Decomposition Products of Phosphine Under Pressure: PH2 Stable and Superconducting?

Prediction of potential hard sodium carbaboride compounds assuming sp3-bonded covalent clathrates

Boron-carbon clathrates have attracted great attention due to their unique sp3-bonded structure and excellent electronic properties. Here, by performing first-principles calculations, we predicted six stoichiometric Na-B-C clathrates (NaBC11, Na2B2C10, NaB2C10, Na2B4C8, NaB4C8, and Na2B6C6) based on Na-doped boron-carbon clathrates. As a result, NaBC11, Na2B2C10, and NaB2C10 were found to become energetically favorable. Under ambient conditions, the electronic structure calculations show that NaBC11 and Na2B2C10 are indirect band gap semiconductors, and NaB2C10, Na2B4C8, and NaB4C8 exhibit metallic features. Na2B2C10 and Na2B4C8 are found to be synthesized at 22.7 and 14.2 GPa, respectively. Interestingly, the formation enthalpies of NaxB2C10 and NaxB4C8 (x = 0, 1, and 2) clathrates decrease in turn with the increased number of Na atoms in the same synthetic paths. Moreover, the ideal indentation strengths of NaBC11, Na2B2C10, and NaB2C10 approach 40 GPa, indicating that they are hard materials with superior hardness. These findings offer valuable insights for advancing the synthesis of boron-carbon clathrates.

Solid-State Investigation, Storage, and Separation of Pyrophoric PH3 and P2 H4 with α-Mg Formate

Phosphane, PH₃ -a highly pyrophoric and toxic gas-is frequently contaminated with H₂ and P₂ H₄ , which makes its handling even more dangerous. The inexpensive metal-organic framework (MOF) magnesium formate, α-[Mg(O₂ CH)₂ ], can adsorb up to 10 wt % of PH₃ . The PH₃ -loaded MOF, PH₃ @α-[Mg(O₂ CH)₂ ], is a non-pyrophoric, recoverable material that even allows brief handling in air, thereby minimizing the hazards associated with the handling and transport of phosphane. α-[Mg(O₂ CH)₂ ] further plays a critical role in purifying PH₃ from H₂ and P₂ H₄ : at 25 °C, H₂ passes through the MOF channels without adsorption, whereas PH₃ adsorbs readily and only slowly desorbs under a flow of inert gas (complete desorption time≈6 h). Diphosphane, P₂ H₄ , is strongly adsorbed and trapped within the MOF for at least 4 months. P₂ H₄ @α-[Mg(O₂ CH)₂ ] itself is not pyrophoric and is air- and light-stable at room temperature.

Pressure-stabilized graphene-like P layer in superconducting LaP2

MgB₂-type superconductors are of great interest in chemistry and condensed matter physics due to their superconductivity dominated by the structural unit of graphene-like B. However, this kind of material is absent in phosphides resulting from the inherent lone pair electrons of phosphorus. Here, we report that a pressure-stabilized LaP₂, isostructural to MgB₂, shows superconductivity with a predicted T_c of 22.2 K, which is the highest among those of already known transition metal phosphides. Besides the electron-phonon coupling of graphene-like P, alike the role of the B layer in MgB₂, La 5d/4f electrons are also responsible for the superconducting transition. The distinct P atomic arrangement is attributed to its sp² hybridization and out-of-plane symmetric distribution of lone pair electrons. On the other hand, its dynamically stabilized pressure reaches as low as 7 GPa, a desirable feature of pressure-induced superconductors. Although P is isoelectronic to N and As, we hereby find the different stable stoichiometries, structures, and electronic properties of La phosphides compared with La nitrides/arsenides at high pressures.

