Simulation and experimental observation of silicon particles' vaporization in RF thermal plasma reactor for preparing Si nano-powder

    Simulation and experimental observation of silicon particles’ vaporization in RF thermal plasma reactor for preparing Si nano-powder Jiaping He, Liuyang Bai, Huacheng Jin, Zhiyuan Jia, Guolin Hou, Fangli Yuan PII: DOI: Reference:

S0032-5910(17)30202-4 doi:10.1016/j.powtec.2017.02.062 PTEC 12400

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Powder Technology

Received date: Revised date: Accepted date:

19 December 2016 13 February 2017 27 February 2017

Please cite this article as: Jiaping He, Liuyang Bai, Huacheng Jin, Zhiyuan Jia, Guolin Hou, Fangli Yuan, Simulation and experimental observation of silicon particles’ vaporization in RF thermal plasma reactor for preparing Si nano-powder, Powder Technology (2017), doi:10.1016/j.powtec.2017.02.062

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Simulation and experimental observation of silicon particles'

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vaporization in RF thermal plasma reactor for preparing Si

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nano-powder

Jiaping Hea,b, Liuyang Baia,*, Huacheng Jina,b, Zhiyuan Jiaa, Guolin Houa, Fangli Yuana,*

University of Chinese Academy of Sciences, Beijing 100049, China

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State Key Laboratory of Multi-Phase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China

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a

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Abstract: Particle size of coarse silicon is a very important parameter in plasma-assisted productions of

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nano-silicon, because an appropriate size cannot only improve nano-silicon's quality, but also reduce the cost of raw materials. In this work, simulations are founded to investigate the effect of particles'

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size on silicon's vaporization process inside radio-frequency (RF) thermal plasma reactor. By counting

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particles' residence time between high temperature region and fully-gasified time inside the reactor, particles' motion and vaporization process can be obtained in statistics. After comparing these two parameters, the gasification ratio of coarse silicon with different size can be finally captured. It is shown that particles below 30 μm all have the gasification ratio above 99.0%, which are suggested as the upper limit of coarse silicon in future experimental works. Moreover, it is also shown that gasification ratios of particles above 30 μm are greatly reduced, illustrating that sacrificing gasification ratio to apply relative bigger particles to prepare silicon nanopowder is inappropriate and uneconomic.

Keywords: particle size, nano-silicon, silicon vaporization, numerical simulation, thermal plasma

Corresponding authors. E-mail address: [email protected] (L. Bai), [email protected] (F. Yuan)

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ACCEPTED MANUSCRIPT 1. Introduction Nano-silicon has been widely applied in many fields [1-5], such as biological technology, industrial

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productions, solar cells, etc. Many methods are thus developed to prepare nano-silicon with high performance, such as laser-assisted electrochemical etching[6], pulsed laser deposition[7], electron

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beam evaporation[8], combustion synthesis[9], radio-frequency (RF) plasma-enhanced vapor deposition [10-12], etc. In these methods, plasma-assisted preparations of nano-silicon has been the

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focus in our laboratory, because of thermal plasma's special superiorities, such as high enthalpy, high

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temperature, highly ionized, and high conductivity [13-17], etc. It has been shown in our previous works that nano-silicon prepared by plasma techniques has very excellent performance[18, 19], coulombic efficiency, low volume variation,

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including high volumetric capacity, ultra-high initial

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good cycling stability, high thermal conductivity, high dielectric constant, etc. However, plasma-assisted preparation works of nano-silicon are faced with a difficult selection--coarse silicon's

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particle size. Although silicon nanpowders have been successfully prepared by the RF plasma-assisted techniques, an appropriate size of coarse silicon cannot only reduce the cost of raw materials, but also eliminate the effect of particles’ vaporization process on the content of silicon nanopowders. Therefore, it is necessary to investigate the relationship between coarse silicon's particle size and vaporization process inside the reactor. To carry out the relationship between coarse silicon's particle size and vaporization process, numerical simulation is much better to be applied in comparison with traditional methods because of its large number of advantages. It can largely reduce the consumption of experimental cost and cycle, and can also provide a great deal of information that cannot be dynamically captured during experimental process, such as instant velocity, residence time, particles tracks, etc. Based on these advantages, it has 2

ACCEPTED MANUSCRIPT been used in many fields, including fluid dynamics[20, 21], heat transfer[22, 23], machinery manufacturing[24], and of course the applications of thermal plasma. Ye et al.[25] founded numerical

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model to analyze the synthesis of alumina nanoparticles for preparing the products with desired size and narrow size distribution in controlled conditions. Jan et al. [26] applied high-voltage circuit

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breakers modelling to analyze the radiation properties of SF6-C2F4 thermal plasmas. Kim et al. [27] modeled the induction plasma process to study the effect of plasma gas composition and operating

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pressure on fullerene synthesis. Therefore, it is concluded that numerical simulation is appropriate to be

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applied to investigate silicon particles' vaporization process.

