Characterization of porosity in lack of fusion pores in selective laser melting using the wavefunction

Selective laser melting (SLM) is used extensively in the manufacture of components for both production and domestic applications. However, the lack of fusion pores is one of the most common defects in the SLM process, affecting the performance and life of the part and hindering the development of the SLM process. Meanwhile, the defects are particularly sensitive to changes in SLM process parameters. The micro-selective laser melting (μ SLM) model was established by molecular dynamics simulation, and the lack of fusion pores in the melt pool was analyzed by a multifunctional wavefunction analyzer to understand the difference of the porosities under different processes. The results show that both laser power and scanning speed can prolong the existence time of the melt pool by changing the input energy density. The melted powder has more time to fill the lack of fusion pores, thus reducing the porosity. The larger scanning spacing hinders the combination of adjacent melt pools, leading to an increase in porosity. Reducing scanning spacing will lead to sintering or remelting, thus improving the bonding quality of adjacent melt pools and effectively reducing porosity.


Introduction
Iron and its alloys are widely used in industrial manufacturing due to their superior properties, making them the most widely used metal in production and life. Conventional manufacturing processes such as machining, casting, forming, and powder metallurgy have restrictions in the production of ferrous parts with complex geometries. The operations are complex and require production tools and long processing times. In recent years, additive manufacturing (AM) has emerged as a new type of manufacturing method that offers new possibilities for metal fabrication. Selective laser melting (SLM) is an AM technique that is a promising manufacturing method for the selective melting and curing of metal powders in a layer-by-layer process by using a high-power laser beam guided by a 2D slice of a 3D CAD model [1]. SLM can also counteract the design freedom of conventional machining methods by creating complex designs without the requirement for expensive tooling limitations.
To explore the relationship between SLM processing conditions and material properties, various factors that affect the performance of parts have been widely studied [2][3][4][5][6][7][8]. Among these factors, the pore is the most influential factor. Therefore, to eliminate the harm of pores to parts, it is necessary to clearly understand how pores are formed. Traditional experiments have been carried out in the field of SLM pore research. Imade et al [9] studied the change of porosity under different energy densities and explored the influence of surface and internal pores on material properties. An et al [10] found that preheating powder can effectively reduce porosity. The layer thickness also plays a decisive role in the formation of pores. The point spacing and filling spacing also have a great influence on the formation of pores, and the difference between the internal porosity and surface porosity of the workpiece under the same process is also significant [11]. Different types of process parameters have different degrees of influence on pores. Shrestha et al [12] studied that laser power has the greatest influence on pores among all parameters.
It is difficult for traditional experiments to know the changes in the melt pool. To further study the formation of pores, the method of combining experiments with simulation came into being [13][14][15][16]. Most scholars used Flow-3D software to establish a physical numerical model to simulate the SLM process, analyze the changes in the molten pool under different energy densities, and explore the formation and evolution of unmelt and improper melt [17]. Although SLM technology is now mature, it is limited to macro-scale applications. As the demand for micro components in modern industry increases, SLM fabrication techniques are gradually moving to the micro-scale. SLM macro fabrication techniques are being scaled down for the manufacture of micro components in a process known as Micro-Selective Laser Melting (μ SLM) [18]. Molecular Dynamics (MD) simulations are processes that focus on the processes of material modeling, motion simulation, and analysis of results [19,20]. MD can be used to simulate the melting and solidification of materials during μ SLM, to observe the metallurgical bonding between powder particles, and to adjust the appropriate processing parameters [21]. Nandy et al [22] investigated the sintering mechanism of two or more AlSi10Mg powders at the same or different sizes using an MD simulation model developed by themselves. In addition, a quasi-twodimensional aluminum nanoparticle powder bed model was developed to simulate the μ SLM process [23]. The melting and solidification processes of aluminum nanoparticles were also analyzed.
However, little research has been done on pores in the μ SLM process. X-ray computed tomography is frequently used in conventional experiments to derive relationships between porosity and manufacturing parameters [24]. The simulation approach is effective in avoiding material waste and effectively shortening the development cycle of production processes. Such quantitative approaches to pore analysis are rare in simulation. Most SLM simulations focus on the process of pore formation and rarely quantify the relationship between the number, size, and shape of pores and the machining parameters. But so far, no attempts have been made to combine these two effective methods of studying pores.
The lack of fusion pores is one of the most common pore defects in the SLM process. The pore shape shows irregularities and is mostly distributed between the melt pool and the melt cell [25]. The lack of fusion pores is generally large and the irregular shape is usually the starting point for cracks, which greatly determines the performance of the part [26]. Hence the present work focuses on the lack of fusion pores.
In this work, the melting of powder particles and the flow and solidification of the melt pool during SLM processing are simulated. The relationship between laser power, scan speed, and scan spacing on the lack of fusion pores was investigated. Guides the fabrication of μ SLM processes.

