Thermoelastic properties of bridgmanite using deep-potential molecular dynamics

The high-pressure Pbnm-perovskite polymorph of ${\mathrm{MgSiO}}_3$, i.e., bridgmanite (Bm), plays a crucial role in the Earth's lower mantle. It is likely responsible for ∼75 vol. % of this region and its properties dominate the properties of this region, especially its elastic properties that are challenging to measure at ambient conditions. This study combines deep-learning potential (DP) with density-functional theory (DFT) to investigate the structural and elastic properties of Bm under lower-mantle conditions. To simulate this system, we developed a series of potentials capable of faithfully reproducing DFT calculations using different functionals, i.e., local density approximation (LDA), Perdew-Burke-Ernzerhof parametrization (PBE), revised PBE for solids (PBEsol), and strongly constrained and appropriately normed (SCAN) meta–generalized-gradient approximation functionals. Our predictions with DP-SCAN exhibit a remarkable agreement with experimental measurements of high-temperature equations of states and elastic properties and highlight its superior performance, closely followed by DP-LDA in accurately predicting. This hybrid computational approach offers a solution to the accuracy-efficiency dilemma in obtaining precise elastic properties at high pressure and temperature conditions for minerals like Bm, opening a way to study the Earth material's thermodynamic properties and related phenomena.

Figure 1

Comparison of DP and ab initio calculations on the potential energy, atomic forces, and stresses with (a) LDA, (b) SCAN, (c) PBE, and (d) PBEsol for all the test data which covers 0–160 GPa and 300–4000 K.

Figure 2

Radial distribution functions of Bm at 4000 K and 120 GPa from DFT-LDA calculations (dotted blue lines) and DP-LDA (solid red lines).

Figure 3

Phonon dispersions of Bm at 0 GPa calculated by DFT-LDA (dotted blue lines) and DP-LDA (solid red lines).

Figure 4

Equation of state of Bm at (a) 300 K and (b) 2000 K. Results from DP-LDA, DP-PBE, DP-PBEsol, and DP-SCAN correspond with blue, red, green, and orange squares, respectively. Experimental data shown as crosses are from Refs. [56, 57, 58, 59, 60, 61, 62, 63, 64, 65]. DFT calculations shown as circles are from Ref. [37].

Figure 5

Relative difference of elastic moduli of Bm at 300 K and 0 GPa. Experimental values are from Refs. [4, 5, 6]. Circles are from previous GGA calculations [19, 66] and previous LDA calculations [10]. Crosses are our DP results with different functionals.

Figure 6

Pressure dependence of the isothermal elastic constants of Bm with (a) DP-LDA and (b) DP-SCAN. Solid lines correspond to our DP results. Open diamonds and open circles represent measurements [4, 6]. Solid symbols are results of previous calculations [17, 19]. Symbol colors denote temperatures.

Figure 7

Relative difference of ${\mathit{c}}_{ij}$ at 40 GPa between DP-SCAN and previous calculations [17] with DP-SCAN as the reference. Symbols denote different temperatures.

Figure 8

Pressure dependence of density ($\rho$), isotropic longitudinal ($V_P=\sqrt{\left(K_T+4G/3\right)/\rho }$), and shear- ($V_S=\sqrt{G/\rho }$) wave velocities, isothermal bulk moduli ($K_T$), and shear ($G$) moduli of Bm. Solid lines in (a) and (c) are our DP-LDA results, while solid lines in (b) and (d) are our DP-SCAN results. Triangles and circles are the experimental results [4, 5, 6]. Symbols connected by squares are the results of previous calculations [17]. Colors denote temperatures. Black crosses are PREM data [71].

Figure 9

(a) Variation of compressional and shear-wave velocities of Bm with different propagation direction at ambient condition. Blue and red open squares are experimental data from Refs. [5, 6]. Pressure and temperature dependence of azimuthal anisotropy for (b) P wave and (c) S wave, alongside pressure and temperature variation of polarization anisotropy for (d) [010], (e) [100], and (f) [001] directions. The black lines indicate the geotherm of the lower mantle [73, 74].