Solute grain boundary segregation during high temperature plastic deformation in a Cr–Mo low alloy steel

Materials Science and Engineering A 528 (2011) 7663–7668

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Solute grain boundary segregation during high temperature plastic deformation in a Cr–Mo low alloy steel X.-M. Chen, S.-H. Song ∗ , L.-Q. Weng, S.-J. Liu Department of Materials Science and Engineering, Shenzhen Graduate School, Harbin Institute of Technology, Xili, Shenzhen 518055, China

a r t i c l e

i n f o

Article history: Received 27 March 2011 Received in revised form 5 June 2011 Accepted 23 June 2011 Available online 6 July 2011 Keywords: Grain boundaries Segregation Deformation Metals and alloys

a b s t r a c t Grain boundary segregation of Cr, Mo and P to austenite grain boundaries in a P-doped 1Cr0.5Mo steel is examined using field emission gun scanning transmission electron microscopy for the specimens undeformed and deformed by 10% with a strain rate of 2 × 10−3 s−1 at 900 ◦ C, and subsequently water quenched to room temperature. Before deformation, there is some segregation for Mo and P, but the segregation is considerably increased after deformation. The segregation of Cr is very small and there is no apparent difference between the undeformed and deformed specimens. Since the thermal equilibrium segregation has been attained prior to deformation, the segregation produced during deformation has a non-equilibrium characteristic. A theoretical model with consideration of site competition in grain boundary segregation between two solutes in a ternary alloy is developed to explain the experimental results. Model predictions are made, which show a reasonable agreement with the observations. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Hot ductility losses of commercial low carbon low alloy steels have received much attention because they can be used to predict the transverse cracking produced in the continuously cast steel during straightening operation which is usually carried out in the range 700–950 ◦ C. It is well known that the precipitation of carbides, nitrides or sulfides [1,2] and the segregation of impurities to grain boundaries [3–5] are the main factors causing ductility deterioration in the austenite range. The ductility can be improved at higher temperatures which may coarsen or remove the particles [1]. Hence, at rather a high temperature, the segregation of undesirable elements plays an important role in ductility losses. Some elements, such as sulfur, phosphorus, tin and antimony, may segregate at grain boundaries, deteriorating the ductility for low carbon low alloy steels [3–5]. Nachtrab and Chou [5] discovered that deformation can enhance the grain boundary segregation of copper, tin and antimony in C–Mn steel at 900 ◦ C, and the addition of these elements can seriously reduce the hot ductility of the steel. Recently, we [6] found that high temperature plastic deformation can induce phosphorus segregation to ferrite grain boundaries in an interstitial free steel, and this deformation-induced segregation increases

∗ Corresponding author. Tel.: +86 755 26033465; fax: +86 755 26033504. E-mail addresses: [email protected], [email protected] (S.-H. Song). 0921-5093/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2011.06.084

with increasing deformation strain until dynamic recrystallization. Also, the deformation-induced segregation is non-equilibrium segregation and cannot be described by equilibrium segregation theories. For this reason, we have proposed a theoretical model for deformation-induced non-equilibrium grain boundary segregation in dilute binary alloys [6,7]. Until now, studies of phosphorus grain boundary segregation during high temperature plastic deformation in an austenite microstructure have been sparse. In the present work, grain boundary segregation of phosphorus and alloying elements during plastic deformation at 900 ◦ C in a P-doped 1Cr0.5Mo steel was examined using field emission gun scanning transmission electron microscopy (FEGSTEM). In addition, a kinetic model with consideration of site competition in grain boundary segregation between two solutes in dilute ternary alloys was established for explanation of the experimental results. 2. Experimental procedure A nominal 1Cr0.5Mo steel doped with 0.054 wt.% P was prepared by vacuum induction melting with an ingot of 50 kg. The chemical composition of the steel (wt.% (at.%)) was 0.098(0.45)C, 0.17(0.34)Si, 0.47(0.48)Mn, 0.054(0.097)P, 0.0065(0.011)S, 1.02(1.09)Cr, 0.44(0.25)Mo, and 0.022(0.019)Cu. The ingot was hot rolled in the range 900–1000 ◦ C into a Plate 18 mm in thickness from which the tensile specimens were

X.-M. Chen et al. / Materials Science and Engineering A 528 (2011) 7663–7668

Fig. 1. FEGSTEM image showing a typical grain boundary analyzed.

