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Numerical simulation of iron whisker growth with changing oxygen content in iron oxide using phase-field method
Computational Materials Science 125 (2016) 263–270
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Numerical simulation of iron whisker growth with changing oxygen content in iron oxide using phase-field method Feng Lu, Liangying Wen ⇑, Jianlong Li, Jin Wei, Jian Xu, Shengfu Zhang College of Materials Science and Engineering, Chongqing University, Chongqing 400030, China
a r t i c l e
i n f o
Article history: Received 7 July 2016 Received in revised form 30 August 2016 Accepted 1 September 2016 Available online 13 September 2016 Keywords: Iron oxide Reduction Iron whiskers Phase-field model Iron-oxygen system
a b s t r a c t Phase-field method is used to simulate the growth of iron whiskers on a gas–solid interface by changing the oxygen content in iron oxide. Results show that oxygen content significantly influences not only the crystal lattice but also the diffusion direction of iron ion vacancies and iron ions, wherein iron ions diffuse to low-oxygen-content areas and iron ion vacancies diffuse to high-oxygen-content areas. The catastrophic swelling of the micro-area volume and the growth of iron whiskers are caused by the enrichment of iron ions in low-oxygen-content areas. The simulation revealed the effects of the reduction rate and the oxygen potential of gas. Iron whiskers are longer and stronger when the oxygen potential of reducing gas decreases from 133.96 kJmol1 to 160.01 kJmol1 or when the reduction rate increases from 6.3 103 mols1 to 7.3 103 mols1. Iron whiskers can appear earlier with a low oxygen potential or a high reduction rate. Both oxygen potential and reduction rate promote the nucleation and growth of iron whiskers. Ó 2016 Elsevier B.V. All rights reserved.
1. Introduction Fluidized bed direct reduction is a non-coke iron-making process that uses iron ore powder at a high reduction rate, making it one of the most developed non-blast furnace processes [1,2]. During reduction, iron ore powder stick in parts of the reactor. Once the sticking becomes too severe, affecting the entire reactor, iron ore powder will lose flow. A previous study showed that during reduction, iron separates from iron ore powder as a fibrous shape and clumps together as a result of the joining of fibrous iron called iron whiskers [3–5]. As the iron oxide is reduced, the change in iron oxide volume accompanied by the decreased in oxygen content is caused by the reconstruction of another crystal lattice by the iron ion Fe2+(Fe3+) and the oxygen ion O2. The growth of iron whiskers during reduction is cited as a major cause of catastrophic swelling at the local micro-area of iron oxide. Reduced temperature, gases, and particle size are among the reduction parameters that reportedly affect iron oxide volume change and iron whisker growth [6–8]. Zhao et al. used in situ observation to study the precipitation morphology of iron and the evolution process of its mineralogical structure; he found that the nucleation and growth of iron whiskers proceed in the conversion of FeO ? Fe [9]. Yoshiaki et al. obtained similar results [10]. Gong et al. established a model for calculating iron whiskers [11]. Researchers agree that ⇑ Corresponding author. E-mail address: [email protected] (L. Wen). http://dx.doi.org/10.1016/j.commatsci.2016.09.003 0927-0256/Ó 2016 Elsevier B.V. All rights reserved.
the growth of iron whiskers is caused by the directed diffusion of iron ions and iron ion vacancies in wustite. In a gas–solid system, iron oxide reacts with carbon monoxide. Movement of the gas–solid interface is caused by the growth of iron whiskers at the local micro-area or the shrinking of the core. The phase-field model has been extensively applied to simulate multiphase changes, such as solidification [12,13], solid state phase transformation [14–16], and metallic corrosion [17]. The phase-field model developed by Ryo Kobayashi [18,19] is used to simulate solidification, in which the parameter m controls the phase change during solidification. In the present study, the growth of iron whiskers is simulated by using a phase-field model without tracking the complex gas–solid interface. The existing experiment results and the iron oxide phase diagram suggest that the oxygen content of iron oxide significantly affects crystal lattice conversion, iron ions, oxygen ions, and iron ion vacancies in directed diffusions in wustite, which control the growth of iron whiskers. In the phase-field model, the parameter m is changed to describe the relationship between oxygen content and iron whisker growth. The reduction rate and oxygen potential are then analyzed. 2. Computational methods and models 2.1. Phase-field model The model includes two main equations: a phase-field /(r, t) and an oxygen-containing field xO(r, t). The /(r, t) is an ordering
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parameter at position r and time t, in which / = 1 indicates solid and / = 0 reduces gas CO/CO2. According to the Ginzburg-Landau phase transition theory [18], the free energy of a gas–solid system can be obtained as follows U(/, m):
Z
U½/; m ¼
1 2 e jr/j2 þ Fð/; mÞdr 2
ð1Þ
Parameter e(ʋ) in Eq. (1), which determines the thickness of the interface, is a function of the outer normal vector at interface ʋ. In the phase-field method, the outer normal vector ʋ is replaced by r/, which indicates that parameter e(ʋ) can be shown as e (r/). Thus, Eq. (1) can be considered as follows:
Z
U½/; m ¼
1 ½eðr/Þ2 jr/j2 þ Fð/; mÞdr; 2
ð2Þ
where F(/, m) is the free energy density. The form of the free energy density in the phase-field model is used to describe the gas–solid system, as shown below:
Fð/; mÞ ¼
1 4 1 1 1 1 / m /3 þ m /2 4 2 3 4 2
ð3Þ
The parameter m is the growth driving force. Combining with ¼ ddtU, the phase-field model can be simplified as equation s @/ @t shown below:
s
@/ @ @/ þ ee0 @y @y @x 1 þ r ðe2 r/Þ þ /ð1 /Þ / þ m ; 2
@/ @ ¼ @t @x
ee0
ð4Þ
rðhÞ ¼ 1 þ d cos½jðh h0 Þ
Thus, the driving force m is another important parameter of phase field because it has a significant effect on the change phase from solid to gas. F(/, m) is a double-well potential which has local minimums at / = 1 and 0 for each m. The profile of F(/, m) changes with m only when jmj 6 1=2, as shown in Fig. 1. Based on the minimum energy principle, the most stable phase at a local place is determined by m. If m is positive, the free energy density is minimum at / = 1. The micro-area would be occupied by solid for the growth of iron whiskers. If m is negative, the micro-area would be a shrinking core. The mechanisms of iron oxide crystal structure change and iron ion, oxygen ion, and vacancy diffusion direction should be studied to establish m function, which could provide the description of the growth of iron whiskers. Oxygen potential of CO/CO2 was less than the oxygen potential of iron oxide, resulting in a reduced iron oxide by CO/CO2. The oxygen content on the surface is decreased by the oxygen ion reaction with CO. The iron whiskers can only grow during wustite reduction. The temperature in the model is over 570 °C, which can maintain the stability of the wustite. As shown in Fig. 2, the crystal lattice conversion of Fe2O3 ? Fe3O4 ? FeO is attributed to the decrease in oxygen content with the same temperature [21]. The particle comprised iron oxide difference; thus, the particle is regarded as one solid phase of oxygen content difference. Experimental studies show that in converting Fe2O3 ? Fe3O4 ? FeO, the volume changes because of the lattice transformation and the iron whiskers which first appeared in the conversion of FeO ? Fe. The growth of iron whiskers or the partial enrichment of iron
where s is a small positive constant, and s = 0.0003 is obtained in the model [18]. Based on the phase-field model, parameter e(h) which is a microscopic interaction length, is placed as Eq. (5) where e is a mean value of the parameter e and r(h) is anisotropy. e0 (h) indicates differentiation with respect to the angle h. The parameter h in the r(h) is the angle between the direction of the growth of iron whiskers and the x-axis. Iron whiskers can grow on the position where CO is preferably adsorbed, indicating that the angle h which determines the direction of the growth of iron whiskers is related with the adsorption site of CO reducing gas. The energy of CO adsorption on the surface of iron oxide is calculated by the firstprinciples method, which shows that CO is easily absorbed on (1 1 1) surface of iron oxide [20]. In two-dimensional space, iron whiskers are more likely to grow in the direction of ±p/4 or ±3p/4. The anisotropy r(h) is obtained as Eq. (6), wherein the initial angle between the growth direction and the x-axis (h0) is p/4, the anisotropy module (j) is 4, and the parameter (d) determining the strength of growth is 0.1.
