International Journal of Heat and Mass Transfer 127 (2018) 394–402 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt Effects of aluminum concentration on the formation of inhibition layer during hot-dip galvanizing Ting Min, Yimin Gao ⇑, Xiaoyu Huang, Zhanpeng Gong, Kemin Li, Shengqiang Ma State Key Laboratory for Mechanical Behavior of Materials, School of Materials Science and Engineering, Xi’an Jiaotong University, 28 Xianning West Road, Xi’an, Shaanxi Province 710049, PR China a r t i c l e i n f o Article history: Received 11 April 2018 Received in revised form 19 July 2018 Accepted 6 August 2018 Keywords: Crystal growth Inhibition layer Mesoscopic simulation Reactive transport Hot-dip galvanizing a b s t r a c t The formation of inhibition layer (IL) during hot-dip galvanizing with Al concentration varying from 0.0 to 0.8 wt pct. is studied by both experiments and numerical simulations. Using EDS and XRD, the IL is identified mainly as Zn-bearing Fe2Al5. SEM results reveal that the IL thickness increases with Al concentration in zinc bath, and the particles of Fe2Al5 on the surface of IL formed in 0.8 wt pct. Al bath are smaller than those formed in 0.2 wt pct. Al bath. On the surface of IL generated in 0.8 wt pct. Al bath there are some tiny particles with size about tens of nanometers randomly dispersing on the larger ones, indicating that the growth of IL is so fast that the growth mode changes and nucleation occurs at the IL/zinc interface. Using a mesoscopic model based on the lattice Boltzmann method, numerical simulations are also performed to study the reactive transport phenomena during IL formation under different Al concentrations. The simulations reveal complex coupled mechanisms between Fe and Al diffusion, Fe dissolution, as well as nucleation and growth of Fe2Al5 and the results agree with the experiments. Ó 2018 Elsevier Ltd. All rights reserved. 1. Introduction During hot-dip galvanizing process, an extremely thin layer of Fe-Al compound with size about tens to hundreds of nanometers, called inhibition layer (IL), forms between the steel substrate and the zinc overlay. This layer serves as a barrier to retard or inhibit the formation of brittle Fe-Zn compounds between steel and molten zinc . Therefore, IL has a critical influence on the microstructure and properties of zinc coating. When Al concentration in the zinc bath is lower than 0.14 wt pct., no Fe-Al compound forms and reaction between Fe and Zn occurs, while when Al concentration is higher than this threshold, the Fe-Al compound forms IL and hinders the formation of Fe-Zn compound [2–4]. The IL formation occurs quickly in only a few seconds, which is affected by various factors including chemical constituent, temperature of molten zinc, substrate material and so on [1,4–10]. Moreover, multiple subprocesses are involved in the IL formation process, including dissolution of Fe, diffusion of Fe and Al in liquid zinc and solid IL, reaction between Fe and Al as well as competition with Fe-Zn reaction [1–5,11]. Thus, study of IL formation is a challenging topic for experimental and theoretical researchers and has drawn great attention [1–18]. ⇑ Corresponding author. E-mail address: firstname.lastname@example.org (Y. Gao). https://doi.org/10.1016/j.ijheatmasstransfer.2018.08.016 0017-9310/Ó 2018 Elsevier Ltd. All rights reserved. The concentration of Al in zinc bath is about 0.13 wt pct. for galvannealing process and about 0.2 wt pct. for galvanizing process, so most of the experiments in the literature focused on the formation and morphologies of IL in bath with Al concentration varying from 0.1 to 0.3 wt pct. at about 460 °C [1–4,11–15]. The typical morphology of IL formed during galvanizing is a double-layer structure, with the lower layer next to substrate containing continuous, compact, roughly equiaxed grains with size about tens of nanometers, and the upper layer adjacent to liquid zinc comprising coarser, larger, elongated grains with size about hundreds of nanometers [1,2,4,6,11–14,18]. To develop more environment friendly galvanizing method, galvanizing steel with scale reduced by heating hydrogen or carbon was suggested by researchers to replace conventional acid pickling [19–22]. The surface of steel with