Scholar] [CrossRef] - Markidonov, A.V.; Gostevskaya, A.N.; Gromov, V.E.; Starostenkov, M.D.; Zykov, P.A. Simulation of the structural changes in the surface layer of a deformed BCC crystal during a short-term external high-intense action. Russ. Metall. (Met.)
**2022**, 2022, 1090–1095. [Google Scholar] [CrossRef] - Markidonov, A.V.; Starostenkov, M.D.; Lubyanoi, D.A.; Zakharov, P.V.; Lipunov, V.N. Modeling of healing cylindrical cavities exposed to shock waves in crystal subjected to shear deformation. Steel Transl.
**2022**, 52, 208–214. [Google Scholar] [CrossRef] - Wang, H.-X.; Chen, X. Three-dimensional modelling of the laser-induced plasma plume characteristics in laser welding. J. Phys. D Appl. Phys.
**2003**, 36, 628–639. [Google Scholar] [CrossRef] - Dudoladov, S.; Larionov, N. The condition for application of the crocco integral in the mathematical description of a laser welding plasma plume. St Petersburg Polytech. Univ. J. Phys. Math.
**2021**, 14, 60–75. [Google Scholar] [CrossRef] - Smallman, R.E.; Ngan, A.H.W. Physical Metallurgy and Advanced Materials; Elsevier: Amsterdam, The Netherlands, 2007. [Google Scholar] [CrossRef]
- Gladkov, S.O.; Bogdanova, S.B. On the theory of nonlinear thermal conductivity. Tech. Phys.
**2016**, 61, 157–164. [Google Scholar] [CrossRef] - Cheilytko, A. Finding of the generalized equation of thermal conductivity for porous heatinsulating materials. Technol. Audit. Prod. Reserves
**2016**, 5, 4–10. [Google Scholar] [CrossRef] - Alexandrov, S.; Jeng, Y.-R. A method of finding stress solutions for a general plastic material under plane strain and plane stress conditions. J. Mech.
**2020**, 37, 100–107. [Google Scholar] [CrossRef] - Lienhard, J.H., IV; Lienhard, J.H., V. A Heat Transfer Textbook, Version 5.10; Phlogiston Press: Cambridge, MA, USA, 2020; pp. 11–761. Available online: https://ahtt.mit.edu/wp-content/uploads/2020/08/AHTTv510.pdf (accessed on 15 September 2021).
- Kamrani, M.; Levitas, V.I.; Feng, B. FEM simulation of large deformation of copper in the quasi-constrain high-pressure-torsion setup. Mater. Sci. Eng. A-Struct. Mater. Prop. Microstruct. Process.
**2017**, 705, 219–230. [Google Scholar] [CrossRef]

**Figure 1.**The scheme illustrates the focusing of the laser beam. The focal plane is situated at a height of 1 mm above the surface of the sample.

**Figure 2.**Sample processing scheme. The lines and arrows show the trajectory and direction of movement of the sample during laser processing. Blue circles are current processing stage. Orange circle are previous processing stage. (

**a**) The first stage of processing with creation of a matrix of nonoverlapping areas. (

**b**) The second stage without overlapping of melted areas. (

**c**) The third stage with overlapping of melted areas. (

**d**) The final stage with full treatment of all surface.

**Figure 3.**(

**a**) Microphotograph of untreated surface. (

**b**) Microphotograph of the irradiated surface. Visible areas of laser melting have the shape of circles with a diameter of 100 mkm.

**Figure 4.**The dependence of the indentation depth on the force: 1—untreated sample; 2—laser-irradiated sample.

**Figure 5.**A model of the geometry of the “triangle” pore system. Points 1, 3, 5 are the boundary areas of the material adjacent to the upper part of the pore. Points 2, 4, 6 are the boundary areas of the material adjacent to the lower part of the pore. Horizontal and vertical distances between pore boundaries are 100 nm.

**Figure 6.**Changes in temperature on a straight line along the height of the triangle ABC drawn from the vertex B to the base AC. S is the distance to the sample surface. The discontinuities on the dependency curves correspond to the pores. Curves: No. 1—10

^{−8}s; No. 2—3 × 10

^{−8}s; No. 3—5 × 10

^{−8}s; No. 4—7 × 10

^{−8}s; No. 5—9 × 10

^{−8}s.

**Figure 8.**Relative temperature difference Δ,K for the first, second, and third pores in the titanium alloy VT18u. N—number of pores from surface of a sample. Curves: No. 1—10

^{−8}s; No. 2—3 × 10

^{−8}s; No. 3—5 × 10

^{−8}s; No. 4—7 × 10

^{−8}s; No. 5—9 × 10

^{−8}s.

**Figure 9.**The main stages of pore healing under the action of a compressive force initiated by a laser pulse/plasma. The red dots show isolated healed areas. Modeling of the healing process was carried out for the pore closest to the surface of the uniformly heated material.

Parameters | Value | Unit |
---|---|---|

Wavelength | 532 | nm |

Energy | 75 | mJ |

Pulse duration (FWHM) | 15–20 | ns |

Pulse repetition rate | 50 | Hz |

Beam divergence (Θ _{0.86}) | ≤0.7 | mrad |

**Table 2.**Microhardness HV and mathematical expectation of the probability of crack formation after loading using Vickers pyramid (P

_{me}) on titanium alloy VT18u before and after treatment with a series of laser pulses.

F, N | Untreated Surface, P_{me} | Laser-Treated Surface, P_{me} | Untreated Surface, HV | Laser-Treated Surface, HV |
---|---|---|---|---|

0.49 ± 0.00735 | 0.2 | 0 | 218 ± 3.27 | 308 ± 4.62 |

0.98 ± 0.0147 | 0.25 | 0 | 250 ± 3.75 | 355 ± 5.325 |

1.47 ± 0.02205 | 0.3 | 0 | 265 ± 3.975 | 360 ± 5.4 |

1.96 ± 0.0294 | 0.35 | 0 | 270 ± 4.05 | 355 ± 5.325 |

2.94 ± 0.0441 | 0.4 | 0 | (260–290) ± 4.125 | (320–380) ± 5.25 |

3.92 ± 0.0588 | 0.45 | 0 | ||

4.9 ± 0.0735 | 0.55 | 0 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wang, Z.; Ushakov, I.V.; Safronov, I.S.; Zuo, J.
Physical Mechanism of Selective Healing of Nanopores in Condensed Matter under the Influence of Laser Irradiation and Plasma. *Nanomaterials* **2024**, *14*, 139.
https://doi.org/10.3390/nano14020139

**AMA Style**

Wang Z, Ushakov IV, Safronov IS, Zuo J.
Physical Mechanism of Selective Healing of Nanopores in Condensed Matter under the Influence of Laser Irradiation and Plasma. *Nanomaterials*. 2024; 14(2):139.
https://doi.org/10.3390/nano14020139

**Chicago/Turabian Style**

Wang, Zhiqiang, Ivan Vladimirovich Ushakov, Ivan Sergeevich Safronov, and Jianping Zuo.
2024. "Physical Mechanism of Selective Healing of Nanopores in Condensed Matter under the Influence of Laser Irradiation and Plasma" *Nanomaterials* 14, no. 2: 139.
https://doi.org/10.3390/nano14020139