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compressive deformations
Accepted Manuscript Title: Effects of twin boundaries in vanadium nitride films subjected to tensile/compressive deformations Authors: Tao Fu, Xianghe Peng, Cheng Huang, Yinbo Zhao, Shayuan Weng, Xiang Chen, Ning Hu PII: DOI: Reference:
S0169-4332(17)32175-X http://dx.doi.org/doi:10.1016/j.apsusc.2017.07.174 APSUSC 36708
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Received date: Revised date: Accepted date:
17-4-2017 24-6-2017 19-7-2017
Please cite this article as: Tao Fu, Xianghe Peng, Cheng Huang, Yinbo Zhao, Shayuan Weng, Xiang Chen, Ning Hu, Effects of twin boundaries in vanadium nitride films subjected to tensile/compressive deformations, Applied Surface Sciencehttp://dx.doi.org/10.1016/j.apsusc.2017.07.174 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Effects of twin boundaries in vanadium nitride films subjected to tensile/compressive deformations Tao Fu1, Xianghe Peng1, 2,*, Cheng Huang1, Yinbo Zhao1, Shayuan Weng1, Xiang Chen3 and Ning Hu1,* 1
College of Aerospace Engineering, Chongqing University, Chongqing 400044, China State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing 400044, China 3 Advanced Manufacturing Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China 2
*Corresponding authors. Address: College of Aerospace Engineering, Chongqing University, Chongqing 400044, China TEL: +86–23–65103755; FAX: +86–23–65102521 E-mail: [email protected] (X. P.); [email protected] (N. H.)
Highlights
The effects of different twin boundary (TB) atoms and tension-compression asymmetry in VN are investigated.
In compression, the migration of TBs with V atoms to that with N atoms contributes to softening.
In tension, fractures occur at the TBs, which does not result in any improvement of fracture toughness and critical stress.
Different deformation mechanisms are responsible for the plastic tension-compression asymmetry in VN.
Abstract: Two kinds of atoms can serve as the twin boundary (TB) atoms in a transition metal nitride (TMN). In this work, we performed molecular dynamics (MD) simulations for the responses of vanadium nitride (VN) films with different kinds of TB atoms (V or N) subjected to uniaxial tensile/compressive deformations, to investigate their effects and the tensile-compressive asymmetry. In compressive deformation, the migration of TBs with V atoms to that with N atoms contributes to softening, while the pile-up of dislocations at TBs contributes to strengthening. During tension, fractures occur at the TBs without distinct nucleation of dislocations, the nature of the brittle fracture, which does not result in any 1
improvement of fracture toughness and critical stress. Different frictional effects, cutoff radii, asymmetrical tensile and compressive nature of the interatomic potential and different deformation mechanisms are responsible for the tension-compression asymmetry in VN.
Keywords: Vanadium nitride; Nanotwin; Twin boundary migration; Tension-compression asymmetry; Molecular dynamics simulation
1. Introduction The effect of grain boundaries (GBs), as an important factor affecting the mechanical behavior of metals and ceramics, is a hot research topic in recent year [1-5]. Much effort has been made in experimental [6-8] and theoretical researches [9-13] for the effects of GBs in metals, and it has been accepted that GBs can improve the strength of the metallic material by impeding the movement of dislocations. GBs can react with and absorb dislocations, reducing dislocation density [3] and resulting in softening [14]. However, in transition metal nitrides and carbides, such as vanadium nitride (VN) and vanadium carbide (VC) [15], which have been widely used as protection coatings materials for molds, tools, and cutting tools, due to their outstanding mechanical and physical properties [16], less progress related to the effects of GBs on their mechanical behavior can be found in the literature. Low energy symmetrical twin boundaries (TBs) are commonly chosen as a typical representative of GBs and have been widely investigated [17, 18]. Lu et al., [19, 20] found that introducing twins into copper (Cu) can increase the strength of Cu without losing toughness, and the strength reaches maximum as the twin thickness decreases to 15 nm. However, it would decrease with the further decrease of twin thickness, implying some different softening mechanism. Zhu and Gao [21] and Lu [22] summarized the three models of dislocation–twin boundary (TB) interactions in FCC materials, related to two hardening modes (Slip transfer and Confined-layer slip) and one softening mode (Twinning partial slip), respectively. The twinning partial slip was formed by the partial dislocations reacting with the TB [21, 22]. Recently, Fu et al. [14] found in the nanoindention on Cu/Ni multilayer that the partial slip parallel with twin boundary can also serve as a softening mechanism, similar to the twinning partial slip. So far most work focused on the effects of TBs in FCC metals, and less 2
attention has been paid to that in ceramics, e.g. vanadium nitride (VN) for it had not been observed in experiment. In the recent work, it was found by first principle calculations that twin boundaries can exist in transition-metal nitrides [23], which was further confirmed in the molecular dynamics (MD) simulation of nanoindentation on VN (111) at 300 K [24]. Moreover, Xue et al [25] identified {111} twin boundary in rocksalt (B1) structure MnS by combing observation by transmission electron microscopy and the result using density functional theory calculation, suggesting the necessity of the study for the role of TBs in such kind of materials. Although transition metal carbides and nitrides with NaCl structure usually have high twin boundary energies (TBEs) [26], it was found recently that TBEs can be reduced by introducing vacancies [27] and alloying elements [28, 29]. However, due to the limit of the interatomic potentials for ternary or more elements, it is still hard to investigate the effects of alloying elements on the mechanical behavior of transition metal carbides and nitrides with the NaCl structure. As for the effects of vacancies, it can be investigated using MD simulations, however, the effects of vacancies including that of atomic type and the location of vacancies, the vacancy density and the ratio of two types of vacancy atoms, are complex. Therefore, in this work, we assume that the TBs have been introduced into the materials before deformation. It is know that the B1 structure VN is a typical structure by nesting two FCC structures, and it would have two possible kinds of atoms (V and N) at the symmetric atomic plane of a TB, in contrast to the twinned FCC metallic where there is only one possible kind of atoms. Therefore, the deformation mechanisms for FCC metals may not be applied to transition-metal nitrides. Moreover, tension-compression asymmetry is also one of the most important phenomena. In this article, we investigate with MD simulation the responses of a single VN and twinned VN films with different kinds of TB atoms subjected to tensile/compressive deformation, for the purpose to explore the effects of different kind of TB atoms on the mechanical properties and the cause of tensile-compressive asymmetry.
2. Simulation details The modified embedded atom method (MEAM) potential [30-32] is adopted in our simulations. The parameters in the potentials for the single elements V and N and those in the 3
binary interatomic potential between V and N have been given by Baskes et al. [31], Lee et al. [32] and Fu et al. [33], respectively. MEAM potentials was found to be able to reproduce the fundamental physical and mechanical properties of materials, such as lattice parameters, cohesive energy, elastic property and surface energy, and have been successfully applied to analyze the fracture behavior of VN films [33] and explore the deformation mechanisms of VN under indentation, incorporating stacking fault energy [24, 34-36]. Figure 1(a), (b) and (c) show the samples with a single crystal, with V termination TBs and with N termination TBs, marked with SC, TBV and TBN, respectively. For SC, there is no twin boundary, and the axes X, Y and Z correspond respectively to lattice orientations 112 ,
110
and
1 11 . For TBV or TBN, TBs are introduced, and the axes X, Y and Z correspond
respectively to the lattice orientations 112 ,
110
and
1 11
for odd layers, and to
1 12 ,
1 10 and 1 11 for even layers. The difference between TBV and TBN lies in the atomic type at the symmetric plane. Before loading, the optimized stable configuration of each sample is achieved using an energy minimization approach based on conjugate gradient (CG) algorithm. Then the isothermal-isobaric NPT ensemble is used to relax the system under a pressure free condition to an equilibration state at T=300 K for 30 ps and T=600 K for 60 ps, respectively. During loading, each sample is stretched/compressed in Z-direction at a strain rate of 109 s−1, the NPT ensemble with Nose/Hoover barostat is employed [37] to keep pressure free in X- and Y- directions. It is known that the total thickness of film is usually of μm-scale, consisting of thousands of TBs. The ratio of the surface area to the volume should be much smaller than that of the interface area to the volume, indicating that surface effect is negligible compared with interface effect (TB effect here). The surface effect would be prominent if non-periodic boundary condition is used in Z- direction. Therefore, periodic boundary condition is applied in Z- direction, considering that there might be thousands of TBs in this direction. As in the lateral directions, periodic boundary conditions are applied to extend the in-plane sizes. Therefore, periodic boundary conditions are applied in X-, Y- and Z-directions. Ko and Lee [38] found that a low radial cut-off distance would result in an unrealistic blunting, and suggested that extending both cut-off distance and truncation range 4
can prevent the unrealistic blunting. Noticing that a larger cut-off distance requires more computational source, we choose a cut-off region of 0.5 nm and a smaller one of 0.5 nm in this work. The centro-symmetry parameter (CSP) [39] is used to analyze the local disorder, which have been extended from pure metals to rock-salt compounds [34, 40]. The CSP for each atom is defined as N /2
2
CSP R i R i N /2 ,
(1)
i 1
where N=6 is the number of the first nearest-neighbors of a central atom in VN with a NaCl structure, and R i and R i +N/2 are the vectors from the central atom to a particular pair of the nearest neighbors. CSP = 0 for an atom whose nearest-neighboring atoms are arranged at their perfect lattice sites, and it would become much larger for an atom of the defect if there is a defect, such as vacancy or dislocation, in the vicinity of the atom. The Open Visualization Tool (OVITO) developed by Stukowski [41] is used to visualize the atomic configurations.
