Density Functional Perturbation Theory Research Articles

Refractory and thermoelectric properties of stabilized Tricalcium aluminate allotrope: A first-principles calculation approach

Tricalcium aluminate (Ca3Al2O6) is an indispensable component of Portland cement due to its high strength and reactivity. This study investigates the equilibrium lattice structure as well as the electronic and refractory properties of a newly discovered allotrope of Ca3Al2O6 using density functional theory and random phase approximation methods. Using density functional perturbation theory, we investigate the phonon dispersion of the refined structure’s experimental stability. In addition, the lattice thermal conductivity and thermoelectric figure of merit are computed by solving the Boltzmann Transport Equation with the modified Debye Callaway model and the Relaxation time Approximation methods. The computed Figure of merit, determined by the carrier concentration, indicates a substantial enhancement of 40 to 100-fold, leading to a superior figure of merit of 0.25 and 0.6 when appropriately doped. As a result, we anticipate that stable allotropes of Ca3Al2O6 in the Pm3̄m phase will be useful as energy-harvesting, convective cooling and infrared radiation shield-based cement materials in the cement and concrete industries.

InAs–InP Superlattice Nanowires with Tunable Phonon Frequencies

AbstractThe control of heat conduction through the manipulation of phonons in solids is of fundamental interest and can be exploited in applications for thermoelectric conversion. In this context, the advent of novel semiconductor nanomaterials with high surface‐to‐volume ratio, e.g. nanowires, offer exciting perspectives, leading to significant leaps forwarding the efficiency of solid‐state thermoelectric converters after decades of stagnation. Beyond the high aspect ratio, the nanowire geometry offers unprecedented possibilities of materials combination and crystal phase engineering not achievable with 2D counterparts. In this work, the growth of long (up to 100 repetitions) wurtzite InAs/InP superlattice nanowires with homogeneous segment thicknesses is reported, with control down to the single digit of nanometer. By means of Raman scattering experiments, clear modifications of the phonon dispersion in superlattice nanowires are found, where both InAs‐like and InP‐like modes are present. The experimentally measured modes are well reproduced by density functional perturbation theory calculations. Remarkably, it is found that the phonon frequencies can be tuned by the superlattice periodicity, opening exciting perspectives for phonon engineering and thermoelectric applications.

Generation of thermal neutron scattering data for GH3535 alloy

Recent studies related to the thermal neutron scattering (TNS) data in reactors were generally focused on fuels and moderators, while the TNS data for structural materials has received little attention. The TNS effect of the GH3535 alloy, a nickel-based alloy widely used in molten salt reactor (MSR), is studied in this work. The partial phonon densities of states (PDOS) for the main metals (Ni, Mo, Cr and Fe) in the alloy, which are required for the TNS data generation, are calculated using the density functional perturbation theory (DFPT) based on a special quasi-random structure (SQS) of the alloy. The TNS cross sections for the main metals in the alloy are generated using the modified NJOY code. To preliminarily validate the TNS data, the calculated scattering cross section, combined with the evaluated absorption cross section of the alloy, is compared with the experimental total cross section, which shows a good agreement. Moreover, an integral neutronics experiment of neutron leakage spectrum is designed to further validate the TNS data. The neutron leakage spectrum is simulated by the Monte Carlo method, which can be compared with the future experimental result. Based on the experiment geometry modeling, the TNS effects of the GH3535 alloy are analyzed at multiple incident neutron energies, sample thicknesses and temperatures, respectively. It is found that the TNS effect of the GH3535 alloy on the neutron leakage spectrum cannot be ignored, and the scattering cross section of the alloy with high precision should be included in designs of MSR.

Demagnetizing Ferromagnetic Catalysts to the Sabatier Optimal of Haber-Bosch Process.

