Molecular Dynamics Simulation of Ti and Ni Particles on Ti Substrate in the Cold Gas Dynamic Spray (CGDS) Process Terence Malama1,a *, Agripa Hamweendo 2,b and Ionel Botef 3,c 1,2,3
University of the Witwatersrand, Johannesburg, Faculty of Engineering and the Built Environment, School of Mechanical, Industrial and Aeronautical Engineering, Johannesburg, South Africa a
[email protected], b
[email protected], c
[email protected],
Keywords: molecular dynamics, simulation, cold gas dynamic spray, cold spray, Titanium, Nickel
Abstract. This paper presents simulation of molecular dynamics for the deposition of Titanium (Ti) and Nickel (Ni) particles on Ti substrate during the Cold Gas Dynamic Spray (CGDS) process. The influencing factors of the deposition process, such as particle incident velocity, particle size and particle temperature are taken into consideration. Ti and Ni were selected because of their potential applications in the aerospace, marine and bio-medical industries. CGDS is preferred because it is a state of the art technique by which coatings are created without significant heating of the sprayed powder. In CGDS, particles are accelerated to supersonic velocities using a high speed gas stream. However, there are inherent difficulties in relating particle deposition characteristics with influencing factors of the deposition process. Moreover, there is limited literature on molecular dynamics simulation of CGDS process. For this reason, this paper develops a simulation process for Ti and Ni particles under influence of many factors using molecular dynamics. In this process, particles are allowed to interact for a short time, giving a view of their motion. The trajectories of these particles are determined by numerically solving the Newton's equations of motion for a system of interacting particles, in which the forces between the particles are defined. The results of the simulation process show that higher incident velocities and larger particle sizes result in stronger interface between the particle and the substrate. Further, higher temperatures of the substrate and particles improve the bond strength. Introduction Cold spraying (CS) of copper (Cu) and aluminum (Al), other than Ti and Ni, has been widely explored in the last decade. It is now of growing interest to the scientific and engineering communities to explore the potential of Ti and Ni and their alloys [1]. Ti as a barrier layer has a great potential for corrosion resistant applications and as a material for near net shaped manufacturing for the aerospace industry where reducing the machining cost is a key factor [2]. Due to its bio-inertness Ti has found applications in the biomedical industry [3], [4]. The difficulties in the conducting of physical CS experiments of Ti are due to its high critical velocity, high reactivity with oxygen and crystal structure. Thus, MD simulation presents a huge potential in the exploration of spray parameters of Ti and Ni. CGDS method possesses several attractive features as a manufacturing process of high quality coatings. This technology was developed in the mid-1980s based on the theory of accelerating particles to a velocity high enough to cause it to plastically deform onto a substrate and thereby forming a bond [5]. In this process, typical particle velocities range from 300 m/s to 1500 m/s and temperatures from 300 K to 1200 K [6], [7]. It is important to note that in CGDS process the high temperature is unnecessary to produce high-density coatings. Low temperatures are useful in generating unique material properties, which otherwise cannot be obtained by traditional methods.
In this study the grain sizes that are used are of the order of 1 nm to 6 nm [8] which is considerably smaller than that of raw particles, assumed to be agglomerated, usually between 1 µm to 50 µm [5], [9], [10]. Computer simulation helps to understand what happens in the CGDS process. Molecular dynamics (MD) technique has been applied in a number of experiments on particle impacts to a substrate [11]–[13]. These studies, however, assumed quite different conditions on the particle size, incident velocity, temperature and compositions. MD simulation is a technique by which one generates the atomic trajectories of a system of N particles by numerical integration of Newton’s equation of motion, for a specific interatomic potential, with certain initial conditions and boundary conditions [14]. It has been applied in the study of, for example, defect formation and migration, fracture, grain boundaries, structural transformations, radiation damage, elastic and plastic mechanical properties, friction, shock waves, molecular crystals and epitaxial growth [11], [15]. The application of MD simulation in CGDS, on the other hand, is scantly reported. In this study, the author carries out the MD simulations on Titanium (Ti) and Nickel (Ni) particle impacts in the CGDS process using Ti as a substrate in both cases. The objective of this work is to understand how influencing factors, such as incident velocity, particle size and temperature affect the deposition process. Experimental Design - Molecular Dynamics Simulation There are a number of