The Growth Characteristics and Kinetics of Metallic Iron in Coal-Based Reduction of Jinchuan Ferronickel Slag

: As the fourth-largest industry waste residue, after iron slag, steel slag, and red mud, in China, the comprehensive utilization of nickel slag is imminent. Coal-based reduction combined with magnetic separation was considered an efﬁcient method to extract iron from nickel slag. During the coal-based reduction of Jinchuan ferronickel slag, the growth characteristics and kinetics of metallic iron were investigated in this paper. The metallisation rate and metal iron grain size gradually increased with the reduction temperature or the reaction time, and the coal-based reduction process was divided into the rapid formation period and the aggregation growth period of the metallic phase. The granularity distribution of metallic iron obeyed the Doseresp sigmoidal function, and the activation energy of grain growth at different stages were 52.482 ± 4.448 kJ · mol − 1 and 26.426 ± 3.295 kJ · mol − 1 , respectively. Meanwhile, a mathematical growth model of the metallic iron grains was also established.


Introduction
Since the economy and the smelting industry developed rapidly, the quantity of smelter slag has been increasing for a long time in China. Common smelting furnace slag includes steel smelting slag, red mud, copper smelting slag, lead slag, ferronickel slag, and sulfuric acid slag, etc. Approximately 30 million tons of ferronickel slag are emitted each year, accounting for more than a fifth of the global production [1][2][3]. The large stockpiles of nickel slag not only occupy land and pollute the environment, but also bring about severe challenges to the sustainable development of the nickel smelting industry [4,5]. Moreover, abundant metal resources are lost in the smelter slag, which is detrimental for the rational development and utilisation of resources. In addition, some non-ferrous metal slag usually contains lead, arsenic, cadmium, mercury, and other harmful substances, which pose a serious threat to the health and survival of residents [6][7][8]. At present, the vast majority of ferronickel slag in China is produced by humus laterite ore in the process of reduction smelting ferronickel in electric furnaces. The composition of ferronickel smelting slag in electric furnaces in different regions is similar. Its main components are FeO, MgO, and SiO 2 , which belong to the FeO-MgO-SiO 2 ternary slag system. Its main mineral components are 2FeO·SiO 2 , FeO·SiO 2 , and MgO·SiO 2 . Therefore, this study has important reference significance for the development and utilization of pyrometallurgical nickel slag at home and abroad. Consequently, it is essential to develop and utilise smelter slag through environmental-friendly technologies [9,10]. However, owing to its complex mineral characteristics, smelter slag is extremely difficult to recycle via the traditional

Materials
The ferronickel slag was collected from Jinchang, Gansu province, China. The 2FeO·SiO 2 (fayalite) was the main iron mineral in the ferronickel slag. The chemical composition analysis of the ferronickel slag is listed in Table 1, which shows the main metallic elements are Fe (45.40%), Ni (0.15%), Co (0.13%), and Cu (0.24%). The primary gangue mineral is SiO 2 (33.50%). Moreover, the contents of CaO and MgO are 0.92% and 4.80%, respectively. Table 2 is the industrial analysis and chemical composition of anthracite collected from Jilin, indicating that coal is a superior reductant for the coal-based reduction experiment owing to the low amount of coal ash, high content of fixed carbon and volatile matter, and the low amount of harmful element sulphur. The microstructure of ferronickel slag is shown in Figure 1.

Experimental Approach
Ferronickel slag and pulverized coal (mass ratio 1:2) were well mixed and placed into a 100 mL crucible. When the temperature in the furnace chamber reached the target temperature, the crucible containing well-mixed ferronickel slag and coal was placed in the resistance furnace. As the temperature reached the given reaction temperature, timing was started, and the temperature was kept constant until the end of the reaction. The reduction products were cooled to 20 • C in water after coal-based reduction. The cooling products were dried, broken, and ground to −0.074 mm accounting for 80%. The reduction products, the SpecoFix resin, and the SpecoFix-20 curing agent were put into a special sampler for 24 h to solidify. The samples were polished to meet the requirements of the image analysis.

