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Deformation induced twinning and phase transition in an interstitial intermetallic compound niobium boride
Acta Materialia 165 (2019) 459e470
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Deformation induced twinning and phase transition in an interstitial intermetallic compound niobium boride Binbin Jiang a, b, 1, Chunjin Chen a, c, 1, Xuelu Wang a, c, Hao Wang d, Weizhen Wang a, e, Hengqiang Ye a, Kui Du a, * a
Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang, 110016, China University of Chinese Academy of Sciences, Beijing, 100049, China School of Materials Science and Engineering, University of Science and Technology of China, China d Division of Titanium Alloys, Institute of Metal Research, Chinese Academy of Sciences, Shenyang, 110016, China e School of Materials Science and Engineering, Northeastern University, Shenyang, 110819, China b c
a r t i c l e i n f o
a b s t r a c t
Article history: Received 11 June 2018 Received in revised form 7 September 2018 Accepted 10 December 2018 Available online 11 December 2018
Interstitial compounds are widely used to improve stiffness, modulus, strength and wear resistance of alloys owing to their high strength and stiffness. Understanding defect evolution and phase transformation processes in interstitial compounds during deformation would therefore provide important guidance for further enhancement of alloy properties. Here, we observed and analyzed the various deformation-induced defects in an NbB crystal using aberration-corrected electron microscopy combined with density functional theory simulations. We identified stable defects such as stacking faults and deformation twins on {110} planes, and (020)[101] planar faults. The stability originates from preservation of the dodecahedron building blocks and B-B covalent bonds. In contrast for the case of (020)[100] planer faults, the crystal structure at planar faults is significantly altered and the B-B bonds are broken, resulting in a deformation-induced phase transition from NbB to Nb phase. These results provide insights on the deformation processes of complex interstitial compounds in general. © 2018 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Keywords: Twinning Phase transition Stacking faults Interstitial compound Scanning transmission electron microscopy
1. Introduction Interstitial compounds such as borides, carbides and nitrides are known for their high strength and stiffness, and thus widely used in alloys [1e8] to improve mechanical properties such as stiffness, modulus, strength and wear resistance [9e15]. Interstitial compounds consist of metal atoms and smaller non-metallic atoms occupying interstitial sites [16,17]. When the radius ratio of the nonmetallic atoms and metal atoms is no more than 0.59, nonmetallic atoms tend to occupy tetrahedral or octahedral interstitial sites, forming simple interstitial compounds [18]. If the radius ratio is higher than 0.59, more complex interstitial sites are introduced to accommodate the relatively large interstitial atoms. For example, complex interstitial compounds NbB, TiB and Fe3C have similar trigonal prism interstitial sites, but their crystal structures can vary depending on different stacking sequence of
* Corresponding author. E-mail address: [email protected] (K. Du). 1 These authors contribute equally to this work. https://doi.org/10.1016/j.actamat.2018.12.011 1359-6454/© 2018 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
trigonal prisms [1,19e23]. In the complex interstitial compound TiB, the two different phases BG and B27 possess the same hexagonal structural units but different stacking orders, analogous to the difference between fcc and hcp structures [1,2,9,11,13,15]. During mechanical deformation, complex interstitial compounds show different defect evolution and phase transformation behaviors. Phase transitions between BG and B27 in TiB particles have been reported previously [1,11,13]. Notably, growth stacking faults and twins are observed running through the entire particles of BG or B27 TiB phase [2e4,9,11]. Meanwhile, for some interstitial compounds, particularly Fe3C particles, dissolution process has been observed after deformation. The dissolution of compounds is reportedly caused by interactions between dislocations and the interstitial atoms or the formation of subgrain boundaries, where the nonmetallic atoms segregate during deformation [6,24e29]. Refractory metal niobium reinforced by stiff interstitial compound second-phases, such as borides or carbides, provides a great opportunity to understand the deformation behavior of complex interstitial compounds. Due to its high melting point (2469 C) and low density compared to nickel-based superalloys, niobium has
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been considered as one of the most promising candidates for high temperature structural applications in jet and turbine engines as well as components for space industry [30,31], and for electromagnetic launchers [32,33]. The strength and wear resistibility of Nb and its alloys are significantly improved by adding stiff interstitial compound second-phases [34e37]. Various stiff secondphases have different deformation behaviors and influence the mechanical properties of the alloys in difference ways [27,28,34]. Due to the complex crystal structure of these compounds, an understanding of their deformation processes remains elusive. In this work, deformation induced defects in NbB crystals are investigated using aberration-corrected and conventional transmission electron microscopy (TEM) in combination with first-principles calculations. We report a new type of stacking faults lying on (020) planes and elucidate the mechanism of a deformation induced phase transition from NbB to Nb. The results will help understand deformation mechanisms of complex structured interstitial compounds.
2. Experiments Nb alloy with about 0.5 wt% boron was synthesized using vacuum induction melting. The diameter of pristine Nb slugs was 31.75 mm. The Nb slugs were then cold-swage-deformed at room temperature down to a diameter of 6.35 mm in one pass. The corresponding strain of the swage deformation is 3.22 [38]. Thin slices were cut from the deformed Nb slug perpendicular to the swage direction, and then mechanical polished down to 20 mm, and later thinned by Ar ion milling with Gatan 691 PIPS under liquid nitrogen cooling. TEM imaging and selected area electron diffraction (SAED) were conducted using a FEI Tecnai F20 electron microscope operated at 200 kV. Atomic resolution high-angle annular dark-field (HAADF) and annular bright-field (ABF) scanning transmission electron microscopy (STEM) was performed using a FEI Titan cubed G2 double aberration-corrected electron microscope operated at 300 kV and a JEM ARM200F probe aberration-corrected electron microscope operated at 200 kV. Energy dispersive spectroscopy (EDS) and electron energy-loss spectroscopy (EELS) were performed using a double aberration-corrected FEI Themis cubed G2 electron microscope equipped with a SuperX-EDS detector and a Gatan 965 energy filtering system and operated at 300 kV. First-principles calculations were performed within the framework of density functional theory (DFT) and the plane-wave pseudopotential approach [39,40], as implemented in the Vienna ab initio Simulation Package (VASP) [41,42]. The Perdew-BurkeErnzerhof functional in generalized gradient approximation (GGA) is used to describe the electronic exchange and correlation [43]. To ensure accurate treatment of the niobium potential, fermi smearing of the electronic occupancy with 0.1eV and a plane-wave kinetic energy cutoff of 450 eV are used. s and p electrons in boron, and s, d and filled-p electrons in niobium, are treated as valence electrons by the projected augmented wave (PAW) potentials [43,44]. The general stacking fault energies (GSFEs) of {110} and {020} planes were calculated by displacing thirteen atomic layers (four atoms in each layer) along [110] and [100] directions, respectively [45]. A 1.2 nm thick vacuum layer was added between periodically repeating slabs. Atom positions of the three atomic layers on both surfaces of the supercell were fixed to prevent impact introduced by the vacuum layer. All the atom positions were relaxed until the energy and force changes on each atom were less than 0.01 meV and 0.01 eV/Å, respectively. The 11 9 1 and 11 11 1 k-point meshes generated in the G-shifted MonkhorstPack scheme are used for supercells of the {110} and {020} staking
faults [46]. GSFE surface (g-surface) of {110} and {020} planes were evaluated along u and v coordinates decomposing ! ! b ¼ u 14 ½110 þ v 12 ½001 and b ¼ u 12 ½110 þ v 12 ½001 , respectively. During the calculation of the GSFE surface, the atomic relaxation is limited within the direction normal to the glide plane. The possible minimum energy paths for stacking faults were determined using climbing image nudged elastic band (CI-NEB) method and the energy barriers were determined as the saddle points of the energy profiles [47,48]. In the NEB calculation, eight finite displacement steps were employed to obtain a high resolution for the estimated GSFE curve. The supercell was the same as the one used in the stacking fault energy calculation. Top (bottom) three atomic layers in each images (replicas) were also fixed to prevent spurious forces generated by crystal drifting. Global force NEB optimization was performed with quick-min ionic optimizer before the Hellmann-Feynman force reaching 0.2 eV/Å. Then the Conjugate Gradient optimizer was performed to reach an accuracy of 0.02 eV/Å. HAADF-STEM image simulations were conducted using QSTEM software based on frozen phonon multislice methods [49]. The parameters used in the simulations were set according to experiment conditions and shown as follows: acceleration voltage is 300 kV, spherical aberration (Cs) is 0 mm, convergence angle is 21.4 mrad, defocus is 0 nm, source size is 0.06 nm and chromatic aberration (Cc) is 1.6 mm. Images were calculated using 60e290 mrad inner and outer angles for HAADF-STEM detector. 3. Results 3.1. Crystal structure of NbB NbB particles are dispersed in Nb matrix, and generally have cuboid shape with the grain size ranging from 0.5 to 5 mm as revealed by bright field (BF) and dark field (DF) TEM (Fig. 1aeb). SAED patterns acquired from different zone axes (Fig. 1cef) confirmed the observed NbB grains have a c-centered orthorhombic structure denoted by space group Cmcm (also known as BG structure) and lattice parameters of a ¼ 0.33 nm, b ¼ 0.87 nm and c ¼ 0.32 nm, consistent with previous report [19]. The abnormal diffraction intensity at the (20-1) Bragg position in SAED pattern obtained along [10-2] axis is attributed to double diffraction in thick specimens [50]. Obvious orientation relationship between NbB particles and the surrounding Nb matrix were not observed from SAED analysis. Atomic resolution HAADF and ABF STEM imaging further confirmed the atomic structure of NbB grains (Fig. 2a). We can consider NbB lattice as stacking of dodecahedron unit comprising ten Nb atoms and two B atoms (Fig. 2d). A dodecahedron contains two connecting Nb trigonal prisms with interstitial B atoms locating at the internal of each trigonal prism. When viewed along the [001] zone axis, each dodecahedron is projected as an elongated hexagon and the lattice can be interpreted as parallel stacking of hexagons (Fig. 2b and c). To better describe the motion of B atoms during deformation processes, the two B atoms in different positions in the dodecahedron are denoted by B1 and B2. The valence charge density distributions of NbB in [001] and [100] projections show that B1 and B2 atoms are strongly bonded with each other, forming a zigzag chain along the [001] axis (Fig. 2eef). 3.2. Stacking faults and deformation twins on {110} planes A large number of planar defects, including stacking faults and
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Fig. 1. (aeb) Dark-field (DF) and bright-field (BF) TEM images of NbB particles in the Nb matrix. The NbB particles are outlined by white dash lines. (cef) Electron diffraction patterns of NbB particles obtained from [001], [101], [10-2] and [116] zone-axis.