3. Results and discussions 3.1 Stability of TBs As mentioned in Introduction, TBs were predicted to exist in transition-metal nitrides [23] using either first principle calculations or MD simulation of nanoindentation on VN (111) at 300 K[24]. However, first principle calculations are usually performed at 0 K [23], which cannot prove that the twin boundaries can exist stably at a higher temperature. Although Fu et al.[24] found in their MD simulations twin structures in the VN under nanoindentation at 300 K, whether such twin structures can exist in VN as it is relaxed at a higher temperature should also be investigated. Table 1 lists the size of each sample after relaxation at 300 K and 600 K, where one can see that the size in Z direction of samples with TBs (TBN and TBV) are larger than that of sample without TBs (SC), which should be attributed to the larger atomic layer spacing near the TBs for the relaxation. The size in the Z direction of TBV is larger than that of TBN, implying that a larger distance is needed for the relaxation of the stress near TB. Twin boundary energy (TBE) is usually used as a stability criterion of TB. We find that the 5
TBE for TBN (0.06 J/m2) is lower than that for TBV (1.11 J/m2), indicating that TBN should be more stable. We did not find any available experimental result that shows whether twins can exist in VN. On the other hand, first principles calculation containing a few dozens of atoms can hardly reflect the effect of temperature. It has been verified that the potentials used in this work can well reproduce the basic physical and mechanical properties of V-N system at 0 K, as well as the coefficient of thermal expansion of VN in a wide range of temperature, therefore, we tried to use MD simulations to relax the TBV and TBN to explore that the TBs can exist stably in VN films at 300 K and 600 K. Figure 2(a) shows the radial distribution functions (RDFs), g(r), for each sample at 300 K and 600 K, where some peaks can be found at the neighbor distances. The first peak in each curve is sharp at the nearest neighbor distance, following by some sharp but lower peaks at larger neighbor distances, indicating that the twinned VN films retain the crystal characteristics. The heights of each peak at 600 K are obvious smaller than that at 300 K, which can be attributed to the appearance of disturbed crystalline structure at the higher temperature. Figures 2(b) and (c) show the atomic configurations in the X−Z planes of TBN and TBV after a full relaxation at 600 K, where TBs can be observed clearly, indicating that they have not been removed during relaxation. Therefore, it can be said that the TBs can exist stably in VN films during relaxation at 300 K and 600 K under the condition of free external pressure.
3.2 Responses and failure modes of VN under tension Figure 3 shows the stress-strain curves of the three samples subjected to uniaxial tension/compression at 300 K and 600K, where the obtained Young's modulus E, critical stress σmax, critical strain εmax and flow stress σflow (GPa) in each case can be determined and are listed in Table 2. E / is defined in the initial deformation stages, where stress increases linearly with the increase of strain. σmax and εmax are defined as the maximum stress and the corresponding strain, respectively. When subjected to tension at 300 K, σmax= 42.96 GPa, 42.55 GPa and 40.74 GPa for SC, TBN and TBV, respectively. It can be found that the critical stresses of the samples with TBs (TBN and TNV) are lower than that of the sample without TBs (SC), and the σmax of TBN is slightly smaller than that of SC, while the difference between the σmax of TBV and that of SC is 2.22 GPa (about 5.17% smaller than 6
SC), indicating that the effect of TBs is significant if the atoms in the symmetric planes of the twins are V atoms, which is consistent with the results obtained at 600 K (Fig. 3(c) and Table 2). The critical strains in SC, TBN and TBV at 300 K are 0.135, 0.129 and 0.115, respectively (Fig. 3(a) and Table 2), where it can be seen that the critical strains in TBN and TBV are smaller than that in SC and compared with the εmax in SC, the reduction of the εmax in TBV is larger than that in TBN, implying smaller ductility of TBV. Young's modulus of SC, TBN and TBV under tension are 322.8 GPa, 332.7 GPa and 363 GPa, indicating that introducing twins into VN may improve Young's modulus, especially as the atoms in the symmetric atomic planes are V atoms, which is different from the tendency of critical stress. Similar phenomenon can also be found in the tension of nanocrystalline copper [42]. Figure 4 shows the CSP distribution and atomic configurations of each sample under different levels of tensile strain. Figures 4(a1), (b1) and (c1) show respectively CSP distributions in SC, TBN and TBV at the sharp drop point in the stress-strain curve of each sample (see Fig. 3), where some cracks can be seen in each sample. The cracks in TBN and TBV are along the TBs, while the cracks in SC are randomly oriented, the corresponding atomic configurations are can be seen in Figures 4(a2), (b2) and (c2), respectively. Figures 4(a3), (b3) and (c3) show the atomic configurations of SC, TBN and TBV at the critical strains, where there are nearly no defects. The increment from the critical strain (Figs. 4(a3), (b3) and (c3)) to the strain at the sharp drop point (Figs. 4(a2), (b2) and (c2)) and critical strain is 0.001. It can be seen that fracture occurs in a very short interval when the strain reaches its critical value. Therefore, brittle fracture should be the main failure mode of the material subjected to tensile deformation. The critical stress is determined by the smaller value between the (111) plane adhesion energy and twin boundary energy (TB adhesion energy here). No nucleation of dislocation is found, which accounts for the insignificant plastic deformation during the tensile deformation. Therefore, twins in VN cannot increase plasticity of the VN subjected to tensile deformation, which differs from that reported in Cu/Ni multilayers [3].
3.3 Responses and failure modes of VN under compression Figures 3(b) and (d) show the compression stress-strain curves of SC, TBN and TBV at 300 K 7
and 600 K, respectively, where each curve ascends with the increase of strain until its critical value is reached, followed by an abrupt drop. Young's modulus E of SC, TBN and TBV subjected to compressive deformation are respectively 354.2 GPa, 356.3 GPa and 383.9 GPa at 300 K, and 356.8 GPa, 362.0 GPa and 384.9 GPa at 600 K, exhibiting similar tendency as that in tensile deformation. Figures 5(a), (b) and (c) show respectively the CSP distributions in SC, TBN and TBV, which are subjected to compressive deformation at 300 K, at the critical strains, where the nucleation and slip of dislocations is insignificant in each sample. Figures 5(d), (e) and (f) show the CSP distributions in SC, TBN and TBV soon after the drop of stress (or at the strain of εmax+0.001), where lots of dislocations nucleate and glide, which dissipate the elastic strain energy and reduce the load-bearing capability of the materials, accounting for the sharp drops in the stress-strain curves. These slips are mainly on {111} planes. After the abrupt drop, the stress-strain curve ascends slowly, as shown in the ellipses in Fig. 3(b), where the external work is stored in the form of elastic strain energy. Thereafter, some new dislocations nucleate and glide, which, together with the interaction between microdefects (dislocations, stacking faults and TBs) affects the flow stress. The flow stress are calculated based on the curves at the strain of 0.25 < ε < 0.35 in Table 2. The maximum stress represents the critical value of dislocation nucleation for the samples without defects, and the flow stress here represents the interaction between dislocations. The flow stresses of samples with TBs (TBN and TBV) are apparent higher than that of SC, which shows that introducing TBs into VN films can improve their flow stress. The flow stress of TBV is higher than that of TBN both at 300 K and 600 K. Another detail that should be noticed is that there is a slight drop in either the stress-strain curve of TBV subjected to compression at 300 K (Fig. 3(b)), or that at 600 K (Fig. 3(d)). The atomic configurations of TBV at ε=0.051 and ε=0.053 are presented in Figs. 6(a) and (b), respectively, where it can be seen that the TB atoms have changed from V to N, which can also be confirmed in Fig. 5(c) that the atoms of TB in TBV become N atoms. For better observation, the X-Z slices with thickness of 2 Å, perpendicular to the TB, at ε= 0.051, 0.052 and 0.053 are presented in Figs. 6(c), (d) and (e), respectively, where the atoms are colored with their CSP values. It can be seen in Fig. 6(c) that the TB-atoms are still V atoms at ε=0.051; however, they become N atoms at ε=0.052, as shown in the rectangle in Fig. 6(d). More atoms assemble above the local TB plane (the 8
ellipse in Fig. 6(d)). But these atoms have small CSP, indicating that the change in local atomic configuration is small, therefore, one can speculate that these atoms may move as a whole and the relative movement is small. With the further increase of strain, the TB plane atoms have all become N atoms, when the migration of the TB is finished. Figure 7 shows the local atomic configuration on X-Z plane. The stacking sequence near the TB of TBV is ...AαBβCγAγCβBαA... (Fig. 7(a)). The distance between the atoms at the TB marked with A
and those at the both sides marked with γ increases as the strain increases from 0.052 to 0.053, although the stacking sequence near the TB in TBV is still ...AαBβCγAγCβBαA... (Fig. 7(b)). With the strain further increases to 0.054, the stacking sequence near the TB becomes ...AαBβCγAαAγCβB... , which results from an in-plane 1/3{111}<112> movement of the atoms in the layer (A) above the TB with respect to their previous position, specifically, γCβBαA... becomes αAγCβB... .