reduced scale is rough and porous [23,24], and a higher Al concentration (0.7 wt pct.) in zinc bath has been proved to be necessary to form a complete IL on such special substrate surfaces . However, to the best of the authors’ knowledge, there are few articles focusing on the IL formation in Zn bath containing Al concentration higher than 0.3 wt pct. in the past two decades . Besides, as a vital process during galvanizing, the formation of IL is affected by Al concentration significantly. It is therefore theoretically and industrially meaningful to explore the influence of Al concentration on the IL formation. T. Min et al. / International Journal of Heat and Mass Transfer 127 (2018) 394–402 As a complementary method to experiments, numerical simulation has been developed not only to predict galvanizing processes at bath scale to capture the fluid flow and transport processes [26– 31], but also at atomic scale to explore the intrinsic properties of compounds forming in zinc bath [32–38]. In the bath-scale simulations, emphasis was put on the evolutions of velocity, temperature and concentration in the whole bath, while the complex reactive transport processes occurring at the surface of steel were simply set as source terms or boundary conditions [26–30]. In atomicscale calculation using first principle or molecular dynamics, some useful physical parameters, such as crystal structure , heat capacity [35,37], diffusivity  and formation energy  were obtained. However, the size of the atomic-scale simulations is limited to a few nanometers. Thus, there is a gap between bath-scale and atomic-scale simulations. A mesoscale model is a bridge which can connect the galvanizing process parameters, variable surface state and the intrinsic properties of involved compounds together. Recently, Min et al.  developed a mesoscale model based on lattice Boltzmann method (LBM) [40–42] to numerically investigate the reactive transport processes during IL formation down to nanoscale. This model not only can take into account the multiple physicochemical processes, but also can capture the dynamic evolutions of IL structure, which is difficult to realize using current experimental techniques . In this paper, this model was also used to explore the effects of Al concentration on the IL formation. The formation of IL can be divided into three steps: (1) dissolution of Fe from substrate into zinc bath, (2) rapid growth of IL by nucleation and growth of Fe-Al until surface is completely covered and (3) diffusion-controlled growth of IL [1,5–10]. A widely used model of IL formation was proposed by Tang  in which he applied classic nucleation theory considering the influence of temperature of bath and strip, thickness of strip, immersion time, heat transfer as well as fluid flow on IL formation process. The IL formation was divided into two stages, high rate of IL formation by continuous nucleation of Fe2Al5 and the growth of the Fe2Al5 limited by the supply of Al through liquid diffusion . This model was elaborated by Giorgi  combining the dissolution of Fe and growth kinetics of Fe2Al5. In this model the surface of substrate is covered by the nucleation and lateral growth of Fe2Al5. Several physical parameters were artificially adjusted because of the lack of experimental and simulated values. Until now, the three stages of IL formation are widely accepted but different mechanisms about each stage are continuously proposed by researchers. Some researchers pointed out the second stage was completed by nucleation [5,7] and others believe that the substrate surface was covered by initial nuclei and their fast growth [8,10]. Some experiments indicate that the initial nucleation is FeAl3 which then transforms to Fe2Al5 . Different factors controlling the IL growth in the third stage have also been proposed in different models including diffusion of Al in the liquid zinc in Refs. [5,7,10] and solid diffusion of Fe in IL in Refs. [4,6,8]. In our previous model, the surface is treated as being covered by nucleation and fast growth of these nuclei; the third stage is controlled by Al diffusion in liquid zinc first and then by Fe diffusion in IL . In the present study, the IL formation in liquid zinc is explored by both experiment and mesoscale simulations. The emphasis is put on the effects of Al concentration. The rest of the paper is arranged as follows. In Section 2, experiment methodology for IL formation is introduced, and then the IL is analyzed using SEM, EDS and XRD. In Section 3, mesoscopic numerical simulations are performed, and time evolutions of IL structure, concentration fields and IL thickness are displayed. In Section 4, the experimental and simulated results are combined with each other and discussed. Finally, a main conclusion is drawn in Section 5. 