A simulation method for femtosecond laser sintering of metal nanoparticles

Abstract

This invention relates to a simulation method for femtosecond laser sintering of metal nanoparticles, belonging to the field of femtosecond laser micro / nano-processing of metal materials technology. The method establishes a metal nanoparticle model at the nanoscale, calculates the evolution of electron temperature distribution and electron-phonon coupling energy within the metal nanoparticles by constructing a two-temperature equation model, and obtains the atomic motion and corresponding sintering process of the metal nanoparticles through molecular dynamics simulation. This invention fully considers the influence of the curved surface of the nanoparticles on laser energy deposition. The simulation results can reveal the sintering mechanism of metal nanoparticles, thereby guiding the processing and avoiding the inability of a single molecular dynamics model to consider the influence of electrons in the material on the laser response.

Description

Technical Field

[0001] This invention belongs to the field of femtosecond laser micro / nano fabrication of metal materials, and specifically relates to a simulation method for femtosecond laser sintering of metal nanoparticles. Background Technology

[0002] Traditional manufacturing methods face numerous challenges in the fabrication of complex micro / nano devices, including limitations in time and spatial resolution. Laser additive manufacturing, a rapidly developing rapid prototyping method, can meet the needs of manufacturing various micro / nano devices. Laser additive manufacturing uses lasers as a heat source, thus the final processing quality is closely related to the laser's performance. Femtosecond lasers, due to their ultrashort interaction time with the processed material and low thermal impact, show great promise in improving processing quality and increasing spatial resolution in laser additive manufacturing. Studies on the interaction mechanism between lasers and raw materials, i.e., nanopowder layers, are not uncommon. However, theoretical research on the formation of sintering necks and gradual sintering between metal nanoparticles under laser induction, especially femtosecond lasers, is limited. Compared to long-pulse lasers, femtosecond lasers can excite non-equilibrium interactions between electrons and the crystal lattice in metal nanoparticles. This non-equilibrium process is multi-stage, involving electrons transferring energy to the lattice and influencing lattice disruption, leading to phase transitions. Therefore, a single model is insufficient to accurately describe the entire process. Current research on femtosecond laser sintering of metal nanoparticles largely focuses on simulating the process using a single molecular dynamics model. This simplifies the femtosecond laser as a heat source, thus simplifying the impact of femtosecond laser irradiation on the thermophysical properties of metal nanoparticles. Furthermore, the simplified femtosecond laser cannot reflect the absorption of laser light by the nanoparticles, affecting the accuracy of the simulation. In reality, femtosecond laser irradiation causes changes in the thermophysical properties of metal nanoparticles, and the shape of the particles also influences laser absorption to varying degrees. Therefore, establishing a simulation method that accurately describes femtosecond laser sintering of metal nanoparticles is essential for explaining the mechanisms of laser micro / nano additive manufacturing and predicting the formation of femtosecond laser-sintered nanoparticles. Summary of the Invention

[0003] In view of the above-mentioned shortcomings of the prior art, the purpose of this invention is to provide a simulation method for femtosecond laser sintering of metal nanoparticles. This method considers the changes in the thermophysical properties of the material caused by laser absorption by the nanoparticles and the deposition of femtosecond laser energy within the metal nanoparticles. This invention can simulate the interaction between different femtosecond lasers and an arbitrary number of spherical nanoparticles by changing laser parameters and particle size, thereby predicting the sintering process of the nanoparticles. Using this simulation method, the sintering process of metal nanoparticles under femtosecond laser irradiation can be predicted with only computational resources, helping researchers select reasonable parameters for experiments, thus effectively saving experimental consumables and reducing experimental costs.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0005] A simulation method for femtosecond laser sintering of metal nanoparticles includes the following steps:

[0006] (1) Establish a model of metal nanoparticles and further subdivide the particles using a fine mesh as the electronic mesh of the nanoparticles.

[0007] Since the simulation is of the process of femtosecond laser sintering of metal nanoparticles, it is necessary to include the spatiotemporal information of this process. Therefore, steps (2) and (3) are described as steps on a time step.

[0008] (2) Since the laser spot radius is much larger than the particle size of the metal nanoparticles, only the attenuation along the laser irradiation direction is considered. The laser energy source term uses a Gaussian distribution, and its expression is as follows:

[0009]

[0010] Where J,t p R and L op These represent laser flux, laser pulse width, the optical properties of the material (reflectivity), and optical transmission depth, respectively. z represents the depth of the laser along the transmission direction, and t represents the duration of laser irradiation.