twin lamellae, were observed in NbB particles using TEM imaging (Fig. 3). The planar defects mostly initiate from interfaces between NbB particles and the surrounding Nb matrix, and terminate inside the NbB particles, which imply that they were induced by mechanical deformation. These planar defects lie predominantly on two types of crystallographic planes, i.e. {110} (including (110) and (110) planes) and {020} planes, as determined by BF, DF TEM imaging, SAED, and HAADF-STEM imaging. For planar defects on the {110} planes, BF and DF TEM images were acquired under different two-beam conditions (Fig. 3aeh). Most of these defects were determined as stacking faults (as indicated by SF1 and SF2 in Fig. 3). The visibilities of SF1 and SF2 under different two-beam conditions are summarized in Table 1. Accordingly, the displacement vector of SF1 should be ¼[110]. The displacement vector of these stacking faults is further determined with the aid of atomic resolution HAADF-STEM imaging. Fig. 4a shows an intrinsic stacking fault lying on (110) plane viewed along the [001] direction. The projected displacement vector of the (110) stacking fault is ¼[110]. The projected Burgers vector of the partial dislocation leading the (110) stacking fault is determined as ¼[110] with the Frank circuit approach [24,51], which is consistent with the measured displacement vector. Hence, the (110) or (110) stacking faults are formed by the glide of ¼[110] or ¼[110] partial dislocations on (110) or (110) plane, respectively. A {110} stacking fault can also be represented by stacking of dodecahedrons. Compared to perfect crystal, projected hexagons have a different orientation at the stacking fault (Fig. 4a). The B1 and B2 atoms are still located at the interstitial sites in Nb trigonal prism. As confirmed by valence charge density distribution of B atoms (Fig. 4d), B1 and B2 atoms still form strong covalent bonds. Twin lamellae along (110) or (110) planes with different lamella thicknesses were observed in NbB particles (Fig. 4bec). Therefore, the twin lamellae can be formed by sequential gliding of ¼[110] or
¼[110] partial dislocations on adjacent (110) or (110) planes, respectively.
3.3. Stacking faults and lamellar Nb phase on (020) planes Two types of (020) planar faults in NbB particles have been identified as (020)[101] and (020)[100] planar faults using atomic resolution images acquired from [001] and [102] zone axes (Figs. 5 and 6). Both planar faults comprise of multiple consecutive layers of intrinsic stacking faults on (020) planes and they look identical along the [001] axis but distinguishable along the [102] axis. The (020)[101] stacking fault has a displacement vector of ½[101], which is projected as ½[100] along the [001] axis and approximately 0.073 nm displacement along the [102] axis (Fig. 5a, c). When viewed along the [102] zone axis, the arrangement of Nb atoms of this planar defect is characterized as a rectangle and a parallelogram (Fig. 5ced). When viewed along the [100] zone axis, we can again use the hexagons from projection of dodecahedrons to better understand atom arrangement at the stacking fault. The dodecahedrons at the stacking fault region are rotated by 90 (Fig. 5eef). The observed (020) planar faults are mostly this type. Another (020) planar fault, the (020)[100] stacking fault, has a displacement vector of ½[100], which is projected as ½[100] along the [001] axis and approximately 0.146 nm displacement along the [102] axis (Fig. 6a, c). When viewed along the [102] zone axis, the arrangement of Nb atoms of this planar defect is characterized as two parallelograms (Fig. 6ced). When viewed along [001] zone axis, the hexagonal structure unit is destroyed at the planar fault, as evidenced by diamond pattern of projected Nb atoms (Fig. 6a). B1 and B2 atoms are located in interstitial sites of octahedrons constructed by six Nb atoms. Consequently, the covalent bonds between B1 and B2 atoms are broken, which is confirmed by the valence charge density distribution of B atoms calculated by the
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Fig. 2. (a) High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) image of NbB crystal taken along the [001] zone axis. The unit cell is outlined by red dash line. The projected hexagonal unit of NbB crystal viewed along [001] axis is outlined by green lines. The inset is annular bright-field (ABF) STEM image of NbB. (b, c) Structural models showing the atomic arrangement of NbB along [001] (b) and [100] (c) axes. Nb atoms are denoted by blue circles and B atoms by orange circles. Solid and open circles represent two different atom layers. The structural units are outlined by green lines. Two B atoms in different positions of the projected hexagonal unit are denoted by B1 and B2. (d) Three-dimensional atomic arrangement of the dodecahedron unit comprising ten Nb atoms and two B atoms, which shows that B atoms are located in the trigonal prism interstitial sites. (eef) The valence charge density distributions of NbB viewed along [001] (e) and [100] (f) axes. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
first principles calculation (Fig. 6e). Noticeably, two {110} stacking faults are observed at both sides of the (020)[100] stacking fault. HAADF-STEM images were simulated using multi-slice method implemented in QSTEM program [49] with NbB supercells containing multiple-layers of (020) stacking faults with either ½[101] or ½[100] displacement vectors (Fig. 5b, d, and 6b, d). The simulated images match very well with experimental HAADF-STEM images acquired from [001] and [102] axes for (020)[101] and (020)[100] stacking faults. Lamellar Nb phase on (020) planes was observed in NbB particles, as determined by HAADF-STEM imaging, EDS and EELS analysis (Figs. 3 and 7). The Nb lamellae generally have a length of more than 200 nm and thicknesses ranging from 2 to 5 nm. The spacing between two paralleled Nb lamellae can be as small as tens of nanometers (Fig. 3). The interfaces between Nb lamellae and surrounding NbB particles are atomically flat and strictly parallel to (020)NbB planes. The orientation relationship between Nb lamellae and NbB grains is (010)Nbk(020)NbB and [001]Nbk[001]NbB (Fig. 7aeb). The lattice parameters of the Nb phase are approximately 0.335 ± 0.004 nm in the <100> direction and 0.333 ± 0.004 nm in the <010> direction when measured using atomic resolution HAADF-STEM images acquired along [001] zone axis. Both numbers agree well with the reported lattice constant of body-centered cubic (BCC) Nb (a ¼ 0.3307 nm) [52]. Chemical analysis using EDS and EELS shows that the Nb concentration increases and the B concentration decreases at Nb lamellae regions
(Fig. 7ced), although line profiles from chemical analysis do not show abrupt changes that should correspond to the interface due to incident electron beam scattering and broadening in thick samples [53]. The Nb lamellae are usually terminated with {110} stacking faults. 3.4. Theoretical analysis Planar fault energies of (110) or (020) planar faults have been calculated using DFT as summarized in Table 2. The results show that (110) stacking fault has the lowest planar fault energies (24.2 mJ/m2), while (020)[100] stacking fault has the highest planar fault energy (1166.3 mJ/m2). Interestingly, intrinsic (110), (020) [101] and (020)[100] stacking faults have comparable stacking fault energy barriers: 1510 mJ/m2, 1470 mJ/m2 and 1695 mJ/m2, respectively (Fig. 9ced and 5i). Here, the GSFE surface of (110) and (020) stacking faults are calculated using classical SFE calculation. The energies of systems before and after boron atoms migrating from the (020)[100] stacking fault regions of NbB to the surrounding Nb matrix were calculated using DFT. The energy difference between these two systems can be considered as the driving force for a boron atom moving from NbB (020)[100] stacking fault region to surrounding Nb matrix. The energy difference of this diffusion process (DE) is described as follows:
DE ¼ ENb lamella þ nENbþB Eð020Þdefect nENb
matrix
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Fig. 3. (a) BF TEM image of planar defects in NbB particles showing (110) stacking faults (SF1), (110) stacking faults (SF2) and lamellar Nb phases (Nb). (bee) BF and DF TEM images of the region in (a) recorded with different two-beam conditions. B ¼ [001]. (f) BF TEM image of (110) stacking faults in NbB particles. (geh) DF TEM images of the region in (f) recorded with different two-beam conditions. B ¼ [101]. (i) BF TEM image of a twin lamella (T) in NbB particles.
