2022 Volume 62 Issue 5 Pages 984-991
Controlling the precipitation of alloy carbides with sizes of a few nanometers in ferritic steels is one of the important issues for designing of high strength steels. In this study, the interfacial atomic structures of nanometer-sized titanium carbides (TiC) in 0.05C-0.5Mn-0.1Ti-3Al (mass%) ferritic steels are investigated using scanning transmission electron microscopy. Plate-like TiC precipitates satisfying Baker-Nutting orientation relationship with the ferrite matrix are observed. High angle annular dark field scanning transmission electron microscopy with atomic resolution reveals the arrangement of Ti atomic columns in TiC and Fe atomic columns in the ferrite matrix. The TiC platelet with ~8 nm in length and ~1 nm in thickness has a coherent planar interface, which length is over the transition size from the lattice mismatch model. The semi-coherent TiC with ~14 nm in length and ~4 nm in thickness has the ledges with misfit dislocations on the planar interface. The lattice spacing of TiC along the coherent planar interface is found to be smaller than the lattice spacing of the semi-coherent broad interface or the value calculated from the lattice constant of bulk TiC.
In order to reduce weight of vehicles for the low fuel consumption and at the same time to improve structural safety, commercial steels have been required to achieve higher strength performance. High strength steel is also expected in several structural bodies such as volts, wires, thick plates, and pipes. Precipitation strengthening method as one of the strengthening techniques is applied to design microstructure of thin and thick plate steels with several kinds of matrix phases such as ferrite, bainite, and martensite.1,2,3,4,5) Although several types of particles can be used according to the purpose of the product, the representative precipitation strengthening steels contain small amounts of carbide-forming alloying elements, such as titanium (Ti), niobium (Nb), and vanadium (V) in the steel products. These alloying elements have low solubility in the ferrite phase, resulting in precipitation in the ferrite as alloy carbides with a NaCl-type crystal structure such as TiC, NbC, and VC, during tempering or cooling processes.6,7,8,9) On the cooling process, these carbides often appear at the moving interphase boundary during the phase transformation from austenite to ferrite, resulting in the dense arranged distribution.
In order to achieve a significant contribution of precipitation strengthening, nanometer-sized alloy carbides should be densely precipitated. Diameters of the alloy carbides in peak aged steels on strength are about 3–6 nm of (Nb, Ti)C, about 12–14 nm of VC, about 2–3 nm of TiC, and about 4 nm of (Nb, Mo)C.10,11,12,13) It may be considered that the diameters of the alloy carbide of 5 nm are close to the transition size of the strengthening mechanism, that is, it may be considered that the interaction between dislocations and the alloy carbides transits from the particle cutting model to the Orowan looping one.14) Kamikawa et al. reported the presence of the dislocation loops around (Ti, Mo)C precipitates having 5.5 nm in diameter in the ferritic steel by transmission electron microscopy (TEM).15) Pereloma et al. show that the step structure at the coherent interface between VC having about 3 nm in diameter and the ferrite matrix after uniaxial tensile test by scanning transmission electron microscopy (STEM) as an evidence of the particle cutting.16) It is suggested that the mismatch of lattice planes between VC and the ferrite matrix is important for dislocations to cut the VC precipitates. Kobayashi et al. evaluated an interaction force between a dislocation and a TiC precipitate in the ferritic steel by APT technique and found that the interaction force increases linearly with particle size until about 2.5 nm in diameter and then becomes constant above the size.12) Since the characters of alloy carbides, such as misfit, modulus, interfacial energy, and friction stress, influence the interaction with a dislocation, the interface coherency on the atomic arrangement should be taken in consider to control the precipitation strengthening of the nanometer-sized alloy carbides.
