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Thermodynamic calculation of the stacking fault energy in Fe-Cr-Mn-C-N steels
Accepted Manuscript Thermodynamic calculation of the stacking fault energy in Fe-Cr-Mn-C-N steels Seung-Joon Lee, Hidetoshi Fujii, Kohsaku Ushioda PII:
S0925-8388(18)31173-3
DOI:
10.1016/j.jallcom.2018.03.296
Reference:
JALCOM 45526
To appear in:
Journal of Alloys and Compounds
Received Date: 26 December 2017 Revised Date:
4 March 2018
Accepted Date: 23 March 2018
Please cite this article as: S.-J. Lee, H. Fujii, K. Ushioda, Thermodynamic calculation of the stacking fault energy in Fe-Cr-Mn-C-N steels, Journal of Alloys and Compounds (2018), doi: 10.1016/ j.jallcom.2018.03.296. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Thermodynamic calculation of the stacking fault energy in
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Fe-Cr-Mn-C-N steels
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Seung-Joon Lee*, Hidetoshi Fujii and Kohsaku Ushioda
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Joining and Welding Research Institute, Osaka University 11-1, Mihogaoka, Ibaraki, Osaka 567-0047, Japan *
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Corresponding author: E-mail: [email protected], Tel./Fax: +81 6 6879 8643
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Abstract
To determine the thermodynamic parameters for the calculation of the accurate stacking
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fault energy (SFE) in Fe-Cr-Mn-C-N steels using the sublattice model, the comparison
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between the calculated and experimental SFE values was conducted. It was realized that the
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relationship between SFE and alloying elements in Fe-Cr-Mn-C-N steels was different from
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that of the conventional Fe-Cr-Ni stainless steels. The SFE increased with the increasing Cr
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concentration up to a critical value, then decreased again with further increased Cr
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concentration. The critical value decreased with the addition of Mn, C and N. In contrast to
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Cr, the addition of Mn continuously increased the SFE, regardless of the additions of C and N.
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Regarding the C and N, they also increased the SFE linearly and the impact of N on the SFE
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was only slightly effective relative to that of C. Accordingly, we realized that the
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thermodynamic calculation using the suggested combination of thermodynamic parameters
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should be considered for more accurate SFE calculation in Fe-Cr-Mn-C-N steels.
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Keywords: Stacking fault energy (SFE); Thermodynamic modeling; Fe-Cr-Mn-C-N steels;
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High-interstitial-alloyed steels
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1. Introduction
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Austenitic Fe-Cr-Mn-C-N steels exhibit the remarkable combination of tensile strength 1
ACCEPTED MANUSCRIPT and ductility of over 60,000 MPa% [1, 2] and corrosion resistance [3] due to the
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transformation- and twinning-induced plasticity (TRIP and TWIP) and the formation of a
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passive film, respectively. The dominant strengthening mechanism is the TRIP when the
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stacking fault energy (SFE) is below 20 mJ m-2, and with an increasing SFE up to ~40 mJ m-2,
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it exhibits the TWIP [4, 5]. Accordingly, the evaluation of an accurate SFE in the Fe-Cr-Mn-
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C-N steels has been actively conducted using the X-ray and neutron diffractometry (XRD and
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ND) [4, 6, 7], transmission electron microscopy (TEM) [8-11] and thermodynamic
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calculation [10, 12, 13].
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Each method has its own disadvantages [4, 14, 15] as follows: (1) For the XRD, the
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limitation of an observation area in the surface of the specimen and the error by the peak
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doublet of Kα1 and Kα2, (2) For the ND, the difficulty to utilize to the equipment and the
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long processing time, (3) For the TEM, the scattering of data caused by the segregation of the
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alloying atoms (C and N) in the stacking fault and the difficulty in measuring the high SFE
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due to the size reduction of the dislocation configurations such as extended node and stacking
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fault tetrahedral, (4) For the thermodynamic calculation, the discrepancy due to different
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thermodynamic databases for the same elements with respect to the authors. It is necessary to
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determine a more reliable SFE based on the comparison between the calculated and measured
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SFE values using the abovementioned techniques. However, the systematic thermodynamic
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calculation of the SFE has not yet been established in the Fe-Cr-Mn-C-N system with respect
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to the alloying elements with a wide range probably due to the presence of various interaction
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parameters on the same elements such as LFe,Mn:Va, LFe:C,Va, LFe:N,Va and LFe:C,N. It leads to a
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difficulty in designing the new Fe-Cr-Mn-C-N steels, considering the strengthening
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mechanisms (TRIP, TWIP) based on the accurate SFE. Although the empirical equations of
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the SFE in conventional Fe-Cr-Ni based stainless steels have been reported [16-18], it is
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difficult to calculate the SFE for Fe-Cr-Mn-C-N steels because of the following reasons; (1)
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ACCEPTED MANUSCRIPT there are difference of the SFE in two systems due to the effect of specific alloying elements
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(Ni, Mo, Si) on the SFE, (2) the range of the alloying elements for the SFE calculation is
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significantly limited, and (3) the dependence of the SFE on the additions of C and/or N over
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~0.3 wt.% for various Fe-Cr-Mn-C-N steels has not been considered.
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Therefore, in the present study, we carried out the thermodynamic calculation of the SFE
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in Fe-Cr-Mn-C-N steels using the sublattice model. This model assumed that each element
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and vacancy separately occupy the substitutional and interstitial sites with random mixing in
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each sublattice to reflect the real crystalline structure, relative to the widely used subregular
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model [12, 14]. It was suggested to use the combination of the thermodynamic databases for
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comparison between the calculated and reported experimental SFEs was preferable for more
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reliable SFE values. Finally, the effect of the alloying elements on the SFE was
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systematically investigated using the thermodynamic calculation, discussed and verified in
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comparison of the results of previous research.
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2. Thermodynamic calculation of stacking fault energy For this purpose, the SFE was calculated based on the classical nucleation theory, because
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the stacking fault is a volumetric embryo of the hcp ε phase in the fcc γ matrix [12, 14]. The
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SFEs were thermodynamically calculated using the sublattice model as follows:
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γ →ε SFE = 2ρ ( ∆Gchγ →ε + ∆Gmg ) + 2σ
(1)
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where ρ is the molar surface density along the atomic plane of (111) in mol m-2 which was
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determined from the equation 4 / ( 3 aγ2 N A ) [12, 14], where NA is Avogardo’s number of
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6.022 ×1023 mol-1 and aγ is the γ lattice parameter given as aγ = 3.5780 + 0.0006 (wt.%Cr) +
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0.00095 (wt.%Mn) + 0.033 (wt.%C) + 0.029 (wt.%N) in Å [19]. Both ∆Gch and ∆Gmg are the
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differences in the chemical and magnetic Gibbs free energies between the γ and ε phases in J 3
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[14]. σ is the γ/ε interfacial energy as the constant value of 10 mJ m-2 [20, 21], which is used
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for the SFE calculation of the high Mn steels [20, 21] as well as the Fe-Cr-Ni stainless steels
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[22].
