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Quantitative analyses of ferrite lattice parameter and solute Nb content in low carbon microalloyed steels
Scripta Materialia 52 (2005) 973–976 www.actamat-journals.com
Quantitative analyses of ferrite lattice parameter and solute Nb content in low carbon microalloyed steels Seok-Jae Lee, Young-Kook Lee
*
Department of Metallurgical Engineering, Yonsei University, Seoul 120-749, Korea Received 19 November 2004; received in revised form 10 January 2005; accepted 21 January 2005
Abstract The effect of solute Nb on the ferrite lattice parameter in low carbon steels was examined using X-ray diffraction and related to atomic size difference. The concentration of solute Nb in ferrite of a furnace-cooled steel was successfully predicted using the measured coefficient of Nb atoms on the ferrite lattice parameter. 2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Solute Nb; Ferrite lattice parameter; XRD; Microalloyed steel
1. Introduction The carbo-nitride-forming elements such as Nb, Ti and V have great influence on microstructure and mechanical properties of low carbon microalloyed steels. A small addition of Nb to low carbon steels is very effective in grain refinement and precipitation hardening as solute Nb atoms or NbC precipitates. The amounts of the solute Nb and NbC precipitates in microalloyed steels have been investigated by using different experimental methods such as inductively coupled plasma atomic emission spectrometry (ICP-AES), transmission electron microscopy (TEM), and stress relaxation [1–4]. Although the size and chemical composition of the precipitates can be evaluated from TEM-EDS work, it is still difficult to acquire the amount of the precipitates, especially in the case of very fine particles less than 100 nm in diameter using TEM, ICP-AES, and mechanical tests. The X-ray diffraction technique is expected to be useful to quantitatively determine the amount of the solute *
Corresponding author. Tel.: +82 2 2123 2831; fax: +82 2 312 5375. E-mail address: [email protected] (Y.-K. Lee).
Nb based on the relationship between the lattice parameters of austenite and ferrite and the concentration of an alloying element as follows [5–7]: ac ðnmÞ ¼ 0:35770 þ 0:00065 C þ 0:00010 Mn 0:00002 Ni þ 0:00006 Cr þ 0:00056 N þ 0:00028 Al 0:00004 Co þ 0:00014 Cu þ 0:00053 Mo þ 0:00079 Nb þ 0:00032 Ti þ 0:00017 V þ 0:00057 W ð1Þ aa ðnmÞ ¼ 0:28664 þ 0:00006 Mn 0:00003 Si 0:00007 Ni þ 0:00005 Cr 0:00010 P 0:00031 Ti þ 0:00027 Ru þ 0:00035 Rh þ 0:00029 Re þ 0:00037 Ir þ 0:00049 Pt
ð2Þ
where ac and aa are the lattice parameters of austenite and ferrite, respectively, and the concentration of each element is in atomic percent.