eðhÞ ¼ e rðhÞ
ð6Þ
ð5Þ
Fig. 1. The profile of F(U, m) changes with m [17].
Fig. 2. Iron oxide phase diagram.
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Fig. 3. Diagram of the wustite reduction mechanism.
Table 1 The lattice constant (1010 m) and the relative volume ratio of the different types of phase [20]. Type of phase
aFe
FeO
Fe3O4
cFe2O3
Oxygen content of micro-area Lattice constant/1010 m Relative volume ratio
0 2.861 2.394
0.5 4.290 0.866
0.57 8.380 0.022
0.6 8.320 0
ion is caused by iron ion directional diffusion. The iron ion vacancy in wustite is more than other iron oxides; thus, the iron ion is active and easier to diffuse [22,23]. The mechanisms of iron ion and iron ion vacancy diffusion are shown in Fig. 3. Iron ion diffuse at a few micro-area of gas–solid interface wherein oxygen content is less than others, whereas iron ion vacancy diffuses into the micro-area inside wherein the oxygen content is more than others. The form of iron ion vacancy in the wustite is shown as 3+ Fe2+ + 1/2O2 = V2 + O2, Fe2þ + 2Fe
and the iron ion vacancy 1=6 1/3 pO2 , concentration in wustite is shown as x V2 = (K1/4 1 ) Fe2þ where K1 is thermodynamic equilibrium constant. The iron ion vacancy concentration is enriched in the high oxygen content [21,24]. The form of iron in the wustite is shown 2 as 1Fe2þ 2Fe3þ V2 + Fe2+ = (2Fe2+2Fe3+ + 2e) + 1/2O2 = Fe2þ O 4Fe + 1/2O2; 1/2O2 + CO = CO2; thus, the iron concentration can be shown as xðFeÞ ¼ ðK2 Þ1=2 p1=4 O2 . Combined with thermodynamic analysis, iron ion in the wustite diffuse to the area of low oxygen potentials and iron ion vacancy diffuse to the area of high oxygen potentials was proven. The iron whiskers first appear in the conversion of FeO ? Fe because iron ion vacancy in wustite is more than other iron oxides,
enabling the free diffusion of iron ion. In addition, oxygen content not only has a significant effect on the crystal lattice but also on the iron ion and iron ion vacancy diffusion direction. The change in oxygen content influences the growth of iron whiskers. Constructing an m function to establish the relationship between the micro-area volume change and micro-area oxygen content in the conversion of Fe2O3 ? Fe3O4 ? FeO ? Fe (with little oxygen) is necessary. The micro-area volume change changes with the oxygen content [25]. The lattice constant of the changing iron oxide with the oxygen content is shown in Table 1 [21]. Based on Table 1 and Fig. 4, there are three steps in the reduction of iron oxide [26,27]. The first step is the swelling fromcFe2O3 to Fe3O4. The second step involves the conversion of Fe2O3 ? Fe3O4, wherein the volume of iron oxides slightly changes because the lattice constant of cFe2O3 is almost the same as Fe3O4 and the relative cell volume ratio m: (mFe3O4 mcFe2O3)/mcFe2O3 = ((8.38)3 (8.32)3)/ (8.32)3 0.022. The second step is shrinking core from Fe3O4 to FeO without growth of iron whiskers. With the decrease in oxygen content, the volume of iron oxides smoothly decreased as a result of relative cell volume ratio m: (mFeO mFe3O4)/mFe3O4 = ((4.290)3 (8.38)3)/(8.38)3 0.866. The last step is shrinking the core from FeO to Fe with the iron whiskers growing on the surface (growth of iron whiskers). The oxygen ion is obtained from
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wustite by carbon monoxide, which provides two electrons, thereby allowing the conversion of two ferric ions (Fe3+) to two ferrous iron (Fe2+). The ferrous iron (Fe2+), whether from iron oxide itself or ferric iron (Fe3+) change, will diffuse from the micro-area of high oxygen content to the micro-area of low oxygen content. Based on the crystal structure change, one FeO unit cell will become four Fe unit cells, resulting in ferrous iron filling the iron ion vacancy to increase the volume of the micro-area as a result of relative cell volume ratio m: (4⁄mFe mFeO)/mFeO = (4⁄(2.861)3 (4.290)3)/(4.290)3 = 2.394. The growth of iron whiskers is limited by the minimum oxygen content of iron oxide. When the oxygen potential of CO/CO2 is similar to iron oxide, the oxygen content is constant. When oxygen content is less than 0.01, the oxygen potential of iron oxide is shown as follows [27]:
lO ¼ 0:5lhO þ RT lnðcO X Omin Þ
ð7Þ
Also, the equation for oxygen potential of CO/CO2 is as follows [21]:
lOðCOCO Þ ¼ 565; 390 þ ½175:17 38:30 lgðpCO =pCO2 ÞT 2
ð8Þ
The minimum oxygen content can be obtained by combining the two equations. Finally, the equation to describe the relationship between the growth driving force m and the relative cell volume ratio mO can be obtained as follows:
a arctan mO þ 0:5 ð/ 1Þ p
m¼/
"
mO ¼ 4v
12 0 6 # X 0O þ X Omin þ g X O þ X Omin þ g ðxO þ X Omin Þ þ g ðxO þ X Omin Þ þ g
ð9Þ
ð10Þ
where X0o is the oxygen content in which iron whiskers start to grow, Xo is the oxygen content of the iron oxide, Xomin is the minimum oxygen content of the iron oxide, and v is the absolute value of the minimum relative volume ratio. Using the data from Table 1, v is 2.450, X0o is 0.023, and g is 0.710. When the oxygen content is less than 0.023, the iron whisker will grow.