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Regarding the ∆Gch using the sublattice model, the γ and ε phases were treated as a
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randomly mixed substitutional solution with two substitutional and interstitial sublattices
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such as (Fe, Cr, Mn)1(C, N, Va)λ, where λ is equal to 1 for the γ, 0.5 for the ε phases [12] and
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the Va indicates a vacancy. The SFE calculation using the sublattice model was discussed in
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ϕ detail by Mosecker et al [12]. The Gch (for φ = γ and ε phases) was adopted by the
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sublattice model, as follows:
ϕ o ϕ o ϕ o ϕ o ϕ o ϕ Gchϕ = yFe yC oGFe :C + yCr yC GCr :C + yMn yC GMn:C + yFe y N GFe: N + yCr y N GCr : N + yMn y N GMn: N ϕ o ϕ o ϕ + yFe yVa oGFe :Va + yCr yVa GCr :Va + yMn yVa GMn:Va + aRT ( yFe ln y Fe + yCr ln yCr + yMn ln yMn )
+ bRT ( yC ln yC + yN ln y N + yVa ln yVa ) + Gexϕ where
Gexϕ = yFe yCr ( yC LϕFe,Cr:C + yN LϕFe,Cr:N + yVa LϕFe,Cr:Va ) + yFe yMn ( yC LϕFe , Mn:C + y N LϕFe , Mn:N + yVa LϕFe , Mn:Va )
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(2)
+ yCr yMn ( yC LϕCr , Mn:C + y N LϕCr , Mn:N + yVa LϕCr , Mn:Va ) + yC yN ( yFe LϕFe:C , N + yCr LϕCr:C , N + yMn LϕMn:C , N ) + yC yVa ( yFe LϕFe:C ,Va + yCr LϕCr:C ,Va + yMn LϕMn:C ,Va ) + yN yVa ( yFe LϕFe:N ,Va + yCr LϕCr:N ,Va + yMn LϕMn:N ,Va )
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+ yFe yCr yMn ( yC LϕFe,Cr , Mn:C + yN LϕFe,Cr , Mn:N + yVa LϕFe ,Cr , Mn:Va )
Giϕ denotes the Gibb free energy of each element i in the γ and ε phases and both a and b
o
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are the site numbers in each sublattice of a = b = 1 for the γ phase and a = 1, b = 0.5 for the ε
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phase. R is the gas constant and T is the temperature in K. The site fractions (yi) of each
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element in the substitutional sublattice are calculated as:
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yi =
xi (1 − xC − xN )
(3)
The site fraction for C and N in the interstitial sublattice is as follows:
yC or N =
xC or N
λ (1 − xC − xN ) 4
(4)
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where x is the mole fraction of each element. The relationship between the site fractions of
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both the substitutional and interstitial sublattices is as follows:
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y Fe + yCr + yMn = yC + y N + yVa = 1
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ϕ In the excess free energy term ( Gexϕ ) in Eq. (2), Li, j:C , N ,Va is the interaction parameter for the
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elements (i and j) in each phase. For the SFE calculation, the recently re-evaluated
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thermodynamic parameters in Fe-Mn-Al-C [14], Fe-Cr-Mn-N [12], Fe-Cr-Mn-C [22] and Fe-
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Cr-C [23] systems were adopted and listed in the Supplementary Information.
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(5)
However, among the thermodynamic parameters, it is essential to verify several parameters
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on a basis of the comparison between the calculated and measured SFEs in the Fe-Cr-Mn-C-
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N system for an accurate SFE. This is because several interaction parameters (LFe,Mn:Va for the
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Fe-Mn system [24, 25] and LFe:C,N, LFe:C,Va, LFe:N,Va for the Fe-N-C system [26, 27]) are
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controversial depending on the authors (Table 1). Namely, for the Fe-Mn system, LFe,Mn:Va
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was recently suggested by Nakano and Jacques [24] and Djurovic et al. [25], and for the Fe-
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C-N system, LFe:C,N, LFe:C,Va and LFe:N,Va are newly proposed by Gӧhring et al. [27], instead of
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the frequently used set of thermodynamic parameters collected by Du and Hillert [26] from
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the literature [28, 29]. Hence, according to the interaction parameters without any change in
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the other parameters, the combinations of thermodynamic databases for the SFE calculations
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can be divided into 3 types and labelled as type I (Nakano-Du), type II (Djurovic-Du) and
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type III (Djurovic-Gӧhring).
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For verification of the calculated SFE, 23 experimentally measured SFEs of austenitic Fe-
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Cr-Mn-C-N steels were collected from the literature [4, 6-11] and listed in Table 2, along
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with the measurement method. The 23 different steels were categorized into three different
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groups based on their C and N concentrations. They are the high C (= 0.6 wt.%)-low N (< 0.1
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wt.%), low C (< 0.1 wt.%)-high N (0.2-0.8 wt.%) and high C (0.2-0.6 wt.%)-high N (0.1-0.4 5
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wt.%) austenitic steels, which are indicated by the black square, red diamond and blue
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triangle in Fig. 1, respectively.
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3. Results and discussion
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3.1. Comparison of the calculated and measured stacking fault energies
Figure 1a through c shows the relationship between the measured and calculated SFEs
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using types I through III, respectively, together with three different indexes of accuracy.
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Parameter E is the average distance between the line in the figure and markers, parameter D
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is the average absolute distance between the line, and the parameter S is the standard error in the figure and markers as follows:
Ei =
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(SFECal . − SFEMea. ) 2
(6)
N
E=
i
i =1
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∑E N
Di = Ei
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(7) (8)
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D=
∑D
i
i =1
N
S=
∑ (SFE i =1
(9)
N
cal .
− SFEmea. ) 2 (10)
N
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where both the SFECal. and SFEMea. are the calculated and measured SFEs, respectively. N is
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the number of steels used. The lower D value indicates a better agreement between SFECal.
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and SFEMea.. The positive E value means a higher SFECal. than SFEMea. on average, or vice
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versa.
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As shown in Fig. 1a, the type I did not work well for both the low C-high N (red circle) 6
ACCEPTED MANUSCRIPT and high C-high N (blue triangle) steels. Overall, the SFECal. using type I was much lower
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than the SFEMea. for most of the steels, except for two steels with the SFECal. over 50 mJ m-2
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(as indicated by the arrows), leading to the highest E, D and S values of -5.9, 8.6 and 13.6,
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respectively. Fig. 2b reveals the relationship between the SFEMea. and the SFECal. using the
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type II. Although the D and S value was improved, relative to that using the type I, the E
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value was similar, implying that the SFECal. using the type II was still underestimated for both
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the low C-high N and high C-high N steels. This is probably because the interaction
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parameters (as collected by Du and Hillert [26]) in both the types I and II did not quite reflect
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the effects of C and N on the SFECal. in the Fe-Cr-Mn-C-N system.
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Accordingly, we calculated the SFECal. using the recently re-evaluated LFe:C,N, LFe:C,Va and
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LFe:N,Va without any change in the other thermodynamic parameters (as indicated by type III)
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and which are plotted in Fig. 1c. Regardless of the C and N concentrations, the SFECal. is in a
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better agreement with the SFEMea., relative to those by both the type I and II, showing the
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lowest E (1.6), D (4.1) and S (6.8) values. The indexes of accuracy seem reasonable,
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considering the possibility of change in the σ value by the addition of alloying elements [15]
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and the experimental error of the SFEMea.. Therefore, the type III is thought to produce more
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accurate thermodynamic calculations of the SFE in the austenitic Fe-Cr-Mn-C-N steels.
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3.2. Effect of alloying elements on the stacking fault energy
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To investigate the dependence of the SFE on the alloying elements in the Fe-Cr-Mn-C-N
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steels, the SFEs were calculated within a wide range of chemical compositions using the type
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III combinations of thermodynamic databases for SFE calculation. Figure 2 shows the change
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in the SFE at 300 K of the Fe-xCr-(10-25)Mn-(0, 0.3)C-(0, 0.3)N steels as a function of the
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Cr concentration. According to the Mn concentration, there are two types of polynomial and
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linear trends of the SFE by the addition of Cr. For the Fe-xCr-10Mn steels (Fig. 2a), the SFE 7
ACCEPTED MANUSCRIPT almost linearly declined with the increasing Cr concentration from zero to 30 wt.%. For the
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Fe-xCr-(15-25)Mn steels (Fig. 2a), the SFE increased as raising the Cr concentration up to a
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critical value, then slightly decreased again with the addition of more Cr. The critical value of
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the Cr concentration increased from ~14 to ~20 wt.% with the increasing Mn concentration
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from 15 to 25 wt.%. As shown in Fig. 2b, the addition of 0.3wt.%C to the Fe-xCr-(10-25)Mn
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steels increased the SFE, showing a similar polynomial trend of the SFE in the Fe-xCr-(15-
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25)Mn steels. The addition of 0.3 wt.%N to the Fe-xCr-(10-25)Mn steels increased the SFE
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and the Fe-xCr-15Mn-0.3N steels changed to have an almost linear decreasing behavior from
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the polynomial trend. The simultaneous additions of 0.3 wt.%C and 0.3 wt.%N to the Fe-xCr-
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(10-25)Mn steels (Fig. 2d) increased the SFE, showing the similar change in the SFE in the
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Fe-xCr-(10-25)Mn-0.3N steels. The distance between the lines decreased with the additions
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of C and/or N, implying that Mn has a more powerful effect on SFE when C or N was added
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to a smaller extent.
