Molecular dynamics simulations have been performed to study the mechanical properties of two-dimensional titanium carbide under tensile deformation. Young modulus was calculated from the linear part of strain-stress curve. From the radial distribution function it is found that the structure of the simulated samples is preserved during the deformation process. Calculated values of the elastic constants are in good agreement with the DFT data

Borysiuk, Vadym Mykolaiovych

Gogotsi, Y.

Mochalin, V.N.

Борисюк, Вадим Миколайович

Борисюк, Вадим Николаевич

Electronic Sumy State University Institutional Repository

PROCEEDINGS OF THE INTERNATIONAL CONFERENCE  NANOMATERIALS: APPLICATIONS AND PROPERTIES Vol. 3 No 1, 01CBNM02(1pp) (2014)   2304-1862/2014/3(1)01CBNM02(1) 01CBNM02-1  2014 Sumy State University Molecular Dynamics Study of the Mechanical Properties of the Grapheme-like  Titanium Carbide Ti2C  V.N. Borysiuk1, 2, V.N. Mochalin2, Y. Gogotsi2, *  1 Sumy State University, 2, Rymsky Korsakov Str., 40007 Sumy, Ukraine 2 A.J. Drexel Nanomaterials Institute, Drexel University, Philadelphia, PA 19104, USA  (Received 10 July 2014; published online 29 August 2014)  Molecular dynamics simulations have been performed to study the mechanical properties of two-dimensional titanium carbide under tensile deformation. Young modulus was calculated from the linear part of strain-stress curve. From the radial distribution function it is found that the structure of the simu-lated samples is preserved during the deformation process. Calculated values of the elastic constants are in good agreement with the DFT data.  Keywords: Two-dimensional material, Titanium carbide, Strain-stress curve, Young modulus   PACS numbers: 81.05.U –, 62.25. – g                                                    * gogotsi@drexel.edu  A new, large family of two-dimensional transition metal carbides and nitrides, known as MXenes has recently been discovered [1, 2]. Their unique properties suggest large area of potential applications [3, 4]. Since the discovery, MXenes are intensively studied by dif-ferent methods and techniques [5-7] with computation-al studies making a large part of these efforts. Here we report the results of an atomistic simulation of the two-dimensional titanium carbide Ti2C.  Atomistic simulations were carried out within clas-sical molecular dynamic techniques. To describe the different types of bonding in the Ti2C monolayer we use the embedded atom model (EAM) [8], Axilrod-Teller (AT) [9] and Lennard-Jones [10] potentials.  During the simulations potential energy of the par-ticles, system temperature and the velocities were rec-orded. The system temperature was maintained at 300 K, using Berendsen thermostat [11]. Mechanical properties of the samples were studied under the tensile deformation with different strain rates. Strain was applied to the Ti2C monolayer by pulling one edge of the sheet while the opposite edge was fixed. Tension was applied to the system up to the destruction of the samples. To detect the changes in the Ti2C structure the radial distribution functions (RDF) were calculated. In the process of tensile load the overall stress in the material was calculated by the virial theorem [12], and the strain-stress curves were obtained.  Obtained strain-stress curves have a similar form with a linear region, related to elastic deformation. At a higher strain, stress continues to increase up to the threshold point of a yield stress, followed by a sharp drop related to the sample destruction. Tensile defor-mation was applied to the system at different strain rates. All the strain-stress curves demonstrate the lin-ear region of elastic deformation, with the slope being independent from the strain rate.  The Young’s modulus values were obtained from the strain-stress curves with the strain 0.01%  by linear regression with the average value 597 55E GPa . These results are in good agreement with the DFT cal-culations [5].  Our simulations have shown that the classical mo-lecular dynamics approach correctly describes mechan-ical behavior of the two-dimensional titanium carbide and may be used in further investigations of the struc-tural and mechanical properties of the MXenes termi-nated by oxygen containing functional groups produced experimentally.   REFERENCES  1. M.  Naguib, M.  Kurtoglu, V.  Presser, J.  Lu, J. J.  Niu, M. Heon, L.  Hultman , Y.  Gogotsi, M.W.  Barsoum, Adv. Mater. 23, 4248 (2011). 2. M.  Naguib, V.N.  Mochalin, M.W.  Barsoum, Y. Gogotsi, Adv. Mater. 26 No 7, 992 (2014). 3. Q. Tang, Z. Zhou, P.W. Shen, J. Am. Chem. Soc. 134 No 40, 16909 (2012).  4. Q. Hu, D. Sun, Q. Wu, H. Wang, L. Wang, B. Liu, A. Zhou, J. Phys. Chem. A 117 No 51, 14253 (2013). 5. M.  Kurtoglu, M.  Naguib, Y.  Gogotsi, M.W.  Barsoum, MRS Communications 2 No 4, 133 (2012). 6. I. R. Shein, A. L. Ivanovskii, Superlattices and Microstruc-tures 52 No 2, 147 (2012). 7. A.N. Enyashin, A. L. Ivanovskii, Computational and Theo-retical Chemistry 989, 27 (2012). 8. X.W. Zhou, H. Wadley, R. Johnson, D. Larson, N. Tabat, A. Cerezo, A. Petford-Long, G. Smith, P.  Clifton, R. Mar-tens, T.  Kelly, Acta Mater.  49, 4005 (2001).  9. B. M. Axilrod,  E. Teller, J. Chem. Phys. 11 No6, 299 (1943); 10. J.E. Lennard-Jones, Proc. R. Soc. Lond. A 106, 463 (1924).  11. H.J.C. Berendsen, J.P.M. Postma, W.F. Vangunsteren, A. Dinola, J.R. Haak, J. Chem. Phys. 81 No8,3684 (1984).  12. D.H. Tsai, J. Chem. Phys.70, 1375 (1979). 