In this work, models are founded to simulate the preparations of nano-silicon inside plasma

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reactor based on the FLUENT software. Since the coarse silicon fed into the reactor is particle group

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instead of single particle, statistical analysis is more accurate and thus used to analyze particles' residence time in heating interval and fully-vaporization time inside the reactor. Residence time of

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silicon particles with different sizes is firstly captured to analyze the differences of particles' motion. Then, particles' fully-gasified time and initial-gasification time are captured to analyze the effect of coarse silicon's particle size on the heating process of silicon. The curve between coarse silicon’s particle size and gasification ratio can be obtained, by comparing these parameters in statistics. It is easy to find out the threshold value of particles' size, which can guide the selections of coarse silicon well. With further analysis of this curve, it can also be found whether it is worthy sacrificing the gasification ratio of coarse silicon to apply big size particles to reduce the cost of raw materials. Finally, experimental works are completed to check the accuracy of the simulations. Based on the accurate simulations, coarse silicon's particle size can be easier and more scientific to be selected in the future plasma-assisted production of silicon nanopowder. 3

ACCEPTED MANUSCRIPT 2. Modelling approach The following hypotheses are assumed in the present simulations:

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(1). Plasma is in local thermodynamic equilibrium (LTE). (2). Particles are regarded as spherical in solid phase and liquid phase.

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(3). Particle’s volume expansion in the process of melting is neglected. (4). Interactions between different particles are neglected.

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(5). Particles are defined as single particle size distribution.

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2.1 Governing equations

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In the LTE condition, particle's heat flux q inside the plasma reactor can be defined as: (1)

d

(2)

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d

where κ is fluid's heat conductivity, including the freeze conductivity κf and the reaction conductivity κr.

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In the calculation of plasma heating without particles' vaporization, the Nusselt dimensionless number, showing the contributions of convection, is defined as: (3)

where q0 is the heat flux without particles' vaporization, κav is the mean heat conductivity, rw is particle's radius and T is the symbol of temperature, including particle's surface temperature Tw and plasma' bulk temperature T∞. Among them, κav is defined as: d

(4)

In the process of convection heating, the relationship between Nu and other dimensionless numbers have been investigated by many researchers [28-30]. Chen et al[31] built a new equation that can reduce the calculation errors well in the applications of plasma modeling: 4

ACCEPTED MANUSCRIPT 0

0

0 3

0

(5)

where Re is the Reynolds of thermal plasma characterizing fluid's flow patterns, Pr is the Prandtl of

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thermal plasma illustrating the contributions of fluid's properties to heat transfer, C is a correction factor of this equation, ∞ represents the position of bulk plasma, w represents the position near

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and C can be calculated by the equations listed below:

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particle's surface, ρ and μ are the density and viscosity of continuous phase. In these parameters, Re, Pr

(6) (7) (8)

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where u∞, cp,∞ and h are the apparent velocity, heat capacity and specific enthalpy of continuous phase.

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As there are phase changes, it is necessary to get the correction factor of particles' vaporization. A simplified correction method is thus applied in this work, which has already been applied by many

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researchers [32-39]:

(9)

0

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In this equation, (q1/q0)nc can be calculated by: d

(10)

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where Lv is silicon's vaporization enthalpy and S is the heat conduction potential of continuous phase. Parameter S is defined as: d

(11)

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In the plasma-assisted production of silicon nanopowders, particle’s heat conservation can be defined as the equation listed below: (12) 5

ACCEPTED MANUSCRIPT where Qs,v is the fully gasification enthalpy, Qs,r is the radiation heat loss, and Qp,c is the convection heat of thermal plasma. Parameter Qs,v can be divided into four parts: temperature-rising process in

parameter Qs,v can be calculated by the equation listed below. d

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(13)

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0

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solid phase, melting process, temperature-rising process in liquid phase and vaporization process. Thus,

where T0 is the room temperature, T1 is silicon's melting point, T2 is silicon's boiling point, cp,s is