[0011] Furthermore, the energy of the laser energy source term deposited in the electronic mesh of the metal nanoparticles is obtained using the following method:

[0012] First, all electron grids are traversed, and electron grids containing atoms are marked.

[0013] Next, the first marked electronic grid along the laser irradiation direction was identified as the surface of the metal nanoparticles irradiated by the laser.

[0014] Then, by traversing all the marked grids, the laser energy deposited in each electronic grid under the femtosecond laser irradiation is calculated using the above formula.

[0015] (3) A two-temperature equation coupled molecular dynamics model was established to simulate the sintering process of metal nanoparticles under femtosecond laser irradiation. The two-temperature equation describes the physical process under femtosecond laser irradiation, where laser photons are first absorbed by electrons in the metal nanoparticles, and then energy is transferred to the crystal lattice through electron-phonon coupling. In this invention, the expression shown in formula (2) is mainly used:

[0016]

[0017] Among them, T e and T l C represents the electron temperature and the lattice temperature, respectively. e k e and G e-ph , respectively, represent electronic heat capacity, electronic thermal conductivity, and electroacoustic coupling coefficient, which are the thermal properties of the metal nanoparticles. S represents the laser energy source term described in formula (1). The electron temperature T in each electron grid under the action of the laser energy source term described in formula (1) is calculated according to formula (2). e This allows us to obtain the electronic temperature distribution of the metal nanoparticles. Simultaneously, we calculate the energy transferred to the lattice by each electronic grid within the nanoparticle through electron-phonon coupling, i.e., the electron-phonon coupling energy.

[0018] Furthermore, the thermal properties of the metal nanoparticles will be calculated using the following expressions:

[0019]

[0020] Among them, a0 to a4 are constants, which are obtained by fitting the electronic heat capacity calculated by quantum processing methods.

[0021] k e =λC e (4)

[0022] Where λ is the thermal diffusivity.

[0023]

[0024] Where G0 is the electroacoustic coupling coefficient of the metallic material at room temperature, and A e and B l These are the electron-electron collision frequencies and the electron-phonon collision frequencies, respectively.

[0025] Subsequently, molecular dynamics coupled with a two-temperature equation was used to calculate the atomic motion information in the nanoparticles. Specifically, the obtained electron-phonon coupling energy was converted into a force and applied to each atom of the nanoparticles for calculation, thereby obtaining the motion information of each atom in the nanoparticles. Furthermore, the lattice temperature distribution in the nanoparticles and the sintering process of the particles were obtained.

[0026] The fundamental equations used in molecular dynamics are as follows:

[0027]

[0028] Where the subscript i represents the i-th atom, m and v represent the mass and velocity of the atom, respectively, and U(r1,…r) n The potential energy of an atomic system is obtained through calculation using the potential function. It is the Langevin force, which represents the force applied to atoms by electron-phonon coupling energy.

[0029] Thermodynamic and kinetic information of femtosecond laser sintering of metal nanoparticles was obtained through steps (2) and (3) in one time step. In the new time step, steps (2) and (3) were repeated to update the corresponding information, and finally the spatiotemporal information of the femtosecond laser sintering of metal nanoparticles was obtained.

[0030] Beneficial effects:

[0031] (1) This invention considers the energy deposition of femtosecond laser inside metal nanoparticles. The femtosecond laser in the simulation has a Gaussian distribution. The femtosecond laser irradiation is no longer regarded as a constant heat flow input. The established energy deposition model considers the interaction between the laser and the metal nanoparticles, which is closer to the actual situation.

[0032] (2) Dynamic material property parameters were used to consider the changes in thermal properties caused by the interaction between femtosecond laser and metal nanoparticles. Based on the two-temperature equation and molecular dynamics simulation, the electronic temperature distribution and lattice temperature distribution of metal nanoparticles can be obtained. Furthermore, the motion information of atoms in metal nanoparticles can be obtained, thereby realizing the simulation of nanoparticle sintering.

[0033] (3) This simulation method can predict the sintering of metal nanoparticles under femtosecond laser irradiation using only computing resources, helping researchers select reasonable parameters for experiments, thereby effectively saving experimental consumables and reducing experimental costs.

