Phonon Calculations Research Articles

Nonlinear Arrhenius behavior of self-diffusion in β−Ti and Mo

While anomalous diffusion coefficients with non-Arrhenius like temperature dependence are observed in a number of metals, a conclusive comprehensive framework of explanation has not been brought forward to date. Here, we use first-principles calculations based on density functional theory to calculate self-diffusion coefficients in the bcc metals Mo and $\beta$-Ti by coupling quasiharmonic transition state theory and large displacement phonon calculations and show that anharmonicity from thermal expansion is the major reason for the anomalous temperature dependence. We use a modified Debye approach to quantify the thermal expansion over the entire temperature range and introduce a method to relax the vacancy structure in a mechanically unstable crystal such as $\beta$-Ti. Thermal expansion is found to weakly affect the activation enthalpy but has a strong effect on the prefactor of the diffusion coefficient, reproducing the non-linear, non-Arrhenius "anomalous" self-diffusion in both bcc systems with good agreement between calculation and experiment. The proposed methodology is general and simple enough to be applicable to other mechanically unstable crystals.

Design of Fe2B-based ductile high temperature ceramics: First-principles calculations and experimental validation

Iron Boride (Fe2B) has significant potential to be used as a wear- and corrosion-resistant ceramic because of its high hardness, good corrosion resistance, and low cost. However, the toughness and elastic heat resistance of Fe2B can be further improved under high-temperature wear conditions. First-principles energetics and phonon calculations showed that Ti, Cr, Mn, Co, Ni, Nb, Mo, Ta, and W can dissolve in Fe2B. Among these, Cr, Mn, and Ni can form a continuous solid solution in (Fe, M)2B. Furthermore, Ti, Cr, Mn, Co, Ni, Cu, Y, Nb, Mo, Ta, and W improved the toughness of Fe2B. The results were validated by the experimental results. It was found that the experimental fracture toughness of Fe2B doped with Cr and Ni reached 4.16 and 4.27 MPa m1/2, respectively, which are higher than 3.64 MPa m1/2 of pure Fe2B. Chemical bond analyses showed that the toughness was improved owing to the stiffening of the B–B bond and the invariability of the Fe–B bond in Fe2B by doping Cr and Ni with increasing pressure. The elastic heat resistance of alloyed Fe2B was related to the degree to which the B–B and Fe–B bonds weakened with temperature. The less these bonds strength weakened with increasing temperature, the better the elastic heat resistance. The bond strength of Fe–B and B–B bonds in Fe2B doped with Cr showed a minimum decrease with increasing temperature, whereas the bond strength of Fe–B and B–B bonds in Fe2B doped with Ta showed a maximum decrease with increasing temperature. This indicates that the alloying element Cr can improve the elastic heat resistance of Fe2B, while Ta decreases the elastic heat resistance of Fe2B.

Phase transition and morphology evolution of superfine NaNbO3 particles synthesized by the hydrothermal method with the assistance of K+

NaNbO3 (NN) is a well-known perovskite-type dielectric material. However, its phase transition is a complex process and the phase transition mechanism is insufficiently investigated yet. Therefore, in the work, the NN superfine particles were synthesized by a hydrothermal method with the assistance of K+ and the microstructures of NN were carefully investigated to understand the strain-driven phase transition and morphology evolution of NN. The results suggest that K+ leads to strong planar bending of NbO6 by influencing the Na + vibration, which accounts for the O-R phase transition as the K+ increases. Once the R phase is triggered, the O-R phase transition proceeds spontaneously based on phonon calculations of orthorhombic (O) NN and R NN. The antiferroelectric nature of rhombohedral (R) NN with the space group R–3H is confirmed through charge density distribution. Additionally, the morphology evolution is deduced on the TEM analysis basis.