machined with a gauge length of 60 mm and a gauge diameter of 10 mm. In this work, both the deformed and undeformed specimens were prepared. The test pieces were initially austenitized at 1000 ◦ C for 1 h, after which they were furnace cooled to 900 ◦ C and held there for 30 min, followed by tensile deformation. Hot tensile deformation was performed using a high temperature tensile testing machine. According to Mclean [8], the holding time is long enough to make grain boundary segregation reach thermal equilibrium. After the specimens were deformed by 10% at a strain rate of 2 × 10−3 s−1 , they were all water quenched to room temperature immediately. The undeformed specimen was maintained for the same time at the same temperature as the deformed one and then water quenched. Disc-shape specimens 3 mm in diameter and 0.5 mm in thickness were cut from the deformed and undeformed specimens using a spark erosion unit. These samples were mechanically polished to approximately 100 ␮m in thickness, followed by dual-jet electropolishing to achieve thin foil regions which are transparent to electrons. A solution of 5% perchloric acid and 95% methanol was used for the electropolishing at −60 ◦ C with a voltage of 25 V. The instrument used to determine the grain boundary composition was JEM-2100F FEGSTEM equipped with an Oxford INCA energy dispersive X-ray spectrometer (EDS). This instrument is an advanced field emission electron microscope featuring ultrahigh spatial resolution. In the FEGSTEM, emission of electron from the very fine tip, results in a very large electron beam current in a very small probe size (nominal probe size: 0.5–1 nm). Microanalysis was carried out under an operating voltage of 200 kV. Grain boundaries selected for analysis were oriented parallel to the incident electron beam and were not decorated with precipitates. The stage controls and microscope power systems were left for more than 10 h to reduce drift and instability to a minimum. The concentrations of Cr, Mo and P were determined by spot analysis and the counting time for data acquisition was 80 s. In the measurements, four grain boundaries were selected for each condition and the mean value of the data points obtained was taken as the measured result.

Measured concentrations at GBs (at.%)

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1.0 GB for undeformed specimen GB for deformed specimen 0.8

0.6

0.4

0.2

0.0 Mo

P

Fig. 2. Grain boundary concentrations of Mo and P, determined by FEGSTEM microanalysis (error bars represent the standard deviation).

than those in the undeformed specimen. Before deformation, the boundary concentration of Mo and P is 0.35 at.% and 0.36 at.%, respectively, and they both increase apparently to 0.70 at.% after deformed by 10% at a strain rate of 2.0 × 10−3 s−1 . Clearly, apparent grain boundary enrichment of these two elements, produced during deformation, is detected since their bulk concentrations are 0.25 at.% and 0.097 at.%, respectively. In crystalline materials, segregation manifests itself in the formation of very thin (often 0.5–1 nm [9]) but high enriched films at grain boundaries, while the spatial resolution for EDS microanalysis is rarely better than ∼2 nm because of beam broadening [10]. Obviously, the measured values are not the accurate results of grain boundary concentrations because the electron interaction volume is larger than the boundary volume, enabling the measured values to be always smaller than the true grain boundary concentrations. It is suggested that the apparent measured value would be a convolution result of the actual compositional distribution around the grain boundary and the distribution of electron density in the probe [11,12]. Faulkner et al. [12] established an analytical convolution method of quantifying the true solute grain boundary concentration. In their research, the incident probe is described as a Gaussian distribution with a standard deviation  and the actual compositional distribution around a grain boundary is assumed as a top-hat function, as shown in Fig. 3, where Cb is the solute concentration in the enriched layer, Cg is the solute concentration in the adjacent matrix, and d0 is the width of the enriched layer. Convoluting the Gaussian distribution function and top-hat function would lead to the observed composition profile, which is expressed as [12] C = Cg +



1 (C − Cg ) × erf 2 b

 x + 0.5d  0 d √  2

− erf

 x − 0.5d  0 d √  2

(1)

3. Results and discussion Fig. 1 shows a typical prior austenite grain boundary observed in FEGSTEM. The selected image shows that there were no precipitates along the grain boundary and the boundary plane was well parallel to the incident electron beam. The grain boundary concentrations of Mo and P in the undeformed and deformed specimens, determined by FEGSTEM microanalysis, are shown in Fig. 2. Since the segregation of Cr is very small (enrichment ratio: ∼1.4) and there is no evdient difference between the undeformed and deformed specimens, the value of Cr is not shown in Fig. 2. As seen, the boundary concentrations of Mo and P in the deformed specimen are much higher

where C represents the observed solute concentration as a function of the distance from the boundary center (xd ). Usually, the effective probe diameter could be defined by a diameter containing 80% of the total probe current (ϕ80 ), i.e., ϕ80 could represent the spatial resolution [12]. The relationship between the standard deviation of electron density distribution () and the beam diameter containing 80% of the current (ϕ80 ) is given by [12]  = 0.279ϕ80

