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Si3N4 ratios
Materials Chemistry and Physics 143 (2013) 223e227
Contents lists available at ScienceDirect
Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys
Atomistic investigation of structural and mechanical properties of silicon carbon nitride with different SiC/Si3N4 ratios Ningbo Liao*, Wei Xue*, Hongming Zhou, Miao Zhang College of Mechanical & Electrical Engineering, Wenzhou University, Wenzhou 325035, PR China
h i g h l i g h t s The nano-domain structure of SiCN is reproduced by large-scale atomistic simulations. The atomic models consist with previous DFT calculation and X-ray/Neutron Diffraction experiments. The calculated Young’s moduli are close to the experimental data and tend to decrease at high temperature. Comparing with the model with high Si3N4 content, the models with the higher SiC content show a larger Young’s modulus. The atomistic model can be used to predict the structural and mechanical properties of SiCN at different compositions.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 29 May 2012 Received in revised form 29 May 2013 Accepted 30 August 2013
Silicon carbon nitride (SiCN) presents good performance at high temperature while it is difficult to ascertain the chemical structure of its nanodomain by experimental techniques. In this work, empirical potential based large-scale atomistic simulations are used to generate the amorphous structures of SiCN. The models obtained by melt-quench simulations reproduce the nano-domain structure of SiCN and the corresponding PDFs consist with previous DFT calculation and X-ray/Neutron Diffraction experiments. The calculated Young’s moduli are comparable to the range of 160e240 GPa in experiments, moreover, it increases with an increasing SiC content and decrease with temperature increases. Ó 2013 Elsevier B.V. All rights reserved.
Keywords: Molecular dynamics Mechanical properties Amorphous materials Nanostructures
1. Introduction Carbon nitride related compounds are promising materials with very high hardness. Among these compounds, silicon carbon nitride (SiCN) ceramics presents good performance at high temperature and has been extensively studied over the past years. However, it is difficult to ascertain the chemical structure of nanodomain of SiCN by microscopic and spectroscopic techniques. SAXS can provide data for the size of the domains but not the molecular structure, NMR can only give information about first nearest neighbors of molecule, and X-ray diffraction also fails as the nanodomains are not crystalline [1]. Further study to understand the molecular structure of the domains is needed and atomistic modeling is a proper way to do it. Amkreutz [2] modeled the atomic structure of a precursorderived amorphous ceramic with the composition Si37C32N31 by
* Corresponding authors. Tel.: þ86 0577 86689138; fax: þ577 86689138. E-mail addresses: [email protected] (N. Liao), [email protected] (W. Xue). 0254-0584/$ e see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.matchemphys.2013.08.055
using a density-functional-based atomistic simulation. Their simulation results show a good consistence with X-ray and Neutron Diffraction results, while the models sizes were limited to several hundreds atoms as density-functional-based calculation is extremely time-consuming. By using empirical potential, the molecular dynamics simulations of SiCN for different compositions were conducted by Resta [3], the results showed when stoichiometric nitrogen/silicon ratio is high enough, the amorphous ceramic separates into C-rich, SiN-rich, and SiC-rich phases. However, their models sizes were still smaller than the feature sizes of the phases in SiCN and thus the corresponding properties could not be investigated properly. Tomar [4] studied the effects of temperature and morphology on mechanical strength of SiCO and SiCN nanocomposites. Their SiCN structures were built up by combining Si3N4 matrix with SiC clusters, the results showed wall placement, wall thickness and size of nanodomain are important factors that directly affect the strength against mechanical deformation. As the morphologies are pre-designed in their models, how does the chemical composition influence these nanodomain structures should be studied further.
