Low-temperature martensitic transformation and deep cryogenic treatment of a tool steel

Materials Science and Engineering A 527 (2010) 7027–7039

Contents lists available at ScienceDirect

Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea

Low-temperature martensitic transformation and deep cryogenic treatment of a tool steel A.I. Tyshchenko a , W. Theisen b , A. Oppenkowski b , S. Siebert b , O.N. Razumov a , A.P. Skoblik a , V.A. Sirosh a , Yu.N. Petrov a , V.G. Gavriljuk a,∗ a b

G.V. Kurdyumov Institute for Metal Physics, 03142 Kiev, Ukraine Ruhr University Bochum, Chair of Materials Technology, 44780 Bochum, Germany

a r t i c l e

i n f o

Article history: Received 23 April 2010 Received in revised form 12 July 2010 Accepted 19 July 2010

Keywords: Martensitic transformation Tool steels Deep cryogenic treatment TEM Mössbauer spectroscopy Internal friction X-ray diffraction

a b s t r a c t The tool steel X220CrVMo 13-4 (DIN 1.2380) containing (mass%) 2.2C, 13Cr, 4V, 1Mo and the binary alloy Fe–2.03 mass% C were studied using transmission electron microscopy, Mössbauer spectroscopy, X-ray diffraction and internal friction with the aim of shedding light on processes occurring during deep cryogenic treatment. It is shown that the carbon atoms are essentially immobile at temperatures below −50 ◦ C, whereas carbon clustering in the virgin martensite occurs during heating above this temperature. An increase in the density of dislocations, the capture of immobile carbon atoms by moving dislocations, the strain-induced partial dissolution of the carbide phase, and the abnormally low tetragonality of the virgin martensite are found and interpreted in terms of plastic deformation that occurs during martensitic transformation at low temperatures where the virgin martensite is sufficiently ductile. © 2010 Elsevier B.V. All rights reserved.

1. Introduction Martensitic transformation in carbon steels at low temperatures has some special features. Kurdyumov and Maximova [1,2] were the first to show that, in contrast to the athermal and burst character of martensitic formation at ambient and elevated temperatures, its kinetics at temperatures below RT are isothermal. Moreover, as shown by studies of steel that has the martensitic point Ms below room temperature [2], rapid cooling in liquid nitrogen retains a fully austenitic structure, whereas the isothermal martensitic transformation starts during subsequent heating with holding at temperatures above 77 K. As firstly obtained in [3], the carbon martensite formed at low temperatures is characterized by an abnormally low c/a ratio, except for steels with high nickel (e.g. [4]) and aluminum (e.g. [5]) contents. The low tetragonality was interpreted by means of two main hypotheses based on ideas about the partial location of carbon atoms in the tetrahedral interstitial sites as a result of the ␥ → ␣

∗ Corresponding author at: Department of Physical Principles for design of Steels and Alloys, G.V. Kurdyumov Institute for Metal Physics, Vernadky Blvd. 36, UA03680, 142 Kiev, Ukraine. Tel.: +380 44 4243310; fax: +380 44 4243310. E-mail address: [email protected] (V.G. Gavriljuk). 0921-5093/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2010.07.056

transformation through the intermediate ␧ phase [6] and that of twinning on the {0 1 1} planes, which shifts some of the carbon atoms in the octahedral sites on the a and/or b axes of the martensitic lattice without changing the location of the metal atoms [7]. The third feature of martensite formed at low temperatures is the precipitation of orthorhombic ␩-carbide, and not hexagonal ␧-carbide, during subsequent tempering (e.g. [8–11]). This precipitation is thought to result from the migration of carbon atoms towards the dislocations during long holding at low temperatures. The carbon clouds around the dislocations serve as nuclei for the ␩-carbide, which is consistent with previous studies by Hirotsu and Nagakura [12] who first observed rod precipitates of ␩-carbide in the vicinity of dislocations in the tempered high-carbon martensite. The ␩-carbide was also found at early stages of decomposition in the iron–carbon martensite using the synchrotron radiation [13]. It is relevant to note that precipitation of orthorhombic carbide in the high-carbon martensite was theoretically predicted by Bagaryatsky [14]. The finely dispersed and evenly distributed ␩-carbide particles are considered to be the main reason for the significantly (more than twice) improved abrasive wear resistance of high-carbon tool steels as a result of deep cryogenic treatment (DCT). At present, little is understood about the physical background of DCT, and a number of published papers contain contradictory and even mutually exclusive data and conclusions.

7028

A.I. Tyshchenko et al. / Materials Science and Engineering A 527 (2010) 7027–7039

For instance, ␩-carbide is found in [10,11] to be precipitated in the freshly formed martensite during its subsequent tempering between 200 and 540 ◦ C. In contrast, as stated in [15], this precipitation already takes place during deep cooling of tool steels. According to [16], additional fine carbides are precipitated as temperature descends to −140 ◦ C. Recently, Das et al. [17] presented data of scanning electron microscopy about two types of secondary carbides existing in the quenched CrMoV tool steel, small and large, both of each increase their fraction with holding time at 77 K. The role of the ␥ → ␣ transformation in the improved wear resistance is also a controversial issue. According to [18], the beneficial effect of DCT is not related to the martensitic transformation because the improvement in the properties is observed if the holding (“soaking”) of steel is carried out at temperatures at which the martensitic transformation is already completed, and the lower the holding temperature the more significant the DCT effect is. Therefore, the relaxation of stresses in martensite is considered to be the main process occurring during DCT (e.g. [19]). Somewhat contradictory to this statement is the observation in [20] that the holding time is more important than the decrease in temperature (163 K for 24 h is more effective than 93 K for 6 h). It is relevant to note that martensitic transformation never goes to completion, and the retained austenite always exists in the structure of high-carbon martensites. This paper aims to present some new results concerning processes taking place during the lowtemperature martensitic transformation in high-carbon steels and thus shed light on some disputed points of deep cryogenic treatment.

ter, which resulted in 32% martensite. Thereafter, the spectra were measured in the transmission mode at the temperature of 65 K after successive heating cycles within the temperature range between 65 and 293 K with holding for 10 min at each temperature. Tetragonality of virgin and aged martensites was measured in CoK␣ radiation using an X-ray diffractometer with the HUBER goniometer –2, having the resolution of 0.005◦ . The fitting of diffraction patterns was carried out using the program ProFit. The samples were also analysed by mechanical spectroscopy to study the interaction between carbon atoms and dislocations. Internal friction spectra were measured in the temperature- and amplitude-dependent damping modes within the temperatures between −196 ◦ C and RT using an inverted pendulum at frequencies of about 1–5 Hz. Setting up of specimens and cooling to −196 ◦ C in the pendulum took less than 15 min. 3. Results 3.1. Transmission electron microscopy of steel X220CrVMo 13-4 The back scattering electron image of martensite as-quenched at room temperature was obtained at a low magnification in order to get a view of the not-dissolved carbide particles (Fig. 1a). Three types of particles different in their size can be distinguished, which is generally consistent with the statement made in [17] about three types of carbides, namely the primary ones and large and small secondary ones. A more detailed view was obtained using the sec-