Design Principles for High-Temperature Superconductors with a Hydrogen-Based Alloy Backbone at Moderate Pressure

Hydrogen-based superconductors provide a route to the long-sought goal of room-temperature superconductivity, but the high pressures required to metallize these materials limit their immediate application. For example, carbonaceous sulfur hydride, the first room-temperature superconductor made in a laboratory, can reach a critical temperature (T_{c}) of 288 K only at the extreme pressure of 267 GPa. The next recognized challenge is the realization of room-temperature superconductivity at significantly lower pressures. Here, we propose a strategy for the rational design of high-temperature superconductors at low pressures by alloying small-radius elements and hydrogen to form ternary H-based superconductors with alloy backbones. We identify a "fluorite-type" backbone in compositions of the form AXH_{8}, which exhibit high-temperature superconductivity at moderate pressures compared with other reported hydrogen-based superconductors. The Fm3[over ¯]m phase of LaBeH_{8}, with a fluorite-type H-Be alloy backbone, is predicted to be thermodynamically stable above 98 GPa, and dynamically stable down to 20 GPa with a high T_{c}∼185  K. This is substantially lower than the synthesis pressure required by the geometrically similar clathrate hydride LaH_{10} (170 GPa). Our approach paves the way for finding high-T_{c} ternary H-based superconductors at conditions close to ambient pressures.

Materials by design at high pressures

Pressure, a fundamental thermodynamic variable, can generate two essential effects on materials. First, pressure can create new high-pressure phases via modification of the potential energy surface. Second, pressure can produce new compounds with unconventional stoichiometries via modification of the compositional landscape. These new phases or compounds often exhibit exotic physical and chemical properties that are inaccessible at ambient pressure. Recent studies have established a broad scope for developing materials with specific desired properties under high pressure. Crystal structure prediction methods and first-principles calculations can be used to design materials and thus guide subsequent synthesis plans prior to any experimental work. A key example is the recent theory-initiated discovery of the record-breaking high-temperature superhydride superconductors H3S and LaH10 with critical temperatures of 200 K and 260 K, respectively. This work summarizes and discusses recent progress in the theory-oriented discovery of new materials under high pressure, including hydrogen-rich superconductors, high-energy-density materials, inorganic electrides, and noble gas compounds. The discovery of the considered compounds involved substantial theoretical contributions. We address future challenges facing the design of materials at high pressure and provide perspectives on research directions with significant potential for future discoveries.

Strong correlation between electronic bonding network and critical temperature in hydrogen-based superconductors

By analyzing structural and electronic properties of more than a hundred predicted hydrogen-based superconductors, we determine that the capacity of creating an electronic bonding network between localized units is key to enhance the critical temperature in hydrogen-based superconductors. We define a magnitude named as the networking value, which correlates with the predicted critical temperature better than any other descriptor analyzed thus far. By classifying the studied compounds according to their bonding nature, we observe that such correlation is bonding-type independent, showing a broad scope and generality. Furthermore, combining the networking value with the hydrogen fraction in the system and the hydrogen contribution to the density of states at the Fermi level, we can predict the critical temperature of hydrogen-based compounds with an accuracy of about 60 K. Such correlation is useful to screen new superconducting compounds and offers a deeper understating of the chemical and physical properties of hydrogen-based superconductors, while setting clear paths for chemically engineering their critical temperatures.

The Li-F-H ternary system at high pressures

Evolutionary crystal structure prediction searches have been employed to explore the ternary Li-F-H system at 300 GPa. Metastable phases were uncovered within the static lattice approximation, with LiF₃H₂, LiF₂H, Li₃F₄H, LiF₄H₄, Li₂F₃H, and LiF₃H lying within 50 meV/atom of the 0 K convex hull. All of these phases contain H_nF_n+1 ^- (n = 1, 2) anions and Li⁺ cations. Other structural motifs such as LiF slabs, H₃ ⁺ molecules, and F^δ- ions are present in some of the low enthalpy Li-F-H structures. The bonding within the H_nF_n+1 ^- molecules, which may be bent or linear, symmetric or asymmetric, is analyzed. The five phases closest to the hull are insulators, while LiF₃H is metallic and predicted to have a vanishingly small superconducting critical temperature. Li₃F₄H is predicted to be stable at zero pressure. This study lays the foundation for future investigations of the role of temperature and anharmonicity on the stability and properties of compounds and alloys in the Li-F-H ternary system.