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N. Liao et al. / Materials Chemistry and Physics 143 (2013) 223e227
In this work, empirical potential based large-scale atomistic simulations were conducted to generate the amorphous structure of SiCN with stoichiometric combination of SiC and Si3N4. The effects of SiC/Si3N4 ratios on structural and temperaturedependent mechanical properties of SiCN were studied. 2. Atomistic model Tersoff potential [5] and the potential parameters of Si3N4 [6] and SiC [5] were used to simulate SiCN in this study. The NeN and CeN attractive interactions in the potential energy are turned off, as there is no NeN and CeN bond presenting in SiCN [6,7] and this modification was successfully used in other MD simulations of SiCN [3,8]. Melt-quench technique is used to generate the amorphous structures of SiCN from random distributed atoms. The system is heat up to 8000 K for 20 ps to avoid the local energy minimum, and then is cooled to 3000 K for 40 ps and equilibrated for 200 ps. Finally the system is cooled to 300K for 1ns and equilibrated for 10 ps. Lammps code [9] is used to implement the simulations. Three SiCN models with different SiC/Si3N4 ratios were studied here, Si10CN12 (25 mol% SiC and 75 mol% Si3N4), Si4CN4 (50 mol% SiC and 50 mol% Si3N4) and Si6C3N4 (75 mol% SiC and 25 mol % Si3N4).
The resulting structures are shown in Fig. 1, it can be observed that the carbon phase presents in different compositions and this consists with Schempp’s experimental results [10]. The Si3N4 and SiCN phases are generally dominant for all the three compositions. The carbon phases are very small in Si10CN12, when SiC content increases, the average sizes of both SiCN and free carbon phases increase while the Si3N4 phase tends to be smaller. These structures consist with the ‘nano-domain’ structures of SiCN [1], and the sizes of carbon, SiC and Si3N4 phases also agree with domains ranges of 1e3 nm in SAXS experiments [1]. 3. Results and discussions The atomic correlations of the SiCN structures are investigated by pair distribution functions (PDF), which are shown in Fig. 2. The bond length of SieN and SieC are determined by the first sharp peaks at rSiN ¼ 1.76 A and rSiC ¼ 1.87 A. For CeC distance, the first peak presents at 1.48 A, the peak is very small for high SiC model while becomes more significant when SiC content decreases, as the presence of free carbon results in a wider CeC distribution. These results consist with DFT calculation [2] and X-ray/Neutron Diffraction experiments [10]. The static structure factor was calculated by Fourier transform of the partial pair distribution functions, which can be directly
Fig. 1. Generated amorphous SiCN structures (The Si, C and N atoms were presented as blue, black and green colors respectively). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
N. Liao et al. / Materials Chemistry and Physics 143 (2013) 223e227
(a)
110
90
4 Si-C 4:1:4 Si-C 6:3:4 Si-C 10:1:12
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total 4:1:4 total 6:3:4 total 10:1:12
7 6
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8 6
2
4 1
2 0
0
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2
4 6 r (Amgstrom)
8
10
0
2
4 6 r (Angstrom)
8
10
Fig. 2. Partial and total pair distribution functions for SiCN.
(a)
1.5
(b)
Si-C 4:1:4 Si-C 6:3:4 Si-C 10:1:12
1
5 C-C 4:1:4 C-C 6:3:4 C-C 10:1:12
4.5 4 3.5 S(q)
S(q)
0.5
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-1 1
-1.5 0
2
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q (Angstrom )
q (Angstrom ) 5
total 4:1:4 total 6:3:4 total 10:1:12
4.5 4 3.5
1 S(q)
S(q)
3
0.5 0
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-0.5
1
-1 -1.5 0
0.5
2
4
6
q (Angstrom )
8
10
0
0
2
4 6 q (Angstrom )
Fig. 3. Static structure factors for the three compositions of SiCN.
8
10
226
N. Liao et al. / Materials Chemistry and Physics 143 (2013) 223e227 0.045
0.06
4:1:4 6:3:4 10:1:12
0.04 0.035
4:1:4 6:3:4 10:1:12
0.05
0.03
0.04
0.025 0.03
0.02 0.015
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0.01 0.01
0.005 0 40
60
80 100 120 140 Si-N-Si Bond Angle (degree)
160
180
0 80
90
100
110 120 130 140 C-C-C Bond Angle (degree)
(a)
150
160
(b)
Fig. 4. Angular distributions of the SiCN structures with different carbon contents.