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silicon's heat capacity in solid phase, cp,l is silicon's capacity in liquid phase, ms is single silicon

calculated by the Stefan-Boltzmann law: 0

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particle's mass, Lm is silicon's melting enthalpy. Silicon particle's radiation heat loss Qs,r can be

d

(14)

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0

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where εs is silicon's radiation coefficient, σ is the Stefan-Boltzmann constant value, As is single silicon particle's surface area, and t0 is silicon particle's fully-gasified time. Since Qp,c can be calculated by the

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heat transfer equations discussed above, silicon particle's integral heat conservation equation can be obtained.

d

ms

d

0 0

0

0

d

d

(15)

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2.2 Plasma process and models foundation Fig.1a is the present RF thermal plasma reactor in our laboratory, consisted by powder injector, inner quartz tube, outer quartz tube, induction coils, reaction area, and cooling chamber. Carrier gas stream is injected by powder injector carrying silicon particles to provide silicon raw materials to plasma reactor. Central gas and sheath gas streams are passing through the branch tubes to provide plasma gas and to protect the reactor. Magnetic field is formed by RF electrical power through 6

ACCEPTED MANUSCRIPT induction coils, which can ionize the plasma gas. Recirculating cooling water is pumped, passing

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through the jackets of both reaction area and cooling chamber, to cool down the continuous phase.

Fig.1. (a). RF plasma reactor in laboratory, (b). RF plasma reactor geometric model

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In the actual experimental works of preparing silicon nanopowder by RF plasma reactor, plasma

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arcing is firstly completed to form the plasma torch inside the reactor. Since silicon can react with many substances in high temperature, such as air, nitrogen, oxygen, etc., both of the gas streams fed

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into the reactor are pure argon in this work. Coarse silicon powders (micro-size silicon powders) with the flow rate of 2.0 g/s, are then injected into plasma torch by carrier gas. With plasma torch's heating,

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coarse silicon powders are vaporized and gaseous silicon is obtained. With cooling chamber's high

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cooling rate, gaseous silicon is crystallized and silicon nanopowders are prepared. By the collection of

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cyclone and bag filter, the products of silicon nanopowders are finally obtained. Since gaseous silicon's crystallization process is affected by cooling chamber's cooling rate, the effect of coarse silicon's particle on the preparations of silicon nanopowder is focused on coarse silicon's vaporization process. Therefore, models applied in the present work are founded to investigate the vaporization process of coarse silicon. To simulate the plasma reactor intuitively, a three-dimensional model is founded based on FLUENT software, which is shown in Fig.1b. Computational domains are focused on the vaporization area of coarse silicon, involving the inner area of quartz tube, reaction area and cooling chamber. It needs to be noted that there is only part of cooling chamber that is added in this model, because the temperature field inside cooling chamber has little contribution to silicon particles' vaporization. The outlet boundary is thus defined as the bottom of cooling chamber. Plasma is added between the bottom 7

ACCEPTED MANUSCRIPT of inner quartz tube and top of reaction area, shown in Fig.1b. In addition, to simplify the calculations, inlet boundary of central gas and sheath gas streams are defined as the top circular cross-sections of

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reactor, instead of the actual branch tubes. Based on these conditions, the foundation of models is thus completed.

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2.3 Calculation specifications

The flow rate of gas streams in this works is listed in Table 1, including mass flow rate and

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volume flow rate. Apart from this data, the other specifications are listed below:

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(1). Working pressure inside plasma reactor is set as atmospheric. (2). RF power is set as 30 kW, similar to the actual experimental condition.

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(3). Component of all the gas streams is set as pure argon.

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(4). Discrete phase model (DPM) is applied to simulate silicon particles' injection.

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(5). Turbulent models are defined as the k- standard model.

Table 1. Gas flow rate set in the simulation

3. Results and discussions 3.1 Fluid fields and particle's trajectories Based on the specifications mentioned above, numerical simulations are completed after some iterations. As it is assumed that discrete phase has no effect on continuous phase, fluid fields inside plasma reactor including temperature field, axial velocity field and radial velocity field, are obviously the same. Thus, the flow fields, shown in Fig.2, can be firstly captured to investigate continuous phase' conditions. Fig.4a is the temperature distributions inside the plasma reactor, which can help finding out the heating interval of silicon. In the central area of quartz tube, most are high temperature regions, 8

ACCEPTED MANUSCRIPT except a cool region near the outlet nozzle of powder injector, which is formed by the impact of carrier gas. As this cool region is only small part of the temperature field, the effect is insignificant and thus is

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neglected. In addition, it is shown that temperature distribution above cooling chamber is all above 4000 K, and that temperature distribution below reaction area is quickly decreased below 2500 K.