combined with the diffusion of iron ion vacancy and iron ion in wustite. The diffusion of the iron ion vacancy and iron ion are determined by the ratio of the decrease in oxygen content. Oxygen ion can rapidly diffuse to the surface for the reaction because it has high diffusivity in iron oxide, thereby improving the diffusion of the iron ion vacancy and the iron ion [9]. The oxygen content is decreased on the gas–solid interface. The oxygen-containing field is represented by the following function:
@xO @/ ¼ r2 Dð/ÞxO þ K @t @t
K @/=@t is the reduction reaction source of the function, in which K is reduction reaction rate. The reduction reaction occurs with the moving gas–solid interface because K @/=@t has a non-zero value only when the interface passes the point. D(/) is the diffusion coefficient with regard to phasefield. When oxygen diffuses inside the iron oxide, diffusion coefficient D(/) is 1 109 with / = 1 [28]. As long as oxygen diffuses on the interface, diffusion coefficient D(/) increase to 1 105 with 0 < / < 1. Moreover, diffusion coefficient D(/) is zero with / = 0 because of the reaction with CO on the interface. Table 2 The parameter in the model. Parameter of the model
Value
Small positive constant of the phase-field model (s) [17] The initial angle between the growth direction and the x-axis (h0) A constant of anisotropy function (j) A constant of anisotropy function (d) A positive constant of the driving force m function (a) [17] Absolute value of the minimum relative volume ratio (v) Minimum oxygen content of the growth of iron whiskers (X0o ) A positive constant of a relative volume ratio function (g) Diffusion coefficient of an oxygen ion in solid (Ds(/)) [22] Diffusion coefficient of an oxygen ion on the interface (Dint(/)) [22]
0.0003 p/4 4 0.1 0.9 2.450 0.023 0.710 1 109 1 105
2.2. Oxygen-containing field The reduction of iron oxide is reacted with the gas–solid interface. Along with iron oxide reduction, the diffusion of oxygen ion is
Fig. 4. The relationship between the changes in rate of volume (VO) and oxygen content (XO).
ð11Þ
Fig. 5. Diagram of the calculation area.
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(a) 700 °C
(b) 800 °C
(c) 900 °C
Fig. 6. The iron whiskers of the experiment results change with different temperatures [9].
(1)ϕ
(2)x o
(3)m
Fig. 7. The growth of the iron whisker, the oxygen content, and the growth of the driving force of simulations when the rate of reduction reaction is 7.3 103 mols1 and the oxygen potential of CO/CO2 is 160.01/kJmol1.
3. Calculation method The growth patterns of iron whiskers under various reduction conditions are presented by two- dimensional simulations. The time step obtained is 0.0002. In the simulation, the system area is regularly shaped to rectangular grids (Dx = Dy). The mean value e of the parameter e corresponding to the thickness of the interface is obtained as 0.02 and the interface layer is shaped with two grids pointing inside. Thus, the grid size Dx obtained is 0.01 and the system size is 300Dx 300Dy for the square region. In the simulation,
one particle is surrounded by reducing gas, and the initial radius R of the particle is obtained as 1. Therefore, the initial value of the phase field and the oxygen-containing field are provided. When the phase field is inside of the iron oxide particle as x2 + y2 6 R2, the phase-field variable / is 1 and initial oxygen content xo is 0.6. On the other hand, when it is outside of the iron oxide particle as x2 + y2 > R2, the phase-field variable / is 0 and initial oxygen content xo is 0. The model parameter is shown in Table 2. Based on the simulation results, the diameter growth, as well as the length growth of the iron whisker, can be obtained. As shown
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μo(CO/CO2)=-143.27/kJ㺃mol-1 Xomin=0.006
μo(CO/CO2)=-133.96/kJ焫mol-1 Xomin=0.01
μo(CO/CO2)=-160.01/kJ㺃mol-1 Xomin=0.002
Fig. 8. The growth of iron whiskers change with the oxygen potential of CO/CO2 in conditions at the same time (t = 0.02 s) and the rate of reduction reaction (K = 7.3 103 mols1).
-1
μΟ(CO/CO2)=-160.01kJ·mol
-1
μΟ(CO/CO2)= -143.27kJ·mol
Diameter of iron whiskers/1
Length of iron whiskers/1
0.20
-1
0.15
μΟ(CO/CO2)= -133.96kJ·mol
0.10 0.05 0.00 0.000
0.005
0.010
0.015
0.020
Time/s Fig. 9. The length of iron whiskers change with oxygen potential mixed with reducing gas CO/CO2 at different times.
in Fig. 5, the length of the iron whisker can be calculated using the formula L = R1 R2, where R1 is the length between the top site of the iron whisker and the center of the particle and R2 is the length between the surface without iron whiskers growing on and the center of the particle. The diameter of the iron whisker is regarded as the arc length of the root of the iron whisker, which can be calculated using the formula D = aR2, where a is the angle of the arc length. 4. Results and discussion 4.1. Growth of iron whiskers In conditions with 7.3 103 mols1 reduction rate and 160.01 kJmol1 oxygen potentials, the growth of iron whiskers during reduction by CO with changing oxygen content was provided in Fig. 7. In the second component of Fig. 7, the oxygen content on the surface decreased at different times during the reduction. Owing to the difference of CO adsorption on the surface, the oxygen content of a few micro-area on (1 1 1) surface decreased less than the oxygen content x0o , in which iron whiskers started growing under the high reduction rate condition. The growth driving force m of these micro-areas converts from negative to positive along with the decreasing oxygen content, as shown in the third component of Fig. 7, resulting in the possible growth of iron whiskers on (1 1 1) surface. Nucleation, growth, and transformation of iron whiskers were provided in the first component of Fig. 7 which are similar to the experiment results in Fig. 6.
0.06
μ(CO/CO2)= -160.01kJ·mol
-1
μ(CO/CO2)= -143.27kJ·mol
-1
μ(CO/CO2)= -133.96kJ·mol
-1
0.04
0.02
0.00 0.000
0.005
0.010
0.015
0.020
Time/s Fig. 10. The diameter of iron whiskers change with oxygen potential mixed with reducing gas CO/CO2 at different times.
4.2. Oxygen potential of reducing gas The growth of iron whiskers during reduction by CO with different oxygen potentials of reducing gas was provided in Fig. 8, which showed that the oxygen potential of reducing gas has a considerable effect on the minimum oxygen content of iron oxide. As the oxygen potential of reducing gas lo(CO/CO2) dropped from 133.96 kJmol1 to 160.01 kJmol1, the iron whiskers grow stronger and longer, accompanied by the increase in the number of iron whiskers. With different oxygen potentials, the calculation results of the diameter and length of the iron whisker at position A were provided in Figs. 9 and 10, wherein time is necessary for the growth of iron whiskers. The time is called nucleation incubation period t0, which shows the difficulty of iron whisker nucleation. As the oxygen potential of reducing gas lo(CO/CO2) dropped from 133.96 kJmol1 to 160.01 kJmol1, the nucleation incubation period t0 decreases from 0.014 s to 0.006 s, indicating that a low oxygen potential results in the nucleation of iron whiskers. The curve slope in Figs. 9 and 10 is calculated to clarify the increasing rate of the length and diameter of iron whiskers. As oxygen potential of reducing gas lo(CO/CO2) dropped from 133.96 kJmol1 to 160.01 kJmol1, the maximum increasing rate of the length of the iron whiskers rLmax changed from 15.00 unit length per second to 33.40 unit length per second and the maximum increasing rate of the diameter of iron whiskers rDmax changed from 5.21 unit length per second to 11.25 unit length per second, thereby resulting in a low oxygen potential which not only improves length but also the diameter of iron whiskers.