Methods
In classical MD simulations, the trajectories of atoms in a system are determined numerically using Newton's equations of motion. The interaction force between atoms is determined by the interaction potential. To better simulate the melting and solidification process of iron, a reliable potential function is important. A modified buried atom method (MEAM) interatomic potential developed by Alireza [27] was used in this work. In the MEAM formalism [28,29], the total energy of a single-element system is given by where F i is the 'embedding energy' function (energy required to embed an atom in the background electron density i r at site i), S ij is the screening factor between atoms at sites i and j, and ij f is the pair interaction between atoms at sites i and j with a separation distance of R ij . This potential function can well represent the melting properties of iron such as latent heat, melting expansion and flow, liquid structure factor, and solid-liquid interface stiffness. The results gained from the potential function simulations match the experimental results to a high degree, thus verifying the accuracy of the developed MEAM parameters. In molecular dynamics simulations, the validation of the potential function is paramount, as seen in many similar works [22][23][24].
Molecular dynamics simulations in this work are all performed using a Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [30]. The open software Ovito [31] is used for the visualization and post-processing of MD simulations. In this work, the Muliwfn [32] software was used for the calculation of the volume of the pores inside the melt pool.
Multiwfn is an extremely powerful program for realizing electronic wavefunction analysis. The Muliwfn software superimposes the electron density of each atom in the free state as a molecular density, which corresponds to the state in which the atoms appear in their corresponding positions in the molecule, but where the electron density has not yet relaxed in its distribution due to bond formation. The electron density is calculated as [32] ( ) where j and h correspond to the natural orbital and its occupation number, respectively. c denotes the basis function, and C is the coefficient matrix. The region inside the equivalence plane of the molecular density is the region inside the molecule, while the region outside this equivalence plane can be regarded as a molecular pore. These pore areas were called free areas and the volume of the free area could be calculated by Multiwfn. The volume of the free area divided by the total volume was the porosity.
A three-dimensional initial model of the iron nanopowder bed is in figure 1(a). Similar powder particle models have been used in similar SLM simulation research work, such as Sorkin et al [21], Zhang et al [33], Wu et al [34] and Qiu et al [35] etc. The powder bed consists of an iron substrate and iron powder particles. Different colors have been chosen to represent them for better differentiation. The dimensions of the iron substrate were 32´28´3 nm 3 and the powder particles were both 4 nm in diameter. Red circles in figure 1(b) indicate the position of the laser beam spot, which had a diameter of 6 nm. The initial x-coordinate of the laser was zero and a single scan was made in the positive direction of the x-axis. At the end of a laser scan, a new single laser scan along the positive x-axis was performed at a specific scan spacing. During the laser scanning process, the iron substrate was kept at 300 K using the Langevin thermostat. The laser source was removed after all laser scanning processes have been completed. The iron substrate was controlled at 300 K using the Langevin thermostat to complete the cooling of the melt pool. The process parameters are shown in table 1. The volumetric energy density (VED (J mm −3 )) was calculated as follows [36] ( ) here P is the laser power, v is the scanning speed, h is the scanning spacing, and t is the layer thickness. Energy density for all simulations was in the same order of magnitude as the experiment [37]. This method of verifying the reasonableness between simulation and experimental results in terms of energy density has been widely used [33,34,38].   The scan spacing is defined as the distance between the laser centers of adjacent passes. As the laser scans the powder particles, the powder particles were heated to change from a solid to a liquid state, forming a molten pool. The flowing molten powder filled the gap in the powder bed, resulting in a reduction in the height of the powder bed. As the laser acted on the powder bed, the substrate also acted on the powder bed, allowing the cooling and solidification process to take place. The laser was scanned in the positive direction of the x-axis in one direction. At the end of one laser scan, a new laser starts scanning in the positive x-axis direction at a specific scanning spacing. After all laser scans have been completed, the laser source is removed. The powder bed continues the cooling and solidification process in the presence of the substrate. Figure 3 shows the melt pool morphology at different laser powers. At low laser power, as in figure 3(a), the energy density input is low, resulting in partial melting of the powder. Figure 3(e) shows the temperature change of the melt pool under different laser power. With the increase of laser power, the temperature of the melt pool rises significantly, and the existence time of the melt pool extends significantly. These incompletely melted particles impede the flow of the melt pool, resulting in a narrow width and short length of the pool. Poor bonding between adjacent melt pools, with the melted powder only filling a small portion of the pore between the particles, eventually led to the creation of irregular pores, as shown in figure 4(a). As the laser power was increased, the energy density input was also increased. The melt pool width and length were increased, the amount of melted powder was increased and most of the pores in the particles were filled. The presence of a lack of fusion pores can still be seen in figures 4(b)-(c) since SLM is a fast-melting and fast solidification process, where the melt pool had limited flow time due to the rapid reduction in temperature and the formation of ovallike pores inside due to the surface tension. In figure 3(d) the laser power is further increased, and the high energy density input allows the melt pool to exist for a further extended period. The width and length of the melt pool were significantly increased, resulting in better bonding between adjacent pools, and no lack of fusion pores was found in figure 4(d). Porosity under different laser power is calculated with Muliwfn software, as shown in figure 4(e). The changing trend of porosity conforms to the changing trend of porosity in figures 4(a)-(d).