High pressure synthesis of phosphine from the elements and the discovery of the missing (PH3)2H2 tile

High pressure reactivity of phosphorus and hydrogen is relevant to fundamental chemistry, energy conversion and storage, and materials science. Here we report the synthesis of (PH3)2H2, a crystalline van der Waals (vdW) compound (I4cm) made of PH3 and H2 molecules, in a Diamond Anvil Cell by direct catalyst-free high pressure (1.2 GPa) and high temperature (T ≲ 1000 K) chemical reaction of black phosphorus and liquid hydrogen, followed by room T compression above 3.5 GPa. Group 15 elements were previously not known to form H2-containing vdW compounds of their molecular hydrides. The observation of (PH3)2H2, identified by synchrotron X-ray diffraction and vibrational spectroscopy (FTIR, Raman), therefore represents the discovery of a previously missing tile, specifically corresponding to P for pnictogens, in the ability of non-metallic elements to form such compounds. Significant chemical implications encompass reactivity of the elements under extreme conditions, with the observation of the P analogue of the Haber-Bosch reaction for N, fundamental bond theory, and predicted high pressure superconductivity in P-H systems.

A Metastable CaSH3 Phase Composed of HS Honeycomb Sheets that is Superconducting Under Pressure

Evolutionary searches have predicted a number of ternary Ca-S-H phases that could be synthesized at pressures of 100-300 GPa. P6₃/mmc CaSH₂, Pnma CaSH₂, Cmc2₁ CaSH₆, and I4̅ CaSH₂₀ were composed of a Ca-S lattice along with H₂ molecules coordinated in a "side-on" fashion to Ca. The H-H bond lengths in these semiconducting phases were elongated because of H₂ σ → Ca d donation, and Ca d → H₂ σ* back-donation, via a Kubas-like mechanism. P6̅m2 CaSH₃, consisting of two-dimensional HS and CaH₂ sheets, was metastable and metallic above 128 GPa. The presence of van Hove singularities increased its density of states at the Fermi level and concomitantly the superconducting critical temperature, which was estimated to be as high as ∼100 K at 128 GPa. This work will inspire the search for superconductivity in materials based upon honeycomb HX (X = S, Se, Te) and MH₂ (M = Mg, Ca, Sr, Ba) layers under pressure.

Navigating the design space of inorganic materials synthesis using statistical methods and machine learning

Data-driven approaches have brought about a revolution in manufacturing; however, challenges persist in their applications to synthetic strategies. Their application to the deterministic navigation of reaction trajectories to stabilize crystalline solids with precise composition, atomic connectivity, microstructural dimensionality, and surface structure remains a frontier in inorganic materials research. The design of synthetic methodologies for the preparation of inorganic materials is often inefficient in terms of exploration of potentially vast design spaces spanning multiple process variables, reaction sequences, as well as structural parameters and reactivities of precursors and structure-directing agents. Reported synthetic methods are further limited in terms of the insight they provide into underlying chemical and physical principles. The recent surge in interest in accelerating the discovery of new materials can be considered as an opportunity to re-evaluate our approach to materials synthesis, and for considering new frameworks for exploration that are systematic and strategic in approach. Herein, we outline with the help of several illustrative examples, the challenges, opportunities, and limitations of data-driven synthesis design. The account collates discussion of design-of-experiments sampling methods, machine learning modeling, and active learning to develop experimental workflows that accelerate the experimental navigation of synthetic landscapes.

Superconducting Zirconium Polyhydrides at Moderate Pressures

Highly compressed hydrides have been at the forefront of the search for high-T_c superconductivity. The recent discovery of record-high T_c's in H₃S and LaH_10±x under high pressure fuels the enthusiasm for finding good superconductors in similar hydride groups. Guided by first-principles structure prediction, we successfully synthesized ZrH₃ and Zr₄H₁₅ at modest pressures (30-50 GPa) in diamond anvil cells by two different reaction routes: ZrH₂ + H₂ at room temperature and Zr + H₂ at ∼1500 K by laser heating. From the synchrotron X-ray diffraction patterns, ZrH₃ is found to have a Pm3̅n structure corresponding to the familiar A15 structure, and Zr₄H₁₅ has an I4̅3d structure isostructural to Th₄H₁₅. Electrical resistance measurement and the dependence of T_c on the applied magnetic field of the sample showed the emergence of two superconducting transitions at 6.4 and 4.0 K at 40 GPa, which correspond to the two T_c's for ZrH₃ and Zr₄H₁₅.

