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(Ti, Nb)C (110) interface: A first-principles investigation
Applied Surface Science 496 (2019) 143742
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The stability, fracture toughness and electronic structure at γ-Ni (101)/(Ti, Nb)C (110) interface: A first-principles investigation
T
Shuting Suna, Hanguang Fua, , Shuangye Chenb, Jiacai Kuangc, Xuelong Pinga, Kaiming Wangd, Yingjun Dengc, Xingye Guoa, Jian Lina, Yongping Leia ⁎
a
Key Laboratory of Advanced Functional Materials, Ministry of Education, School of Materials Science and Engineering, Beijing University of Technology, Beijing 100124, PR China b Faculty of Information Technology, Beijing University of Technology, Beijing 100124, PR China c School of Automotive and Mechanical Engineering, Changsha University of Science and Technology, Changsha 410114, Hunan Province, PR China d State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, PR China
ARTICLE INFO
ABSTRACT
Keywords: γ-Ni/(Ti, Nb)C interface First principles Interface stability Interfacial fracture toughness Electronic structure
(Ti, Nb)C particles reinforced Ni45 coatings were made by a fiber laser system. The atomic structure, interfacial stability, interfacial fracture toughness, electronic structure and bonding nature of γ-Ni/(Ti, Nb)C were systematically analyzed using first principles calculations. TEM results showed that the interface orientation relationship of γ-Ni/(Ti, Nb)C was [010](202)//[001](220). For the γ-Ni/(Ti, Nb)C interfaces, the stacking sites have much influence than the substitution position of Ti, the center-site stacking interfaces shower higher adhesion work and lower interface energy, indicating the interfacial alloying or new phases were prone to formed. According to the interfacial fracture toughness results, the mechanical failure of γ-Ni/(Ti, Nb)C may initiate at the interface or close to γ-Ni rather than (Ti, Nb)C. The bonding behavior of γ-Ni/(Ti, Nb)C was a blend of covalent bond and partial ionic bond. The chemical bonding properties of interfacial atoms were also discussed in view of electronic structure and partial density of states (PDOS) results.
1. Introduction As a promising surface treatment technology, laser cladding has become a major method in the surface modification field [1,2]. Especially, the combination of laser cladding and metal matrix composite (MMC) have many advantages, the fabricated coatings not only exhibit the high toughness and strength of metal matrix material, but also show the high modulus and wear resistance of reinforcement phases [3,4]. Thus they have been widely applied in the aerospace, automotive die repair, chemical industries and other fields [5–8]. However, the reinforcement phase/matrix interface has become a core issue of coatings, the current research is mainly focuses on the microstructures, phase composition and element distribution [9–11], there is still a lack of indepth research on the intrinsic characteristics of interface physical phenomena such as interface behavior and interface structure. In recent years, with the rapid development of computer technology, remarkable results of interfaces have been achieved by first principles calculations. Li et al. [12] studied the interface properties of TiC(111)/α-Ti(0001) by first principles, they found the maximum
interfacial fracture toughness was 4.8 MPa m1/2, and the interfacial bonding mainly consist of TieTi metallic interaction and CeTi covalent bonds. Sawada et al. [13] investigated the interface energy of Fe/NbC using first principles, the strain energy around the precipitate was also estimated by a classical molecular dynamics method. Gong et al. [14] studied the reinforcing effects of Ni/Ni3Al interface induced by Re, Co, Ru, Ta, Cr, W and Mo elements, they found the best reinforcing effect was attributed to rare earth Re, while W, Ta and Co elements appeared to be less potent. Sun et al. [15] discussed the temperature influence on the adhesion work of TiC/Al interface, they found the adhesion increased with the increase of temperature (973–1273 K). The adhesive energy of 4Al/5TiC-Ti, 4Al/5TiC-C, 5Al/4TiC-Ti and 5Al/4TiC-C was about 1 J/m2, which was less than 1Al/1TiC-C. Grytsyuk et al. [16] studied the interface structure and stability of CoO(111)/Ni(111), they found Ni atoms in the transition layer become more metallic and less magnetic moments as the number grows from 25 to 36, the optimal comprise of Ni atoms was 31 or 33. It can be concluded that it is suitable to analyze the interfaces of materials by first principles, but there are still no systematic studies on
⁎ Corresponding author at: School of Materials Science and Engineering, Beijing University of Technology, Number 100, Pingle Garden, Chaoyang District, Beijing 100124, PR China. E-mail address: [email protected] (H. Fu).
https://doi.org/10.1016/j.apsusc.2019.143742 Received 16 April 2019; Received in revised form 26 July 2019; Accepted 19 August 2019 Available online 20 August 2019 0169-4332/ © 2019 Elsevier B.V. All rights reserved.
Applied Surface Science 496 (2019) 143742
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Table 1 The composition of substrate and Ni45 powders.
Ni45 Cr12MoV
C
S
P
Mn
Si
B
Cr
Fe
Mo
Cu
V
Ni
0.33 1.45
– 0.01
– 0.02
– 0.21
3.05 0.27
1.89 –
10.01 12.30
5.28 Bal.
– 0.55
– 0.13
– 0.27
Bal. 0.11
Fig. 1. Elemental distribution of the coating.
the γ-Ni/(Ti, Nb)C interface. Based on the previous work [17,18], (Ti, Nb)C particles were synthesized in the Ni45 coatings. In present study, the interface orientation relation of γ-Ni/(Ti, Nb)C was identified by transmission electron microscopy (TEM), and the stability (adhesion work and interface energy), fracture toughness, electronic structure and interfacial bonding nature was calculated by first principles calculations. The results are expected to further understand the intrinsic characteristics of γ-Ni/(Ti, Nb)C interface.