(2)

Michael et al. [13] proposed a modified definition of spatial resolution, R, based on the Gaussian model and experimental mea-

X.-M. Chen et al. / Materials Science and Engineering A 528 (2011) 7663–7668

Fig. 3. Top-hat function depicting the compositional distribution around a grain boundary (Cb is the solute concentration in the enriched layer; Cg is the solute concentration in the adjacent matrix; and d0 is the width of the enriched layer).

surements, which is considered as the best available definition of the X-ray spatial resolution by Williams et al. [14]. R is given by R=

d+



b2 + d2 2

(3)

where d is the beam diameter and b is the beam spreading amount. Williams et al. and Goldstein et al. [14,15] assume that each electron undergoes a single scattering event in the middle of the foil, resulting in a conservative estimate of the beam broadening, b (in cm), which is given by b = 6.25 × 105

 Z    1/2 E0

A

h3/2

(4)

where  is the specimen density in g/cm3 ; A is the atomic weight; Z is the atomic number; E0 is the operating voltage in V, and h is the specimen thickness in cm. It has been experimentally demonstrated that the foil thickness is around 100 nm [16]. As a result, the beam spreading amount in the iron matrix may be obtained as 9.60 nm. When xd is taken as naught, Eq. (1) may be used in conjunction with Eqs. (2)–(4) to determine the true grain boundary concentration of the solute (Cb ). In the present work, the nominal probe size is about 1 nm, and thus the spatial resolution could be 5.33 nm. Assuming that the boundary thickness is 1 nm and the solute concentration in the matrix adjacent to the boundary is equal to the bulk concentration, using the measured results shown in Fig. 2 one can acquire the corrected concentrations of Mo and P, which are visually represented in Fig. 4. Clearly, the corrected values are much higher than the measured ones. After the correction, the enrichment ratios for Mo and P in the undeformed specimen are 2.5 and 11.3, respectively. After deformed by 10%, the enrichment ratios are 7.8 and 24.6 for Mo and P, respectively. It is claimed that plastic deformation can encourage Mo and P to segregate at grain boundaries.

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Fig. 4. Grain boundary (GB) concentrations of Mo and P in the specimens undeformed and deformed (ε = 10%, ε˙ = 2 × 10−3 s−1 ) at 900 ◦ C, determined by FEGSTEM microanalysis and corrected by the convolution method. The concentrations of Mo and P in the matrix are also plotted for comparison.

segregation mechanism. During high temperature plastic deformation, two types of non-equilibrium segregation have been reported in previous studies, namely, deformation-induced nonequilibrium segregation [5–7] and non-equilibrium segregation during recrystallization [19]. Fig. 5 shows a typical engineering stress ()-engineering strain (ε) curve for the specimen at 900 ◦ C with a strain rate of 8.3 × 10−4 s−1 in which the true stress (S)–true strain (e) curve is also plotted for comparison. It is suggested [20] that the engineering stress peak indicates the occurrence of dynamic recrystallization, while Poliak and Jonas [21] demonstrated that the inflection in the strain hardening rate ( = ∂S/∂e) – true stress (S) plot, ln  – true strain (e) plot, or ln  – ln S plot indicates the onset of dynamic recrystallization. In the present work, the ln  − e plot, as shown in Fig. 6, was used to predict the initiation of dynamic recrystallization. It should be noted that, to find the inflection of ln  − e plot accurately, it is necessary to determine the maximum in (d ln /de)–e plot which is insetted in Fig. 6. Obviously, the maximum is attained at about 12% true strain which is equal to 12.7% engineering strain. Therefore, no recrystallization has occurred after10% engineering strain. Moreover, it is suggested [22] that recrystallization can be delayed by higher strain rates, further demonstrating that there is no recrystallization present in the specimen deformed at a higher strain rate of 2.0 × 10−3 s−1 . Accordingly, there is only deformation-induced non-equilibrium

4. Theoretical prediction Grain boundary segregation is classified into two types: equilibrium segregation [8] and non-equilibrium segregation [17,18]. As is well known [8], the equilibrium segregation is a thermodynamic process. The maximum equilibrium boundary concentration of solute depends merely on the temperature and decreases with increasing temperature. Hence, the preceding experimental results cannot be reasonably explained by the equilibrium

Fig. 5. Stress–strain curve for the specimen deformed at 900 ◦ C with a strain rate of 8.3 × 10−4 s−1 .