As shown in Fig. 5, the main deformation mechanism for the stress drop is the nucleation and slip of dislocations; and the nucleation stress are determined by the stacking fault energy. In a uniaxial compression at a constant temperature, the critical stress and strain are mainly determined by the angle of slip plane and loading direction, i.e., the Schmid factor. Therefore, the critical stress and strain of SC and TBN are very close to each other (Table 2). The lower critical stress of TBV should be ascribed to the migration of TBs with V atoms to that with N atoms.
3.4 Tension-compression asymmetry Figure 8 shows the comparisons between the tensile and compressive stress-strain curves of each sample, where distinct tension-compression asymmetry can be observed. The Young's modulus of each sample obtained in compression are slightly larger than that obtained in tension, as shown in Table 2, which has also been observed in FCC single crystal with an EAM potential [43]. This elastic asymmetry can be ascribed to two factors. (1) Higher friction in compression. In theory, the stresses normal to slip plane can affect the friction between the atomic planes, i.e., the friction would be larger in compression due to compressive normal 9
stress to the slip planes, and smaller in tension due to tensile normal stress to the slip planes [43]; (2) The effects of the cutoff distance used for potential. As we know, a cutoff distance for atomic potential is usually used in a MD simulation, which is an approximate processing method by neglecting insignificant long distance effect to save computing time. There is no doubt that during deformation the distance between some pair of atoms may reach a critical value that is very close to the cutoff distance prescribed. In tensile case the critical value may increase and just slightly exceeds the cutoff distance due to the stretch between the pair of atoms, so that the interaction between them would be ignored, while in compressive case it would still be taken into consideration, because the critical value may decrease due to the compaction between the pair of atoms due to compression. It can be seen that the linear elastic asymmetry is moderate, and the largest error between Young’s modulus obtained by tension and compression is less than 10%. However, the tension-compression asymmetry of curves at nonlinear elastic region, after the linear elastic stage and before the critical strain, is much severer, besides the two previously mentioned factors, the asymmetry of the potential should also be an important one, because failure may occur at a state far from equilibrium, where compressive deformation should be more difficult. On the other hand, the critical stress of each sample in compression are larger than that in tension, which can mainly be ascribed to the different deformation mechanisms, i.e., brittle fracture in tension and the dislocation nucleation and glide for compression, although the previously mentioned three factors for elastic asymmetry are also existed. The critical strains of tension and compression are very close for SC and TBN, which shows that at this strain the bond strength and resolved shear stress reach their critical value. However, for TBV the difference between the tensile critical strain and compressive critical strain is larger, which results from the lower adhesion energy of the twin boundary in TBV. Another important difference for tension and compression is the flow stress. Because of brittle fracture in tension, there is no flow stress; however, the dislocation nucleation and glide are the main deformation mechanisms of the materials under compression, which, together with the reactions between defect including the dislocations, stacking faults and TBs, accounting for the limited flow stress.
10
4. Conclusions In this work, uniaxial tension and compression are performed with MD simulations to investigate the effects of different kinds of TB atoms (V and N) and tension-compression asymmetry in twinned VN. During compressive deformation the migration of TBs with V atoms to that with N atoms contributes to softening, although dislocations blocking by TBs results in strengthening. In tensile deformation, fractures take place from the TBs without nucleation of dislocations, thus no improvement in fracture toughness and fracture stress can be observed. Distinct tension-compression asymmetry can be found in VN, which can be attributed to different frictional effect, cutoff radii, asymmetrical tensile and compressive nature of the interatomic potential and different deformation mechanisms. The results obtained are of fundamental significance not only help us to gain an insight into the effect of twin boundaries on the mechanical properties of transition metal nitrides, but can also provide available information for a better understanding of the effect of grain boundaries on such kinds of materials.
Acknowledgements The authors acknowledge the financial supports from National Natural Science Foundation of China (grant no. 11332013), Chongqing New Star Cultivation Project of Science and Technology, Graduate Scientific Research and Innovation Foundation of Chongqing (grant no. CYB16023), and Chongqing Research Program of Basic Research and Frontier Technology (grant no. cstc2015jcyjA50008 and cstc2016jcyjA0366).
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References [1] T. Fu, X. Peng, C. Huang, S. Weng, Y. Zhao, Z. Wang, N. Hu, Strain rate dependence of tension and compression behavior in nano-polycrystalline vanadium nitride, Ceramics International, (2017), DOI: https://doi.org/10.1016/j.ceramint.2017.05.342. [2] T. Fu, X.P. Peng, C.H. Huang, H. Xiang, S. Weng, Z. Wang, N. Hu, In-plane anisotropy and twin boundary effects in vanadium nitride under nanoindentation, Scientific reports, (2017),DOI: 10.1038/s41598-017-05062-0. [3] S. Weng, H. Ning, N. Hu, C. Yan, T. Fu, X. Peng, S. Fu, J. Zhang, C. Xu, D. Sun, Y. Liu, L. Wu, Strengthening effects of twin interface in Cu/Ni multilayer thin films – A molecular dynamics study, Materials & Design, 111 (2016) 1-8. [4] S.A. Shao, S.N. Medyanik, Dislocation-interface interaction in nanoscale fcc metallic bilayers, Mechanics Research Communications, 37 (2010) 315-319. [5] S. Shao, H.M. Zbib, I. Mastorakos, D.F. Bahr, Effect of Interfaces in the Work Hardening of Nanoscale Multilayer Metallic Composites During Nanoindentation: A Molecular Dynamics Investigation, Journal of Engineering Materials and Technology, 135 (2013) 021001. [6] R. Daniel, M. Meindlhumer, W. Baumegger, J. Zalesak, B. Sartory, M. Burghammer, C. Mitterer, J. Keckes, Grain boundary design of thin films: Using tilted brittle interfaces for multiple crack deflection toughening, Acta Materialia, 122 (2017) 130-137. [7] M. Mohr, L. Daccache, S. Horvat, K. Brühne, T. Jacob, H.-J. Fecht, Influence of grain boundaries on elasticity and thermal conductivity of nanocrystalline diamond films, Acta Materialia, 122 (2017) 92-98. [8] C. Zhang, G.Z. Voyiadjis, Rate-dependent size effects and material length scales in nanoindentation near the grain boundary for a bicrystal FCC metal, Materials Science and Engineering: A, 659 (2016) 55-62. [9] W.S. Yu, S.P. Shen, Energetics of point defect interacting with grain boundaries undergone plastic deformations, International Journal of Plasticity, 85 (2016) 93-109. [10] J. Li, J. Guo, H. Luo, Q. Fang, H. Wu, L. Zhang, Y. Liu, Study of nanoindentation mechanical response of nanocrystalline structures using molecular dynamics simulations, Applied Surface Science, 364 (2016) 190-200. 12