Achieving the Sabatier optimal of a chemical reaction has been the central topic in heterogeneous catalysis for a century. However, this ultimate goal was greatly hindered in previous catalyst design strategies since the active sites indeed changed. Fortunately, the magneto-catalytic effect (MCE) provides a promising solution to this long-standing challenge. Recent research suggests that the performance of ferromagnetic catalysts is capable to be promoted without changing its chemical structure. Herein, we use time-dependent density functional perturbation theory (TDDFPT) calculations to elucidate that a partially demagnetized (DM) ferromagnet could be a Sabatier optimal catalyst. Using ammonia synthesis as the model reaction, we determined the activity of Cobalt at each DM state by including the magnetic thermal excitations via magnon analysis, making the 55% DM Co to the genuine Sabatier optimal. As an essential but underexcavated phenomenon in heterogeneous catalysis, the MCE will open a new avenue to design high-performance catalysts.

Nanoscale Localized Phonons at Al2O3 Grain Boundaries.

Nanoscale defects like grain boundaries (GBs) would introduce local phonon modes and affect the bulk materials' thermal, electrical, optical, and mechanical properties. It is highly desirable to correlate the phonon modes and atomic arrangements for individual defects to precisely understand the structure-property relation. Here we investigated the localized phonon modes of Al2O3 GBs by combination of the vibrational electron energy loss spectroscopy (EELS) in scanning transmission electron microscope and density functional perturbation theory (DFPT). The differences between GB and bulk obtained from the vibrational EELS show that the GB exhibited more active vibration at the energy range of <50 meV and >80 meV, and further DFPT results proved the wide distribution of bond lengths at GB are the main factor for the emergence of local phonon modes. This research provides insights into the phonon-defect relation and would be of importance in the design and application of polycrystalline materials.

Lattice thermal conductivity in half-Heusler compounds XNiSn (X=Ti, Zr, Hf) using Slack's model

Reducing lattice thermal conductivity (κl) that reflects the material’s heat-carrying capacity through lattice phonon vibrations is crucial for optimizing the figure of merit (zT). Using density functional theory (DFT) and density functional perturbation theory (DFPT), present work considers the structural, electronic, magnetic, and phonon properties of the XNiSn (X=Ti, Zr, Hf ) half Heusler (hH) compounds. TiNiSn, ZrNiSn, and HfNiSn are identified as semiconductors with indirect band gaps of 0.43 eV, 0.47 eV and 0.39 eV, respectively, exhibiting dynamical stability. The temperature- dependent κl of hH XNiSn are compared using Slack’s model with two approaches for analyzing phonon velocity: elastic constants from quasi- harmonic approximation (QHA) as implemented in the Thermo_pw code and slope of phonon bands based on DFPT. At room temperature, TiNiSn, ZrNiSn and HfNiSn have κl values of 28.61 Wm−1K−1, 34.61 Wm−1K−1 and 29.85 Wm−1K−1 respectively using phonon velocity from slopes of phonon bands based on DFPT. These values show deviation of 1.48%, 6.29%, and 5.82% to those κl values 29.01 Wm−1K−1’, 36.79 Wm−1K−1 and 31.59 Wm−1K−1 for TiNiSn, ZrNiSn and HfNiSn respectively using QHA.

Electronic and vibrational properties of MgCu2O3

AbstractThe vibrational properties of orthorhombic MgCu2O3 compound have been investigated within the framework of the density functional perturbation theory (DFPT) as well as experimentally, to validate the computational results. MgCu2O3 was synthesized by solid‐state reaction and characterized by synchrotron‐based X‐ray diffraction, Raman spectroscopy, and Fourier transform infrared spectroscopy. The DFT + U‐based first principle calculations were performed to obtain the correct electronic ground state and the band structure of this compound. The same DFT + U methodology was employed along with DFPT calculations for obtaining vibrational properties: phonon density of states and phonon band structure. The atomic vibrations for each mode were also analyzed, and the Raman and the IR active modes are identified. Experimentally observed Raman and infrared (IR) spectra agree well with the computed ones.

Strain-induced modification in thermal properties of monolayer 1T-ZrS2 and ZrS2/ZrSe2 heterojunction.