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Fig. 11. The growth of iron whiskers in conditions with similar oxygen potential (lo(CO/CO2) = 160.01/kJ) changes with the rate of reduction reaction at different times.
Diameter of iron whiskers/1
Length of iron whiskers/1
0.07
K=7.3×10-3mol·s -1 K=6.3×10-3mol·s -1
0.20 0.15 0.10 0.05 0.00 0.000
0.005
0.010
0.015
0.020
0.05 0.04 0.03 0.02 0.01 0.00 -0.01
Time/s Fig. 12. Changes in length of the iron whiskers with the rate of reduction reaction K at different times.
4.3. Rate of reduction reaction Based on the research on experiments, the form of iron reduced from the iron oxides is related to reduction rate. With the increase in reduction rate, the form of iron is converted from layer iron to iron whiskers [9]. The growth of iron whiskers during reduction by CO with different reduction rates was provided in Fig. 11, wherein the reduction rate controlling the rate of decreasing oxygen content has an effect on the growth of iron whiskers. As the reduction rate decreased from 7.3 103 mols1 to 6.3 103 mols1, iron whiskers grow shorter and smaller. With the continued decrease of reduction rate to 4.3 103 mols1 in the model, iron whiskers were not found in the lower reduction rate condition, which is the same with the experiment studies. With different reduction rates, the calculation results of the diameter and length of the iron whisker at position B were provided in Figs. 12 and 13. As the reduction rate K decreased from
K=7.3×10-3mol·s-1 K=6.3×10-3mol·s-1
0.06
0.000
0.005
0.010
0.015
0.020
Time/s Fig. 13. Changes in the diameter of iron whiskers with the rate of reduction reaction K at different times.
7.3 103 mols1 to 6.3 103 mols1, the nucleation incubation period t0 increased from 0.006 s to 0.010 s. A high reduction rate resulted in the nucleation of iron whiskers, in which the maximum increasing rate of the length of iron whiskers rLmax changed from 33.40 unit length per second to 15.00 unit length per second and maximum increasing rate of the diameter of iron whiskers rDmax changed from 11.25 unit length per second to 3.75 unit length per second. Therefore, a high reduction can improve the length and diameter of iron whiskers.
5. Conclusion The simulated results showed that the oxygen content of iron oxide has an effect on the diffusion of iron ion (Fe2+or Fe3+) and iron ion vacancy. The growth of iron whiskers can be attributed
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to the catastrophic swelling of micro-area volume, wherein the iron ion of the high oxygen area diffuses to the low -oxygen area during the wustite reduction, changing the relative cell volume ratio m from 0.866 to 2.394. The iron whiskers cannot grow until iron oxide has already been reduced, in which low oxygen potential or high reduction rate can decrease the initial time of iron whiskers growth t0 to promote the iron whiskers nucleation. The iron whiskers are longer and stronger, increasing the growth rate under the low oxygen potential or high reduction rate. Acknowledgments This work is supported by the Natural Science Foundation Project of China (51374263, 51304257). References [1] J.L. Schenk, Recent status of fluidized bed technologies for producing iron input materials for steelmaking, Particuology 9 (1) (2011) 14–23. [2] J. Fang, X. Wang, Y. Shi, Technology and Theory of Non-Blast Furnace IronMaking, Metallurgical Industry Press, Beijing, 2010, pp. 30–34. [3] Mirko Komatina, H.W. Gudenau, The sticking problem during direct reduction of fine iron ore in the fluidized bed, Metalurgija 10 (4) (2004) 309. [4] R. Degel, Eisenerzreduktion in der Wirbelschiht Mit Wasserstoffreichem Gas: Sticking und Ansatz[D], Iehk, RWTH Aachen, 1996. [5] H.W. Gudenau, M. Hirsch, H. Denecke, et al., The direct reduction of iron ore by the fluidized bed under hydrogen atmosphere, Stahl. Eisen. 117 (4) (1997) 91. [6] Shigeji Taniguchi, Munekazu Ohmi, The variation in the crushing strength of metallised iron pellets with basicity after hydrogen reduction, Trans. Jpn. Inst. Met. 21 (7) (1980) 433–440. [7] A.A. El-Geassy, V. Rajakumar, Gaseous reduction of wustite with H2, CO and H2-CO mixtures, J. Iron Steel Inst. Jpn. Int. 25 (10) (1985) 449–458. [8] A.A. El-Geassy, V. Rajakumar, Influence of particle size on the gaseous reduction of wustite at 900–1100 °C, ISIJ Int. 25 (1985) 1202–1211. [9] Zhilong Zhao, Huiqing Tang, Zhancheng Guo, Micro-behavior of the precipitation of metallic Fe in the reduction of Fe2O3 under CO atmosphere, J. Iron Steel Res. 24 (11) (2012) 26–28. [10] Yoshiaki Iguchi, Yu-ichi Uyeda, Keisuke Goto, Shoji Hayashi, In situ observation of nucleation and growth of iron whiskers from supersaturated wustite, Oxid. Met. 42 (1) (1994) 103–108.