(SCF) procedure to implement the electronic minimization, the ground state can be found. To ensure the convergence accuracy of total energy to 2.0 × 10−6 eV/atom, Monkhorst-Pack k-point grid and plane-wave cut off energy was 5 × 7 × 1 and 320 eV, respectively. The root-mean square stress was less than 0.1 GPa. In addition, NbC and Ni are all cubic structures (Space group: FM-3 M), which belong to NaCl crystal structure, aNbC = 4.47 Å [22,23], aNi = 3.535 Å [24]. 3. Results
2. Experimental
3.1. Interface orientation relationship
In this study, the substrate was Cr12MoV die steel, the cladding materials were Ni45 powders, Nb powders (99 wt%Nb), Cr3C2 powders (15wt%C and 85 wt%Cr) and Ti powders (30 wt%Ti and 69 wt%Fe). The diameter of above powders was 75-105 μm. Table 1 listed the composition of substrate and Ni45 powders. On the basis of the Ti/Nb mole ratio of 1:1, the (Ti, Nb)C particles were made by an IPG fiber laser system (YLS-6000) with continuous wave, which laser beam size is 5 mm × 5 mm [18]. The parameters were as follows: powder feeding rate k = 15 g/min, scanning speed ν = 4 mm/s, laser power P = 2000 W, flow rate of high-purity argon shielding gas ν′ = 15 L/min. In addition, the polished and etched was conducted on the cross section of coatings. A Scanning electron microscope (HITACHI S-3400, SEM) was used to observe the microstructure characteristics and elemental distribution, TEM (JEM-2100) equipped with energy dispersive spectrometer (Apollo XLT SDD, EDS) was used to further identify the phases and interface orientation relation. γ-Ni/(Ti, Nb)C interface was estimated by first-principles calculations [19,20]. The ground state and electronic minimization was implemented by Kohn-Sham equation, as performed in CASTEP code [21]. In this study, GGA (generalized gradient approximation) was used to dispose the exchange correlation energy. The Kleinman-Bylander ultrasoft pseudopotentials were implemented to depict the interactions between valence electrons and ionic cores. The valence electrons of Ni, Nb, C, Ti were 3d8 4s2, 4s2 4p6 4d4 5s1, 2s2 2p2, 3s2 3p6 3d2 4s2, respectively. By solving Kohn-Sham equation with the selfconsistent field
Fig. 1 exhibited the EDS mapping scanning of coatings. The microstructure was mainly composed of striped phases, lump phases and matrix. Ti, Nb and C atoms were coincided with the lump structures, C and Cr atoms were concentrated on the striped phases, and Ni, Si and Fe atoms were enriched in the matrix. Based on the previous work [17,18], they were (Ti, Nb)C, chromium carbides and γ-Ni matrix. TEM was carried out to further identify the γ-Ni and (Ti, Nb)C, as shown in Fig. 2. Fig. 2(a) exhibited the microstructure of γ-Ni and (Ti, Nb)C, as well as the corresponding SADP (selected area diffraction pattern), the lump phase was marked A, and the adjacent part was marked B. EDS point scanning results of A and B were showed in Fig. 2 (c) and Fig. 2 (d). It can be confirmed that A was (Ti, Nb)C, B was γ-Ni. In addition, the (Ti, Nb)C size was about 2.3 μm, and it was a continuous structure owing to the consistent reciprocal lattice. The results were also consistent with Li et al. [25]. However, the structure of (Ti, Nb)C was approximate to NbC because of the burn ability of Ti powders. Fig. 2 (b) showed the SADP of γ-Ni/(Ti, Nb)C interface, it can be concluded that the interface orientation relationship of them was [010](202)//[001](220). 3.2. γ-Ni/(Ti, Nb)C interface model The interface was modeled according to the above interface orientation relationship of γ-Ni/(Ti, Nb)C. As the lattice constant of (Ti, Nb)C was similar to NbC, NbC(110) and Ni(101) free surfaces were 2
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Fig. 2. TEM micrographs of interface (a) bright-field TEM micrograph of (Ti, Nb)C (110)/ γ-Ni (101) interface; (b) the SADP of interface in (a); (c)-(d) EDS of Point A and Point B.
where Eslab and Ebulk are the total energy of free surface slab and single atom (or molecular formula), respectively. n is atomic (or molecular formula) number, A is the surface area. In this study, the γsurf of NbC(110) and Ni(101) with different atoms (from 3 to 7) were calculated, respectively. Table 2 listed the γsurf convergence results with respect to the atom layers. It can be seen that it converged well when the surface cell contains more than four layers for NbC(110) and Ni (101). The five layers of NbC(110) and Ni(101) is enough thick to ensure the bulk like interior. In addition, to minimize the interface mismatch and interface stress, Ni(101) 2 × 1 × 1 supercell and NbC(110) were employed to model the interfaces, and the interface mismatch was less than 6%. Two stacking sites (case I and case II) illustrated in Fig. 3 were considered: the interfacial Nb atoms of NbC(110) were located at the top-site and center-site, respectively. In addition, a small number of atoms were dissolved in the γ-Ni as shown in Fig. 2, and Fe atoms has the higher content. In the Ni(101) models, Fe atom was apt to replace the center site of Ni by lower energy. Fig. 4 and Fig. 5 exhibited the γNi/(Ti, Nb)C interfaces, (Ti, Nb)C (110) interface was modeled by replacing Nb atoms of NbC(110) with Ti [32].