Metallisation Rate of Coal-Based Reduction
The metallisation rate is the specific value of metal iron (MFe) content and total iron (TFe) content, and it is used to characterise the reduction degree of iron oxide, as shown in Equation (1). The content of MFe and TFe were determined through titration three times to decrease the errors.
where M represents the metallisation rate of the coal-based reduction; w(MFe) represents the mass fraction of metallic iron (%); w(TFe) is the mass fraction of total iron (%).

Scanning Electron Microscopy Analysis
In this study, scanning electron microscopy (SEM) (SSX-550, Shimadzu, Japan) was used to observe the apparent morphology of the coal-based reduction products at an acceleration voltage of 15 kV. An EDS (Inca, Oxford, UK) was used to analyse the differences between the various components before and after the coal-based reduction.

Size Measurement of Metal Particles
Due to the metallic iron and the slag being closely integrated in the reduction sample and the particle size being diverse, it is difficult to separate the metallic iron and slag phase without destroying the shape and size of the metallic phase. In recent years, with the rapid development of image processing technology and computer vision technology, image analysis technology is widely used for the detection of particle size [23,24]. The optical microscopy (BX51, OLYMPUS, Shinjuku, Tokyo, Japan) image analysis technology was used to measure the granularity of metallic iron. The image was divided equally into 177 areas, and was collected from the middle of each grid to ensure the representativeness of the image, as shown in Figure 2. Figure 3 demonstrates the image processing. More than 5000 metal particles were counted using the metallographic image analysis system OLYCIA M3 in each coal-based reduction product. The image was analyzed by the OLYCIA M3 metallographic image analysis system. The image (Figure 3a) was collected and reversed to obtain the negative image of the original image ( Figure 3b). The particles were extracted from the image through the binarization process ( Figure 3c). The particle profiles were automatically recognised and marked in order to count and screen the particle numbers ( Figure 3d). In order to ensure representativeness of the measured data, the statistical numbers of metallic particle size in the reduced sample at each test point were more than 5000.
used to observe the apparent morphology of the coal-based reduction products at an acceleration voltage of 15 kV. An EDS (Inca, Oxford, UK) was used to analyse the differences between the various components before and after the coal-based reduction.

Size Measurement of Metal Particles
Due to the metallic iron and the slag being closely integrated in the reduction sample and the particle size being diverse, it is difficult to separate the metallic iron and slag phase without destroying the shape and size of the metallic phase. In recent years, with the rapid development of image processing technology and computer vision technology, image analysis technology is widely used for the detection of particle size [23,24]. The optical microscopy (BX51, OLYMPUS, Shinjuku, Tokyo, Japan) image analysis technology was used to measure the granularity of metallic iron. The image was divided equally into 177 areas, and was collected from the middle of each grid to ensure the representativeness of the image, as shown in Figure 2. Figure 3 demonstrates the image processing. More than 5000 metal particles were counted using the metallographic image analysis system OLYCIA M3 in each coal-based reduction product. The image was analyzed by the OLYCIA M3 metallographic image analysis system. The image (Figure 3a) was collected and reversed to obtain the negative image of the original image ( Figure 3b). The particles were extracted from the image through the binarization process ( Figure 3c). The particle profiles were automatically recognised and marked in order to count and screen the particle numbers (Figure 3d). In order to ensure representativeness of the measured data, the statistical numbers of metallic particle size in the reduced sample at each test point were more than 5000.      The frequency distribution and cumulative distribution of particle numbers were adopted to characterise the test data, as shown in Equations (2) and (3).
where f (D i ) represented the frequency distribution of size interval D i (%). n i was the number of particles in the size interval D i . N represented the total number of particles.
where Q(d) represented the cumulative frequency of particle number (%). n(d < d i ) was the number of particles size smaller than d i . d i was the size interval boundary. N represented the total number of particles.