Optimal alloying in hydrides: Reaching room-temperature superconductivity in LaH10

Doping represents one of the most promising avenues for optimizing superconductors, such as high-pressure conventional superconductors with record-breaking critical temperatures. In this work, we perform an extensive search for substitutional dopants in ${\mathrm{LaH}}_{10}$, looking for elements that enhance its electronic structure. In total, 70 elements were investigated as possible substitutions of La-sites at doping ratio of 12.5% under high pressure. To accelerate the screening of the ternary phases, our protocol to scan the chemical space is 1) to be constrained to highly symmetric patterns of hydrogen atoms, 2) focusing on phases with compact basis of lanthanum atoms (minimize enthalpy) and 3) to choose candidate dopants that preserve the van Hove singularity around the Fermi level. We found Ca as the best candidate dopants, which shift the van Hove singularity and increase the electronic DOS at the Fermi level. By using harmonic-level phonon calculations and performing first-principles calculation of ${T}_{\mathrm{c}}$, Ca-doped ${\mathrm{LaH}}_{10}$ shows ${T}_{\mathrm{c}}$ which is 15% higher than the one of ${\mathrm{LaH}}_{10}$. It provides a promising route to reach room-temperature superconductivity in pressurized hydrides by doping.

In-silico synthesis of lowest-pressure high-Tc ternary superhydrides

We report the theoretical prediction of two high-performing hydride superconductors BaSiH8 and SrSiH8. They are thermodynamically stable above pressures of 130 and 174 GPa, respectively, and metastable below that. Employing anharmonic phonon calculations, we determine the minimum pressures of dynamical stability to be around 3 GPa for BaSiH8 and 27 GPa for SrSiH8, and using the fully anisotropic Migdal-Eliashberg theory, we predict Tc’s around 71 and 126 K, respectively. We also introduce a method to estimate the lowest pressure of synthesis, based on the calculation of the enthalpy barriers protecting the BaSiH8Fmbar{3}m structure from decomposition at various pressures. This kinetic pressure threshold is sensibly higher than the one based on dynamic stability, but gives a much more rigorous limit for synthesizability.

Transport properties of binary phosphide AgP2 denoting high Hall mobility and low lattice thermal conductivity

This study found that polycrystalline AgP2 shows intrinsic semiconducting electrical conductivity with Hall mobility of 51 cm2 V−1 s−1, which is as high as that of Mg2Si, and lattice thermal conductivity of 1.2 W K−1 m−1, which is as low as that of Bi2Te3. First-principles calculations theoretically indicate AgP2 as an intrinsic semiconductor, and indicate the estimated carrier relaxation time τ as 3.3 fs, which is long for a polycrystalline material. Moreover, the effective mass of hole m* is approximately 0.11 times that of free electrons. These results indicate that long τ and light m* of the carrier are the origins of the high experimentally obtained Hall mobility. Phonon calculations indicate that the Ag atoms in AgP2 exhibit highly anharmonic phonon modes with mode Grüneisen parameters of more than 2 in the 50–100 cm−1 low-frequency range. The large anharmonic vibrations of the Ag atoms reduce the phonon mean free path. Moreover, the lattice thermal conductivity was found, experimentally and theoretically, to be as low as approx. 1.2 W K−1 m−1 at room temperature by phonon–phonon and grain-boundary scattering.

Intermediate spin state and the B1−B2 transition in ferropericlase

Ferropericlase (fp), (Mg$_{1-x}$Fe$_x$)O, the second most abundant mineral in the Earth's lower mantle, is expected to be an essential component of super-Earths' mantles. Here we present an ab initio investigation of the structure and magnetic ground state of fp up to $\sim$ 3 TPa with iron concentrations (x$_{Fe}$) varying from 0.03 to 0.12. Calculations were performed using LDA+U$_{sc}$ and PBE exchange-correlation functionals to elucidate the pressure range for which the Hubbard U (U$_{sc}$) is required. Similar to the end-members FeO and MgO, fp also undergoes a B1 to B2 phase transition that should be essential for modeling the structure and dynamics of super-Earths' mantles. This structural transition involves a simultaneous change in magnetic state from a low spin (LS) B1 phase with iron total spin S=0 to an intermediate spin (IS) B2 phase with S=1. This is a rare form of pressure/strain-induced magnetism produced by local cation coordination changes. Phonon calculations confirm the dynamical stability of the iron B2-IS state. Free energy calculations are then carried out including vibrational effects and electronic and magnetic entropy contributions. The phase diagram is then obtained for low concentration fp using a quasi-ideal solid solution model. For x$_{Fe}$ > 0.12 this approach is no longer valid. At ultra-high pressures, there is an IS to LS spin state change in Fe in the B2 phase, but the transition pressure depends sensitively on thermal electronic excitations and on x$_{Fe}$.