Table 2 The surface energy (γsurf) convergence results with respect to the atom layers. Atom layers / n
2 3 4 5 6 7
Surface energy (γs) / J/m2 NbC (110)
γ-Ni (101)
1.2 1.4 1.3 1.4 1.4 1.4
1.0 1.1 1.0 1.1 1.1 1.1
modeled with supercell slabs. 8 Å vacuum layers were added to the free surface slabs to represent the bulk-like interior. To ensure the calculating efficiency and precision, convergence tests were conducted for appropriate atom layers [26]. During the convergence tests, the surface energy was used to represent the surface stability, the energy required of a new surface was calculated when a crystal was divided into two halves along a crystal plane [27,28]. The surface energy (γsurf) can be defined by eq. (1) [29–31]: surf
=
Eslab
nEbulk 2A
3.3. Adhesion work
(1)
The ideal adhesion work (Wad) was used to estimate the mechanical 3
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Fig. 3. The interface models for γ-Ni (101)/NbC (110).
Fig. 4. The interface models for γ-Ni (101)/(Ti, Nb)C (110) in Case I.
properties of interfaces, which described the reversible work of separating into two free surfaces, and it can be expressed by eq. (2) [33,34]:
Wad =
Eslab, + Eslab, S
E
/
interfacial distance (d), the curve's peaks correspond the optimal distances and max adhesion work [35]. Based on the appropriate distances, fully relaxed calculation of the interfaces was carried out. Fig. 6 and Fig. 7 showed the UBER curves of Wad versus d, and Table 3 listed the adhesion work and interfacial distance results with two different methods (UBER and fully relaxed). It can be seen that Case II showed larger Wad than Case I from the two methods, indicating that the stacking sites have much influence on the Wad and d than the substitution position of Ti. The Case II-1, Case II-2, Case II-3, Case II-4 and
(2)
where Eslab,α and Eslab,β are the total energy of slab α and β with different layers, Eslab,α/β is the total energy of α/β interface, S is the interface area. In this study, a UBER (Universal Binding Energy Relation) method was utilized to obtain the Wad, which calculated by a serial 4
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Fig. 5. The interface models for γ-Ni (101)/(Ti, Nb)C (110) in Case II.
Fig. 6. UBER curves for different γ-Ni (101)/(Ti, Nb)C (110) interfaces in Case I.
Fig. 7. UBER curves for different γ-Ni (101)/(Ti, Nb)C (110) interfaces in Case II.
Case II-5 interfaces showed stronger interfacial bonding, interaction and thermodynamic stability. In addition, the Wad of Case I-4 and Case II-3 were larger in the case I and case II models, respectively.
Table 3 The adhesion work (Wad) and interfacial distance (d) of different interfaces with two method.
3.4. Interface energy
Stacking site
Interface energy is a quantity to describe the interface thermodynamic stability, which essentially came from the structure strain and interfacial chemical bonding [33]. In this study, (Ti, Nb)C and Ni are similar materials, resulting in a negative interface energy. Generally, a negative interface energy will promote the diffusion of interface atoms, which maybe bring into the interfacial alloying or new phases [36,37]. The interface energy (γint) can be estimated by [38]: int
=
Etotal
NNi µNi
NFe µFe
NTi µ Ti S
NNb µNb
NC µ C
(Ti,Nb)C
Top-site
Center-site
Ni
(3)
5
Interface
Case Case Case Case Case Case Case Case Case Case
I-1 I-2 I-3 I-4 I-5 II-1 II-2 II-3 II-4 II-5
UBER
Fully relaxed
d
Wad
d
Wad
~2.05 ~2.05 ~2.05 ~2.1 ~2.1 ~1.5 ~1.7 ~1.7 ~1.5 ~1.7
0.246 0.249 0.205 0.340 0.327 0.503 0.530 0.564 0.414 0.496
1.855 1.857 1.854 1.878 1.879 0.956 1.141 1.138 1.098 1.142
1.110 1.131 1.057 1.164 1.156 1.652 1.760 1.859 1.652 1.732
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interface energy of different models. It can be seen that the interface energy were all negative. The center-site stacking interfaces showed lower interface energy than the top-site, indicating that interfacial alloying was apt to occur in the Case II. In addition, the relationship of interface energy (γint) and adhesion work (Wad) can be expressed by eq. (4) [12,33]:
Table 4 The interface energy of different models. Stacking site
Interface
Interface energy γint (J/m2)
Top-site
Case Case Case Case Case Case Case Case Case Case
−2.623 −2.637 −2.618 −2.638 −2.601 −3.024 −3.122 −3.160 −3.051 −3.128
Center-site
I-1 I-2 I-3 I-4 I-5 II-1 II-2 II-3 II-4 II-5
Wad =
+
int
(4)
It can be concluded that a smaller γint corresponds to a larger Wad. The lower surface energy of Case I-4 and Case II-3 in the case I and case II models was observed, respectively, which was consistent with the results of adhesion work. 4. Discussion
where Etotal is the total energy of fully relaxed interface, NNi, NFe, NTi, NNb and NC are the numbers of Ni, Fe, Ti, Nb and C atoms, respectively. μNi, μFe, μTi, μNb and μC are the chemical potentials of Ni, Fe, Ti, Nb and C atoms, respectively. S′ is the interface area. γ(Ti, Nb)C and γγ-Ni are the surface energy of (Ti, Nb)C and γ-Ni. Table 4 listed
4.1. Interfacial fracture toughness The interfaces between matrix and reinforcement phases have a significant effect on mechanical properties, while the fracture
Fig. 8. The charge density distributions for interfaces: the fully relaxed models of Case I-4 (a) and Case II-3 (d); the charge density distributions of Case I-4 (b-c) and Case II-3 (e-f).