[11] R.G. Hoagland, S.M. Valone, Emission of dislocations from grain boundaries by grain boundary dissociation, Philosophical Magazine, 95 (2015) 112-131. [12] C. Huang, X. Peng, T. Fu, X. Chen, H. Xiang, Q. Li, N. Hu, Molecular dynamics simulation of BCC Ta with coherent twin boundaries under nanoindentation, Materials Science and Engineering: A, 700C (2017) 609-616. [13] A. Stukowski, K. Albe, D. Farkas, Nanotwinned fcc metals: Strengthening versus softening mechanisms, Physical Review B, 82 (2010). [14] T. Fu, X. Peng, X. Chen, S. Weng, N. Hu, Q. Li, Z. Wang, Molecular dynamics simulation of nanoindentation on Cu/Ni nanotwinned multilayer films using a spherical indenter, Scientific reports, 6 (2016) 35665. [15] G. Dehm, H.P. Wörgötter, S. Cazottes, J.M. Purswani, D. Gall, C. Mitterer, D. Kiener, Can micro-compression testing provide stress–strain data for thin films?: A comparative study using Cu, VN, TiN and W coatings, Thin Solid Films, 518 (2009) 1517-1521. [16] W. Wolf, R. Podloucky, T. Antretter, F.D. Fischer, First-principles study of elastic and thermal properties of refractory carbides and nitrides, Philosophical Magazine Part B, 79 (1999) 839-858. [17] H. Dong, J. Xiao, R. Melnik, B. Wen, Weak phonon scattering effect of twin boundaries on thermal transmission, Scientific reports, 6 (2016) 19575. [18] H. Dong, B. Wen, Y. Zhang, R. Melnik, Low thermal conductivity in Si/Ge hetero-twinned superlattices, RSC Advances, 7 (2017) 29959-29965. [19] L. Lu, X. Chen, X. Huang, K. Lu, Revealing the maximum strength in nanotwinned copper, Science, 323 (2009) 607-610. [20] K. Lu, L. Lu, S. Suresh, Strengthening Materials by Engineering Coherent Internal Boundaries at the Nanoscale, Science, 324 (2009) 349-352. [21] T. Zhu, H.J. Gao, Plastic deformation mechanism in nanotwinned metals: An insight from molecular dynamics and mechanistic modeling, Scripta Mater., 66 (2012) 843-848. [22] K. Lu, Stabilizing nanostructures in metals using grain and twin boundary architectures, Nature Reviews Materials, (2016) 16019. [23] T.F. Li, T.M. Liu, H.M. Wei, S. Hussain, J.X. Wang, W. Zeng, X.H. Peng, Z.C. Wang, First-principles calculations of the twin boundary energies and adhesion energies of interfaces 13
for cubic face-centered transition-metal nitrides and carbides, Applied Surface Science, 355 (2015) 1132-1135. [24] T. Fu, X.H. Peng, Y.B. Zhao, T.F. Li, Q.B. Li, Z.C. Wang, Molecular dynamics simulation of deformation twin in rocksalt vanadium nitride, Journal of Alloys and Compounds, 675 (2016) 128-133. [25] Y.B. Xue, Y.T. Zhou, D. Chen, X.L. Ma, Structural stability and electronic structures of (111) twin boundaries in the rock-salt MnS, Journal of Alloys and Compounds, 582 (2014) 181-185. [26] T.F. Li, T.M. Liu, L.Q. Zhang, T. Fu, H.M. Wei, First-principles investigation on slip systems and twinnability of TiC, Computational Materials Science, 126 (2017) 103-107. [27] W.T. Hu, S.C. Liu, B. Wen, J.Y. Xiang, F.S. Wen, B. Xu, J.L. He, D.L. Yu, Y.J. Tian, Z.Y. Liu, {111}-specific twinning structures in nonstoichiometric ZrC0.6 with ordered carbon vacancies, Journal of Applied Crystallography, 46 (2013) 43-47. [28] R. Yu, Q. Zhan, L.L. He, Y.C. Zhou, H.Q. Ye, Si-induced twinning of TiC and formation of Ti3SiC2 platelets, Acta Materialia, 50 (2002) 4127-4135. [29] R. Yu, L.L. He, H.Q. Ye, Effects of Si and Al on twin boundary energy of TiC, Acta Materialia, 51 (2003) 2477-2484. [30] M.I. Baskes, J.S. Nelson, A.F. Wright, Semiempirical modified embedded-atom potentials for silicon and germanium, Physical review. B, Condensed matter, 40 (1989) 6085-6100. [31] M.I. Baskes, Modified embedded-atom potentials for cubic materials and impurities, Physical review. B, Condensed matter, 46 (1992) 2727-2742. [32] Y.-M. Kim, B.-J. Lee, M.I. Baskes, Modified embedded-atom method interatomic potentials for Ti and Zr, Physical Review B, 74 (2006) 014101. [33] T. Fu, X. Peng, Y. Zhao, C. Feng, S. Tang, N. Hu, Z. Wang, First-principles calculation and molecular dynamics simulation of fracture behavior of VN layers under uniaxial tension, Physica E: Low-dimensional Systems and Nanostructures, 69 (2015) 224-231. [34] T. Fu, X.H. Peng, C. Huang, D.Q. Yin, Q.B. Li, Z.C. Wang, Molecular dynamics simulation of VN thin films under indentation, Applied Surface Science, 357 (2015) 643-650. [35] T. Fu, X. Peng, C. Wan, Z. Lin, X. Chen, N. Hu, Z. Wang, Molecular dynamics 14
simulation of plasticity in VN(001) crystals under nanoindentation with a spherical indenter, Applied Surface Science, 392 (2017) 942-949. [36] T. Fu, X.H. Peng, Y.B. Zhao, R. Sun, D.Q. Yin, N. Hu, Z.C. Wang, Molecular dynamics simulation of the slip systems in VN, Rsc Advances, 5 (2015) 77831-77838. [37] W.G. Hoover, CONSTANT-PRESSURE EQUATIONS OF MOTION, Physical Review A, 34 (1986) 2499-2500. [38] W.-S. Ko, B.-J. Lee, Origin of unrealistic blunting during atomistic fracture simulations based on MEAM potentials, Philosophical Magazine, 94 (2014) 1745-1753. [39] C.L. Kelchner, S.J. Plimpton, J.C. Hamilton, Dislocation nucleation and defect structure during surface indentation, Physical Review B, 58 (1998) 11085-11088. [40] T. Fu, X.H. Peng, Y.B. Zhao, R. Sun, S.Y. Weng, C. Feng, Z.C. Wang, Molecular dynamics simulation of TiN (001) thin films under indentation, Ceramics International, 41 (2015) 14078-14086. [41] A. Stukowski, Structure identification methods for atomistic simulations of crystalline materials, Modelling and Simulation in Materials Science and Engineering, 20 (2012) 045021. [42] G.J. Tucker, S.M. Foiles, Quantifying the influence of twin boundaries on the deformation of nanocrystalline copper using atomistic simulations, International Journal of Plasticity, 65 (2015) 191-205. [43] I. Salehinia, D.F. Bahr, Crystal orientation effect on dislocation nucleation and multiplication in FCC single crystal under uniaxial loading, International Journal of Plasticity, 52 (2014) 133-146.
15
Fig. 1. Initial atomic configurations in X−Z plane, (a) SC; (b) TBV; (c) TBN. Bigger red and smaller blue balls represent V and N atoms, respectively.
Fig. 2. (a) Radial distribution functions (RDFs) of samples at 300 K and 600 K; the atomic configurations in X−Z plane after full relaxation at 600 K: (b) TBN and (c) TBV.
Fig. 3. Uniaxial tensile and compressive tress-strain curves at 300 K and 600K. (a) tension at 300 K, (b) compression at 300K; (c) tension at 600 K, (d) compression at 600K.
Fig. 4. Atomic configurations of fractured samples, colored with CSP values.
Fig. 5. Atomic configurations at critical stresses (upper row) and at drop points (lower row) of samples subjected to compression at 300 K, colored with atomic type, the atoms with the CSP<1.0 have been removed for clarity. (a) and (d) for SC at ε=0.140 and 0.141; (b) and (e) for TBN at ε=0.140 and 0.141; and (c) and (f) for TBV at ε=0.143 and 0.144. The bigger red and smaller blue balls represent V and N atoms, respectively.
Fig. 6. Evolution of TBs in TBV. (a) and (b) atomic configurations at ε=0.051 and 0.053, respectively colored with atomic type, atoms with CSP<1.0 have been removed for clarity; (c)-(e) atomic configurations in X-Z slices at ε=0.051, 0.052 and 0.053, respectively, colored with CSP.
Fig. 7. Migration of TBs with V atoms to that with N atoms. Atomic arrangement on X-Z plane at strains of (a) 0.051, (b) 0.052, (c) 0.053.
Fig. 8. Stress-strain curves of each sample during uniaxial tension and compression. (a)-(c) SC, TBV and TBN at 300 K; (d)-(f) SC, TBV and TBN at 600 K
16
Figure 1
(a)
or
(b)
or
(c) V
N
or
or
or
Figure 2
(a)
(b)
(c)
17
Figure 3
=0.052
=0.054
18
Figure 4
(a1)
(a2)
(b2)
(b1)
(a3)
Slice TB Crack
Crack Crack TB
Slice
Crack TB SC ε=0.136
(b3)
SC ε=0.136
SC ε=0.135
TBN ε=0.129
(c3)
(c2)
(c1)
TBN ε=0.129
Crack
TB
Crack
Slice
TBN ε=0.128
TBV ε=0.115
TBV ε=0.115
19
TBV ε=0.114
Figure 5 (a)
(c)
(b)
N
SC ε=0.140
TBN ε=0.140
TBV ε=0.143
(f)
(e)
(d)
N
Slip {111} Slip {111}
Slips {111} Slips {111}
Slips {111}
Slip {111}
TBN ε=0.141
SC ε=0.141
TBV ε=0.144
Figure 6 (c)
(b)
(a)
V TB
TB TBV ε=0.051
(d) TB
TB
N
TBV ε=0.052
N
V TB
V
(e)
TB
N TBV ε=0.051
TBV ε=0.053
20
TBV ε=0.053
Figure 7
(a)
(b)
A
A
A
C
A
C
B
C
A
B
A
Figure 8
21
A
C
A A
C
A
C
C
A
B
B
B
C
B
A
A
C
B
B
A
B
(c)
A
A
B
C
C
B
C B
Table 1 Size of samples after relaxation at 300 K and 600 K. Lx, Ly and Lz represent edge lengths in three directions.
