Journal of Materials Science 【-逻*辑*与-】amp; Technology, 2020, 49(0): 126-132 doi: 10.1016/j.jmst.2019.12.025

Research Article

## Twinned substructure in lath martensite of water quenched Fe-0.2 %C and Fe-0.8 %C steels

Haidong Suna, Yuhui Wanga, Zuohua Wanga, Ning Liub, Yan Penga, Xiujuan Zhaoc, Ruiming Renc, Hongwang Zhang,a,*

a National Engineering Research Center for Equipment and Technology of Cold Strip Rolling, College of Mechanical Engineering, Yanshan University,Qinhuangdao, 066004, China

b Liren College of Yanshan University, Yanshan University, Qinhuangdao, 066004, China

c School of Materials Science & Engineering, Dalian Jiaotong University, Dalian, 116028, China

Corresponding authors: * E-mail address:hwzhang@ysu.edu.cn(H. Zhang).

Received: 2019-11-9   Accepted: 2019-12-24   Online: 2020-07-15

Abstract

In the present investigation, twinned substructures within lath martensite of two water quenched steels (0.2 wt. %C and 0.8 wt. %C) were studied. The lath martensite has typical hierarchical packet-block-lath with dislocation substructure. Besides, laths that are misoriented by <011>/70.5° or <111>/60° and bordered by {011} plane, namely twinned laths, are observed, of which the density increases and the scale decreases as more carbons were presented. Such twinned laths have body centered cubic (bcc) crystal structure, belonging to twinned variants following the classical Kurdjumov-Sachs (K-S) orientation relationship with respect to the parent austenite. Unlike bcc {112}<111> twins, twinned variants produce strong double diffraction and in turn the extra diffraction spots that are commonly observed in the martensite in steels with wide range of carbon contents.

Keywords： Twinned variant ; Lath martensite ; Double electron diffraction ; Orientation relationship ; Steels

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Haidong Sun, Yuhui Wang, Zuohua Wang, Ning Liu, Yan Peng, Xiujuan Zhao, Ruiming Ren, Hongwang Zhang. Twinned substructure in lath martensite of water quenched Fe-0.2 %C and Fe-0.8 %C steels. Journal of Materials Science & Technology[J], 2020, 49(0): 126-132 doi:10.1016/j.jmst.2019.12.025

## 1. Introduction

Lath martensite is the common quenched product of overwhelming industrial significance for most heat-treated commercial low and medium carbon steels [1,2], having hierarchical structure with packet (a group of parallel laths with the same habit plane), block (a group of laths of the same orientation) and laths [3]. Lath martensite is known as dislocation martensite as it has dislocation substructure, reflecting the accommodation of the volume change by dislocation slip [4]. However, it is interesting that twinned substructure is also observed within lath martensite and becomes more and more significant with an increase of carbon content [2,[5], [6], [7]]. Concerning the common suggestion that twinning replaces dislocation slip as the dominant stain accommodation mode when the martensitic start temperature (Ms) becomes low at high carbon content [[8], [9], [10]], the formation of twinned substructure in lath martensite with high Ms point inspires the interest in detailing the twinned martensitic substructure in steels.

The twinned substructure in lath martensite, as that for high carbon martensite, has body centered cubic (bcc) structure, and was commonly believed to be {112}<111>-twins [11]. Bcc-{112}<111>-twins were directly supported by the electron diffraction pattern that is composed of two overlapped mirror symmetric patterns with respect to (112) plane normal, i.e. the typical diffraction for bcc {112}<111>twin [12]. However, twinning relationship in lath martensite is presented among martensitic laths, unlike the locally appeared twins close to midrib for lenticular martensite [13] and inside the thin plate martensite [14]. Besides, extra diffraction spots always occur at the positions where diffraction is absent for bcc {112}<111>-twins, for instance n/3 (n is integer) of (112) as the incident beam is parallel with [$\bar{1}$10] [15,16]. The origin of these extra diffraction spots has been extensively investigated and many contributions were proposed, including double diffraction of twin-matrix for bcc {112}<111>-twins [16], the retained austenite [16], carbide [17,18] or the hexagonal ω-phase [19]. Unfortunately, the nature of the twinned martensitic substructure still remains unclear.