Machine-learning correction to density-functional crystal structure optimization

Density functional theory is routinely applied to predict crystal structures. The most common exchange-correlation functionals used to this end are the Perdew–Burke–Ernzerhof (PBE) approximation and its variant PBEsol. We investigate the performance of these functionals for the prediction of lattice parameters and show how to enhance their accuracy using machine learning. Our data set is constituted by experimental crystal structures of the Inorganic Crystal Structure Database matched with PBE-optimized structures stored in the materials project database. We complement these data with PBEsol calculations. We demonstrate that the accuracy and precision of PBE/PBEsol volume predictions can be noticeably improved a posteriori by employing simple, explainable machine learning models. These models can improve PBE unit cell volumes to match the accuracy of PBEsol calculations, and reduce the error of the latter with respect to experiment by 35 percent. Further, the error of PBE lattice constants is reduced by a factor of 3–5. A further benefit of our approach is the implicit correction of finite temperature effects without performing phonon calculations.Impact statementKnowledge about the crystal structure of solids is essential for describing their elastic and electronic properties. In particular, their accurate prediction is essential to predict the electronic properties of not-yet-synthesized materials. Lattice parameters are most commonly calculated by density functional theory using the Perdew–Burke–Ernzerhof (PBE) approximation and its variant PBEsol as exchange-correlation functional. They are successful in describing materials properties but do, however, not always achieve the desired accuracy in comparison with experiments. We propose a computationally efficient scheme based on interpretable machine learning to optimize crystal structures. We demonstrate that the accuracy of PBE- and PBEsol-structures can be, therewith, enhanced noticeably. In particular, the PBE unit cells, available in materials databases, can be improved to the level of the more accurate PBEsol calculations and the error of the latter with respect to the experiment can be reduced by 35 percent. An additional advantage of our scheme is the implicit inclusion of finite temperature corrections, which makes expensive phonon calculations unnecessary.Graphical abstract

High-energy-density metal nitrides with armchair chains

Polymeric nitrogen has attracted much attention owing to its possible application as an environmentally safe high-energy-density material. Based on a crystal structure search method accelerated by the use of machine learning and graph theory and on first-principles calculations, we predict a series of metal nitrides with chain-like polynitrogen (P21-AlN6, P21-GaN6, P-1-YN6, and P4/mnc-TiN8), all of which are estimated to be energetically stable below 40.8 GPa. Phonon calculations and ab initio molecular dynamics simulations at finite temperature suggest that these nitrides are dynamically stable. We find that the nitrogen in these metal nitrides can polymerize into two types of poly-N42− chains, in which the π electrons are either extended or localized. Owing to the presence of the polymerized N4 chains, these metal nitrides can store a large amount of chemical energy, which is estimated to range from 4.50 to 2.71 kJ/g. Moreover, these compounds have high detonation pressures and detonation velocities, exceeding those of conventional explosives such as TNT and HMX.

A new transition metal diphosphide α-MoP2 synthesized by a high-temperature and high-pressure technique

Monoclinic α-MoP2, with the OsGe2-type structure (space group C2/m, Z = 4) and lattice parameters a = 8.7248(11) Å, b = 3.2322(4) Å, c = 7.4724(9)Å, and β = 119.263°, was synthesized under a pressure of 4~GPa at a temperature between 1100 °C and 1200 °C. The structure of α-MoP2 and its relationship to other transition metal diphosphides are discussed. Surprisingly, the ambient pressure phase orthorhombic β-MoP2 (space group Cmc21) is denser in structure than α-MoP2. Room-temperature high-pressure x-ray diffraction studies exclude the possibility of phase transition from β-MoP2 to α-MoP2, suggesting that α-MoP2 is a stable phase at ambient conditions; this is also supported by the total energy and phonon calculations.