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Fig. 9. The difference electron density distributions for interfaces: (a-b):Case I-4; (c-d): Case II-3.
toughness is mainly depended on the phases and interfaces. According to the Griffith fracture theory, the fracture work (G) of bulk materials along a certain lattice plane can be expressed by G~2γ, where γ is the surface energy. If G < Wad, the fracture will occur in the bulk material; if G > Wad, the fracture will occur at the interface. The fracture work of γ-Ni (101) and (Ti, Nb)C (110) was 2.11 J/m2 and 3.08–3.29 J/ m2, which was all larger than the adhesion work (1.06–1.86 J/m2). In addition, the fracture work of (Ti, Nb)C along (110) plane was larger than γ-Ni (101), and (Ti, Nb)C showed higher breaking strength in the ten interfaces. It can be concluded that the mechanical failure of γ-Ni/ (Ti, Nb)C may initiate at the interface or close to γ-Ni rather than the reinforcement phase (Ti, Nb)C. The resistance of materials to deformation can be defined by Young's modulus, Kim et al. [39] and Zhao et al. [40] calculated the elastic properties of Ni and (Ti, Nb)C by first-principles calculations, respectively, they found the Young's modulus of (Ti, Nb)C was 472–497 GPa, which was higher than Ni (265 GPa). It can be concluded that (Ti, Nb)C showed more resistant to deformation. Li et al. [41] conducted a first principles study of interfacial fracture toughness of Fe/WC, they also found reinforcement phase showed higher breaking strength, and W-HCP interface failure is more likely to occur at the interface. Similarly, Li et al. [12] also found the reinforcement phase showed higher breaking strength than Ti in the Ti(0001)/TiC(111) interface, indicating that the interface failure may occurs at the interface or near the matrix, it was consistence with our study.
distance of Case II-3 was less than Case I-4, resulting more tighter interface. Ionic bond features were observed from the Ni and Nb atoms of interfaces as shown in Fig. 8(b) and Fig. 8(e). In addition, the charge accumulation was occurred in the Ni and C atoms, resulting more polar covalent features and stronger bonding characteristics. Meanwhile C atoms and Ti atoms also exhibited covalent characteristics as shown in Fig. 8(c) and Fig. 8(f). Therefore, the chemical bonding of interface was a mixture of covalent bond with partial ionic bond. Besides, the distance of atoms around the interface in Case II-3 was larger, while showed higher Wad. It can be attributed to the C or Nb atoms interacted with four atoms around it, resulting in stronger interfacial bonding force. Fig. 9 showed the difference electron density distributions of Case I4 and Case II-3 interfaces. The legend illustrated in the lower right corner showed the relationship between the charge and colors. The localized electron density is mainly concentrated on the interface and its vicinity. The loss and gain of electrons can be also obtained from Fig. 9. The electrons of interface were shifted from Ni, Ti and Nb atoms to C atoms, the stronger charge transfer and electron interaction generated covalent bonding, as well as certain ionic characteristics, which was consistent with results of total electron density distribution. 4.3. Interfacial bonding The bonding nature of γ-Ni/(Ti, Nb)C was studied by the partial density of states (PDOS). Fig. 10 and Fig. 11 illustrated the PDOS of Case I-4 and Case II-3. The PDOS of interfacial C atom all exhibited new peaks, and the PDOS height in the first layer was much lower comparing with other layers, indicating that the charge shift between C and Ni atoms, as well as C and Nb atoms. Moreover, Nb and C atoms were resonant with peaks of −3.5 eV (Case I-4) and −3.8 eV (Case II-3), and the overlapping states contributed to the hybridization of C-2p and Nb3d orbital, so as to form NieC and NbeC covalent bonds. Comparing other layers of Ni, the PDOS of Ni in the first layer shifted toward negative levels (especially in Case II-3), indicating the obvious electron transfer from Ni to C atoms. The interface also showed ionic characteristics owing to higher Fermi level values. It should be noted that more overlapping states between C and Nb/Ti atoms were observed in the interior of (Ti, Nb)C than the interface, suggesting that the bonding
4.2. Electronic structure The atomic bonding characteristics of interface has an great influence on the mechanical properties. The distribution of total electron density and difference electron density calculated in this study was utilized to study the interfacial bonding characteristics of γ-Ni/(Ti, Nb)C. To observe the effect of Nb and Ti atoms intuitively, the directions of case I and Case II along (011) plane were chosen. Case I-4 and Case II-3 has great influence in the Case I and Case II models, respectively. Fig. 8 exhibited the total electron density distribution of fully relaxed Case I-4 and Case II-3 interfaces, respectively. Two bonding methods (NbeNi and CeNi) were observed in each stacking site interfaces. As can be seen from Fig. 8(a) and Fig. 8(d), the interface
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Fig. 10. Partial density of states (PDOS) in Case I-4.
in the (Ti, Nb)C was stronger than the interface. As a result of which, the mechanical failure of interface was easily occurred at the interface, it was agreement with the results of interfacial fracture toughness.
were cubic structures, and the interface orientation relationship of them was [001](220)//[010](202). (2) The stacking sites have much influence than the substitution position of Ti, the center-site stacking interfaces shower higher adhesion work and lower interface energy. The mechanical failure of γ-Ni/ (Ti, Nb)C may initiate at the interface or close to γ-Ni. (3) The electronic structure and PDOS results suggest that the bonding behavior of γ-Ni/(Ti, Nb)C was a mixture of covalent bond with partial ionic bond, which was mainly contributed from NieC, NbeC and NbeNi interaction.
5. Conclusions In this study, the interface properties of γ-Ni/(Ti, Nb)C were studied, the interface orientation relationship was identified by TEM firstly, and then ten interfaces of γ-Ni (101)/(Ti, Nb)C (110) were calculated by first principles. The main conclusions are as follows: (1) The in-situ (Ti, Nb)C compound was a composite carbide with consistent reciprocal lattice. In the SADP of γ-Ni and (Ti, Nb)C, they
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Fig. 11. Partial density of states (PDOS) in Case II-3.