Results and Discussion
3.1. Formation and Microstructure of Metal Phase 3.1.1. Metallisation Process Figure 4 demonstrates the metallisation rate of the coal-based reduction for different reduction times and temperatures, which shows that the metallisation rate of the reduction samples at different reduction temperatures exhibits the same tendency. The metallisation rate increased rapidly and then slowly until it stabilised with the reduction time. For example, when the reduction temperature was 1473 K, the metallisation rate increased rapidly from 18.47% to 61.23% as the reduction time was extended from 10 min to 40 min. Nevertheless, the metallisation rate increased slowly from 61.23% to 73.2% with the reduction time extending from 40 min to 100 min. Consequently, the metallisation process of the reduction products was divided into two stages: the rapid formation of the metallic phase and the relatively stable content of the metallic phase.
Minerals 2021, 11, x of the reduction products was divided into two stages: the rapid formation phase and the relatively stable content of the metallic phase. According to the TG weight-loss curve of ore sample ( Figure 5), the s basically did not change with the increase in temperature, indicating tha obvious weight-loss process. It could be seen from the DSC curve that wi According to the TG weight-loss curve of ore sample ( Figure 5), the sample quality basically did not change with the increase in temperature, indicating that there was no obvious weight-loss process. It could be seen from the DSC curve that with the increase in temperature, the DSC curve gradually increased without obvious peaks and troughs, i.e., there were no obvious endothermic and exothermic peaks, but the slope of the curve changes at about 1100 • C (1373 K). The change of slope was completed in the temperature range from 1050~1150 • C. There was no obvious slope change point, indicating that the slag was a melt rather than a crystal, and there was no fixed melting point; additionally, the phase transition occurred in the temperature range from 1050~1150 • C. It was solid before 1050 • C and liquid after 1150 • C. The results of thermogravimetric and differential thermal analysis showed that the composition of the slag was relatively single, there was basically no weight loss, and the melting temperature of the ore was about 1373 K.  Figure 4 indicates that the reduction temperature significantly influenced the metallisation process of the ferronickel slag. The metallisation rate gradually rose with the rise of temperature. As the coal-based reduction reached a certain extent, the gradient of the metallisation rate decreased with the reduction time. At the reduction time of 20 min, the metallisation rate increased from 59.76% to 89.08% as the reduction temperature rose from 1523 K to 1623 K, whereas the metallisation rate merely improved from 81.79% to 97.16% for the reduction time 40 min. Meanwhile, the time for the metallisation rate to reach the stable stage shortened as the reduction temperature elevated.

Microstructure of Metal Phase
The metal phase microstructure of the coal-based reduction was analysed using SEM. Figures 6 and 7 show the SEM images and EDS spectra of the reduction samples, respectively. Figure 8 shows the SEM image of the coal-based reduction samples for the reduction temperature of 1523 K, CaO content of 15%, and reduction times of 10, 20, 40, and 60 min, respectively.
As shown in Figure 6, the metallic iron granularity gradually increased as the time and reduction temperature increased, which promoted the growth of the metallic iron. The prolongation of the reduction time accelerated the reduction of iron minerals when the reduction time was less than 40 min, and supplied sufficient time for the aggregation of metallic phase. The distinct boundary between the metallic particles and the slag matrix were generated owing to the addition of CaO, which was also beneficial for the formation of the metallic particles. stable stage shortened as the reduction temperature elevated.