Fig. 5. A typical interfacial structure between free carbon and SieN regions. The SieC, SieN and CeC bonds are presented as purple, green and black respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
compared to neutron and/or X-ray diffraction experiments. Fig. 3 shows the partial and total structure factors for the three compositions of SiCN. As shown in the total S (q), the peak at 5 A1 is related to the short range order in real space. Si10CN12 and Si4CN4 show a peak at 2.8 A1, while peak of Si6C3N4 shift to 2.25 A1, corresponds to real space correlation of 2.24 A and 2.79 A respectively. The peaks at lower q are responsible for the real space correlation beyond 4 A and can be associated with an intermediate range order. The peaks positions and heights are in agreement with the experimental structure factor [10]. Further information about the local structural is provided by the angular distribution, as shown in Fig. 4. The SieNeSi distribution shows a peak at 119 , which is comparable with the peak at 121 for Si3N4 in experiments [11]. However, there is an additional peak presents at 64.5 and this may relate to the SieN bonds near the carbon regions. The CeCeC angular distribution shows a main peak at 120 which presents the sp2 carbon character. A typical interfacial structure between free carbon and SieN regions is shown in Fig. 5, it can be observed that the Si-centered tetrahedrons SieCxN4x (x ¼ 1e4) also present in SiCN structure. By a tetrahedron statistics shown in Fig. 6, the most popular case is SieN4, which consists with the domain characteristic shown in Fig. 1. Moreover, the increasing of Si3N4 content increases the proportion of SieN4 tetrahedrons while discourage the formation of other two tetrahedrons, as shown in Fig. 6(a). Another dominant tetrahedron is SieC/N (silicon bonds to a mixture of C and N), as shown in Fig. 1, these tetrahedrons generally present at the
100% 90% 80%
Si10CN12
90%
Si4CN4
80%
Si6C3N4
70%
70%
60%
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50%
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20%
20%
10%
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Si10CN12 Si4CN4 Si6C3N4
0
0 Si-N4
Si-C4
Si-C/N
Si-CN3
Fig. 6. Statistics of Si-centered tetrahedrons.
Si-C2N2
Si-C3N
N. Liao et al. / Materials Chemistry and Physics 143 (2013) 223e227
280 4:1:4 6:3:4 10:1:12
Young's modulus (GPa)
260
240
220
227
amorphous structures generated by melt-quench simulations consist with previous DFT calculation and X-ray/Neutron Diffraction experiments. The Si-centered tetrahedrons also present in SiCN structure, the tetrahedron statistics gives detailed information on interfacial structure of Si3N4 and free carbon. The calculated Young’s moduli are close to the experimental data and tend to decrease at high temperature. The atomistic model here can be used to predict the structural and mechanical properties of SiCN at different compositions.
200
Acknowledgement 180
160
300K
500K
700K
900K
1100K 1300K 1500K
Fig. 7. Temperature-dependent Young’s moduli of SiCN.
interface of Si3N4 and free carbon. In mixture tetrahedrons Sie CxN4x (x ¼ 1e3), SieCN3 is dominant and is more popular in the structures with high Si3N4 content, as shown in Fig. 6(b). The mechanical properties were studied by tensile simulation. Periodic boundary conditions were applied to all the three dimensions. In every 10 ps, the simulation box was displaced in z direction with strain of 0.0025 and the structure was dynamically relaxed. The Young’s moduli of SiCN are calculated by the stresse strain curves of the tensile simulations. The temperaturesdependent Young’s moduli are shown in Fig. 7, it generally increases with an increasing SiC content and decreases with temperature increases. At room temperature, the Young’s moduli range from 236 GPa to 269 GPa for different SiC/Si3N4 ratios, which are comparable to the range of 160e240 GPa in experiments [12,13]. 4. Conclusions Empirical potential based large-scale atomistic simulations were conducted to study the structural and mechanical properties of silicon carbon nitride with different SiC/Si3N4 ratios. The