It is well established that lath martensite (m) obeys Kurdjumov-Sachs (K-S) orientation relationship with respect to the parent austenite (A): (011)m//(111)A, [1$\bar{1}$1]m//[$\bar{1}$01]A) [20]. K-S relationship predicates 24 equivalent martensitic variants, among which certain pairs like V1-V2, V3-V4, V5-V6,…are twin-related with axis/angle of <011>/70.5° or <111>/60°, namely, twinned variants. Under a random arrangement, 24 out of 576 pairs are twin-related, accounting for a number fraction of ~4%. Twinned variants have been found strengthening with an increase of carbon content [21], a decrease of Ms point [22] and an enhancement of the applied pressure [23]. It should be noted that unlike the bcc {112}<111> twin with {112} boundary between twin-matrix, twinned variants have the boundaries of {011}m as their {011}m planes are parallel with the parent austenite {111}A planes. Twinned variant can thus be viewed as an alternative origin for the twinned substructures in lath martensite, which will in the present investigation be addressed based on the characterization of the twinned substructure within lath martensite in two typical low- and medium-carbon steels.

## 2. Experimental

Two steels with 0.2 wt. %C and 0.8 wt. %C were chosen as the experimental materials, hereafter denoted as Fe-0.2C and Fe-0.8C, respectively. The two steel samples were made into cylindrical shape with a dimension of φ5 mm × 5 mm and subjected to heating in air furnace at 1100 °C for 10 min (Fe-0.2 wt.%C) and 850 °C for 30 min (Fe-0.8 wt.%C), respectively, followed by quenching into water. The microstructures of the final products were characterized on the longitudinal section by optical microscopy (OM), X-ray diffraction (XRD), scanning electron microscopy (SEM) and transmission electron microscopy (TEM). XRD examination was performed on a D/max 2400 diffractometer with Co target, while SEM and TEM were operated on FEI-Scios and FEI-Talos 200 FX, respectively. Orientation relationship between martensite and austenite was determined by means of electron back-scattered diffraction technique (EBSD) with a scanning step size of 20 nm. Samples for EBSD examination were prepared following the general route of mechanical polishing with sand papers and electrochemical polishing (temperature: room temperature, voltage: 10 V, duration: 20 s, solution of 10 vol. % HClO4 + 90 vol. %C2H5OH).

## 3. Results and discussion

From Fig. 1, the induced products in both quenched Fe-0.2C and Fe-0.8C samples have dominant XRD peaks that can be indexed as bcc (110) and (200) (α-Fe), respectively. These two peaks keep the same positions as those of the starting materials, implying the formation of bcc martensite with almost unchanged lattice parameter. The diffraction peaks are broadened owing to the generation of crystal defects like dislocations, and the reduction of structural scale. Comparatively, Fe-0.8C sample shows more significant peak broadening, pointing to the more effective structural refinement and higher density of crystal defects, which will in the following be addressed by TEM characterization. Extra phases like carbide (Fe3C) or ω-Fe were not detected in both samples, while face centered cubic (fcc) phase are presented in the quenched Fe-0.8C sample, indicating that small amount of high temperature austenite (γ-Fe) was retained in the quenched medium carbon steel sample.

Fig. 1.   XRD profiles of the starting and quenched Fe-0.2C and Fe-0.8C steel samples. The standard diffraction peaks for several common phases in steels were inserted for comparison.