Microstructure of Metal Phase
The metal phase microstructure of the coal-based reduction was analysed using SEM. Figures 6 and 7 show the SEM images and EDS spectra of the reduction samples, respectively. Figure 8 shows the SEM image of the coal-based reduction samples for the reduction temperature of 1523 K, CaO content of 15%, and reduction times of 10, 20, 40, and 60 min, respectively.  As shown in Figure 6, the metallic iron granularity gradually increased as the time and reduction temperature increased, which promoted the growth of the metallic iron. The prolongation of the reduction time accelerated the reduction of iron minerals when the reduction time was less than 40 min, and supplied sufficient time for the aggregation of metallic phase. The distinct boundary between the metallic particles and the slag matrix   Figure 9 demonstrates the cumulative distribution of metallic grain under different reduction times and temperatures. Figure 9 indicates that the largest frequency distribution appears in the 5-10 μm size range in each curve, and the frequency distribution of the 0-5 μm size range is somewhat less than that of 5-10 μm. The frequency distribution of each size range decreased rapidly with particle diameter. The reduction temperature and time significantly influenced the metallisation process of the ferronickel slag. The percentage content of the larger-sized particles increased with increasing reduction time. At reduction temperature 1473 K, the frequency of 5-10 μm particles decreased from 36.06% to 28.26% with the reduction time extending from 20 min to 100 min, while the frequency of 15-20 μm particles increased from 7.94% to 10.21%. Figure 9 also suggests that the cumulative curve of metallic iron grain gradually moved to the right with the prolongation of the reduction time. Owing to the increase in the reduction time, the ferronickel slag was reduced more thoroughly to promote the growth of the metallic phase. The distribution frequency of smaller iron grain decreased as the temperature increased, while the distribution frequency of the coarse iron grain enlarged gradually.  Figure 9 indicates that the largest frequency distribution appears in the 5-10 µm size range in each curve, and the frequency distribution of the 0-5 µm size range is somewhat less than that of 5-10 µm. The frequency distribution of each size range decreased rapidly with particle diameter. The reduction temperature and time significantly influenced the metallisation process of the ferronickel slag. The percentage content of the larger-sized particles increased with increasing reduction time. At reduction temperature 1473 K, the frequency of 5-10 µm particles decreased from 36.06% to 28.26% with the reduction time extending from 20 min to 100 min, while the frequency of 15-20 µm particles increased from 7.94% to 10.21%. Figure 9 also suggests that the cumulative curve of metallic iron grain gradually moved to the right with the prolongation of the reduction time. Owing to the increase in the reduction time, the ferronickel slag was reduced more thoroughly to promote the growth of the metallic phase. The distribution frequency of smaller iron grain decreased as the temperature increased, while the distribution frequency of the coarse iron grain enlarged gradually. Figure 10a,b indicate the average diameter of the equal-area circle and the roundness of the iron grain at different reduction temperatures and reduction times. Figure 10 indicates that the granularity increased with the reduction temperature. At the reduction time of 40 min, the average diameter of the equal-area circle of the metallic particles increased from 14.17 µm to 19.88 µm with the reduction temperature varying from 1473 K to 1623 K; meanwhile, the roundness enlarged from 0.57 to 0.68. Consequently, the granularity of metallic iron improved gradually with the reduction temperature. In addition, the appearance of the metallic particles verged toward a spherical shape. The diffusion rate of the metallic iron accelerated due to the increase of temperature, which promoted the diffusion migration of the metallic iron. Meanwhile, the viscosity and the interfacial tension of the ferronickel slag declined with the reduction temperature. Therefore, the metallic iron particles aggregated more easily to acquire the spherical appearance on account of the interfacial energy effect.  Figure 10a,b indicate the average diameter of the equal-area circle and the roundness of the iron grain at different reduction temperatures and reduction times. Figure 10 indicates that the granularity increased with the reduction temperature. At the reduction time of 40 min, the average diameter of the equal-area circle of the metallic particles increased from 14.17 μm to 19.88 μm with the reduction temperature varying from 1473 K to 1623 K; meanwhile, the roundness enlarged from 0.57 to 0.68. Consequently, the granularity of metallic iron improved gradually with the reduction temperature. In addition, the appearance of the metallic particles verged toward a spherical shape. The diffusion rate of the metallic iron accelerated due to the increase of temperature, which promoted the diffusion migration of the metallic iron. Meanwhile, the viscosity and the interfacial tension of the ferronickel slag declined with the reduction temperature. Therefore, the metallic iron particles aggregated more easily to acquire the spherical appearance on account of the interfacial energy effect.    Figure 10a,b indicate the average diameter of the equal-area circle and the roundness of the iron grain at different reduction temperatures and reduction times. Figure 10 indicates that the granularity increased with the reduction temperature. At the reduction time of 40 min, the average diameter of the equal-area circle of the metallic particles increased from 14.17 μm to 19.88 μm with the reduction temperature varying from 1473 K to 1623 K; meanwhile, the roundness enlarged from 0.57 to 0.68. Consequently, the granularity of metallic iron improved gradually with the reduction temperature. In addition, the appearance of the metallic particles verged toward a spherical shape. The diffusion rate of the metallic iron accelerated due to the increase of temperature, which promoted the diffusion migration of the metallic iron. Meanwhile, the viscosity and the interfacial tension of the ferronickel slag declined with the reduction temperature. Therefore, the metallic iron particles aggregated more easily to acquire the spherical appearance on account of the interfacial energy effect.