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The maximum boundary concentration of solute during deformation, Cbm , is given by [7] Cbm = Ceq + Cg

Fig. 6. Natural logarithm value of strain hardening rate (ln ) as a function of true strain (e) for the experimental steel deformed at 900 ◦ C with a strain rate of 8.3 × 10−4 s−1 . The inset is corresponding derivative curve.

 t Cex (t) = 0

+

˝0 ˙ s ε Qf

Dv s2 ˇ

2 2 b20

 exp

 1 − exp

x − ˇ

 −

−

x ˇ

Dv s2 ˇ

2 2 b20

 +

Cj ˝0

 exp

4b30 t − ˇ

ε˙



 exp

Dv s2

2 2 b20

 Q  def RT

Cex Cth



(7)

Mo = Ceq

CgMo exp(QMo /kT )

P and C Mo are the maximum equilibrium boundary where Ceq eq concentrations of P and Mo, respectively; CgP and CgMo are the concentrations of P and Mo in the matrix, respectively; QP and QMo are the segregation energies of P and Mo, respectively. In the present case, the maximum equilibrium grain boundary segregation is equal to the corrected values of solute boundary concentration in the undeformed specimen. The non-equilibrium segregation of P and Mo are dealt with by the following method. As described in Ref. [27], by the complex mechanism described above they first segregate to the grain boundary independently to obtain segregation levels CbP and CbMo , and then distribute there in accordance with their binding energies with the grain boundary (equilibrium segregation energies). The final levels of deformation-induced grain boundary segregation of P and Mo, CbP∗ and CbMo∗ , may be evaluated by [28]



P CbP∗ = (CbP − Ceq )

CgP exp(QP /kT ) CgP exp(QP /kT ) + CgMo exp(QMo /kT )

(5)

where A0 , a and n are empirical constants, and Qdef is the apparent activation energy for deformation.

(9)

1 + CgP exp(QP /kT ) + CgMo exp(QMo /kT )



(6)

(8)

exp(QP /kT ) + CgMo exp(QMo /kT )

Mo CbMo∗ = (CbMo − Ceq )

where  is a constant associated with the mechanical production of jogs; ˝0 is the atomic volume; Qf is the vacancy formation energy; ˇ is the characteristic time which is related to the deformation condition; b0 is the Burgers vector; Dv is the diffusion coefficient of vacancies; is a structural parameter describing the distribution of dislocations;  is the shear modulus; L is the grain size; Cj is the concentration of thermal jogs, given by exp(− Ej /kT) [23] where k is the Boltzmann constant and Ej is the jog formation energy being calculated by 0.1b30 [24]; is a parameter which describes the neutralization effect produced by the presence of vacancy emitting and vacancy absorbing jogs and may be calculated by 0.5 − 10Cj if Cj < 0.05, and else is equal to 0 [23]; and  s is the saturation stress which may be modeled using a hyperbolic sine law [23,25] ε˙ = A0 [sinh(as )]n exp −

1+

CgP exp(QP /kT ) 1 + CgP

(x − t)



Dv + 2 (x − t) dx L



where Ceq is the maximum equilibrium boundary concentration at a given temperature; Qsv is the vacancy-solute binding energy; Cth is the thermal equilibrium vacancy concentration, given by B exp(− Qf /kT) [23] where B is a constant associated with the vibrational frequency of atoms around a vacancy. In the present work, Cr, Mo is the main alloy elements in the experimental 1Cr0.5Mo steel, and P is the main impurity element. The FEGSTEM results indicate that there is no apparent boundary enrichment of Cr in the deformed and undeformed specimens. Since apparent boundary segregation of P and Mo are detected, competition between these two elements at the grain boundary must be considered in the theoretical treatment. In a dilute ternary alloy, the maximum equilibrium grain boundary concentrations of P and Mo at a given temperature T may be given by [26] P = Ceq

segregation existing in the deformed specimen in addition to some thermal equilibrium segregation. Deformation-induced non-equilibrium segregation is a kinetic process and relies on the formation of excess quantities of vacancysolute complexes [7]. During deformation at a high temperature, solute atoms, vacancies and their complexes are in dynamic equilibrium each other. Cascades of vacancies can be produced during plastic deformation, and as a result the vacancy concentration exceeds its thermal equilibrium value in the matrix, leading the complexes to be supersaturated. However, at grain boundaries which are sinks of vacancies, the vacancy concentration approaches its thermal equilibrium value, making the complex concentration be equilibrium. Consequently, a concentration gradient of complexes is formed between the boundary and the grain center, which drives the complexes to diffuse towards the grain boundary, causing non-equilibrium segregation. Chen and Song [6] have established a theoretical model to predict deformation-induced non-equilibrium grain boundary segregation in a dilute binary ˙ and temperature (T), the excess conalloy. At a given strain rate (ε) centration of vacancies, Cex (t), which is dependent on deformation time, is given by [6]