As shown by Fig. 2a and c, the starting Fe-0.2C sample has typical hypoeutectoid structure consisting of ferrite and pearlite, while Fe-0.8C sample is eutectoid structure of pearlite. Water quenching induces lath martensite in both samples, Fig. 2b and d, of which the basic structural units are the parallel laths with varied extending directions. Following Ref. [3], a group of parallel laths was defined as a packet, and closely-oriented laths form blocks showing bright or dark contrast in the optical micrograph. The hierarchical packet-block-lath structure was demonstrated in Fig. 2b, where a packet (marked by thick line) within a prior austenite grain (bordered by dotted line) is composed of alternatively distributed dark and bright groups of parallel laths (block). Such hierarchical structure is the common feature for lath martensite in the quenched steels with medium to low carbon contents [3,24,25]. Note that as more carbons were presented, both packet and blocks become so small that the hierarchical structure is not readily resolved by optical microscope.

Fig. 2.   Optical micrographs of the starting and the quenched samples. (a, b): Fe-0.2C steel, (c, d): Fe-0.8C steel. Dotted line in (b) encloses martensite packets (indicated by the thick lines) and blocks within a prior austenite grain.

The lath martensite was further characterized by EBSD, and the variant analysis was performed according to K-S relationship (Table 1) [20]. A packet in Fe-0.2C steel samples was shown in Fig. 3a, containing blocks with different orientations (different colors). The distribution of these orientations in the {001} pole figure (black dots) agrees well with that (red triangles) of the 6 martensitic variants (indicated by the number) calculated by K-S relationship by arbitrarily selecting one orientation as V1 (for instance the purple in the IPF image). According to standard angle/axis pair among the six variants of V1 to V6 (Table 2), the variant combination in Fig. 3a was determined and Bain groups that were previously reported in lath martensite in low carbon steel [3] were indicated by black rectangle and arrows, showing axis/angle pair of [011]/10.53°, i.e. V1-V4, V2-V5, V3-V6. Besides, twin-related groups (indicated by red rectangle and arrows) were frequently observed, having axis/angle pair of [1$\bar{1}$1]/60°, for instance V1-V2, V3-V4, V5-V6. For Fe-0.8C steel sample, the lath martensite also follows the K-S relationship, as demonstrated by the good agreement of the experimentally measured orientation distribution with those calculated by K-S relationship (Fig. 3d). Martensitic variants of both Bain group and twin-related are also presented (Fig. 3c). From Fig. 3e, distribution of misorientation angle of neighbor pixels for Fe-0.8C resembles that of the misorientation between variant pairs predicated theoretically from K-S relationship. Note that the distributions around 5-10° and 60° were enhanced compared to that of the K-S theoretical distribution. It should be noted that it is a low-bound estimation, since certain number of twin-related variants were excluded for statistics as the step size (20 nm) during EBSD scanning is much bigger than that of the variant size (several nanometers, see below).

Table 1   24 martensitic variants in the K-S orientation relationship and the misorientation axis/angle between V1 and the rest variants [3,20].