Table 1 The visibility (v) and invisibility (i) of {110} SFs under different two-beam conditions. The values of g$R for all SFs are calculated under two-beam conditions. g
SF1 (110)
SF2 (110)
R1 ¼ ¼ [110]
200 040 1e30 130 1e11 131
R2 ¼ ¼ [110]
v/i
g,R1
v/i
g,R2
v i v i i i
1/2 1 1/2 1 0 1
v i i v
1/2 1 1 1/2
Here, ENb matrix is the energy of surrounding Nb matrix. E(020) means the energy of NbB supercell containing three layers of (020)[100] intrinsic stacking faults. ENbþB indicates the energy of surrounding Nb matrix containing one boron atom. ENb lamella indicates the energy of Nb lamella transformed from (020)[100]
defect
stacking faults of NbB after removing one boron atom. n indicates the number of migrated boron atoms. Prior calculation shows that a single B atom energetically favors the octahedral interstitial site over the tetrahedral interstitial site, and thus boron atoms were assigned at octahedral interstitial sites of a 2 2 10 Nb supercell for the calculation. Compression strain along the [020] crystallographic direction ranging from 0% to 10% was applied on the (020) [100] stacking fault region by changing the length of [020] direction of supercell, meanwhile, the other two orthogonal directions are relaxed to minimize the total energy. The result of the energy difference shows that the phase transition is thermodynamically feasible when the compression strain higher than 3.79% (Fig. 8). From first principles calculations, the lattice parameters of the unit cell of the (020)[100] stacking fault structure are estimated to be a ¼ 0.330 nm, b ¼ 0.925 nm and c ¼ 0.327 nm. Compared with NbB crystal (b ¼ 0.878 nm), the lattice expands along b axis ([010]NbB direction). As the (020) stacking faults form completely
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Fig. 4. (a) HAADF-STEM image of an intrinsic stacking fault lying on (110) plane, taken along [001] zone axis. The projected units of the matrix and stacking fault are outlined by green and red hexagons, respectively. (bec) HAADF-STEM images of (110) twin lamellae with different thickness. (d) The valence charge density distribution of (110) stacking fault in NbB viewed along [001] axis. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
coherent and epitaxial interface within NbB crystal, a compressive strain (approximately 5.1%) is expected to exist in the (020) stacking faults region. 4. Discussion The planar fault energies of (020)[100] stacking faults are much higher than those of (110) and (020)[101] stacking faults, while the general stacking fault energy barriers of intrinsic (110), (020)[101] and (020)[100] stacking faults are similar. We need to mention that the kinetics governing formation of stacking faults (by dislocation slip) is mainly controlled by general stacking fault energy barriers, while the thermodynamic stability of stacking faults is related to planar fault energies [54]. Therefore, the stresses required to form (110), (020)[101] or (020)[100] stacking faults are comparable, although (020)[100] stacking faults are thermodynamic unstable compared with the other stacking faults. Stacking faults with general stacking fault energy barriers ranging from 1470 to 1700 mJ/m2 can be formed during mechanical deformation, according to previous researches in titanium nitride (TiN). An even higher estimation of stacking fault energy barrier of TiN ranging from 1480 to 2520 mJ/m2 was reported [55]. Significant dislocation activities were observed in TiN phases under a working condition of 0.05e0.07 plastic strain at room temperature [56,57]. As the strain of samples (a true strain of 3.22) in this work is much higher than the plastic strain of the TiN samples, while the local strain of samples can be even higher, (110), (020)[101] and (020)[100] stacking faults should likely form in NbB particles during the
deformation. The type of planar defects generated in the NbB crystal may mainly depend on the local strain state during the deformation. (110) and (020)[101] stacking faults are thermodynamic stable, while (020)[100] stacking faults are unstable due to their high planar fault energies. For (110) and (020)[101] stacking faults, the structural units are the same as that of the NbB crystal with the two boron atoms forming strong bonds similar to the NbB crystal. On the contrary, at (020)[100] stacking faults, B1 and B2 atoms are located in the octahedral interstitial sites of Nb atoms and they cannot form covalent bonds to lower the total energy. As described above, the Nb lamellae observed in NbB crystal usually have a uniform thickness and strictly parallel to the (020)NbB plane, initiated from the interface between NbB particles and the Nb matrix, and terminated inside the NbB particles (Figs. 3 and 7). These features are similar to the unstable (020)[100] stacking faults. In Fig. 3c, the spacing between two paralleled Nb lamellae is approximately 11 nm while each lamella is more than 200 nm long. It is unlikely to form two long paralleled cracks with such small spacing between them during mechanical deformation. Hence, the origin of such Nb lamellae is likely related to the phase transition from multilayered (020)[100] stacking faults of NbB rather than the diffusion of Nb element from the surrounding matrix into micro-cracks in NbB crystals. Multiple layers of (020)[100] stacking faults can form by gliding of ½[100] partial dislocations on adjacent (020) planes at regions with high local stress, e.g. induced by piled-up dislocations in surrounding Nb matrix at the NbB/Nb interfaces during
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Fig. 5. (a, c) HAADF-STEM images of an extrinsic (020)[101] stacking fault on (020) plane, taken along [001] and [102] zone axes. The projected units of the matrix and stacking fault are outlined by green and magenta lines. (b, d) HAADF-STEM image simulations of multiple-layered (020)[101] stacking fault with ½[101] displacement vector taken along [001] and [102] axes. (eeg) Structure models of the (020)[101] stacking fault along [001], [100] and [010] axes, respectively. The dashed and solid circles indicate positions of Nb atoms in the up-layer before and after the formation of the (020)[101] stacking fault, respectively, in (g). (h) The valence charge density distribution of a (020)[101] stacking fault in NbB viewed along [001] axis. (i) The calculated (020) general stacking fault energy (GSFE) surface of the NbB crystal. The minimum-energy path (MEP) is marked with a red arrow, which can form (020)[101] stacking fault. Another possible pathway is marked with a black arrow, which can form (020)[100] stacking fault. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
deformation. At the same time, the characteristic hexagonal units are destroyed and the covalent bonds between B1 and B2 atoms are broken. Consequently, boron atoms become more mobile. Under compressive strain, these B atoms may diffuse out of the deformed
structure through the interface between NbB particles and the surrounding Nb matrix, leading to a phase transition from NbB (020)[100] stacking faults to Nb phase. This process is thermodynamically feasible according to the DFT calculations of the energy
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Fig. 6. (a, c) HAADF-STEM images of multiple-layered (020)[100] stacking fault on (020) plane, taken along [001] and [102] zone axes. The projected units of the matrix and stacking fault are outlined by green and magenta lines. (b, d) HAADF-STEM image simulations of multiple-layered (020)[100] stacking fault with ½[100] displacement vector taken along [001] and [102] axes. (e) The valence charge density distribution of (020)[100] stacking fault in NbB viewed along [001] axis. (feh) Structure models of (020)[100] stacking fault along [001], [100] and [010] axes. The dashed and solid circles indicate positions of Nb atoms in the up-layer before and after the formation of the (020)[100] stacking fault, respectively, in (h). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
difference of diffusion processes (Fig. 8). The calculations show that the compression strain (approximately 5.1%) in the defective NbB phase is higher than the critical compression strain (3.79%) above which diffusion process is energetically favorable. (020)[100] stacking fault (Fig. 6) can be stabilized when the stacking fault is pinned by two {110} stacking faults on both sides inside a NbB particle, and thus is not connected to the interface between the NbB particle and surrounding Nb matrix. The phase transition from NbB (020)[100] stacking fault to Nb phase can be divided to two steps: orthorhombic to BCT transition, and BCT to BCC transition. NbB (020)[100] stacking faults can be considered as a simple orthorhombic structure with two Nb atoms and two B atoms in the unit cell. After B atoms migrate to the surrounding Nb matrix, the stacking of (020) planes of the remaining Nb atoms is denoted as ababab in the defective phase and the remaining Nb atoms form a simple orthorhombic structure (Pmnm) with lattice parameters of a ¼ 0.331 nm, b ¼ 0.4393 nm, c ¼ 0.317 nm and two Nb atoms in the unit cell, at (0, 0, 0) and (0.5, 0.418, 0.5). The lattice parameters are calculated based on the crystal structure of (020)[100] stacking faults. DFT calculations show that this orthorhombic structure is unstable and spontaneously transforms into a BCT structure with the lattice parameters of a ¼ 0.331 nm, b ¼ 0.355 nm, c ¼ 0.317 nm. The two Nb atoms are at (0, 0, 0) and (0.5, 0.5, 0.5) in the BCT unit cell. It is notable that the lattice parameter of the b axis decreases spontaneously during the relaxation of the supercell. The lattice parameters of the BCT structure are comparable to those of the BCC
structure of Nb (a ¼ 0.3307 nm). As the thickness of the Nb lamellae becomes sufficiently high, the Nb atoms prefer to form the BCC structure, to lower the total energy [58,59]. That can also lead to degradation of interfacial coherency between Nb lamellae and NbB matrix. Rearrangement of B atoms are required for the slip of ¼[110] partial dislocations on (110) planes, resulting in formation of {110} stacking faults and twins. Nudge elastic band (NEB) calculations were performed on two possible slip processes (Fig. 9). The first possible slip process involves movement of the upper half-crystal from left to right along [110] direction relative to the lower half. The bonding between B1 and B2 atoms in one dodecahedron breaks, and then the B2 atom combines with the B1 atom in the adjacent dodecahedron to form a new bond. Another slip process requires that the upper half-crystal moves in the opposite direction, where the B2 atoms move from the right to the left side of B1 atoms. The calculation results show that the first slip process has a significantly lower energy barrier. This is in consistent with the crystallographic analysis on the formation process of (110) stacking fault in TiB [2]. The deformation-induced defects investigated in this work are mostly terminated inside NbB particles and likely formed by the glide of partial dislocations. They are substantially different from the growth defects in TiB particles reported in previous works, which usually run through entire TiB particles [1e4,13]. The commonly observed B274BG phase transitions in TiB crystals only change the stacking of the hexagonal units from zigzag to parallel or vice versa, which is analogous to the transition between hcp and
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Fig. 7. (aeb) HAADF-STEM images of Nb lamellae in NbB particles, taken along [001] zone axis. The Nb lamellae are outlined by white solid lines. The (110) intrinsic stacking faults are indicated by white dash lines. The blue and orange lines marked in (b) indicate the routes along which chemical compositions are profiled. (c) Energy dispersive spectroscopy (EDS) line-scan profile of Nb element along the blue line across the Nb lamella. (d) Electron energy-loss spectroscopy (EELS) line-scan profile of B element along the orange line across the Nb lamella. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
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Table 2 The planar fault energies of (110), (020)[101] or (020)[100] stacking faults in NbB crystals calculated by the first principles calculation. The one, two and three layer faults are equivalent to the intrinsic stacking fault, extrinsic stacking fault and three intrinsic stacking faults on consecutive planes for (110), (020)[101] or (020)[100], respectively. Planar fault energy (mJ/m2)
One layer
Two layers
Three layers
(110) plane (020)[101] (020)[100]
24.2 184.6 1166.3
31.1 322.0 2048.8
33.8 449.4 2742.1
fcc structures [1,2,11]. This is different from the phase transition from the defective NbB phase to Nb crystals, which changes both the atomic arrangement as well as the chemical composition. The NbB crystal can be considered as a typical example of complex interstitial compounds, where the interstitial atoms (B) are situated at interstitial sites of Nb trigonal prisms [19,20]. Such interstitial sites are also commonly found in other practically important compounds, such as TiB and Fe3C [1,19e22]. During mechanical deformation, these trigonal prism structural units and the environment of interstitial atoms may be altered by certain dislocation slips [60], and this will lead to diffusion of the interstitial atoms and consequent phase transitions. From this point of view, the results reported in this work could be helpful for an understanding of deformation processes of complex interstitial compounds in general. 5. Conclusions
Fig. 8. The energy difference of diffusion process calculated by the first principles calculation for the phase transition from the defected NbB phase to Nb phase under different compression strain.