Qsv Qf



P + Ceq

CgMo exp(QMo /kT ) CgP exp(QP /kT ) + CgMo exp(QMo /kT )

(10)

Mo + Ceq

(11) The above approach to describing the site competition at the grain boundary between two solutes in ternary systems could be acceptable. Since deformation-induced non-equilibrium segregation is a kinetic process, the complexes leading to this segregation may diffuse independently to the grain boundary. In a manner similar to equilibrium segregation, the two solutes, however, need to redistribute at the grain boundary in the light of their binding energies with the boundary. With Eqs. (8)–(11), one can obtain P ) CbP∗ = (CbP − Ceq

P Ceq P Ceq

Mo ) CbMo∗ = (CbMo − Ceq

Mo + Ceq

P + Ceq

Mo Ceq P Ceq

Mo + Ceq

Mo + Ceq

(12)

(13)

As mentioned above, Eq. (7) evaluates the maximum concentration of non-equilibrium segregation in dilute binary alloys. As

X.-M. Chen et al. / Materials Science and Engineering A 528 (2011) 7663–7668

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Table 1 Data used in the theoretical calculations.  ˝o (m3 ) Qf (eV)

ˇ (s)  (Jm−3 ) b0 (m) DcP (m2 s−1 ) DcMo (m2 s−1 ) DsP (m2 s−1 ) DsMo (m2 s−1 )

0.1 [23] 1.21 × 10−29 [23] 1.73 [32,33] 72.5 [34] 5.86 [25] 8.1 × 1010 (1–0.91(T-300)/1810) [23] 2.58 × 10−10 [23] 1.1 × 10−5 exp (–1.63/kT) [23,35] 1.1 × 10−5 exp (–1.49/kT) [23,35] 2.83 × 10−6 exp (–3.03/kT) [36] 1.55 × 10−3 exp (–2.73/kT) [36]

L (␮m) P Qsv (eV) Mo Qsv (eV) d0 (nm) Dv (m2 s−1 ) ı B A0 (s−1 ) Qdef (eV) n a (MPa−1 )

stated in Ref. [29], the absolute concentration of complexes is proportional to the solute concentration and the exponential term containing the solute-vacancy binding energy. Thus, the maximum concentrations of non-equilibrium grain boundary segregation of P and C Mo , could be evaluated by P and Mo in a ternary system, Cbm bm [28] P P Cbm = Ceq + CgP

 ×

P Qsv Qf



1+

Cex Cth





P /kT ) CgP exp(Qsv

(14)

P /kT ) + C Mo exp(Q Mo /kT ) CgP exp(Qsv g sv

Mo Mo Cbm = Ceq + CgMo

 ×

Mo Qsv Qf



1+

Cex Cth



Mo /kT ) CgMo exp(Qsv

(15)

P /kT ) + C Mo exp(Q Mo /kT ) CgP exp(Qsv g sv

P and Q Mo are the phosphorus-vacancy and molybdenumwhere Qsv sv vacancy binding energies, respectively. The process to gain the maximum concentration is controlled by the diffusion of complexes, and the kinetic equation is described by [7,8,28] i Cbi (t) − Ceq i i Cbm − Ceq

 = 1 − exp

4Dci t ˛2i d0

2



erfc

2

Dci t ˛i d0



(i = P, Mo)

(16)

where Cbi (t) is the boundary concentration of P or Mo at time t, Dci is the diffusion coefficient of P-vacancy complexes or Mo-vacancy complexes in the matrix; d0 is the boundary thickness, and ˛i is i /C i . In Eq. (16), the enrichment ratio of P or Mo, given by ˛i = Cbm g erfc(x) = 1 − erf(x), where erf(x) is the error function of x. A further refinement to the model is made by introducing the concept of a critical time. At this critical time, the supply of solute atoms from the grain interior becomes exhausted. After that, the forward flux of complexes to the grain boundary is balanced by the backward flux of solute atoms caused by the non-equilibrium concentration gradient created by segregation. The factors controlling the critical time are the diffusivities for both complexes and solute atoms in the matrix as well as the grain size (L). The critical time is expressed as [7,30] tci =