Molecular Dynamics Study of the Mechanical Properties of the Grapheme-like  Titanium Carbide Ti2C

SocioEconomic Challenges Journal (Sumy State University)

PROCEEDINGS OF THE INTERNATIONAL CONFERENCE  
NANOMATERIALS: APPLICATIONS AND PROPERTIES 
Vol. 3 No 1, 01CBNM02(1pp) (2014) 
 
 
2304-1862/2014/3(1)01CBNM02(1) 01CBNM02-1  2014 Sumy State University 
Molecular Dynamics Study of the Mechanical Properties of the Grapheme-like  
Titanium Carbide Ti2C 
 
V.N. Borysiuk1, 2, V.N. Mochalin2, Y. Gogotsi2, * 
 
1 Sumy State University, 2, Rymsky Korsakov Str., 40007 Sumy, Ukraine 
2 A.J. Drexel Nanomaterials Institute, Drexel University, Philadelphia, PA 19104, USA 
 
(Received 10 July 2014; published online 29 August 2014) 
 
Molecular dynamics simulations have been performed to study the mechanical properties of two-
dimensional titanium carbide under tensile deformation. Young modulus was calculated from the linear 
part of strain-stress curve. From the radial distribution function it is found that the structure of the simu-
lated samples is preserved during the deformation process. Calculated values of the elastic constants are in 
good agreement with the DFT data. 
 
Keywords: Two-dimensional material, Titanium carbide, Strain-stress curve, Young modulus 
 
 PACS numbers: 81.05.U –, 62.25. – g 
 
 
                                                 