Deformation-induced planar defects have been investigated in NbB crystals. Stacking faults and twins on {110} planes are formed by gliding of one or more ¼[110] or ¼[110] partial dislocations on adjacent {110} planes. Having the same dodecahedron building blocks of NbB crystal without breaking B-B bonds, these {110} stacking faults and twins are stable in NbB grains. On (020) planes, both (020)[101] and (020)[100] planar faults have been observed. The (020)[101] planar faults preserve the dodecahedron building blocks and B-B bonds. On the contrary, unstable (020)[100] planer faults of NbB phase can form by gliding of ½[100] partial dislocations on (020) planes, breaking dodecahedron building blocks and B-B bonds. In this case, the B atoms residing at octahedral interstitial sites become mobile and tend to diffuse out under
Fig. 9. Results of the NEB calculations for the slip process of forming {110} stacking fault. (a) The atomic configurations show that the upper half-crystal moves from left to right relative to the lower half along [110] direction (type 1). (b) The atomic configurations show that the upper half-crystal moves from right to left relative to the lower half along [110] direction (type 2). (c) Energy profiles obtained by NEB and classical SFE calculations. (d) The calculated {110} GSFE surface of the NbB crystal. The MEP is marked with a red arrow. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
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compression stress, leading to a deformation-induced phase transition from the defective NbB to Nb metal. Acknowledgements We thank the National Natural Science Foundation of China (grants nos 51521091 and 51771203), Chinese Academy of Sciences (grant no QYZDJ-SSW-JSC024) and National Key Research and Development Program of China (grant no 2017YFA0700701) for the financial support. We are also grateful to B. Wu, C.B. Jiang and Q.M. Hu for their support on electron microscopes and first-principles calculations, and M. Debangshu, X.H. Sang and Y.X. Du for their contributions on the language editing. References € fvander, C. Mccullough, C.G. Levi, The evolution of [1] M. De Graef, J.P.A. Lo metastable BG borides in a Ti-Al-B alloy, Acta Metall. Mater. 40 (1992) 3395e3406. [2] B.J. Kooi, Y.T. Pei, J.T.M. De Hosson, The evolution of microstructure in a laser clad TiBeTi composite coating, Acta Mater. 51 (2003) 831e845. [3] Y.K. Min, J.S. Park, K.P. Min, K.T. Kim, S.H. Hong, Effect of aspect ratios of in situ formed TiB whiskers on the mechanical properties of TiB w/Tie6Ale4V composites, Scripta Mater. 66 (2012) 487e490. €nisch, M. Calin, L.C. Zhang, S. Scudino, J. Eckert, Selective laser [4] H. Attar, M. Bo melting of in situ titaniumetitanium boride composites: processing, microstructure and mechanical properties, Acta Mater. 76 (2014) 13e22. [5] M. Ozerov, M. Klimova, A. Kolesnikov, N. Stepanov, S. Zherebtsov, Deformation behavior and microstructure evolution of a Ti/TiB metal-matrix composite during high-temperature compression tests, Mater. Des. 112 (2016) 17e26. [6] L.S. Vasil’ev, I.L. Lomaev, E.P. Elsukov, On the analysis of the mechanisms of the strain-induced dissolution of phases in metals, Phys. Met. Metallogr. 102 (2006) 186e197. [7] S.A. Mantri, T. Alam, D. Choudhuri, C.J. Yannetta, C.V. Mikler, P.C. Collins, R. Banerjee, The effect of boron on the grain size and texture in additively manufactured b-Ti alloys, J. Mater. Sci. 52 (2017) 12455e12466. [8] M. Ozerov, M. Klimova, A. Vyazmin, N. Stepanov, S. Zherebtsov, Orientation relationship in a Ti/TiB metal-matrix composite, Mater. Lett. 186 (2017) 168e170. [9] D.X. Li, D.H. Ping, Y.X. Lu, H.Q. Ye, Characterization of the microstructure in TiB-whisker reinforced Ti alloy matrix composite, Mater. Lett. 16 (1993) 322e326. [10] C. Schuh, D.C. Dunand, Load transfer during transformation superplasticity of Tie6Ale4V/TiB whisker-reinforced composites, Scripta Mater. 45 (2001) 631e638. [11] A. Genç, R. Banerjee, D. Hill, H.L. Fraser, Structure of TiB precipitates in laser deposited in situ, Ti-6Al-4VeTiB composites, Mater. Lett. 60 (2006) 859e863. [12] R. Ribeiro, S. Ingole, M. Usta, C. Bindal, A.H. Ucisik, H. Liang, Tribological characteristics of boronized niobium for biojoint applications, Vacuum 80 (2006) 1341e1345. [13] Q. Meng, H. Feng, G. Chen, R. Yu, D. Jia, Y. Zhou, Defects formation of the in situ reaction synthesized TiB whiskers, J. Cryst. Growth 311 (2009) 1612e1615. €nisch, M. Calin, L.C. Zhang, K. Zhuravleva, A. Funk, S. Scudino, [14] H. Attar, M. Bo C. Yang, J. Eckert, Comparative study of microstructures and mechanical properties of in situ Ti-TiB composites produced by selective laser melting, powder metallurgy, and casting technologies, J. Mater. Res. 29 (2014) 1941e1950. €ber, A. Funk, M. Calin, L.C. Zhang, K.G. Prashanth, S. Scudino, [15] H. Attar, L. Lo Y.S. Zhang, J. Eckert, Mechanical behavior of porous commercially pure Ti and TieTiB composite materials manufactured by selective laser melting, Mater. Sci. Eng., A 625 (2015) 350e356. [16] W. Hume-Rothery, G.V. Raynor, The Structure of Metals and Alloys, Institute of Metlals, 1962. [17] C.S. Barrett, T.B. Massalski, Structure of Metals: Crystallographic Methods, Principles, and Data, McGraw-Hill, 1966. [18] G.S. Rohrer, Structure and Bonding in Crystalline Materials, Cambridge University Press, 2001. €m, I. Higashi, Crystal Growth of the New [19] S. Okada, K. Hamano, T. Lundstro Compound Nb2B3, and the Borides NbB, Nb5B6, Nb3B4, and NbB2, Using the Copper-flux Method, American Institute of Physics Conference Series, 1991, pp. 456e459. [20] Y.Q. Chai, Y.G. Tang, Study on the electronic structure of superconduct of NbB, J. Hebei Normal Univ. 28 (2004) 263e268. [21] I.G. Wood, L. Vo cadlo, K.S. Knight, G.D. Price, Thermal expansion and crystal structure of cementite, Fe3C, between 4 and 600K determined by time-offlight neutron powder diffraction, J. Appl. Crystallogr. 37 (2004) 82e90. [22] Z. Nishiyama, A. Kore'Eda, S. Katagiri, Study of plane defects in the cementite by transmission electron microscopy, Trans. Japan Inst. Met. 5 (1964) 115e121. [23] C.L. Yeh, W.H. Chen, A comparative study on combustion synthesis of NbeB
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Deformation induced twinning and phase transition in an interstitial intermetallic compound niobium boride Binbin Jiang a, b, 1, Chunjin Chen a, c, 1, Xuelu Wang a, c, Hao Wang d, Weizhen Wang a, e, Hengqiang Ye a, Kui Du a, * a
Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang, 110016, China University of Chinese Academy of Sciences, Beijing, 100049, China School of Materials Science and Engineering, University of Science and Technology of China, China d Division of Titanium Alloys, Institute of Metal Research, Chinese Academy of Sciences, Shenyang, 110016, China e School of Materials Science and Engineering, Northeastern University, Shenyang, 110819, China b c
a r t i c l e i n f o
a b s t r a c t
Article history: Received 11 June 2018 Received in revised form 7 September 2018 Accepted 10 December 2018 Available online 11 December 2018
Interstitial compounds are widely used to improve stiffness, modulus, strength and wear resistance of alloys owing to their high strength and stiffness. Understanding defect evolution and phase transformation processes in interstitial compounds during deformation would therefore provide important guidance for further enhancement of alloy properties. Here, we observed and analyzed the various deformation-induced defects in an NbB crystal using aberration-corrected electron microscopy combined with density functional theory simulations. We identified stable defects such as stacking faults and deformation twins on {110} planes, and (020)[101] planar faults. The stability originates from preservation of the dodecahedron building blocks and B-B covalent bonds. In contrast for the case of (020)[100] planer faults, the crystal structure at planar faults is significantly altered and the B-B bonds are broken, resulting in a deformation-induced phase transition from NbB to Nb phase. These results provide insights on the deformation processes of complex interstitial compounds in general. © 2018 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Keywords: Twinning Phase transition Stacking faults Interstitial compound Scanning transmission electron microscopy
1. Introduction Interstitial compounds such as borides, carbides and nitrides are known for their high strength and stiffness, and thus widely used in alloys [1e8] to improve mechanical properties such as stiffness, modulus, strength and wear resistance [9e15]. Interstitial compounds consist of metal atoms and smaller non-metallic atoms occupying interstitial sites [16,17]. When the radius ratio of the nonmetallic atoms and metal atoms is no more than 0.59, nonmetallic atoms tend to occupy tetrahedral or octahedral interstitial sites, forming simple interstitial compounds [18]. If the radius ratio is higher than 0.59, more complex interstitial sites are introduced to accommodate the relatively large interstitial atoms. For example, complex interstitial compounds NbB, TiB and Fe3C have similar trigonal prism interstitial sites, but their crystal structures can vary depending on different stacking sequence of