This paper systematically analyzes the phonon dispersion curves of single-layer ZrS2, ZrSe2, and ZrS2/ZrSe2 heterostructures under different strains. The phonon spectra and thermal parameters of the three structures were obtained based on the density functional perturbation theory method. The upper limits of strain that different monolayers and heterojunctions can withstand were studied. The monolayers ZrSe2 and ZrS2 can withstand up to 8% biaxial tensile strain, and the ZrS2/ZrSe2 heterojunction can withstand up to 6% biaxial tensile strain. In addition, the van der Waals force of the heterojunction may cause phonon tearing in the vertical direction. The application of biaxial tensile strain can adjust the thermal properties of the system to a large extent, which is similar to the strain effect in the pristine case. When the temperature rises, the entropy enthalpy of the three structures also gradually increases, the free energy gradually decreases, and the heat capacity of the system gradually increases until it tends to be stable. Taking single-layer ZrS2 as an example, we analyzed the change curve of thermal properties of single-layer ZrS2 under tensile strain. The results show that with the gradual increase of strain, the crystal's entropy, enthalpy, and free energy change differently. In addition, the heat capacity increases slowly under high temperatures. When all systems reach the limit strain, the phonon spectrum appears to have an imaginary frequency, and the thermal properties decrease significantly. This paper uses the first-principle calculation method based on density functional theory, and the PBE exchange-correlation function based on generalized gradient approximation (GGA) is selected for a specific calculation. The density functional perturbation theory (DFPT) calculates the full kinetic matrix. Because the lattice constants of ZrS2 and ZrSe2 are similar and have similar periodicity, the corresponding unit cells are used for structural optimization and property calculation. The Brillouin zone is integrated using the K points generated by the Monkhorst-pack method. For single-layers ZrS2 and ZrSe2, 8 × 8 × 1K-point grid is selected, and for ZrS2/ZrSe2 heterojunction, 8 × 8 × 2K-point grid is selected. A vacuum layer of 30Å was added in the vertical direction to avoid interlayer interaction. The non-conservative pseudopotential method is used to optimize the structure, and the optimization convergence is set as follows: the cutoff energy is set to 700eV, the convergence threshold of the maximum force between atoms is 0.01eV/Å, the convergence threshold of the maximum energy change is set to 1 × 10-9eV, and the convergence threshold of the maximum displacement is 0.001Å.

Machine Learning K-Means Clustering in Interpolative Separable Density Fitting Algorithm: Advancing Accurate and Efficient Cubic-Scaling Density Functional Perturbation Theory Calculations within Plane Waves.

Density functional perturbation theory (DFPT) is a crucial tool for accurately describing lattice dynamics. The adaptively compressed polarizability (ACP) method reduces the computational complexity of DFPT calculations from O(N4) to O(N3) by combining the interpolative separable density fitting (ISDF) algorithm. However, the conventional QR factorization with column pivoting (QRCP) algorithm, used for selecting the interpolation points in ISDF, not only incurs a high cubic-scaling computational cost, O(N3), but also leads to suboptimal convergence. This convergence issue is particularly pronounced when considering the complex interplay between the external potential and atomic displacement in ACP-based DFPT calculations. Here, we present a machine learning K-means clustering algorithm to select the interpolation points in ISDF, which offers a more efficient quadratic-scaling O(N2) alternative to the computationally intensive cubic-scaling O(N3) QRCP algorithm. We implement this efficient K-means-based ISDF algorithm to accelerate plane-wave DFPT calculations in KSSOLV, which is a MATLAB toolbox for performing Kohn-Sham density functional theory calculations within plane waves. We demonstrate that this K-means algorithm not only offers comparable accuracy to QRCP in ISDF but also achieves better convergence for ACP-based DFPT calculations. In particular, K-means can remarkably reduce the computational cost of selecting the interpolation points by nearly 2 orders of magnitude compared to QRCP in ISDF.

Deep-Learning Density Functional Perturbation Theory.

Calculating perturbation response properties of materials from first principles provides a vital link between theory and experiment, but is bottlenecked by the high computational cost. Here, a general framework is proposed to perform density functional perturbation theory (DFPT) calculations by neural networks, greatly improving the computational efficiency. Automatic differentiation is applied on neural networks, facilitating accurate computation of derivatives. High efficiency and good accuracy of the approach are demonstrated by studying electron-phonon coupling and related physical quantities. This work brings deep-learning density functional theory and DFPT into a unified framework, creating opportunities for developing abinitio artificial intelligence.