[11] Xuzhong Gong, Ben Zhang, Zhi Wang, Zhancheng Guo, Insight of iron whisker sticking mechanism from iron atom diffusion and calculation of solid bridge radius, Metall. Mater. Trans. B 45 (6) (2014) 1–7. [12] Seong Gyoon Kim, Won Tae Kim, Toshio Suzuki, Machiko Ode, Phase-field modeling of eutectic solidification, J. Cryst. Growth 261 (1) (2004) 135–158. [13] S.L. Wang, R.F. Sekerka, A.A. Wheeler, et al., Thermodynamically-consistent phase-field models for solidification, Physica D 69 (s 1–2) (1993) 189–200. [14] A. Bhattacharya, C.S. Upadhyay, S. Sangal, Phase-field model for mixed-mode of growth applied to austenite to ferrite transformation, Metall. Mater. Trans. A 46 (2) (2014) 926–936. [15] I. Loginova, J. Odqvist, G. Amberg, J. Agren, The phase-field approach and solute drag modeling of the transition to massive c-a transformation in binary Fe-C alloys, Acta Mater. 51 (2003) 1327–1339. [16] Yongbiao Wang, Liming Peng, Yujuan Wu, et al., Phase-field modeling the effect of misfit on the precipitation of the second-phase particles and grain coarsening, Comput. Mater. Sci. 100 (2015) 166–172. [17] You-Hai Wen, Long-Qing Chen, Jeffrey A. Hawk, Phase-field modeling of corrosion kinetics under dual-oxidants, Modell. Simul. Mater. Sci. Eng. 20 (3) (2012) 35013–35024. [18] Ryo Kobayashi, Modeling and numerical simulations of dendritic crystal growth, Physica D 63 (1993) 410–423. [19] Ryo Kobayashi, A numerical approach to three-dimensional dendritic solidification, Exp. Math. 3 (1) (2012) 59–81. [20] Hong Zhong, Liangying Wen, Chong Zou, Shengfu Zhang, Chengguang Bai, Density functional theory study on the carbon- adhering reaction on Fe3O4(1 1 1) surface, Metall. Mater. Trans. B 46 (5) (2015) 2288–2295. [21] Xihu Huang, Ferrous Metallurgy Theory, Metallurgical Industry Press, Beijing, 2008, pp. 239–261. [22] L.Y. Liang, L. Guang-Hong, Phase-field modeling of vacancy cluster evolution in Fe, Acta Phys. Sinica 62 (18) (2013) 182801. [23] Helmut Mehrer, Diffusion in Solids, Springer, Berlin, Heidelberg, New York, 2007, pp. 76–133. [24] Kun Huang, Solid State Physics, Higher Education Press, Beijing, 2014, pp. 42– 78. [25] A.A. El-Geassy, M.I. Nasr, M.M. Hessien, Effect of reducing gas on the volume change during reduction of iron oxide compacts, J. Iron Steel Inst. Jpn. Int. 36 (6) (1996) 640–649. [26] W. Schweika, A. Hoser, M. Martin, Defect structure of ferrous oxide Fe1xO, Phys. Rev. B: Condens. Matter 51 (51) (1995) 15722–15777. [27] Taufiq Hidayat, Denis Shishin, Evgueni Jak, Sergei A. Decterov, Thermodynamic reevaluation of the Fe-O system, CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 48 (2015) 131–144. [28] Paul Shewmon, Diffusion in Solids, Ohio State University: Department of Metallurgical Engineering, 1991, pp. 54–172.
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Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Numerical simulation of iron whisker growth with changing oxygen content in iron oxide using phase-field method Feng Lu, Liangying Wen ⇑, Jianlong Li, Jin Wei, Jian Xu, Shengfu Zhang College of Materials Science and Engineering, Chongqing University, Chongqing 400030, China
a r t i c l e
i n f o
Article history: Received 7 July 2016 Received in revised form 30 August 2016 Accepted 1 September 2016 Available online 13 September 2016 Keywords: Iron oxide Reduction Iron whiskers Phase-field model Iron-oxygen system
a b s t r a c t Phase-field method is used to simulate the growth of iron whiskers on a gas–solid interface by changing the oxygen content in iron oxide. Results show that oxygen content significantly influences not only the crystal lattice but also the diffusion direction of iron ion vacancies and iron ions, wherein iron ions diffuse to low-oxygen-content areas and iron ion vacancies diffuse to high-oxygen-content areas. The catastrophic swelling of the micro-area volume and the growth of iron whiskers are caused by the enrichment of iron ions in low-oxygen-content areas. The simulation revealed the effects of the reduction rate and the oxygen potential of gas. Iron whiskers are longer and stronger when the oxygen potential of reducing gas decreases from 133.96 kJmol1 to 160.01 kJmol1 or when the reduction rate increases from 6.3 103 mols1 to 7.3 103 mols1. Iron whiskers can appear earlier with a low oxygen potential or a high reduction rate. Both oxygen potential and reduction rate promote the nucleation and growth of iron whiskers. Ó 2016 Elsevier B.V. All rights reserved.
1. Introduction Fluidized bed direct reduction is a non-coke iron-making process that uses iron ore powder at a high reduction rate, making it one of the most developed non-blast furnace processes [1,2]. During reduction, iron ore powder stick in parts of the reactor. Once the sticking becomes too severe, affecting the entire reactor, iron ore powder will lose flow. A previous study showed that during reduction, iron separates from iron ore powder as a fibrous shape and clumps together as a result of the joining of fibrous iron called iron whiskers [3–5]. As the iron oxide is reduced, the change in iron oxide volume accompanied by the decreased in oxygen content is caused by the reconstruction of another crystal lattice by the iron ion Fe2+(Fe3+) and the oxygen ion O2. The growth of iron whiskers during reduction is cited as a major cause of catastrophic swelling at the local micro-area of iron oxide. Reduced temperature, gases, and particle size are among the reduction parameters that reportedly affect iron oxide volume change and iron whisker growth [6–8]. Zhao et al. used in situ observation to study the precipitation morphology of iron and the evolution process of its mineralogical structure; he found that the nucleation and growth of iron whiskers proceed in the conversion of FeO ? Fe [9]. Yoshiaki et al. obtained similar results [10]. Gong et al. established a model for calculating iron whiskers [11]. Researchers agree that ⇑ Corresponding author. E-mail address: [email protected] (L. Wen). http://dx.doi.org/10.1016/j.commatsci.2016.09.003 0927-0256/Ó 2016 Elsevier B.V. All rights reserved.
the growth of iron whiskers is caused by the directed diffusion of iron ions and iron ion vacancies in wustite. In a gas–solid system, iron oxide reacts with carbon monoxide. Movement of the gas–solid interface is caused by the growth of iron whiskers at the local micro-area or the shrinking of the core. The phase-field model has been extensively applied to simulate multiphase changes, such as solidification [12,13], solid state phase transformation [14–16], and metallic corrosion [17]. The phase-field model developed by Ryo Kobayashi [18,19] is used to simulate solidification, in which the parameter m controls the phase change during solidification. In the present study, the growth of iron whiskers is simulated by using a phase-field model without tracking the complex gas–solid interface. The existing experiment results and the iron oxide phase diagram suggest that the oxygen content of iron oxide significantly affects crystal lattice conversion, iron ions, oxygen ions, and iron ion vacancies in directed diffusions in wustite, which control the growth of iron whiskers. In the phase-field model, the parameter m is changed to describe the relationship between oxygen content and iron whisker growth. The reduction rate and oxygen potential are then analyzed. 2. Computational methods and models 2.1. Phase-field model The model includes two main equations: a phase-field /(r, t) and an oxygen-containing field xO(r, t). The /(r, t) is an ordering
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parameter at position r and time t, in which / = 1 indicates solid and / = 0 reduces gas CO/CO2. According to the Ginzburg-Landau phase transition theory [18], the free energy of a gas–solid system can be obtained as follows U(/, m):
Z
U½/; m ¼
1 2 e jr/j2 þ Fð/; mÞdr 2
ð1Þ
Parameter e(ʋ) in Eq. (1), which determines the thickness of the interface, is a function of the outer normal vector at interface ʋ. In the phase-field method, the outer normal vector ʋ is replaced by r/, which indicates that parameter e(ʋ) can be shown as e (r/). Thus, Eq. (1) can be considered as follows:
Z
U½/; m ¼
1 ½eðr/Þ2 jr/j2 þ Fð/; mÞdr; 2
ð2Þ
where F(/, m) is the free energy density. The form of the free energy density in the phase-field model is used to describe the gas–solid system, as shown below:
Fð/; mÞ ¼
1 4 1 1 1 1 / m /3 þ m /2 4 2 3 4 2
ð3Þ
The parameter m is the growth driving force. Combining with ¼ ddtU, the phase-field model can be simplified as equation s @/ @t shown below:
s
@/ @ @/ þ ee0 @y @y @x 1 þ r ðe2 r/Þ þ /ð1 /Þ / þ m ; 2
@/ @ ¼ @t @x
ee0
ð4Þ
rðhÞ ¼ 1 þ d cos½jðh h0 Þ
Thus, the driving force m is another important parameter of phase field because it has a significant effect on the change phase from solid to gas. F(/, m) is a double-well potential which has local minimums at / = 1 and 0 for each m. The profile of F(/, m) changes with m only when jmj 6 1=2, as shown in Fig. 1. Based on the minimum energy principle, the most stable phase at a local place is determined by m. If m is positive, the free energy density is minimum at / = 1. The micro-area would be occupied by solid for the growth of iron whiskers. If m is negative, the micro-area would be a shrinking core. The mechanisms of iron oxide crystal structure change and iron ion, oxygen ion, and vacancy diffusion direction should be studied to establish m function, which could provide the description of the growth of iron whiskers. Oxygen potential of CO/CO2 was less than the oxygen potential of iron oxide, resulting in a reduced iron oxide by CO/CO2. The oxygen content on the surface is decreased by the oxygen ion reaction with CO. The iron whiskers can only grow during wustite reduction. The temperature in the model is over 570 °C, which can maintain the stability of the wustite. As shown in Fig. 2, the crystal lattice conversion of Fe2O3 ? Fe3O4 ? FeO is attributed to the decrease in oxygen content with the same temperature [21]. The particle comprised iron oxide difference; thus, the particle is regarded as one solid phase of oxygen content difference. Experimental studies show that in converting Fe2O3 ? Fe3O4 ? FeO, the volume changes because of the lattice transformation and the iron whiskers which first appeared in the conversion of FeO ? Fe. The growth of iron whiskers or the partial enrichment of iron
where s is a small positive constant, and s = 0.0003 is obtained in the model [18]. Based on the phase-field model, parameter e(h) which is a microscopic interaction length, is placed as Eq. (5) where e is a mean value of the parameter e and r(h) is anisotropy. e0 (h) indicates differentiation with respect to the angle h. The parameter h in the r(h) is the angle between the direction of the growth of iron whiskers and the x-axis. Iron whiskers can grow on the position where CO is preferably adsorbed, indicating that the angle h which determines the direction of the growth of iron whiskers is related with the adsorption site of CO reducing gas. The energy of CO adsorption on the surface of iron oxide is calculated by the firstprinciples method, which shows that CO is easily absorbed on (1 1 1) surface of iron oxide [20]. In two-dimensional space, iron whiskers are more likely to grow in the direction of ±p/4 or ±3p/4. The anisotropy r(h) is obtained as Eq. (6), wherein the initial angle between the growth direction and the x-axis (h0) is p/4, the anisotropy module (j) is 4, and the parameter (d) determining the strength of growth is 0.1.
eðhÞ ¼ e rðhÞ
ð6Þ
ð5Þ
Fig. 1. The profile of F(U, m) changes with m [17].
Fig. 2. Iron oxide phase diagram.
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Fig. 3. Diagram of the wustite reduction mechanism.
Table 1 The lattice constant (1010 m) and the relative volume ratio of the different types of phase [20]. Type of phase
aFe
FeO
Fe3O4
cFe2O3
Oxygen content of micro-area Lattice constant/1010 m Relative volume ratio
0 2.861 2.394
0.5 4.290 0.866
0.57 8.380 0.022
0.6 8.320 0
ion is caused by iron ion directional diffusion. The iron ion vacancy in wustite is more than other iron oxides; thus, the iron ion is active and easier to diffuse [22,23]. The mechanisms of iron ion and iron ion vacancy diffusion are shown in Fig. 3. Iron ion diffuse at a few micro-area of gas–solid interface wherein oxygen content is less than others, whereas iron ion vacancy diffuses into the micro-area inside wherein the oxygen content is more than others. The form of iron ion vacancy in the wustite is shown as 3+ Fe2+ + 1/2O2 = V2 + O2, Fe2þ + 2Fe
and the iron ion vacancy 1=6 1/3 pO2 , concentration in wustite is shown as x V2 = (K1/4 1 ) Fe2þ where K1 is thermodynamic equilibrium constant. The iron ion vacancy concentration is enriched in the high oxygen content [21,24]. The form of iron in the wustite is shown 2 as 1Fe2þ 2Fe3þ V2 + Fe2+ = (2Fe2+2Fe3+ + 2e) + 1/2O2 = Fe2þ O 4Fe + 1/2O2; 1/2O2 + CO = CO2; thus, the iron concentration can be shown as xðFeÞ ¼ ðK2 Þ1=2 p1=4 O2 . Combined with thermodynamic analysis, iron ion in the wustite diffuse to the area of low oxygen potentials and iron ion vacancy diffuse to the area of high oxygen potentials was proven. The iron whiskers first appear in the conversion of FeO ? Fe because iron ion vacancy in wustite is more than other iron oxides,
enabling the free diffusion of iron ion. In addition, oxygen content not only has a significant effect on the crystal lattice but also on the iron ion and iron ion vacancy diffusion direction. The change in oxygen content influences the growth of iron whiskers. Constructing an m function to establish the relationship between the micro-area volume change and micro-area oxygen content in the conversion of Fe2O3 ? Fe3O4 ? FeO ? Fe (with little oxygen) is necessary. The micro-area volume change changes with the oxygen content [25]. The lattice constant of the changing iron oxide with the oxygen content is shown in Table 1 [21]. Based on Table 1 and Fig. 4, there are three steps in the reduction of iron oxide [26,27]. The first step is the swelling fromcFe2O3 to Fe3O4. The second step involves the conversion of Fe2O3 ? Fe3O4, wherein the volume of iron oxides slightly changes because the lattice constant of cFe2O3 is almost the same as Fe3O4 and the relative cell volume ratio m: (mFe3O4 mcFe2O3)/mcFe2O3 = ((8.38)3 (8.32)3)/ (8.32)3 0.022. The second step is shrinking core from Fe3O4 to FeO without growth of iron whiskers. With the decrease in oxygen content, the volume of iron oxides smoothly decreased as a result of relative cell volume ratio m: (mFeO mFe3O4)/mFe3O4 = ((4.290)3 (8.38)3)/(8.38)3 0.866. The last step is shrinking the core from FeO to Fe with the iron whiskers growing on the surface (growth of iron whiskers). The oxygen ion is obtained from
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wustite by carbon monoxide, which provides two electrons, thereby allowing the conversion of two ferric ions (Fe3+) to two ferrous iron (Fe2+). The ferrous iron (Fe2+), whether from iron oxide itself or ferric iron (Fe3+) change, will diffuse from the micro-area of high oxygen content to the micro-area of low oxygen content. Based on the crystal structure change, one FeO unit cell will become four Fe unit cells, resulting in ferrous iron filling the iron ion vacancy to increase the volume of the micro-area as a result of relative cell volume ratio m: (4⁄mFe mFeO)/mFeO = (4⁄(2.861)3 (4.290)3)/(4.290)3 = 2.394. The growth of iron whiskers is limited by the minimum oxygen content of iron oxide. When the oxygen potential of CO/CO2 is similar to iron oxide, the oxygen content is constant. When oxygen content is less than 0.01, the oxygen potential of iron oxide is shown as follows [27]:
lO ¼ 0:5lhO þ RT lnðcO X Omin Þ
ð7Þ
Also, the equation for oxygen potential of CO/CO2 is as follows [21]:
lOðCOCO Þ ¼ 565; 390 þ ½175:17 38:30 lgðpCO =pCO2 ÞT 2
ð8Þ
The minimum oxygen content can be obtained by combining the two equations. Finally, the equation to describe the relationship between the growth driving force m and the relative cell volume ratio mO can be obtained as follows:
a arctan mO þ 0:5 ð/ 1Þ p
m¼/
"
mO ¼ 4v
12 0 6 # X 0O þ X Omin þ g X O þ X Omin þ g ðxO þ X Omin Þ þ g ðxO þ X Omin Þ þ g
ð9Þ
ð10Þ
where X0o is the oxygen content in which iron whiskers start to grow, Xo is the oxygen content of the iron oxide, Xomin is the minimum oxygen content of the iron oxide, and v is the absolute value of the minimum relative volume ratio. Using the data from Table 1, v is 2.450, X0o is 0.023, and g is 0.710. When the oxygen content is less than 0.023, the iron whisker will grow.