Acknowledgement
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The stability, fracture toughness and electronic structure at γ-Ni (101)/(Ti, Nb)C (110) interface: A first-principles investigation
T
Shuting Suna, Hanguang Fua, , Shuangye Chenb, Jiacai Kuangc, Xuelong Pinga, Kaiming Wangd, Yingjun Dengc, Xingye Guoa, Jian Lina, Yongping Leia ⁎
a
Key Laboratory of Advanced Functional Materials, Ministry of Education, School of Materials Science and Engineering, Beijing University of Technology, Beijing 100124, PR China b Faculty of Information Technology, Beijing University of Technology, Beijing 100124, PR China c School of Automotive and Mechanical Engineering, Changsha University of Science and Technology, Changsha 410114, Hunan Province, PR China d State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, PR China
ARTICLE INFO
ABSTRACT
Keywords: γ-Ni/(Ti, Nb)C interface First principles Interface stability Interfacial fracture toughness Electronic structure
(Ti, Nb)C particles reinforced Ni45 coatings were made by a fiber laser system. The atomic structure, interfacial stability, interfacial fracture toughness, electronic structure and bonding nature of γ-Ni/(Ti, Nb)C were systematically analyzed using first principles calculations. TEM results showed that the interface orientation relationship of γ-Ni/(Ti, Nb)C was [010](202)//[001](220). For the γ-Ni/(Ti, Nb)C interfaces, the stacking sites have much influence than the substitution position of Ti, the center-site stacking interfaces shower higher adhesion work and lower interface energy, indicating the interfacial alloying or new phases were prone to formed. According to the interfacial fracture toughness results, the mechanical failure of γ-Ni/(Ti, Nb)C may initiate at the interface or close to γ-Ni rather than (Ti, Nb)C. The bonding behavior of γ-Ni/(Ti, Nb)C was a blend of covalent bond and partial ionic bond. The chemical bonding properties of interfacial atoms were also discussed in view of electronic structure and partial density of states (PDOS) results.
1. Introduction As a promising surface treatment technology, laser cladding has become a major method in the surface modification field [1,2]. Especially, the combination of laser cladding and metal matrix composite (MMC) have many advantages, the fabricated coatings not only exhibit the high toughness and strength of metal matrix material, but also show the high modulus and wear resistance of reinforcement phases [3,4]. Thus they have been widely applied in the aerospace, automotive die repair, chemical industries and other fields [5–8]. However, the reinforcement phase/matrix interface has become a core issue of coatings, the current research is mainly focuses on the microstructures, phase composition and element distribution [9–11], there is still a lack of indepth research on the intrinsic characteristics of interface physical phenomena such as interface behavior and interface structure. In recent years, with the rapid development of computer technology, remarkable results of interfaces have been achieved by first principles calculations. Li et al. [12] studied the interface properties of TiC(111)/α-Ti(0001) by first principles, they found the maximum
interfacial fracture toughness was 4.8 MPa m1/2, and the interfacial bonding mainly consist of TieTi metallic interaction and CeTi covalent bonds. Sawada et al. [13] investigated the interface energy of Fe/NbC using first principles, the strain energy around the precipitate was also estimated by a classical molecular dynamics method. Gong et al. [14] studied the reinforcing effects of Ni/Ni3Al interface induced by Re, Co, Ru, Ta, Cr, W and Mo elements, they found the best reinforcing effect was attributed to rare earth Re, while W, Ta and Co elements appeared to be less potent. Sun et al. [15] discussed the temperature influence on the adhesion work of TiC/Al interface, they found the adhesion increased with the increase of temperature (973–1273 K). The adhesive energy of 4Al/5TiC-Ti, 4Al/5TiC-C, 5Al/4TiC-Ti and 5Al/4TiC-C was about 1 J/m2, which was less than 1Al/1TiC-C. Grytsyuk et al. [16] studied the interface structure and stability of CoO(111)/Ni(111), they found Ni atoms in the transition layer become more metallic and less magnetic moments as the number grows from 25 to 36, the optimal comprise of Ni atoms was 31 or 33. It can be concluded that it is suitable to analyze the interfaces of materials by first principles, but there are still no systematic studies on
⁎ Corresponding author at: School of Materials Science and Engineering, Beijing University of Technology, Number 100, Pingle Garden, Chaoyang District, Beijing 100124, PR China. E-mail address: [email protected] (H. Fu).
https://doi.org/10.1016/j.apsusc.2019.143742 Received 16 April 2019; Received in revised form 26 July 2019; Accepted 19 August 2019 Available online 20 August 2019 0169-4332/ © 2019 Elsevier B.V. All rights reserved.
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Table 1 The composition of substrate and Ni45 powders.
Ni45 Cr12MoV
C
S
P
Mn
Si
B
Cr
Fe
Mo
Cu
V
Ni
0.33 1.45
– 0.01
– 0.02
– 0.21
3.05 0.27
1.89 –
10.01 12.30
5.28 Bal.
– 0.55
– 0.13
– 0.27
Bal. 0.11
Fig. 1. Elemental distribution of the coating.
the γ-Ni/(Ti, Nb)C interface. Based on the previous work [17,18], (Ti, Nb)C particles were synthesized in the Ni45 coatings. In present study, the interface orientation relation of γ-Ni/(Ti, Nb)C was identified by transmission electron microscopy (TEM), and the stability (adhesion work and interface energy), fracture toughness, electronic structure and interfacial bonding nature was calculated by first principles calculations. The results are expected to further understand the intrinsic characteristics of γ-Ni/(Ti, Nb)C interface.