Experimental and theoretical study of Gd2O3 added pseudo-tetragonal Bi3TaTiO9-based ceramics for ferroelectric, electric and high-temperature piezoelectric applications

The present global energy crisis, along with the development of modern technologies, has compelled the scientists to search for smart materials, which possess the multifunctional properties simultaneously. Among such materials, bismuth-layered structure ferroelectrics (BLSFs) containing a perovskite structure have demonstrated the tendency to play a vital role. Herein, we report an engineered Gd2O3 added Bi3TiTa0·5Nb0·5O9 (BTTN) based material with composition Bi3TiTa0·5Nb0·5O9:xwt%Gd2O3 (BTTN:xGd) with x = 0–0.20 ceramics to investigate the ferroelectric, electric, piezoelectric and dielectric properties of the material. Highly dense (relative density of ∼96%) BTTN:0.15Gd has shown the best merits among all other compositions with improved remnant polarization (Pr ∼ 7.86 μC/cm2), energy conversion efficiency (ƞ) of ∼63.48%, resistance of ∼2.2 × 1010 Ω and high piezoelectric co-efficient (d33 ∼ 25 pC/N) at room temperature, which are much improved than pure BTTO or BTTN ceramics. Nonetheless, ceramic has shown the stable resistivity of ∼104 Ω at 500 °C, with a stable d33 value of 22 pC/N (just 12% drop) after annealing at 600 °C. The ferroelectric to paraelectric phase transition of ceramic with the highest dielectric constant is reported at Curie temperature (TC) of 859 °C. Additionally, Density-Functional-Theory (DFT) and Density-Functional-Perturbation-Theory (DFPT) measurements are performed by employing generalized gradient approximation using the Quantum-ESPRESSO code. Structural, ferroelectric and electronic properties of BTTO, BTTN and Gd-added BTTN compounds are investigated. The calculated formation energies confirmed the thermodynamic stability of pseudo-tetragonal Gd-added BTTN compounds. Using the Berry-phase approach for piezoelectric materials, the calculated maximum polarization is 54.00 μC/cm2, which is in agreement with values obtained experimentally. Mentioned outcomes of the material clearly represent the potential of the BTTN:0.15Gd ceramic for the utilization in high-temperature piezoelectric devices.

Bistability between π-diradical open-shell and closed-shell states in indeno[1,2-a]fluorene.

Indenofluorenes are non-benzenoid conjugated hydrocarbons that have received great interest owing to their unusual electronic structure and potential applications in nonlinear optics and photovoltaics. Here we report the generation of unsubstituted indeno[1,2-a]fluorene on various surfaces by the cleavage of two C-H bonds in 7,12-dihydroindeno[1,2-a]fluorene through voltage pulses applied by the tip of a combined scanning tunnelling microscope and atomic force microscope. On bilayer NaCl on Au(111), indeno[1,2-a]fluorene is in the neutral charge state, but it exhibits charge bistability between neutral and anionic states on the lower-workfunction surfaces of bilayer NaCl on Ag(111) and Cu(111). In the neutral state, indeno[1,2-a]fluorene exhibits one of two ground states: an open-shell π-diradical state, predicted to be a triplet by density functional and multireference many-body perturbation theory calculations, or a closed-shell state with a para-quinodimethane moiety in the as-indacene core. We observe switching between open- and closed-shell states of a single molecule by changing its adsorption site on NaCl.

Ultraviolet active novel chalcogenides BAlTe2 (B = Rb, Cs): the structural, optoelectronic, mechanical, and vibrational properties for energy harvesting applications through first principles approach

In this study, ternary aluminum-based chalcogenide materials are discussed since these are found to be very appealing for multifunction devices. Here, the structural, optoelectronic, mechanical, and vibrational properties of RbAlTe2 and CsAlTe2 are observed via density functional theory (DFT). An indirect energy band gap is noted to be increased from 1.33 eV to 1.96 eV for RbAlTe2 and 1.28 eV to 1.83 eV for CsAlTe2 by employing improved functional as modified by Trans and Blaha. The calculated formation energy appears to be decreasing, such as -4.39 and -3.83 eV for RbAlTe2 and CsAlTe2, respectively. The investigation of PDOS revealed that Rb-d, Cs-p, Al-p/s, and Te-p orbitals are located prominently and contribute mainly to boosting the conduction mechanism. The optical results declare CsAlTe2 as the strongest absorptive substance, which may be used to devise optoelectronic and photovoltaic devices. Moreover, six independent elastic constants show that these are mechanically stable materials, their brittle nature is confirmed by obeying Born’s stability requirements. According to the density functional perturbation theory (DFPT) approach used for analyzing phonon dispersion, there is no imaginary phonon frequency in both cases (RbAlTe2 and CsAlTe2). The overall results show that the studied materials are potential candidates for applications in photovoltaic and optoelectronic devices.