Samples SC TBN TBV
300 K
600 K
Lx
Ly
Lz
Lx
Ly
Lz
60.7456 60.7189 60.516
58.4365 58.4286 58.2286
171.783 172.291 173.545
60.9223 60.9205 60.7264
58.641 58.617 58.4292
172.328 172.797 173.995
Table 2 Young's modulus E, critical stress σmax, critical strain εmax and flow stress τflow of samples subjected to tension/compression at 300 K and 600 K. σmax (GPa)
εmax
600
300
600
300
600
300
600
322.8 354.2
322.4 356.8
42.96 71.14
42.15 65.41
0.135 0.140
0.139 0.137
0 15.04±0.83
0 14.42±0.86
Tension Compression
332.7 358.3
331.0 362.0
42.55 71.51
41.91 66.01
0.129 0.140
0.136 0.137
0 15.41±0.72
0 16.22±0.67
Tension Compression
363.0 383.9
354.4 384.9
40.74 69.51
38.54 63.96
0.115 0.143
0.115 0.139
0 17.26±1.06
0 16.76±1.14
Properties
E (GPa)
Temperature (K)
300
SC
Tension Compression
TBN TBV
σflow (GPa)
Samples
22
S0169-4332(17)32175-X http://dx.doi.org/doi:10.1016/j.apsusc.2017.07.174 APSUSC 36708
To appear in:
APSUSC
Received date: Revised date: Accepted date:
17-4-2017 24-6-2017 19-7-2017
Please cite this article as: Tao Fu, Xianghe Peng, Cheng Huang, Yinbo Zhao, Shayuan Weng, Xiang Chen, Ning Hu, Effects of twin boundaries in vanadium nitride films subjected to tensile/compressive deformations, Applied Surface Sciencehttp://dx.doi.org/10.1016/j.apsusc.2017.07.174 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Effects of twin boundaries in vanadium nitride films subjected to tensile/compressive deformations Tao Fu1, Xianghe Peng1, 2,*, Cheng Huang1, Yinbo Zhao1, Shayuan Weng1, Xiang Chen3 and Ning Hu1,* 1
College of Aerospace Engineering, Chongqing University, Chongqing 400044, China State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing 400044, China 3 Advanced Manufacturing Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China 2
*Corresponding authors. Address: College of Aerospace Engineering, Chongqing University, Chongqing 400044, China TEL: +86–23–65103755; FAX: +86–23–65102521 E-mail: [email protected] (X. P.); [email protected] (N. H.)
Highlights
The effects of different twin boundary (TB) atoms and tension-compression asymmetry in VN are investigated.
In compression, the migration of TBs with V atoms to that with N atoms contributes to softening.
In tension, fractures occur at the TBs, which does not result in any improvement of fracture toughness and critical stress.
Different deformation mechanisms are responsible for the plastic tension-compression asymmetry in VN.
Abstract: Two kinds of atoms can serve as the twin boundary (TB) atoms in a transition metal nitride (TMN). In this work, we performed molecular dynamics (MD) simulations for the responses of vanadium nitride (VN) films with different kinds of TB atoms (V or N) subjected to uniaxial tensile/compressive deformations, to investigate their effects and the tensile-compressive asymmetry. In compressive deformation, the migration of TBs with V atoms to that with N atoms contributes to softening, while the pile-up of dislocations at TBs contributes to strengthening. During tension, fractures occur at the TBs without distinct nucleation of dislocations, the nature of the brittle fracture, which does not result in any 1
improvement of fracture toughness and critical stress. Different frictional effects, cutoff radii, asymmetrical tensile and compressive nature of the interatomic potential and different deformation mechanisms are responsible for the tension-compression asymmetry in VN.
Keywords: Vanadium nitride; Nanotwin; Twin boundary migration; Tension-compression asymmetry; Molecular dynamics simulation
1. Introduction The effect of grain boundaries (GBs), as an important factor affecting the mechanical behavior of metals and ceramics, is a hot research topic in recent year [1-5]. Much effort has been made in experimental [6-8] and theoretical researches [9-13] for the effects of GBs in metals, and it has been accepted that GBs can improve the strength of the metallic material by impeding the movement of dislocations. GBs can react with and absorb dislocations, reducing dislocation density [3] and resulting in softening [14]. However, in transition metal nitrides and carbides, such as vanadium nitride (VN) and vanadium carbide (VC) [15], which have been widely used as protection coatings materials for molds, tools, and cutting tools, due to their outstanding mechanical and physical properties [16], less progress related to the effects of GBs on their mechanical behavior can be found in the literature. Low energy symmetrical twin boundaries (TBs) are commonly chosen as a typical representative of GBs and have been widely investigated [17, 18]. Lu et al., [19, 20] found that introducing twins into copper (Cu) can increase the strength of Cu without losing toughness, and the strength reaches maximum as the twin thickness decreases to 15 nm. However, it would decrease with the further decrease of twin thickness, implying some different softening mechanism. Zhu and Gao [21] and Lu [22] summarized the three models of dislocation–twin boundary (TB) interactions in FCC materials, related to two hardening modes (Slip transfer and Confined-layer slip) and one softening mode (Twinning partial slip), respectively. The twinning partial slip was formed by the partial dislocations reacting with the TB [21, 22]. Recently, Fu et al. [14] found in the nanoindention on Cu/Ni multilayer that the partial slip parallel with twin boundary can also serve as a softening mechanism, similar to the twinning partial slip. So far most work focused on the effects of TBs in FCC metals, and less 2
attention has been paid to that in ceramics, e.g. vanadium nitride (VN) for it had not been observed in experiment. In the recent work, it was found by first principle calculations that twin boundaries can exist in transition-metal nitrides [23], which was further confirmed in the molecular dynamics (MD) simulation of nanoindentation on VN (111) at 300 K [24]. Moreover, Xue et al [25] identified {111} twin boundary in rocksalt (B1) structure MnS by combing observation by transmission electron microscopy and the result using density functional theory calculation, suggesting the necessity of the study for the role of TBs in such kind of materials. Although transition metal carbides and nitrides with NaCl structure usually have high twin boundary energies (TBEs) [26], it was found recently that TBEs can be reduced by introducing vacancies [27] and alloying elements [28, 29]. However, due to the limit of the interatomic potentials for ternary or more elements, it is still hard to investigate the effects of alloying elements on the mechanical behavior of transition metal carbides and nitrides with the NaCl structure. As for the effects of vacancies, it can be investigated using MD simulations, however, the effects of vacancies including that of atomic type and the location of vacancies, the vacancy density and the ratio of two types of vacancy atoms, are complex. Therefore, in this work, we assume that the TBs have been introduced into the materials before deformation. It is know that the B1 structure VN is a typical structure by nesting two FCC structures, and it would have two possible kinds of atoms (V and N) at the symmetric atomic plane of a TB, in contrast to the twinned FCC metallic where there is only one possible kind of atoms. Therefore, the deformation mechanisms for FCC metals may not be applied to transition-metal nitrides. Moreover, tension-compression asymmetry is also one of the most important phenomena. In this article, we investigate with MD simulation the responses of a single VN and twinned VN films with different kinds of TB atoms subjected to tensile/compressive deformation, for the purpose to explore the effects of different kind of TB atoms on the mechanical properties and the cause of tensile-compressive asymmetry.
2. Simulation details The modified embedded atom method (MEAM) potential [30-32] is adopted in our simulations. The parameters in the potentials for the single elements V and N and those in the 3
binary interatomic potential between V and N have been given by Baskes et al. [31], Lee et al. [32] and Fu et al. [33], respectively. MEAM potentials was found to be able to reproduce the fundamental physical and mechanical properties of materials, such as lattice parameters, cohesive energy, elastic property and surface energy, and have been successfully applied to analyze the fracture behavior of VN films [33] and explore the deformation mechanisms of VN under indentation, incorporating stacking fault energy [24, 34-36]. Figure 1(a), (b) and (c) show the samples with a single crystal, with V termination TBs and with N termination TBs, marked with SC, TBV and TBN, respectively. For SC, there is no twin boundary, and the axes X, Y and Z correspond respectively to lattice orientations 112 ,
110
and
1 11 . For TBV or TBN, TBs are introduced, and the axes X, Y and Z correspond
respectively to the lattice orientations 112 ,
110
and
1 11
for odd layers, and to
1 12 ,
1 10 and 1 11 for even layers. The difference between TBV and TBN lies in the atomic type at the symmetric plane. Before loading, the optimized stable configuration of each sample is achieved using an energy minimization approach based on conjugate gradient (CG) algorithm. Then the isothermal-isobaric NPT ensemble is used to relax the system under a pressure free condition to an equilibration state at T=300 K for 30 ps and T=600 K for 60 ps, respectively. During loading, each sample is stretched/compressed in Z-direction at a strain rate of 109 s−1, the NPT ensemble with Nose/Hoover barostat is employed [37] to keep pressure free in X- and Y- directions. It is known that the total thickness of film is usually of μm-scale, consisting of thousands of TBs. The ratio of the surface area to the volume should be much smaller than that of the interface area to the volume, indicating that surface effect is negligible compared with interface effect (TB effect here). The surface effect would be prominent if non-periodic boundary condition is used in Z- direction. Therefore, periodic boundary condition is applied in Z- direction, considering that there might be thousands of TBs in this direction. As in the lateral directions, periodic boundary conditions are applied to extend the in-plane sizes. Therefore, periodic boundary conditions are applied in X-, Y- and Z-directions. Ko and Lee [38] found that a low radial cut-off distance would result in an unrealistic blunting, and suggested that extending both cut-off distance and truncation range 4
can prevent the unrealistic blunting. Noticing that a larger cut-off distance requires more computational source, we choose a cut-off region of 0.5 nm and a smaller one of 0.5 nm in this work. The centro-symmetry parameter (CSP) [39] is used to analyze the local disorder, which have been extended from pure metals to rock-salt compounds [34, 40]. The CSP for each atom is defined as N /2
2
CSP R i R i N /2 ,
(1)
i 1
where N=6 is the number of the first nearest-neighbors of a central atom in VN with a NaCl structure, and R i and R i +N/2 are the vectors from the central atom to a particular pair of the nearest neighbors. CSP = 0 for an atom whose nearest-neighboring atoms are arranged at their perfect lattice sites, and it would become much larger for an atom of the defect if there is a defect, such as vacancy or dislocation, in the vicinity of the atom. The Open Visualization Tool (OVITO) developed by Stukowski [41] is used to visualize the atomic configurations.