Granularity Distribution Function of Iron Grain
To characterise the granularity distribution of the iron grain, four frequency distribution functions were adopted: Gaussian distribution, Langevin exponential function, Doseresp sigmoidal function, and Power function, as shown in Equations (4)- (8).
where f (x) represented the distribution frequency (%) for particle size x (µm). µ represented the geometric average particle size (µm). σ was the geometric standard deviation.
Origin Pro 8.0 software was used to ascertain the relationship between the four functions and the granularity distribution of the iron grain. The determinate coefficient R 2 with the value range [0, 1] was used to evaluate the goodness of fit. R 2 close to 1 indicates a more precise degree of fit. Conversely, R 2 close to 0 indicates a worse degree of fit. The fitting results of the size distribution of iron grain were listed in Table 3, which shows that the R 2 of the Doseresp sigmoidal function was closest to 1.0, thus identifying the Doseresp sigmoidal function as the optimal functional model for characterising the distribution of iron grain granularity.

Effect of Temperature and Time on the Growth of Iron Particles
Increasing the temperature and prolonging the time could promote the growth of metallic iron grain. To further clarify the growth process of the iron grain and describe the growth characteristics of the metallic iron quantitatively, the average size of the metallic particles under different reduction conditions was calculated according to the image analysis datas. Equation (9) shows the calculation equation for the average particle size.
where d represents the average size of the metallic iron (µm). N was the total number of measured grain. d j represents the diameter of the metallic grain (µm). m j was the number of metallic iron with the diameter d j . Figure 11 shows that the time and reduction temperature significantly affected the average granularity of the iron grain. The average size of the metallic iron grain increased evidently with the temperature and time. At the reduction time 40 min, the average size of the iron grain improved from 14.17 µm to 19.88 µm when the temperature rose from 1473 K to 1623 K. With the reduction time varying from 10 min to 100 min, the average size of the metallic grain improved from 10.33 µm to 22.03 µm at the reduction temperature 1573 K. At the reduction temperature of 1523 K, the average granularity of the iron particles improved from 11.45 µm to 16.07 µm as the time was extended from 20 min to 40 min. While the reduction time was extended from 40 min to 100 min, the average granularity enlarged from 16.07 µm to 18.47 µm. The increments in the average size for the two stages were 4.62 µm and 2.67 µm, thus indicating that the mechanism and growth rate of the iron grain were diverse in different coal-based reduction stages. Increasing the temperature and prolonging the time could promote the growth of metallic iron grain. To further clarify the growth process of the iron grain and describe the growth characteristics of the metallic iron quantitatively, the average size of the metallic particles under different reduction conditions was calculated according to the image analysis datas. Equation (9) shows the calculation equation for the average particle size.
where d represents the average size of the metallic iron (μm). N was the total number of measured grain. dj represents the diameter of the metallic grain (μm). mj was the number of metallic iron with the diameter dj. Figure 11 shows that the time and reduction temperature significantly affected the average granularity of the iron grain. The average size of the metallic iron grain increased evidently with the temperature and time. At the reduction time 40 min, the average size of the iron grain improved from 14.17 μm to 19.88 μm when the temperature rose from 1473 K to 1623 K. With the reduction time varying from 10 min to 100 min, the average size of the metallic grain improved from 10.33 μm to 22.03 μm at the reduction temperature 1573 K. At the reduction temperature of 1523 K, the average granularity of the iron particles improved from 11.45 μm to 16.07 μm as the time was extended from 20 min to 40 min. While the reduction time was extended from 40 min to 100 min, the average granularity enlarged from 16.07 μm to 18.47 μm. The increments in the average size for the two stages were 4.62 μm and 2.67 μm, thus indicating that the mechanism and growth rate of the iron grain were diverse in different coal-based reduction stages. Figure 11. Effect of temperature and time on the average particle size of iron grain.