* Corresponding author. E-mail address: [email protected] (K. Du). 1 These authors contribute equally to this work. https://doi.org/10.1016/j.actamat.2018.12.011 1359-6454/© 2018 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
trigonal prisms [1,19e23]. In the complex interstitial compound TiB, the two different phases BG and B27 possess the same hexagonal structural units but different stacking orders, analogous to the difference between fcc and hcp structures [1,2,9,11,13,15]. During mechanical deformation, complex interstitial compounds show different defect evolution and phase transformation behaviors. Phase transitions between BG and B27 in TiB particles have been reported previously [1,11,13]. Notably, growth stacking faults and twins are observed running through the entire particles of BG or B27 TiB phase [2e4,9,11]. Meanwhile, for some interstitial compounds, particularly Fe3C particles, dissolution process has been observed after deformation. The dissolution of compounds is reportedly caused by interactions between dislocations and the interstitial atoms or the formation of subgrain boundaries, where the nonmetallic atoms segregate during deformation [6,24e29]. Refractory metal niobium reinforced by stiff interstitial compound second-phases, such as borides or carbides, provides a great opportunity to understand the deformation behavior of complex interstitial compounds. Due to its high melting point (2469 C) and low density compared to nickel-based superalloys, niobium has
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been considered as one of the most promising candidates for high temperature structural applications in jet and turbine engines as well as components for space industry [30,31], and for electromagnetic launchers [32,33]. The strength and wear resistibility of Nb and its alloys are significantly improved by adding stiff interstitial compound second-phases [34e37]. Various stiff secondphases have different deformation behaviors and influence the mechanical properties of the alloys in difference ways [27,28,34]. Due to the complex crystal structure of these compounds, an understanding of their deformation processes remains elusive. In this work, deformation induced defects in NbB crystals are investigated using aberration-corrected and conventional transmission electron microscopy (TEM) in combination with first-principles calculations. We report a new type of stacking faults lying on (020) planes and elucidate the mechanism of a deformation induced phase transition from NbB to Nb. The results will help understand deformation mechanisms of complex structured interstitial compounds.
2. Experiments Nb alloy with about 0.5 wt% boron was synthesized using vacuum induction melting. The diameter of pristine Nb slugs was 31.75 mm. The Nb slugs were then cold-swage-deformed at room temperature down to a diameter of 6.35 mm in one pass. The corresponding strain of the swage deformation is 3.22 [38]. Thin slices were cut from the deformed Nb slug perpendicular to the swage direction, and then mechanical polished down to 20 mm, and later thinned by Ar ion milling with Gatan 691 PIPS under liquid nitrogen cooling. TEM imaging and selected area electron diffraction (SAED) were conducted using a FEI Tecnai F20 electron microscope operated at 200 kV. Atomic resolution high-angle annular dark-field (HAADF) and annular bright-field (ABF) scanning transmission electron microscopy (STEM) was performed using a FEI Titan cubed G2 double aberration-corrected electron microscope operated at 300 kV and a JEM ARM200F probe aberration-corrected electron microscope operated at 200 kV. Energy dispersive spectroscopy (EDS) and electron energy-loss spectroscopy (EELS) were performed using a double aberration-corrected FEI Themis cubed G2 electron microscope equipped with a SuperX-EDS detector and a Gatan 965 energy filtering system and operated at 300 kV. First-principles calculations were performed within the framework of density functional theory (DFT) and the plane-wave pseudopotential approach [39,40], as implemented in the Vienna ab initio Simulation Package (VASP) [41,42]. The Perdew-BurkeErnzerhof functional in generalized gradient approximation (GGA) is used to describe the electronic exchange and correlation [43]. To ensure accurate treatment of the niobium potential, fermi smearing of the electronic occupancy with 0.1eV and a plane-wave kinetic energy cutoff of 450 eV are used. s and p electrons in boron, and s, d and filled-p electrons in niobium, are treated as valence electrons by the projected augmented wave (PAW) potentials [43,44]. The general stacking fault energies (GSFEs) of {110} and {020} planes were calculated by displacing thirteen atomic layers (four atoms in each layer) along [110] and [100] directions, respectively [45]. A 1.2 nm thick vacuum layer was added between periodically repeating slabs. Atom positions of the three atomic layers on both surfaces of the supercell were fixed to prevent impact introduced by the vacuum layer. All the atom positions were relaxed until the energy and force changes on each atom were less than 0.01 meV and 0.01 eV/Å, respectively. The 11 9 1 and 11 11 1 k-point meshes generated in the G-shifted MonkhorstPack scheme are used for supercells of the {110} and {020} staking
faults [46]. GSFE surface (g-surface) of {110} and {020} planes were evaluated along u and v coordinates decomposing ! ! b ¼ u 14 ½110 þ v 12 ½001 and b ¼ u 12 ½110 þ v 12 ½001 , respectively. During the calculation of the GSFE surface, the atomic relaxation is limited within the direction normal to the glide plane. The possible minimum energy paths for stacking faults were determined using climbing image nudged elastic band (CI-NEB) method and the energy barriers were determined as the saddle points of the energy profiles [47,48]. In the NEB calculation, eight finite displacement steps were employed to obtain a high resolution for the estimated GSFE curve. The supercell was the same as the one used in the stacking fault energy calculation. Top (bottom) three atomic layers in each images (replicas) were also fixed to prevent spurious forces generated by crystal drifting. Global force NEB optimization was performed with quick-min ionic optimizer before the Hellmann-Feynman force reaching 0.2 eV/Å. Then the Conjugate Gradient optimizer was performed to reach an accuracy of 0.02 eV/Å. HAADF-STEM image simulations were conducted using QSTEM software based on frozen phonon multislice methods [49]. The parameters used in the simulations were set according to experiment conditions and shown as follows: acceleration voltage is 300 kV, spherical aberration (Cs) is 0 mm, convergence angle is 21.4 mrad, defocus is 0 nm, source size is 0.06 nm and chromatic aberration (Cc) is 1.6 mm. Images were calculated using 60e290 mrad inner and outer angles for HAADF-STEM detector. 3. Results 3.1. Crystal structure of NbB NbB particles are dispersed in Nb matrix, and generally have cuboid shape with the grain size ranging from 0.5 to 5 mm as revealed by bright field (BF) and dark field (DF) TEM (Fig. 1aeb). SAED patterns acquired from different zone axes (Fig. 1cef) confirmed the observed NbB grains have a c-centered orthorhombic structure denoted by space group Cmcm (also known as BG structure) and lattice parameters of a ¼ 0.33 nm, b ¼ 0.87 nm and c ¼ 0.32 nm, consistent with previous report [19]. The abnormal diffraction intensity at the (20-1) Bragg position in SAED pattern obtained along [10-2] axis is attributed to double diffraction in thick specimens [50]. Obvious orientation relationship between NbB particles and the surrounding Nb matrix were not observed from SAED analysis. Atomic resolution HAADF and ABF STEM imaging further confirmed the atomic structure of NbB grains (Fig. 2a). We can consider NbB lattice as stacking of dodecahedron unit comprising ten Nb atoms and two B atoms (Fig. 2d). A dodecahedron contains two connecting Nb trigonal prisms with interstitial B atoms locating at the internal of each trigonal prism. When viewed along the [001] zone axis, each dodecahedron is projected as an elongated hexagon and the lattice can be interpreted as parallel stacking of hexagons (Fig. 2b and c). To better describe the motion of B atoms during deformation processes, the two B atoms in different positions in the dodecahedron are denoted by B1 and B2. The valence charge density distributions of NbB in [001] and [100] projections show that B1 and B2 atoms are strongly bonded with each other, forming a zigzag chain along the [001] axis (Fig. 2eef). 3.2. Stacking faults and deformation twins on {110} planes A large number of planar defects, including stacking faults and
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Fig. 1. (aeb) Dark-field (DF) and bright-field (BF) TEM images of NbB particles in the Nb matrix. The NbB particles are outlined by white dash lines. (cef) Electron diffraction patterns of NbB particles obtained from [001], [101], [10-2] and [116] zone-axis.