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Since silicon's boiling point is 2628 K, it is indicated that the main heating interval is between the

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outlet nozzle of powder injector and the bottom of reaction area.

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Fig.2 Fluid fields: (a). Temperature field, (b). Axial velocity field, (c). Radial velocity field Velocity field inside plasma reactor is split into two parts to study continuous phase's motion in

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axial direction and radial direction, exhibited in Fig.2b and Fig.2c. It is shown that axial velocity ranges

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from 0 to 12.083 m/s, and that radial velocity ranges from -0.928 m/s to 2.345 m/s. For axial velocity, large range can greatly affect particles' motion in axial direction, which can greatly affect particles'

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residence time in high temperature regions. For radial velocity, its existence can bring out particles' diffusion in radial direction. Since temperature field distributed in the wall regions is much lower than central area, diffused particles' heat transfer temperature differences (HTTDs) are lower than non-diffused particles. In general, it is concluded that the effect of continuous phase's velocity field is great and is needed to be taken seriously. Simulations of silicon with different sizes ranging from

μm to 0 μm are then completed.

Particle trajectories are captured to study silicon particles' motion, involving particles' velocity distributions and continuous phase's temperature distributions, which are displayed in Fig.3. It is shown that particles' diffusion intensity is greatly reduced depending on particle size. When silicon particles are below 0 μm, their trajectories can fully fill the bottom cross-section of outer quartz tube. When 9

ACCEPTED MANUSCRIPT silicon particles are below 30 μm, their trajectories can fully fill the bottom cross-section of reaction area. However, when silicon particles are above 40 μm, the trajectories cannot even fully fill the outlet

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boundary of computational domain. As diffused particles' HTTDs are lower than non-diffused particles,

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it can be concluded that big particles' HTTDs are bigger than small particles.

Fig.3. Particle trajectories: (a). 5 μm, (b). 10 μm, (c). 15 μm, (d). 20 μm, (e). 25 μm, (f). 30 μm, (g).

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35 μm, (h). 40 μm, (i). 45 μm, (j). 50 μm

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This result can just be explained by the existence of radial velocity, which has been mentioned above. When silicon particles are passing through the reactor with continuous phase, most are affected

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by vapor phase's drag force in radial direction, which is complied with the Stokes equation.

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(16) (17)

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where FD is the drag force of vapor phase, ζ is the drag coefficient, ds is silicon particle's diameter, and us,r is the relative velocity between continuous phase and silicon particle in radial direction. Then, particle's acceleration -dus,r/dt in radial direction can be obtained. d d

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(18)

It can be found that particle's acceleration is inversely proportional to particles' diameter. Since radial velocity distribution is constant based on the simulation assumptions, it is concluded that small particles are easier to be affected by radial velocity than big particles. Therefore, big particles' diffusion is obviously slighter that small particles.

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ACCEPTED MANUSCRIPT 3.2 Particles' motion and vaporization process 3.2.1 Particles residence time

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For illustrating particles' vaporization process intuitively, particles' motion in high temperature region is very necessary to be studied. As it has been discussed above that the heating interval of silicon

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particles is between the outlet nozzle of powder injector and the bottom of reaction area, residence time of particles with different sizes in this interval is firstly captured. Since the actual coarse silicon are a

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group of particles instead of single particle or several particles, particles' residence time in statistics is

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more accurate, which is shown in Fig.4a.

By comparing the distributions of particles' residence time, it is easily found that the residence

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time of most particles, above 80%, are between 0.020 s and 0.035 s, although the diameter of these

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particles is obviously different. It means that particle size cannot significantly affect the residence time of most silicon particles. And it is also found that the overall range of small particles' residence time is

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much wider than that of big particles When particles are above 0 μm, the residence time ranges from 0 0 7 s to 0 0

s When particles are above 0 μm, the residence time ranges from 0.016 s to 0.070 s.

However, when particles are below 0 μm, the residence time of part silicon particles can be even more than 0.100 s. Although there are only small part particles obtaining the residence time below 0.020 s or above 0.035 s, it can be indicated that small particles can be easier to be affected by continuous phase.

