Stability and electronic properties of complex structures of silicon and carbon under pressure: Density-functional calculations

Toward Superior Stiffness in Carbon: The Interplay between Bond Strength and Anisotropic Response

Carbon's ability to form diverse structures with varying hybridizations motivates the search for novel materials surpassing diamond's exceptional mechanical rigidity. We analyze previously predicted superhard phases and find that some exhibit average bond stiffness and density higher than those of diamond, hinting at potentially superior stiffness. However, these structures show a lower bulk modulus. We delve into this contradiction and demonstrate that it stems from the structures' anisotropic response to isotropic deformation. The concept of strain anisotropy is introduced to quantify this phenomenon. Our findings reveal a key connection between bond stiffness and bulk modulus in carbon materials, highlighting the importance of considering anisotropic behavior for a comprehensive understanding of the mechanical properties.

Double-Shock Compression Pathways from Diamond to BC8 Carbon

Carbon is one of the most important elements for both industrial applications and fundamental research, including life, physics, chemistry, materials, and even planetary science. Although theoretical predictions on the transition from diamond to the BC8 (Ia3[over ¯]) carbon were made more than thirty years ago, after tremendous experimental efforts, direct evidence for the existence of BC8 carbon is still lacking. In this study, a machine learning potential was developed for high-pressure carbon fitted from first-principles calculations, which exhibited great capabilities in modeling the melting and Hugoniot line. Using the molecular dynamics based on this machine learning potential, we designed a thermodynamic pathway that is achievable for the double shock compression experiment to obtain the elusive BC8 carbon. Diamond was compressed up to 584 GPa after the first shock at 20.5  km/s. Subsequently, in the second shock compression at 24.8 or 25.0  km/s, diamond was compressed to a supercooled liquid and then solidified to BC8 in around 1 ns. Furthermore, the critical nucleus size and nucleation rate of BC8 were calculated, which are crucial for nano-second x-ray diffraction measurements to observe BC8 carbon during shock compressions. The key to obtaining BC8 carbon lies in the formation of liquid at a sufficient supercooling. Our work provides a feasible pathway by which the long-sought BC8 phase of carbon can be reached in experiments.

Hexagonal Si-Ge Class of Semiconducting Alloys Prepared by Using Pressure and Temperature

Multi-anvil and laser-heated diamond anvil methods have been used to subject Ge and Si mixtures to pressures and temperatures of between 12 and 17 GPa and 1500-1800 K, respectively. Synchrotron angle dispersive X-ray diffraction, precession electron diffraction and chemical analysis using electron microscopy, reveal recovery at ambient pressure of hexagonal Ge-Si solid solutions (P6₃ /mmc). Taken together, the multi-anvil and diamond anvil results reveal that hexagonal solid solutions can be prepared for all Ge-Si compositions. This hexagonal class of solid solutions constitutes a significant expansion of the bulk Ge-Si solid solution family, and is of interest for optoelectronic applications.

Metastability of diamond ramp-compressed to 2 terapascals

Carbon is the fourth-most prevalent element in the Universe and essential for all known life. In the elemental form it is found in multiple allotropes, including graphite, diamond and fullerenes, and it has long been predicted that even more structures can exist at pressures greater than those at Earth's core^1-3. Several phases have been predicted to exist in the multi-terapascal regime, which is important for accurate modelling of the interiors of carbon-rich exoplanets^4,5. By compressing solid carbon to 2 terapascals (20 million atmospheres; more than five times the pressure at Earth's core) using ramp-shaped laser pulses and simultaneously measuring nanosecond-duration time-resolved X-ray diffraction, we found that solid carbon retains the diamond structure far beyond its regime of predicted stability. The results confirm predictions that the strength of the tetrahedral molecular orbital bonds in diamond persists under enormous pressure, resulting in large energy barriers that hinder conversion to more-stable high-pressure allotropes^1,2, just as graphite formation from metastable diamond is kinetically hindered at atmospheric pressure. This work nearly doubles the highest pressure at which X-ray diffraction has been recorded on any material.

All-Silicon Topological Semimetals with Closed Nodal Line

Because of the natural compatibility with current semiconductor industry, silicon allotropes with diverse structural and electronic properties provide promising platforms for next-generation Si-based devices. After screening 230 all-silicon crystals in the zeolite frameworks by first-principles calculations, we disclose two structurally stable Si allotropes (AHT-Si₂₄ and VFI-Si₃₆) containing open channels as topological node-line semimetals with Dirac nodal points forming a nodal loop in the k _z = 0 plane of the Brillouin zone. Interestingly, their nodal loops protected by inversion and time-reversal symmetries are robust against SU(2) symmetry breaking because of the very weak spin-orbit coupling of Si. When the nodal lines are projected onto the (001) surface, flat surface bands can be observed because of the nontrivial topology of the bulk band structures. Our discoveries extend the topological physics to the three-dimensional Si materials, highlighting the possibility of realizing low-cost, nontoxic, and semiconductor-compatible Si-based electronics with topological quantum states.

