Determination of shear modulus and out of plane Young's modulus of layered materials by raman spectroscopy
Event details
| Date | 24.04.2015 |
| Hour | 14:15 |
| Speaker |
Silvia Milana, Cambridge Graphene Centre, University of Cambridge, UK Bio: Silvia Milana is a Research Associate in Cambridge University Engineering Department and Pembroke College. She is in the Nanomaterials and Spectroscopy Group in the Electrical Engineering Division. |
| Location | |
| Category | Conferences - Seminars |
The set of elastic constants of a material describes its response to applied external forces [1]. The elastic constants relate such external forces, described by the stress tensor, to the resulting deformation, described by the strain tensor, and an in-depth knowledge of them is essential to gain insight on the nature of crystal structure and bonding forces [1]. In crystals with uniaxial hexagonal layered structure, the elasticity matrix describing mechanical properties contains five non-vanishing, independent terms: C11, C12, C13, C33, and C44 [1]. C44 represents the shear modulus of the layer-layer interface, accounting for displacement of the planes with respect to each other [1]. C33 determines the Young’s modulus in the normal direction, thus describing the out-of-plane compression or expansion of the layers [1]. Raman spectroscopy is the prime non-destructive characterization tool for graphene and related layered materials (LMs) [2]. The shear (C) [3] and layer breathing modes (LBMs) [4, 5, 6] are due to relative motions of the planes, either perpendicular or parallel to their normal. It is therefore possible to associate these Raman modes to their respective elastic constants accounting for such displacements. Here we consider three examples of LMs, namely NLG, NL-MoS2 and NL-hBN (N being the number of layers), which can be regarded as representative metallic, semiconducting and insulating templates, respectively. Similarly to the C mode of NLG and NL-hBN, the first-order C and LBMs of MoS2 are directly accessible at room temperature, whereas we gain insight on the LBM dynamics in NLG by measuring its combinations with the D' peak. We find that the positions of the observed C and LBMs in these materials depend strongly on N. A general linear-chain model, based on an interlayer force constant per unit area, can account for the observed trends, allowing a direct evaluation of C44 and C33, with applicability to any layered materials. For NLG we find C44 ~4.3 GPa and C33 ~37GPa. The C44 and C33 of NL- MoS2 are found to be ~18.9 GPa and ~59.6 GPa, respectively, whereas the C44 of NL-hBN is ~6.5 GPa.
[1] G. Grimvall, North-Holland (1986).
[2] A. C. Ferrari, D. M. Basko, Nat. Nanotechnol., 8 (2013) 235.
[3] P. H. Tan, W. P. Han, W. J. Zhao, Z. H. Wu, K. Chang, H. Wang, T. F. Wang, N. Bonini, N. Marzari, N. Pugno, G. Savini, A. Lombardo, A. C. Ferrari, Nat. Mater. 11 (2012) 294.
[4] X. Zhang, W. P. Han, J. B. Wu, S. Milana, Y. Lu, Q. Q. Li, A. C. Ferrari, P. H. Tan, Phys. Rev. B 87 (2013) 115413.
[5] F. Bonaccorso, P.H. Tan, A.C. Ferrari, 7(3) ACS Nano (2013) 1838.
[6] F. Herziger, P. May, J. Maultzsch, Phys. Rev. B, 85 (2012) 235447.
Host: Oleg Yazyev
[1] G. Grimvall, North-Holland (1986).
[2] A. C. Ferrari, D. M. Basko, Nat. Nanotechnol., 8 (2013) 235.
[3] P. H. Tan, W. P. Han, W. J. Zhao, Z. H. Wu, K. Chang, H. Wang, T. F. Wang, N. Bonini, N. Marzari, N. Pugno, G. Savini, A. Lombardo, A. C. Ferrari, Nat. Mater. 11 (2012) 294.
[4] X. Zhang, W. P. Han, J. B. Wu, S. Milana, Y. Lu, Q. Q. Li, A. C. Ferrari, P. H. Tan, Phys. Rev. B 87 (2013) 115413.
[5] F. Bonaccorso, P.H. Tan, A.C. Ferrari, 7(3) ACS Nano (2013) 1838.
[6] F. Herziger, P. May, J. Maultzsch, Phys. Rev. B, 85 (2012) 235447.
Host: Oleg Yazyev
Practical information
- Informed public
- Free
Organizer
- ICMP (Arnaud Magrez and Raphaël Butté)
Contact
- Oleg Yazyev ([email protected])