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Regarding the Mn, the Fe-(10-25)Cr-xMn systems have an approximately linear
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increasing trend with the addition of Mn from 10 to 30 wt.% (Fig. 3). The gap between the
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lines by the addition of Cr ranging from 10 to 25 wt.% was not as high as that by the addition
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of Mn in the Fe-xCr-(10-25)Mn-(0, 0.3)C-(0, 0.3)N systems, indicating that the addition of
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Cr has a minor effect on the SFE relative to Mn.
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In order to investigate the effects of C and N on the SFE, the SFEs of the Fe-18Cr-10Mn-
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(0-0.4)C-(0-0.4)N steels were plotted versus the C and N concentrations in Fig. 4a and b,
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respectively. The reason why the Fe-18Cr-10Mn based steels were selected is because the
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SFECal. of the Fe-10Cr-18Mn-xC-yN and Fe-15Cr-15Mn-xC-yN systems (not shown here)
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have a trend similar to the SFECal. of the Fe-18Cr-10Mn-xC-yN system, regardless of the
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addition of Cr and Mn. Both C and N almost linearly increased the SFE. The effect of N on
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the SFE was more effective than that of C, indicating both the increase in the distance 8
ACCEPTED MANUSCRIPT between the lines in Fig. 4a and the higher slope in Fig. 4b. In addition, the synergetic effect
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of C and N on the SFE was not seen yet and, for example, the SFE (22 mJ m-2) of the Fe-
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18Cr-10Mn-0.6N steel was higher than that (15.9 mJ m-2) of the Fe-18Cr-10Mn-0.3C-0.3N
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steel. According to Lee et al.’s study [7], the measured SFE (19.3 mJ m-2) using the ND in
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the Fe-18.3Cr-9.7Mn-0.3Si-0.61N (wt.%) steel was lower than the SFE (22.5 mJ m-2) of the
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Fe-18.1Cr-9.6Mn-0.1Si-0.30C-0.32N (wt.%) steel due to slightly effective impact of C on the
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SFE relative to N. This difference between the present and previous studies is probably due to
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the difficulty to sufficiently reflect the interaction between the substitutional and interstitial
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elements caused by the lack of the interaction parameters, such as LMn:C,N, LCr:C,N and
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LFe,Mn,Cr:C.
Looking into the relationship between the alloying elements and SFE in the Fe-Cr-Ni
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based stainless steels for the comparison with that of the Fe-Cr-Mn-C-N steels, Meric de
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Bellefon et al. [18] have recently reported the SFE equation in austenitic stainless steels.
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Their new expression to predict the SFE from the chemical composition was obtained using
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the linear regression with random intercepts of 144 measured SFEs from previous reports,
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given as SFE (mJ m-2) = 2.2+1.9Ni-2.9Si+0.77Mo+0.5Mn+40C-0.016Cr-3.6N (wt.%). It is
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difficult to predict the SFE using this equation for the Fe-Cr-Mn-C-N steels due to the
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discrepancy in the effect of alloying elements, such as Cr, Mn and N, on the SFE. This is due
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to both the dependence of the SFE on other alloying elements (Ni, Mo and Si) and the
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difference in the concentrations of Mn, C and N of the reported Fe-Cr-Ni steels for the
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prediction equation. Therefore, the suggested combination (type III) of the thermodynamic
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parameters is suitable to calculate more reliable SFE for the Fe-Cr-Mn-C-N steels.
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4. Conclusion In the present study, we investigated the thermodynamic calculations of the accurate 9
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stacking fault energy (SFE) in Fe-Cr-Mn-C-N steels using the sublattice model based on the
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comparison between the calculated and experimentally measured SFEs. (1) The calculated SFE more closely agreed with the measured SFE when using the
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combination of thermodynamic databases based on the interaction parameters
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(LFe,Mn:Va, LFe:C,N, LFe:C,Va and LFe:N,Va) suggested by Djurovic et al. [25] and Gӧhring
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et al. [27].
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(2) The change in the SFE of the Fe-Cr-Mn-C-N steels was different from that of the Fe-
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Cr-Ni austenitic steels. The influence of Cr on the SFE was complex; the trend in the
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SFE by the addition of Cr showed two types of behavior such as polynomial and
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linear, depending on the amount of Mn, C and N. In contrast to Cr, the addition of
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Mn, C and N increased the SFE continuously.
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Figure caption
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Fig. 1. Relationship between the thermodynamically-calculated stacking fault energy (SFE)
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using the combination of (a) type I, (b) type II and (c) type III, and the experimentally
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measured SFE in the Fe-Cr-Mn-C-N steels. The black arrow in Fig. 1(a) denotes the
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overestimated data by the SFE calculation. The legends, such as 0.6C-(0-0.1)N, 0C-(0.2-
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0.8)N and (0.2-0.6)C-(0.1-0.4)N, in Fig. 1 indicate the Fe-Cr-Mn steels containing high C-
19
low N, low C-high N and high C-high N, respectively, and the details of the chemical
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composition are listed in Table 2. All the parameters (E, D and S) are the indexes of accuracy
21
in Eqs. (6-10).
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Fig. 2. Variations in the calculated stacking fault energy (SFE) using the type III in (a) Fe-
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xCr-(10-25)Mn, (b) Fe-xCr-(10-25)Mn-0.3C, (c) Fe-xCr-(10-25)Mn-0.3N and (d) Fe-xCr-
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(10-25)Mn-0.3C-0.3N (wt.%) steels with the increasing Cr concentration from 0 to 30 wt.%. 10
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Fig. 3. Variations in the calculated stacking fault energy (SFE) using the type III in (a) Fe-
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(10-25)Cr-xMn, (b) Fe-(10-25)Cr-xMn-0.3C, (c)Fe-(10-25)Cr-xMn-0.3N and (d) Fe-(10-
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25)Cr-xMn-0.3C-0.3N (wt.%) steels with the increasing Mn concentration from 10 to 30
5
wt.%.
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Fig. 4. Variations in the calculated stacking fault energy (SFE) using the type III in (a) Fe-
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18Cr-10Mn-xC-(0-0.4)N and (b) Fe-18Cr-10Mn-(0-0.4)C-xN (wt.%) steels with the
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increasing C or N concentrations from zero to 0.6 wt.%.
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Acknowledgements
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This study was partly supported by the New Energy and Industrial Technology Development
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Organization (NEDO) under the “Innovation Structural Materials Project (Future Pioneering
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Projects)” and a Grant-in-Aid for Science Research from the Japan Society for the Promotion
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of Science. LSJ acknowledges support from the “Basic Science Research Program through
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the National Research Foundation of Korea (NRF) funded by the Ministry of Education
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(2017R1A6A3A03002080)”.
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[7] T.-H. Lee, H.-Y. Ha, B. Hwang, S.-J. Kim, E. Shin, Effect of carbon fraction on stacking
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fault energy of austenitic stainless steels, Metall. Mater. Trans. A, 43A (2012) 4455-4459.
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[8] V. Gavriljuk, Y. Petrov, B. Shanina, Effect of nitrogen on the electron structure and
13
stacking fault energy in austenitic steels, Scripta Mater. 55 (2006) 537-540.
14
[9] L. Bracke, J. Penning, N. Akdut, The influence of Cr and N additions on the mechanical
15
properties of FeMnC steels, Metall. Mater. Trans. A. 38 (2007) 520-528.
