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Brillouin Scattering of Layered & 2D Materials

Below are values of elastic stiffnesses of 2D and layered materials as determined by Brillouin light scattering. Note that there are only a few measurements that have managed to determine all stiffness coefficients. Most measurements are done using a scattering geometry of 180 degrees and an equal-angle scattering geometry such as 90a. Part of this is due to the reflective nature of these samples, but also the difficulty inherent in making these measurements.
Brillouin scattering of graphite has been measured by several sources but there is little agreement between meeasurements and it has been the source of contention. A measurement worth mentioning for graphite is that of S.A. Lee and S.M. Lindsay. Phys. Stat. Sol. (b) 157, K83 (1990). The cutoff of the author's shutter (Sandercock tandem Febry-Perot Interferometer) is misassigned as a graphite peak (oops!). Grimsditch notes in a correction, he also made an error with accounting for the solid angle of collection on HOPG (M. Grimsditch. J. Phys. C: Solid State Phys. 16, L143 (1983).). Grimsditch notes a c44 = 3.25 GPa.

Halides:
[GPa]
PbI2
CdI2
BiI3
SbI3
c11 27.7 +/- 0.5 43.1 +/- 0.9 29 15
c33 202.2 +/- 0.4 22.5 +/- 0.5 26 9.3
c44 6.2 +/- 0.2 5.5 +/- 0.3 7 4.7
c12 9.6 +/- 0.9 20.4 +/- 1.0 5 -5
c13 11.3 +/- 0.6 8.9 +/- 0.5 9 4
c14 3.0 +/- 0.2 0 2 1
c13
c25 0 2.5
Crystal Class Trigonal Trigonal rhombohedral rhombohedral
Space Group P3m1 P3m1 R-3 R-3
Reference [1] [1] [2] [2]
Sesqui-chalcogenides:
[GPa]
As2S3
Bi2Se3
Bi2Te3
Sb2Te3
c11 99.6 +/- 1.0
c22 27.1 +/- 0.3
c33 21.9 +/- 1.4 98 +/- 7 52 +/- 5 72 +/- 3
c44 1.1 +/- 0.2 37 +/- 10 25 +/- 2
c55 24.0 +/- 0.8
c66 0.7+/- 0.2
c12
c13 20.6 +/- 1.9
c23
c46 0.2+/- 0.2
Crystal Class Monoclinic rhombohedral trigonal trigonal
Space Group P2_1/n R-3m R-3m R-3m
Reference [6] [7] [7] [7]
Dichalcogenides:
[GPa]
SnS2
SnSe2
2H-TaSe2
1T-TiSe2
2H-NbSe2
1T-TaS2
c11 146 +/- 3.0
c33 27.2 +/- 0.5 208.5 108 108 58.5
c44 8.3 +/- 0.2 5.5 10.98 13.2 11.3 8.5
c12 41.5 +/- 1.5
c13 13.3 +/- 1.1
c14 0
c25
c46
Crystal Class Trigonal Trigonal hexagonal Trigonal hexagonal Trigonal
Space Group P3m1 P3m1 hP6 P-3m1 P63mmc P-3m1
Reference [1] [1] [2] [2] [2] [2]
Mono-chalcogenides and Nitrides:
[GPa]
InSe
GaSe
GaS
h-BN
h-BN
c11 68.4 +/- 2.7 111 +/- 2.2 122 788 819 +/- 10
c33 29.2 +/- 0.7 35.3 +/- 0.7 38 24.5 27.6 +/- 0.2
c44 6.27 +/- 0.45 10.2 +/- 0.3 9.8 385 +/- 11
c12 28.2 +/- 3.2 32.6 +/- 1.2 33.4
c13 12.2 +/- 2.6 12.0 +/- 0.9 8.9
c15 -0.3 +/- 0.8
c35 -1.2 +/- 0.9
Crystal Class hexagonal hexagonal hexagonal hexagonal hexagonal
Space Group hexagonal hexagonal hexagonal P6_3/mmc P6_3/mmc
Reference [5] [1] [11] [4] [12]
Layered Oxides
[GPa]
V2O5
MoO3
c11 231 +/- 13 156 +/- 2
c22 230 +/- 14 128.7 +/- 0.8
c33 42.2 +/- 0.4 241 +/- 2
c44 23.6 +/- 0.3 51.6 +/- 0.3
c55 25.7 +/- 0.3 60 +/- 1
c66 38.0 +/- 0.2
c12 -13 +/- 2
c13 51.4 +/- 1.2 31 +/- 2
c23 41.9 +/- 1.5 35 +/- 2
Crystal Class orthorhombic orthorhombic
Space Group Pmmn Pbnm
Reference [9] [10]
References
[1] J Sandercock, Festkorperprobleme, 15, 183 (1975)
[2] Tato, Eiji, Teruo Komatsu, and Yozo Kaifu. J Phys Soc Japan, 54, 3597-3604 (1985)
[3] Nakashima, S., et al. Sol. State Commun. 31, 913-916 (1979)
[4] Jimenez-Rioboo, Rafael J., et al. Appl. Phys. Lett. 112, 051905 (2018)
[5] Panella, V., et al.  J Phys: Condens. Matter 9, 5575 (1997)
[6] McNeil, L. E., and M. Grimsditch. Phys Rev B 44, 4174 (1991)
[7] Alnofiay, Jamal Najr.Diss. Memorial University of Newfoundland, 2014
[8] Harley, R. T., and P. A. Fleury, J Phys C: Sol State Phys 12, L863 (1979)
[9] Reed, Bryan W., Koski, Kristie J. et al. Phys. Rev. B 102, 054109 (2020)
[10] Reed, Bryan W., Koski, Kristie J. et al. Nano Lett. 19, 4406-4412 (2019)
[11] Polian, A., Besson, J.M., et al. Phys. Rev. B 25, 2767-2775 (1982)
[12] Reed, B.W., Tran, C., Koski, K.J. Phys. Rev. Mat. 7, 044003 (2023)