2. Experimental A tool steel X220CrVMo 13-4 (DIN 1.2380) containing (mass%) 2.2C, 13Cr, 4V, 1Mo was used for the studies. The specimens used for TEM and X-ray diffraction had the size of 10 mm × 10 mm × 0.1 mm, those for Mössbauer spectroscopy and internal friction measurements were 10 mm × 10 mm × 0.03 mm and 0.8 mm × 0.8 mm × 60 mm, respectively. These specimens were solution-treated at 1080 ◦ C for 20 min under protective pure argon atmosphere and cooled using the flow of the cold argon. Immediately after cooling, some of the specimens were cooled to −196 or −150 ◦ C with holding at these temperatures for 24, 36 or 48 h. A JEM-2000 FXII transmission electron microscope, operating at a voltage of 200 kV, was used for structural studies in the transmission mode, as well as for obtaining the back-scattered electron or secondary electron images. A computer program LINK EDP served for the analysis of diffraction patterns. The energy dispersive X-ray spectrometer (EDS) and the quantitative program LINK RTS 2/FLS with a virtual standard package were used for the local chemical analysis. The maximum error did not exceed ±5%. Mössbauer spectra were recorded in the transmission mode. A WISSEL Mössbauer spectrometer and a source of ␥ quanta 57 Co in the Cr matrix with an activity of 100 mCi were used for measurements. The equipment was characterized by the line-width of 0.22 mm/s for the ␥ quanta source. The distribution of hyperfine fields was obtained using the programme DISTRI developed by Prof. Rusakov, Moscow State University, Russia. In order to exclude the effect of alloying elements and carbide particles, which make Mössbauer spectra rather complicated, we studied the state of the carbon atoms in the virgin martensite using a binary Fe–C solid solution. A pure iron foil of 20 ␮m in thickness was carburized at 1150 ◦ C under flowing methane followed by quenching in water, which allowed us to obtain the fully austenitic state at RT. According to X-ray diffraction data, the carbon content in the obtained austenite was 2.03 mass%. The specimen was then cooled to 4.5 K in the cryostat of the Mössbauer spectrome-

Fig. 1. (a) Back scattering electron image of steel X220CrVMo 13-4 after solution treatment at 1080 ◦ C for 20 min and quenching in water; (b) the same: secondary electron image.

A.I. Tyshchenko et al. / Materials Science and Engineering A 527 (2010) 7027–7039

7029

Fig. 2. (a) Carbide Me7 C3 in steel X220CrVMo 13-4 after holding in liquid nitrogen for 48 h. Points of local chemical analysis are marked by 1–3; (b) the electron ¯ hcp . diffraction from carbide particle, the zone axis [1 0 2]

ondary electron image (Fig. 1b). The local chemical analysis of these particles revealed a different content of Cr, V and Mo (see Table 1). Their nature was clarified using transmission mode with the corresponding chemical analysis (see Figs. 2–4 and Table 1). The primary carbide, as particles of 5–10 ␮m in size, was identified as Me7 C3 carbide with the hcp crystal lattice (Fig. 2). The small secondary carbide particles of 0.1–1 ␮m in size belong to the cubic carbide MeC (Fig. 3), whereas the large secondary carbide precipitated as globules with size of 1–3 ␮m is the hexagonal carbide Me2 C (Fig. 4). It is relevant to note that weaker reflections in the diffraction patterns of MeC

Fig. 3. (a) Carbide MeC in steel X220CrVMo 13-4 after holding in liquid nitrogen for 48 h. Points of local chemical analysis are marked by 1–3; (b) the electron diffraction ¯ fcc . from carbide particle, the zone axis [1 0 1]

and Me2 C carbides, as compared to that of Me7 C3 carbide, can be due to their stronger chemical stability, which results in a higher thickness of particles and, correspondingly, a weaker penetrability for electrons and stronger diffuse electron scattering. Fig. 5 demonstrates a difference in the structure of martensites obtained at room and low temperatures. A high density of twins along with dislocations and the rather large size of martensitic

7030

A.I. Tyshchenko et al. / Materials Science and Engineering A 527 (2010) 7027–7039

Table 1 Identification of carbides and the content (at.%) of Cr, V, Mo in the carbides and in the matrix (see points 1–3 in Figs. 2–4). Figure