(SCF) procedure to implement the electronic minimization, the ground state can be found. To ensure the convergence accuracy of total energy to 2.0 × 10−6 eV/atom, Monkhorst-Pack k-point grid and plane-wave cut off energy was 5 × 7 × 1 and 320 eV, respectively. The root-mean square stress was less than 0.1 GPa. In addition, NbC and Ni are all cubic structures (Space group: FM-3 M), which belong to NaCl crystal structure, aNbC = 4.47 Å [22,23], aNi = 3.535 Å [24]. 3. Results
2. Experimental
3.1. Interface orientation relationship
In this study, the substrate was Cr12MoV die steel, the cladding materials were Ni45 powders, Nb powders (99 wt%Nb), Cr3C2 powders (15wt%C and 85 wt%Cr) and Ti powders (30 wt%Ti and 69 wt%Fe). The diameter of above powders was 75-105 μm. Table 1 listed the composition of substrate and Ni45 powders. On the basis of the Ti/Nb mole ratio of 1:1, the (Ti, Nb)C particles were made by an IPG fiber laser system (YLS-6000) with continuous wave, which laser beam size is 5 mm × 5 mm [18]. The parameters were as follows: powder feeding rate k = 15 g/min, scanning speed ν = 4 mm/s, laser power P = 2000 W, flow rate of high-purity argon shielding gas ν′ = 15 L/min. In addition, the polished and etched was conducted on the cross section of coatings. A Scanning electron microscope (HITACHI S-3400, SEM) was used to observe the microstructure characteristics and elemental distribution, TEM (JEM-2100) equipped with energy dispersive spectrometer (Apollo XLT SDD, EDS) was used to further identify the phases and interface orientation relation. γ-Ni/(Ti, Nb)C interface was estimated by first-principles calculations [19,20]. The ground state and electronic minimization was implemented by Kohn-Sham equation, as performed in CASTEP code [21]. In this study, GGA (generalized gradient approximation) was used to dispose the exchange correlation energy. The Kleinman-Bylander ultrasoft pseudopotentials were implemented to depict the interactions between valence electrons and ionic cores. The valence electrons of Ni, Nb, C, Ti were 3d8 4s2, 4s2 4p6 4d4 5s1, 2s2 2p2, 3s2 3p6 3d2 4s2, respectively. By solving Kohn-Sham equation with the selfconsistent field
Fig. 1 exhibited the EDS mapping scanning of coatings. The microstructure was mainly composed of striped phases, lump phases and matrix. Ti, Nb and C atoms were coincided with the lump structures, C and Cr atoms were concentrated on the striped phases, and Ni, Si and Fe atoms were enriched in the matrix. Based on the previous work [17,18], they were (Ti, Nb)C, chromium carbides and γ-Ni matrix. TEM was carried out to further identify the γ-Ni and (Ti, Nb)C, as shown in Fig. 2. Fig. 2(a) exhibited the microstructure of γ-Ni and (Ti, Nb)C, as well as the corresponding SADP (selected area diffraction pattern), the lump phase was marked A, and the adjacent part was marked B. EDS point scanning results of A and B were showed in Fig. 2 (c) and Fig. 2 (d). It can be confirmed that A was (Ti, Nb)C, B was γ-Ni. In addition, the (Ti, Nb)C size was about 2.3 μm, and it was a continuous structure owing to the consistent reciprocal lattice. The results were also consistent with Li et al. [25]. However, the structure of (Ti, Nb)C was approximate to NbC because of the burn ability of Ti powders. Fig. 2 (b) showed the SADP of γ-Ni/(Ti, Nb)C interface, it can be concluded that the interface orientation relationship of them was [010](202)//[001](220). 3.2. γ-Ni/(Ti, Nb)C interface model The interface was modeled according to the above interface orientation relationship of γ-Ni/(Ti, Nb)C. As the lattice constant of (Ti, Nb)C was similar to NbC, NbC(110) and Ni(101) free surfaces were 2
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Fig. 2. TEM micrographs of interface (a) bright-field TEM micrograph of (Ti, Nb)C (110)/ γ-Ni (101) interface; (b) the SADP of interface in (a); (c)-(d) EDS of Point A and Point B.
where Eslab and Ebulk are the total energy of free surface slab and single atom (or molecular formula), respectively. n is atomic (or molecular formula) number, A is the surface area. In this study, the γsurf of NbC(110) and Ni(101) with different atoms (from 3 to 7) were calculated, respectively. Table 2 listed the γsurf convergence results with respect to the atom layers. It can be seen that it converged well when the surface cell contains more than four layers for NbC(110) and Ni (101). The five layers of NbC(110) and Ni(101) is enough thick to ensure the bulk like interior. In addition, to minimize the interface mismatch and interface stress, Ni(101) 2 × 1 × 1 supercell and NbC(110) were employed to model the interfaces, and the interface mismatch was less than 6%. Two stacking sites (case I and case II) illustrated in Fig. 3 were considered: the interfacial Nb atoms of NbC(110) were located at the top-site and center-site, respectively. In addition, a small number of atoms were dissolved in the γ-Ni as shown in Fig. 2, and Fe atoms has the higher content. In the Ni(101) models, Fe atom was apt to replace the center site of Ni by lower energy. Fig. 4 and Fig. 5 exhibited the γNi/(Ti, Nb)C interfaces, (Ti, Nb)C (110) interface was modeled by replacing Nb atoms of NbC(110) with Ti [32].