1359-6462/$ - see front matter 2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.scriptamat.2005.01.028
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S.-J. Lee, Y.-K. Lee / Scripta Materialia 52 (2005) 973–976
Eq. (1) includes the effect of Nb on the lattice parameter of austenite and the coefficient of Nb is 0.00079 nm per atomic percent. However, there are few articles about the effect of Nb on the lattice parameter of ferrite. The purpose of this study is to quantitatively investigate the coefficient of Nb on the lattice parameter of ferrite to evaluate the amount of the solute Nb in low carbon microalloyed steels. 2. Experimental procedure The five ingots of Fe–X%C–0.2%Si–1.2%Mn–Y%Nb steels were prepared using a vacuum induction furnace. The chemical composition of homogenized ingots is listed in Table 1. The ingots were hot-rolled to 10 mm thick plates, from which the specimens of 15 · 15 · 2 mm3 were machined, solution-treated at 1170 C for 10 min in a vacuum furnace to fully dissolve Nb particles, which might form during hot rolling, and then furnace-cooled down to the room temperature. The samples were mechanically polished by using Emery papers of different grit sizes and the cloth pasted with alumina powders of about 1 lm. Finally, the samples were chemically polished using a chemical mixture of acetic acid 90% and perchloric acid 10%. To examine the lattice parameter of ferrite, X-ray diffraction (XRD) tests were performed at room temperature after the calibration of the standard Si powders using ‘‘Rigaku D/Max-RC’’ diffractometer with the Cu ˚ . The scantarget whose Ka wavelength k is 1.540562 A ning angle 2 was between 35 and 140 and the step size was 0.01. The lattice parameters were first calculated by applying the Nelson–Riley function [8] to each peak having different diffraction angles (2h), and then final lattice parameter of the ferrite was determined by fitting the different lattice parameters obtained at each peak by using the least square method, and was listed with an error range in Table 1. 3. Results and discussion 3.1. Effect of Nb on ferrite lattice parameter The effect of Nb on the lattice parameter of ferrite in the ultra-low carbon microalloyed steels (A1, A2, A3, A4
in Table 1) was examined by X-ray diffraction tests. Because the carbon content of the steels (0.003 wt.%) is too low to form NbC precipitates during furnace cooling, all Nb atoms can be assumed to remain as solutes in ferrite matrix. Strictly speaking, however, the distribution of the solute Nb atoms would be unlikely uniform in the ferrite matrix during furnace cooling, because the segregation of Nb atoms to the grain boundaries can occur at such a slow cooling rate [9]. Nevertheless, the lattice parameters of polycrystalline materials have been widely measured as a function of the average solute content by using X-ray diffraction [10–12]. The variation in lattice parameter of ferrite is plotted against Nb content in atomic percent in Fig. 1. The lattice parameter of ferrite is almost linearly proportional to the Nb concentration and the slope (kNb = 0.000625 (nm/at.%)) is the coefficient of Nb on the lattice parameter of ferrite. The intersection point between a fitted straight line and y-axis indicates the lattice parameter of ferrite without Nb atoms (0.286768 nm), which can also be calculated using Eq. (2) containing the coefficients of alloying elements such as C, Mn and Si on the lattice parameter of ferrite. The calculated lattice parameter of ferrite without Nb atoms (0.286707 nm) is in a good agreement with the experimental one of 0.286767 nm. The lattice parameter of ferrite of pure iron is taken as 0.28664 nm at 25 C (JCPDS, Card 6-0696). 3.2. Effect of the difference in atomic radius between Fe and an alloying element on lattice parameters Assuming that the variation in lattice parameters of austenite and ferrite with the addition of an alloying element is closely related to the difference in atomic radius [13] between Fe and the alloying element, the coefficients of alloying elements on the austenite lattice parameter in Eq. (1) are plotted against the difference in atomic radius between Fe and alloying elements in Fig. 2. The coefficient of the alloying element on the lattice parameter of austenite is increased with the increase in difference in atomic radius between Fe and the alloying element. Specially, the coefficient of Nb in Eq. (1) does not seem different from that of Nb calculated using a fitted curve in Fig. 2.
Table 1 Chemical composition and ferrite lattice parameters of the experimental steels (wt.%) Steel
C
Si
Mn
Nb
N
aa (nm)
A1 A2 A3 A4 A5
0.003 0.003 0.003 0.003 0.040
0.20 0.20 0.20 0.20 0.20
1.21 1.21 1.21 1.20 1.22
– 0.020 0.050 0.080 0.082
0.0035 0.0037 0.0041 0.0036 0.0045
0.286767 ± 0.0000073 0.286778 ± 0.0000048 0.286786 ± 0.0000039 0.286797 ± 0.0000041 0.286788 ± 0.0000021
S.-J. Lee, Y.-K. Lee / Scripta Materialia 52 (2005) 973–976
Fig. 1. Variation in the lattice parameter of ferrite with Nb concentration at 25 C in ultra-low carbon microalloyed steels (A1, A2, A3, and A4).
Fig. 2. Relationship between the coefficient of an alloying element on austenite lattice parameter and the difference in atomic radius between Fe and the alloying element [9].