No.[m]//[A]Axis(indexed by martensite)Angle (deg.)
PI
(111) A//(011)m
V1[-101]//[-1 -11]
V2[-101]//[-11 -1][0.5774 -0.5774 0.5774]60.00
V3[01 -1]//[-1 -11][0.0000 -0.7071 -0.7071]60.00
V4[01 -1]//[-11 -1][0.0000 0.7071 0.7071]10.53
V5[1 -10]//[-1 -11][0.0000 0.7071 0.7071]60.00
V6[1 -10]//[-11 -1][0.0000 -0.7071 -0.7071]49.47
PII
(1-11) A//(011)m
V7[10 -1]//[-1 -11][-0.5774 -0.5774 0.5774]49.47
V8[10 -1]//[-11 -1][0.5774 -0.5774 0.5774]10.53
V9[-1 -10]//[-1 -11][-0.1862 0.7666 0.6145]50.51
V10[-1 -10]//[-11 -1][-0.4904 -0.4625 0.7387]50.51
V11[011]//[-1 -11][0.3543 -0.9329 -0.0650]14.88
V12[011]//[-11 -1][0.3568 -0.7136 0.6029]57.21
PIII
(1-11) A//(011)m
V13[0 -11]//[-1 -11][0.9329 0.3543 -0.0650]14.88
V14[0 -11]//[-11 -1][-0.7387 0.4625 -0.4904]50.51
V15[-10 -1]//[-1 -11][-0.2461 -0.6278 -0.7384]57.21
V16[-10 -1]//[-11 -1][0.6589 0.6589 0.3628]20.61
V17[110]//[-1 -11][-0.6589 0.3628 -0.6589]60.00
V18[110]//[-11 -1][-0.3022 -0.6255 -0.7193]47.11
PIV
(1-11) A//(011)m
V19[-110]//[-1 -11][-0.6145 0.1862 -0.7666]50.51
V20[-110]//[-11 -1][-0.3568 -0.6029 -0.7136]57.21
V21[0 -1 -1]//[-1 -11][0.9551 0.0000 -0.2962]20.61
V22[0 -1 -1]//[-11 -1][-0.7193 0.3022 -0.6255]47.11
V23[101]//[-1 -11][-0.7384 -0.2461 0.6278]57.21
V24[101]//[-11 -1][0.9121 0.4100 0.0000]21.06

Table 2   Variant combinations among V1 to V6 following K-S relationship [3,20].

GroupVar. PairAxis/angle pair (r/θ)
Twin-relatedV1-V2; V3-V4; V5-V6;[0.57735 -0.57735 0.57735]/60°
Bain groupV1-V4; V2-V5; V3-V6;[0 0.70711 0.70711]/10.53°
OthersV1-V3; V2-V4; V4-V6 ; V5-V1; V3-V5; V6-V2[0 0.70711 0.70711]/60°
V1-V6; V3-V2; V5-V4[0 0.70711 0.70711]/49.47°

### Fig. 3.

Fig. 3.   EBSD characterizations of the lath martensite in Fe-0.2C (a, b) and Fe-0.8C (c, d, e) steel samples. In the inverse pole figure (IPF) images (a, c), twin-related variant groups like V1-V2, V3-V4, V5-V6 were marked by red rectangle and arrows, while Bain groups, i.e. V1-V4, V2-V5, V3-V6 were marked by black rectangle and arrows. {001} pole figures in b and d show the experimental (black dots) and calculated (red triangles) orientation distribution according to K-S relationship. Histograms (e) show the experimental and theoretical misorientation distribution between 24 variants following K—S relationship. See text for detailed information.

The martensitic substructures of Fe-0.2C and Fe-0.8C samples were detailed by TEM, with special attention paid to the twinned substructure. As shown by the bright field TEM images in Fig. 4a and c, a packet contains blocks with straight and parallel laths of same contrast (same orientated). Some blocks contain more laths, while others have only one lath. The dark and bright blocks are twin-related, as demonstrated by the selected area electron diffraction (SAED) patterns (Figs. 4b, and e) obtained from the circle areas in Fig. 4a and d. Here the dark blocks were tiled with their [$\bar{1}$10] parallel with the incident electron beam, two overlapped [$\bar{1}$10] single crystal diffraction patterns were obtained. One pattern from the dark block was indexed as [$\bar{1}$10]V1 and the other from the bright one was indexed as [$\bar{1}$10]V2. Pattern [$\bar{1}$10]V1 is mirror symmetric with respect to [$\bar{1}$10 V2 around the common plane normal of (112) plane, which can be viewed as rotation counterclockwise around [$\bar{1}$10] by 70.5°. It is the typical feature of SAED patterns for bcc {112}<111> twin and matrix as the electron is parallel with <110> [15]. However, extra diffraction spots occur at n/3 (n is integer) of (112), which is absent for bcc {112}<111> twins [15]. Second phases for instance fcc austenite [16], carbide [17,18] and/or ω-phase [19] are not presented. This is further supported by the fact that as the sample was tilted with its [11$\bar{1}$] parallel with the electron beam, a single crystal SAED pattern of bcc Fe (Fig. 4c and f) was obtained from roughly same position as that in Fig. 4a and c. Besides, the lath boundaries reach edge-on position as the electron beam is parallel with [11$\bar{1}$], under which boundary plane between twinned-blocks in both Fe-0.2C and Fe-0.8C samples was determined to be (011). On the contrary, bcc {112}<111> twin boundary of (112) reaches edge-on as the electron beam is parallel with [$\bar{1}$10]. According to the crystallography, when the electron beam is parallel with the [$\bar{1}$10], (011) may project a strip on the phosphor screen (($\bar{1}$10) plane), which makes block boundaries look thicker, as observed in many lath martensite with different carbon contents [4,26,27]. Since both (011) and (112) are intersected with ($\bar{1}$10) by [1$\bar{1}$1], the thick strip is easily misinexed as the trace of the (112) twin plane and in turn the mirror symmetric crystallites were mistaken for bcc {112}<111> twin. The electron diffraction of the twin-related variants with {011} boundary will in the following be discussed, paying more attention to the double diffraction behaviors.