experimental conditions that can be considered in the CGDS process such as the particle size, incident velocity and angle to the substrate, temperature of the substrate, etc. In order to perform the MD simulation, one must consider other atomistic conditions such as the crystal orientation of the particles and the substrate. In the actual CGDS process, particles strike against the substrate at randomly distributed crystal orientations and order. In the present study, MD simulations are executed on solitary particle impacts to the substrate by assuming several selected conditions such as incident velocity. In the first experimental setup, pure Ti is selected as the composition of the particle and the substrate. In the second experimental setup, pure Ni is the composition of the particle while pure Ti, is maintained as the substrate. The interatomic potentials proposed by Ackland for Ti and Ni [16], [17] are adopted. Since the crystal phase of Ti and Ni at the temperature of the CGDS process are Hexagonal Close Packed (hcp) and Face Centered Cubic (fcc), initial atomic configurations are prepared as hcp and fcc phases, respectively. The incident particle is assumed to have a spherical shape of which experimental radii are taken to be 0.68 nm, 1.70 nm, 2.38 nm, and 3.06 nm, for both Ti and Ni. The substrate is also assumed to be Ti and is modelled by a rectangular shape of 6.8 x 9.5 x 13.6 nm. The maximum numbers of atoms used in the particle and in the substrate are about 2013 and 60760, respectively. Simulation cell A Schematic diagram of the MD cell structure is given in Fig. 1. A rectangular MD Particle simulation cell and three-dimensional periodic boundary conditions are assumed. The v(y) Substrate horizontal (x–z) dimensions of the MD simulation cell are the same to those of the Pressure layer v(0) y substrate. The vertical (y) dimension of 6.8 nm z is assumed. The vertical periodicity is x necessary for the Ewald summations [18], [19]. In order to fix the position of the Fig. 1 – Schematic diagram of MD simulation cell. substrate against the particle impact force, v(y) is particle incident velocity. v(0) is the velocity of atoms in the pressure layer (shown in Fig. 1) the substrate.
are frozen with a null set-force in all directions, that is, x, y and z. The impact incident angle of the particle is zero. The particle is assumed to move without any rotational motion before contact with the substrate. The initial temperatures and incident Table 1 – MD Simulation setup – for Ti Particle and Ti velocities of the particle and the substrate were Substrate and Ni Particle and Ti Substrate set as in Table 1, which is a simulations’ setup Event code Particle Parameters for Ti-Ti particle-substrate and Ni-Ti particleVelocity Temperature Diameter Ti Ni substrate combinations. Incident speeds larger [m/s] [K] [nm] than 1250 m/s are unlikely to be used in the 1Ti-0 250 750 2.38 actual spray process but are adopted in order 1Ti-1 1Ni-1 500 750 2.38 to observe high-energy impact circumstances 1Ti-2 1Ni-2 750 750 2.38 corresponding to large particle sizes. MD 1Ti-3 1Ni-3 1000 750 2.38 1Ti-4 1Ni-4 1250 750 2.38 simulation is carried out at npt integration 1500 750 2.38 conditions with full control of temperature and 1Ti-5 750 350 2.38 pressure [20]. Each of the simulation events 2Ti-1 2Ni-1 2Ti-2 2Ni-2 750 500 2.38 take between 300 ns to 716.1 ns (depending 750 750 2.38 on the applied time steps), at 21.7 as 2Ti-3 2Ni-3 2Ti-4 2Ni-4 750 1000 2.38 (attosecond) timesteps. 750 750 0.68 At the beginning of the the simulation, an 3Ti-1 3Ni-1 750 750 1.70 energy minimisation of the system is performed 3Ti-2 3Ni-2 3Ti-3 3Ti-4
3Ni-3 3Ni-4
750 750
750 750
2.38 3.06
until local atom potential energies are minimised and stable (also known as the equilibrate state) [21]–[23]. Fig. 2 shows a MD cell comprising of an atom packed particle and substrate after 273 ps of minimisation. During the simulations, snapshots of system temperature and atom positions (projectiles) are captured at time-step intervals of 434 ps and are retrived at the end of each simulation for analysis.
Results Table 2 presents results for MD simulation cells for Ti-Ti particle-substrate combinations, captured at 290 ns for velocity and 350 ns for temperature and diameter. The first set shows the effect of varying velocity; the second set shows the effect of varying temperature; and the third set shows the effect of varying diameters. Corresponding temperature-time graphs, a few nanoseconds before and after impact, are reported in Fig. 3, 4 & 5. Likewise, Table 3 presents results for MD simulation cells for Ti-Ni particle-substrate combinations. Their corresponding temperature-time graphs are shown in Fig. 6, 7 & 8. In each of the temperature-time graphs, is a legend of the plots, which can be traced from the simulation “event codes” from Table 1. For example, code 1Ti-3 is a simulation of impact of a 2.38 nm diameter Ti particle with initial temperature and velocity of 750 K and 1000 m/s, respectively. The 3D view of this event (1Ti-3), caught at 290 ns, is shown in Table 2. Further, Fig. 3 shows temperature (drop) during impact (observed from legend line 1Ti-3).