The authors would like to acknowledge the support of the National Natural Science Foundation of China (51202164), Postdoctoral Science Foundation of China (2012M521006), Qianjiang Talent Project of Zhejiang Province (2013R10068), Natural Science Foundation of Zhejiang Province (Y1111140), Research project of Educational Commission of Zhejiang Province (Y201223855), Innovative Research Team Program of Wenzhou City (C2012000206) and High Performance Computing System of Wenzhou University. References [1] A. Saha, R. Raj, D.L. Williamson, H.J. Kleebe, J. Am. Ceram. Soc. 88 (2005) 232e 234. [2] M. Amkreutz, T. Frauenheim, Phys. Rev. B 65 (2002) 134113. [3] N. Resta, C. Kohler, H.R. Trebin, J. Am. Ceram. Soc. 86 (2003) 1409e1414. [4] V. Tomar, M. Gan, H.S. Kim, J. Euro. Cera. Soc. 30 (2010) 2223e2237. [5] J. Tersoff, Phys. Rev. B 39 (1989) 5566e5568. [6] F.D.B. Mota, J.F. Justo, A. Fazzio, Phys. Rev. B 58 (1998) 8323e8328. [7] M. Seher, J. Bill, R. Riedel, F. Aldinger, Key Eng. Mater. 89 (1994) 101e106. [8] K. Matsunaga, Y. Iwamoto, C.A.J. Fisher, H. Matsubara, J. Ceram. Soc. Jpn. 107 (1999) 1025e1031. [9] S.J. Plimpton, J. Comp. Phys. 117 (1995) 1e19. [10] S. Schempp, J. Durr, P. Lamparter, J. Bill, F. Aldinger, Z. Naturforsch. A Phys. Sci. 53 (1998) 127e133. [11] M. Misawa, T. Fukinga, K. Nihara, T. Hirai, K. Suzuki, J. Non-Cryst. Solids 34 (1979) 313e321. [12] G. Lehmann, P. Hess, J.-J. Wu, C.-T. Wu, T.-S.-S. Wong, K.-H. Chen, L.-C. Chen, H.-Y. Lee, M. Amkreutz, T. Frauenham, Phys. Rev. B 64 (2001) 165305. [13] Y. Awad, M.A.E. Khakani, C. Aktik, J. Mouine, N. Camiré, M. Lessard, M. Scarlete, H.A.A. Abadleh, R. Smirani, Surf. Coat. Tech. 204 (2009) 539e545.
Contents lists available at ScienceDirect
Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys
Atomistic investigation of structural and mechanical properties of silicon carbon nitride with different SiC/Si3N4 ratios Ningbo Liao*, Wei Xue*, Hongming Zhou, Miao Zhang College of Mechanical & Electrical Engineering, Wenzhou University, Wenzhou 325035, PR China
h i g h l i g h t s The nano-domain structure of SiCN is reproduced by large-scale atomistic simulations. The atomic models consist with previous DFT calculation and X-ray/Neutron Diffraction experiments. The calculated Young’s moduli are close to the experimental data and tend to decrease at high temperature. Comparing with the model with high Si3N4 content, the models with the higher SiC content show a larger Young’s modulus. The atomistic model can be used to predict the structural and mechanical properties of SiCN at different compositions.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 29 May 2012 Received in revised form 29 May 2013 Accepted 30 August 2013
Silicon carbon nitride (SiCN) presents good performance at high temperature while it is difficult to ascertain the chemical structure of its nanodomain by experimental techniques. In this work, empirical potential based large-scale atomistic simulations are used to generate the amorphous structures of SiCN. The models obtained by melt-quench simulations reproduce the nano-domain structure of SiCN and the corresponding PDFs consist with previous DFT calculation and X-ray/Neutron Diffraction experiments. The calculated Young’s moduli are comparable to the range of 160e240 GPa in experiments, moreover, it increases with an increasing SiC content and decrease with temperature increases. Ó 2013 Elsevier B.V. All rights reserved.