Carbide type, size

Crystal lattice

Point of analysis

Cr

V

Mo

Fe

Fig. 2

Me7 C3 5–10 ␮m

hcp

Fig. 3

MeC 0.1–1 ␮m

fcc

Fig. 4

Me2 C 1–3 ␮m

hcp

1 2 3 1 2 3 1 2 3

46.6 8.7 8.8 19.6 8.3 8.9 11.3 7.3 7.9

12.3 0.8 0.8 63.2 0.6 0.7 84.1 0.3 0.3

1.1 0.5 0.6 2.3 0.6 0.6 2.5 0.6 0.7

40.0 90.0 89.8 14.9 90.5 90.7 2.2 91.8 91.1

domains are typical for the martensite quenched at RT (Fig. 5a). Finer twinning and a smaller size of the martensitic domains are distinguishing features of martensite transformed at −150 ◦ C (Fig. 5b). The analysis of electron diffraction has disclosed a number of fine cementite particles in the martensite obtained by water quenching (see Fig. 6). Such cementite particles could also be observed after deep cryogenic treatment. Again, the intensity of cementite reflections is rather poor (Fig. 6b), which is not surprising taking into account the small cementite fraction. Nevertheless, it is sufficient for obtaining the dark field image (Fig. 6c), which is the first observation of cementite in the as-quenched not tempered martensite of tool steels. 3.2. Carbon in the virgin Fe–2.03%C martensite A binary Fe–C solid solution was used in order to shed light on the mobility of carbon atoms in the virgin martensite, which can be important for the interpretation of phenomena occurring during DCT and for discussion of mechanisms responsible for the abnormally low tetragonality of virgin Fe–C martensite. Fig. 7 shows transmission Mössbauer spectra of the binary Fe–2.03 mass% C alloy after quenching from 1150 ◦ C in water followed by cooling to liquid helium and successive heating to different temperatures with a holding time of 10 min at each temperature. All measurements were carried out at −208 ◦ C. The hyperfine structure parameters are given in Table 2 for the virgin and aged martensites. Fig. 8 shows the outer line of the Mössbauer spectrum (nuclear transition −1/2 → −3/2) after holding at above mentioned temperatures. As seen in Figs. 7 and 8, the spectrum of virgin martensite consists of six sextets with different values of the hyperfine field, isomer shift and quadrupole interaction (see Table 2). Sextets 1, 2 and 3, 4, and 5, 6 can be combined into groups A, B, C, respectively, as carried out in many recent studies of Fe–C martensites. The seventh component with Hi = 34.6 T, which is close to that in pure iron measured at −208 ◦ C, appears after aging at RT. 3.2.1. Interpretation of Mössbauer spectra The virgin and aged Fe–C martensites were measured in a number of Mössbauer studies (see e.g. [21–30]). So far, it is hardly possible to carry out ab initio calculations to obtain hyperfine

structure parameters in such multicomponent nuclear gamma resonance spectra. It is thus not surprising that the available interpretations differ significantly with respect to attributing spectral components to possible atomic configurations of iron and carbon atoms. Gielen and Kaplow [21] studied only aged Fe–C martensite and interpreted the spectrum as consisting of two sextets corresponding to pure iron atoms Fe0 and iron atoms having two carbon atoms as nearest neighbors, Fe2 (see schemas in Fig. 9). Moriya et al. [22], as well as Lesoille and Gielen [23] applied the hypothesis given in [6] to the carbon distribution in the virgin martensite and attributed component B to iron atoms with carbon in the tetrahedral sites. It is relevant to note that neutron diffraction studies (e.g. [24]) do not reveal carbon in the tetrahedral sites of virgin martensite. Furthermore, the location of some carbon atoms in the tetrahedral sites would cause two additional sextets in the spectra of the virgin martensite that should disappear during ageing, which was not observed. Choo and Kaplow [25] and de Cristopharo and Kaplow [26] suggested a repulsive distribution of carbon in the virgin martensite and interpreted components A, B, C as correspondingly belonging to the iron atoms as third, second, and first neighbors of a carbon atom in the octahedral site. Ino et al. [27] also attributed the components C and B to the iron atoms as first and second neighbors of iron atoms. One of the arguments in this interpretation was that the C component cannot belong to iron atoms in carbon clusters because they do not exist in the virgin martensite. According to [25–27], carbon clustering occurs only at room temperature resulting in the formation of an Fe4 Cx structure. However, as shown in [28], where the Monte Carlo simulation of the Fe–C solid solution for obtaining the C–C interaction energies in the first and second co-ordination spheres, which could be consistent with Mössbauer data, were performed, the pairs of carbon atoms in neighboring interstitial sites exist in the Fe–C austenite. Therefore, such pairs should be inherited by the virgin martensite as a result of the diffusionless transformation. A detailed interpretation was given by Genin et al. [29,30], who fitted the spectra of the virgin and aged Fe–C martensites using a combination of E, A, Ba , Bc , C, D, F components. According to [29,30], the component E with the highest hyperfine field of 37.6 T represents an “extended” Fe–C multiplet in which an iron atom has two carbon atoms at the shortest possible distances of 2.0 A˚ and sev-

Table 2 Patrameters of hyperfine structure in Mössbauer spectrum of Fe–2.03 mass% C for the virgin martensite. Sextet 7 appears after ageing at 20 ◦ C. Measurements at −208 ◦ C. Sextet

Hyperfine field (T)

1 2 3 4 5 6 7

37.4 35.7 33.5 31.6 28.0 27.8 34.6

a

In relation to ␣-iron.

± ± ± ± ± ± ±

0.2 0.3 0.4 0.4 0.3 0.3 0.15

Isomer shift,a ı ± 0.005 (mm/s)

Quadrupol interaction 4ε (mm/s)

0.207 0.157 0.124 0.229 0.197 0.185 0.096

0.027 0.012 0.076 −0.210 −0.512 0.273 0.009

± ± ± ± ± ± ±

0.005 0.005 0.01 0.01 0.01 0.01 0.01

A.I. Tyshchenko et al. / Materials Science and Engineering A 527 (2010) 7027–7039

Fig. 4. (a) Carbide Me2 C in steel X220CrVMo 13-4 after holding in liquid nitrogen for 48 h. Points of local chemical analysis are marked by 1–3; (b) the electron diffraction from carbide particle, the zone axis [1 6 4]hcp .

˚ Genin et al. eral iron atoms at enlarged distances of 2.86 and 2.66 A. suppose that this dilatation of the iron lattice is sufficient to counterbalance the effect of two carbon neighbors which, in the absence of dilatation, should decrease the hyperfine field at the iron nucleus at least by 6 T (see a corresponding relation in [31]). The component A with Hi = 36.2 T is interpreted by Genin et al. as belonging to “pure” iron atoms located sufficiently far from the carbon atoms. The components Ba and Bc with Hi equal to 33.1

7031

Fig. 5. (a) Structure of martensite in steel X220CrVMo 13-4 as-quenched at RT; (b) the same after subsequent holding at −150 ◦ C for 24 h.

and 33.4 T are attributed to the iron atoms with an isolated carbon atom (like Fe1 and Fe1 in Fig. 9a). In other words, the authors [29,30] suggest that the overlapping of wave electron functions is the same in the atomic pairs Fe1 –C and Fe1 –C, in spite of the fact that carbon atoms located in the octahedral sites push Fe1 atoms much more strongly than Fe1 atoms, thereby creating tetragonality in the iron lattice.

7032

A.I. Tyshchenko et al. / Materials Science and Engineering A 527 (2010) 7027–7039

¯ of the orthorhombic lattices (c) dark Fig. 6. (a) Structure of martensite as-quenched at RT; (b) diffraction pattern, the zone axis [1¯ 1 1] of the body centered cubic and [3 6¯ 1] field image in the light of cementite reflection [2 1 0] .

Finally, the components C and D with Hi equal to 28.3 and 26.2 T are attributed to “isolated multiplets”, i.e. to iron atoms having two carbon atoms in the nearest neighborhood (Fe2 in Fig. 9c or d). The difference between C and D configurations is thought to come from the effect of next carbon neighbors in the D case. There also exists

a weak component F with Hi = 16.5 T, which is ascribed to the iron atoms with three carbon nearest neighbors. One can conclude from the above-performed analysis that, so far, in relation to Mössbauer spectra of virgin and aged Fe–C martensites, there is no interpretation that is fully satisfactory.

