Elastic constants of cubic boron phosphide and boron arsenide

Sushant Mahat, Sheng Li, Hanlin Wu, Pawan Koirala, Bing Lv, and David G. Cahill

Phys. Rev. Materials 5, 033606 – Published 16 March 2021

Abstract

We report the room temperature elastic constants of boron phosphide (BP) and boron arsenide (BAs) single crystals derived from Brillouin frequencies measured by picosecond interferometry. The synthesis of BP and BAs with thermal conductivity as high as 540 and $1000 W m^{– 1} K^{– 1}$ , respectively, has made them promising materials for thermal management. Accurate measurements of elastic constants are needed to assess the accuracy of computational modeling of the lattice dynamics. The crystals are cut and polished in different orientations to access waves traveling along different directions. The surface normal orientations of the crystals are determined using electron backscattering diffraction. We studied the Brillouin frequencies of quasilongitudinal waves in five different orientations of BP and BAs crystals. Quasishear waves were observed in two orientations of BP and one orientation of BAs. The propagation directions and acoustic velocities are used to construct Christoffel equations which are then solved for the elastic constants. We report $C_{11}$ , $C_{12}$ , and $C_{44}$ values of 354 ± 5 GPa, 83 ± 15 GPa, and 190 ± 8 GPa for BP and 291 ± 5 GPa, 76 ± 13 GPa, and 173 ± 6 GPa for BAs. The measured elastic constants for BAs differ by less than 5% and 17% from calculated elastic constants obtained through local density approximation and Perdew-Burke-Ernzerhof density functional calculations, respectively. In most cases, the measured elastic constants are larger than the calculated elastic constants.

Received 20 November 2020
Accepted 24 February 2021

DOI:https://doi.org/10.1103/PhysRevMaterials.5.033606

Physics Subject Headings (PhySH)

Elastic deformation Mechanical & acoustical properties Stress propagation Structural properties

Acoustic techniques Interferometry Laser techniques Optical interferometry

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Sushant Mahat ^1,*, Sheng Li², Hanlin Wu², Pawan Koirala ², Bing Lv², and David G. Cahill¹

¹Department of Materials Science and Engineering and Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
²Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080, USA

^*smahat2@illinois.edu

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 5, Iss. 3 — March 2021

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Summary of EBSD measurements. Inverse pole figures (001) showing all indexed points for (a) BP and (b) BAs crystal faces. Approximately one hundred points over a $\sim 10 \times 10 − μ m^{2}$ area were indexed from the exposed faces. All indexed points with a good confidence index ( $CI > 0.1$ ) are shown and points from different faces have been assigned different colors. Average orientation and spread in orientation were calculated for each face. The average orientation of each face is labeled using a hkl notation. Orientations where we were able to detect secondary waves are underlined in the figures.
Reuse & Permissions
Figure 2
Picosecond interferometry measurements. (a) Example data sets showing change in reflectivity vs delay time between the probe and the pump pulse for two BAs samples. Both data sets contain Brillouin oscillations from quasilongitudinal acoustic waves (QL) while oscillations from quasishear (QS) acoustic waves are only present in the (−2 −20 5) data set. Miller indices (hkl) for the crystallographic plane of the probed surfaces are shown. (b) Fourier transformation of the acoustic contributions showing frequencies of Brillouin oscillations present in the data sets from (a).
Reuse & Permissions
Figure 3
Summary of elastic constant measurements and comparisons to prior experiments and computational results. Over the range of elastic constant values shown, Christoffel matrices were constructed using elastic constant combination at each point of the plots (step size 0.5 GPa between points) using direction cosines of BP and BAs samples and were solved for quasilongitudinal and quasishear velocities. (a),(b) Contour plots showing sum of absolute differences ( $Σ_{Δ V}$ ) between quasilongitudinal velocities $v_{L}$ measured using picosecond interferometry vs $v_{L}$ calculated using different combinations of $C_{11}$ and $C_{12} + 2 C_{44}$ . The filled circle marks the combination of elastic constants with the lowest $Σ_{Δ V}$ and contour lines for $Σ_{Δ V}$ values of 2% and 5% of average $v_{L}$ are shown. A 2% uncertainty is expected in our velocity measurements, mostly from the uncertainty in our measurements of refractive indices. (c),(d) $Σ_{Δ V}$ between measured and calculated quasishear velocities as a function of $C_{12}$ and $C_{44}$ . $C_{11}$ was held constant at 354 GPa and 291 GPa for BP and BAs respectively for the shear velocity calculations. The blue line encloses the expected value of $C_{12} + 2 C_{44}$ from $v_{L}$ measurements, and the area enclosed by the black line include the $Σ_{Δ V}$ values lower than the uncertainty expected in an average shear velocity measurement. Previous experimental values are shown as filled squares [10, 15] and values calculated from ab initio calculations using local density approximation (LDA) and Perdew, Burke, and Ernzerhof (PBE) functionals are included for comparison [37].
Reuse & Permissions

Physical Review Materials