16
[10] L. Mujica, S. Weber, W. Theisen, The stacking fault energy and its dependence on the
17
interstitial content in various austenitic steels, Mater. Sci. For. 706-709 (2012) 2193-2198.
18
[11] L. Mosecker, D.T. Pierce, A. Schwedt, M. Beighmohamadi, J. Mayer, W. Bleck, J.E.
19
Wittig, Temperature effect on deformation mechanisms and mechanical properties of a high
20
manganese C+N alloyed austenitic stainless steel, Mater. Sci. Eng. A, 642 (2015) 71-83.
21
[12] L. Mosecker, A. Saeed-Akbari, Nitrogen in chromium-manganese stainless steels: A
22
review on the evaluation of stacking fault energy by computational thermodynamics, Sci.
23
Technol. Adv. Mater. 14 (2013) 033001.
24
[13] S. Curtze, V.T. Kuokkala, A. Oikari, J. Talonen, H. Hänninen, Thermodynamic modeling
25
of the stacking fault energy of austenitic steels, Acta Mater. 59 (2011) 1068-1076.
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ACCEPTED MANUSCRIPT [14] D.T. Pierce, J.A. Jiménez, J. Bentley, D. Raabe, C. Oskay, J.E. Wittig, The influence of
2
manganese content on the stacking fault and austenite/ε-martensite interfacial energies in Fe-
3
Mn-(Al-Si) steels investigated by experiment and theory, Acta Mater. 68 (2014) 238-253.
4
[15] D.T. Pierce, J.A. Jiménez, J. Bentley, D. Raabe, J.E. Wittig, The influence of stacking
5
fault energy on the microstructural and strain-hardening evolution of Fe-Mn-Al-Si steels
6
during tensile deformation, Acta Mater. 100 (2015) 178-190.
7
[16] R.E. Schramm, R.P. Reed, Stacking fault energies of seven commercial austenitic
8
stainless steels, Metall. Trans. A, 6 (1975) 1345-1351.
9
[17] T. Yonezawa, K. Suzuki, S. Ooki, A. Hashimoto, The effect of chemical composition and
10
heat treatment conditions on stacking fault energy for Fe-Cr-Ni austenitic stainless steel,
11
Metall. Mater. Trans. A, 44 (2013) 5884-5896.
12
[18] G. Meric de Bellefon, J.C. van Duysen, K. Sridharan, Composition-dependence of
13
stacking fault energy in austenitic stainless steels through linear regression with random
14
intercepts, J. Nucl. Mater. 492 (2017) 227-230.
15
[19] N.C.S. Srinivas, V.V. Kutumbarao, On the discontinuous precipitation of Cr2N in Cr-Mn-
16
N austenitic stainless steels, Scripta Mater. 37 (1997) 285-291.
17
[20] S.-J. Lee, J. Han, S. Lee, S.H. Kang, S.M. Lee, Y.-K. Lee, Design for Fe-high Mn alloy
18
with an improved combination of strength and ductility, Sci. Rep. 7 (2017) 3573.
19
[21] S.-J. Lee, J. Han, C.-Y. Lee, I.-J. Park, Y.-K. Lee, Elastic strain energy induced by
20
epsilon martensitic transformation and its contribution to the stacking-fault energy of
21
austenite in Fe-15Mn-xC alloys, J. Alloys Compd. 617 (2014) 588-596.
22
[22] B.-J. Lee, On the stability of Cr carbides, CALPHAD 16 (1992) 121-149.
23
[23] A.V. Khvan, B. Hallstedt, C. Broeckmann, A thermodynamic evaluation of the Fe-Cr-C
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system, CALPHAD 46 (2014) 24-33.
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[24] J. Nakano, P.J. Jacques, Effects of the thermodynamic parameters of the hcp phase on
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ACCEPTED MANUSCRIPT the stacking fault energy calculations in the Fe-Mn and Fe-Mn-C systems, CALPHAD 34
2
(2010) 167-175.
3
[25] D. Djurovic, B. Hallstedt, J. Von Appen, R. Dronskowski, Thermodynamic assessment
4
of the Fe-Mn-C system, CALPHAD 35 (2011) 479-491.
5
[26] H. Du, M. Hillert, Assessment of the Fe-C-N system, Z. Metallkde. 82 (1991) 310-316.
6
[27] H. Göhring, O. Fabrichnaya, A. Leineweber, E.J. Mittemeijer, Thermodynamics of the
7
Fe-N and Fe-N-C systems: The Fe-N and Fe-N-C phase diagrams revisited, Metall. Mater.
8
Trans. A, 47 (2016) 6173-6186.
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[28] P. Gustafson, Thermodynamic evaluation of the Fe-C system, Scand. J. Metall. 14 (1985)
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259-267.
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[29] K. Frisk, A thermodynamic evaluation of the Cr-N, Fe-N, Mo-N and Cr-Mo-N systems,
12
CALPHAD 15 (1991) 79-106.
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Table 1 Various interaction parameters according to the authors. All values are given in SI unit, J, mol and K. hcp ε
-7762+3.865T-259(yFe-yMn) LFe,Mn:Va
-26150
LFe:C,N
-53059-38756(yC-yVa)
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Djurovic
et al. [25]
Du & Hillert [26] Göhring et al. [27]
10345-19.71T-
Du & Hillert
(11130-11.84T)(yN-yVa)
[26]
8186-18.127T-
Göhring
(24378-24.959T)(yN-yVa)
et al. [27]
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-14545
Jacques [24]
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LFe:N,Va
(14271.46-13.884T)(yFe-yMn)
-17335
LFe:C,Va
-26150
Nakano &
-5748+3.865T-273(yFe-yMn)
-34671 -34671
69.41+2.836T-
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-7762+3.865T-259(yFe-yMn)
Ref.
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fcc γ
Parameter
-20772-32.504T-28839(yC-yN)
Du & Hillert [26] Göhring et al.
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Table 2 Stacking fault energy (SFE) of Fe-Cr-Mn-C-N steels reported in the literature. Chemical composition (wt.%)
SFE
Mn
C
N
(mJ m-2)
2.0
14.8
0.60
0.02
14.6
High C-Low N
2.0
14.5
0.59
0.03
15.5
:0.6C-(0-0.1)N
1.8
15.0
0.59
0.07
17.1
1.8
15.0
0.62
0.09
19.6
15.1
17.2
-
0.23
26.4
15.1
17.2
-
0.48
21.3
15.1
17.2
-
0.8
17.8
9.7
0.03
0.39
18.1
9.7
0.03
0.44
12.2
17.7
9.6
0.03
0.51
17.1
17.5
9.8
0.03
0.69
22.8
18.3
9.7
0.02
0.61
19.3
:(0-0.1)C(0.2-0.8)N
5.6 9.7
:(0.2-0.6)C-
12.0
0.21
neutron
diffraction
Lee et al. [6]
Gavrlijuk
TEM
et al. [8]
33.1
Neutron
Lee et al.
diffraction
[4,7]
X-ray & neutron diffraction
0.25
0.11
5.0
19
0.24
0.20
20.0
20.0
0.24
0.32
36.0
25.0
0.3
0.40
31.0
TEM
TEM
Lee et al. [6] Bracke et al. [9] Mujica et al. [10]
12.0
30.0
0.3
0.40
43.3
14.6
16.0
0.31
0.29
21.0
18.0
10.2
0.15
0.42
20.1
18.1
9.7
0.38
0.38
27.6
Neutron
Lee et al.
18.1
9.5
0.24
0.35
20.8
diffraction
[4,7]
18.1
9.6
0.3
0.32
22.5
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(0.1-0.4)N
12.0
0.56
Ref.
10.4
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High C-high N
14.9
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2.5
X-ray &
41.0
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Method
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Cr
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2
TEM
Mosecker et al. [11]
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ACCEPTED MANUSCRIPT Highlights • Stacking fault energy in Fe-Cr-Mn-C-N steels was thermodynamically calculated. • For accurate stacking fault energy, measured and predicted energies were compared.