A.I. Tyshchenko et al. / Materials Science and Engineering A 527 (2010) 7027–7039

7033

Fig. 7. Mössbauer spectra of the alloy Fe–2.03 mass%C after quenching in water, cooling to 4.5 K (as-quenched), and subsequent holding for 10 min at −150, 0, and 20 ◦ C. All measurements were carried out at 65 K.

The change in the spectra caused by heating the virgin martensite from −208 ◦ C to RT provides some hints for their interpretation. This change is seen after heating at −50 ◦ C and higher temperatures (see Figs. 7 and 8). The component B essentially disappears, whereas the component C increases in its intensity. Due to ageing at RT, the outer lines are shifted to the gravity center of the spectrum, which is obviously caused by a new component 7. As a result, component 1, with the highest hyperfine field, becomes more visible. Based on the above presented data and taking into account the change in the spectra due to the ageing of martensite, an interpretation of the Mössbauer spectra can be proposed which is similar to that in [29,30], but with some essential distinctions. Sextet 1 belongs to pure iron atoms that are located far away from the carbon atoms as nearest neighbors. The increase in the hyperfine field in comparison with the ␣-iron is obviously caused by lattice dilatation. This is component E in [29,30], that was attributed to iron atoms having two carbon neighbors at the closest distances. We do not believe that lattice dilatation can counterbalance the giant decrease, about 6 T, in the hyperfine field caused by carbon atoms as nearest neighbors. Sextets 2–4 come from the iron atoms as third, second, and first neighbors of a single carbon atom in the octahedral site on the c  axis (iron atoms Fe1 , Fe1 , Fe in Fig. 9a). It is hardly possible that 1 sextets 2 and 3 (Ba and Bc in [29,30]) could have the same hyperfine fields because overlapping of the iron and carbon electron shells is quite different for the Fe1 and Fe1 atoms. It also follows from the spectra in Figs. 7 and 8 that partitioning of single carbon atoms on the c and a or b axes, as proposed in [7] for interpretation of abnormally low tetragonality, has no place. This would lead to an increase in the number of corre-

Fig. 8. The outer line (nuclear transition −1/2 → −3/2) of the Mössbauer spectra of the alloy Fe–2.03 mass%C after quenching in water, cooling to 4.5 K (as-quenched) and subsequent holding for 10 min at −150, −100, −50, 0, 20 ◦ C. All measurements were carried out at 65 K.

Fig. 9. Configurations of iron and carbon atoms as derived from the interpretation of Mössbauer spectra. H is the axis of easy magnetization, q is the electric field gradient.

7034

A.I. Tyshchenko et al. / Materials Science and Engineering A 527 (2010) 7027–7039

Fig. 10. (a) Mössbauer spectrum of steel X220CrVMo 13-4 after solution treatment at 1080 ◦ C and quenching at RT; (b) distribution of hyperfine fields in the martensite.

Fig. 11. (a) Mössbauer spectrum of steel X220CrVMo 13-4 after solution treatment at 1080 ◦ C, quenching at RT and subsequent holding at −196 ◦ C for 48 h; (b) distribution of hyperfine fields in the martensite.

sponding sextets due to the difference in quadrupole interactions ε = e2 qQ(3 cos2  − 1)/8, where e and Q are the electron charge and the iron nuclear quadrupole moment, respectively, and  is the angle between the electric field gradient q and the direction of easy

magnetization axis H. The angle  should be equal to zero for the iron atoms on the c axis (see Fig. 9a) and 90◦ for those on the a or b axes (see Fig. 9b). An additional argument was given by Ino et al. [27], who have shown that the exchange energy for keeping the

Fig. 12. (a) Mössbauer spectrum of steel X220CrVMo 13-4 after solution treatment at 1080 ◦ C, quenching at RT and subsequent holding at −150 ◦ C for 24 h; (b) distribution of hyperfine fields in the martensite.

A.I. Tyshchenko et al. / Materials Science and Engineering A 527 (2010) 7027–7039

7035

Fig. 13. Mössbauer spectrum of steel X220CrVMo 13-4 after solution treatment at 1080 ◦ C, quenching at RT, ageing at RT for 1 week and subsequent holding at −196 ◦ C for 24 h.

spins parallel each other on the c axis is two orders of magnitude higher than the anisotropic energy by which the direction of a spin is turned toward a carbon atom located on the a or b axes. Thus, the pairs of non-parallel spins in the martensite cannot be formed. Sextets 5 and 6 belong to the iron atoms having two carbon atoms as nearest neighbors with the angle  equal to zero (Fig. 9c for sextet 5) and 90◦ (Fig. 9d for sextet 6, see also the values of ε in Table 2). This is similar to the interpretation of C and D components in [29,30] with the only difference that sextets 5 and 6 have the same hyperfine field but different values of quadrupole interaction because of different  values. 3.2.2. Carbon distribution in the virgin and aged martensites Based on the proposed interpretation of Mössbauer spectra, the following preliminary characteristics of carbon distribution in the virgin martensite and carbon behavior during ageing can be assumed: (i) The hypotheses attributing the abnormally low tetragonality of virgin martensite to the occurrence of carbon atoms in the tetrahedral sites [6] or their distribution on the a, b, or c sublattices of octahedral sites [7] are not consistent with the hyperfine structure of Mössbauer spectra and their evolution during the heating of virgin martensite. (ii) It is clear from the spectra presented in Figs. 7 and 8 that, at holding temperatures below −50 ◦ C, nothing changes in the virgin martensite, i.e. the carbon atoms remain immobile. If account is taken of the fact that carbon migration exponentially decreases with decreasing temperature, it can be concluded that carbon atoms cannot move towards the dislocations during deep cryogenic treatment of tool steels, as has been suggested in a number of DCT studies (see Section 1). (iii) The decrease in intensity of sextets 3 and 4 and the growth of sextets 5 and 6 starting from holding at −50 ◦ C is evidence of carbon clustering, which is consistent with the available observations of the modulated structure in the aged highcarbon martensites (e.g. [32,33]). Sextet 7, with the hyperfine field approaching that of pure iron, appears due to carbon clustering. Sextet 1 with the increased hyperfine field in comparison with the pure ␣-iron remains after ageing, which can be attributed to dilatation at the coherent boundaries between the carbon-rich and carbon-depleted areas in the modulated aged martensite.