Table 2 The surface energy (γsurf) convergence results with respect to the atom layers. Atom layers / n
2 3 4 5 6 7
Surface energy (γs) / J/m2 NbC (110)
γ-Ni (101)
1.2 1.4 1.3 1.4 1.4 1.4
1.0 1.1 1.0 1.1 1.1 1.1
modeled with supercell slabs. 8 Å vacuum layers were added to the free surface slabs to represent the bulk-like interior. To ensure the calculating efficiency and precision, convergence tests were conducted for appropriate atom layers [26]. During the convergence tests, the surface energy was used to represent the surface stability, the energy required of a new surface was calculated when a crystal was divided into two halves along a crystal plane [27,28]. The surface energy (γsurf) can be defined by eq. (1) [29–31]: surf
=
Eslab
nEbulk 2A
3.3. Adhesion work
(1)
The ideal adhesion work (Wad) was used to estimate the mechanical 3
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Fig. 3. The interface models for γ-Ni (101)/NbC (110).
Fig. 4. The interface models for γ-Ni (101)/(Ti, Nb)C (110) in Case I.
properties of interfaces, which described the reversible work of separating into two free surfaces, and it can be expressed by eq. (2) [33,34]:
Wad =
Eslab, + Eslab, S
E
/
interfacial distance (d), the curve's peaks correspond the optimal distances and max adhesion work [35]. Based on the appropriate distances, fully relaxed calculation of the interfaces was carried out. Fig. 6 and Fig. 7 showed the UBER curves of Wad versus d, and Table 3 listed the adhesion work and interfacial distance results with two different methods (UBER and fully relaxed). It can be seen that Case II showed larger Wad than Case I from the two methods, indicating that the stacking sites have much influence on the Wad and d than the substitution position of Ti. The Case II-1, Case II-2, Case II-3, Case II-4 and
(2)
where Eslab,α and Eslab,β are the total energy of slab α and β with different layers, Eslab,α/β is the total energy of α/β interface, S is the interface area. In this study, a UBER (Universal Binding Energy Relation) method was utilized to obtain the Wad, which calculated by a serial 4
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Fig. 5. The interface models for γ-Ni (101)/(Ti, Nb)C (110) in Case II.
Fig. 6. UBER curves for different γ-Ni (101)/(Ti, Nb)C (110) interfaces in Case I.
Fig. 7. UBER curves for different γ-Ni (101)/(Ti, Nb)C (110) interfaces in Case II.
Case II-5 interfaces showed stronger interfacial bonding, interaction and thermodynamic stability. In addition, the Wad of Case I-4 and Case II-3 were larger in the case I and case II models, respectively.
Table 3 The adhesion work (Wad) and interfacial distance (d) of different interfaces with two method.
3.4. Interface energy
Stacking site
Interface energy is a quantity to describe the interface thermodynamic stability, which essentially came from the structure strain and interfacial chemical bonding [33]. In this study, (Ti, Nb)C and Ni are similar materials, resulting in a negative interface energy. Generally, a negative interface energy will promote the diffusion of interface atoms, which maybe bring into the interfacial alloying or new phases [36,37]. The interface energy (γint) can be estimated by [38]: int
=
Etotal
NNi µNi
NFe µFe
NTi µ Ti S
NNb µNb
NC µ C
(Ti,Nb)C
Top-site
Center-site
Ni
(3)
5
Interface
Case Case Case Case Case Case Case Case Case Case
I-1 I-2 I-3 I-4 I-5 II-1 II-2 II-3 II-4 II-5
UBER
Fully relaxed
d
Wad
d
Wad
~2.05 ~2.05 ~2.05 ~2.1 ~2.1 ~1.5 ~1.7 ~1.7 ~1.5 ~1.7
0.246 0.249 0.205 0.340 0.327 0.503 0.530 0.564 0.414 0.496
1.855 1.857 1.854 1.878 1.879 0.956 1.141 1.138 1.098 1.142
1.110 1.131 1.057 1.164 1.156 1.652 1.760 1.859 1.652 1.732
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interface energy of different models. It can be seen that the interface energy were all negative. The center-site stacking interfaces showed lower interface energy than the top-site, indicating that interfacial alloying was apt to occur in the Case II. In addition, the relationship of interface energy (γint) and adhesion work (Wad) can be expressed by eq. (4) [12,33]:
Table 4 The interface energy of different models. Stacking site
Interface
Interface energy γint (J/m2)
Top-site
Case Case Case Case Case Case Case Case Case Case
−2.623 −2.637 −2.618 −2.638 −2.601 −3.024 −3.122 −3.160 −3.051 −3.128
Center-site
I-1 I-2 I-3 I-4 I-5 II-1 II-2 II-3 II-4 II-5
Wad =
+
int
(4)
It can be concluded that a smaller γint corresponds to a larger Wad. The lower surface energy of Case I-4 and Case II-3 in the case I and case II models was observed, respectively, which was consistent with the results of adhesion work. 4. Discussion
where Etotal is the total energy of fully relaxed interface, NNi, NFe, NTi, NNb and NC are the numbers of Ni, Fe, Ti, Nb and C atoms, respectively. μNi, μFe, μTi, μNb and μC are the chemical potentials of Ni, Fe, Ti, Nb and C atoms, respectively. S′ is the interface area. γ(Ti, Nb)C and γγ-Ni are the surface energy of (Ti, Nb)C and γ-Ni. Table 4 listed
4.1. Interfacial fracture toughness The interfaces between matrix and reinforcement phases have a significant effect on mechanical properties, while the fracture
Fig. 8. The charge density distributions for interfaces: the fully relaxed models of Case I-4 (a) and Case II-3 (d); the charge density distributions of Case I-4 (b-c) and Case II-3 (e-f).