In the same way, the coefficient of Nb on the lattice parameter of ferrite is estimated by fitting the coefficients of alloying elements against the difference in atomic radius between Fe and the alloying elements in ferrite [5]. The estimated coefficient of Nb (0.00064 nm per atomic percent) is almost the same to that of Nb (0.000625 nm per atomic percent) measured by X-ray diffraction tests, as shown in Fig. 3. 3.3. Quantitative analysis of solute Nb content using the ferrite lattice parameter The quantitative analysis of solute Nb in ferrite of the steel A5, which was never used for the coefficient of Nb on the lattice parameter of ferrite, was investigated by measuring the lattice parameter of ferrite of the steel from X-ray diffraction tests. The steel A5 was solution treated at 1170 C for 10 min. and furnace-cooled so that NbC particles and cementite probably form and the carbon concentration in ferrite is almost identical to its solubility limit in ferrite at room temperature
975
Fig. 3. Relationship between the coefficient of an alloying element on ferrite lattice parameter and the difference in atomic radius between Fe and the alloying element [9].
Fig. 4. Quantitative analysis of the amount of solute Nb in ferrite using the relationship between ferrite lattice parameter and solute Nb concentration.
[14]. The measured lattice parameter of ferrite is proportional to the average solute Nb content in ferrite, although the solute Nb content is not homogeneous locally because of the depletion of Nb atoms around the NbC particles. The measured ferrite lattice parameter is plotted as a square mark together with those of the ultra-low carbon microalloyed steels in Fig. 4. The ferrite lattice parameter of the steel A5, whose initial Nb content is 0.048 at.%, corresponds to that of the specimen containing the solute Nb content of 0.033 at.%, indicating that approximately 30% of Nb atoms probably joined precipitation during furnace-cooling.
4. Conclusions The coefficient of the solute Nb on ferrite lattice parameter is 0.000625 nm per atomic percent. The variation in lattice parameters of austenite and ferrite with the addition of an alloying element is strongly dependent upon the difference in atomic radius between Fe
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and the alloying element. The solute Nb concentration in ferrite of a furnace-cooled low carbon microalloyed steel can be determined using the ferrite lattice parameter of the specimen measured from X-ray diffraction tests and the coefficient of solute Nb on ferrite lattice parameter. Acknowledgments This research was performed as a part of the POSCO project titled ‘‘Development of Simulator for Predicting Phase Transformations and Mechanical Properties of Microalloyed and Low Alloy Steels’’. References [1] Samuel FH, Ouellet P, Samuel AM, Doty HW. Metall Mater Trans A 1998;29A:2871.
[2] Mishra(Pathak) SK, Das S, Ranganathan S. Mater Sci Eng A 2002;323A:285. [3] Soto R, Saikaly W, Bano X, Issartel C, Rigaut G, Charai A. Acta Mater 1999;47:3475. [4] Garcı´a-Mateo C, Lo´pez B, Rodriguez-Ibabe JM. Mater Sci Eng A 2001;303A:216. [5] Leslie WC. The physical metallurgy of steels. New York: McGraw-Hill; 1982. p. 111. [6] Pearson WB. A hand book of lattice spacings and structure of metals and alloys, vol. 2. London: Pergamon Press; 1967. p. 908. [7] Dyson DJ, Holmes B. JISI 1970;208:469. [8] Cullity BD. Elements of X-ray diffraction 2nd ed. Reading: Addison-Wesley; 1967. p. 350. [9] Lee YK, Hong JM, Choi CS, Lee JK. Mat Sci Forum 2005;475– 479:65. [10] Hos James P, McCormick Paul G. Scr Mater 2003;48:85. [11] Gobran HA, Liua KW, Hegerb D, Mu¨cklich F. Scr Mater 2003;49:1097. [12] Smith NA, Sekido N, Perepezko JH, Ellis AB, Crone WC. Scr Mater 2004;51:423. [13] Van Vlack, Lawrence H. Elements of materials science and engineering. Addison-Wesley; 1989. p. 554. [14] Bepari MA, Whiteman JA. J Mater Proc Technol 1996;56:834.