[0034] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and will become apparent from the description or may be learned by practice of the invention. Attached Figure Description

[0035] Figure 1 Simulation method calculation flowchart;

[0036] Figure 2 The established aluminum nanoparticle model;

[0037] Figure 3 Schematic diagram of energy deposition of aluminum nanoparticles under femtosecond laser irradiation;

[0038] Figure 4 Evolution of electron temperature and lattice temperature of aluminum nanoparticles under femtosecond laser irradiation;

[0039] Figure 5 A snapshot of the atomic evolution of aluminum nanoparticles under femtosecond laser irradiation. Detailed Implementation

[0040] The embodiments of the present invention are described in detail below. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0041] Combination Figures 1 to 4 The present invention further illustrates the simulation method for femtosecond laser irradiation sintering of metal nanoparticles according to the present invention through numerical examples. Figure 1 The diagram shows a simulation flowchart for the sintering of metal nanoparticles using femtosecond laser irradiation. The implementation examples of this invention require the following conditions: specified femtosecond laser parameters, namely a laser pulse width of 100 fs and an absorbed laser flux of 250 J / m². 2 The simulation calculates the melting process of a 6nm aluminum nanoparticle under a specified metal nanoparticle, and outputs an atomic snapshot of the sintering process. The specific simulation steps are as follows:

[0042] (1) Establish a metal nanoparticle model and perform mesh generation on it as the electronic mesh of the model.

[0043] Create an .in file to build a model of aluminum nanoparticles with a diameter of 6 nm and a lattice constant of . Initially located at the center of the simulation space, the model's boundaries are defined. An embedded atomic potential function is chosen as the potential function to describe the material. The model is then initialized and relaxed at room temperature. Next, during mesh generation, the entire simulation space is meshed, and the mesh covered by the particles is assigned an initial electronic temperature as the electronic mesh. The established aluminum nanoparticle model is as follows: Figure 2 As shown.

[0044] (2) Obtain the energy of femtosecond laser deposition in the electronic grid of metal nanoparticles based on the established metal nanoparticle model.

[0045] First, all electron grids are traversed, and those containing atoms are marked. Then, the first marked electron grid along the laser irradiation direction is identified as the surface of the metal nanoparticle under laser irradiation. Next, by traversing all marked grids, the energy deposited in each electron grid under femtosecond laser irradiation is calculated using the following laser energy source term formula. The energy distribution of femtosecond laser deposition in the electron grid of metal nanoparticles is illustrated below. Figure 3 As shown.

[0046]

[0047] In the formula J,t p R and L op These represent laser flux, laser pulse width, the optical properties of the material (reflectivity), and optical transmission depth, respectively. z represents the depth of the laser along the transmission direction, and t represents the duration of laser irradiation.

[0048] (3) Obtain the distribution of electron temperature and lattice temperature in nanoparticles under femtosecond laser irradiation and sintering information.

[0049] The molecular dynamics coupled two-temperature equations were solved on the model. Based on the two-temperature equations, the electronic temperature distribution of the metal nanoparticles under the influence of the laser energy source term in step (2) was calculated, and the electron-phonon coupling energy transferred from the nanoparticle electronic grid to the lattice was obtained. The obtained electron-phonon coupling energy was converted into a force and applied to each atom of the nanoparticle using molecular dynamics, thereby calculating the motion information of each atom in the nanoparticle, obtaining the lattice temperature distribution in the nanoparticle, and the melting process of the particle. The formulas used are shown below:

[0050]

[0051]

[0052] In the formula, T e and T l C represents the electron temperature and the lattice temperature, respectively. e k e and G e-ph Representing electronic heat capacity, electronic thermal conductivity, and electroacoustic coupling coefficient, respectively, these are the thermal properties of metal nanoparticles. S represents the laser energy source term, the subscript i represents the i-th atom, m and v represent the mass and velocity of the atom, respectively, and U(r1,…r) represents the electron heat capacity, electronic thermal conductivity, and electroacoustic coupling coefficient, respectively. n The potential energy of an atomic system is obtained through calculation using the potential function. This refers to the Langevin force, which represents the force exerted on the atom by the electron-phonon coupling energy. The thermal properties of metallic nanoparticles will be calculated using the following formula:

[0053] Electronic heat capacity:

[0054]

[0055] Among them, a0 to a4 are constants, which are obtained by fitting the electronic heat capacity calculated by quantum processing methods.