On the other hand, the nanometer-sized alloy carbides are important to improve the resistance of hydrogen embrittlement in high strength steels.17,18,19,20) The alloy carbides act as a trapping site for hydrogen and reduce diffusible hydrogen in high strength steels. There are several kinds of proposed trapping sites, such as strain field, coherent interface, misfit dislocations at semi-coherent interface, incoherent interface, and carbon vacancies.18,21,22,23,24,25,26,27) Most of the trapping sites is influenced by an interfacial structure originated by coherent or incoherent properties between the alloy carbide and the ferrite matrix. The interfacial coherency of the alloy carbide in the ferrite matrix is considered to be one of the important factors for the optimization of hydrogen trapping ability to enhance the resistant of the hydrogen embrittlement in high strength steels.
It is well known that the NaCl-type alloy carbides (MC) have a Baker-Nutting orientation relationship (B-N OR) with the ferrite (α) matrix.28,29) The B-N OR is described as (100)MC||(100)α and [011]MC||[001]α. The typical shape of the alloy carbides is a thin plate having the habit planes of {100}α. The interface between {100}MC and {100}α is a planar face of the thin plate due to smaller lattice misfit than lattice misfit along the lateral interface. It has been considered that the alloy carbide is perfectly coherent with the ferrite matrix on both the planar and the lateral interface at the initial stage of precipitation and the coherent interfaces change into semi-coherent interfaces during growth.21) There are some studies investigating the presence of misfit dislocations at the interface between nanometer-sized alloy carbides and a ferrite matrix using high resolution TEM (HRTEM).18,20,27,29) Wei et al. revealed that misfit dislocations existed on both the planar and the lateral interfaces of TiC having 6 nm in length and 2.3 nm in thickness in a tempered martensitic steel.29) Takahashi et al. reported that misfit dislocations existed on the lateral interface of VC having 30 nm in length and 1 nm in thickness in a ferritic steel and misfit dislocations were rarely observed on the planar interface.27) However, the interface structure of nanometer-sized alloy carbides in ferritic steels remains to be elucidated even though HRTEM is applied, because the image simulation of the assumed structure model is necessary to interpret the atomic arrangements in HRTEM images. In contrast, in high angle annular dark field (HAADF) STEM, the atomic columns can be always observed as bright dots.30) HAADF-STEM images provide an intuitive interpretation of the atomic arrangement. Aberration correction of the TEM probe forming drastically improves the spatial resolution of STEM imaging. It allows access to the complicated atomic structure such as interfaces. Recently, only the step structure of VC in a ferrite matrix is observed by aberration corrected HAADF-STEM.16,31)
In the present study, we prepared a Ti-bearing low carbon steel containing 3 mass% Al to investigate the interface structure of TiC precipitating in polygonal ferrite during heat treatment. The addition of the Al to the steel is to stabilize ferrite phase during solid solution treatment, as already reported by other group.12) The atomic structure of TiC precipitates in the ferritic steel is characterized using aberration corrected HAADF-STEM. Furthermore, the transition from coherent to semi-coherent interface with the growth of TiC is discussed, in comparison with the case of TiC precipitate in the tempered low carbon martensite.29)
A 30 kg ingot of Fe-low C-Mn-high Al alloy with a small amount of additional alloying elements to disperse the fine TiC precipitates was melted in a laboratory vacuum induction furnace. The composition is chemically analyzed as Fe-0.05C-0.50Mn-0.10Ti-3.0Al-0.0009N in mass%. The ingot was homogenized at 1523 K for 7.2 ks, hot rolled from 110 to 30 mm in thickness at about 1273 K, and then rapidly cooled by spraying water. The size of the hot rolled plate is around 110 × 1000 × 30 mm3. Cylindrical samples of 8 mm in diameter and 12 mm in length are prepared from the hot-rolled plate. After the samples were heated in vacuum at 1523 K for 600 s for solid solution treatment, they were quenched by blowing helium (He) gas. Then, they were aged in vacuum between 853 K and 1133 K for 3.6–172.8 ks, and quenched by blowing He gas.