Establishment of Iron Particle Growth Kinetics Model
The classical kinetic equation of particle growth was used to clarify the growth mechanism of the particles [25], as shown in Equation (10). Figure 11. Effect of temperature and time on the average particle size of iron grain.

Establishment of Iron Particle Growth Kinetics Model
The classical kinetic equation of particle growth was used to clarify the growth mechanism of the particles [25], as shown in Equation (10).
where D t and D 0 represents the particle size at time t (µm) and time t = 0 (µm), respectively. n represents the particle growth index. K 0 is the growth rate constant of the particle. t represents the growth time of the particle (min). Q represents the activation energy of particle growth (kJ·mol −1 ). T and R are the thermodynamic temperature (K) and gas constant (J·mol −1 ·K −1 ), respectively. Based on the classical kinetic equation of particle growth, the growth behaviour of the iron grain was investigated in detail in this study. As there was no metallic phase generated at the reduction time t = 0, Equations (11) and (12) were obtained. From Equation (12), the slope of ln(D t ) and ln(t) was used to calculate the particle growth index n. The slope of ln(D t ) and 1/T represents the activation energy of particle growth Q. K 0 was obtained according to the particle growth index n and activation energy of particle growth Q.
According to Figure 4, the coal-based reduction process of ferronickel slag is divided into two stages, the rapid rise period of 0-40 min and the stable period of 40-100 min. Therefore, linear fitting was carried out for the two stages respectively, as shown in Figure 12. According to the results of the linear regression, the two stages of the coal-based reduction exhibited a close linear relationship. Based on the slope of the regression line, indices, denoted by n, were 2.016 ± 0.076 and 5.960 ± 2.060 at the two stages of the coal-based reduction.
Based on the classical kinetic equation of particle growth, the growth behaviour of the iron grain was investigated in detail in this study. As there was no metallic phase generated at the reduction time t = 0, Equations (11) and (12) were obtained. From Equation (12), the slope of ln(Dt) and ln(t) was used to calculate the particle growth index n. The slope of ln(Dt) and 1/T represents the activation energy of particle growth Q. K0 was obtained according to the particle growth index n and activation energy of particle growth Q.
According to Figure 4, the coal-based reduction process of ferronickel slag is divided into two stages, the rapid rise period of 0-40 min and the stable period of 40-100 min. Therefore, linear fitting was carried out for the two stages respectively, as shown in Figure  12. According to the results of the linear regression, the two stages of the coal-based reduction exhibited a close linear relationship. Based on the slope of the regression line, indices, denoted by n, were 2.016 ± 0.076 and 5.960 ± 2.060 at the two stages of the coalbased reduction. As shown in Figure 13, the values of the activation energy of particle growth Q were 52.482 ± 4.448 kJ·mol −1 and 26.426 ± 3.295 kJ·mol −1 . The calculated results of activation energy indicated that the activation energy of iron particles growth at the reduction time t ≤ 40 min was higher than that for the reduction time t > 40 min. The high surface energy generated owing to the small particle size promoted the formation of a stronger driving As shown in Figure 13, the values of the activation energy of particle growth Q were 52.482 ± 4.448 kJ·mol −1 and 26.426 ± 3.295 kJ·mol −1 . The calculated results of activation energy indicated that the activation energy of iron particles growth at the reduction time t ≤ 40 min was higher than that for the reduction time t > 40 min. The high surface energy generated owing to the small particle size promoted the formation of a stronger driving force of grain growth and a faster growth rate. Moreover, the growth rate constants, denoted by K 0 , for the two stages were 30.33 ± 1.92 and 21.30 ± 1.45, respectively. Consequently, the growth kinetics model of the iron grain is expressed in Equations (13) and (14).  Figure 14 shows the predicted value and experimental values of the iron grain. From Figure 14, all model prediction values were evenly distributed near the line y = x, indicating that the predicted value was consistent with the experimentally measured value. Therefore, the accuracy of the growth kinetics model of the iron particles was verified via Figure 14. Figure 14 shows the predicted value and experimental values of the iron grain. From Figure 14, all model prediction values were evenly distributed near the line y = x, indicating that the predicted value was consistent with the experimentally measured value. Therefore, the accuracy of the growth kinetics model of the iron particles was verified via Figure 14.     Figure 14 shows the predicted value and experimental values of the iron grain. From Figure 14, all model prediction values were evenly distributed near the line y = x, indicating that the predicted value was consistent with the experimentally measured value. Therefore, the accuracy of the growth kinetics model of the iron particles was verified via Figure 14.