Quantitative analyses of ferrite lattice parameter and solute Nb content in low carbon microalloyed steels Seok-Jae Lee, Young-Kook Lee
*
Department of Metallurgical Engineering, Yonsei University, Seoul 120-749, Korea Received 19 November 2004; received in revised form 10 January 2005; accepted 21 January 2005
Abstract The effect of solute Nb on the ferrite lattice parameter in low carbon steels was examined using X-ray diffraction and related to atomic size difference. The concentration of solute Nb in ferrite of a furnace-cooled steel was successfully predicted using the measured coefficient of Nb atoms on the ferrite lattice parameter. 2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Solute Nb; Ferrite lattice parameter; XRD; Microalloyed steel
1. Introduction The carbo-nitride-forming elements such as Nb, Ti and V have great influence on microstructure and mechanical properties of low carbon microalloyed steels. A small addition of Nb to low carbon steels is very effective in grain refinement and precipitation hardening as solute Nb atoms or NbC precipitates. The amounts of the solute Nb and NbC precipitates in microalloyed steels have been investigated by using different experimental methods such as inductively coupled plasma atomic emission spectrometry (ICP-AES), transmission electron microscopy (TEM), and stress relaxation [1–4]. Although the size and chemical composition of the precipitates can be evaluated from TEM-EDS work, it is still difficult to acquire the amount of the precipitates, especially in the case of very fine particles less than 100 nm in diameter using TEM, ICP-AES, and mechanical tests. The X-ray diffraction technique is expected to be useful to quantitatively determine the amount of the solute *
Corresponding author. Tel.: +82 2 2123 2831; fax: +82 2 312 5375. E-mail address: [email protected] (Y.-K. Lee).
Nb based on the relationship between the lattice parameters of austenite and ferrite and the concentration of an alloying element as follows [5–7]: ac ðnmÞ ¼ 0:35770 þ 0:00065 C þ 0:00010 Mn 0:00002 Ni þ 0:00006 Cr þ 0:00056 N þ 0:00028 Al 0:00004 Co þ 0:00014 Cu þ 0:00053 Mo þ 0:00079 Nb þ 0:00032 Ti þ 0:00017 V þ 0:00057 W ð1Þ aa ðnmÞ ¼ 0:28664 þ 0:00006 Mn 0:00003 Si 0:00007 Ni þ 0:00005 Cr 0:00010 P 0:00031 Ti þ 0:00027 Ru þ 0:00035 Rh þ 0:00029 Re þ 0:00037 Ir þ 0:00049 Pt
ð2Þ
where ac and aa are the lattice parameters of austenite and ferrite, respectively, and the concentration of each element is in atomic percent.
1359-6462/$ - see front matter 2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.scriptamat.2005.01.028
974
S.-J. Lee, Y.-K. Lee / Scripta Materialia 52 (2005) 973–976
Eq. (1) includes the effect of Nb on the lattice parameter of austenite and the coefficient of Nb is 0.00079 nm per atomic percent. However, there are few articles about the effect of Nb on the lattice parameter of ferrite. The purpose of this study is to quantitatively investigate the coefficient of Nb on the lattice parameter of ferrite to evaluate the amount of the solute Nb in low carbon microalloyed steels. 2. Experimental procedure The five ingots of Fe–X%C–0.2%Si–1.2%Mn–Y%Nb steels were prepared using a vacuum induction furnace. The chemical composition of homogenized ingots is listed in Table 1. The ingots were hot-rolled to 10 mm thick plates, from which the specimens of 15 · 15 · 2 mm3 were machined, solution-treated at 1170 C for 10 min in a vacuum furnace to fully dissolve Nb particles, which might form during hot rolling, and then furnace-cooled down to the room temperature. The samples were mechanically polished by using Emery papers of different grit sizes and the cloth pasted with alumina powders of about 1 lm. Finally, the samples were chemically polished using a chemical mixture of acetic acid 90% and perchloric acid 10%. To examine the lattice parameter of