395 2. Experiments 2.1. Experimental method The specimens used in this study were polycrystalline pure iron. All of them were cut into 70 mm 10 mm 4 mm and degreased in a 2.0 wt pct. alkaline solution at 80 °C for 15 min, which were rinsed first and then pickled in 15 vol pct. hydrochloric acid for 3 min to remove oxide and rinsed. Next the specimens were prefluxed in a solution of NH4Cl and ZnCl2 for 3 min at 60 °C, and then were dried in heater immediately before immersion in zinc bath. The solution of NH4Cl and ZnCl2 is a traditional activating agent in galvanizing, which can clean the surface further and maintain an un-oxidized surface before immersion in zinc bath. Pure zinc ingots were melted in a graphite crucible first and then pure Al wire and pure iron was added after zinc ingots totally melted. Four zinc baths saturated with Fe and Al were prepared with Al concentration as 0.0, 0.1, 0.2, 0.5, 0.8 wt pct., respectively, and for each bath three specimens were immersed for about 10 s at 460 °C one by one after Al wire was completely dissolved. The cross sections of galvanized samples were cut from the middle of galvanized specimens, grinded and polished for observation using SEM and EDS. A mixture of glacial acetic acid and hydrogen peroxide with volume ratio 4:1 was used to expose the top view of IL by stripping off the zinc layer. The etching solution can remove zinc and leave the Fe-Al intermetallic phases . The proceeding solution was also used to extract the particles of IL. X-ray diffraction analysis was performed on top view after the Zn layer was removed using Bruker D8AA25X with Cu Ka radiation and the monochromatic operated at 40 kV and 40 mA. The diffraction scans were performed using a parallel beam geometry X-ray diffractometer with an incident angle of 1.0°. The speed was set as 30 s/degree and the step as 0.02°. 2.2. Results Fig. 1(a) and (b) shows the top-view morphology and EDS spectrum of IL after stripping the overlying zinc obtained in a 0.20 wt pct. Al bath at 460 °C. The typical double-layer structure of IL  was observed from top-view (Fig. 1(a)), where some larger grains disperse on the top of compact and fine ones. The EDS result further proves that this layer is rich in Fe, Al and Zn (Fig. 1(b)). The phase identification was implemented using GIXRD from top-view after stripping the overlying zinc. As shown in Fig. 1(c), except the substrate iron, only Fe2Al5 was detected, indicating that the dominant phase in IL should be Fe2Al5. Combing with EDS results, IL mainly consists of Zn-bearing Fe2Al5 compound. Fig. 1 (d) displays the extracted particles of IL formed in 0.2 wt pct. Al bath, most of which are irregular polygon particles and the size varies in the range of tens to hundreds of nanometers. The SEM BES images and elemental distributions of Al in crosssection of ILs formed in Zn baths containing 0.0, 0.1, 0.2, 0.5 and 0.8 wt pct. Al are shown in Fig. 2. Al-rich area is hardly examined when the Al concentration is 0.0 or 0.1 wt pct., and thus no elemental distribution is given for these two cases. When the Al concentration is 0.2 wt pct. or higher, there is a band of dark contrast between substrate and coating zinc because of the formation of IL. This dark band is confirmed to be an Al-rich layer as shown in the EDS mapping (Fig. 2(d, f, h)). According to the Fe-Al-Zn ternary phase diagram , Fe2Al5 can form when the Al concentration is higher than about 0.14 wt pct. The results obtained here are in coincidence with the ternary phase diagram . Moreover, as shown in Fig. 2(c, e, g), when the Al concentration increases the Al-rich layer becomes thicker. Limited by the resolution of BES in SEM, it is hard to measure the IL thickness quantitatively. 