# Elastic moduli, anisotropy and refractive index of γ-Ge3N4 via laser ultrasonics, Brillouin light scattering, and first-principles calculations

Chen-Hui Li, Philippe Djemia, Nikolay Chigarev, Siham Sodki, Y. Roussigné, Samuel Raetz, Vitalyi Gusev, Andreas Zerr

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Chen-Hui Li, Philippe Djemia, Nikolay Chigarev, Siham Sodki, Y. Roussigné, et al., Elastic moduli, anisotropy and refractive index of γ-Ge3N4 via laser ultrasonics, Brillouin light scattering, and first-principles calculations. The Joint 28th AIRAPT and 60th EHPRG International Conference 2023, Jul 2023, Edinburgh, United Kingdom. pp.17. [hal-04241737](https://hal.science/hal-04241737v1)

HAL Id: hal-04241737

https://hal.science/hal-04241737v1

Submitted on 13 Oct 2023

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Elastic moduli, anisotropy and refractive index of γ-Ge₃N₄ via laser
ultrasonics, Brillouin light scattering, and first-principles calculations

Dr. Chen-Hui Li¹, Prof. Philippe Djemia¹, Dr. Nikolay Chigarev², Ms. Siham Sodki¹,
Prof. Yves Roussigné¹, Prof. Samuel Raetz², Prof. Vitalyi E. Gusev², **Dr. Andreas Zerr**¹

¹Laboratoire des Sciences des Procédés et des Matériaux - CNRS, Villetaneuse, France, ²Laboratoire d'Acoustique de l'Université du Mans, Le Mans, France

Poster Session 2 and Refreshments, July 27, 2023, 16:00–17:30

Germanium nitride having cubic spinel structure, γ-Ge₃N₄, is a wide band-gap semiconductor, Eg=3.65(5) eV, with a large exciton binding energy [1,2] which exhibits high hardness, elastic moduli and elevated thermal stability to ~700°C. Experimental data on its bulk and shear moduli (B₀ and G₀, respectively) are strongly limited [3–6], inconsistent and, thus, require verification. Moreover, earlier first-principles density functional calculations provided significantly scattering B₀ values but consistently predicted G₀ much higher than the experimental one [7–9]. Here, we investigated the elastic behaviour of γ-Ge₃N₄ experimentally, using the techniques of laser ultrasonics (LU) and Brillouin light scattering (BLS), and theoretically, using the first-principles calculations. We measured velocities of the Rayleigh surface acoustic waves (RSAWs) and of the longitudinal acoustic waves (LAWs) in our low-porosity polycrystalline sample using the LU-technique and derived its isotropic elastic moduli Bp and Gp (here and below, the subscripts p and 0 indicate values for the porous and densified sample, respectively). Applying the Hashin-Shtrikman approach, we obtained B₀=322(44) GPa and G₀=188(7) GPa for the dense γ-Ge₃N₄. The significant error in B₀ is explained by the low amplitude of the LAW-signals in our LU-measurements. Nevertheless, it agrees, within experimental uncertainties, with the B₀=295(5) GPa [3] obtained from the EOS measured upon quasi-hydrostatic compression. Both the previous and the present first-principles calculations underestimated B₀ while the GGA-PBEsol functional with a hard PAW potential showed the least deviation from the experiment.

Our experimental G₀ exceeds by ~1.5 times the previous experimental value, G₀=124-129 GPa derived
from the nanoindentation testing [4, 5]. The calculated G₀ values, typically around 170 GPa, were
underestimated but much less significant than the B₀, between 211-269 GPa. However, G₀=186(10)
GPa calculated using the GGA-PBEsol functional with a hard PAW potential agreed with our
measurements. Comparison of the RSAW-velocity values, VR₀, measured using the LU- and BLS
techniques confirmed the theoretically-predicted elastic anisotropy of γ-Ge₃N₄. The anisotropy led to
the asymmetric RSAW peaks in our BLS measurements resulting in the VR₀ underestimation by ~10%.
Combining our LU- and BLS results for the LAWs, we determined the refractive index of the dense
γ-Ge₃N₄ to be n₀=2.4(1). This value ranks γ-Ge₃N₄ in the class of very-high-refractive-index materials
transparent for visible light, such as diamond, GaN or TiO₂ having anatase structure.

[1] Boyko T.D., et al., Phys. Rev. Lett. 111, 097402 (2013)

[2] Feldbach E., et al., Electron. Mater. Lett. 17, 315-323 (2021)

[3] Somayazulu M.S., et al., in Proceedings of AIRAPT-17, M. Manghnani, W.J. Nellis, M. Nicol, 663-666 (2000)

[4] Shemkunas M.P., et al., J. Mater. Res. 19, 1392-1399 (2004)

[5] Zerr A., J. Mater. Res. 23, 3273-3274 (2008)

[6] Nishiyama N., et al., J. Am. Ceram. Soc. 102, 2195-2202 (2019)

[7] Dong J.J., et al., Phys. Rev. B 67, 094104 (2003)

[8] Luo Y.S., et al., Comput. Condens. Matter 1, 1-7 (2014)

[9] Xiang H.M., et al., Sci. Rep. 8, 14374 (2018)
28th AIRAPT and 60th EHPRG

23-28 July 2023

Edinburgh International Conference Centre,
Edinburgh, UK

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