Chemically Tuning Stability and Superconductivity of P-H Compounds

Experimental evidence has revealed superconductivity with a critical temperature, T_c, around 100 K in compressed solid phosphine, but theoretical studies have hitherto found no stable structure in any binary P-H system, leaving the characterization of the new superconductor unsettled. Here we present the findings of an advanced structure search and first-principles calculations unveiling the effect of Li as an electron donor that stabilizes the crystal structure and produces robust phonon-mediated superconductivity in the resulting Li-P-H compounds in wide ranges of stoichiometry and pressure. We showcase a trigonal LiP₂H₁₄ phase that reaches T_c of 169 K at 230 GPa and then decreases with rising pressure, which can be remedied by substituting Li with Be or Na, which considerably enhances T_c. These findings highlight the intricate and effective chemical tuning of stabilizing the crystal structure and enhancing the superconductivity in a distinct class of ternary hydrides, opening new avenues for designing and optimizing new high-T_c hydride superconductors.

Stoichiometric evolutions of PH3 under high pressure: implication for high-T c superconducting hydrides

The superconductivity of hydrides under high pressure has attracted a great deal of attention since the recent observation of the superconducting transition at 203 K in strongly compressed H2S. It has been realized that the stoichiometry of hydrides might change under high pressure, which is crucial in understanding the superconducting mechanism. In this study, PH3 was studied to understand its superconducting transition and stoichiometry under high pressure using Raman, IR and X-ray diffraction measurements, as well as theoretical calculations. PH3 is stable below 11.7 GPa and then it starts to dehydrogenate through two dimerization processes at room temperature and pressures up to 25 GPa. Two resulting phosphorus hydrides, P2H4 and P4H6, were verified experimentally and can be recovered to ambient pressure. Under further compression above 35 GPa, the P4H6 directly decomposed into elemental phosphorus. Low temperature can greatly hinder polymerization/decomposition under high pressure and retains P4H6 up to at least 205 GPa. The superconductivity transition temperature of P4H6 is predicted to be 67 K at 200 GPa, which agrees with the reported result, suggesting that it might be responsible for superconductivity at higher pressures. Our results clearly show that P2H4 and P4H6 are the only stable P-H compounds between PH3 and elemental phosphorus, which is helpful for shedding light on the superconducting mechanism.

Mechanism for the Structural Transformation to the Modulated Superconducting Phase of Compressed Hydrogen Sulfide

A comprehensive description of crystal and electronic structures, structural transformations, and pressure-dependent superconducting temperature (Tc) of hydrogen sulfide (H2S) compressed from low pressure is presented through the analysis of the results from metadynamics simulations. It is shown that local minimum metastable crystal structures obtained are dependent on the choice of pressure-temperature thermodynamic paths. The origin of the recently proposed 'high-Tc' superconducting phase with a modulated structure and a diffraction pattern reproducing two independent experiments was the low pressure Pmc21 structure. This Pmc21 structure is found to transform to a Pc structure at 80 K and 80 GPa which becomes metallic and superconductive above 100 GPa. This structure becomes dynamically unstable above 140 GPa beyond which phonon instability sets in at about a quarter in the Γ to Y segment. This explains the transformation to a 1:3 modulation structure at high pressures proposed previously. The pressure trend of the calculated Tc for the Pc structure is consistent with the experimentally measured 'low-Tc phase'. Fermi surface analysis hints that pressurized hydrogen sulfide may be a multi-band superconductor. The theoretical results reproduced many experimental characteristics, suggesting that the dissociation of H2S is unrequired to explain the superconductivity of compressed H2S at any pressure.

Predicted Pressure-Induced Superconducting Transition in Electride Li_{6}P

Electrides are unique compounds where most of the electrons reside at interstitial regions of the crystal behaving as anions, which strongly determines its physical properties. Interestingly, the magnitude and distribution of interstitial electrons can be effectively modified either by modulating its chemical composition or external conditions (e.g., pressure). Most of the electrides under high pressure are nonmetallic, and superconducting electrides are very rare. Here we report that a pressure-induced stable Li_{6}P electride, identified by first-principles swarm structure calculations, becomes a superconductor with a predicted superconducting transition temperature T_{c} of 39.3 K, which is the highest among the already known electrides. The interstitial electrons in Li_{6}P, with dumbbell-like connected electride states, play a dominant role in the superconducting transition. Other Li-rich phosphides, Li_{5}P, Li_{11}P_{2}, Li_{15}P_{2}, and Li_{8}P, are also predicted to be superconducting electrides, but with a lower T_{c}. Superconductivity in all these compounds can be attributed to a combination of a weak electronegativity of phosphorus (P) with a strong electropositivity of lithium (Li), and opens up the interest to explore high-temperature superconductivity in similar binary compounds.