ferrite, X-ray diffraction (XRD) tests were performed at room temperature after the calibration of the standard Si powders using ‘‘Rigaku D/Max-RC’’ diffractometer with the Cu ˚ . The scantarget whose Ka wavelength k is 1.540562 A ning angle 2 was between 35 and 140 and the step size was 0.01. The lattice parameters were first calculated by applying the Nelson–Riley function [8] to each peak having different diffraction angles (2h), and then final lattice parameter of the ferrite was determined by fitting the different lattice parameters obtained at each peak by using the least square method, and was listed with an error range in Table 1. 3. Results and discussion 3.1. Effect of Nb on ferrite lattice parameter The effect of Nb on the lattice parameter of ferrite in the ultra-low carbon microalloyed steels (A1, A2, A3, A4
in Table 1) was examined by X-ray diffraction tests. Because the carbon content of the steels (0.003 wt.%) is too low to form NbC precipitates during furnace cooling, all Nb atoms can be assumed to remain as solutes in ferrite matrix. Strictly speaking, however, the distribution of the solute Nb atoms would be unlikely uniform in the ferrite matrix during furnace cooling, because the segregation of Nb atoms to the grain boundaries can occur at such a slow cooling rate [9]. Nevertheless, the lattice parameters of polycrystalline materials have been widely measured as a function of the average solute content by using X-ray diffraction [10–12]. The variation in lattice parameter of ferrite is plotted against Nb content in atomic percent in Fig. 1. The lattice parameter of ferrite is almost linearly proportional to the Nb concentration and the slope (kNb = 0.000625 (nm/at.%)) is the coefficient of Nb on the lattice parameter of ferrite. The intersection point between a fitted straight line and y-axis indicates the lattice parameter of ferrite without Nb atoms (0.286768 nm), which can also be calculated using Eq. (2) containing the coefficients of alloying elements such as C, Mn and Si on the lattice parameter of ferrite. The calculated lattice parameter of ferrite without Nb atoms (0.286707 nm) is in a good agreement with the experimental one of 0.286767 nm. The lattice parameter of ferrite of pure iron is taken as 0.28664 nm at 25 C (JCPDS, Card 6-0696). 3.2. Effect of the difference in atomic radius between Fe and an alloying element on lattice parameters Assuming that the variation in lattice parameters of austenite and ferrite with the addition of an alloying element is closely related to the difference in atomic radius [13] between Fe and the alloying element, the coefficients of alloying elements on the austenite lattice parameter in Eq. (1) are plotted against the difference in atomic radius between Fe and alloying elements in Fig. 2. The coefficient of the alloying element on the lattice parameter of austenite is increased with the increase in difference in atomic radius between Fe and the alloying element. Specially, the coefficient of Nb in Eq. (1) does not seem different from that of Nb calculated using a fitted curve in Fig. 2.
Table 1 Chemical composition and ferrite lattice parameters of the experimental steels (wt.%) Steel
C
Si
Mn
Nb
N
aa (nm)
A1 A2 A3 A4 A5
0.003 0.003 0.003 0.003 0.040
0.20 0.20 0.20 0.20 0.20
1.21 1.21 1.21 1.20 1.22
– 0.020 0.050 0.080 0.082
0.0035 0.0037 0.0041 0.0036 0.0045
0.286767 ± 0.0000073 0.286778 ± 0.0000048 0.286786 ± 0.0000039 0.286797 ± 0.0000041 0.286788 ± 0.0000021
S.-J. Lee, Y.-K. Lee / Scripta Materialia 52 (2005) 973–976
Fig. 1. Variation in the lattice parameter of ferrite with Nb concentration at 25 C in ultra-low carbon microalloyed steels (A1, A2, A3, and A4).
Fig. 2. Relationship between the coefficient of an alloying element on austenite lattice parameter and the difference in atomic radius between Fe and the alloying element [9].