combined with the diffusion of iron ion vacancy and iron ion in wustite. The diffusion of the iron ion vacancy and iron ion are determined by the ratio of the decrease in oxygen content. Oxygen ion can rapidly diffuse to the surface for the reaction because it has high diffusivity in iron oxide, thereby improving the diffusion of the iron ion vacancy and the iron ion [9]. The oxygen content is decreased on the gas–solid interface. The oxygen-containing field is represented by the following function:
@xO @/ ¼ r2 Dð/ÞxO þ K @t @t
K @/=@t is the reduction reaction source of the function, in which K is reduction reaction rate. The reduction reaction occurs with the moving gas–solid interface because K @/=@t has a non-zero value only when the interface passes the point. D(/) is the diffusion coefficient with regard to phasefield. When oxygen diffuses inside the iron oxide, diffusion coefficient D(/) is 1 109 with / = 1 [28]. As long as oxygen diffuses on the interface, diffusion coefficient D(/) increase to 1 105 with 0 < / < 1. Moreover, diffusion coefficient D(/) is zero with / = 0 because of the reaction with CO on the interface. Table 2 The parameter in the model. Parameter of the model
Value
Small positive constant of the phase-field model (s) [17] The initial angle between the growth direction and the x-axis (h0) A constant of anisotropy function (j) A constant of anisotropy function (d) A positive constant of the driving force m function (a) [17] Absolute value of the minimum relative volume ratio (v) Minimum oxygen content of the growth of iron whiskers (X0o ) A positive constant of a relative volume ratio function (g) Diffusion coefficient of an oxygen ion in solid (Ds(/)) [22] Diffusion coefficient of an oxygen ion on the interface (Dint(/)) [22]
0.0003 p/4 4 0.1 0.9 2.450 0.023 0.710 1 109 1 105
2.2. Oxygen-containing field The reduction of iron oxide is reacted with the gas–solid interface. Along with iron oxide reduction, the diffusion of oxygen ion is
Fig. 4. The relationship between the changes in rate of volume (VO) and oxygen content (XO).
ð11Þ
Fig. 5. Diagram of the calculation area.
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(a) 700 °C
(b) 800 °C
(c) 900 °C
Fig. 6. The iron whiskers of the experiment results change with different temperatures [9].
(1)ϕ
(2)x o
(3)m
Fig. 7. The growth of the iron whisker, the oxygen content, and the growth of the driving force of simulations when the rate of reduction reaction is 7.3 103 mols1 and the oxygen potential of CO/CO2 is 160.01/kJmol1.
3. Calculation method The growth patterns of iron whiskers under various reduction conditions are presented by two- dimensional simulations. The time step obtained is 0.0002. In the simulation, the system area is regularly shaped to rectangular grids (Dx = Dy). The mean value e of the parameter e corresponding to the thickness of the interface is obtained as 0.02 and the interface layer is shaped with two grids pointing inside. Thus, the grid size Dx obtained is 0.01 and the system size is 300Dx 300Dy for the square region. In the simulation,
one particle is surrounded by reducing gas, and the initial radius R of the particle is obtained as 1. Therefore, the initial value of the phase field and the oxygen-containing field are provided. When the phase field is inside of the iron oxide particle as x2 + y2 6 R2, the phase-field variable / is 1 and initial oxygen content xo is 0.6. On the other hand, when it is outside of the iron oxide particle as x2 + y2 > R2, the phase-field variable / is 0 and initial oxygen content xo is 0. The model parameter is shown in Table 2. Based on the simulation results, the diameter growth, as well as the length growth of the iron whisker, can be obtained. As shown
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μo(CO/CO2)=-143.27/kJ㺃mol-1 Xomin=0.006
μo(CO/CO2)=-133.96/kJ焫mol-1 Xomin=0.01
μo(CO/CO2)=-160.01/kJ㺃mol-1 Xomin=0.002
Fig. 8. The growth of iron whiskers change with the oxygen potential of CO/CO2 in conditions at the same time (t = 0.02 s) and the rate of reduction reaction (K = 7.3 103 mols1).
-1
μΟ(CO/CO2)=-160.01kJ·mol
-1
μΟ(CO/CO2)= -143.27kJ·mol
Diameter of iron whiskers/1
Length of iron whiskers/1
0.20
-1
0.15
μΟ(CO/CO2)= -133.96kJ·mol
0.10 0.05 0.00 0.000
0.005
0.010
0.015
0.020
Time/s Fig. 9. The length of iron whiskers change with oxygen potential mixed with reducing gas CO/CO2 at different times.
in Fig. 5, the length of the iron whisker can be calculated using the formula L = R1 R2, where R1 is the length between the top site of the iron whisker and the center of the particle and R2 is the length between the surface without iron whiskers growing on and the center of the particle. The diameter of the iron whisker is regarded as the arc length of the root of the iron whisker, which can be calculated using the formula D = aR2, where a is the angle of the arc length. 4. Results and discussion 4.1. Growth of iron whiskers In conditions with 7.3 103 mols1 reduction rate and 160.01 kJmol1 oxygen potentials, the growth of iron whiskers during reduction by CO with changing oxygen content was provided in Fig. 7. In the second component of Fig. 7, the oxygen content on the surface decreased at different times during the reduction. Owing to the difference of CO adsorption on the surface, the oxygen content of a few micro-area on (1 1 1) surface decreased less than the oxygen content x0o , in which iron whiskers started growing under the high reduction rate condition. The growth driving force m of these micro-areas converts from negative to positive along with the decreasing oxygen content, as shown in the third component of Fig. 7, resulting in the possible growth of iron whiskers on (1 1 1) surface. Nucleation, growth, and transformation of iron whiskers were provided in the first component of Fig. 7 which are similar to the experiment results in Fig. 6.