3. Results and discussions 3.1 Stability of TBs As mentioned in Introduction, TBs were predicted to exist in transition-metal nitrides [23] using either first principle calculations or MD simulation of nanoindentation on VN (111) at 300 K[24]. However, first principle calculations are usually performed at 0 K [23], which cannot prove that the twin boundaries can exist stably at a higher temperature. Although Fu et al.[24] found in their MD simulations twin structures in the VN under nanoindentation at 300 K, whether such twin structures can exist in VN as it is relaxed at a higher temperature should also be investigated. Table 1 lists the size of each sample after relaxation at 300 K and 600 K, where one can see that the size in Z direction of samples with TBs (TBN and TBV) are larger than that of sample without TBs (SC), which should be attributed to the larger atomic layer spacing near the TBs for the relaxation. The size in the Z direction of TBV is larger than that of TBN, implying that a larger distance is needed for the relaxation of the stress near TB. Twin boundary energy (TBE) is usually used as a stability criterion of TB. We find that the 5
TBE for TBN (0.06 J/m2) is lower than that for TBV (1.11 J/m2), indicating that TBN should be more stable. We did not find any available experimental result that shows whether twins can exist in VN. On the other hand, first principles calculation containing a few dozens of atoms can hardly reflect the effect of temperature. It has been verified that the potentials used in this work can well reproduce the basic physical and mechanical properties of V-N system at 0 K, as well as the coefficient of thermal expansion of VN in a wide range of temperature, therefore, we tried to use MD simulations to relax the TBV and TBN to explore that the TBs can exist stably in VN films at 300 K and 600 K. Figure 2(a) shows the radial distribution functions (RDFs), g(r), for each sample at 300 K and 600 K, where some peaks can be found at the neighbor distances. The first peak in each curve is sharp at the nearest neighbor distance, following by some sharp but lower peaks at larger neighbor distances, indicating that the twinned VN films retain the crystal characteristics. The heights of each peak at 600 K are obvious smaller than that at 300 K, which can be attributed to the appearance of disturbed crystalline structure at the higher temperature. Figures 2(b) and (c) show the atomic configurations in the X−Z planes of TBN and TBV after a full relaxation at 600 K, where TBs can be observed clearly, indicating that they have not been removed during relaxation. Therefore, it can be said that the TBs can exist stably in VN films during relaxation at 300 K and 600 K under the condition of free external pressure.
3.2 Responses and failure modes of VN under tension Figure 3 shows the stress-strain curves of the three samples subjected to uniaxial tension/compression at 300 K and 600K, where the obtained Young's modulus E, critical stress σmax, critical strain εmax and flow stress σflow (GPa) in each case can be determined and are listed in Table 2. E / is defined in the initial deformation stages, where stress increases linearly with the increase of strain. σmax and εmax are defined as the maximum stress and the corresponding strain, respectively. When subjected to tension at 300 K, σmax= 42.96 GPa, 42.55 GPa and 40.74 GPa for SC, TBN and TBV, respectively. It can be found that the critical stresses of the samples with TBs (TBN and TNV) are lower than that of the sample without TBs (SC), and the σmax of TBN is slightly smaller than that of SC, while the difference between the σmax of TBV and that of SC is 2.22 GPa (about 5.17% smaller than 6
SC), indicating that the effect of TBs is significant if the atoms in the symmetric planes of the twins are V atoms, which is consistent with the results obtained at 600 K (Fig. 3(c) and Table 2). The critical strains in SC, TBN and TBV at 300 K are 0.135, 0.129 and 0.115, respectively (Fig. 3(a) and Table 2), where it can be seen that the critical strains in TBN and TBV are smaller than that in SC and compared with the εmax in SC, the reduction of the εmax in TBV is larger than that in TBN, implying smaller ductility of TBV. Young's modulus of SC, TBN and TBV under tension are 322.8 GPa, 332.7 GPa and 363 GPa, indicating that introducing twins into VN may improve Young's modulus, especially as the atoms in the symmetric atomic planes are V atoms, which is different from the tendency of critical stress. Similar phenomenon can also be found in the tension of nanocrystalline copper [42]. Figure 4 shows the CSP distribution and atomic configurations of each sample under different levels of tensile strain. Figures 4(a1), (b1) and (c1) show respectively CSP distributions in SC, TBN and TBV at the sharp drop point in the stress-strain curve of each sample (see Fig. 3), where some cracks can be seen in each sample. The cracks in TBN and TBV are along the TBs, while the cracks in SC are randomly oriented, the corresponding atomic configurations are can be seen in Figures 4(a2), (b2) and (c2), respectively. Figures 4(a3), (b3) and (c3) show the atomic configurations of SC, TBN and TBV at the critical strains, where there are nearly no defects. The increment from the critical strain (Figs. 4(a3), (b3) and (c3)) to the strain at the sharp drop point (Figs. 4(a2), (b2) and (c2)) and critical strain is 0.001. It can be seen that fracture occurs in a very short interval when the strain reaches its critical value. Therefore, brittle fracture should be the main failure mode of the material subjected to tensile deformation. The critical stress is determined by the smaller value between the (111) plane adhesion energy and twin boundary energy (TB adhesion energy here). No nucleation of dislocation is found, which accounts for the insignificant plastic deformation during the tensile deformation. Therefore, twins in VN cannot increase plasticity of the VN subjected to tensile deformation, which differs from that reported in Cu/Ni multilayers [3].
3.3 Responses and failure modes of VN under compression Figures 3(b) and (d) show the compression stress-strain curves of SC, TBN and TBV at 300 K 7
and 600 K, respectively, where each curve ascends with the increase of strain until its critical value is reached, followed by an abrupt drop. Young's modulus E of SC, TBN and TBV subjected to compressive deformation are respectively 354.2 GPa, 356.3 GPa and 383.9 GPa at 300 K, and 356.8 GPa, 362.0 GPa and 384.9 GPa at 600 K, exhibiting similar tendency as that in tensile deformation. Figures 5(a), (b) and (c) show respectively the CSP distributions in SC, TBN and TBV, which are subjected to compressive deformation at 300 K, at the critical strains, where the nucleation and slip of dislocations is insignificant in each sample. Figures 5(d), (e) and (f) show the CSP distributions in SC, TBN and TBV soon after the drop of stress (or at the strain of εmax+0.001), where lots of dislocations nucleate and glide, which dissipate the elastic strain energy and reduce the load-bearing capability of the materials, accounting for the sharp drops in the stress-strain curves. These slips are mainly on {111} planes. After the abrupt drop, the stress-strain curve ascends slowly, as shown in the ellipses in Fig. 3(b), where the external work is stored in the form of elastic strain energy. Thereafter, some new dislocations nucleate and glide, which, together with the interaction between microdefects (dislocations, stacking faults and TBs) affects the flow stress. The flow stress are calculated based on the curves at the strain of 0.25 < ε < 0.35 in Table 2. The maximum stress represents the critical value of dislocation nucleation for the samples without defects, and the flow stress here represents the interaction between dislocations. The flow stresses of samples with TBs (TBN and TBV) are apparent higher than that of SC, which shows that introducing TBs into VN films can improve their flow stress. The flow stress of TBV is higher than that of TBN both at 300 K and 600 K. Another detail that should be noticed is that there is a slight drop in either the stress-strain curve of TBV subjected to compression at 300 K (Fig. 3(b)), or that at 600 K (Fig. 3(d)). The atomic configurations of TBV at ε=0.051 and ε=0.053 are presented in Figs. 6(a) and (b), respectively, where it can be seen that the TB atoms have changed from V to N, which can also be confirmed in Fig. 5(c) that the atoms of TB in TBV become N atoms. For better observation, the X-Z slices with thickness of 2 Å, perpendicular to the TB, at ε= 0.051, 0.052 and 0.053 are presented in Figs. 6(c), (d) and (e), respectively, where the atoms are colored with their CSP values. It can be seen in Fig. 6(c) that the TB-atoms are still V atoms at ε=0.051; however, they become N atoms at ε=0.052, as shown in the rectangle in Fig. 6(d). More atoms assemble above the local TB plane (the 8
ellipse in Fig. 6(d)). But these atoms have small CSP, indicating that the change in local atomic configuration is small, therefore, one can speculate that these atoms may move as a whole and the relative movement is small. With the further increase of strain, the TB plane atoms have all become N atoms, when the migration of the TB is finished. Figure 7 shows the local atomic configuration on X-Z plane. The stacking sequence near the TB of TBV is ...AαBβCγAγCβBαA... (Fig. 7(a)). The distance between the atoms at the TB marked with A
and those at the both sides marked with γ increases as the strain increases from 0.052 to 0.053, although the stacking sequence near the TB in TBV is still ...AαBβCγAγCβBαA... (Fig. 7(b)). With the strain further increases to 0.054, the stacking sequence near the TB becomes ...AαBβCγAαAγCβB... , which results from an in-plane 1/3{111}<112> movement of the atoms in the layer (A) above the TB with respect to their previous position, specifically, γCβBαA... becomes αAγCβB... .