Fig.4. (a). Distributions of particles' residence time: 5.0 μm~50.0 μm, (b). Mean and minimum residence time of silicon particles: 5.0 μm~50.0 μm To further realize the effect of particle's size on the residence time, the minimum residence time and mean residence time are separately listed out, which are shown in Fig.4b. It is shown that the 11

ACCEPTED MANUSCRIPT minimum residence time is increased slowly by particles' size, and that residence time is firstly decreased quickly and then increased slowly by particle size. For minimum residence time, the range is

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about 25.18% of their average value, which is greatly smaller than the change of particle size. And it is interesting that small particles' minimum residence time is lower than big particles. For mean residence

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time, the range is about 18.91% of their average value, which is greatly smaller than the change of particle size, too. And it is also interesting that small particles' mean residence time is lower than big μm

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particles, when particles are above

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These results can also be explained based on the Stokes equation. In axial direction, silicon particles are affected by three forces--gravity, continuous phase's buoyancy and drag force. As particles

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are all flowing downwards, the equation of particles' relative velocity us,a can thus be defined as: 3

d

3

3

(19)

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d

where -dus,r/dt is particle's acceleration in axial direction. Since continuous phase's density is very low

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in comparison with silicon's density, continuous phase's buoyancy is neglected. Then, to study the effect of continuous phase's drag force on particles' residence time, the ratio between drag force and gravity γ is improved and listed below:

3

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(20)

With pre-calculation of particles' Reynolds Rep, silicon particles’ motion is located in the Stokes area. In this area, the drag coefficient ζ is complied with the equations listed below. (21) (22) Then, the ratio between drag force and gravity γ can be further simplified. 7 (23) 12

ACCEPTED MANUSCRIPT Since the initial velocity of particles are 0, the relative velocity us,a can be bigger than 10.0 m/s. Although silicon particles have been accelerated by continuous phase in powder injector, relative

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velocity us,a is still above 1.0 m/s. Based on this condition, the ratios γ of particles with different sizes can be finally estimated, ranging from 2.63×104 to 2.63×106. It is indicated that gravity's effect is trace

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in comparison with continuous phase's drag force. As the ratios γ are too big, particles' acceleration section is only occupying a small part of the track line in heating interval. This result can finely explain

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the phenomena that the residence time cannot be greatly affected by particle size. In addition, as the

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ratio γ is inversely proportional to the square of particles' diameter, it is indicated that small particles can be easier to be affected by continuous phase. Thus, small particles' residence time is lower than big

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particles, which is finely meeting with the results listed above. However, when particles are below 25

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μm, there's another impact that can greatly affect particles' residence time--particles' diffusion. It has been discussed above that small particles' diffusion intensity is obviously higher than big particles. And

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high diffusion intensity means wider range of residence time. Therefore, when particles' are below 25 μm, particles' mean residence time is increasing instead of decreasing depending on particle size. In general, regardless of these sight changes, it is concluded that drag force always plays the most important role in particles' motion, especially the residence time. It is worth mentioning that particles' residence time is not changeless. Although the residence time cannot be greatly influenced by particle size, it can be improved by the change of some other parameters, such as the flow rate of gas streams, plasma reactor's geometric parameters, RF power, etc. Since continuous phase's effect plays the most important role, optimization of gas streams' flow rates is the most effective method. This work will soon be continued in the future.

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ACCEPTED MANUSCRIPT 3.2.2 Particles' fully-gasified time For illustrating particles' vaporization process, calculations based on particles' heat transfer

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equations listed above are then completed. Particles' fully-gasified time is then obtained, which is shown in Fig.5a. The minimum fully-gasified time and mean fully-gasified time is also separately listed

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out, which is shown in Fig.5b. Particles' fully-gasified time is growing greatly and that the distributions are all very narrow. Although part of particles is diffused toward regions, their fully-gasified time is not

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change too much. It means that particles' size plays the most important role in particles' vaporization

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process. This result is obviously similar to the actual experimental results.