twin lamellae, were observed in NbB particles using TEM imaging (Fig. 3). The planar defects mostly initiate from interfaces between NbB particles and the surrounding Nb matrix, and terminate inside the NbB particles, which imply that they were induced by mechanical deformation. These planar defects lie predominantly on two types of crystallographic planes, i.e. {110} (including (110) and (110) planes) and {020} planes, as determined by BF, DF TEM imaging, SAED, and HAADF-STEM imaging. For planar defects on the {110} planes, BF and DF TEM images were acquired under different two-beam conditions (Fig. 3aeh). Most of these defects were determined as stacking faults (as indicated by SF1 and SF2 in Fig. 3). The visibilities of SF1 and SF2 under different two-beam conditions are summarized in Table 1. Accordingly, the displacement vector of SF1 should be ¼[110]. The displacement vector of these stacking faults is further determined with the aid of atomic resolution HAADF-STEM imaging. Fig. 4a shows an intrinsic stacking fault lying on (110) plane viewed along the [001] direction. The projected displacement vector of the (110) stacking fault is ¼[110]. The projected Burgers vector of the partial dislocation leading the (110) stacking fault is determined as ¼[110] with the Frank circuit approach [24,51], which is consistent with the measured displacement vector. Hence, the (110) or (110) stacking faults are formed by the glide of ¼[110] or ¼[110] partial dislocations on (110) or (110) plane, respectively. A {110} stacking fault can also be represented by stacking of dodecahedrons. Compared to perfect crystal, projected hexagons have a different orientation at the stacking fault (Fig. 4a). The B1 and B2 atoms are still located at the interstitial sites in Nb trigonal prism. As confirmed by valence charge density distribution of B atoms (Fig. 4d), B1 and B2 atoms still form strong covalent bonds. Twin lamellae along (110) or (110) planes with different lamella thicknesses were observed in NbB particles (Fig. 4bec). Therefore, the twin lamellae can be formed by sequential gliding of ¼[110] or
¼[110] partial dislocations on adjacent (110) or (110) planes, respectively.
3.3. Stacking faults and lamellar Nb phase on (020) planes Two types of (020) planar faults in NbB particles have been identified as (020)[101] and (020)[100] planar faults using atomic resolution images acquired from [001] and [102] zone axes (Figs. 5 and 6). Both planar faults comprise of multiple consecutive layers of intrinsic stacking faults on (020) planes and they look identical along the [001] axis but distinguishable along the [102] axis. The (020)[101] stacking fault has a displacement vector of ½[101], which is projected as ½[100] along the [001] axis and approximately 0.073 nm displacement along the [102] axis (Fig. 5a, c). When viewed along the [102] zone axis, the arrangement of Nb atoms of this planar defect is characterized as a rectangle and a parallelogram (Fig. 5ced). When viewed along the [100] zone axis, we can again use the hexagons from projection of dodecahedrons to better understand atom arrangement at the stacking fault. The dodecahedrons at the stacking fault region are rotated by 90 (Fig. 5eef). The observed (020) planar faults are mostly this type. Another (020) planar fault, the (020)[100] stacking fault, has a displacement vector of ½[100], which is projected as ½[100] along the [001] axis and approximately 0.146 nm displacement along the [102] axis (Fig. 6a, c). When viewed along the [102] zone axis, the arrangement of Nb atoms of this planar defect is characterized as two parallelograms (Fig. 6ced). When viewed along [001] zone axis, the hexagonal structure unit is destroyed at the planar fault, as evidenced by diamond pattern of projected Nb atoms (Fig. 6a). B1 and B2 atoms are located in interstitial sites of octahedrons constructed by six Nb atoms. Consequently, the covalent bonds between B1 and B2 atoms are broken, which is confirmed by the valence charge density distribution of B atoms calculated by the
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Fig. 2. (a) High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) image of NbB crystal taken along the [001] zone axis. The unit cell is outlined by red dash line. The projected hexagonal unit of NbB crystal viewed along [001] axis is outlined by green lines. The inset is annular bright-field (ABF) STEM image of NbB. (b, c) Structural models showing the atomic arrangement of NbB along [001] (b) and [100] (c) axes. Nb atoms are denoted by blue circles and B atoms by orange circles. Solid and open circles represent two different atom layers. The structural units are outlined by green lines. Two B atoms in different positions of the projected hexagonal unit are denoted by B1 and B2. (d) Three-dimensional atomic arrangement of the dodecahedron unit comprising ten Nb atoms and two B atoms, which shows that B atoms are located in the trigonal prism interstitial sites. (eef) The valence charge density distributions of NbB viewed along [001] (e) and [100] (f) axes. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
first principles calculation (Fig. 6e). Noticeably, two {110} stacking faults are observed at both sides of the (020)[100] stacking fault. HAADF-STEM images were simulated using multi-slice method implemented in QSTEM program [49] with NbB supercells containing multiple-layers of (020) stacking faults with either ½[101] or ½[100] displacement vectors (Fig. 5b, d, and 6b, d). The simulated images match very well with experimental HAADF-STEM images acquired from [001] and [102] axes for (020)[101] and (020)[100] stacking faults. Lamellar Nb phase on (020) planes was observed in NbB particles, as determined by HAADF-STEM imaging, EDS and EELS analysis (Figs. 3 and 7). The Nb lamellae generally have a length of more than 200 nm and thicknesses ranging from 2 to 5 nm. The spacing between two paralleled Nb lamellae can be as small as tens of nanometers (Fig. 3). The interfaces between Nb lamellae and surrounding NbB particles are atomically flat and strictly parallel to (020)NbB planes. The orientation relationship between Nb lamellae and NbB grains is (010)Nbk(020)NbB and [001]Nbk[001]NbB (Fig. 7aeb). The lattice parameters of the Nb phase are approximately 0.335 ± 0.004 nm in the <100> direction and 0.333 ± 0.004 nm in the <010> direction when measured using atomic resolution HAADF-STEM images acquired along [001] zone axis. Both numbers agree well with the reported lattice constant of body-centered cubic (BCC) Nb (a ¼ 0.3307 nm) [52]. Chemical analysis using EDS and EELS shows that the Nb concentration increases and the B concentration decreases at Nb lamellae regions
(Fig. 7ced), although line profiles from chemical analysis do not show abrupt changes that should correspond to the interface due to incident electron beam scattering and broadening in thick samples [53]. The Nb lamellae are usually terminated with {110} stacking faults. 3.4. Theoretical analysis Planar fault energies of (110) or (020) planar faults have been calculated using DFT as summarized in Table 2. The results show that (110) stacking fault has the lowest planar fault energies (24.2 mJ/m2), while (020)[100] stacking fault has the highest planar fault energy (1166.3 mJ/m2). Interestingly, intrinsic (110), (020) [101] and (020)[100] stacking faults have comparable stacking fault energy barriers: 1510 mJ/m2, 1470 mJ/m2 and 1695 mJ/m2, respectively (Fig. 9ced and 5i). Here, the GSFE surface of (110) and (020) stacking faults are calculated using classical SFE calculation. The energies of systems before and after boron atoms migrating from the (020)[100] stacking fault regions of NbB to the surrounding Nb matrix were calculated using DFT. The energy difference between these two systems can be considered as the driving force for a boron atom moving from NbB (020)[100] stacking fault region to surrounding Nb matrix. The energy difference of this diffusion process (DE) is described as follows:
DE ¼ ENb lamella þ nENbþB Eð020Þdefect nENb
matrix
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Fig. 3. (a) BF TEM image of planar defects in NbB particles showing (110) stacking faults (SF1), (110) stacking faults (SF2) and lamellar Nb phases (Nb). (bee) BF and DF TEM images of the region in (a) recorded with different two-beam conditions. B ¼ [001]. (f) BF TEM image of (110) stacking faults in NbB particles. (geh) DF TEM images of the region in (f) recorded with different two-beam conditions. B ¼ [101]. (i) BF TEM image of a twin lamella (T) in NbB particles.