Thin plates of about 8 × 12 × 2 mm3 were mechanically cut from center of the samples aged in several conditions. For Vickers hardness test and microstructure observation, the machined surface was polished by waterproof emery papers. The final polishing was done using a diamond abrasive slurry and colloidal silica solutions. The Vickers hardness tests were performed with a force of 4.9 N (0.5 kgf). Scanning electron microscope (SEM) observation and electron backscatter diffraction (EBSD) analysis were carried out using the JSM-7001F with 15 kV accelerated electron beam.
On the procedure of sample preparation for the transmission electron microscope (TEM), lamellae with dimensions of about 15 × 10 × 3 μm3 were picked up and attached on molybdenum (Mo) grid using a dual beam system of the Helios Nanolab 600i. A focused ion beam (FIB) with an accelerating voltage of 30 kV was used to thin the lamellae to a thickness of ~200 nm. In addition, an argon (Ar) ion beam was irradiated while the accelerating voltage was gradually decreased from 1 to 0.3 kV to remove the damaged layer produced by the FIB process. TEM observation was performed by the FEI Titan3 60–300 equipped with the energy dispersive X-ray spectrometer (EDS); the accelerating voltage of the TEM was 300 kV. In order to obtain drift corrected atomic resolution STEM images for measuring lattice spacing, dozens of STEM images with a scanning time of 0.5 s or 1 s per frame were integrated using the statistically determined spatial drift (SDSD) correction program.32)
The microstructure of the sample aged at 933 K for 3.6 ks is composed of polygonal ferrite with grain size of 300–500 μm, as shown in Fig. 1. Figure 1(a) represents the microstructure of all samples used in the present study. The crystal orientation of polygonal ferrite is random, as indicated by the inverse pole figure map of Fig. 1(b) using SEM-EBSD system. Other microstructures such as pearlite, bainite and martensite are not found in any of samples, except of original inclusions such as MnS introduced during the casting.
a) SEM image of the TiC precipitating steel aged at 933 K for 28.8 ks and b) an inverse pole figure map of ferrite. (Online version in color.)
Figure 2 shows change in Vickers hardness of the aged samples. The plots in the figures show the average hardness values of 10 tests for each sample with error bars determined by standard deviation of the 10 tests. In Fig. 2(a), the Vickers hardness decreases monotonically from 250 to 206 HV on increasing of aging time at 933 K. In Fig. 2(b), the hardness value also decreases from 250 to 168 HV with increasing aging temperature for 3.6 ks. Judging from the high value of Vickers hardness and the change with further heat treatments, the strength of the ferrite steels is originated by the precipitation strengthening effect of TiC precipitates, as discussed in detail later.
The change in Vickers hardness a) as a function of aging time at 933 K and b) as a function of aging temperature for 3.6 ks in the TiC precipitating steels.
Figures 3(a) and 3(b) show distribution of TiC precipitates in the ferritic steels aged at 933 K for 28.8 ks and at 1133 K for 3.6 ks, respectively. The both images in Fig. 3 are low angle annular dark field (LAADF) STEM micrographs taken by the condition of a detection range from about 20 to 80 mrad. The incident electron beam direction is parallel to [001]α, so the perpendicular directions of [100]α and [010]α are indicated in both images. Particles with bright contrast in the ferrite matrix are determined to be TiC precipitates by EDS analysis in the TEM. It is clear that the size of the TiC precipitates increases with the same morphology by further aging treatment of high temperature conditions. The plate-shaped TiC precipitates have crystal habit planes of (100)α and (010)α in the ferrite matrix and there are some of the TiC precipitates with near square shape in Fig. 3(a). Figure 4 shows the magnified LAADF-STEM image of the square TiC and the intensity map of Ti Kα line obtained by the EDS mapping measurement. The size of the square TiC precipitate is about 10 nm, and the lateral planes are parallel to (100)α and (010)α. The elemental mapping image shows that Ti atoms are homogeneously distributed in the square particle, as seen in Fig. 4(b).