In the same way, the coefficient of Nb on the lattice parameter of ferrite is estimated by fitting the coefficients of alloying elements against the difference in atomic radius between Fe and the alloying elements in ferrite [5]. The estimated coefficient of Nb (0.00064 nm per atomic percent) is almost the same to that of Nb (0.000625 nm per atomic percent) measured by X-ray diffraction tests, as shown in Fig. 3. 3.3. Quantitative analysis of solute Nb content using the ferrite lattice parameter The quantitative analysis of solute Nb in ferrite of the steel A5, which was never used for the coefficient of Nb on the lattice parameter of ferrite, was investigated by measuring the lattice parameter of ferrite of the steel from X-ray diffraction tests. The steel A5 was solution treated at 1170 C for 10 min. and furnace-cooled so that NbC particles and cementite probably form and the carbon concentration in ferrite is almost identical to its solubility limit in ferrite at room temperature
975
Fig. 3. Relationship between the coefficient of an alloying element on ferrite lattice parameter and the difference in atomic radius between Fe and the alloying element [9].
Fig. 4. Quantitative analysis of the amount of solute Nb in ferrite using the relationship between ferrite lattice parameter and solute Nb concentration.
[14]. The measured lattice parameter of ferrite is proportional to the average solute Nb content in ferrite, although the solute Nb content is not homogeneous locally because of the depletion of Nb atoms around the NbC particles. The measured ferrite lattice parameter is plotted as a square mark together with those of the ultra-low carbon microalloyed steels in Fig. 4. The ferrite lattice parameter of the steel A5, whose initial Nb content is 0.048 at.%, corresponds to that of the specimen containing the solute Nb content of 0.033 at.%, indicating that approximately 30% of Nb atoms probably joined precipitation during furnace-cooling.
4. Conclusions The coefficient of the solute Nb on ferrite lattice parameter is 0.000625 nm per atomic percent. The variation in lattice parameters of austenite and ferrite with the addition of an alloying element is strongly dependent upon the difference in atomic radius between Fe
976
S.-J. Lee, Y.-K. Lee / Scripta Materialia 52 (2005) 973–976
and the alloying element. The solute Nb concentration in ferrite of a furnace-cooled low carbon microalloyed steel can be determined using the ferrite lattice parameter of the specimen measured from X-ray diffraction tests and the coefficient of solute Nb on ferrite lattice parameter. Acknowledgments This research was performed as a part of the POSCO project titled ‘‘Development of Simulator for Predicting Phase Transformations and Mechanical Properties of Microalloyed and Low Alloy Steels’’. References [1] Samuel FH, Ouellet P, Samuel AM, Doty HW. Metall Mater Trans A 1998;29A:2871.
[2] Mishra(Pathak) SK, Das S, Ranganathan S. Mater Sci Eng A 2002;323A:285. [3] Soto R, Saikaly W, Bano X, Issartel C, Rigaut G, Charai A. Acta Mater 1999;47:3475. [4] Garcı´a-Mateo C, Lo´pez B, Rodriguez-Ibabe JM. Mater Sci Eng A 2001;303A:216. [5] Leslie WC. The physical metallurgy of steels. New York: McGraw-Hill; 1982. p. 111. [6] Pearson WB. A hand book of lattice spacings and structure of metals and alloys, vol. 2. London: Pergamon Press; 1967. p. 908. [7] Dyson DJ, Holmes B. JISI 1970;208:469. [8] Cullity BD. Elements of X-ray diffraction 2nd ed. Reading: Addison-Wesley; 1967. p. 350. [9] Lee YK, Hong JM, Choi CS, Lee JK. Mat Sci Forum 2005;475– 479:65. [10] Hos James P, McCormick Paul G. Scr Mater 2003;48:85. [11] Gobran HA, Liua KW, Hegerb D, Mu¨cklich F. Scr Mater 2003;49:1097. [12] Smith NA, Sekido N, Perepezko JH, Ellis AB, Crone WC. Scr Mater 2004;51:423. [13] Van Vlack, Lawrence H. Elements of materials science and engineering. Addison-Wesley; 1989. p. 554. [14] Bepari MA, Whiteman JA. J Mater Proc Technol 1996;56:834.