Table 1 The visibility (v) and invisibility (i) of {110} SFs under different two-beam conditions. The values of g$R for all SFs are calculated under two-beam conditions. g
SF1 (110)
SF2 (110)
R1 ¼ ¼ [110]
200 040 1e30 130 1e11 131
R2 ¼ ¼ [110]
v/i
g,R1
v/i
g,R2
v i v i i i
1/2 1 1/2 1 0 1
v i i v
1/2 1 1 1/2
Here, ENb matrix is the energy of surrounding Nb matrix. E(020) means the energy of NbB supercell containing three layers of (020)[100] intrinsic stacking faults. ENbþB indicates the energy of surrounding Nb matrix containing one boron atom. ENb lamella indicates the energy of Nb lamella transformed from (020)[100]
defect
stacking faults of NbB after removing one boron atom. n indicates the number of migrated boron atoms. Prior calculation shows that a single B atom energetically favors the octahedral interstitial site over the tetrahedral interstitial site, and thus boron atoms were assigned at octahedral interstitial sites of a 2 2 10 Nb supercell for the calculation. Compression strain along the [020] crystallographic direction ranging from 0% to 10% was applied on the (020) [100] stacking fault region by changing the length of [020] direction of supercell, meanwhile, the other two orthogonal directions are relaxed to minimize the total energy. The result of the energy difference shows that the phase transition is thermodynamically feasible when the compression strain higher than 3.79% (Fig. 8). From first principles calculations, the lattice parameters of the unit cell of the (020)[100] stacking fault structure are estimated to be a ¼ 0.330 nm, b ¼ 0.925 nm and c ¼ 0.327 nm. Compared with NbB crystal (b ¼ 0.878 nm), the lattice expands along b axis ([010]NbB direction). As the (020) stacking faults form completely
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Fig. 4. (a) HAADF-STEM image of an intrinsic stacking fault lying on (110) plane, taken along [001] zone axis. The projected units of the matrix and stacking fault are outlined by green and red hexagons, respectively. (bec) HAADF-STEM images of (110) twin lamellae with different thickness. (d) The valence charge density distribution of (110) stacking fault in NbB viewed along [001] axis. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
coherent and epitaxial interface within NbB crystal, a compressive strain (approximately 5.1%) is expected to exist in the (020) stacking faults region. 4. Discussion The planar fault energies of (020)[100] stacking faults are much higher than those of (110) and (020)[101] stacking faults, while the general stacking fault energy barriers of intrinsic (110), (020)[101] and (020)[100] stacking faults are similar. We need to mention that the kinetics governing formation of stacking faults (by dislocation slip) is mainly controlled by general stacking fault energy barriers, while the thermodynamic stability of stacking faults is related to planar fault energies [54]. Therefore, the stresses required to form (110), (020)[101] or (020)[100] stacking faults are comparable, although (020)[100] stacking faults are thermodynamic unstable compared with the other stacking faults. Stacking faults with general stacking fault energy barriers ranging from 1470 to 1700 mJ/m2 can be formed during mechanical deformation, according to previous researches in titanium nitride (TiN). An even higher estimation of stacking fault energy barrier of TiN ranging from 1480 to 2520 mJ/m2 was reported [55]. Significant dislocation activities were observed in TiN phases under a working condition of 0.05e0.07 plastic strain at room temperature [56,57]. As the strain of samples (a true strain of 3.22) in this work is much higher than the plastic strain of the TiN samples, while the local strain of samples can be even higher, (110), (020)[101] and (020)[100] stacking faults should likely form in NbB particles during the
deformation. The type of planar defects generated in the NbB crystal may mainly depend on the local strain state during the deformation. (110) and (020)[101] stacking faults are thermodynamic stable, while (020)[100] stacking faults are unstable due to their high planar fault energies. For (110) and (020)[101] stacking faults, the structural units are the same as that of the NbB crystal with the two boron atoms forming strong bonds similar to the NbB crystal. On the contrary, at (020)[100] stacking faults, B1 and B2 atoms are located in the octahedral interstitial sites of Nb atoms and they cannot form covalent bonds to lower the total energy. As described above, the Nb lamellae observed in NbB crystal usually have a uniform thickness and strictly parallel to the (020)NbB plane, initiated from the interface between NbB particles and the Nb matrix, and terminated inside the NbB particles (Figs. 3 and 7). These features are similar to the unstable (020)[100] stacking faults. In Fig. 3c, the spacing between two paralleled Nb lamellae is approximately 11 nm while each lamella is more than 200 nm long. It is unlikely to form two long paralleled cracks with such small spacing between them during mechanical deformation. Hence, the origin of such Nb lamellae is likely related to the phase transition from multilayered (020)[100] stacking faults of NbB rather than the diffusion of Nb element from the surrounding matrix into micro-cracks in NbB crystals. Multiple layers of (020)[100] stacking faults can form by gliding of ½[100] partial dislocations on adjacent (020) planes at regions with high local stress, e.g. induced by piled-up dislocations in surrounding Nb matrix at the NbB/Nb interfaces during
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Fig. 5. (a, c) HAADF-STEM images of an extrinsic (020)[101] stacking fault on (020) plane, taken along [001] and [102] zone axes. The projected units of the matrix and stacking fault are outlined by green and magenta lines. (b, d) HAADF-STEM image simulations of multiple-layered (020)[101] stacking fault with ½[101] displacement vector taken along [001] and [102] axes. (eeg) Structure models of the (020)[101] stacking fault along [001], [100] and [010] axes, respectively. The dashed and solid circles indicate positions of Nb atoms in the up-layer before and after the formation of the (020)[101] stacking fault, respectively, in (g). (h) The valence charge density distribution of a (020)[101] stacking fault in NbB viewed along [001] axis. (i) The calculated (020) general stacking fault energy (GSFE) surface of the NbB crystal. The minimum-energy path (MEP) is marked with a red arrow, which can form (020)[101] stacking fault. Another possible pathway is marked with a black arrow, which can form (020)[100] stacking fault. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
deformation. At the same time, the characteristic hexagonal units are destroyed and the covalent bonds between B1 and B2 atoms are broken. Consequently, boron atoms become more mobile. Under compressive strain, these B atoms may diffuse out of the deformed
structure through the interface between NbB particles and the surrounding Nb matrix, leading to a phase transition from NbB (020)[100] stacking faults to Nb phase. This process is thermodynamically feasible according to the DFT calculations of the energy
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Fig. 6. (a, c) HAADF-STEM images of multiple-layered (020)[100] stacking fault on (020) plane, taken along [001] and [102] zone axes. The projected units of the matrix and stacking fault are outlined by green and magenta lines. (b, d) HAADF-STEM image simulations of multiple-layered (020)[100] stacking fault with ½[100] displacement vector taken along [001] and [102] axes. (e) The valence charge density distribution of (020)[100] stacking fault in NbB viewed along [001] axis. (feh) Structure models of (020)[100] stacking fault along [001], [100] and [010] axes. The dashed and solid circles indicate positions of Nb atoms in the up-layer before and after the formation of the (020)[100] stacking fault, respectively, in (h). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
difference of diffusion processes (Fig. 8). The calculations show that the compression strain (approximately 5.1%) in the defective NbB phase is higher than the critical compression strain (3.79%) above which diffusion process is energetically favorable. (020)[100] stacking fault (Fig. 6) can be stabilized when the stacking fault is pinned by two {110} stacking faults on both sides inside a NbB particle, and thus is not connected to the interface between the NbB particle and surrounding Nb matrix. The phase transition from NbB (020)[100] stacking fault to Nb phase can be divided to two steps: orthorhombic to BCT transition, and BCT to BCC transition. NbB (020)[100] stacking faults can be considered as a simple orthorhombic structure with two Nb atoms and two B atoms in the unit cell. After B atoms migrate to the surrounding Nb matrix, the stacking of (020) planes of the remaining Nb atoms is denoted as ababab in the defective phase and the remaining Nb atoms form a simple orthorhombic structure (Pmnm) with lattice parameters of a ¼ 0.331 nm, b ¼ 0.4393 nm, c ¼ 0.317 nm and two Nb atoms in the unit cell, at (0, 0, 0) and (0.5, 0.418, 0.5). The lattice parameters are calculated based on the crystal structure of (020)[100] stacking faults. DFT calculations show that this orthorhombic structure is unstable and spontaneously transforms into a BCT structure with the lattice parameters of a ¼ 0.331 nm, b ¼ 0.355 nm, c ¼ 0.317 nm. The two Nb atoms are at (0, 0, 0) and (0.5, 0.5, 0.5) in the BCT unit cell. It is notable that the lattice parameter of the b axis decreases spontaneously during the relaxation of the supercell. The lattice parameters of the BCT structure are comparable to those of the BCC
structure of Nb (a ¼ 0.3307 nm). As the thickness of the Nb lamellae becomes sufficiently high, the Nb atoms prefer to form the BCC structure, to lower the total energy [58,59]. That can also lead to degradation of interfacial coherency between Nb lamellae and NbB matrix. Rearrangement of B atoms are required for the slip of ¼[110] partial dislocations on (110) planes, resulting in formation of {110} stacking faults and twins. Nudge elastic band (NEB) calculations were performed on two possible slip processes (Fig. 9). The first possible slip process involves movement of the upper half-crystal from left to right along [110] direction relative to the lower half. The bonding between B1 and B2 atoms in one dodecahedron breaks, and then the B2 atom combines with the B1 atom in the adjacent dodecahedron to form a new bond. Another slip process requires that the upper half-crystal moves in the opposite direction, where the B2 atoms move from the right to the left side of B1 atoms. The calculation results show that the first slip process has a significantly lower energy barrier. This is in consistent with the crystallographic analysis on the formation process of (110) stacking fault in TiB [2]. The deformation-induced defects investigated in this work are mostly terminated inside NbB particles and likely formed by the glide of partial dislocations. They are substantially different from the growth defects in TiB particles reported in previous works, which usually run through entire TiB particles [1e4,13]. The commonly observed B274BG phase transitions in TiB crystals only change the stacking of the hexagonal units from zigzag to parallel or vice versa, which is analogous to the transition between hcp and
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Fig. 7. (aeb) HAADF-STEM images of Nb lamellae in NbB particles, taken along [001] zone axis. The Nb lamellae are outlined by white solid lines. The (110) intrinsic stacking faults are indicated by white dash lines. The blue and orange lines marked in (b) indicate the routes along which chemical compositions are profiled. (c) Energy dispersive spectroscopy (EDS) line-scan profile of Nb element along the blue line across the Nb lamella. (d) Electron energy-loss spectroscopy (EELS) line-scan profile of B element along the orange line across the Nb lamella. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
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Table 2 The planar fault energies of (110), (020)[101] or (020)[100] stacking faults in NbB crystals calculated by the first principles calculation. The one, two and three layer faults are equivalent to the intrinsic stacking fault, extrinsic stacking fault and three intrinsic stacking faults on consecutive planes for (110), (020)[101] or (020)[100], respectively. Planar fault energy (mJ/m2)
One layer
Two layers
Three layers
(110) plane (020)[101] (020)[100]
24.2 184.6 1166.3
31.1 322.0 2048.8
33.8 449.4 2742.1
fcc structures [1,2,11]. This is different from the phase transition from the defective NbB phase to Nb crystals, which changes both the atomic arrangement as well as the chemical composition. The NbB crystal can be considered as a typical example of complex interstitial compounds, where the interstitial atoms (B) are situated at interstitial sites of Nb trigonal prisms [19,20]. Such interstitial sites are also commonly found in other practically important compounds, such as TiB and Fe3C [1,19e22]. During mechanical deformation, these trigonal prism structural units and the environment of interstitial atoms may be altered by certain dislocation slips [60], and this will lead to diffusion of the interstitial atoms and consequent phase transitions. From this point of view, the results reported in this work could be helpful for an understanding of deformation processes of complex interstitial compounds in general. 5. Conclusions
Fig. 8. The energy difference of diffusion process calculated by the first principles calculation for the phase transition from the defected NbB phase to Nb phase under different compression strain.