LAADF-STEM images showing distribution of TiC precipitates in ferritic steels aged at a) 933 K for 28.8 ks and b) 1133 K for 3.6 ks.
a) A LAADF-STEM image and b) a Ti elemental map of TiC with a habit plane of (001)α. (Online version in color.)
Figure 5 is a series of atomic-resolution STEM images with [001]α incident direction and corresponding fast Fourier transformed (FFT) patterns obtained from the samples aged at different conditions such as 853 K for 28.8 ks, 933 K for 28.8 ks, and 1033 K for 3.6 ks. In Fig. 5(a), the HAADF-STEM image and the FFT pattern show no clear interfacial contrast of a TiC precipitate and its diffraction pattern, but it is considered that fine TiC platelets of ~2 nm in length can be recognized as strain contrast in the bright field STEM image. In Figs. 5(b) and 5(c), the arrangements of Ti atomic columns are clearly shown as the NaCl-type crystal structure with a [011]TiC projected direction and corresponding FFT patterns indicate the B-N OR between TiC and the ferrite matrix. The TiC platelet in Fig. 5(b) has an almost exact B-N OR, while the TiC platelet in Fig. 5(c) is slightly rotated around [001]α axis. Note that the fine TiC platelets may be present in the ferrite matrix along the projection direction since the thickness of TEM thin foils is more than 20 nm. If the fine particle in Fig. 5(a) have the NaCl-type crystal structure, the Ti atomic columns may be barely observed due to small occupation along the projection direction.
Atomic-resolution HAADF-STEM images and their FFT patterns of TiC precipitates in the ferritic steels aged a) at 853 K for 28.8 ks, b) at 933 K for 28.8 ks, and c) at 1033 K for 3.6 ks.
Figure 6 shows a drift corrected HAADF-STEM image of the TiC platelet in the ferritic steel aged at 933 K for 28.8 ks. The length of TiC along the planar interface is about 8 nm, corresponding with 27 unit cells of the ferrite lattice, and the thickness of precipitate is about 1 nm, corresponding with 4 or 6 atomic layers of (100)TiC. The planar interface of the TiC platelet consists of (100)α and (100)TiC. The matching of the lattice planes of (010)α and (011)TiC on the planar interface is perfectly coherent. On the other hand, the lateral interface is not a flat but a facet morphology along (110)α and (110)α planes in ferrite. The corresponding crystal planes of TiC along the lateral interfaces are (111)TiC and (111)TiC. The lattice plane matching of (100)α and (100)TiC on the lateral interfaces shows the presence of two extra planes of (100)α. Lattice spacing of the TiC platelet in Fig. 6 is measured directly from the HAADF-STEM image. The lattice spacing of (011)TiC along the planar interface is 1.019 ± 0.027 times as large as that of (010)α. The lattice spacing of (100)TiC along the lateral interface is 1.480 ± 0.009 times as large as that of (100)α.
A HAADF-STEM image of TiC in the ferritic steel aged at 933 K for 28.8 ks. Sold lines indicate lattice planes of ferrite and dashed lines indicate lattice planes of TiC. T-shape mark represents a misfit dislocation. A dark dot at the top-right corner is an irradiated damage by electron beam.