First-principles calculations on mechanical and electronical properties of AlB[formula omitted]-type CaB[formula omitted]

In the present study, we focused on studying the properties of CaB2 in the hexagonal AlB2-phase. To determine the characteristics of the material, it is crucial to use first-principles calculation methods. Therefore, we used the Density Functional Perturbation Theory to calculate the elastic constants, phonon frequencies, and electron–phonon coupling properties of CaB2, which are important for understanding its superconducting and mechanical behaviors. Additionally, we analyzed Fermi surfaces and electronic band structures and compared them to those of MgB2. Our calculations showed that there is a close relationship between electron–phonon coupling and the superconducting properties of the material. We discovered that the critical superconducting transition temperature value is 24.71 K. In a remarkable finding, the presence of a Dirac cone at the Fermi level was observed in the electronic band structure, which may indicate that the material may be a topological semi-metal.

Variational density functional perturbation theory for metals

Variational density functional perturbation theory for metals

Phonons from density-functional perturbation theory using the all-electron full-potential linearized augmented plane-wave method FLEUR * *Dedicated to the memory of Henry Krakauer (1947–2023).

Phonons are quantized vibrations of a crystal lattice that play a crucial role in understanding many properties of solids. Density functional theory provides a state-of-the-art computational approach to lattice vibrations from first-principles. We present a successful software implementation for calculating phonons in the harmonic approximation, employing density-functional perturbation theory within the framework of the full-potential linearized augmented plane-wave method as implemented in the electronic structure package FLEUR. The implementation, which involves the Sternheimer equation for the linear response of the wave function, charge density, and potential with respect to infinitesimal atomic displacements, as well as the setup of the dynamical matrix, is presented and the specifics due to the muffin-tin sphere centered linearized augmented plane-wave basis-set and the all-electron nature are discussed. As a test, we calculate the phonon dispersion of several solids including an insulator, a semiconductor as well as several metals. The latter are comprised of magnetic, simple, and transition metals. The results are validated on the basis of phonon dispersions calculated using the finite displacement approach in conjunction with the FLEUR code and the phonopy package, as well as by some experimental results. An excellent agreement is obtained.

Emergence of superconductivity by intercalation of alkali metals and alkaline earth metals in Janus transition-metal dichalcogenide heterostructures.

Superconductivity in two-dimensional materials has attracted considerable attention. A new material belonging to the family of Janus transition metal dichalcogenides with out-of-plane structural asymmetry has been recently found to show interesting physical and chemical properties. Using density functional theory and density functional perturbation theory, within the generalized gradient approximation with van der Waals correction, we performed a detailed investigation of the electronic structure, phonon dispersion, Eliashberg spectral function, and electron-phonon coupling of Janus MSSe bilayers (M = Mo or W) and the Janus MoSSe/WSSe heterostructure intercalated with alkali metals (Li, Na, and K) or alkaline earth metals (Mg, Ca, and Sr). We found that the Janus MoSSe bilayer, Janus WSSe bilayer, and Janus MoSSe/WSSe heterostructure transform from a direct band gap semiconductor to a metal or semimetal due to charge transfer from intercalated atoms to the Se and S planes. We showed that all compounds are dynamically stable conventional superconductors. In addition, the Janus heterostructure MoSSe/WSSe intercalated with K exhibits the highest electron-phonon coupling of about 2.12 and the highest superconducting transition temperature of about 14.77 K. Our results indicate the potential application of the Janus materials we investigated in superconductivity.

Phonon softening induced phase transition of CeSiO4: a density functional theory study.