3.3. Change in the phases of steel X220CrVMo 13-4 due to cryogenic treatment Mössbauer spectra of steel X220CrVMo 13-4 (DIN 1.2380) were measured after solution treatment at 1080 ◦ C followed by quenching at RT and subsequent holding in liquid nitrogen or at −150 ◦ C. As example, some data are presented in Figs. 10–13. The spectra consist of a single line, which belongs to the retained austenite, a doublet with a quadrupole splitting of about 0.6 mm/s, which is attributed to the carbide phase, and four sextets of martensite. The fitting of the martensitic component by four sextets was made based on the distribution of hyperfine fields (see Fig. 10b–13b). The areas under spectra components, as determined from Mössbauer spectra, are given in Table 3. The mean square amplitude of atomic vibrations is not remarkably different in the austenitic and martensitic phases, however it is significantly decreased in the carbide lattice because of prevailing covalent interatomic bonds. Therefore, the probability of gamma quanta absorption is much higher in the carbide phase, so that the relative area under carbide doublet in Mössbauer spectrum is higher than the fraction of carbides in the studied steel. Thus, the change in the area under spectra components due to cryogenic treatment allows to only obtain a knowledge about the change of fractions of corresponding phases, not their precise amount. In relation to the martensitic phase (see Figs. 10b–13b), the distribution of hyperfine fields reveals four intensive components in the martensitic spectrum with a rather large half-width of lines that are in fact attributed to several overlapped components, which is due to the effect of first, second, and so on, neighboring solute atoms of different kinds on the hyperfine field at the nuclei of the iron atoms. Each single carbon atom as the nearest neighbor of an iron atom in the martensite lattice decreases the hyperfine field at Table 3 Relative areas (%) under components of martensite, retained austenite and casrbide and under the lines Fe0 and Fe1 in the martensitic component of Mössbauer spectra in steel X220CrVMo 13-4. Data for Fe0 and Fe1 are normalized to 100% of martensite. Cooling after solution treatment

Martensite

RA

Carbide

Fe0

Fe1

Quenching at RT RT → −196 ◦ C (24 h) RT → −196 ◦ C (36 h) RT → −196 ◦ C (48 h) RT → −150 ◦ C (24 h) RT(1 week) → −196 ◦ C (24 h)

81.7 86.6 87.0 87.3 89.1 85.6

7.7 4.1 3.9 3.7 3.5 5.8

10.6 9.3 9.1 9.0 7.4 8.6

27.2 24.3 22.8 19.9 15.2 21.2

34.0 37.3 38.8 43.3 46.3 36.5

7036

A.I. Tyshchenko et al. / Materials Science and Engineering A 527 (2010) 7027–7039

its nucleus by nearly 3.0 T (e.g. [31,34]). For chromium in ␣-iron, this effect is equal to ∼2.7 T [35], and for vanadium it is ∼2.6 T [36]. A detailed interpretation of the hyperfine field distribution in the FeCrVC martensite is not reliable owing to the high complexity of its chemical composition and problems concerned with the occurrence of the carbide phase. As a rough approximation, in accordance with their hyperfine fields, four resolved sextets of the spectrum are denoted as belonging, respectively, to iron atoms having no carbon, chromium, and vanadium (Fe0 ) and one (Fe1 ), two (Fe2 ) or three (Fe3 ) carbon or chromium or vanadium atoms in the nearest neighborhood. This interpretation does not pretend to be any exact clarification of the atomic distribution in the studied martensite; however, it allows us to derive some important features of processes occurring during the low-temperature martensitic transformation. As expected, the fraction of retained austenite decreases after cooling below room temperature (compare Fig. 10a with Figs. 11a and 12a). However, it is unusual that, in spite of the same conditions of solution treatment, the cooling in liquid nitrogen was accompanied by a decrease in the carbide fraction (see Table 3). This result suggests that the carbide retained after the solution treatment and quenching at RT is partly dissolved in the course of the low-temperature martensitic transformation and the larger the fraction of freshly formed martensite the more intense is the low-temperature carbide dissolution. The attempt was made to test whether the observed effect of deep cryogenic treatment occurs if the retained austenite is stabilized due to ageing at RT before cooling to low temperatures. Fig. 13 presents a Mössbauer spectrum obtained after ageing for 1 week at RT and subsequent holding at −196 ◦ C for 24 h. In comparison with the data for the same cryogenic treatment without preliminary ageing at RT (see Table 3), one can see that the stabilization of the retained austenite decreased the amount of the low-temperature martensite, which is natural. Unexpected is that, in case of preliminary ageing at RT, the effect of carbide dissolution increases. The change in the relative intensities of martensitic components Fe0 and Fe1 with increasing time of holding at −196 ◦ C and after holding for 24 h at −150 ◦ C is shown in Figs. 10b–12b and in Fig. 14 where the outer lines of the martensitic spectrum (nuclear transition +1/2 → +3/2) are presented. The numerical data are given in Table 3. It can be seen that, with increasing fraction of transformed virgin martensite, the intensity of component Fe0 decreases and the component Fe1 becomes more intensive. In other words, the content of alloying elements in the martensitic solid solution increases in the course of cryogenic treatment. This result is obviously related to the partial dissolution of carbides during the low-temperature martensitic transformation. It is also remarkable (see Figs. 11, 12, 14b and 14c, and Table 3) that, in relation to the concentration change in the martensitic solid solution and carbide dissolution, the treatment at −150 ◦ C is more effective than that in liquid nitrogen. 3.4. Interaction between carbon atoms and dislocations The amplitude- and temperature-dependent internal friction in steel X220CrVMo 13-4 was measured in order to study dislocation pinning by carbon atoms. In the absence of relaxation or hysteretic processes, the damping background is caused by the vibrations of dislocation segments (e.g. [37,38]). It is proportional to the area swept by dislocations for one cycle of vibrations, i.e. to dislocation velocity. With increasing strain amplitude, this area is expected to increase if the dislocations are free to move. Fig. 15 presents the amplitude-dependent internal friction in the studied steel measured immediately after cooling to the liquid nitrogen temperature and after subsequent holding at this temperature for 12 h. Holding

Fig. 14. Outer line Fe0 (nuclear transition +1/2 → +3/2) in the martensitic component of Mössbauer spectra measured after quenching of steel X220CrVMo 13-4 at RT (a) and holding at −196 ◦ C for 48 h (b) and at −150 ◦ C for 24 h (c).

in liquid nitrogen decreases the damping, particularly at increased strain amplitudes. This result suggests that the mobility of the dislocations decreases as the low-temperature holding time increases. The evolution of internal friction during heating after cooling in liquid nitrogen is shown in Fig. 16 at two different vibration frequencies. There are two peaks, the positions of which do not depend on the frequency. Thus, both of them are not associated with any relaxation processes. The first one is obviously caused by the isothermal martensitic transformation, i.e. it has a hysteretic nature. As a result of thermal