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• Mn, C and N continuously increase stacking fault energy.
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• Cr increases stacking fault energy, then decreases it again over a critical value.
S0925-8388(18)31173-3
DOI:
10.1016/j.jallcom.2018.03.296
Reference:
JALCOM 45526
To appear in:
Journal of Alloys and Compounds
Received Date: 26 December 2017 Revised Date:
4 March 2018
Accepted Date: 23 March 2018
Please cite this article as: S.-J. Lee, H. Fujii, K. Ushioda, Thermodynamic calculation of the stacking fault energy in Fe-Cr-Mn-C-N steels, Journal of Alloys and Compounds (2018), doi: 10.1016/ j.jallcom.2018.03.296. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Thermodynamic calculation of the stacking fault energy in
2
Fe-Cr-Mn-C-N steels
3
Seung-Joon Lee*, Hidetoshi Fujii and Kohsaku Ushioda
4
Joining and Welding Research Institute, Osaka University 11-1, Mihogaoka, Ibaraki, Osaka 567-0047, Japan *
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Corresponding author: E-mail: [email protected], Tel./Fax: +81 6 6879 8643
6 7
Abstract
To determine the thermodynamic parameters for the calculation of the accurate stacking
9
fault energy (SFE) in Fe-Cr-Mn-C-N steels using the sublattice model, the comparison
10
between the calculated and experimental SFE values was conducted. It was realized that the
11
relationship between SFE and alloying elements in Fe-Cr-Mn-C-N steels was different from
12
that of the conventional Fe-Cr-Ni stainless steels. The SFE increased with the increasing Cr
13
concentration up to a critical value, then decreased again with further increased Cr
14
concentration. The critical value decreased with the addition of Mn, C and N. In contrast to
15
Cr, the addition of Mn continuously increased the SFE, regardless of the additions of C and N.
16
Regarding the C and N, they also increased the SFE linearly and the impact of N on the SFE
17
was only slightly effective relative to that of C. Accordingly, we realized that the
18
thermodynamic calculation using the suggested combination of thermodynamic parameters
19
should be considered for more accurate SFE calculation in Fe-Cr-Mn-C-N steels.
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Keywords: Stacking fault energy (SFE); Thermodynamic modeling; Fe-Cr-Mn-C-N steels;
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High-interstitial-alloyed steels
23 24
1. Introduction
25
Austenitic Fe-Cr-Mn-C-N steels exhibit the remarkable combination of tensile strength 1
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2
transformation- and twinning-induced plasticity (TRIP and TWIP) and the formation of a
3
passive film, respectively. The dominant strengthening mechanism is the TRIP when the
4
stacking fault energy (SFE) is below 20 mJ m-2, and with an increasing SFE up to ~40 mJ m-2,
5
it exhibits the TWIP [4, 5]. Accordingly, the evaluation of an accurate SFE in the Fe-Cr-Mn-
6
C-N steels has been actively conducted using the X-ray and neutron diffractometry (XRD and
7
ND) [4, 6, 7], transmission electron microscopy (TEM) [8-11] and thermodynamic
8
calculation [10, 12, 13].
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Each method has its own disadvantages [4, 14, 15] as follows: (1) For the XRD, the
10
limitation of an observation area in the surface of the specimen and the error by the peak
11
doublet of Kα1 and Kα2, (2) For the ND, the difficulty to utilize to the equipment and the
12
long processing time, (3) For the TEM, the scattering of data caused by the segregation of the
13
alloying atoms (C and N) in the stacking fault and the difficulty in measuring the high SFE
14
due to the size reduction of the dislocation configurations such as extended node and stacking
15
fault tetrahedral, (4) For the thermodynamic calculation, the discrepancy due to different
16
thermodynamic databases for the same elements with respect to the authors. It is necessary to
17
determine a more reliable SFE based on the comparison between the calculated and measured
18
SFE values using the abovementioned techniques. However, the systematic thermodynamic
19
calculation of the SFE has not yet been established in the Fe-Cr-Mn-C-N system with respect
20
to the alloying elements with a wide range probably due to the presence of various interaction
21
parameters on the same elements such as LFe,Mn:Va, LFe:C,Va, LFe:N,Va and LFe:C,N. It leads to a
22
difficulty in designing the new Fe-Cr-Mn-C-N steels, considering the strengthening
23
mechanisms (TRIP, TWIP) based on the accurate SFE. Although the empirical equations of
24
the SFE in conventional Fe-Cr-Ni based stainless steels have been reported [16-18], it is
25
difficult to calculate the SFE for Fe-Cr-Mn-C-N steels because of the following reasons; (1)
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2
(Ni, Mo, Si) on the SFE, (2) the range of the alloying elements for the SFE calculation is
3
significantly limited, and (3) the dependence of the SFE on the additions of C and/or N over
4
~0.3 wt.% for various Fe-Cr-Mn-C-N steels has not been considered.
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Therefore, in the present study, we carried out the thermodynamic calculation of the SFE
6
in Fe-Cr-Mn-C-N steels using the sublattice model. This model assumed that each element
7
and vacancy separately occupy the substitutional and interstitial sites with random mixing in
8
each sublattice to reflect the real crystalline structure, relative to the widely used subregular
9
model [12, 14]. It was suggested to use the combination of the thermodynamic databases for
10
comparison between the calculated and reported experimental SFEs was preferable for more
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reliable SFE values. Finally, the effect of the alloying elements on the SFE was
12
systematically investigated using the thermodynamic calculation, discussed and verified in
13
comparison of the results of previous research.
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2. Thermodynamic calculation of stacking fault energy For this purpose, the SFE was calculated based on the classical nucleation theory, because
17
the stacking fault is a volumetric embryo of the hcp ε phase in the fcc γ matrix [12, 14]. The
18
SFEs were thermodynamically calculated using the sublattice model as follows:
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γ →ε SFE = 2ρ ( ∆Gchγ →ε + ∆Gmg ) + 2σ
(1)
20
where ρ is the molar surface density along the atomic plane of (111) in mol m-2 which was
21
determined from the equation 4 / ( 3 aγ2 N A ) [12, 14], where NA is Avogardo’s number of
22
6.022 ×1023 mol-1 and aγ is the γ lattice parameter given as aγ = 3.5780 + 0.0006 (wt.%Cr) +
23
0.00095 (wt.%Mn) + 0.033 (wt.%C) + 0.029 (wt.%N) in Å [19]. Both ∆Gch and ∆Gmg are the
24
differences in the chemical and magnetic Gibbs free energies between the γ and ε phases in J 3
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2
[14]. σ is the γ/ε interfacial energy as the constant value of 10 mJ m-2 [20, 21], which is used
3
for the SFE calculation of the high Mn steels [20, 21] as well as the Fe-Cr-Ni stainless steels
4
[22].