396 T. Min et al. / International Journal of Heat and Mass Transfer 127 (2018) 394–402 500 nm keV (b) (a) (c) (d) Fig. 1. Top view morphology of inhibition layer (IL) (a) SEM, (b) EDS spectrum operated at 5 kV accelerate voltage, (c) XRD pattern of IL using GIXRD, (d) morphologies of extracted particles in IL formed in 0.20 wt pct. Al bath at 460 °C. To compare the morphologies of ILs formed in zinc bath with high and low concentrations of Al, the top-view SEM SE images of ILs formed in 0.2 and 0.8 wt pct. Al baths are displayed in Fig. 3. The particles in IL forming in 0.8 wt pct. Al bath are smaller those formed in 0.2 wt pct. Al bath, and both of ILs contain compact fine polyhedral grains with some dispersing larger ones. Another difference between surfaces of these two ILs is that there are some tiny particles, about tens of nanometers as marked using red1 circles, distributing in IL formed in 0.8 wt pct. Al bath. 3. Numerical study 3.1. Simulation method Mesoscopic simulations are performed to simulate the coupled reactive transport process during IL growth process, with emphasis on the effects of Al concentration. After the steel sheet enters the Zn-Al bath, Fe dissolves from the steel surface into the liquid zinc bath. Then the precipitation reaction of Fe2Al5 takes place, which consumes Fe and Al. Nucleation and subsequent crystal growth of Fe2Al5 occur on the steel surface, and IL is generated [5–10]. IL formation is characterized by short-time, nanoscale, and multiple physicochemical processes involved, making it one of the most challenging problems in material science. In our previous study, 1 For interpretation of color in Fig. 3, the reader is referred to the web version of this article. a mesoscopic model based on the LBM was developed to study IL formation . In this model, Fe and Al mass transport in liquid zinc as well as in solid IL were simulated using the LBM, and structure evolution of IL due to nucleation and crystal growth of IL was captured by a cellular automaton (CA) method. Different mechanisms in the literature were explored using the model. IL Doublelayer structures as well as typical IL thickness were successfully captured by the model . In the present study, the LB mesoscopic model is further employed to investigate the effects of Al concentration. The computational domain is a rectangle with size of 1000 1000 nm as shown in Fig. 4. Part of the domain near the left is Fe with size of 100 1000 nm, while the remaining part of the domain is liquid zinc. According to the phase identification by GIXRD and EDS, IL consists mainly of Zn-bearing Fe2Al5. Therefore, following [5,7,10], the precipitation reaction of Fe2Al5 on the steel surface in contact with the liquid zinc is described by the following formula 1 2Fe þ 5Al ! Fe2 Al5 ; DG ¼ 283; 470 þ 84:8T J mol ð1Þ where DG is the free energy change associated with this reaction, which is a function of temperature, T. This reaction takes place only if two conditions are satisfied based on the Zn-Al-Fe phase diagram . First, there is a threshold value of Al concentration in the zinc bath, below which Fe2Al5 cannot be generated and the inhibition breaks down, leading to the generation of Fe-Zn intermetallic compounds . This threshold value is set as 0.14 wt pct. at T = 733 K T. Min et al. / International Journal of Heat and Mass Transfer 127 (2018) 394–402 (a) 0.0 wt. pct. Al, SEM (b) 0.1 wt. pct. Al, SEM (c) 0.2 wt. pct. Al, SEM (d) 0.2 wt. pct. Al, EDS (e) 0.5 wt. pct. Al, SEM (f) 0.5 wt. pct. Al, EDS (g) 0.8 wt. pct. Al, SEM (h) 0.8 wt. pct. Al, EDS 397 Fig. 2. Cross sectional morphologies and elemental distributions of ILs obtained in (a) 0.0 wt pct., (b) 0.1 wt pct., (c, d) 0.2 wt pct., (e, f) 0.5 wt pct. and (g, h) 0.8 wt pct. Al baths. 