* gogotsi@drexel.edu  
A new, large family of two-dimensional transition 
metal carbides and nitrides, known as MXenes has 
recently been discovered [1, 2]. Their unique properties 
suggest large area of potential applications [3, 4]. Since 
the discovery, MXenes are intensively studied by dif-
ferent methods and techniques [5-7] with computation-
al studies making a large part of these efforts. Here we 
report the results of an atomistic simulation of the two-
dimensional titanium carbide Ti2C.  
Atomistic simulations were carried out within clas-
sical molecular dynamic techniques. To describe the 
different types of bonding in the Ti2C monolayer we use 
the embedded atom model (EAM) [8], Axilrod-Teller 
(AT) [9] and Lennard-Jones [10] potentials.  
During the simulations potential energy of the par-
ticles, system temperature and the velocities were rec-
orded. The system temperature was maintained at 300 
K, using Berendsen thermostat [11]. 
Mechanical properties of the samples were studied 
under the tensile deformation with different strain 
rates. Strain was applied to the Ti2C monolayer by 
pulling one edge of the sheet while the opposite edge 
was fixed. Tension was applied to the system up to the 
destruction of the samples. To detect the changes in the 
Ti2C structure the radial distribution functions (RDF) 
were calculated. 
In the process of tensile load the overall stress in 
the material was calculated by the virial theorem [12], 
and the strain-stress curves were obtained.  
Obtained strain-stress curves have a similar form 
with a linear region, related to elastic deformation. At 
a higher strain, stress continues to increase up to the 
threshold point of a yield stress, followed by a sharp 
drop related to the sample destruction. Tensile defor-
mation was applied to the system at different strain 
rates. All the strain-stress curves demonstrate the lin-
ear region of elastic deformation, with the slope being 
independent from the strain rate.  
The Young’s modulus values were obtained from the 
strain-stress curves with the strain 0.01%  by linear 
regression with the average value 597 55E GPa . 
These results are in good agreement with the DFT cal-
culations [5].  
Our simulations have shown that the classical mo-
lecular dynamics approach correctly describes mechan-
ical behavior of the two-dimensional titanium carbide 
and may be used in further investigations of the struc-
tural and mechanical properties of the MXenes termi-
nated by oxygen containing functional groups produced 
experimentally. 
 
 
REFERENCES 
 
1. M.  Naguib, M.  Kurtoglu, V.  Presser, J.  Lu, J. J.  Niu, 
M. Heon, L.  Hultman , Y.  Gogotsi, M.W.  Barsoum, Adv. 
Mater. 23, 4248 (2011). 
2. M.  Naguib, V.N.  Mochalin, M.W.  Barsoum, Y. Gogotsi, 
Adv. Mater. 26 No 7, 992 (2014). 
3. Q. Tang, Z. Zhou, P.W. Shen, J. Am. Chem. Soc. 134 
No 40, 16909 (2012).  
4. Q. Hu, D. Sun, Q. Wu, H. Wang, L. Wang, B. Liu, A. Zhou, 
J. Phys. Chem. A 117 No 51, 14253 (2013). 
5. M.  Kurtoglu, M.  Naguib, Y.  Gogotsi, M.W.  Barsoum, 
MRS Communications 2 No 4, 133 (2012). 
6. I. R. Shein, A. L. Ivanovskii, Superlattices and Microstruc-
tures 52 No 2, 147 (2012). 
7. A.N. Enyashin, A. L. Ivanovskii, Computational and Theo-
retical Chemistry 989, 27 (2012). 
8. X.W. Zhou, H. Wadley, R. Johnson, D. Larson, N. Tabat, 
A. Cerezo, A. Petford-Long, G. Smith, P.  Clifton, R. Mar-
tens, T.  Kelly, Acta Mater.  49, 4005 (2001).  
9. B. M. Axilrod,  E. Teller, J. Chem. Phys. 11 No6, 299 
(1943); 
10. J.E. Lennard-Jones, Proc. R. Soc. Lond. A 106, 463 (1924).  
11. H.J.C. Berendsen, J.P.M. Postma, W.F. Vangunsteren, 
A. Dinola, J.R. Haak, J. Chem. Phys. 81 No8,3684 (1984).  
12. D.H. Tsai, J. Chem. Phys.70, 1375 (1979). 


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Molecular Dynamics Study of the Mechanical Properties of the Grapheme-like Titanium Carbide Ti2C

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