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Regarding the ∆Gch using the sublattice model, the γ and ε phases were treated as a
6
randomly mixed substitutional solution with two substitutional and interstitial sublattices
7
such as (Fe, Cr, Mn)1(C, N, Va)λ, where λ is equal to 1 for the γ, 0.5 for the ε phases [12] and
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the Va indicates a vacancy. The SFE calculation using the sublattice model was discussed in
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ϕ detail by Mosecker et al [12]. The Gch (for φ = γ and ε phases) was adopted by the
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sublattice model, as follows:
ϕ o ϕ o ϕ o ϕ o ϕ o ϕ Gchϕ = yFe yC oGFe :C + yCr yC GCr :C + yMn yC GMn:C + yFe y N GFe: N + yCr y N GCr : N + yMn y N GMn: N ϕ o ϕ o ϕ + yFe yVa oGFe :Va + yCr yVa GCr :Va + yMn yVa GMn:Va + aRT ( yFe ln y Fe + yCr ln yCr + yMn ln yMn )
+ bRT ( yC ln yC + yN ln y N + yVa ln yVa ) + Gexϕ where
Gexϕ = yFe yCr ( yC LϕFe,Cr:C + yN LϕFe,Cr:N + yVa LϕFe,Cr:Va ) + yFe yMn ( yC LϕFe , Mn:C + y N LϕFe , Mn:N + yVa LϕFe , Mn:Va )
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(2)
+ yCr yMn ( yC LϕCr , Mn:C + y N LϕCr , Mn:N + yVa LϕCr , Mn:Va ) + yC yN ( yFe LϕFe:C , N + yCr LϕCr:C , N + yMn LϕMn:C , N ) + yC yVa ( yFe LϕFe:C ,Va + yCr LϕCr:C ,Va + yMn LϕMn:C ,Va ) + yN yVa ( yFe LϕFe:N ,Va + yCr LϕCr:N ,Va + yMn LϕMn:N ,Va )
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+ yFe yCr yMn ( yC LϕFe,Cr , Mn:C + yN LϕFe,Cr , Mn:N + yVa LϕFe ,Cr , Mn:Va )
Giϕ denotes the Gibb free energy of each element i in the γ and ε phases and both a and b
o
13
are the site numbers in each sublattice of a = b = 1 for the γ phase and a = 1, b = 0.5 for the ε
14
phase. R is the gas constant and T is the temperature in K. The site fractions (yi) of each
15
element in the substitutional sublattice are calculated as:
16
17
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yi =
xi (1 − xC − xN )
(3)
The site fraction for C and N in the interstitial sublattice is as follows:
yC or N =
xC or N
λ (1 − xC − xN ) 4
(4)
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where x is the mole fraction of each element. The relationship between the site fractions of
2
both the substitutional and interstitial sublattices is as follows:
3
y Fe + yCr + yMn = yC + y N + yVa = 1
4
ϕ In the excess free energy term ( Gexϕ ) in Eq. (2), Li, j:C , N ,Va is the interaction parameter for the
5
elements (i and j) in each phase. For the SFE calculation, the recently re-evaluated
6
thermodynamic parameters in Fe-Mn-Al-C [14], Fe-Cr-Mn-N [12], Fe-Cr-Mn-C [22] and Fe-
7
Cr-C [23] systems were adopted and listed in the Supplementary Information.
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However, among the thermodynamic parameters, it is essential to verify several parameters
9
on a basis of the comparison between the calculated and measured SFEs in the Fe-Cr-Mn-C-
10
N system for an accurate SFE. This is because several interaction parameters (LFe,Mn:Va for the
11
Fe-Mn system [24, 25] and LFe:C,N, LFe:C,Va, LFe:N,Va for the Fe-N-C system [26, 27]) are
12
controversial depending on the authors (Table 1). Namely, for the Fe-Mn system, LFe,Mn:Va
13
was recently suggested by Nakano and Jacques [24] and Djurovic et al. [25], and for the Fe-
14
C-N system, LFe:C,N, LFe:C,Va and LFe:N,Va are newly proposed by Gӧhring et al. [27], instead of
15
the frequently used set of thermodynamic parameters collected by Du and Hillert [26] from
16
the literature [28, 29]. Hence, according to the interaction parameters without any change in
17
the other parameters, the combinations of thermodynamic databases for the SFE calculations
18
can be divided into 3 types and labelled as type I (Nakano-Du), type II (Djurovic-Du) and
19
type III (Djurovic-Gӧhring).
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For verification of the calculated SFE, 23 experimentally measured SFEs of austenitic Fe-
21
Cr-Mn-C-N steels were collected from the literature [4, 6-11] and listed in Table 2, along
22
with the measurement method. The 23 different steels were categorized into three different
23
groups based on their C and N concentrations. They are the high C (= 0.6 wt.%)-low N (< 0.1
24
wt.%), low C (< 0.1 wt.%)-high N (0.2-0.8 wt.%) and high C (0.2-0.6 wt.%)-high N (0.1-0.4 5
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wt.%) austenitic steels, which are indicated by the black square, red diamond and blue
2
triangle in Fig. 1, respectively.
3
3. Results and discussion
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3.1. Comparison of the calculated and measured stacking fault energies
Figure 1a through c shows the relationship between the measured and calculated SFEs
7
using types I through III, respectively, together with three different indexes of accuracy.
8
Parameter E is the average distance between the line in the figure and markers, parameter D
9
is the average absolute distance between the line, and the parameter S is the standard error in the figure and markers as follows:
Ei =
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(SFECal . − SFEMea. ) 2
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N
E=
i
i =1
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12
∑E N
Di = Ei
13
(7) (8)
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D=
∑D
i
i =1
N
S=
∑ (SFE i =1
(9)
N
cal .
− SFEmea. ) 2 (10)
N
16
where both the SFECal. and SFEMea. are the calculated and measured SFEs, respectively. N is
17
the number of steels used. The lower D value indicates a better agreement between SFECal.
18
and SFEMea.. The positive E value means a higher SFECal. than SFEMea. on average, or vice
19
versa.
20
As shown in Fig. 1a, the type I did not work well for both the low C-high N (red circle) 6
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2
than the SFEMea. for most of the steels, except for two steels with the SFECal. over 50 mJ m-2
3
(as indicated by the arrows), leading to the highest E, D and S values of -5.9, 8.6 and 13.6,
4
respectively. Fig. 2b reveals the relationship between the SFEMea. and the SFECal. using the
5
type II. Although the D and S value was improved, relative to that using the type I, the E
6
value was similar, implying that the SFECal. using the type II was still underestimated for both
7
the low C-high N and high C-high N steels. This is probably because the interaction
8
parameters (as collected by Du and Hillert [26]) in both the types I and II did not quite reflect
9
the effects of C and N on the SFECal. in the Fe-Cr-Mn-C-N system.
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Accordingly, we calculated the SFECal. using the recently re-evaluated LFe:C,N, LFe:C,Va and
11
LFe:N,Va without any change in the other thermodynamic parameters (as indicated by type III)
12
and which are plotted in Fig. 1c. Regardless of the C and N concentrations, the SFECal. is in a
13
better agreement with the SFEMea., relative to those by both the type I and II, showing the
14
lowest E (1.6), D (4.1) and S (6.8) values. The indexes of accuracy seem reasonable,
15
considering the possibility of change in the σ value by the addition of alloying elements [15]
16
and the experimental error of the SFEMea.. Therefore, the type III is thought to produce more
17
accurate thermodynamic calculations of the SFE in the austenitic Fe-Cr-Mn-C-N steels.
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20
To investigate the dependence of the SFE on the alloying elements in the Fe-Cr-Mn-C-N
21
steels, the SFEs were calculated within a wide range of chemical compositions using the type
22
III combinations of thermodynamic databases for SFE calculation. Figure 2 shows the change
23
in the SFE at 300 K of the Fe-xCr-(10-25)Mn-(0, 0.3)C-(0, 0.3)N steels as a function of the
24
Cr concentration. According to the Mn concentration, there are two types of polynomial and
25
linear trends of the SFE by the addition of Cr. For the Fe-xCr-10Mn steels (Fig. 2a), the SFE 7
ACCEPTED MANUSCRIPT almost linearly declined with the increasing Cr concentration from zero to 30 wt.%. For the
2
Fe-xCr-(15-25)Mn steels (Fig. 2a), the SFE increased as raising the Cr concentration up to a
3
critical value, then slightly decreased again with the addition of more Cr. The critical value of
4
the Cr concentration increased from ~14 to ~20 wt.% with the increasing Mn concentration
5
from 15 to 25 wt.%. As shown in Fig. 2b, the addition of 0.3wt.%C to the Fe-xCr-(10-25)Mn
6
steels increased the SFE, showing a similar polynomial trend of the SFE in the Fe-xCr-(15-
7
25)Mn steels. The addition of 0.3 wt.%N to the Fe-xCr-(10-25)Mn steels increased the SFE
8
and the Fe-xCr-15Mn-0.3N steels changed to have an almost linear decreasing behavior from
9
the polynomial trend. The simultaneous additions of 0.3 wt.%C and 0.3 wt.%N to the Fe-xCr-
10
(10-25)Mn steels (Fig. 2d) increased the SFE, showing the similar change in the SFE in the
11
Fe-xCr-(10-25)Mn-0.3N steels. The distance between the lines decreased with the additions
12
of C and/or N, implying that Mn has a more powerful effect on SFE when C or N was added
13
to a smaller extent.