Figure 7 shows a series of drift-corrected HAADF-STEM images of the TiC platelets obtained from the ferritic steel aged at 1133 K for 3.6 ks. The length of TiC along the planar interface was approximately 14 nm and the thickness was approximately 4 nm. In Fig. 7(a), a few atomic-layer steps can be observed on the planar interface. The contrast of the atomic columns near the interfaces is blurred because of the presence of step-like structures along the projection direction of the incident beam. To clarify the atomic columns, an inverse FFT (IFFT) technique was applied to the HAADF-STEM image. A masked pattern is created from the FFT pattern shown in Fig. 7(b), following which the IFFT image of Fig. 7(c) is obtained from the rectangular part indicated in Fig. 7(a). The matching of (010)α and (011)TiC was analyzed by counting each plane. The counting started from the left side, where (010)α and (011)TiC are continuous. The number on the right side, where (010)α matches (011)TiC, is 63 lines for ferrite and 60 lines for TiC. The planar interface of the TiC platelet in Fig. 7(a) is not a coherent interface, but a semi-coherent interface. Figure 7(d) is a vertically reduced version of Fig. 7(c), where the extra (010)α planes are more clearly visible. The matching between (010)α and (011)TiC gradually changes from matching to mismatching, as evident by the wavy part in the middle of Fig. 7(d). The mismatch appears to be larger at the position indicated by the black arrows, and there are extra half plane of (010)α in the ferrite region. On the other hand, extra planes of (100)α can be seen at the ledge structures with a height of one or two atomic layers of TiC, as indicated by white arrows in Fig. 7(c). Since it is difficult to determine the exact position of the ledge structure because of atom positions projected in the incident beam direction, each ledge position assumed is indicated by the white arrow and the corresponding stepped line profile on the micrograph. The positions of the black arrows seem to be in correspondence with the ledge structure indicated by the white arrows in Fig. 7(c). The lattice spacing of the TiC platelets in Fig. 7(a) was also measured. The lattice spacing of (011)TiC along the planar interface was 1.053 ± 0.031 times larger than that of (010)α. The lattice spacing of (100)TiC along the lateral interface was 1.533 ± 0.030 times larger than that of (100)α.
A titanium carbide with semi-coherent interface in the ferritic steel aged at 1133 K for 3.6 ks. a) A HAADF-STEM image of the TiC in the ferrite matrix, b) a FFT pattern of (a), c) a noise-reduction image of the white rectangle part showed in (a), and d) the image reduced along a vertical direction of (c). White arrows show extra planes of (100)α at the planar interface. Black arrows show extra planes of (010)α at the planar interface.
The characteristics of nanometer-sized TiC precipitate is very important issue in the precipitation strengthening technique, and the experimental evaluation of the particle size dependence has been done by atom probe tomography (APT) analysis using in ferrite steels with similar composition.12) As the result, the strongest effect is realized by the TiC precipitation with about 2 nm in average diameter in the ferrite steel aged at 853 K for 28.8 ks. In the present study, the same sized TiC precipitate is observed in the sample aged at 853 K for 28.8 ks, as seen in Fig. 5(a). Although it is difficult to make clear the crystal structure by APT, the atomic arrangement of TiC particle itself is not made clear even by the HAADF-STEM, in which only the strain contrast is recognized around the nanometer-sized TiC precipitate in the ferrite matrix. It is noted here that the exact atomic structure of the most effective nanometer-sized TiC precipitates for the strength remains a future subject even in the field of TEM study. Since there are nanometer-sized TiC precipitates with different sizes dispersed in the samples showing the high strength, however, the understanding of the interfacial atomic structure of the nanometer-sized TiC precipitates in the ferrite matrix is important on the view point of the interaction of dislocations. As the hydrogen trapping site in the high strength ferritic steels, furthermore, the change in the interfacial atomic structure of the TiC precipitates during growth should be made clear.
As indicated by Vickers hardness measurement in Fig. 2, the hardness values of all samples are higher than 168 HV, gradually decreased by several kinds of aging treatments. As seen in Fig. 1, the present ferrite steels are the polygonal ferrite with random grain orientation, having the grain size of about 300–500 μm. Based on the change in the hardness values and ferrite microstructure, all of samples are strengthened by the dispersion of the nanometer-sized TiC precipitates in the ferrite matrix. As seen in Fig. 5(b), the atomic structure of the TiC precipitates has been clearly visible by HAADF-STEM in the sample aged at 933 K for 28.8 ks. The morphology of the TiC precipitates is of platelet with B-N OR, and the initial shape recognized as the precipitates in the STEM imaging is the square shape with a habit plane of (001)α, as shown in Fig. 4.