Keywords: Molecular dynamics Mechanical properties Amorphous materials Nanostructures
1. Introduction Carbon nitride related compounds are promising materials with very high hardness. Among these compounds, silicon carbon nitride (SiCN) ceramics presents good performance at high temperature and has been extensively studied over the past years. However, it is difficult to ascertain the chemical structure of nanodomain of SiCN by microscopic and spectroscopic techniques. SAXS can provide data for the size of the domains but not the molecular structure, NMR can only give information about first nearest neighbors of molecule, and X-ray diffraction also fails as the nanodomains are not crystalline [1]. Further study to understand the molecular structure of the domains is needed and atomistic modeling is a proper way to do it. Amkreutz [2] modeled the atomic structure of a precursorderived amorphous ceramic with the composition Si37C32N31 by
* Corresponding authors. Tel.: þ86 0577 86689138; fax: þ577 86689138. E-mail addresses: [email protected] (N. Liao), [email protected] (W. Xue). 0254-0584/$ e see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.matchemphys.2013.08.055
using a density-functional-based atomistic simulation. Their simulation results show a good consistence with X-ray and Neutron Diffraction results, while the models sizes were limited to several hundreds atoms as density-functional-based calculation is extremely time-consuming. By using empirical potential, the molecular dynamics simulations of SiCN for different compositions were conducted by Resta [3], the results showed when stoichiometric nitrogen/silicon ratio is high enough, the amorphous ceramic separates into C-rich, SiN-rich, and SiC-rich phases. However, their models sizes were still smaller than the feature sizes of the phases in SiCN and thus the corresponding properties could not be investigated properly. Tomar [4] studied the effects of temperature and morphology on mechanical strength of SiCO and SiCN nanocomposites. Their SiCN structures were built up by combining Si3N4 matrix with SiC clusters, the results showed wall placement, wall thickness and size of nanodomain are important factors that directly affect the strength against mechanical deformation. As the morphologies are pre-designed in their models, how does the chemical composition influence these nanodomain structures should be studied further.
224
N. Liao et al. / Materials Chemistry and Physics 143 (2013) 223e227
In this work, empirical potential based large-scale atomistic simulations were conducted to generate the amorphous structure of SiCN with stoichiometric combination of SiC and Si3N4. The effects of SiC/Si3N4 ratios on structural and temperaturedependent mechanical properties of SiCN were studied. 2. Atomistic model Tersoff potential [5] and the potential parameters of Si3N4 [6] and SiC [5] were used to simulate SiCN in this study. The NeN and CeN attractive interactions in the potential energy are turned off, as there is no NeN and CeN bond presenting in SiCN [6,7] and this modification was successfully used in other MD simulations of SiCN [3,8]. Melt-quench technique is used to generate the amorphous structures of SiCN from random distributed atoms. The system is heat up to 8000 K for 20 ps to avoid the local energy minimum, and then is cooled to 3000 K for 40 ps and equilibrated for 200 ps. Finally the system is cooled to 300K for 1ns and equilibrated for 10 ps. Lammps code [9] is used to implement the simulations. Three SiCN models with different SiC/Si3N4 ratios were studied here, Si10CN12 (25 mol% SiC and 75 mol% Si3N4), Si4CN4 (50 mol% SiC and 50 mol% Si3N4) and Si6C3N4 (75 mol% SiC and 25 mol % Si3N4).
The resulting structures are shown in Fig. 1, it can be observed that the carbon phase presents in different compositions and this consists with Schempp’s experimental results [10]. The Si3N4 and SiCN phases are generally dominant for all the three compositions. The carbon phases are very small in Si10CN12, when SiC content increases, the average sizes of both SiCN and free carbon phases increase while the Si3N4 phase tends to be smaller. These structures consist with the ‘nano-domain’ structures of SiCN [1], and the sizes of carbon, SiC and Si3N4 phases also agree with domains ranges of 1e3 nm in SAXS experiments [1]. 3. Results and discussions The atomic correlations of the SiCN structures are investigated by pair distribution functions (PDF), which are shown in Fig. 2. The bond length of SieN and SieC are determined by the first sharp peaks at rSiN ¼ 1.76 A and rSiC ¼ 1.87 A. For CeC distance, the first peak presents at 1.48 A, the peak is very small for high SiC model while becomes more significant when SiC content decreases, as the presence of free carbon results in a wider CeC distribution. These results consist with DFT calculation [2] and X-ray/Neutron Diffraction experiments [10]. The static structure factor was calculated by Fourier transform of the partial pair distribution functions, which can be directly
Fig. 1. Generated amorphous SiCN structures (The Si, C and N atoms were presented as blue, black and green colors respectively). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
N. Liao et al. / Materials Chemistry and Physics 143 (2013) 223e227
(a)
110
90
4 Si-C 4:1:4 Si-C 6:3:4 Si-C 10:1:12
3.5
80
3
70
2.5
60
g(r)
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8 6
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4 1
2 0
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2
4 6 r (Amgstrom)
8
10
0
2
4 6 r (Angstrom)
8
10
Fig. 2. Partial and total pair distribution functions for SiCN.