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Fig.5. (a). Distributions of particles' fully-gasified time: 5.0 μm~50.0 μm, (b). Mean and minimum

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fully-gasified time of silicon particles: 5.0 μm~50.0 μm 3.2.3 Fully-vaporized particles ratio and gasification ratio of coarse silicon

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As every particle stream's residence time and fully-gasified time have been obtained, it is easy to capture the fully-vaporized particles ratio in statistics, shown in Fig.6a. Obviously, when residence time is longer than fully-gasified time, particles can be fully vaporized. However, when residence time is shorter than fully-gasified time, it doesn’t mean that there's no gaseous silicon. In fact, only if residence time is sufficiently shorter than fully-gasified time, there would be no fully-vaporized silicon. The threshold value is another specific time--the initial-gasification time, which can provide enough time for particles to complete the processes of temperature-rising in solid phase, melting and temperature-rising in liquid phase. Mean initial-gasification time of silicon particles with different sizes is then listed out, which is shown in Fig.6b, coupled with the mean fully-gasified time. It is easily found that initial-gasification time is only about 20.0% of fully-gasified time. This result indicates that 14

ACCEPTED MANUSCRIPT most heat is consumed by particles' vaporization enthalpy. With consideration of this specific time, the

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gasification ratios of coarse silicon with different sizes are easily captured, which is exhibited in Fig.6a.

Fig.6. (a). Gasification ratio of silicon particles: 5.0 μm~50.0 μm, (b). Mean initial-gasification

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time and mean fully-gasified time: 5.0 μm~50.0 μm

It is shown in Fig.6a that both fully-vaporized particle ratios and gasification ratios of coarse

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silicon are greatly reduced with particle size increasement.When particles are below

μm, all the

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gasification ratios are 100%, illustrating that particles are fully vaporized. When particles are between μm and 30 μm, the gasification ratios are above 99.0% and reducing slowly. However, when

0 μm, there are almost no fully vaporized particle. In the plasma-assisted preparation,

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above

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particles are above 30 μm, the ratios are quickly reducing below 90 0% Especially, when particles are

productions are absolutely acceptable for applications when the content of nano-silicon is above 99.0%.

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Thus, although the fully-vaporized particles ratio of 30 μm particles are less than 99.0%, the threshold of coarse silicon's particle size can be confirmed as 30 μm With consideration of raw materials' cost, particles between

0 μm and 30 μm are suggested to be applied in the actual productions. As

gasification ratios are reducing greatly when particles are above 30 μm, sacrificing particles' gasification ratios to apply bigger particles bring a new problem--the separation of silicon nanopowders. Since nano-size particles' separations are very complex and costly, it is not very advisable to select particles above 30 μm as raw materials In addition, what needs to be noted is that the threshold value--30 μm--is also not changeless. As it has been discussed above that particles' residence time can be optimized, it has possibilities to improve this threshold value within an appropriate range.

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ACCEPTED MANUSCRIPT 3.3 Experiment results of silicon particles' vaporization Since this work has some assumptions that are different with the actual operation, experiments are

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then completed to check the accuracy of the simulation results. As the coarse silicon on sale is in the distribution with wide range instead of single distribution,and the screening process of micro-size

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particles is very difficult, 0 μm and 30 μm are finally selected in the experiments SEM images of coarse silicon are firstly obtained, shown in Fig.7a and Fig.7b. After the preparation of silicon

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nanopowders, SEM images of final productions are obtained, shown in Fig.7c and Fig.7d. Furthermore,

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to characterize silicon nanopowders' size distributions more intuitively, particle size analyzing (PSA) is

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then completed and the size distributions are shown in Fig.8a and Fig.8b.

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Fig.7. SEM images: (a). 30 μm coarse silicon, (b). 10 μm coarse silicon, (c). 30 μm vaporization

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result, (d). 10 μm vaporization result

Fig.8. PSA results: (a). 30 μm size distribution, (b). 10 μm size distribution

For 30 μm coarse silicon, it is shown in Fig.7c that most particles are below 500 nm. And it is also shown in Fig.8a that the mass fraction of silicon nanopowders below 500 nm is above 99.0%. For 10 μm coarse silicon, it is shown in Fig.7d that all particles are below 200 nm. And it is also shown in Fig.8b that the mass fraction of silicon nanopowders below 200 nm is 100.0%. It has been discussed above that the gasification ratio of 30 μm coarse silicon is above 99.0% and that the gasification ratio of 10 μm coarse silicon is 100.0%. The relative big part particles (near 500 nm), exhibited in Fig.8a, can just characterize the incompletely-vaporized particles. Thus, without the effect of gaseous silicon's crystallization, the experiment results are almost completely similar to the simulation results. In general, 16

ACCEPTED MANUSCRIPT it is concluded that the simulation results are correct, which can guide the selections of raw materials in the future experimental works.

