Diamond’s third-order elastic constants: ab initio calculations and experimental investigation

First-Principles Calculation of Third-Order Elastic Constants via Numerical Differentiation of the Second Piola-Kirchhoff Stress Tensor

“…The calculated SOECs and TOECs are reported in Table I together with experimental data measured at finite temperature. Our results shown in Table I compare well with both experimental data [3, 6-8, 10, 27] and previous DFT calculations [9,10]. The agreement with the experiments is very good in the case of silicon and the metals, whereas it is satisfactory in case of diamond, for which the reported data show large variations and experimental uncertainties (Table I).…”

“…In addition, TOECs are far more structure sensitive than the second-order elastic constants (SOECs), and sample quality is known to introduce variability in the experimental data [2,[7][8][9][10]. As a result, so far TOECs have been measured for only a relatively few bulk materials [2,[7][8][9][10]. In recent years, nanoindentation experiments have also been used to probe linear and nonlinear elastic properties of 2D materials [11,12].…”

“…To demonstrate the validity and accuracy of our method, we consider the case of diamond, whose TOECs have been repeatedly measured and calculated over the past years [9,10,16]. Figure 1 shows the energy density and component P 1 ↔ P xx of the 2 nd -PK stress tensor of a diamond crystal at 0 K under uniaxial strain in the x direction.…”

“…Figure 1 shows the energy density and component P 1 ↔ P xx of the 2 nd -PK stress tensor of a diamond crystal at 0 K under uniaxial strain in the x direction. These energy and pressure data allow to calculate C (2) 11 and C (3) 111 [9,10,16]. A fitting of the energy curve gives values of 1037 GPa and -5876 GPa, respectively.…”

Effects of Induced Stress on Seismic Waves: Validation Based on Ab Initio Calculations

“…One focuses on stress effects on preexisting or induced cracks, which manifest themselves in the form of seismic anisotropy (e.g., Bruner, ; Henyey & Pomphrey, ; Nur, ; O'Connell & Budiansky, ; Zheng, ). In the other context of mineral physics, the effects of stress changes are frequently captured based on third‐order elasticity theory (Bogardus, ; Egle & Bray, ; Hughes & Kelly, ; Murnaghan, ; Wang & Li, ), requiring knowledge of higher‐order elastic constants, which are not easily measured in the laboratory (e.g., Renaud et al, ; Telichko et al, ). We propose an alternative approach in the latter context without introducing higher‐order derivatives.…”