4.2. Change in Lattice Spacing at the Early Precipitation Stage of TiC Precipitate in the Ferrite MatrixIn this study, it is found that the planar interface of the TiC platelet with a length of about 8 nm is still coherent to the corresponding ferrite matrix. The lattice mismatch model proposed by Wei et al. predicts that the size of the coincidence of TiC lattice in ferrite matrix is about 15 times of the spacing of the (010)α plane, that is 4.22 nm.29) The present result is not explained by the lattice mismatch model, which assumes the lattice constant of TiC precipitates in the ferrite matrix is the same as 0.4329 nm of bulk TiC. As clearly seen in Fig. 6, the ratios of the lattice spacing, especially the ratio of the lattice spacing between (011)TiC and (010)α along the planar interface, is smaller than that of the bulk TiC. Since the exact measurement of lattice spacing is difficult to determine from the TEM image, the lattice spacing ratio between the TiC and ferrite is obtained from the same HAADF image, resulting in the summary in Table 1. It is found from the present observation that the crystal structure of the TiC precipitate is compressed at the early precipitation stage in the ferritic steel. The semi-coherent TiC precipitate in the ferrite matrix still have slightly smaller lattice spacing of (011)TiC than that of bulk TiC. Constraint in the ferrite matrix still influence to the semi-coherent TiC precipitates.
Two mechanisms for the reduction of the lattice spacing of (011)TiC are considered. One is the dependence of the lattice constant on carbon vacancies in the TiC precipitate itself. Titanium carbide is known to have nonstoichiometric compound with C vacancies. The lower C concentration, the smaller lattice constant; the relationship between C concentration and lattice constant has been reported by X-ray diffraction measurement of synthesized TiC.33) If the ratio is calculated for the lattice spacing of (011)TiC using the lattice constant of TiC0.25, the lattice spacing ratio decreases to be about 1.057. If there are many C vacancies in the coherent TiC platelet in the ferrite matrix, however, the effect of C vacancy on the lattice spacing is too small to explain the present result of 1.019.
The other is the elastic relaxation of the TiC lattice in the ferrite matrix. Elastic relaxation effect of the precipitate lattice in the matrix has been reported in ab initio calculation for a system of Mo2C in a Mo matrix.34) The lattice constant of Mo2C along the interface is 0.29907 nm and that of Mo is 0.31520 nm, which is 1.054 times larger than the lattice constant of Mo2C. In the report, it is proposed that Mo2C initially grows with the same lattice constant of the Mo matrix and that of Mo2C approaches the original value of Mo2C during growth of thickness. This is an example showing the change of lattice constant of precipitate affected by that of matrix. In order to consider the possibility of an elastic relaxation of TiC in the ferrite matrix, the elastic strain energy of a TiC with bulk lattice constant is calculated by the Eshelby’s ellipsoidal inclusion theory.35) The calculation conditions are as follows. The shear modulus is 182 GPa and the Poisson’s ratio is 0.20 for TiC.36) The shear modulus is 81.8 GPa and the Poisson’s ratio is 0.29 for ferrite.37) Eshelby’s tensor for thin ellipsoidal inclusion with the aspect ratio of 0.1 and the Poisson ratio of 0.33 reported by Shibata et al. is used.38) TiC and ferrite is approximated as a homogeneous isotropic elastic medium. The thin ellipsoidal shape of the coherent TiC is assigned by 7.7 nm in diameter and 1.0 nm in thickness as seen in Fig. 6. The eigenstrain is 0.068. Using of these parameters, the elastic strain energy is tentatively estimated at 0.61 J m−2.