L2 ln(Dci /Dsi∗ ) 4ı(Dci − Dsi∗ )

(i = P, Mo)

70 0.41 [37] 0.30 [37] 1 [9,27] 3.3 × 10−5 exp(−1.49/kT) [23] 11.5 [30] 2.7 [23] 1.56 × 1011 [25] 3.24 [25] 5.1 [25] 1.2 × 10−2 [25]

effect of deformation-induced supersaturated vacancy enhanced diffusion is dominant [31], and the vacancy enhanced diffusion coefficient is given by [27,31]



Dsi∗ = Dsi 1 +

Cex Cth



(i = P, Mo)

(18)

where Dsi is the diffusion coefficient of P or Mo in the matrix. As mentioned above, there is no dynamic recrystallization occurring in the specimen deformed by 10% at a strain rate of 2 × 10−3 s−1 . Therefore, the theoretical model is valid to predict the non-equilibrium segregation levels of phosphorus and molybdenum during tensile deformation. Data used in the calculations are listed in Table 1. The predicted boundary concentrations of phosphorus and molybdenum are shown in Fig. 7 as a function of deformation strain with a strain rate of 2 × 10−3 s−1 at 900 ◦ C. The experimental values are also plotted for comparison. Clearly, there is quite a reasonable fit between predictions and observations. As shown in Fig. 7, the boundary concentrations of P and Mo are evidently enhanced after hot deformation (10% strain) at 2 × 10−3 s−1 . During deformation, the boundary levels of P and Mo increase evidently with increasing strain at the beginning of deformation. After then, they increase slightly with further increasing strain until a steady value is achieved at about 6% strain. As seen in Eqs. (14) and (15), the deformation-induced non-equilibrium segregation depends on the formation of vacancy-solute complexes, which is strongly related to the solute-vacancy binding energy. According to Ref. [37], the chromium-vacancy binding energy in ␥-Fe is 0.036 eV which is much smaller than the phosphorus-vacancy binding energy (0.41 eV) and molybdenum-vacancy binding energy

(17)

where tci is the critical time of P or Mo; ı is a dimensionless material constant, termed the critical time constant; Dsi∗ is the deformationenhanced diffusion coefficient of P or Mo. During high-temperature plastic deformation, supersaturated vacancies were produced and also dislocation density was increased drastically by multiplication. In general, solute diffusion in a dilute alloy may be enhanced by supersaturated vacancies and pipe diffusion along dislocations. It is demonstrated that the

Fig. 7. Predicted P and Mo boundary concentrations as a function of deformation strain at 900 ◦ C. The experimental values determined by FEGSTEM microanalysis and corrected by the convolution method are also plotted for comparison.

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(0.30 eV). Therefore, deformation-induced grain boundary segregation of Cr should be much smaller as compared with P and Mo, so that the non-equilibrium segregation phenomenon of Cr was not detected. As seen in Fig. 7, there is some discrepancy between the predicted and experimental values. Normally, the model prediction result is highly dependent on the accuracy of data used in the calculations. Unfortunately, the values of some parameters, such as vacancy-solute binding energy and diffusion coefficient of vacancysolute complexes for the experimental 1Cr0.5Mo steel, are not available and just estimated from the relevant literature. This may be the main reason for the discrepancy between the predicted and experimental results. 5. Conclusions Non-equilibrium grain boundary segregation of Mo and P during high temperature plastic deformation was studied by FEGSTEM microanalysis for a P-doped 1Cr0.5Mo low alloy steel. Prior to deformation at 900 ◦ C, there was some equilibrium segregation for Mo and P, while the segregation was evidently enhanced for the specimens deformed by 10% at a strain rate of 2 × 10−3 s−1 . A kinetic model with consideration of site competition in grain boundary segregation between two solutes was established to explain the present experimental results. Model predictions show a reasonable fit with the observations. Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant No. 50671033) and the Science and Technology Foundation of Shenzhen (Grant No. JC200903120199A). References [1] B. Mintz, ISIJ Int. 39 (1999) 833. [2] K. Yasumoto, Y. Maehara, S. Ura, Y. Ohmori, Mater. Sci. Technol. 1 (1985) 111.

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