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Regarding the Mn, the Fe-(10-25)Cr-xMn systems have an approximately linear
15
increasing trend with the addition of Mn from 10 to 30 wt.% (Fig. 3). The gap between the
16
lines by the addition of Cr ranging from 10 to 25 wt.% was not as high as that by the addition
17
of Mn in the Fe-xCr-(10-25)Mn-(0, 0.3)C-(0, 0.3)N systems, indicating that the addition of
18
Cr has a minor effect on the SFE relative to Mn.
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In order to investigate the effects of C and N on the SFE, the SFEs of the Fe-18Cr-10Mn-
20
(0-0.4)C-(0-0.4)N steels were plotted versus the C and N concentrations in Fig. 4a and b,
21
respectively. The reason why the Fe-18Cr-10Mn based steels were selected is because the
22
SFECal. of the Fe-10Cr-18Mn-xC-yN and Fe-15Cr-15Mn-xC-yN systems (not shown here)
23
have a trend similar to the SFECal. of the Fe-18Cr-10Mn-xC-yN system, regardless of the
24
addition of Cr and Mn. Both C and N almost linearly increased the SFE. The effect of N on
25
the SFE was more effective than that of C, indicating both the increase in the distance 8
ACCEPTED MANUSCRIPT between the lines in Fig. 4a and the higher slope in Fig. 4b. In addition, the synergetic effect
2
of C and N on the SFE was not seen yet and, for example, the SFE (22 mJ m-2) of the Fe-
3
18Cr-10Mn-0.6N steel was higher than that (15.9 mJ m-2) of the Fe-18Cr-10Mn-0.3C-0.3N
4
steel. According to Lee et al.’s study [7], the measured SFE (19.3 mJ m-2) using the ND in
5
the Fe-18.3Cr-9.7Mn-0.3Si-0.61N (wt.%) steel was lower than the SFE (22.5 mJ m-2) of the
6
Fe-18.1Cr-9.6Mn-0.1Si-0.30C-0.32N (wt.%) steel due to slightly effective impact of C on the
7
SFE relative to N. This difference between the present and previous studies is probably due to
8
the difficulty to sufficiently reflect the interaction between the substitutional and interstitial
9
elements caused by the lack of the interaction parameters, such as LMn:C,N, LCr:C,N and
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LFe,Mn,Cr:C.
Looking into the relationship between the alloying elements and SFE in the Fe-Cr-Ni
12
based stainless steels for the comparison with that of the Fe-Cr-Mn-C-N steels, Meric de
13
Bellefon et al. [18] have recently reported the SFE equation in austenitic stainless steels.
14
Their new expression to predict the SFE from the chemical composition was obtained using
15
the linear regression with random intercepts of 144 measured SFEs from previous reports,
16
given as SFE (mJ m-2) = 2.2+1.9Ni-2.9Si+0.77Mo+0.5Mn+40C-0.016Cr-3.6N (wt.%). It is
17
difficult to predict the SFE using this equation for the Fe-Cr-Mn-C-N steels due to the
18
discrepancy in the effect of alloying elements, such as Cr, Mn and N, on the SFE. This is due
19
to both the dependence of the SFE on other alloying elements (Ni, Mo and Si) and the
20
difference in the concentrations of Mn, C and N of the reported Fe-Cr-Ni steels for the
21
prediction equation. Therefore, the suggested combination (type III) of the thermodynamic
22
parameters is suitable to calculate more reliable SFE for the Fe-Cr-Mn-C-N steels.
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4. Conclusion In the present study, we investigated the thermodynamic calculations of the accurate 9
ACCEPTED MANUSCRIPT 1
stacking fault energy (SFE) in Fe-Cr-Mn-C-N steels using the sublattice model based on the
2
comparison between the calculated and experimentally measured SFEs. (1) The calculated SFE more closely agreed with the measured SFE when using the
4
combination of thermodynamic databases based on the interaction parameters
5
(LFe,Mn:Va, LFe:C,N, LFe:C,Va and LFe:N,Va) suggested by Djurovic et al. [25] and Gӧhring
6
et al. [27].
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(2) The change in the SFE of the Fe-Cr-Mn-C-N steels was different from that of the Fe-
8
Cr-Ni austenitic steels. The influence of Cr on the SFE was complex; the trend in the
9
SFE by the addition of Cr showed two types of behavior such as polynomial and
10
linear, depending on the amount of Mn, C and N. In contrast to Cr, the addition of
11
Mn, C and N increased the SFE continuously.
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Figure caption
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Fig. 1. Relationship between the thermodynamically-calculated stacking fault energy (SFE)
15
using the combination of (a) type I, (b) type II and (c) type III, and the experimentally
16
measured SFE in the Fe-Cr-Mn-C-N steels. The black arrow in Fig. 1(a) denotes the
17
overestimated data by the SFE calculation. The legends, such as 0.6C-(0-0.1)N, 0C-(0.2-
18
0.8)N and (0.2-0.6)C-(0.1-0.4)N, in Fig. 1 indicate the Fe-Cr-Mn steels containing high C-
19
low N, low C-high N and high C-high N, respectively, and the details of the chemical
20
composition are listed in Table 2. All the parameters (E, D and S) are the indexes of accuracy
21
in Eqs. (6-10).
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Fig. 2. Variations in the calculated stacking fault energy (SFE) using the type III in (a) Fe-
24
xCr-(10-25)Mn, (b) Fe-xCr-(10-25)Mn-0.3C, (c) Fe-xCr-(10-25)Mn-0.3N and (d) Fe-xCr-
25
(10-25)Mn-0.3C-0.3N (wt.%) steels with the increasing Cr concentration from 0 to 30 wt.%. 10
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Fig. 3. Variations in the calculated stacking fault energy (SFE) using the type III in (a) Fe-
3
(10-25)Cr-xMn, (b) Fe-(10-25)Cr-xMn-0.3C, (c)Fe-(10-25)Cr-xMn-0.3N and (d) Fe-(10-
4
25)Cr-xMn-0.3C-0.3N (wt.%) steels with the increasing Mn concentration from 10 to 30
5
wt.%.
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Fig. 4. Variations in the calculated stacking fault energy (SFE) using the type III in (a) Fe-
8
18Cr-10Mn-xC-(0-0.4)N and (b) Fe-18Cr-10Mn-(0-0.4)C-xN (wt.%) steels with the
9
increasing C or N concentrations from zero to 0.6 wt.%.
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Acknowledgements
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This study was partly supported by the New Energy and Industrial Technology Development
13
Organization (NEDO) under the “Innovation Structural Materials Project (Future Pioneering
14
Projects)” and a Grant-in-Aid for Science Research from the Japan Society for the Promotion
15
of Science. LSJ acknowledges support from the “Basic Science Research Program through
16
the National Research Foundation of Korea (NRF) funded by the Ministry of Education
17
(2017R1A6A3A03002080)”.
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[3] H.-Y. Ha, T.-H. Lee, C.-S. Oh, S.-J. Kim, Effects of combined addition of carbon and
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[4] T.-H. Lee, E. Shin, C.-S. Oh, H.-Y. Ha, S.-J. Kim, Correlation between stacking fault
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[7] T.-H. Lee, H.-Y. Ha, B. Hwang, S.-J. Kim, E. Shin, Effect of carbon fraction on stacking
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[8] V. Gavriljuk, Y. Petrov, B. Shanina, Effect of nitrogen on the electron structure and
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[9] L. Bracke, J. Penning, N. Akdut, The influence of Cr and N additions on the mechanical
15
properties of FeMnC steels, Metall. Mater. Trans. A. 38 (2007) 520-528.