398 T. Min et al. / International Journal of Heat and Mass Transfer 127 (2018) 394–402 SFe ¼ 8 > > > >0 > < if ðC Fe Þ2 ðC Al Þ5 < ðC Fe;sat Þ2 ðC Al;sat Þ5 or C Al < C Al;critical > > ðC Fe Þ2 ðC Al Þ5 > > 1 2k > p 2 5 : ðC Fe;sat Þ ðC Al;sat Þ if ðC Fe Þ2 ðC Al Þ5 P ðC Fe;sat Þ2 ðC Al;sat Þ5 and C Al P C Al;critical ð2aÞ SAl ¼ 500 nm 8 > > > > 0 > < if ðC Fe Þ2 ðC Al Þ5 < ðC Fe;sat Þ2 ðC Al;sat Þ5 or C Al < C Al;critical > > ðC Fe Þ2 ðC Al Þ5 > > 1 5k > p : ðC Fe;sat Þ2 ðC Al;sat Þ5 if ðC Fe Þ2 ðC Al Þ5 P ðC Fe;sat Þ2 ðC Al;sat Þ5 and C Al P C Al;critical ð2bÞ (a) 0.5 wt. pct. Al 500 nm (b) 0.8 wt. pct. Al Fig. 3. Top-view morphologies of ILs after stripping zinc layer in 0.2 wt pct. (a) and 0.8 wt pct. (b) Al bath at 460 °C. where kp is the precipitation reaction rate constant, C the molar concentration in the bath, Csat the saturation molar concentration and CAl,critical the threshold concentration of Al below which Fe2Al5 cannot form. Note that in the present study, C denotes the concentration with unit of mol m3, while w is weight percent with unit of wt pct. In the generated solid IL, heterogeneous diffusion containing both lattice diffusion and grain boundary diffusion is considered. The lattice diffusion is the slow diffusion within a grain. The grain boundary diffusion (or short circuit diffusion) refers to diffusion along the grain boundaries in a polycrystalline, and is greatly faster than the lattice diffusion [4,43]. In a polycrystalline with smaller crystal size, there are abundant of grain boundaries, leading to greatly larger diffusivity in nano-crystals than the corresponding bulk counterpart . This is the case in the Fe–Al compound IL with crystal size of tens to hundreds of nanometers. Therefore, Chen et al.  adopted a grain boundary diffusivity 500 times higher than lattice diffusivity to theoretically estimate the IL growth. Following our previous study , two values of solid diffusivity (4.0 1012 m2 s1 and 4.0 1011 m2 s1) are randomly assigned to the IL solid nodes with 50% probability of each value. Under a certain temperature T, the relationship between Fe saturated weight percent and that of Al is as follows  33066 ðwFe;sat Þ2 ðwAl;sat Þ5 ¼ exp 28:1 T ð3Þ where wi,sat is saturated weight percent of i. For more details of the model, one can refer to our previous study [39,44]. Initially, the bath is saturated with aluminum and iron. At the top and bottom boundaries, periodic boundary conditions are adopted. At the right boundary, concentrations of Fe and Al are set as the saturation concentrations . At the steel interface, boundary condition for Al is no flux boundary condition. For Fe at this interface, if the interface is not covered by IL, the dissolution reaction follows [8,10], DFe Fig. 4. Evolutions of IL structures and Fe concentration for the case with Al concentration as 0.2 wt pct. [3,5]. Second, product of Fe and Al concentrations, namely, should be higher than ðC Fe;sat Þ2 ðC Al;sat Þ5 , otherwise only liquid phase can exist . In other words, the crystal growth requires supersaturation. Therefore, source terms for the Fe and Al concentrations SFe and SAl are as follows @C Fe ¼ kd ðC 0Fe;sat C Fe Þ @n ð4Þ where DFe is the diffusivity of Fe in liquid zinc, n the direction normal to the reactive surface pointing to the void space, kd with unit of m s1 the dissolution reaction rate constant, C 0Fe;sat the saturation concentration of Fe in liquid zinc bath without Al. On the other hand, if a computational node at interface is occupied by IL, the concentration of Fe there is set as the C 0Fe;sat [5,8,10] C Fe ¼ C 0Fe;sat ð5Þ The values of physicochemical variables adopted in the simulation are listed in Table 1. T. Min et al. / International Journal of Heat and Mass Transfer 127 (2018) 394–402 399 Table 1 Values of physicochemical variables used in the simulations. Physicochemical variables Values Density of liquid Zn, qZn Saturated weight percent Fe in liquid Zn at T = 733 K, w0Fe;sat 6570 kg m3 0.04 wt pct. Dissolution rate constant of Fe at the Fe-liquid Zn interface, kd Density of Fe2Al5 with dissolved Zn, qFe2 Al5 Molar volume of the IL component, VIL Precipitation rate constant of IL, kp 1.75 102 m s1 4720 kg m3 6.61 105 m3 mol1 10000 mol m3 s1 3.2. Evolution of IL under various Al concentrations Fig. 4 shows the evolutions of IL structures and Fe concentration for the case with Al weight percent as 0.2 wt pct. In Fig. 4, black is steel, brown triangle denotes IL, and the contour is for Fe weight percent. Before the formation of IL, the source for the Fe into the bath is steel dissolution given by Eq. (4), and it is expected that weight percent of Fe decreases from bath-steel interface to the right boundary (t = 0.001 