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Although simulation results are accurate, it is necessary to analyze the calculation errors for further investigating silicon's vaporization process. It is shown in the SEM images of coarse silicon that particles are above 10 μm or 30 μm because of the wide distributions, and that the shape factor of

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part

coarse silicon is all irregular instead of spherical. In addition, particles' crystallization process can also

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affect the quality of final productions. Therefore, the errors can be split into three parts: size

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distributions, shape factor, and crystallization process. For size distributions, when particles are sufficient small, wide distributions have no effect on vaporization results, because the relative big

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particles are still below 30 μm. However, when particles are near 30 μm, the relative big particles can

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be above the threshold value and cannot be fully vaporized. Thus, in the actual productions, it is necessary to screen out these relative big particles. For particles' shape factor, as spherical particles

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have the smallest specific surface area, heat transfer area of non-spherical particles is bigger than that of spherical particles. Moreover, shape factor can also affect particles' drag force, leading to the differences of residence time between non-spherical and spherical particles. Thus, it can be concluded that the shape factor also plays an important role in particles' vaporization process. For particles' crystallization process, it has great influence on the plasma-assisted preparation of silicon nanopowders, because this process is neglected in the present work. Furthermore, it is worth mentioning that some other parameters, such as the gas streams, equipment structure, particles' flow rate, etc., also cannot be neglected. Therefore, it is necessary to investigate both of these parameters in our future works.

4. Conclusions Selections of coarse silicon's particle size are very important in plasma-assisted productions of 17

ACCEPTED MANUSCRIPT nano-silicon. Numerical simulations are founded in this work to investigate the impact of particle size on coarse silicon's vaporization process. Several conclusions can be drawn from the discussions:

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(1). Models are founded to simulate the plasma-assisted preparation of nano-silicon. The motions of continuous phase and silicon particles inside plasma reactor are then captured. Particle trajectories

effect of continuous phase's drag force in radial direction.

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show that big particles' diffusion intensity is obviously lower than small particles, resulting from the

μm to 0 μm, are obtained in statistics The residence time has no significant

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interval, ranging from

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(2). Residence time distributions of silicon particles with different sizes between the heating

difference, which is most between 0.020 s and 0.035 s. Particle’s velocity equations in axial direction,

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drag force, instead of gravity.

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finely explaining this result, show that micro-size particles are mainly affected by continuous phase's

(3). Fully-gasified time of silicon particles with different sizes, coupled with the

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initial-gasification time, is obtained based on particles' heat transfer equations inside the reactor. It is shown that both of the fully-gasified time and the initial gasification time are greatly increased depending on particles' size, which is similar to the actual experimental results. (4). Fully-vaporized particles ratios and gasification ratios of coarse silicon are captured based on the comparison between the residence time, initial-gasification time and fully-gasified time. It is illustrated that all the ratios are greatly affected by particles' size Particles below 30 μm have the gasification ratios of above 99.0%, acceptable for the actual applications, which is suggested to be applied in the actual preparation When particles are above 30 μm, particles' gasification ratio is greatly reduced, leading the cost of nano-silicon's separation. Thus, sacrificing gasification ratios to apply bigger particles as coarse silicon is not very advisable. 18

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Experimental works, applying

0 μm and 30 μm as coarse silicon's particle size, are

completed to check the accuracy of simulation results. SEM images and PSA results show that

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vaporization results are almost completely similar to numerical simulations. Therefore, it is concluded that the simulation results are correct and can guide the selections of coarse silicon in the

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plasma-assisted production of silicon nanopowders.

Acknowledgements

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This work was supported by the National Natural Science Foundation of China (NSFC, no.

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11535003).

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ACCEPTED MANUSCRIPT Table 1. Gas flow rate set in the simulation Parameters

Carrier gas

Mass flow rate/g·s-1 3

Sheath gas

0.0924

0.9235

1.8471

0.20

2.00

4.00

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Volume flow rate/m ·h

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Central gas

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Graphical abstract

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ACCEPTED MANUSCRIPT Highlights 1. Model was built to simulate silicon's vaporization inside plasma reactor.

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2. Silicon's residence time and fully-gasified time in the reactor was obtained. 3. Main force of micro-particle's motion was confirmed as drag force.

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4. Gasification ratios of raw materials with different size were obtained.

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Threshold particle size of raw materials was confirmed as 30 μm

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