An insight into structural, electronic and optical characteristics of Mo1-xMxO3 (M = Zr, Y, ZrY) for the formation of conducting filaments in optoelectronic memory devices: A first principles study

In the present work, we have theoretically investigated the structural, electronic and optical characteristics of Mo1−xMxO3 (M = Zr, Y, co-doped (ZrY)) for Optoelectronic Resistive Random-Access Memory (ORRAM) devices and associated applications. Density functional theory within Heyd-Scuseria-Ernzerhof (HSE06) functional has been employed to better estimate optoelectronic parameters. The structural outcomes, findings of the energy band structure, spin resolved total density of states (TDOS), three dimensional iso-surface electron charge density, electron localization function and Bader charge analysis unveil thatMo1−x(ZrY)xO3 is comparatively more suitable composite with enhanced charge conductance for ORRAM devices. The partial density of states (PDOS) and Bader charge analysis results reveals that noticeable orbital contribution of the constituent atoms mainly in increasing conductivity through hybridization. Formation energy and phonon calculations confirmed that studied structures are stable. The photo absorption behavior shows that Mo1−x(ZrY)xO3 can absorb a broad electromagnetic radiations wavelength range from ultraviolet (UV) to infrared (IR) coherent with the charge conduction property which has been found a most fitted candidate for ORRAM and associated applications.

Fermi surface topology and anisotropic superconducting gap in electron-doped hydride compounds at high pressure

The recent theoretical discovery of the predicted high-temperature superconductivity (superconducting transition temperature ${T}_{\mathrm{c}}\ensuremath{\sim}351\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ at 300 GPa) in clathrate ${\mathrm{Li}}_{2}\mathrm{Mg}{\mathrm{H}}_{16}$ is an important advance toward room-temperature superconductors. Here we use first-principle approaches to identify a new ternary hydride of clathrate structure of $Fd\overline{3}m\text{\ensuremath{-}}{\mathrm{Rb}}_{2}\mathrm{Mg}{\mathrm{H}}_{16}$ by Rb-doped $\mathrm{Mg}{\mathrm{H}}_{16}$ at 300 GPa. We first verified the thermal and dynamic stability for the $Fd\overline{3}m\text{\ensuremath{-}}{\mathrm{Rb}}_{2}\mathrm{Mg}{\mathrm{H}}_{16}$ through the formation enthalpy and phonon calculations, respectively. Next, we showcased that $Fd\overline{3}m\text{\ensuremath{-}}{\mathrm{Rb}}_{2}\mathrm{Mg}{\mathrm{H}}_{16}$ has two Fermi surface (FS) sheets, which are both dominated by the H2 $s$ orbital. Using the Eliashberg formalism, the ${T}_{\mathrm{c}}$ of $Fd\overline{3}m\text{\ensuremath{-}}{\mathrm{Rb}}_{2}\mathrm{Mg}{\mathrm{H}}_{16}$ was calculated to be 130 K at 300 GPa. Furthermore, the calculations of the electronic, phonon, and superconducting properties reveal that $Fd\overline{3}m\text{\ensuremath{-}}{\mathrm{Li}}_{2}\mathrm{Mg}{\mathrm{H}}_{16}$ has four FS sheets with mixed H1 $s$ and H2 $s$ orbital character and reaches the ${T}_{\mathrm{c}}$ of 352 K at 300 GPa. Compared with $Fd\overline{3}m\text{\ensuremath{-}}{\mathrm{Rb}}_{2}\mathrm{Mg}{\mathrm{H}}_{16}$, $Fd\overline{3}m\text{\ensuremath{-}}{\mathrm{Li}}_{2}\mathrm{Mg}{\mathrm{H}}_{16}$ produces high-frequency phonon softening, leading to the enhancement of ${T}_{\mathrm{c}}$. Moreover, it is demonstrated that Rb substitution for Li produces the reduction of contribution of H orbitals to the FS sheets and the decrease in FS sheets in number, which tend to decrease the electron-phonon coupling strength and ${T}_{\mathrm{c}}$. Our observed FS sheets and their associated superconducting gap will provide key insights into the understanding of the superconductivity mechanism in these and related systems.

Proposal to improve Ni-based superconductors via enhanced charge transfer

Recently discovered superconductivity in hole-doped nickelate Nd$_{0.8}$Sr$_{0.2}$NiO$_2$ has attracted intensive attention in the field. An immediate question is how to improve its superconducting properties. Guided by the key characteristics of electronic structures of the cuprates and the nickelates, we propose that nickel chalcogenides with a similar lattice structure should be a promising family of materials. Using NdNiS$_2$ as an example, through first-principle structural optimization and phonon calculation, we find this particular crystal structure a stable one. We justify our proposal by comparing with CaCuO$_2$ and NdNiO$_2$ with regard to strength of the charge-transfer characteristics and the trend in their low-energy many-body effective Hamiltonians of doped hole carriers. This analysis indicates that nickel chalcogenides host low-energy physics closer to that of the cuprates, with stronger magnetic interaction than the nickelates, and thus they deserve further experimental exploration. Our proposal also opens up the possibility of a wide range of parameter tuning through ligand substitution among chalcogenides, to further improve superconducting properties.