Fig. 4.   TEM characterization of the lath martensite induced in Fe-0.2C steel (a-c) and Fe-0.8C steel (d-f). Dashed circles in TEM image (a, d) indicate the areas where SAED patterns of (b, c) and (e, f), respectively, were obtained. As the sample was tilted with [$\bar{1}$10] and [$\bar{1}$11], respectively, parallel with the electron beam, circled laths in (a, d) give rise to mirror symmetric diffraction patterns and extra diffraction spots. See text for detail.

We begin with the electron diffraction of an edge-on bcc {112}<111> twin, namely, letting the incident electron beam parallel with [$\bar{1}$10] and (112) (Fig. 5a). Under such condition, planes that are belonging to [$\bar{1}$10] zone axis, for instance (110) from matrix (M) and twin (T) will generate primary diffraction beams (110)DM and (110)DT as Bragg diffraction condition was met [28]: 2dsin(θ) = λ, where d is the interplanar distance (0.202 nm for (110) and 0.143 nm for (002) for bcc iron), θ is the angle between incident electron beam and the diffraction plane, λ is the wave length of electron that is dependent upon the TEM accelerating voltage (0.00251 nm under 200 KV). The diffraction spots of same-index planes for instance (110)M and (110)T from matrix and twin are mirror symmetric with respect to the common (112) plane normal. When the primary diffraction beams from matrix enter the adjacent twin, double diffraction may occur and extra diffraction spots could be generated in case the diffraction condition was met again. Double diffraction follows the same diffraction principles as that for primary diffraction and the diffraction patterns for double diffraction are same as that of the primary diffraction but with the transmitting beam moved to the corresponding primary diffraction beams [29]. As the [$\bar{1}$10] is parallel with the incident electron beam, double diffraction pattern induced by primary diffraction beam can be obtained by translating the primary [$\bar{1}$10] pattern from 000 to the corresponding diffraction spots. As shown by Fig. 5a and c, when the primary diffraction (110)DM and (1$\bar{1}$0)DM of matrix are able to enter the adjacent twin and induce double diffraction, the double diffraction patterns can be obtained by translating the 000 of the primary diffraction units of twin (blue dashed rectangle) to (110)DM and (1$\bar{1}$0)DM, respectively. Consequently, the double diffraction of (110)DT and (002)DT produces extra diffraction spots that occur exactly at 2/3 and 1/3 of the (112)DMT, respectively. Primary diffraction of twin may also enter the matrix and induce double diffraction that can be obtained by the above graphic method. Consequently, all the potential extra diffractions induced by double diffraction may appear in the positions indicated by “x” in Fig. 5c. Unfortunately, bcc {112}<111> twins are actually unable to induce detectable double diffraction. This is because the incident angle θ is so small (~0.1°) that the diffraction beams can be viewed approximately parallel with the incident beam. It means that unless very close to the edge-on twin plane, the primary diffraction beams from either twin or matrix will pass through the sample without entering the adjacent crystal to activate double diffraction. According to the sample thickness t and the incident angle θ, the width of the region that is able to induce double diffraction can be roughly estimated: ttg(θ), being 0.05-0.5 nm for typical sample thickness of 10-100 nm and θ of 0.3°. Such small volume of crystal may induce double diffraction spots that are too weak to be detected. This is supported by previous investigations that extra diffraction spots never appear in the <110> diffraction pattern for both bcc {112}<111> twin [7] and fcc {111}<112> twins of either (sub)micron- or nano-scale [30,31].

