Exploring the High-Pressure Materials Genome

A thorough in situ characterization of materials at extreme conditions is challenging, and computational tools such as crystal structural search methods in combination with ab initio calculations are widely used to guide experiments by predicting the composition, structure, and properties of high-pressure compounds. However, such techniques are usually computationally expensive and not suitable for large-scale combinatorial exploration. On the other hand, data-driven computational approaches using large materials databases are useful for the analysis of energetics and stability of hundreds of thousands of compounds, but their utility for materials discovery is largely limited to idealized conditions of zero temperature and pressure. Here, we present a novel framework combining the two computational approaches, using a simple linear approximation to the enthalpy of a compound in conjunction with ambient-conditions data currently available in high-throughput databases of calculated materials properties. We demonstrate its utility by explaining the occurrence of phases in nature that are not ground states at ambient conditions and by estimating the pressures at which such ambient-metastable phases become thermodynamically accessible, as well as guiding the exploration of ambient-immiscible binary systems via sophisticated structural search methods to discover new high-pressure phases.

Popular Summary

Understanding how materials behave under extreme pressure has a range of benefits, from the design of exotic materials to a better understanding of planetary interiors. Researchers typically use computational tools to guide experiments by predicting composition, structure, and properties of materials under pressure. However, these techniques are computationally expensive. Data-driven approaches using large databases of materials are useful for analyzing hundreds of thousands of compounds, but their utility for materials discovery is largely limited to idealized conditions of zero temperature and pressure. Here, we present a novel framework combining these two approaches to provide an efficient assessment of the thermodynamic stability of materials at nonzero pressure.

Our approach uses a simple linear approximation to the enthalpy of a compound in conjunction with data on ambient conditions currently available in high-throughput databases of calculated materials properties. We find that we can readily explain the occurrence of phases in nature that are not ground states at ambient conditions. In conjunction with crystal structure search schemes, our approach effectively predicts new high-pressure phases that can be realized with existing high-pressure experimental methods.

This framework paves a route toward robust exploration of the entire high-pressure materials genome based on emerging materials big data, leading to accelerated materials discovery at nonambient pressures.

Figure 1

(a) A schematic energy-volume ($E–V$) diagram with three phases [the ground state (GS), and two metastable phases A and B] and their EOS, each represented by a parabola. The negative slope of the common tangent to two adjacent EOS (dashed grey lines) represents the pressure at which the two phases are in equilibrium. The LAE approximates the common tangent with a line connecting the ambient-condition equilibrium volumes and energies of two adjacent phases (solid black line connecting filled circles). (b) A schematic $N–V–E$ convex hull for a model binary system. Individual phases are represented by spheres, and convex hull boundaries are indicated with solid red and dotted black lines. On the left is the conventional zero-pressure $N–E$ hull, a projection of the extended $N–V–E$ convex hull on the right. Phases that are thermodynamically stable at zero pressure lie on the $N–E$ convex hull (blue spheres). Metastable phases that are stable at some nonambient pressure lie above the $N–E$ hull but on the $N–V–E$ convex hull (teal spheres). A phase that is truly unstable at any pressure lies above the $N–V–E$ hull (orange sphere).

Figure 2

The pressure range of stability of high-pressure phases of elemental (a) silicon and (b) bismuth. Explicitly computed transition pressures using DFT-calculated formation enthalpies are labeled “DFT” (top bar in each panel), and those based on the LAE are denoted with “LAE” (second bar in each panel). In addition, we show transition pressures calculated using the expansion of the enthalpy to second order (“QUA”) and the Murnaghan EOS (“MUR”) [51, 52], for comparison. The crystal structures of the silicon and bismuth allotropes were taken from Refs. [44, 45, 46, 47, 48, 49, 50] and [53, 54, 55, 56, 57, 58, 59], respectively.

Figure 3

Comparison between the explicitly computed phase diagrams with the ones derived from the LAE model for binary systems. Panels (a)–(c) correspond to the Fe–Bi, Cu–Bi, and Ni–Bi systems, respectively. Explicitly calculated transition pressures using DFT are denoted with “DFT” (top bar), and results based on the LAE are denoted with “LAE” (bottom bar).

Figure 4

Comparison between the explicitly computed phase diagrams and the ones calculated using the LAE model for two oxide systems. Panels (a) and (b) correspond to the Zr–O and the Ge–O systems, respectively. Explicitly calculated transition pressures using DFT are denoted with “DFT” (top bar), and results based on the LAE are denoted with “LAE” (bottom bar). The arrow denotes the displacive phase transformation.

Figure 5

Comparison of predictions of high-pressure elemental phases from the LAE model against experiment. For each element, the number of (a) unique phases reported experimentally and (b) those predicted by the linear enthalpy model to be thermodynamically stable at nonambient pressures are indicated by the color of the bottom-left and top-right halves, respectively, of the corresponding tile in the periodic table. Overall, the model correctly predicts about 75% of the high-pressure phases in the ICSD to be thermodynamically stable at nonambient pressures.

Figure 6

(a) Fraction of metastable phases that become thermodynamically stable with incremental increase/decrease in pressure, with respect to 0 GPa. The horizontal dashed lines indicate the fraction of metastable phases that do not lie on the $N–V–E$ convex hull at any pressure. (b) Fraction of ambient-metastable phases that cannot be accessed thermodynamically at any pressure larger than pressure $p$, equivalent to 1- (fraction of phases that can be accessed at some pressure larger than pressure $p$).

Figure 7

The convex hulls of formation enthalpy of ten ambient-immiscible binary systems calculated using structural search at 50 GPa via the MHM. Each cross denotes a phase sampled with the MHM. In all but the Zn-Ga system, we find at least one thermodynamically stable high-pressure phase.