A.I. Tyshchenko et al. / Materials Science and Engineering A 527 (2010) 7027–7039

Fig. 15. Amplitude-dependent internal friction in steel X220CrVMo 13-4 after quenching at RT followed by cooling in liquid nitrogen (filled circles) and subsequent holding at this temperature for 12 h (open circles). Measurements were carried out at 85 K.

activation, the martensitic transformation is retarded or proceeds slowly at −196 ◦ C and is activated during subsequent heating. The same behavior of magnetic saturation was observed in [2]) during the holding of steel 100Mn6 at low temperatures. The second peak is located close to the temperature range of the ␥ relaxation (∼280 K) in the bcc iron, which is caused by the paired kink formation at screw dislocations (see e.g. [39]). However, such kinds of relaxation exist only in pure metals and disappear in the interstitial solid solutions. This is why, in contrast to the ␥ relaxation peak, the temperature of the second peak does not depend on the frequency. Taking into account that the mobility of dislocations increases with increasing temperature and, as follows from Mössbauer spectra (see Figs. 7 and 8), the carbon atoms in the iron–carbon martensite become sufficiently mobile starting from −50 ◦ C, this non-relaxation peak can thus be attributed to dislocations which become sufficiently mobile to move at temperatures above −100 ◦ C increasing thereby the damping background. The ageing of virgin martensite at temperatures above −50 ◦ C limits the amplitude of their vibrations. This interpretation suggests that, in spite of carbide dissolution in the course of cryogenic treatment, some part of dislocations produced by low-temperature martensitic transformation remains sufficiently free of carbon atoms. 3.5. Tetragonality of marensite after deep cryogenic treatment X-ray diffraction patterns of steel X220CrVMo 13-4 after quenching at RT and holding at −196 ◦ C for 24 h are shown in

Fig. 16. Change of internal friction with increasing temperature in steel X220CrVMo 13-4 with preliminary cooling in liquid nitrogen. Measurements were carried out at two frequencies 0.8 and 4.9 Hz, the strain amplitude is 0.5 × 10−5 .

7037

Fig. 17. Fragments of X-ray diffraction patterns of steel X220CrVMo 13-4 after quenching at RT (open circles) and holding at −196 ◦ C for 24 h (filled circles). Table 4 Tetragonality of martensites after quenching at RT and cryogenic treatment. Treatment

c/a

Quenching at RT RT → −196 ◦ C (24 h)

1.022 1.012

Fig. 17. It is seen that the cryogenic treatment causes a decrease in the tetragonality of martensite (see also Table 4). This result is consistent with many studies of the martensite in steels having the martensitic start temperature Ms below −50 ◦ C (see e.g. [3]). According to these observations, the martensite formed at low temperatures acquires a decreased tetragonality which increases during subsequent heating to RT, but does not reach the value obtained for steels with the same carbon content if the martensite is formed at RT. 4. Discussion 4.1. A model for processes occurring during the low-temperature martensitic transformation Questions regarding the physical nature of deep cryogenic treatment can be formulated as follows: (i) What is the reason for the increase in the density of dislocations due to holding at low temperatures, as it is manifested in a number of studies of DCT? (ii) If the clouds of carbon atoms at dislocations are the sites for precipitation of finely dispersed ␩-carbide at subsequent tempering, how the carbon atoms can reach the dislocations at low temperatures? (iii) What happens with carbide phases in the course of deep cryogenic treatment? The obtained experimental data are at variance with the available interpretations of DCT which are described in the Introduction. First, the martensitic transformation is not finished at temperatures of about −80 ◦ C that is the highest temperature for so-called “conventional treatment”. Moreover, at all, the full austenite-tomartensite transformation does not occur in the studied steel, as well as in any high-carbon steel. Second, the carbon atoms are essentially immobile at temperatures below −50 ◦ C and, therefore, they cannot migrate towards the dislocations for formation of carbon segregations which should be nuclei for subsequent ␩-carbide precipitation during tempering.

7038

A.I. Tyshchenko et al. / Materials Science and Engineering A 527 (2010) 7027–7039

Based on the analysis of the available data and taking into account the results obtained in the present study, the following model is proposed. The freshly formed virgin martensite is characterized by a decreased strength and comparatively high ductility (see e.g. [40–42]). The hardness, brittleness, and even microcracking [43] are acquired due to subsequent ageing at RT. Therefore, the plastic deformation is expected to occur during the martensitic transformation at low temperatures due to the volume effect of the martensitic transformation. In addition, the dislocation creep can proceed due to stresses caused by differing thermal coefficients of dilatation for austenite and martensite. The plastic deformation of virgin martensite should lead to two important consequences: (i) an increase in the dislocation density and (ii) the capture and transport of immobile carbon atoms by moving dislocations. The transport of interstitial atoms by the gliding dislocations is usually discussed in relation to hydrogen in metals (see e.g. [44]). A theoretical analysis for the dislocation transfer of interstitial atoms in crystals was recently made in [45]. Thus, the carbon clouds around the dislocations are not formed due to the migration of carbon atoms towards dislocations. They result from the capture of carbon atoms by dislocations generated and gliding during the plastic deformation. Because of high enthalpy of binding between carbon atoms and dislocations in the ␣-iron (about 0.8 eV, see e.g. [46]), these carbon clouds do not take part in the formation of the modulated structure during aging of virgin martensite and become the sites for the nucleation of the ␩-carbide particles at subsequent tempering, which is consistent with TEM studies of ␩ nucleation during tempering of a high-carbon martensite [12]. The results of the amplitude-dependent internal friction measurements in liquid nitrogen (Fig. 15) support the idea of carbon segregation at the dislocations during the low-temperature gliding of dislocations. The increase in the holding time in liquid nitrogen decreases the mobility of dislocations, which, at such a low temperature, can only result from the capture of immobile carbon atoms by moving dislocations. A reason for their movement is plastic deformation during the isothermal martensitic transformation and dislocation creep. 4.2. Carbide precipitates and their behavior in the course of cryogenic treatment The studied tool steel contains particles of primary carbide Me7 C3 , which is enriched in Cr, secondary carbides MeC and Me2 C, enriched in V, and fine cementite precipitates. The cubic MeC carbide obviously plays the role of the intermediate phase in the course of Me2 C precipitation. The presence of cementite is rather intriguing. It is reasonably to suppose that it precipitates within the temperature range between the martensitic point Ms and RT, where the cooling rate is rather low. The partial dissolution of the carbide phase, as follows from the decrease in the intensity of paramagnetic doublet in Mössbauer spectra, can be related to the effect of plastic deformation in the course of the low-temperature martensitic transformation. The strain-induced dissolution of cementite during plastic deformation of plain carbon steels was observed in 1972 using Mössbauer spectroscopy [47]. A review of the experimental data is given in [48,49]. In the 1990s, this effect was studied using the 3d APFIM technique (e.g. [50,51]]). In relation to the partial strain-induced dissolution of special carbides, it seems to be hardly possible for MeC and Me2 C carbides because they contain much vanadium. Even be dissolved in cementite, vanadium decreases its strain-induced dissolution because of strong increase of the interatomic bonds in cementite lattice