The elastic strain energy of coherent TiC in the ferrite matrix has been calculated by the classical molecular dynamics (MD) simulation.39) The value is proportionally extrapolated to be 2.0 J m−2 in the case of a similar size of precipitate, which is considerably large value than the above tentative estimation. It must be pointed here that the coherent TiC with the same lattice constant of the bulk TiC is used on the MD simulation. Although the chemical composition is different, there is an interesting data in the case of Mo2C precipitation in the Mo matrix. It is reported that the elastic strain energies of 0.694–1.974 J m−2 of coherent Mo2C in the Mo matrix by the ab initio calculation, especially, the value of 0.694 J m−2 is obtained by the condition of the average lattice constant of Mo and Mo2C.34) The strain energy calculated for Mo2C is similar order of the estimated value of 0.61 J m−2 for the present TiC precipitate in the ferrite matrix.
It is reasonable that the TiC precipitates with large lattice constant in the bulk state has appeared in the ferrite matrix with small lattice constant by strong elastic relaxation. That is, elastic relaxation may be one of the reasons for the smaller lattice spacing of the (011)TiC in coherent TiC platelet with a thickness of 1 nm. As the result, it is expected that the large elastic strain has been yielded at the coherent planar interfaces for the thin plate TiC precipitate.
4.3. The Interface Structure Change from Coherent to Semi-coherent along the Planar InterfaceAs shown in Figs. 4 and 6, the coherent TiC platelet in ferrite with B-N OR has a square shape with considerable flat facets of (100)TiC as the planar interface and angled facet planes of {111}TiC as the lateral interface. The structure model of a coherent TiC platelet in the ferrite matrix is proposed as indicated in Fig. 8. Since it is not made clear, there are two possibilities that the {111}TiC lattice plane is terminated by a C atomic layer or a Ti atomic layer. In the HAADF-STEM images with atomic resolution, the carbon atomic columns are not visible. However, it is reported by ab initio calculations that Fe atom forms the strong bonds with C atom on the interface between (100)TiC and (100)α, resulting in stabilizing the interface.39,40) It is expected that the interface of {111}TiC terminated with C atoms can form bonds with Fe atoms and becomes more stable than the interface terminated with Ti atoms. The result is schematically indicated in the Fig. 8. As discussed in section 4.2, there is large elastic strain field around the planar interfaces, and then the two different misfit dislocations are introduced on the lateral interfaces. It is clearly seen in the HAADF-STEM image of Fig. 6, and also such kinds of misfit dislocations at the lateral interfaces are reported by the observation of Wei et al.29) At the early stage of TiC precipitation, the atomic structure of lateral interfaces is correspondence with the argument in literature, while the atomic arrangement of the planar interfaces is not still resolved.
A schematic of a platelet TiC with the coherent planar interface in the ferrite matrix. (Online version in color.)
In the present study, the transition from coherent to semi-coherent along the planar interface structure is proposed. The TiC precipitates with semi-coherent interface has slightly small lattice spacing of bulk TiC precipitate as seen in Fig. 7, resulting in the corresponding ledge structure with two kinds of misfit dislocations. Figure 9 shows a schematic edge-on interface model with a projection direction of [001]α to explain the relationship between ledges and misfit dislocations on the planar interface. There are 16 unit cells of ferrite and the corresponding TiC lattices. The lattice planes of (010)α and (011)TiC are almost coincident at left and right edges. There is a ledge structure with a height of one atomic layers of (100)TiC. One lattice plane of (100)α exists as an extra plane at the ledge structure. Although the exact position of the ledge structure is difficult, but it is made clear from the Fig. 7(c) that two directional extra half planes exist at the ledge position. Thus, two kinds of misfit dislocations are schematically indicated in Fig. 9. The strong interaction between Fe atom and C atom on the interface between TiC and ferrite is predicted by the ab initio calculations.40) The bonding between Fe atom and C atom is preferable to that between Fe atom and Ti atom, and then the Fe atoms approach to the C atoms on the interface.39) As the result, as shown by red arrows in Fig. 9, the Fe atoms at the interface are migrating toward the closest C atoms at the interface. In the ledges, the direction of Fe migration is reversed, and one lattice plane of (010)α exists as an extra plane. The ledge structures have misfit dislocations with Burgers vectors of 1/2[111]α and 1/2[111]α. Looking at the entire structure of Fig. 9, the Burgers vector of misfit dislocations is [010]α. It is suggested that a misfit dislocation is accompanied by the ledge structure on the semi-coherent planar interface due to the relaxation of Fe atoms.