[0056] Electronic thermal conductivity:

[0057] k e =λC e

[0058] Where λ is the thermal diffusivity.

[0059] Electroacoustic coupling coefficient:

[0060]

[0061] Where G0 is the electroacoustic coupling coefficient of the metallic material at room temperature, and A e and B l These represent the electron-electron collision frequencies and the electron-phonon collision frequencies, respectively. By solving the above model, we can obtain, as follows: Figure 4 The electron lattice temperature distribution of aluminum nanoparticles under femtosecond laser irradiation is shown. Figure 5 The aluminum nanoparticles shown melt under femtosecond laser irradiation due to the destruction of their crystal structure caused by the intense thermal motion of atoms.

[0062] As can be seen from the above examples, those skilled in the art can clearly understand that the present invention can be implemented using software and necessary general-purpose hardware platforms. The above examples are merely illustrative and not intended to limit the method of the present invention. Any equivalent substitutions or modifications made to the technical solutions and inventive concepts of the present invention should be covered within the protection scope of the present invention.

Claims

1. A simulation method for femtosecond laser sintering of metal nanoparticles, characterized in that... Includes the following steps: The first step is to establish a model of metal nanoparticles and further subdivide the particles using a fine mesh as the electronic mesh for the nanoparticles. The second step is to obtain the energy deposited in the electronic mesh of metal nanoparticles under the action of the laser energy source term for the established model. The third step involves establishing a two-temperature equation coupled with molecular dynamics to simulate the process of femtosecond laser sintering of metal nanoparticles. Based on the two-temperature equation, the electron temperature T in each electron grid is calculated under the influence of the laser energy source term. e This allows us to obtain the electronic temperature distribution of the metal nanoparticles and calculate the energy transferred to the lattice by each electronic grid in the nanoparticle through electron-phonon coupling, i.e., the electron-phonon coupling energy. Based on the obtained electron-phonon coupling energy and combined with molecular dynamics, we can calculate the motion information of each atom in the nanoparticles, thereby obtaining the lattice temperature distribution in the nanoparticles and the sintering process of the particles, thus completing the simulation of femtosecond laser sintering of metal nanoparticles. The laser energy source term uses a Gaussian distribution, and its expression is as follows: J abs ,t p , and L op These represent laser flux, laser pulse width, and optical transmission depth, respectively, where z is the depth of the laser along the transmission direction, and t is the optical transmission depth. p The duration of laser irradiation; The expression for the two-temperature equation coupled with the molecular dynamics model is as follows: Among them, T e and T l C represents the electron temperature and the lattice temperature, respectively. e k e and G e-ph represent electronic thermal capacity, electronic thermal conductivity and electro-acoustic coupling coefficient, respectively, which are the thermal properties of metal nanoparticles; S represents the laser energy source term; in formula (3), the subscript i represents the i-th atom, m and v represent the mass and velocity of the atom, respectively, and U(r1,…r…) represents the mass and velocity of the atom. n The potential energy of an atomic system is obtained through calculation using the potential function. It is the Langevin force, which represents the energy of electroacoustic coupling being applied to atoms in the form of a force.

2. The simulation method for femtosecond laser sintering of metal nanoparticles as described in claim 1, characterized in that: The energy of laser energy source deposited in the electronic grid of metal nanoparticles is obtained by the following method: First, all electronic grids are traversed and electronic grids containing atoms are marked; then, the first marked electronic grid along the laser irradiation direction is identified as the surface of the metal nanoparticles irradiated by the laser energy source; then, by traversing all marked grids, the energy deposited in each electronic grid under the irradiation of the femtosecond laser energy source is calculated using Equation (1).

3. The simulation method for femtosecond laser sintering of metal nanoparticles as described in claim 1, characterized in that: The thermal properties of metal nanoparticles will be calculated using the following expressions: Electronic heat capacity: Among them, a0 to a4 are constants, which are obtained by fitting the electronic heat capacity calculated by quantum processing methods; Electronic thermal conductivity: k e =λC e (5) Where λ is the thermal diffusivity; Electroacoustic coupling coefficient: Where G0 is the electroacoustic coupling coefficient of the metallic material at room temperature, and A e and B l These are the electron-electron collision frequencies and the electron-phonon collision frequencies, respectively.

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