6
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Fig. 9. The difference electron density distributions for interfaces: (a-b):Case I-4; (c-d): Case II-3.
toughness is mainly depended on the phases and interfaces. According to the Griffith fracture theory, the fracture work (G) of bulk materials along a certain lattice plane can be expressed by G~2γ, where γ is the surface energy. If G < Wad, the fracture will occur in the bulk material; if G > Wad, the fracture will occur at the interface. The fracture work of γ-Ni (101) and (Ti, Nb)C (110) was 2.11 J/m2 and 3.08–3.29 J/ m2, which was all larger than the adhesion work (1.06–1.86 J/m2). In addition, the fracture work of (Ti, Nb)C along (110) plane was larger than γ-Ni (101), and (Ti, Nb)C showed higher breaking strength in the ten interfaces. It can be concluded that the mechanical failure of γ-Ni/ (Ti, Nb)C may initiate at the interface or close to γ-Ni rather than the reinforcement phase (Ti, Nb)C. The resistance of materials to deformation can be defined by Young's modulus, Kim et al. [39] and Zhao et al. [40] calculated the elastic properties of Ni and (Ti, Nb)C by first-principles calculations, respectively, they found the Young's modulus of (Ti, Nb)C was 472–497 GPa, which was higher than Ni (265 GPa). It can be concluded that (Ti, Nb)C showed more resistant to deformation. Li et al. [41] conducted a first principles study of interfacial fracture toughness of Fe/WC, they also found reinforcement phase showed higher breaking strength, and W-HCP interface failure is more likely to occur at the interface. Similarly, Li et al. [12] also found the reinforcement phase showed higher breaking strength than Ti in the Ti(0001)/TiC(111) interface, indicating that the interface failure may occurs at the interface or near the matrix, it was consistence with our study.
distance of Case II-3 was less than Case I-4, resulting more tighter interface. Ionic bond features were observed from the Ni and Nb atoms of interfaces as shown in Fig. 8(b) and Fig. 8(e). In addition, the charge accumulation was occurred in the Ni and C atoms, resulting more polar covalent features and stronger bonding characteristics. Meanwhile C atoms and Ti atoms also exhibited covalent characteristics as shown in Fig. 8(c) and Fig. 8(f). Therefore, the chemical bonding of interface was a mixture of covalent bond with partial ionic bond. Besides, the distance of atoms around the interface in Case II-3 was larger, while showed higher Wad. It can be attributed to the C or Nb atoms interacted with four atoms around it, resulting in stronger interfacial bonding force. Fig. 9 showed the difference electron density distributions of Case I4 and Case II-3 interfaces. The legend illustrated in the lower right corner showed the relationship between the charge and colors. The localized electron density is mainly concentrated on the interface and its vicinity. The loss and gain of electrons can be also obtained from Fig. 9. The electrons of interface were shifted from Ni, Ti and Nb atoms to C atoms, the stronger charge transfer and electron interaction generated covalent bonding, as well as certain ionic characteristics, which was consistent with results of total electron density distribution. 4.3. Interfacial bonding The bonding nature of γ-Ni/(Ti, Nb)C was studied by the partial density of states (PDOS). Fig. 10 and Fig. 11 illustrated the PDOS of Case I-4 and Case II-3. The PDOS of interfacial C atom all exhibited new peaks, and the PDOS height in the first layer was much lower comparing with other layers, indicating that the charge shift between C and Ni atoms, as well as C and Nb atoms. Moreover, Nb and C atoms were resonant with peaks of −3.5 eV (Case I-4) and −3.8 eV (Case II-3), and the overlapping states contributed to the hybridization of C-2p and Nb3d orbital, so as to form NieC and NbeC covalent bonds. Comparing other layers of Ni, the PDOS of Ni in the first layer shifted toward negative levels (especially in Case II-3), indicating the obvious electron transfer from Ni to C atoms. The interface also showed ionic characteristics owing to higher Fermi level values. It should be noted that more overlapping states between C and Nb/Ti atoms were observed in the interior of (Ti, Nb)C than the interface, suggesting that the bonding
4.2. Electronic structure The atomic bonding characteristics of interface has an great influence on the mechanical properties. The distribution of total electron density and difference electron density calculated in this study was utilized to study the interfacial bonding characteristics of γ-Ni/(Ti, Nb)C. To observe the effect of Nb and Ti atoms intuitively, the directions of case I and Case II along (011) plane were chosen. Case I-4 and Case II-3 has great influence in the Case I and Case II models, respectively. Fig. 8 exhibited the total electron density distribution of fully relaxed Case I-4 and Case II-3 interfaces, respectively. Two bonding methods (NbeNi and CeNi) were observed in each stacking site interfaces. As can be seen from Fig. 8(a) and Fig. 8(d), the interface
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Fig. 10. Partial density of states (PDOS) in Case I-4.
in the (Ti, Nb)C was stronger than the interface. As a result of which, the mechanical failure of interface was easily occurred at the interface, it was agreement with the results of interfacial fracture toughness.
were cubic structures, and the interface orientation relationship of them was [001](220)//[010](202). (2) The stacking sites have much influence than the substitution position of Ti, the center-site stacking interfaces shower higher adhesion work and lower interface energy. The mechanical failure of γ-Ni/ (Ti, Nb)C may initiate at the interface or close to γ-Ni. (3) The electronic structure and PDOS results suggest that the bonding behavior of γ-Ni/(Ti, Nb)C was a mixture of covalent bond with partial ionic bond, which was mainly contributed from NieC, NbeC and NbeNi interaction.
5. Conclusions In this study, the interface properties of γ-Ni/(Ti, Nb)C were studied, the interface orientation relationship was identified by TEM firstly, and then ten interfaces of γ-Ni (101)/(Ti, Nb)C (110) were calculated by first principles. The main conclusions are as follows: (1) The in-situ (Ti, Nb)C compound was a composite carbide with consistent reciprocal lattice. In the SADP of γ-Ni and (Ti, Nb)C, they
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Fig. 11. Partial density of states (PDOS) in Case II-3.
Acknowledgement
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