[48,49]. Stability of vanadium carbides should be much higher in comparison with the vanadium-containing cementite. The dispersed cementite particles can be obviously dissolved due to deformation in the course of low-temperature martensitic transformation. They are also observed after cryogenic treatment, and the exact extent of cementite dissolution cannot be determined by means of transmission electron microscopy. The strain-induced dissolution of the primary Me7 C3 carbides is a controversial issue. Chromium in the pearlitic carbon steels assists the dissolution of cementite under cold work [48,49] because it increases the enthalpy of binding between carbon atoms and dislocations [46], whereas its contribution to strengthening of interatomic bonds in the carbide lattice is not so large in comparison with vanadium. The change in the intensities of the martensite components due to the low-temperature martensitic transformation, namely weakening of the component Fe0 (see Fig. 14 and also Figs. 10b–12b), gives the evidence that the concentration of alloying elements in the martensite increases due to carbide dissolution. In accordance with the mechanism of strain-induced carbide dissolution, the carbon atoms of dissolved carbides are captured by dislocations and cannot affect the intensities of martensitic lines in Mössbauer spectra. Therefore, only substitutional atoms like Cr, V and Mo can be responsible for the decrease in the fraction of “pure iron” due to cryogenic treatment. The content of these elements in cementite cannot be different from their average content in steel, if to take into account that the fine cementite particles are precipitated during self-tempering below Ms temperature. Thus, the increase in the concentration of substitutional alloying elements in the solid solution occurs and it can be only due to dissolution of special carbides, most likely Me7 C3 . While discussing the obtained TEM images of carbide phases (Figs. 2–4), it is relevant to note that their partial dissolution due to plastic deformation cannot be clearly identified using TEM, which is a reason why the phenomenon of strain-induced cementite dissolution was first discovered not using TEM, but Mössbauer spectroscopy. Under cold work of pearlitic steels, the cementite is dissolved due to dislocations pulling the carbon atoms from the surface of cementite plates and, to a smaller extent, due to their cutting accompanied by the carrying-out of carbon atoms by the gliding dislocations. This is why the only effect observed by means of TEM is the blurred contrast at the ferrite-cementite interface (see e.g. [52]). The same blurred contrast can be observed at the surface of Me7 C3 (see Fig. 2a) and even in MeC and Me2 C (Figs. 3a and 4a) particles. Thus, the observed change in Mössbauer spectra of martensite due to cryogenic treatment can be interpreted in terms of partial dissolution of cementite and some special carbides. 4.3. Abnormally low tetragonality of virgin martensite It follows from the analysis of Mössbauer spectra of the virgin binary Fe–2.03%C martensite that carbon atoms do not occupy tetrahedral sites or octahedral sites in their b or c sublattices, which is at variance with the corresponding hypotheses of the low c/a ratio. The results obtained in the present study are interpreted in terms of plastic deformation of the virgin martensite leading to the partial capture of carbon atoms by moving dislocations. This suggests that the segregation of carbon atoms at the dislocations is the real reason for the decreased tetragonality of the virgin martensite. It is worth noting that the subsequent increase in the c/a ratio during ageing of the virgin martensite at room temperature, which was first observed in [3] and repeated in other similar studies, is not due to dilution of carbon clouds around the dislocations. The binding enthalpy between carbon atoms and dislocations in the pure bcc iron is about 0.8 eV and it increases due to the alloying with

A.I. Tyshchenko et al. / Materials Science and Engineering A 527 (2010) 7027–7039

elements like Cr [46]. Thus, it is hardly possible that carbon atmospheres around the dislocations can be exhausted during ageing of martensite. A more plausible explanation for this partial recovery of tetragonality is based on the coherent stresses at the boundaries between the carbon-rich and carbon-depleted areas in the aged martensite, similar to tetragonality of Ni–Ti martensite containing Ni3 Ti precipitates [53]. It is also worth noting that the capture of carbon atoms by gliding dislocations during the cryogenic treatment and corresponding decrease of the carbon content in the martensite should result in the increase of the fraction of iron atoms having no carbon as nearest neighbors (the component Fe0 in Mössbauer spectra). The opposite effect of the decrease in the intensity of the component Fe0 , as observed in this study, is due to the strain-induced dissolution of the carbide phases and should be absent in studies of steels having no carbides. 5. Conclusions 1. Martensitic transformation in high-carbon steels at low temperatures is accompanied by plastic deformation of virgin martensite, which is a physical reason for beneficial effect of deep cryogenic treatment of tool steels. 2. An important consequence of plastic deformation is the capture of immobile carbon atoms by moving dislocations and the formation of carbon clusters that can serve as sites for nucleation of fine ␩-carbide particles during subsequent tempering. 3. Plastic deformation occurring during the low-temperature martensitic transformation causes partial dissolution of carbide particles. 4. The abnormally low tetragonality of the virgin martensite transformed at low temperatures can be attributed to the capture of carbon atoms by moving dislocations, thus decreasing the carbon content in the martensitic solid solution. 5. The obtained results can be used to deepen our understanding of the processes occurring during deep cryogenic cooling of tool steels. References [1] [2] [3] [4] [5] [6] [7] [8] [9]

G.V. Kurdyumov, Dokl. Akad. Nauk. SSSR 60 (1948) 1543–1546. G.V. Kurdyumov, O.P. Maksimova, Dokl. Akad. Nauk. SSSR 61 (1948) 83–86. L.I. Lysak, Ya.I. Vovk, Fiz. Met. Metalloved. 20 (1965) 540–545. L.I. Lysak, S.A. Artemyuk, Yu.M. Polishchuk, Fiz. Met. Metalloved. 35 (1973) 1098–1101. M. Watanabe, C.M. Wayman, Scripta Mater. 5 (1971) 109–116. L.I. Lysak, B.I. Nikolin, Fiz. Met. Metalloved. 22 (1966) 730–736. A.L. Roitburd, A.G. Khachaturyan, Fiz. Met. Metalloved. 30 (1970) 1189–1199. F. Meng, K. Tagashira, R. Azuma, H. Sohma, ISIJ Int. 34 (1994) 205–210. P.-L. Yen, D.J. Kamody, Ind. Heat. 64 (1997) 40–44.