A schematic of the semi-coherent planar interface of TiC in the ferrite matrix with ledge structures. T-shaped symbols represent misfit dislocations. (Online version in color.)
At the initial stage of precipitation, TiC platelets have a coherent planar interface. According to the present study, the coherent TiC platelet elastically relaxes in the ferrite matrix and the lattice spacing of (011)TiC along the planar interface becomes smaller than that of bulk TiC. The thickness of a precipitate is important factor for the elastic relaxation as mentioned in section 4.2. The TiC platelet is considered to grow in thickness by the terrace-ledge-kink (TLK) model.41) In the TLK model, a ledge or kink structure is formed at the edge of new TiC layer on the planar interface. In the ledge or kink structure, Ti and C atoms jump into the TiC crystal. The TiC platelet then grows in the thickness direction, increasing of the thickness partially on layer by layer. During growth in the thickness direction, the elastic energy for the relaxation of TiC increases. The lattice spacing of (011)TiC gradually expands because of the balance of the elastic relaxation between TiC and the ferrite matrix. However, the TLK model does not predict the lattice rotation from the B-N OR as seen in Fig. 5. The factor for the lattice rotation is discussed in below.
The small rotation from the B-N orientation relationship should occur because of the expansion of the TiC lattice spacing. The spacing of (011)TiC along [010]α become smaller by the cosine of the rotation angle. The rotation from the B-N orientation relationship helps the reduction of the elastic strain energy to keep the coherent interface. When the thickness of the coherent TiC platelet reaches the critical thickness, however, misfit dislocations should be introduced to release the stored elastic energy and the lattice constant of the TiC platelet changes into the constant of the bulk TiC. Therefore, a transition from coherent to semi-coherent occurs along the planar interface. In order to discuss the effect of the lattice rotation in detail, the further investigation of the elastic strain energy will be expected in near future.
Atomic scale interfacial structure of nanometer-sized TiC precipitates has been investigated with heating treatments in 0.05C-0.5Mn-0.1Ti-3Al (mass%) ferritic steel using a HAADF-STEM imaging technique. The following conclusions are obtained.
(1) All of the TiC precipitates have a thin plate morphology with (100)α plane at the planar interface and {110}α facets at the lateral interface with the Baker-Nutting orientation relationship. The initial morphology of the precipitate is a square plate.
(2) The TiC precipitated at 933 K for 28.8 ks with about 8 nm in length and 1 nm in thickness is characterized by a coherent interface along the planar interface, and by the presence of misfit dislocations on the lateral interface.
(3) The grown TiC precipitated at 1133 K for 3.6 ks has the semi-coherent planar interface with a set of ledge structure, in the dimension of 14 nm in length and 4 nm in thickness. The misfit dislocation having one extra plane of (010)α on the planar interface is observed at near part of ledge structures with one extra plane of (100)α. The Burgers vectors of misfit dislocations at the ledge structures are 1/2[111]α and 1/2[111]α and as the entire structure, the Burgers vector is considered to be [010]α on the semi-coherent planar interface.
(4) In comparison with the ratio of lattice spacing between (011)TiC and (010)α, the coherent TiC precipitates at the early stage of precipitation are compressed by the ferrite matrix. Although the lattice spacing of bulk TiC is 1.07 times as large as that of ferrite matrix, the lattice spacing of (011)TiC is only 1.02 times as large as that of (010)α in the coherent TiC with a thickness of about 1 nm. The ratio is increased to be about 1.05 times in the semi-coherent TiC with a thickness of about 4 nm.
The authors thank Dr. Hideaki Sawada and Dr. Kazuto Kawakami for their useful discussion about results of ab initio calculations.