0.06
μ(CO/CO2)= -160.01kJ·mol
-1
μ(CO/CO2)= -143.27kJ·mol
-1
μ(CO/CO2)= -133.96kJ·mol
-1
0.04
0.02
0.00 0.000
0.005
0.010
0.015
0.020
Time/s Fig. 10. The diameter of iron whiskers change with oxygen potential mixed with reducing gas CO/CO2 at different times.
4.2. Oxygen potential of reducing gas The growth of iron whiskers during reduction by CO with different oxygen potentials of reducing gas was provided in Fig. 8, which showed that the oxygen potential of reducing gas has a considerable effect on the minimum oxygen content of iron oxide. As the oxygen potential of reducing gas lo(CO/CO2) dropped from 133.96 kJmol1 to 160.01 kJmol1, the iron whiskers grow stronger and longer, accompanied by the increase in the number of iron whiskers. With different oxygen potentials, the calculation results of the diameter and length of the iron whisker at position A were provided in Figs. 9 and 10, wherein time is necessary for the growth of iron whiskers. The time is called nucleation incubation period t0, which shows the difficulty of iron whisker nucleation. As the oxygen potential of reducing gas lo(CO/CO2) dropped from 133.96 kJmol1 to 160.01 kJmol1, the nucleation incubation period t0 decreases from 0.014 s to 0.006 s, indicating that a low oxygen potential results in the nucleation of iron whiskers. The curve slope in Figs. 9 and 10 is calculated to clarify the increasing rate of the length and diameter of iron whiskers. As oxygen potential of reducing gas lo(CO/CO2) dropped from 133.96 kJmol1 to 160.01 kJmol1, the maximum increasing rate of the length of the iron whiskers rLmax changed from 15.00 unit length per second to 33.40 unit length per second and the maximum increasing rate of the diameter of iron whiskers rDmax changed from 5.21 unit length per second to 11.25 unit length per second, thereby resulting in a low oxygen potential which not only improves length but also the diameter of iron whiskers.
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Fig. 11. The growth of iron whiskers in conditions with similar oxygen potential (lo(CO/CO2) = 160.01/kJ) changes with the rate of reduction reaction at different times.
Diameter of iron whiskers/1
Length of iron whiskers/1
0.07
K=7.3×10-3mol·s -1 K=6.3×10-3mol·s -1
0.20 0.15 0.10 0.05 0.00 0.000
0.005
0.010
0.015
0.020
0.05 0.04 0.03 0.02 0.01 0.00 -0.01
Time/s Fig. 12. Changes in length of the iron whiskers with the rate of reduction reaction K at different times.
4.3. Rate of reduction reaction Based on the research on experiments, the form of iron reduced from the iron oxides is related to reduction rate. With the increase in reduction rate, the form of iron is converted from layer iron to iron whiskers [9]. The growth of iron whiskers during reduction by CO with different reduction rates was provided in Fig. 11, wherein the reduction rate controlling the rate of decreasing oxygen content has an effect on the growth of iron whiskers. As the reduction rate decreased from 7.3 103 mols1 to 6.3 103 mols1, iron whiskers grow shorter and smaller. With the continued decrease of reduction rate to 4.3 103 mols1 in the model, iron whiskers were not found in the lower reduction rate condition, which is the same with the experiment studies. With different reduction rates, the calculation results of the diameter and length of the iron whisker at position B were provided in Figs. 12 and 13. As the reduction rate K decreased from
K=7.3×10-3mol·s-1 K=6.3×10-3mol·s-1
0.06
0.000
0.005
0.010
0.015
0.020
Time/s Fig. 13. Changes in the diameter of iron whiskers with the rate of reduction reaction K at different times.
7.3 103 mols1 to 6.3 103 mols1, the nucleation incubation period t0 increased from 0.006 s to 0.010 s. A high reduction rate resulted in the nucleation of iron whiskers, in which the maximum increasing rate of the length of iron whiskers rLmax changed from 33.40 unit length per second to 15.00 unit length per second and maximum increasing rate of the diameter of iron whiskers rDmax changed from 11.25 unit length per second to 3.75 unit length per second. Therefore, a high reduction can improve the length and diameter of iron whiskers.
5. Conclusion The simulated results showed that the oxygen content of iron oxide has an effect on the diffusion of iron ion (Fe2+or Fe3+) and iron ion vacancy. The growth of iron whiskers can be attributed
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to the catastrophic swelling of micro-area volume, wherein the iron ion of the high oxygen area diffuses to the low -oxygen area during the wustite reduction, changing the relative cell volume ratio m from 0.866 to 2.394. The iron whiskers cannot grow until iron oxide has already been reduced, in which low oxygen potential or high reduction rate can decrease the initial time of iron whiskers growth t0 to promote the iron whiskers nucleation. The iron whiskers are longer and stronger, increasing the growth rate under the low oxygen potential or high reduction rate. Acknowledgments This work is supported by the Natural Science Foundation Project of China (51374263, 51304257). References [1] J.L. Schenk, Recent status of fluidized bed technologies for producing iron input materials for steelmaking, Particuology 9 (1) (2011) 14–23. [2] J. Fang, X. Wang, Y. Shi, Technology and Theory of Non-Blast Furnace IronMaking, Metallurgical Industry Press, Beijing, 2010, pp. 30–34. [3] Mirko Komatina, H.W. Gudenau, The sticking problem during direct reduction of fine iron ore in the fluidized bed, Metalurgija 10 (4) (2004) 309. [4] R. Degel, Eisenerzreduktion in der Wirbelschiht Mit Wasserstoffreichem Gas: Sticking und Ansatz[D], Iehk, RWTH Aachen, 1996. [5] H.W. Gudenau, M. Hirsch, H. Denecke, et al., The direct reduction of iron ore by the fluidized bed under hydrogen atmosphere, Stahl. Eisen. 117 (4) (1997) 91. [6] Shigeji Taniguchi, Munekazu Ohmi, The variation in the crushing strength of metallised iron pellets with basicity after hydrogen reduction, Trans. Jpn. Inst. Met. 21 (7) (1980) 433–440. [7] A.A. El-Geassy, V. Rajakumar, Gaseous reduction of wustite with H2, CO and H2-CO mixtures, J. Iron Steel Inst. Jpn. Int. 25 (10) (1985) 449–458. [8] A.A. El-Geassy, V. Rajakumar, Influence of particle size on the gaseous reduction of wustite at 900–1100 °C, ISIJ Int. 25 (1985) 1202–1211. [9] Zhilong Zhao, Huiqing Tang, Zhancheng Guo, Micro-behavior of the precipitation of metallic Fe in the reduction of Fe2O3 under CO atmosphere, J. Iron Steel Res. 24 (11) (2012) 26–28. [10] Yoshiaki Iguchi, Yu-ichi Uyeda, Keisuke Goto, Shoji Hayashi, In situ observation of nucleation and growth of iron whiskers from supersaturated wustite, Oxid. Met. 42 (1) (1994) 103–108.
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