s). As the precipitation reaction continues, the first layer of IL forms (t = 0.2 s), and the entire steel surface is covered by IL, leading to the supply mechanisms of Fe into the bath shifted to the slow solid diffusion. Such slow diffusion becomes the constraint of IL growth later. Due to the heterogeneous diffusivity (including lattice diffusion and grain boundary diffusion) of Fe in the IL, IL grows relatively quicker at some sites with high values of diffusivity, and the surface of IL is no longer smooth but becomes rough (t = 5 s). The Fe weight percent gradient is still obvious at t = 5.0 s, which means Fe still can diffuse away from the IL/liquid zinc interface as be consumed by reaction. Fig. 5 shows the evolutions of IL structures and the Fe weight percent in 0.8 wt pct. Al bath. It can be seen that in a very short time of 0.001 s the first layer of IL forms. At t = 0.1 s, more than five layers of IL have been generated, with effects of the heterogeneous diffusion clearly observed. The IL generated in the 0.8 wt pct. Al bath is much thicker than that in the 0.2 wt pct. Al bath and the concentration gradient of Fe in zinc bath is negligible in the 0.8 wt pct. Al bath when immersion time is 5 s, which means all of Fe diffusing from substrate is completely consumed by the IL formation and Fe seldom can diffuse away from the interface. Fig. 6. Time evolutions of the average concentration of Fe in molten zinc with different Al concentration. Fig. 6 gives the time evolution of average Fe concentration in 0.2 and 0.8 wt pct. Al bath. The Fe concentration increases dramatically fast initially due to the dissolution of substrate, and then decreases slowly to their saturation concentration resulting from the formation of IL, which can reduce the dissolution of Fe by covering substrate surface and consume Fe dissolved in liquid zinc simultaneously. At final stage the Fe concentration in 0.8 wt pct. Al bath is slightly lower than its saturation concentration due to reaction overshoot. Comparing the two cases, the dissolution time of Fe in 0.8 wt pct. Al bath is much shorter than that in 0.2 wt pct. Al and the Fe concentration approaches to the saturation concentration earlier in 0.8 wt pct. Al bath. Fig. 7 further shows the solid structures of IL for four cases with different values of wAl;sat . First, as wAl;sat increases, IL grows faster and becomes thicker, coincident with the experimental results shown in Fig. 2. Under a low wAl;sat , the upper layer of the IL is relatively flat; under a high wAl;sat , the upper layer of IL are coarser agree with Fig. 2(g). Fig. 8 illustrates the time evolutions of the IL thickness. For the case with 0.2 wt pct. Al, the thickness of IL at t = 5 s is about 50 nm, while for the 0.8 wt pct. case, the thickness of IL at t = 5 s can be as high as 390 nm. 4. Discussion Fig. 5. Evolutions of IL structures and Fe concentration for the case with Al concentration as 0.8 wt pct. The experimental observation of IL formed in zinc bath results from underlying coupled physicochemical processes, and is influenced by multiple factors such as Al concentration, immersion time, temperature, etc. Numerical simulations can provide details of the distributions and evolutions of important variables such as concentration, and thus serve as a complementary tool for experiments. Combining the experimental observations and simulation results, there are three typical variations of IL with Al concentration: (1) the IL grows faster as Al concentration increases, (2) the final IL thickness of IL increases with the increasing of Al concentration and (3) the particles of Fe2Al5 become smaller and some finer particles disperse on the top morphology of IL when the Al concentration increases to 0.8 wt pct. The IL forming in 0.2 wt pct. Al bath has been observed and discussed by many researchers [2,4,11–15,17,45,46] and recently it was successfully captured by mesoscopic simulations . Therefore, the emphasis will be put on the morphology variation of IL with Al concentration between 400 T. Min et al. / International Journal of Heat and Mass Transfer 127 (2018) 394–402 Fig. 7. Evolutions of IL structure under different Al concentration. 