Investigating Electronic, Optical, and Phononic Properties of Bulk γ-M2ON2 and β-M7O8N4 (M = Hf and Zr) Insulators Using Density Functional Theory.

Hafnium and zirconium oxynitrides have similar properties, yet a consolidated investigation of their intrinsic properties has not been carried out. In this paper, we perform first-principles density functional theory calculations of γ- and β-phase hafnium and zirconium oxynitrides, which show that the γ-M2ON2 (M = Hf and Zr) is an indirect band-gap (Eg) insulator, while the β-M7O8N4 has a “pseudo-direct” type of Eg. β-phase has higher Eg than γ-phase, with concomitant disappearance of the conduction band tail. Optical properties in γ-M2ON2 show that the anisotropy is negligible, and the optical constant values are in the range of other superhard materials. Phonon calculations present peculiar characteristics such as a small phonon band gap in γ-Hf2ON2 and imaginary phonon frequencies in β-phases relating to lattice instability. The phononic properties are unfavorable for their potential use as an absorber material of the hot carrier solar cell—an emerging photovoltaic concept.

First-principles phonon calculations for lattice dynamics, thermal expansion and lattice thermal conductivity of CoSi in the high temperature region

This study presents the first-principles phonon calculations to understand the experimental thermal expansion () and lattice thermal conductivity of CoSi in the high temperature region. Phonon dispersion is computed using the finite displacement method and supercell approach by taking the equilibrium crystal structures obtained from DFT. The calculation of is done under quasi-harmonic approximation. The is calculated using first-principle anharmonic lattice dynamics calculations under single-mode relaxation time approximation. The calculated in the temperature range 0–1300 K gives a good match with existing experimental data. The calculated value of (∼8.0 W/mK) at 300 K is found to be in good agreement with the experimental value of ∼8.3 W/mK. The temperature dependence of phonon lifetime due to phonon-phonon interaction is calculated to understand the behaviour of . The present study suggests that ground state phonon dispersion obtained from DFT-based methods gives reasonably good explanation of experimental and .

Thermodynamics of spin crossover in ferropericlase: an improved LDA + Usc calculation

We present LDA + Usc calculations of high-spin (HS) and low-spin (LS) states in ferropericlase (fp) with an iron concentration of 18.75%. The Hubbard parameter U is determined self-consistently with structures optimized at arbitrary pressures. We confirm a strong dependence of U on the pressure and spin state. Static calculations confirm that the antiferromagnetic configuration is more stable than the ferromagnetic one in the HS state, consistent with low-temperature measurements. Phonon calculations guarantee the dynamical stability of HS and LS states throughout the pressure range of the Earth mantle. Compression curves for HS and LS states agree well with experiments. Using a non-ideal mixing model for the HS to LS states solid solution, we obtain a crossover starting at ∼45 GPa at room temperature and considerably broader than previous results. The spin-crossover phase diagram is calculated, including vibrational, magnetic, electronic, and non-ideal HS–LS entropic contributions. Our results suggest the mixed-spin state predominates in fp in most of the lower mantle.

Vibrational properties of SrVO2H with large spin-phonon coupling

The antiferromagnetic transition metal oxyhydride ${\mathrm{SrVO}}_{2}\mathrm{H}$ is distinguished by its stoichiometric composition and an ordered arrangement of H atoms. The tetragonal structure is related to the cubic perovskite and consists of alternating layers of ${\mathrm{VO}}_{2}$ and SrH. ${d}^{2}$ V(III) attains a sixfold coordination by four O and two H atoms. The latter are arranged in a trans fashion, which produces H--V--H chains along the tetragonal axis. Here, we investigate the vibrational properties of ${\mathrm{SrVO}}_{2}\mathrm{H}$ by inelastic neutron scattering and infrared spectroscopy combined with phonon calculations based on density functional theory. The H-based vibrational modes divide into a degenerate bending motion perpendicular to the H--V--H chain direction and a highly dispersed stretching motion along the H--V--H chain direction. The bending motion, with a vibrational frequency of approximately 800 ${\mathrm{cm}}^{\ensuremath{-}1}$, is split into two components separated by about 50 ${\mathrm{cm}}^{\ensuremath{-}1}$, owing to the doubled unit cell from the antiferromagnetic structure. Interestingly, spin-phonon coupling stiffens the H-based modes by $50\ensuremath{-}100\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ although super-exchange coupling via H is very small. Frequency shifts of the same order of magnitude also occur for V--O modes. It is inferred that ${\mathrm{SrVO}}_{2}\mathrm{H}$ displays the hitherto largest recognized coupling between magnetism and phonons in a material.