As shown in Fig. 5, the main deformation mechanism for the stress drop is the nucleation and slip of dislocations; and the nucleation stress are determined by the stacking fault energy. In a uniaxial compression at a constant temperature, the critical stress and strain are mainly determined by the angle of slip plane and loading direction, i.e., the Schmid factor. Therefore, the critical stress and strain of SC and TBN are very close to each other (Table 2). The lower critical stress of TBV should be ascribed to the migration of TBs with V atoms to that with N atoms.
3.4 Tension-compression asymmetry Figure 8 shows the comparisons between the tensile and compressive stress-strain curves of each sample, where distinct tension-compression asymmetry can be observed. The Young's modulus of each sample obtained in compression are slightly larger than that obtained in tension, as shown in Table 2, which has also been observed in FCC single crystal with an EAM potential [43]. This elastic asymmetry can be ascribed to two factors. (1) Higher friction in compression. In theory, the stresses normal to slip plane can affect the friction between the atomic planes, i.e., the friction would be larger in compression due to compressive normal 9
stress to the slip planes, and smaller in tension due to tensile normal stress to the slip planes [43]; (2) The effects of the cutoff distance used for potential. As we know, a cutoff distance for atomic potential is usually used in a MD simulation, which is an approximate processing method by neglecting insignificant long distance effect to save computing time. There is no doubt that during deformation the distance between some pair of atoms may reach a critical value that is very close to the cutoff distance prescribed. In tensile case the critical value may increase and just slightly exceeds the cutoff distance due to the stretch between the pair of atoms, so that the interaction between them would be ignored, while in compressive case it would still be taken into consideration, because the critical value may decrease due to the compaction between the pair of atoms due to compression. It can be seen that the linear elastic asymmetry is moderate, and the largest error between Young’s modulus obtained by tension and compression is less than 10%. However, the tension-compression asymmetry of curves at nonlinear elastic region, after the linear elastic stage and before the critical strain, is much severer, besides the two previously mentioned factors, the asymmetry of the potential should also be an important one, because failure may occur at a state far from equilibrium, where compressive deformation should be more difficult. On the other hand, the critical stress of each sample in compression are larger than that in tension, which can mainly be ascribed to the different deformation mechanisms, i.e., brittle fracture in tension and the dislocation nucleation and glide for compression, although the previously mentioned three factors for elastic asymmetry are also existed. The critical strains of tension and compression are very close for SC and TBN, which shows that at this strain the bond strength and resolved shear stress reach their critical value. However, for TBV the difference between the tensile critical strain and compressive critical strain is larger, which results from the lower adhesion energy of the twin boundary in TBV. Another important difference for tension and compression is the flow stress. Because of brittle fracture in tension, there is no flow stress; however, the dislocation nucleation and glide are the main deformation mechanisms of the materials under compression, which, together with the reactions between defect including the dislocations, stacking faults and TBs, accounting for the limited flow stress.
10
4. Conclusions In this work, uniaxial tension and compression are performed with MD simulations to investigate the effects of different kinds of TB atoms (V and N) and tension-compression asymmetry in twinned VN. During compressive deformation the migration of TBs with V atoms to that with N atoms contributes to softening, although dislocations blocking by TBs results in strengthening. In tensile deformation, fractures take place from the TBs without nucleation of dislocations, thus no improvement in fracture toughness and fracture stress can be observed. Distinct tension-compression asymmetry can be found in VN, which can be attributed to different frictional effect, cutoff radii, asymmetrical tensile and compressive nature of the interatomic potential and different deformation mechanisms. The results obtained are of fundamental significance not only help us to gain an insight into the effect of twin boundaries on the mechanical properties of transition metal nitrides, but can also provide available information for a better understanding of the effect of grain boundaries on such kinds of materials.
Acknowledgements The authors acknowledge the financial supports from National Natural Science Foundation of China (grant no. 11332013), Chongqing New Star Cultivation Project of Science and Technology, Graduate Scientific Research and Innovation Foundation of Chongqing (grant no. CYB16023), and Chongqing Research Program of Basic Research and Frontier Technology (grant no. cstc2015jcyjA50008 and cstc2016jcyjA0366).
11
References [1] T. Fu, X. Peng, C. Huang, S. Weng, Y. Zhao, Z. Wang, N. Hu, Strain rate dependence of tension and compression behavior in nano-polycrystalline vanadium nitride, Ceramics International, (2017), DOI: https://doi.org/10.1016/j.ceramint.2017.05.342. [2] T. Fu, X.P. Peng, C.H. Huang, H. Xiang, S. Weng, Z. Wang, N. Hu, In-plane anisotropy and twin boundary effects in vanadium nitride under nanoindentation, Scientific reports, (2017),DOI: 10.1038/s41598-017-05062-0. [3] S. Weng, H. Ning, N. Hu, C. Yan, T. Fu, X. Peng, S. Fu, J. Zhang, C. Xu, D. Sun, Y. Liu, L. Wu, Strengthening effects of twin interface in Cu/Ni multilayer thin films – A molecular dynamics study, Materials & Design, 111 (2016) 1-8. [4] S.A. Shao, S.N. Medyanik, Dislocation-interface interaction in nanoscale fcc metallic bilayers, Mechanics Research Communications, 37 (2010) 315-319. [5] S. Shao, H.M. Zbib, I. Mastorakos, D.F. Bahr, Effect of Interfaces in the Work Hardening of Nanoscale Multilayer Metallic Composites During Nanoindentation: A Molecular Dynamics Investigation, Journal of Engineering Materials and Technology, 135 (2013) 021001. [6] R. Daniel, M. Meindlhumer, W. Baumegger, J. Zalesak, B. Sartory, M. Burghammer, C. Mitterer, J. Keckes, Grain boundary design of thin films: Using tilted brittle interfaces for multiple crack deflection toughening, Acta Materialia, 122 (2017) 130-137. [7] M. Mohr, L. Daccache, S. Horvat, K. Brühne, T. Jacob, H.-J. Fecht, Influence of grain boundaries on elasticity and thermal conductivity of nanocrystalline diamond films, Acta Materialia, 122 (2017) 92-98. [8] C. Zhang, G.Z. Voyiadjis, Rate-dependent size effects and material length scales in nanoindentation near the grain boundary for a bicrystal FCC metal, Materials Science and Engineering: A, 659 (2016) 55-62. [9] W.S. Yu, S.P. Shen, Energetics of point defect interacting with grain boundaries undergone plastic deformations, International Journal of Plasticity, 85 (2016) 93-109. [10] J. Li, J. Guo, H. Luo, Q. Fang, H. Wu, L. Zhang, Y. Liu, Study of nanoindentation mechanical response of nanocrystalline structures using molecular dynamics simulations, Applied Surface Science, 364 (2016) 190-200. 12