Fig. 5.   Schematic illustration of the primary and double diffraction of bcc {112}<111> twin (a, c) and twinned variants (b, d) as the incident electron beam is parallel with [$\bar{1}$10]. The potential extra positions by double diffraction were marked by red “×” in (c) and red solid circles in (d).

Here the extra diffraction spots of high intensity are actually resulted from overlapped twinned variants. Taking V1 and V2 for example (applicable for other twin-related pairs), twinned variants have the interface of (011) plane that is inclined by 30° to the (112) plane (Fig. 5b). This arrangement leads to an overlapped region of V1 and V2, which makes incident beams and primary diffraction beams firstly pass through V1 and then enter V2. The width of overlapped region can be roughly estimated according to the sample thickness (t) and the inclination angle between (011) and ($\bar{1}$10): tctg(60°), being 6-60 nm for typical TEM sample thickness of 10-100 nm. Within this overlapped region, primary diffraction beam from V1 planes will act as incident beam to induce double diffraction in V2. The double diffraction process resembles the aforementioned process (Fig. 5a and c) but with the intensity that can be orders of magnitude stronger, owing to the much enlarged double diffraction region. By translating the 000 of the V2 primary diffraction pattern to the corresponding primary diffraction spots of V1, all the double diffraction spots can be generated as indicated by the red thick circles in Fig. 5d, matching exactly the extra diffraction spots in Fig. 4b and e. It should be noted that as the incident electron beam is parallel with [11$\bar{1}$], the (011) boundary between V1 and V2 reaches edge-on position, and double diffraction becomes insignificant. Furthermore, as [11$\bar{1}$] is parallel with incident beam, the primary diffraction patterns for both V1 and V2 are six-folded symmetric and fully coincident, while the double diffraction patterns for V2 are also coincident with that of the primary diffraction pattern. This means that even double diffraction was induced, extra diffraction spots will not appear in the SAED pattern.

Extra diffraction spots have previously been attributed to the double diffraction of austenite [16] and/or the presence of extra phases like carbide [17,18] or ω-phase [19]. In case austenite is presented, double diffraction spots of austenite may occur between the martensite matrix and the primary diffraction spots of retained austenite. K-S orientation relationship between austenite and the martensite makes the primary diffraction pattern of <111>A overlap with <110>m. However, such overlapping was indeed not observed, as demonstrated by Fig. 4b and e that the pattern can solely be indexed as <110>m. Double diffraction of austenite is thus unlikely inducing the extra diffraction, which is supplemented with XRD profile without austenite for Fe-0.2 C sample (Fig. 1). It is further supported by the operation of tilting the sample to [11$\bar{1}$] zone axis, Fig. 4c and f, where single crystal diffraction was obtained. Here the presence of extra phases like carbide or ω-phase can also be ruled out, since fully coincident diffraction patterns of martensite, austenite, carbide and ω-phase is impossible as they have different lattice structures and/or lattice parameters and in turn the different diffraction patterns. The present study thus underpins the origin of the extra diffraction spots, being the double diffraction of bcc twinned substructures.