Metallic Phase Growth Process and Description of Limiting Links
The ferronickel slag existed in a liquid state at the reduction temperature range of 1473-1623 K, and CO was the reductant during the coal-based reduction. Therefore, the coalbased reduction first occurred at the interface between the liquid state and gaseous states. The metallic iron appeared on the liquid surface of the ferronickel slag and aggregated to generate the metallic particles assisted by the collision and diffusion effects. Considering the influence of gravity, the metallic iron particles separated from the reaction interface with the increase in the particle size. As the viscosity has a great influence on the falling speed of particles, the Stokes equation Equation (15) was adopted to ascertain the average falling speed of the iron particles.
where ν was the average falling speed of the metallic iron particles (m·s −1 ). r represented the radius of the metallic iron (m). η S was the viscosity of the slag (Pa·s). ρ M and ρ S represented the bulk densities of the metal and slag, respectively (kg·m −3 ). g was the gravitational acceleration (m·s −2 ). Figure 15 shows that the viscosity values of the slag were diverse at different metallisation rates. The viscosity of the slag increased to 1900 Pa·s owing to the high mass fraction of SiO 2 at the metallisation rate of 80%. Figure 15 suggests that the metallic iron particles generated in the initial stage were separated from the reaction interface to produce small metallic particles due to the surface tension and lower viscosity ( Figure 16). Meanwhile, the 2FeO·SiO 2 in the slag diffused to the reaction interface and reduced to metallic iron particles [25]. In the intermediate stage, the concentration of 2FeO·SiO 2 in the slag and the reaction interface decreased. Consequently, the number of metallic iron atoms in the reaction interface and the probability of producing larger particles declined. Nevertheless, the falling speed of the metallic iron particles decreased because the viscosity increased with the metallisation rate [19,26]. The residence time of the iron grain at the reaction interface and the probability of producing larger iron granules increased. In the later stage, the concentration of 2FeO·SiO 2 diffused to the reaction interface further decreased, resulting in a smaller particle size of metallic iron at the reaction interface [18,21,27]. Moreover, many small iron granules appeared on the surface of the slag at the end of the reduction reaction owing to the increase of the slag viscosity and the slower falling speed.  According to the description of the growth process and theoretical calculation, the distribution characteristics of the metallic particles were highly consistent with the measured ones. Consequently, the sizes of most of the particles varied approximately from 10-15 μm, and most of the metal particles were less than 50 μm.
The reduction product with an iron grade of 29.43% and metallisation rate of 98.22% was obtained at carbon addition coefficient 2.0, reduction temperature 1573 K, reduction time 60 min, the particle size of coal and ferronickel slag −2.0 mm, and CaO content 15%. The reduction products were ground and separated to obtain concentrate products, and  According to the description of the growth process and theoretical calculation, the distribution characteristics of the metallic particles were highly consistent with the measured ones. Consequently, the sizes of most of the particles varied approximately from 10-15 μm, and most of the metal particles were less than 50 μm.
The reduction product with an iron grade of 29.43% and metallisation rate of 98.22% was obtained at carbon addition coefficient 2.0, reduction temperature 1573 K, reduction time 60 min, the particle size of coal and ferronickel slag −2.0 mm, and CaO content 15%. In the initial stage, more iron grains appeared in the reaction interface. Nevertheless, the metallic iron particles were separated from the reaction interface on account of the short reaction time and lower viscosity of the slag, which indicated the formation of larger iron grain was difficult. In the intermediate stage, the granularity remained within a certain range owing to the influence of the 2FeO·SiO 2 concentration and slag viscosity ( Figure 17).