Deformation-induced planar defects have been investigated in NbB crystals. Stacking faults and twins on {110} planes are formed by gliding of one or more ¼[110] or ¼[110] partial dislocations on adjacent {110} planes. Having the same dodecahedron building blocks of NbB crystal without breaking B-B bonds, these {110} stacking faults and twins are stable in NbB grains. On (020) planes, both (020)[101] and (020)[100] planar faults have been observed. The (020)[101] planar faults preserve the dodecahedron building blocks and B-B bonds. On the contrary, unstable (020)[100] planer faults of NbB phase can form by gliding of ½[100] partial dislocations on (020) planes, breaking dodecahedron building blocks and B-B bonds. In this case, the B atoms residing at octahedral interstitial sites become mobile and tend to diffuse out under
Fig. 9. Results of the NEB calculations for the slip process of forming {110} stacking fault. (a) The atomic configurations show that the upper half-crystal moves from left to right relative to the lower half along [110] direction (type 1). (b) The atomic configurations show that the upper half-crystal moves from right to left relative to the lower half along [110] direction (type 2). (c) Energy profiles obtained by NEB and classical SFE calculations. (d) The calculated {110} GSFE surface of the NbB crystal. The MEP is marked with a red arrow. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
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compression stress, leading to a deformation-induced phase transition from the defective NbB to Nb metal. Acknowledgements We thank the National Natural Science Foundation of China (grants nos 51521091 and 51771203), Chinese Academy of Sciences (grant no QYZDJ-SSW-JSC024) and National Key Research and Development Program of China (grant no 2017YFA0700701) for the financial support. We are also grateful to B. Wu, C.B. Jiang and Q.M. Hu for their support on electron microscopes and first-principles calculations, and M. Debangshu, X.H. Sang and Y.X. Du for their contributions on the language editing. References € fvander, C. Mccullough, C.G. Levi, The evolution of [1] M. De Graef, J.P.A. Lo metastable BG borides in a Ti-Al-B alloy, Acta Metall. Mater. 40 (1992) 3395e3406. [2] B.J. Kooi, Y.T. Pei, J.T.M. De Hosson, The evolution of microstructure in a laser clad TiBeTi composite coating, Acta Mater. 51 (2003) 831e845. [3] Y.K. Min, J.S. Park, K.P. Min, K.T. Kim, S.H. Hong, Effect of aspect ratios of in situ formed TiB whiskers on the mechanical properties of TiB w/Tie6Ale4V composites, Scripta Mater. 66 (2012) 487e490. €nisch, M. Calin, L.C. Zhang, S. Scudino, J. Eckert, Selective laser [4] H. Attar, M. Bo melting of in situ titaniumetitanium boride composites: processing, microstructure and mechanical properties, Acta Mater. 76 (2014) 13e22. [5] M. Ozerov, M. Klimova, A. Kolesnikov, N. Stepanov, S. Zherebtsov, Deformation behavior and microstructure evolution of a Ti/TiB metal-matrix composite during high-temperature compression tests, Mater. Des. 112 (2016) 17e26. [6] L.S. Vasil’ev, I.L. Lomaev, E.P. Elsukov, On the analysis of the mechanisms of the strain-induced dissolution of phases in metals, Phys. Met. Metallogr. 102 (2006) 186e197. [7] S.A. Mantri, T. Alam, D. Choudhuri, C.J. Yannetta, C.V. Mikler, P.C. Collins, R. Banerjee, The effect of boron on the grain size and texture in additively manufactured b-Ti alloys, J. Mater. Sci. 52 (2017) 12455e12466. [8] M. Ozerov, M. Klimova, A. Vyazmin, N. Stepanov, S. Zherebtsov, Orientation relationship in a Ti/TiB metal-matrix composite, Mater. Lett. 186 (2017) 168e170. [9] D.X. Li, D.H. Ping, Y.X. Lu, H.Q. Ye, Characterization of the microstructure in TiB-whisker reinforced Ti alloy matrix composite, Mater. Lett. 16 (1993) 322e326. [10] C. Schuh, D.C. Dunand, Load transfer during transformation superplasticity of Tie6Ale4V/TiB whisker-reinforced composites, Scripta Mater. 45 (2001) 631e638. [11] A. Genç, R. Banerjee, D. Hill, H.L. Fraser, Structure of TiB precipitates in laser deposited in situ, Ti-6Al-4VeTiB composites, Mater. Lett. 60 (2006) 859e863. [12] R. Ribeiro, S. Ingole, M. Usta, C. Bindal, A.H. Ucisik, H. Liang, Tribological characteristics of boronized niobium for biojoint applications, Vacuum 80 (2006) 1341e1345. [13] Q. Meng, H. Feng, G. Chen, R. Yu, D. Jia, Y. Zhou, Defects formation of the in situ reaction synthesized TiB whiskers, J. Cryst. Growth 311 (2009) 1612e1615. €nisch, M. Calin, L.C. Zhang, K. Zhuravleva, A. Funk, S. Scudino, [14] H. Attar, M. Bo C. Yang, J. Eckert, Comparative study of microstructures and mechanical properties of in situ Ti-TiB composites produced by selective laser melting, powder metallurgy, and casting technologies, J. Mater. Res. 29 (2014) 1941e1950. €ber, A. Funk, M. Calin, L.C. Zhang, K.G. Prashanth, S. Scudino, [15] H. Attar, L. Lo Y.S. Zhang, J. Eckert, Mechanical behavior of porous commercially pure Ti and TieTiB composite materials manufactured by selective laser melting, Mater. Sci. Eng., A 625 (2015) 350e356. [16] W. Hume-Rothery, G.V. Raynor, The Structure of Metals and Alloys, Institute of Metlals, 1962. [17] C.S. Barrett, T.B. Massalski, Structure of Metals: Crystallographic Methods, Principles, and Data, McGraw-Hill, 1966. [18] G.S. Rohrer, Structure and Bonding in Crystalline Materials, Cambridge University Press, 2001. €m, I. Higashi, Crystal Growth of the New [19] S. Okada, K. Hamano, T. Lundstro Compound Nb2B3, and the Borides NbB, Nb5B6, Nb3B4, and NbB2, Using the Copper-flux Method, American Institute of Physics Conference Series, 1991, pp. 456e459. [20] Y.Q. Chai, Y.G. Tang, Study on the electronic structure of superconduct of NbB, J. Hebei Normal Univ. 28 (2004) 263e268. [21] I.G. Wood, L. Vo cadlo, K.S. Knight, G.D. Price, Thermal expansion and crystal structure of cementite, Fe3C, between 4 and 600K determined by time-offlight neutron powder diffraction, J. Appl. Crystallogr. 37 (2004) 82e90. [22] Z. Nishiyama, A. Kore'Eda, S. Katagiri, Study of plane defects in the cementite by transmission electron microscopy, Trans. Japan Inst. Met. 5 (1964) 115e121. [23] C.L. Yeh, W.H. Chen, A comparative study on combustion synthesis of NbeB
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