Effect of laser power on the pore
Increasing the laser power eliminates the creation of a lack of fusion pores. 3.3. Effect of scanning speed on pore Figure 5 shows the morphology of the melt pool at different scanning speeds. Figures 5(a)-(d), the scanning speed decreases sequentially. Figure 5(e) shows the temperature change of the melt pool at different scanning  speeds. Figure 6(e) shows the change of porosity at different scanning speeds. In figure 5(a), at high scanning speed, the laser stay on the powder was short and resulted in a discontinuous and small size of the melt pool. The high scanning speed led to a low energy density input, a low amount of melted powder, and the inability of adjacent melt pools to combine. The discontinuous melt pool led to the creation of large-sized open pores, as shown in figure 6(a) when the pores inside the melt pool are dominated by open pores. In figure 5(b), the scanning speed was reduced, allowing the melt pool to exist for a longer period, but the molten powder was unable to diffuse sufficiently in a short period, leading to the creation of irregular pores. However, the porosity still decreases. As shown in figure 6 i i is the distance travelled by any specific particle in time t. Figure 7 shows the MSD curves for different machining parameters. As the laser acted on the particles, the powder particles began to melt, and the MSD would increase dramatically. When the laser has scanned, the melt pool starts to cool, the movement space for atomic diffusion had diminished and the MSD will remain at a stable value. In figure 7(a), the mean square displacement increases as the laser power ramps up. Since the increase in laser power gives the atoms higher kinetic energy, the atoms have more room to move so that to fill more porous areas. Figure 7(b) shows the mean square displacement curves for different scanning speeds. The lower the scanning speed, the longer the laser acts on the powder and the more energy the atoms gain. The degree of atomic diffusion is greatly increased in this case, the pores are filled more, and the porosity is reduced. Figure 8 shows the morphology of the melt pool at different scanning spacings. Figure 8(e) shows the change in the temperature of the first melt pool at different scanning spacing under the adjacent laser scanning, while the other process parameters remain unchanged. When the scanning spacing was small, the temperature of the first melt pool was affected by the second laser, so there will be two peaks. If the scanning spacing was too large, the subsequent laser scanning had little effect on the previous melt pool temperature. Figure 9(e) shows the change of porosity at different scanning spacings. In figure 8(d), the spacing between adjacent melt pools was too large at the high scanning spacing. With such a large spacing, the adjacent melt pools were unable to bond with each other and many un-melted particles were present in the adjacent melt pools, resulting in many open pores existing between the melt pools, as shown in figure 9(d). In figure 8(c), the scanning spacing was reduced and adjacent melt pools were in contact with each other with a small overlap, effectively reducing the generation of  open pores. In figure 9(c) it was seen that the pores were mainly irregular. In figure 8(b) the scanning spacing was further reduced, at which point the overlapping area of adjacent melt pools increased. As the temperature in the edge region of the melt pool was lower than the temperature in the central region, sintering would mainly occur  in the overlapping region at this point [40]. Sintering occured at the edge of the previous melt pool due to the reprocessing of the latter laser, which enhanced the bond between adjacent melt pools. Currently, the internal pores of the melt pool were mainly ellipsoidal-like pores, as shown in figure 9(b). In figure 8(a), the scanning spacing was further reduced and the overlap area between adjacent melt pools was further increased, at which point remelting occurs in the overlap area [41]. When adjacent lasers were scanned, the latter laser also scanned most of the area of the preceding melt pool, at which point the overlapping area also melted. Remelting causes the pores inside the melt pool to be filled with melted powder and the lack of fusion pores was eliminated [42], as shown in figure 9(a).

Conclusions
The SLM process of iron powder particles was simulated by MD, the volume of the lack of fusion pores in the melt pool was obtained by Muliwfn software, and the porosity was obtained. The effects of different process parameters on the porosity in the final molten pool were analyzed. As a result of the above work, conclusions can be drawn as follows.
(1) Based on the capabilities of the wave function analyzer, a quantitative characterization between SLM simulated the lack of fusion pores and process parameters can be achieved. This function has great potential for future molecular dynamics methods to simulate pores.
(2) The effect of processing parameters on porosity is studied by this new method. The results show that increasing laser power and decreasing scanning speed will lead to an increase in energy density. This increases the maximum temperature of the molten pool and increases the duration of the molten pool. The molten powder has more time to fill pores, thereby reducing pores.
(3) The high scanning spacing can prevent the adhesion between adjacent molten pools, resulting in the inability of molten powder to fill the pores and a large lack of fusion pores. The low scan spacing allows sintering and remelting, and the molten powder better fills the pores, thereby reducing the pores. These conclusions are consistent with the experimental results.