Density functional theory plus Hubbard U (DFT+U) methodology was used to calculate the structures and energetic landscapes of CeSiO4, including its stetindite and scheelite phases from ambient pressure to ∼24 GPa. To ensure accurate simulations of the high-pressure structures, assessments of strain-stress methods and stress-strain methods were conducted in prior, with the former found to have a better agreement with the experimental result. From DFT calculations the equation of states (EOS) of both stetindite and scheelite were further obtained, with the fitted bulk moduli being 182(2) GPa and 190.0(12) GPa, respectively. These results were found to be consistent with the experimental values of 177(5) GPa and 222(40) GPa. Furthermore, the calculated energetics suggest that the stetindite structure is more thermodynamically stable than the scheelite structure at a pressure lower than 8.35 GPa. However, the stetindite → scheelite phase transition was observed experimentally at a much higher pressure of ∼15 GPa. A further phonon spectra investigation by the density functional perturbation theory (DFPT) indicated the Eg1 mode is being softened with pressure and becomes imaginary after 12 GPa, which is a sign of the lattice instability. Consequently, it was concluded that the stetindite → scheelite transition is predominantly initiated by the lattice instability under high-pressure.

Electron-phonon interactions at the topological edge states in single bilayer Bi(111).

An intriguing feature of two-dimensional topological insulators is the topologically protected electronic edge state, which allows one-way carrier transport without backscattering. Although this feature has strong potential applications in lossless electronics, the ideal behavior of the edge states may be fragile due to electron-phonon (e-ph) interactions at room temperatures. Using density functional perturbation theory calculations for single bilayer Bi(111) as a prototypical 2D topological insulator, we show that e-ph scattering can be a significant source of backscattering at the topological edge states. We also show that e-ph interactions strongly correlate to the dispersions of the electronic edge states. In particular, the e-ph interactions increase significantly with temperature and are much stronger at the nonlinearly dispersed edge states of native edges compared to the linearly dispersed edge states of passivated edges, causing a significant energy dissipation in the temperature range of 200-400 K. Overall, we argue that the e-ph interactions can be a crucial factor at finite temperatures in controlling the electronic transport at the topologically protected edge states.

First-Principles study of the structural, electronic, elastic, lattice dynamics and thermoelectric properties of the newly predicted half-heusler alloys NaYZ (Z = Si, Ge, Sn)

In this study, we applied Density Functional Theory (DFT) and Boltzmann Transport Theory to investigate the structural, electronic, lattice dynamic, elastic and thermometric properties of new half-Heusler compounds NaYZ (Z = Si, Ge, Sn). The structural optimization calculations revealed that the ZXY (1/4,1/2,0) phase have the most stable state with the least energy among others. Our calculated lattice constants in (Å) are found to be 6.861, 6.899, and 7.284 for NaYZ (Z = Si, Ge, Sn). Also, the calculated elastic constants satisfied the Born-Huang criteria and were found to be mechanically and elastically stable. The Density Functional Perturbation Theory (DFPT) was used to examined the lattice dynamics of the compounds and the results shown non-existence of negative frequencies all through dispersion band structures, thus all the compounds are dynamically stable. The Seebeck coefficient of the compounds at room temperature for the p-type (n-type) are 143.79 (−48.91) μ V/K, 132.49 (−48.86) μ V/K, 154.75 (−60.24) μ V/k for NaYZ (Z = Si, Ge, Sn). The modified Slack's approach was used to compute lattice thermal conductivity (kp) within the experimental range and the kp values obtained for NaYZ (Z = Si, Ge, Sn) at room temperature are 17.265 Wm −1 K −1, 14.671 W m−1K−1, 10.693 W m−1K−1, respectively. The computations of charge carriers relaxation time (τ = F(T)) as a function of temperature through deformation potential theory and the effective mass of charge carriers were used to evaluate the figure of merit (zT) for p-type and n-type of the materials. The maximum zT at 1200 K of τ = F(T) (τ = 10−13 s) are 1.76 (1.67), 1.73 (1.65), and 1.91 (1.88). These results show that τ = F(T) has improvement in determining the figure of merit as compared to the constant relaxation time (τ).