[11] R.G. Hoagland, S.M. Valone, Emission of dislocations from grain boundaries by grain boundary dissociation, Philosophical Magazine, 95 (2015) 112-131. [12] C. Huang, X. Peng, T. Fu, X. Chen, H. Xiang, Q. Li, N. Hu, Molecular dynamics simulation of BCC Ta with coherent twin boundaries under nanoindentation, Materials Science and Engineering: A, 700C (2017) 609-616. [13] A. Stukowski, K. Albe, D. Farkas, Nanotwinned fcc metals: Strengthening versus softening mechanisms, Physical Review B, 82 (2010). [14] T. Fu, X. Peng, X. Chen, S. Weng, N. Hu, Q. Li, Z. Wang, Molecular dynamics simulation of nanoindentation on Cu/Ni nanotwinned multilayer films using a spherical indenter, Scientific reports, 6 (2016) 35665. [15] G. Dehm, H.P. Wörgötter, S. Cazottes, J.M. Purswani, D. Gall, C. Mitterer, D. Kiener, Can micro-compression testing provide stress–strain data for thin films?: A comparative study using Cu, VN, TiN and W coatings, Thin Solid Films, 518 (2009) 1517-1521. [16] W. Wolf, R. Podloucky, T. Antretter, F.D. Fischer, First-principles study of elastic and thermal properties of refractory carbides and nitrides, Philosophical Magazine Part B, 79 (1999) 839-858. [17] H. Dong, J. Xiao, R. Melnik, B. Wen, Weak phonon scattering effect of twin boundaries on thermal transmission, Scientific reports, 6 (2016) 19575. [18] H. Dong, B. Wen, Y. Zhang, R. Melnik, Low thermal conductivity in Si/Ge hetero-twinned superlattices, RSC Advances, 7 (2017) 29959-29965. [19] L. Lu, X. Chen, X. Huang, K. Lu, Revealing the maximum strength in nanotwinned copper, Science, 323 (2009) 607-610. [20] K. Lu, L. Lu, S. Suresh, Strengthening Materials by Engineering Coherent Internal Boundaries at the Nanoscale, Science, 324 (2009) 349-352. [21] T. Zhu, H.J. Gao, Plastic deformation mechanism in nanotwinned metals: An insight from molecular dynamics and mechanistic modeling, Scripta Mater., 66 (2012) 843-848. [22] K. Lu, Stabilizing nanostructures in metals using grain and twin boundary architectures, Nature Reviews Materials, (2016) 16019. [23] T.F. Li, T.M. Liu, H.M. Wei, S. Hussain, J.X. Wang, W. Zeng, X.H. Peng, Z.C. Wang, First-principles calculations of the twin boundary energies and adhesion energies of interfaces 13
for cubic face-centered transition-metal nitrides and carbides, Applied Surface Science, 355 (2015) 1132-1135. [24] T. Fu, X.H. Peng, Y.B. Zhao, T.F. Li, Q.B. Li, Z.C. Wang, Molecular dynamics simulation of deformation twin in rocksalt vanadium nitride, Journal of Alloys and Compounds, 675 (2016) 128-133. [25] Y.B. Xue, Y.T. Zhou, D. Chen, X.L. Ma, Structural stability and electronic structures of (111) twin boundaries in the rock-salt MnS, Journal of Alloys and Compounds, 582 (2014) 181-185. [26] T.F. Li, T.M. Liu, L.Q. Zhang, T. Fu, H.M. Wei, First-principles investigation on slip systems and twinnability of TiC, Computational Materials Science, 126 (2017) 103-107. [27] W.T. Hu, S.C. Liu, B. Wen, J.Y. Xiang, F.S. Wen, B. Xu, J.L. He, D.L. Yu, Y.J. Tian, Z.Y. Liu, {111}-specific twinning structures in nonstoichiometric ZrC0.6 with ordered carbon vacancies, Journal of Applied Crystallography, 46 (2013) 43-47. [28] R. Yu, Q. Zhan, L.L. He, Y.C. Zhou, H.Q. Ye, Si-induced twinning of TiC and formation of Ti3SiC2 platelets, Acta Materialia, 50 (2002) 4127-4135. [29] R. Yu, L.L. He, H.Q. Ye, Effects of Si and Al on twin boundary energy of TiC, Acta Materialia, 51 (2003) 2477-2484. [30] M.I. Baskes, J.S. Nelson, A.F. Wright, Semiempirical modified embedded-atom potentials for silicon and germanium, Physical review. B, Condensed matter, 40 (1989) 6085-6100. [31] M.I. Baskes, Modified embedded-atom potentials for cubic materials and impurities, Physical review. B, Condensed matter, 46 (1992) 2727-2742. [32] Y.-M. Kim, B.-J. Lee, M.I. Baskes, Modified embedded-atom method interatomic potentials for Ti and Zr, Physical Review B, 74 (2006) 014101. [33] T. Fu, X. Peng, Y. Zhao, C. Feng, S. Tang, N. Hu, Z. Wang, First-principles calculation and molecular dynamics simulation of fracture behavior of VN layers under uniaxial tension, Physica E: Low-dimensional Systems and Nanostructures, 69 (2015) 224-231. [34] T. Fu, X.H. Peng, C. Huang, D.Q. Yin, Q.B. Li, Z.C. Wang, Molecular dynamics simulation of VN thin films under indentation, Applied Surface Science, 357 (2015) 643-650. [35] T. Fu, X. Peng, C. Wan, Z. Lin, X. Chen, N. Hu, Z. Wang, Molecular dynamics 14
simulation of plasticity in VN(001) crystals under nanoindentation with a spherical indenter, Applied Surface Science, 392 (2017) 942-949. [36] T. Fu, X.H. Peng, Y.B. Zhao, R. Sun, D.Q. Yin, N. Hu, Z.C. Wang, Molecular dynamics simulation of the slip systems in VN, Rsc Advances, 5 (2015) 77831-77838. [37] W.G. Hoover, CONSTANT-PRESSURE EQUATIONS OF MOTION, Physical Review A, 34 (1986) 2499-2500. [38] W.-S. Ko, B.-J. Lee, Origin of unrealistic blunting during atomistic fracture simulations based on MEAM potentials, Philosophical Magazine, 94 (2014) 1745-1753. [39] C.L. Kelchner, S.J. Plimpton, J.C. Hamilton, Dislocation nucleation and defect structure during surface indentation, Physical Review B, 58 (1998) 11085-11088. [40] T. Fu, X.H. Peng, Y.B. Zhao, R. Sun, S.Y. Weng, C. Feng, Z.C. Wang, Molecular dynamics simulation of TiN (001) thin films under indentation, Ceramics International, 41 (2015) 14078-14086. [41] A. Stukowski, Structure identification methods for atomistic simulations of crystalline materials, Modelling and Simulation in Materials Science and Engineering, 20 (2012) 045021. [42] G.J. Tucker, S.M. Foiles, Quantifying the influence of twin boundaries on the deformation of nanocrystalline copper using atomistic simulations, International Journal of Plasticity, 65 (2015) 191-205. [43] I. Salehinia, D.F. Bahr, Crystal orientation effect on dislocation nucleation and multiplication in FCC single crystal under uniaxial loading, International Journal of Plasticity, 52 (2014) 133-146.
15
Fig. 1. Initial atomic configurations in X−Z plane, (a) SC; (b) TBV; (c) TBN. Bigger red and smaller blue balls represent V and N atoms, respectively.
Fig. 2. (a) Radial distribution functions (RDFs) of samples at 300 K and 600 K; the atomic configurations in X−Z plane after full relaxation at 600 K: (b) TBN and (c) TBV.
Fig. 3. Uniaxial tensile and compressive tress-strain curves at 300 K and 600K. (a) tension at 300 K, (b) compression at 300K; (c) tension at 600 K, (d) compression at 600K.
Fig. 4. Atomic configurations of fractured samples, colored with CSP values.
Fig. 5. Atomic configurations at critical stresses (upper row) and at drop points (lower row) of samples subjected to compression at 300 K, colored with atomic type, the atoms with the CSP<1.0 have been removed for clarity. (a) and (d) for SC at ε=0.140 and 0.141; (b) and (e) for TBN at ε=0.140 and 0.141; and (c) and (f) for TBV at ε=0.143 and 0.144. The bigger red and smaller blue balls represent V and N atoms, respectively.
Fig. 6. Evolution of TBs in TBV. (a) and (b) atomic configurations at ε=0.051 and 0.053, respectively colored with atomic type, atoms with CSP<1.0 have been removed for clarity; (c)-(e) atomic configurations in X-Z slices at ε=0.051, 0.052 and 0.053, respectively, colored with CSP.
Fig. 7. Migration of TBs with V atoms to that with N atoms. Atomic arrangement on X-Z plane at strains of (a) 0.051, (b) 0.052, (c) 0.053.
Fig. 8. Stress-strain curves of each sample during uniaxial tension and compression. (a)-(c) SC, TBV and TBN at 300 K; (d)-(f) SC, TBV and TBN at 600 K
16
Figure 1
(a)
or
(b)
or
(c) V
N
or
or
or
Figure 2
(a)
(b)
(c)
17
Figure 3
=0.052
=0.054
18
Figure 4
(a1)
(a2)
(b2)
(b1)
(a3)
Slice TB Crack
Crack Crack TB
Slice
Crack TB SC ε=0.136
(b3)
SC ε=0.136
SC ε=0.135
TBN ε=0.129
(c3)
(c2)
(c1)
TBN ε=0.129
Crack
TB
Crack
Slice
TBN ε=0.128
TBV ε=0.115
TBV ε=0.115
19
TBV ε=0.114
Figure 5 (a)
(c)
(b)
N
SC ε=0.140
TBN ε=0.140
TBV ε=0.143
(f)
(e)
(d)
N
Slip {111} Slip {111}
Slips {111} Slips {111}
Slips {111}
Slip {111}
TBN ε=0.141
SC ε=0.141
TBV ε=0.144
Figure 6 (c)
(b)
(a)
V TB
TB TBV ε=0.051
(d) TB
TB
N
TBV ε=0.052
N
V TB
V
(e)
TB
N TBV ε=0.051
TBV ε=0.053
20
TBV ε=0.053
Figure 7
(a)
(b)
A
A
A
C
A
C
B
C
A
B
A
Figure 8
21
A
C
A A
C
A
C
C
A
B
B
B
C
B
A
A
C
B
B
A
B
(c)
A
A
B
C
C
B
C B
Table 1 Size of samples after relaxation at 300 K and 600 K. Lx, Ly and Lz represent edge lengths in three directions.
Samples SC TBN TBV
300 K
600 K
Lx
Ly
Lz
Lx
Ly
Lz
60.7456 60.7189 60.516
58.4365 58.4286 58.2286
171.783 172.291 173.545
60.9223 60.9205 60.7264
58.641 58.617 58.4292
172.328 172.797 173.995
Table 2 Young's modulus E, critical stress σmax, critical strain εmax and flow stress τflow of samples subjected to tension/compression at 300 K and 600 K. σmax (GPa)
εmax
600
300
600
300
600
300
600
322.8 354.2
322.4 356.8
42.96 71.14
42.15 65.41
0.135 0.140
0.139 0.137
0 15.04±0.83
0 14.42±0.86
Tension Compression
332.7 358.3
331.0 362.0
42.55 71.51
41.91 66.01
0.129 0.140
0.136 0.137
0 15.41±0.72
0 16.22±0.67
Tension Compression
363.0 383.9
354.4 384.9
40.74 69.51
38.54 63.96
0.115 0.143
0.115 0.139
0 17.26±1.06
0 16.76±1.14
Properties
E (GPa)
Temperature (K)
300
SC
Tension Compression
TBN TBV
σflow (GPa)
Samples
22