The Structure and Properties of Magnesium-Phosphorus Compounds Under Pressure

Inspired by the emergence of compounds with novel structures and unique properties (i.e., superconductivity and hardness) under high pressure, we systematically explored a binary Mg-P system under pressure, combining first-principles calculations with structure prediction. Several stoichiometries (Mg₃ P, Mg₂ P, MgP, MgP₂ , and MgP₃ ) were predicted to be stable under pressure. Especially, the P-P bonding patterns are different in the P-rich compounds and the Mg-rich compounds: in the former, the P-P bonding patterns form P₂ , P₃ , quadrilateral units, P-P⋅⋅⋅P chains or disordered "graphene-like" sublattice, while in the latter, the P-P bonding patterns eventually evolve isolated P ions. The analysis of integrated-crystal orbital Hamilton populations reveals that the P-P interactions are mainly responsible for the structural stability. The P-rich compounds with stoichiometries of MgP, MgP₂ and MgP₃ exhibit superconductive behaviors, and these phases show T_c in the range of 4.3-20 K. Our study provides useful information for understanding the Mg-P binary compounds at high pressure.

Potential high-Tc superconducting lanthanum and yttrium hydrides at high pressure

A systematic structure search in the La-H and Y-H systems under pressure reveals some hydrogen-rich structures with intriguing electronic properties. For example, LaH₁₀ is found to adopt a sodalite-like face-centered cubic (fcc) structure, stable above 200 GPa, and LaH₈ a C2/m space group structure. Phonon calculations indicate both are dynamically stable; electron phonon calculations coupled to Bardeen-Cooper-Schrieffer (BCS) arguments indicate they might be high-T_c superconductors. In particular, the superconducting transition temperature T_c calculated for LaH₁₀ is 274-286 K at 210 GPa. Similar calculations for the Y-H system predict stability of the sodalite-like fcc YH₁₀ and a T_c above room temperature, reaching 305-326 K at 250 GPa. The study suggests that dense hydrides consisting of these and related hydrogen polyhedral networks may represent new classes of potential very high-temperature superconductors.

Quantitative analysis of nonadiabatic effects in dense H3S and PH3 superconductors

The comparison study of high pressure superconducting state of recently synthesized H₃S and PH₃ compounds are conducted within the framework of the strong-coupling theory. By generalization of the standard Eliashberg equations to include the lowest-order vertex correction, we have investigated the influence of the nonadiabatic effects on the Coulomb pseudopotential, electron effective mass, energy gap function and on the 2Δ(0)/T_C ratio. We found that, for a fixed value of critical temperature (178 K for H₃S and 81 K for PH₃), the nonadiabatic corrections reduce the Coulomb pseudopotential for H₃S from 0.204 to 0.185 and for PH₃ from 0.088 to 0.083, however, the electron effective mass and ratio 2Δ(0)/T_C remain unaffected. Independently of the assumed method of analysis, the thermodynamic parameters of superconducting H₃S and PH₃ strongly deviate from the prediction of BCS theory due to the strong-coupling and retardation effects.

Structure and superconductivity of hydrides at high pressures

Hydrogen atoms can provide high phonon frequencies and strong electron–phonon coupling in hydrogen-rich materials, which are believed to be potential high-temperature superconductors at lower pressure than metallic hydrogen. Especially, recently both of theoretical and experimental reports on sulfur hydrides under pressure exhibiting superconductivity at temperatures as high as 200 K have further stimulated an intense search for room-temperature superconductors in hydrides. This review focuses on crystal structures, stabilities, pressure-induced transformations, metallization, and superconductivity of hydrogen-rich materials at high pressures.