7039

[10] M. Pellizari, A. Molinari, in: J. Bergström, et al. (Eds.), Proceedings of the 6th International Tooling Conference, Karlstad University, Karlstad, Sweden, September 10–13, 2002, pp. 547–557. [11] T. Yugandhar, P.K. Krishnan, C.V. Bhaskar Rao, R. Kalidas, in: J. Bergström, et al. (Eds.), Proceedings of the 6th International Tooling Conference, Karlstad University, Karlstad, Sweden, September 10–13, 2002, pp. 559–569. [12] Y. Hirotsu, S. Nagakura, Acta Metall. 20 (1972) 645–655. [13] M.J. Van Cenderen, A. Böttger, R.J. Cernik, E.J. Mittemeijer, Metall. Trans. A 24 (1993) 1965–1973. [14] Yu.A. Bagaryatsky, Dokl. Akad. Nauk. SSSR 63 (1950) 1161–1164. [15] D. Jun, X. Hohgshen, Heat Treat. Met. 25 (1998) 55–59. [16] C.L. Gogte, M.I. Kumar, R.K. Paretkar, in: M. Rosso, M. Actis Grande, D. Ugues (Eds.), Proceedings of 7th International Tooling Conference, Politechnico di Torino, Torino, Italy, May 2–5, 2006, pp. 151–158. [17] D. Das, A.K. Dutta, K.K. Ray, Wear 266 (2009) 297–309. [18] D.N. Collins, Heat Treat. Met. 2 (1996) 40–42. [19] R.G. Tated, S.R. Kajale, K. Iyer, in: M. Rosso, M. Actis Grande, D. Ugues (Eds.), Proceedings of 7th International Tooling Conference, Politechnico di Torino, Torino, Italy, May 2–5, 2006, pp. 135–145. [20] D. Mohan Lal, S. Renganarayanan, A. Kalanidhi, Cryogenics 41 (2001) 149–155. [21] P.M. Gielen, R. Kaplow, Acta Metal. 15 (1967) 49–63. [22] T. Moriya, H. Ino, F.E. Fujita, J. Phys. Soc. Jpn. 24 (1968) 60–68. [23] M. Lesoille, P.M. Gielen, Metall. Trans. 3 (1972) 2681–2689. [24] R.I. Entin, V.A. Somenkov, S.S. Shilstein, Dokl. Akad. Nauk. SSSR 206 (1972) 1096–1099 (in Russian). [25] W.K. Choo, R.W. Kaplow, Acta Metall. 21 (1973) 725–732. [26] N. de Cristopharo, R. Kaplow, Metal. Trans. A 8 (1977) 35–44. [27] H. Ino, T. Ito, S. Nasu, U.A. Gonser, Acta Metall. 30 (1982) 9–20. [28] A.L. Soziniv, A.G. Balanyuk, V.G. Gavriljuk, Acta Mater. 45 (1997) 225–232. [29] J.-M. Genin, Metal. Trans. A 18 (1987) 1371–1388. [30] O.N.C. Uwakweh, J.Ph. Bauer, J.-M.R. Genin, Metall. Trans. A 21 (1990) 589–602. [31] J. Foct, J.P. Senateur, J.M. Dubois, G. Le Caer, J. Phys. Suppl. 40 (1979) C2-467. [32] R.A. Taylor, L. Chang, G.B. Olson, G.D.W. Smith, M. Cohen, J.B. Wander Sande, Metall. Trans. A 20 (1989) 2717–2737. [33] Ya. Omori, I. Tamura, Metall. Trans. A 23 (1992) 2147–2158. [34] V.G. Gavriljuk, A.V. Tarasenko, A.I. Tyshchenko, Scripta Mater. 43 (2000) 233–238. [35] I. Vincze, I.A. Campbell, J. Phys. F: Met. Phys. 3 (1973) 647–663. [36] G.K. Wertheim, V. Jaccarino, J.H. Wernick, D.N.E. Buchanan, Phys. Rev. Lett. 12 (1964) 24–27. [37] G. Schoeck, E. Bisogni, J. Shyne, Acta Metall. 12 (1964) 1466–1468. [38] A. Rivière, J.P. Amirault, J. Woirgard, Nuovo Cimento 33 (1976) 398–407. [39] D. Brunner, J. Diehl, Phys. Stat. Sol. (a) 124 (1991) 155–170. [40] A.J. McEvily, R.C. Ku, T.L. Johnston, Trans. Metal. Soc. AIME 236 (1966) 108–114. [41] J. Pietikainen, J. Iron Steel Inst. 206 (1968) 74–78. [42] J.T. Eldis, M. Cohen, Metall. Trans. A 14 (1983) 1007–1012. [43] J. Pietikainen, Trans. ISIJ 25 (1985) 340–344. [44] J.K. Tien, A.W. Thompson, I.M. Bernstein, R.J. Richards, Metall. Trans. A 7 (1976) 821–829. [45] I.N. Karnaukhov, A.E. Pogorelov, M.S. Chernolevsky, Metallofiz Noveishie Technol. 29 (2007) 748–754 (in Russian). [46] V.G. Gavriljuk, N.P. Kushnareva, V.G. Prokopenko, Phys. Met. Metallogr. 42 (1976) 1288–1293. [47] V.N. Gridnev, V.G. Gavriljuk, I.Ya. Dekhtyar, V.G. Prokopenko, P.S. Nizin, Phys. Stat. Sol. (a) 14 (1972) 689–694. [48] V.N. Gridnev, V.G. Gavriljuk, Met. Phys. 4 (1982) 74–87. [49] V.G. Gavriljuk, Mater. Sci. Eng. A 345 (2003) 81–89. [50] H.G. Read, W.T. Reynolds, K. Hono, T. Tarui, Scripta Mater. 37 (1997) 1221–1230. [51] X. Sauvage, J. Copreaux, F. Danoix, D. Blavette, Phil. Mag. A 80 (2000) 781–796. [52] V.G. Gavriljuk, Carbon Distribution in Steel, Edition “Naukova Dumka”, Kiev, 1987 (in Russian). [53] Yu.N. Koval, V.V. Kokorin, Fiz. Met. Metalloved. 38 (1975) 1044–1048 (in Russian).