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[10] L. Mujica, S. Weber, W. Theisen, The stacking fault energy and its dependence on the
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interstitial content in various austenitic steels, Mater. Sci. For. 706-709 (2012) 2193-2198.
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[11] L. Mosecker, D.T. Pierce, A. Schwedt, M. Beighmohamadi, J. Mayer, W. Bleck, J.E.
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Wittig, Temperature effect on deformation mechanisms and mechanical properties of a high
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manganese C+N alloyed austenitic stainless steel, Mater. Sci. Eng. A, 642 (2015) 71-83.
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[12] L. Mosecker, A. Saeed-Akbari, Nitrogen in chromium-manganese stainless steels: A
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23
Technol. Adv. Mater. 14 (2013) 033001.
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[13] S. Curtze, V.T. Kuokkala, A. Oikari, J. Talonen, H. Hänninen, Thermodynamic modeling
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of the stacking fault energy of austenitic steels, Acta Mater. 59 (2011) 1068-1076.
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ACCEPTED MANUSCRIPT [14] D.T. Pierce, J.A. Jiménez, J. Bentley, D. Raabe, C. Oskay, J.E. Wittig, The influence of
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manganese content on the stacking fault and austenite/ε-martensite interfacial energies in Fe-
3
Mn-(Al-Si) steels investigated by experiment and theory, Acta Mater. 68 (2014) 238-253.
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[15] D.T. Pierce, J.A. Jiménez, J. Bentley, D. Raabe, J.E. Wittig, The influence of stacking
5
fault energy on the microstructural and strain-hardening evolution of Fe-Mn-Al-Si steels
6
during tensile deformation, Acta Mater. 100 (2015) 178-190.
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[16] R.E. Schramm, R.P. Reed, Stacking fault energies of seven commercial austenitic
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stainless steels, Metall. Trans. A, 6 (1975) 1345-1351.
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[17] T. Yonezawa, K. Suzuki, S. Ooki, A. Hashimoto, The effect of chemical composition and
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heat treatment conditions on stacking fault energy for Fe-Cr-Ni austenitic stainless steel,
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Metall. Mater. Trans. A, 44 (2013) 5884-5896.
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[18] G. Meric de Bellefon, J.C. van Duysen, K. Sridharan, Composition-dependence of
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stacking fault energy in austenitic stainless steels through linear regression with random
14
intercepts, J. Nucl. Mater. 492 (2017) 227-230.
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N austenitic stainless steels, Scripta Mater. 37 (1997) 285-291.
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[20] S.-J. Lee, J. Han, S. Lee, S.H. Kang, S.M. Lee, Y.-K. Lee, Design for Fe-high Mn alloy
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with an improved combination of strength and ductility, Sci. Rep. 7 (2017) 3573.
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[21] S.-J. Lee, J. Han, C.-Y. Lee, I.-J. Park, Y.-K. Lee, Elastic strain energy induced by
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epsilon martensitic transformation and its contribution to the stacking-fault energy of
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austenite in Fe-15Mn-xC alloys, J. Alloys Compd. 617 (2014) 588-596.
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[22] B.-J. Lee, On the stability of Cr carbides, CALPHAD 16 (1992) 121-149.
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[23] A.V. Khvan, B. Hallstedt, C. Broeckmann, A thermodynamic evaluation of the Fe-Cr-C
24
system, CALPHAD 46 (2014) 24-33.
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[24] J. Nakano, P.J. Jacques, Effects of the thermodynamic parameters of the hcp phase on
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ACCEPTED MANUSCRIPT the stacking fault energy calculations in the Fe-Mn and Fe-Mn-C systems, CALPHAD 34
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(2010) 167-175.
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[25] D. Djurovic, B. Hallstedt, J. Von Appen, R. Dronskowski, Thermodynamic assessment
4
of the Fe-Mn-C system, CALPHAD 35 (2011) 479-491.
5
[26] H. Du, M. Hillert, Assessment of the Fe-C-N system, Z. Metallkde. 82 (1991) 310-316.
6
[27] H. Göhring, O. Fabrichnaya, A. Leineweber, E.J. Mittemeijer, Thermodynamics of the
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Fe-N and Fe-N-C systems: The Fe-N and Fe-N-C phase diagrams revisited, Metall. Mater.
8
Trans. A, 47 (2016) 6173-6186.
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[28] P. Gustafson, Thermodynamic evaluation of the Fe-C system, Scand. J. Metall. 14 (1985)
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[29] K. Frisk, A thermodynamic evaluation of the Cr-N, Fe-N, Mo-N and Cr-Mo-N systems,
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CALPHAD 15 (1991) 79-106.
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Table 1 Various interaction parameters according to the authors. All values are given in SI unit, J, mol and K. hcp ε
-7762+3.865T-259(yFe-yMn) LFe,Mn:Va
-26150
LFe:C,N
-53059-38756(yC-yVa)
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Djurovic
et al. [25]
Du & Hillert [26] Göhring et al. [27]
10345-19.71T-
Du & Hillert
(11130-11.84T)(yN-yVa)
[26]
8186-18.127T-
Göhring
(24378-24.959T)(yN-yVa)
et al. [27]
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Jacques [24]
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(14271.46-13.884T)(yFe-yMn)
-17335
LFe:C,Va
-26150
Nakano &
-5748+3.865T-273(yFe-yMn)
-34671 -34671
69.41+2.836T-
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-7762+3.865T-259(yFe-yMn)
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Parameter
-20772-32.504T-28839(yC-yN)
Du & Hillert [26] Göhring et al.
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Table 2 Stacking fault energy (SFE) of Fe-Cr-Mn-C-N steels reported in the literature. Chemical composition (wt.%)
SFE
Mn
C
N
(mJ m-2)
2.0
14.8
0.60
0.02
14.6
High C-Low N
2.0
14.5
0.59
0.03
15.5
:0.6C-(0-0.1)N
1.8
15.0
0.59
0.07
17.1
1.8
15.0
0.62
0.09
19.6
15.1
17.2
-
0.23
26.4
15.1
17.2
-
0.48
21.3
15.1
17.2
-
0.8
17.8
9.7
0.03
0.39
18.1
9.7
0.03
0.44
12.2
17.7
9.6
0.03
0.51
17.1
17.5
9.8
0.03
0.69
22.8
18.3
9.7
0.02
0.61
19.3
:(0-0.1)C(0.2-0.8)N
5.6 9.7
:(0.2-0.6)C-
12.0
0.21
neutron
diffraction
Lee et al. [6]
Gavrlijuk
TEM
et al. [8]
33.1
Neutron
Lee et al.
diffraction
[4,7]
X-ray & neutron diffraction
0.25
0.11
5.0
19
0.24
0.20
20.0
20.0
0.24
0.32
36.0
25.0
0.3
0.40
31.0
TEM
TEM
Lee et al. [6] Bracke et al. [9] Mujica et al. [10]
12.0
30.0
0.3
0.40
43.3
14.6
16.0
0.31
0.29
21.0
18.0
10.2
0.15
0.42
20.1
18.1
9.7
0.38
0.38
27.6
Neutron
Lee et al.
18.1
9.5
0.24
0.35
20.8
diffraction
[4,7]
18.1
9.6
0.3
0.32
22.5
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(0.1-0.4)N
12.0
0.56
Ref.
10.4
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14.9
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2.5
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41.0
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Cr
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TEM
Mosecker et al. [11]
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ACCEPTED MANUSCRIPT Highlights • Stacking fault energy in Fe-Cr-Mn-C-N steels was thermodynamically calculated. • For accurate stacking fault energy, measured and predicted energies were compared.
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• Mn, C and N continuously increase stacking fault energy.
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• Cr increases stacking fault energy, then decreases it again over a critical value.