Conclusions
(1) The reduction time and reduction temperature have prominent effects on the coalbased reduction of ferronickel slag. The metallisation process includes two stages, i.e., the rapid formation and aggregate growth of the metallic phase. The time required for the metallisation rate to reach the stable stage decreases with the reduction temperature. (2) With the increase of temperature or reaction time, the metallisation rate increases, and the average size of the spherical iron grain grows. The reduction time and temperature significantly influence the frequency distribution of thec iron granules. The frequency distribution of the iron granules follows the Doseresp sigmoidal function. (3) The growth kinetic models of the iron grain in the coal-based reduction of ferronickel slag are established according to the classical kinetic equation of particle growth. The growth characteristic and mechanism of iron grain during the coal-based reduction are complex. A faster growth rate and stronger growth driving force of metallic iron particles are generated owing to the smaller particle size and larger surface energy at the initial stage. The coal-based reduction rate decreases as the reduction time exceeds 40 min, and the growth of the iron grain is restricted to the interfacial chemical reaction. According to the description of the growth process and theoretical calculation, the distribution characteristics of the metallic particles were highly consistent with the measured ones. Consequently, the sizes of most of the particles varied approximately from 10-15 µm, and most of the metal particles were less than 50 µm.
The reduction product with an iron grade of 29.43% and metallisation rate of 98.22% was obtained at carbon addition coefficient 2.0, reduction temperature 1573 K, reduction time 60 min, the particle size of coal and ferronickel slag −2.0 mm, and CaO content 15%. The reduction products were ground and separated to obtain concentrate products, and the analysis of main chemical elements is shown in Table 4.

Conclusions
(1) The reduction time and reduction temperature have prominent effects on the coal-based reduction of ferronickel slag. The metallisation process includes two stages, i.e., the rapid formation and aggregate growth of the metallic phase. The time required for the metallisation rate to reach the stable stage decreases with the reduction temperature. (2) With the increase of temperature or reaction time, the metallisation rate increases, and the average size of the spherical iron grain grows. The reduction time and temperature significantly influence the frequency distribution of thec iron granules. The frequency distribution of the iron granules follows the Doseresp sigmoidal function.  The growth characteristic and mechanism of iron grain during the coal-based reduction are complex. A faster growth rate and stronger growth driving force of metallic iron particles are generated owing to the smaller particle size and larger surface energy at the initial stage. The coal-based reduction rate decreases as the reduction time exceeds 40 min, and the growth of the iron grain is restricted to the interfacial chemical reaction.