Table 2 - 3D view results of MD simulation cells of impacting Ti particles and Ti substrates under varying velocity, temperature and diameter particle conditions 3D views of the MD simulations
1Ti-2 - 750 m/s
1Ti-3 - 1000 m/s
2Ti-2 – 500 K
2Ti-3 – 750 K
2Ti-4 – 1000 K
3Ti-2 – 1.70 nm
3Ti-3 – 2.38 nm
3Ti-4 – 3.06 nm
1Ti-0 - 250 m/s
1Ti-1 - 500 m/s
1Ti-4 - 1250 m/s
1Ti-5 - 1500 m/s
2Ti-1 – 350 K
3Ti-1 – 0.68 nm
Diameters at 350 ns
Temperature at 350 ns
Velocity at 290 ns
Varying facto r
Table 3 - 3D view results of MD simulation cells of impacting Ni particles and Ti substrates under varying velocity, temperature and diameter particle conditions Varying factor
1Ni-1 – 500 m/s
1Ni-2 – 750 m/s
1Ni-3 – 1000 m/s
1Ni-4 – 1250 m/s
2Ni-1 – 350 K
2Ni-2 – 500 K
2Ni-3 – 750 K
2Ni-4 – 1000 K
Diameters at 350 ns
Temperature at 350 ns
Velocity at 290 ns
3D views of the MD simulations
3Ni-1 - 0.68 nm
3Ni-2 – 1.70 nm
3Ni-3 - 2.38 nm
3Ni-4 - 3.06 nm
Discussion Velocity: From Table 2 & 3, it can be observed that, for velocities below 750 m/s, the incident particle maintains its spherical shape, and the atomic arrangement in the substrate is fairly in good order. Above 750 m/s, on the other hand, the lower parts of the particles are considerably deformed, and a few planer defects can be recognized in the substrates. Moreover, a trend can be observed; with higher impact particle velocity, there is a corresponding increase in the flattening ratio. This results in an increase in the contact area on the particle-substrate interface. Thus, from Fig. 3 & 6, a rapid temperature decrease of the particle is observed during impact. However, with velocities above 1250 m/s, the atoms of the particle tend to shutter and bounce off the substrate, leaving a dent and thus less deposition.
Fig 3 - Effect of particle impact velocity for Ti particle and Ti substrate
Fig 5 - Effect of particle diameter for Ti particle and Ti substrate
Fig 4 - Effect of particle temperature for Ti particle and Ti substrate
Fig 6 - Effect of particle impact velocity for Ni particle and Ti substrate
Fig 7 - Effect of particle temperature for Ni particle and Ti substrate
Fig 8 - Effect of particle diameter for Ni particle and Ti substrate
Temperature: Table 2 & 3 show the elaborate influence temperature has on the particle deposition. The higher the temperature of the particle, the higher the flatening ratio, and thus, the corresponding increase in the contact area. This causes a rapid temperature decrease of the particle during impact as can be obseved from Fig. 4 & 7. The effect is most remarkable for the 750 K and 1000 K simulations. This occurs for both Ti and Ni particles. Particle size: Table 2 & 3 shows the effect of particle size on the deposition. Bigger particles create a larger contact area on the substrate. Hence during impact, the particle temperature drops at a higher rate with bigger particles. This can be observed from Fig. 5 & 8. Again, this occurs for both Ti and Ni particles. Future work: To conduct MD simulations on impacts of Titanium Nitride (TiN) particles on Ti substrate in the CGDS process; to use the Taguachi approach [24], [25] in conducting of MD simulations in CGDS process so as to obtain quantifiable spray prameters. Conclusion This paper has demonstrated the application of the MD simulations of Ti and Ni particles on a Ti Substrate in the CGDS process. It can therefore be concluded that: particle deposition increases with incident velocity, the higher the temperature of the incident particle the better the deposition, and the smaller the particle, the lower deposition. These results are concurrent with experimental results of critical CGDS parameters for Ti and Ni [4], [5], [26]–[28]. Acknowledgement Authors of this paper wish to acknowledge the support of the DST-NRF Centre of Excellence in Strong Materials (CoE-SM) towards this research. Opinions expressed and conclusions made, are the authors’ and not attributable to the CoE-SM. References [1]
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