0.2 and 0.8 wt pct. The formation of IL can be considered as three steps: the dissolution of Fe from substrate before IL formation, the fast growth controlled by initial nucleation and the fast growth of the nuclei before the substrate surface is completely covered by IL, and the slow IL growth controlled by diffusion. We will discuss the IL formation process step by step. The dissolution of Fe from the substrate can be described by Eq. (4). Increasing the Fe concentration gradient at the interface can enhance the dissolution rate. According to Eq. (3), the higher the wAl, sat, the lower the wFe, sat. With temperature as 733 K, if wAl, sat is 0.2 wt pct. (CAl, sat is 486.67 mol m3), wFe, sat is 0.011 wt pct. (CFe, sat is 12.87 mol m3). As wAl, sat increases to 0.8 wt pct. (CAl, sat is 1216.67 mol m3), wFe, sat greatly reduces to 3.4 104 wt pct. (CFe, Fig. 8. Time evolution of the IL thickness under different Al concentration. sat is 0.40 mol m3). Because C 0Fe;sat in Eq. (4) (or w0Fe;sat ) is a constant for a given temperature, it is obvious that a lower wFe, sat leads to a higher Fe dissolution rate. Therefore, for the higher wAl, sat case, Fe dissolution is accelerated. On the other hand, the Al concentration also affects the Fe dissolution by accelerating nucleation and growth of Fe2Al5, which can cover the substrate surface, reduce the dissolution area, and consume Fe near the interface in liquid zinc. According to Figs. 4 and 5, the T. Min et al. / International Journal of Heat and Mass Transfer 127 (2018) 394–402 dissolution time before the formation of the first layer of IL varies from 0.2 s to 0.001 s, hence the amount of Fe dissolution into Zn bath reduces rapidly with Al concentration, as shown in Fig. 6. It can be deduced from Fig. 6 that part of Fe dissolved from substrate is precipitated in the form of Fe2Al5 and the remaining part of Fe dissolved into zinc bath raising the Fe concentration near the interface, as shown in Figs. 4 and 5. The nucleation of Fe2Al5 begins when the Fe concentration near the interface is high enough and the product of Fe and Al concentrations exceeds their saturated concentration product according to Eq. (3). Here, the model improved by Dutta  is used to describe the nucleation rate N. In Dutta’s model  the activation energy of Fe diffusion across the substrate/zinc interface is included. The nucleation rate N can be calculated by [5,9] DG þDGD ; N ¼ n0 v 0 s C Al exp kT DG ¼ 3 8p Dcpl 3 DG2 ð6Þ where n0 is the number of Fe atoms on the surface of substrate, v0 the lattice vibration frequency (1013), s⁄ the total number of atoms surrounding the critical nucleus, DG⁄ the energy barrier of nucleation, GD the activation energy for diffusion across the substrate/ melt interface (21 kJ mol1), k Boltzmann constant, T the temperature, and Dcpl the interface energy change for a semi-sphere nucleus on the substrate. According to Eq. (6), the nucleation rate is determined by CAl and T. For a given temperature T, the nucleation rate N is exclusively affected by CAl. A higher Al concentration results in faster nucleation, and further leads to smaller particles of Fe2Al5, which is consistent with experimental observation shown in Fig. 3. Besides nucleation of Fe2Al5, the fast growth of existing nuclei occurs simultaneously in the second stage. The growth rate of Fe2Al5 particles vgrowth can be described by the following formula " v growth kp ðC Fe Þ2 ðC Al Þ5 ðC Fe;sat Þ2 ðC Al;sat Þ5 # 1 ð7Þ According to Eq. (3), ðC Fe;sat Þ2 ðC Al;sat Þ5 is constant for a given temperature, and thus the growth rate of particles, vgrowth, raises exponentially with the Al and Fe concentrations at the interface. Due to higher Al concentration and the faster dissolution of Fe for the case with higher Al concentration the growth of nuclei is accelerated significantly in the second stage, which results in a much shorter time for complete coverage of substrate surface in the 0.8 wt pct. Al case. This process completed in less than 0.001 s is very challenging, if possible, to be directly observed by experiments, but is consistent with the top-view morphologies shown in Fig. 3. Fig. 3 shows the morphology of IL changes when Al concentration varies from 0.2 to 0.8 wt pct. The dispersed tiny crystals sticking to the surface of IL formed in 0.8 wt pct. Al