Twinned substructures within lath martensite of the water quenched Fe-0.2C and Fe-0.8C steel samples are the twinned variants. Twinned substructures may have two origins: i) crystal structure change induced by displacive transformation and ii) the accommodation of invariant plane strain and/or the collision between inclined martensite plates [32]. The first origin relates the twinned martensitic variants, while the second one is responsible for the deformation twins and/or mechanical twins. As we have demonstrated that twinned variants rather than bcc {112}<111> twins induce double diffraction of high intensity, producing extra diffraction spots at n/3 (n is integer) of the (112) diffraction spot as [$\bar{1}$10] is parallel with the incident electron beam, the first origin was thus evidenced. Bcc {112}<111> twins are unlikely, since substructure of the lath martensite in both Fe-0.2C and Fe-0.8C steel samples is characterized by dislocations, owing to the high Ms point where dislocation slip rather than twinning acts as the dominant strain accommodation mode [3]. The great resemblance for the electron pattern reported in the lath martensite with very small amount of carbon [21] implies that twinned substructure in such martensite is also very likely twinned martensitic variants. The present lath martensite for both Fe-0.2C and Fe-0.8C samples has typical hierarchical packet-block-lath structure, obeys the K-S orientation relationship with respect to the parent austenite. All the features follow the common characteristics of lath martensite in steels [3]. Twinned substructure is occasionally observed in Fe-0.2C sample, while for Fe-0.8C sample it becomes very prevalent. For martensite with low content of carbon, blocks commonly contain more variants, for instance V1-V4, V2-V5, V3-V6, the twinned blocks can be related to the adjacent twinned variants in different blocks, for instance V1-V2, V3-V4, V5-V6. As more carbons are presented, blocks frequently contain only one single variant that is twin-related to the adjacent one. Preferential selecting of twinned variants has previously been observed [21], where an increase of the carbon content from 0 to 0.35, 0.75 wt% makes twinned variants (V1-V2) gradually replacing V1-V4 as the dominant variant combination. Besides, twinned variants could be strengthened as the formation temperature is low and high pressure is applied. During the investigation on the variant pairing of low-carbon bainite, the decrease of formation temperature from 853 K to 773 K and 723 K leads to an increase of V1-V2 fraction from 2% to 25 % and finally 48 % [22]. Our recent investigation found that as pure iron was slowly cooled from 1050 °C at 10 °C/s under a high pressure of 3 GPa, lath martensite was induced in a pure iron, containing high density of twinned substructure with the length scale as small as 3.8 nm [26].

## 4. Conclusion

Two steels with 0.2 wt. %C and 0.8 wt. %C, respectively, were quenched from high temperature into water, and the microstructure of the final products were investigated. The following conclusions were reached:

1)Both Fe-0.2C and Fe-0.8C samples form lath martensite. The martensite is characterized by typical hierarchical packet-block-lath structure and obeys K-S orientation relationship with respect to the parent austenite. Comparatively, martensitic substructure of Fe-0.8C is finer than that of Fe-0.2C sample.

2)Twinned substructure was observed among the lath martensite. This structure is observed occasionally inside the Fe-0.2C sample but prevalent in the Fe-0.8C samples.

3)The twinned substructure has the origin related to the twinned variants. Twinned variants are martensitic variants that are misoriented by <011>/70.5° or <111>/60° but with {011} boundary.

4)The commonly observed extra diffraction spots in the electron diffraction pattern for martensite with wide range of carbon contents can be attributed to the double diffraction of twinned martensitic variants rather than the bcc {112}<111> twins or extra phases like austenite, carbide or ω-phase.

## Acknowledgments

This work was supported financially by the Hundred Outstanding Creative Talents Projects in Hebei University, China, the Project Program of Heavy Machinery Collaborative Innovation Center, the National Natural Science Foundation (Grant No. 51231006, 51171182 and 51471039). One of the authors (H.W. Zhang) would like to acknowledge Prof. Z.N. Yang from Yanshan University for the assistance of conducting XRD experiment and Prof. C.H. Chen from Dalian Jiaotong University for the useful discussions. We would like to thank reviewers and editor for valuable comments and suggestions.

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