(a)
1.5
(b)
Si-C 4:1:4 Si-C 6:3:4 Si-C 10:1:12
1
5 C-C 4:1:4 C-C 6:3:4 C-C 10:1:12
4.5 4 3.5 S(q)
S(q)
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0
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-1.5 0
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6
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10
q (Angstrom )
q (Angstrom ) 5
total 4:1:4 total 6:3:4 total 10:1:12
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1 S(q)
S(q)
3
0.5 0
2.5 2 1.5
-0.5
1
-1 -1.5 0
0.5
2
4
6
q (Angstrom )
8
10
0
0
2
4 6 q (Angstrom )
Fig. 3. Static structure factors for the three compositions of SiCN.
8
10
226
N. Liao et al. / Materials Chemistry and Physics 143 (2013) 223e227 0.045
0.06
4:1:4 6:3:4 10:1:12
0.04 0.035
4:1:4 6:3:4 10:1:12
0.05
0.03
0.04
0.025 0.03
0.02 0.015
0.02
0.01 0.01
0.005 0 40
60
80 100 120 140 Si-N-Si Bond Angle (degree)
160
180
0 80
90
100
110 120 130 140 C-C-C Bond Angle (degree)
(a)
150
160
(b)
Fig. 4. Angular distributions of the SiCN structures with different carbon contents.
Fig. 5. A typical interfacial structure between free carbon and SieN regions. The SieC, SieN and CeC bonds are presented as purple, green and black respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
compared to neutron and/or X-ray diffraction experiments. Fig. 3 shows the partial and total structure factors for the three compositions of SiCN. As shown in the total S (q), the peak at 5 A1 is related to the short range order in real space. Si10CN12 and Si4CN4 show a peak at 2.8 A1, while peak of Si6C3N4 shift to 2.25 A1, corresponds to real space correlation of 2.24 A and 2.79 A respectively. The peaks at lower q are responsible for the real space correlation beyond 4 A and can be associated with an intermediate range order. The peaks positions and heights are in agreement with the experimental structure factor [10]. Further information about the local structural is provided by the angular distribution, as shown in Fig. 4. The SieNeSi distribution shows a peak at 119 , which is comparable with the peak at 121 for Si3N4 in experiments [11]. However, there is an additional peak presents at 64.5 and this may relate to the SieN bonds near the carbon regions. The CeCeC angular distribution shows a main peak at 120 which presents the sp2 carbon character. A typical interfacial structure between free carbon and SieN regions is shown in Fig. 5, it can be observed that the Si-centered tetrahedrons SieCxN4x (x ¼ 1e4) also present in SiCN structure. By a tetrahedron statistics shown in Fig. 6, the most popular case is SieN4, which consists with the domain characteristic shown in Fig. 1. Moreover, the increasing of Si3N4 content increases the proportion of SieN4 tetrahedrons while discourage the formation of other two tetrahedrons, as shown in Fig. 6(a). Another dominant tetrahedron is SieC/N (silicon bonds to a mixture of C and N), as shown in Fig. 1, these tetrahedrons generally present at the
100% 90% 80%
Si10CN12
90%
Si4CN4
80%
Si6C3N4
70%
70%
60%
60%
50%
50%
40%
40%
30%
30%
20%
20%
10%
10%
Si10CN12 Si4CN4 Si6C3N4
0
0 Si-N4
Si-C4
Si-C/N
Si-CN3
Fig. 6. Statistics of Si-centered tetrahedrons.