bath indicate that the concentration product of Fe and Al at the interface is very high resulting in a faster growth mode and nucleation on the growing particles occurs during their growth. This phenomenon is seldom reported in the literature [1–4,11–18,25,46,47]. Once the surface of substrate is completely covered by Fe2Al5, the third stage of IL formation starts. At the beginning of the third stage, Fe near the interface is still supersaturated with Fe2Al5 as shown in Figs. 4(b) and 5(a). As the growth proceeds the Fe concentration near the interface is diminished to its saturation point and the only Fe source for reaction becomes the diffusion of Fe across IL from substrate, as shown in Figs. 4(d) and 5(d). The IL growth is limited by the slow solid diffusion of Fe in IL. For a given thickness of IL, the amount of Fe diffusing across IL is the same, but the growth rate of IL in 0.8 wt pct. Al bath is larger due to the higher Al concentration, which is the mainly reason why IL thickness increases with Al concentration, as shown in Fig. 2. With the thickening of the IL, the effect of Al concentration on the growth rate 401 gradually becomes insignificant, as shown in Fig. 8, where the gradient of all of growth curves is close to an extremely small value. 5. Conclusion During hot-dip galvanizing, a small amount of Al is added into the molten zinc bath, leading to the formation of Zn-bearing Fe2Al5 inhibition layer (IL) between the substrate and the zinc coating. Investigating effects of Al concentration on the IL formation is important for both scientific researches and industrial applications. In this study, both experiments and numerical simulations are conducted to investigate crystal growth during IL formation in bath with Al concentration varying from 0 to 0.8 wt pct. Several techniques including SEM, EDS and XRD are employed to investigate the morphologies and composition of the ILs. There is no IL formed in the 0 and 0.1 wt pct. Al baths, consistent with the conclusion in the literature that below a threshold value of 0.14 wt pct. Al the IL cannot form. Above this threshold value, the experimental results show that IL thickness increases as Al concentration raises. Besides, it is also observed from the SEM images that the particles in IL formed in 0.8 wt pct. Al bath are smaller than those formed in 0.2 wt pct. Al bath, while some tiny crystals distribute on the surface of IL formed in the 0.8 wt pct. Al bath, indicating that the nucleation and growth occur simultaneously. Currently, it is challenging to experimentally observe the time evolution of IL, which completes in several seconds and involves different physicochemical processes. Simulations help to get a comprehensive understanding of evolutions and distributions of important variables. Therefore, numerical simulations are implemented using a mesoscopic model based on the LBM. In this model, coupled processes of Fe and Al diffusion, Fe dissolution reaction, IL nucleation and crystal growth are considered. Time evolutions of the IL structures as well as Fe concentration are presented and discussed in detail. It is found that as Al concentration increases, iron dissolution and IL growth are accelerated, leading to quicker IL formation and thicker IL. For the physicochemical variables adopted in the present study, the final IL thickness is about 50 nm for 0.2 wt pct. Al case, which is relatively high as about 390 nm for the 0.8 wt pct. case. Accordingly, the formation and structures of IL is depended on Al concentration and immersion time based on the Fe and Al diffusion. Conflict of interest We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled. Acknowledgement Yimin Gao thanks the support of the Science and Technology Project of Guangdong Province in China (2015B010122003, 2015B090926009), the Science and Technology Project of Guangzhou City in China (201604046009). Shengqiang Ma thanks the National Natural Science Foundation of China (51771143). Ting Min thanks Dr. Jiuhong Wang at State Key Laboratory for Manufacturing Systems Engineering for the help of GIXRD and Mr. Zijun Ren at Instrument Analysis Center of Xi’an Jiaotong University for the help of SEM observation. 402 T. 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