Superconducting Open-Framework Allotrope of Silicon at Ambient Pressure

Diamond Si is a semiconductor with an indirect band gap that is the basis of modern semiconductor technology. Although many metastable forms of Si were observed using diamond anvil cells for compression and chemical precursors for synthesis, no metallic phase at ambient conditions has been reported thus far. Here we report the prediction of pure metallic Si allotropes with open channels at ambient pressure, unlike a cubic diamond structure in covalent bonding networks. The metallic phase termed P6/m-Si_{6} can be obtained by removing Na after pressure release from a novel Na-Si clathrate called P6/m-NaSi_{6}, which is predicted through first-principles study at high pressure. We identify that both P6/m-NaSi_{6} and P6/m-Si_{6} are stable and superconducting with the critical temperatures of about 13 and 12 K at ambient pressure, respectively. The prediction of new Na-Si and Si clathrate structures presents the possibility of exploring new exotic allotropes useful for Si-based devices.

BC8 Silicon (Si-III) is a Narrow-Gap Semiconductor

Large-volume, phase-pure synthesis of BC8 silicon (Ia3[over ¯], cI16) has enabled bulk measurements of optical, electronic, and thermal properties. Unlike previous reports that conclude BC8-Si is semimetallic, we demonstrate that this phase is a direct band gap semiconductor with a very small energy gap and moderate carrier concentration and mobility at room temperature, based on far- and midinfrared optical spectroscopy, temperature-dependent electrical conductivity, Seebeck and heat capacity measurements. Samples exhibit a plasma wavelength near 11  μm, indicating potential for infrared plasmonic applications. Thermal conductivity is reduced by 1-2 orders of magnitude depending on temperature as compared with the diamond cubic (DC-Si) phase. The electronic structure and dielectric properties can be reproduced by first-principles calculations with hybrid functionals after adjusting the level of exact Hartree-Fock (HF) exchange mixing. These results clarify existing limited and controversial experimental data sets and ab initio calculations.

A low-surface energy carbon allotrope: the case for bcc-C6

Graphite may be viewed as a low-surface-energy carbon allotrope with little layer–layer interaction.

Carbon under extreme conditions: phase boundaries and electronic properties from first-principles theory

At high pressure and temperature, the phase diagram of elemental carbon is poorly known. We present predictions of diamond and BC8 melting lines and their phase boundary in the solid phase, as obtained from first-principles calculations. Maxima are found in both melting lines, with a triple point located at approximately 850 GPa and approximately 7,400 K. Our results show that hot, compressed diamond is a semiconductor that undergoes metalization upon melting. In contrast, in the stability range of BC8, an insulator to metal transition is likely to occur in the solid phase. Close to the diamond/liquid and BC8/liquid boundaries, molten carbon is a low-coordinated metal retaining some covalent character in its bonding up to extreme pressures. Our results provide constraints on the carbon equation of state, which is of critical importance for devising models of Neptune, Uranus, and white dwarf stars, as well as of extrasolar carbon-rich planets.

Carbon phase diagram from ab initio molecular dynamics

We compute the free energy of solid and liquid diamond from first-principles electronic structure theory using efficient thermodynamic integration techniques. Our calculated melting curve is in excellent agreement with the experimental estimate of the graphite-diamond-liquid triple point and is consistent with shock wave experiments. We predict the phase diagram of diamond at pressures and temperatures that are difficult to access experimentally. We confirm early speculations on the presence of a reentrant point in the diamond melting line but find no evidence for a first order liquid-liquid phase transition near the reentrant point.

Melting of Diamond at High Pressure

Melting of diamond at high pressure and the properties of liquid carbon at pressures greater than 1 megabar were investigated with a first-principles molecular dynamics technique. The results indicate an increase of the diamond melting temperature with pressure, which is opposite to the behavior of silicon and germanium. This is contrary to long-held assumptions, but agrees with recent experiments, and has important implications for geology and astrophysics. As is the case for the solid phase of carbon at low temperature, which changes greatly with pressure from graphite to diamond, the structural and bonding properties of liquid carbon vary strongly with pressure.