Si-C2N2
Si-C3N
N. Liao et al. / Materials Chemistry and Physics 143 (2013) 223e227
280 4:1:4 6:3:4 10:1:12
Young's modulus (GPa)
260
240
220
227
amorphous structures generated by melt-quench simulations consist with previous DFT calculation and X-ray/Neutron Diffraction experiments. The Si-centered tetrahedrons also present in SiCN structure, the tetrahedron statistics gives detailed information on interfacial structure of Si3N4 and free carbon. The calculated Young’s moduli are close to the experimental data and tend to decrease at high temperature. The atomistic model here can be used to predict the structural and mechanical properties of SiCN at different compositions.
200
Acknowledgement 180
160
300K
500K
700K
900K
1100K 1300K 1500K
Fig. 7. Temperature-dependent Young’s moduli of SiCN.
interface of Si3N4 and free carbon. In mixture tetrahedrons Sie CxN4x (x ¼ 1e3), SieCN3 is dominant and is more popular in the structures with high Si3N4 content, as shown in Fig. 6(b). The mechanical properties were studied by tensile simulation. Periodic boundary conditions were applied to all the three dimensions. In every 10 ps, the simulation box was displaced in z direction with strain of 0.0025 and the structure was dynamically relaxed. The Young’s moduli of SiCN are calculated by the stresse strain curves of the tensile simulations. The temperaturesdependent Young’s moduli are shown in Fig. 7, it generally increases with an increasing SiC content and decreases with temperature increases. At room temperature, the Young’s moduli range from 236 GPa to 269 GPa for different SiC/Si3N4 ratios, which are comparable to the range of 160e240 GPa in experiments [12,13]. 4. Conclusions Empirical potential based large-scale atomistic simulations were conducted to study the structural and mechanical properties of silicon carbon nitride with different SiC/Si3N4 ratios. The
The authors would like to acknowledge the support of the National Natural Science Foundation of China (51202164), Postdoctoral Science Foundation of China (2012M521006), Qianjiang Talent Project of Zhejiang Province (2013R10068), Natural Science Foundation of Zhejiang Province (Y1111140), Research project of Educational Commission of Zhejiang Province (Y201223855), Innovative Research Team Program of Wenzhou City (C2012000206) and High Performance Computing System of Wenzhou University. References [1] A. Saha, R. Raj, D.L. Williamson, H.J. Kleebe, J. Am. Ceram. Soc. 88 (2005) 232e 234. [2] M. Amkreutz, T. Frauenheim, Phys. Rev. B 65 (2002) 134113. [3] N. Resta, C. Kohler, H.R. Trebin, J. Am. Ceram. Soc. 86 (2003) 1409e1414. [4] V. Tomar, M. Gan, H.S. Kim, J. Euro. Cera. Soc. 30 (2010) 2223e2237. [5] J. Tersoff, Phys. Rev. B 39 (1989) 5566e5568. [6] F.D.B. Mota, J.F. Justo, A. Fazzio, Phys. Rev. B 58 (1998) 8323e8328. [7] M. Seher, J. Bill, R. Riedel, F. Aldinger, Key Eng. Mater. 89 (1994) 101e106. [8] K. Matsunaga, Y. Iwamoto, C.A.J. Fisher, H. Matsubara, J. Ceram. Soc. Jpn. 107 (1999) 1025e1031. [9] S.J. Plimpton, J. Comp. Phys. 117 (1995) 1e19. [10] S. Schempp, J. Durr, P. Lamparter, J. Bill, F. Aldinger, Z. Naturforsch. A Phys. Sci. 53 (1998) 127e133. [11] M. Misawa, T. Fukinga, K. Nihara, T. Hirai, K. Suzuki, J. Non-Cryst. Solids 34 (1979) 313e321. [12] G. Lehmann, P. Hess, J.-J. Wu, C.-T. Wu, T.-S.-S. Wong, K.-H. Chen, L.-C. Chen, H.-Y. Lee, M. Amkreutz, T. Frauenham, Phys. Rev. B 64 (2001) 165305. [13] Y. Awad, M.A.E. Khakani, C. Aktik, J. Mouine, N. Camiré, M. Lessard, M. Scarlete, H.A.A. Abadleh, R. Smirani, Surf. Coat. Tech. 204 (2009) 539e545.