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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:
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
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 [1]. 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: (Y. Gao).
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 [19]. 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 [25]. 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
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 [36], heat
capacity [35,37], diffusivity [38] and formation energy [32] 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. [39] 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 [39]. 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 [5] 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 [5]. This model was
elaborated by Giorgi [8] 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 [4]. 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 [39].
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.
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 [15].
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 [4]
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 [3], 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 [3]. 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.
T. Min et al. / International Journal of Heat and Mass Transfer 127 (2018) 394–402
500 nm
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,
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 [39]. 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 [39].
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
2Fe þ 5Al ! Fe2 Al5 ; DG ¼ 283; 470 þ 84:8T J mol
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
[3]. 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 [3]. 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
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
T. Min et al. / International Journal of Heat and Mass Transfer 127 (2018) 394–402
SFe ¼
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
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
SAl ¼
500 nm
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
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
(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 [13]. This is the case in the Fe–Al compound IL
with crystal size of tens to hundreds of nanometers. Therefore, Chen
et al. [4] adopted a grain boundary diffusivity 500 times higher than
lattice diffusivity to theoretically estimate the IL growth. Following
our previous study [39], 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 [10]
ðwFe;sat Þ2 ðwAl;sat Þ5 ¼ exp 28:1 T
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 [8]. 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],
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 [3]. 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
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
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
Table 1
Values of physicochemical variables used in the simulations.
Physicochemical variables
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 [39]. Therefore, the emphasis will be put
on the morphology variation of IL with Al concentration between
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.
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 [9] is used to
describe the nucleation rate N. In Dutta’s model [9] the activation
energy of Fe diffusion across the substrate/zinc interface is
included. The nucleation rate N can be calculated by [5,9]
N ¼ n0 v 0 s C Al exp kT
DG ¼
8p Dcpl
3 DG2
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
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
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.
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.
T. Min et al. / International Journal of Heat and Mass Transfer 127 (2018) 394–402
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