Theoretical Insights into the Hydrogen Evolution Reaction on VGe2N4 and NbGe2N4 Monolayers.

Catalytically active sites at the basal plane of two-dimensional monolayers for hydrogen evolution reaction (HER) are important for the mass production of hydrogen. The structural, electronic, and catalytic properties of two-dimensional VGe2N4 and NbGe2N4 monolayers are demonstrated using the first-principles calculations. The dynamical stability is confirmed through phonon calculations, followed by computation of the electronic structure employing the hybrid functional HSE06 and PBE+U. Here, we introduced two strategies, strain and doping, to tune their catalytic properties toward HER. Our results show that the HER activity of VGe2N4 and NbGe2N4 monolayers are sensitive to the applied strain. A 3% tensile strain results in the adsorption Gibbs free energy (ΔGH*) of hydrogen for the NbGe2N4 monolayer of 0.015 eV, indicating better activity than Pt (−0.09 eV). At the compressive strain of 3%, the ΔGH* value is −0.09 eV for the VGe2N4 monolayer, which is comparable to that of Pt. The exchange current density for the P doping at the N site of the NbGe2N4 monolayer makes it a promising electrocatalyst for HER (ΔGH* = 0.11 eV). Our findings imply the great potential of the VGe2N4 and NbGe2N4 monolayers as electrocatalysts for HER activity.

High-Pressure Properties of Wolframite-Type ScNbO4

In this work, we used Raman spectroscopic and optical absorption measurements and first-principles calculations to unravel the properties of wolframite-type ScNbO4 at ambient pressure and under high pressure. We found that monoclinic wolframite-type ScNbO4 is less compressible than most wolframites and that under high pressure it undergoes two phase transitions at ∼5 and ∼11 GPa, respectively. The first transition induces a 9% collapse of volume and a 1.5 eV decrease of the band gap energy, changing the direct band gap to an indirect one. According to calculations, pressure induces symmetry changes (P2/c–Pnna–P2/c). The structural sequence is validated by the agreement between phonon calculations and Raman experiments and between band structure calculations and optical absorption experiments. We also obtained the pressure dependence of Raman modes and proposed a mode assignment based upon calculations. They also provided information on infrared modes and elastic constants. Finally, noncovalent and charge analyses were employed to analyze the bonding evolution of ScNbO4 under pressure. They show that the bonding nature of ScNbO4 does not change significantly under pressure. In particular, the ionicity of the wolframite phase is 61% and changes to 63.5% at the phase transition taking place at ∼5 GPa.

High Energy Density Polymeric Nitrogen Nanotubes inside Carbon Nanotubes

Polymeric nitrogen as a new class of high energy density materials has promising applications. We develop a new scheme of crystal structure searching in a confined space using external confining potentials fitted from first-principles calculations. As a showcase, this method is employed to systematically explore novel polymeric nitrogen structures confined in single-walled carbon nanotubes. Several quasi-one-dimensional single-bonded polymeric nitrogen structures are realized, two of them are composed of nanotubes instead of chains. These new polymeric nitrogen phases are mechanically stable at ambient pressure and temperature according to phonon calculations and ab initio molecular dynamics simulations. It is revealed that the stabilization of zigzag and armchair chains confined in carbon nanotubes are mostly attributed to the charge transfer from carbon to nitrogen. However, for the novel nitrogen nanotube systems, electrons overlapping in the middle space provide strong Coulomb repulsive forces, which not only induce charge transfer from the middle to the sides but also stabilize the polymeric nitrogen. Our work provides a new strategy for designing novel high-energy-density polymeric nitrogen materials, as well as other new materials with the help of confined space inside porous systems, such as nanotubes, covalent organic frameworks, and zeolites.