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Advancing simulations of coupled electron and phonon nonequilibrium dynamics using adaptive and multirate time integration

Electronic structure calculations in the time domain provide a deeper understanding of nonequilibrium dynamics in materials. The real-time Boltzmann equation (rt-BTE), used in conjunction with accurate interactions computed from first principles, has enabled reliable predictions of coupled electron and lattice dynamics. However, the timescales and system sizes accessible with this approach are still limited, with two main challenges being the different timescales of electron and phonon interactions and the cost of computing collision integrals. As a result, only a few examples of these calculations exist, mainly for two-dimensional (2D) materials. Here we leverage adaptive and multirate time integration methods to achieve a major step forward in solving the coupled rt-BTEs for electrons and phonons. Relative to conventional (non-adaptive) time-stepping, our approach achieves a 10x speedup for a target accuracy, or greater accuracy by 3–6 orders of magnitude for the same computational cost, enabling efficient calculations in both 2D and bulk materials. This efficiency is showcased by computing the coupled electron and lattice dynamics in graphene up to ~100 ps, as well as modeling ultrafast lattice dynamics and thermal diffuse scattering maps in bulk materials (silicon and gallium arsenide). In addition to improved efficiency, our adaptive method can resolve the characteristic rates of different physical processes, thus naturally bridging different timescales. This enables simulations of longer timescales and provides a framework for modeling multiscale dynamics of coupled degrees of freedom in matter. Our work opens new opportunities for quantitative studies of nonequilibrium physics in materials, including driven lattice dynamics with phonons coupled to electrons, spin, and other degrees of freedom.

Yao, Jia [California Institute of Technology (CalT↗

Electron-phonon interaction on optical spectra of nanoelectronic devices

Information obtained on the solid-state lattice dynamics by electron-phonon interaction between lattice phonons and electrons could open up to learn more about lattice dynamics and to apply it in nanoelectronic devices including software reliability, nano-size capacitors, master clock sources, as well as non-contact temperature probes on nano-electronic and photonicdevices.

electron-phonon interactions lattice dynamics SrTi↗

Coupled Vortex-Lattice Flight Dynamic Model with Aeroelastic Finite-Element Model of Flexible Wing Transport Aircraft with Variable Camber Continuous Trailing Edge Flap for Drag Reduction

This paper presents a coupled vortex-lattice flight dynamic model with an aeroelastic finite-element model to predict dynamic characteristics of a flexible wing transport aircraft. The aircraft model is based on NASA Generic Transport Model (GTM) with representative mass and stiffness properties to achieve a wing tip deflection about twice that of a conventional transport aircraft (10% versus 5%). This flexible wing transport aircraft is referred to as an Elastically Shaped Aircraft Concept (ESAC) which is equipped with a Variable Camber Continuous Trailing Edge Flap (VCCTEF) system for active wing shaping control for drag reduction. A vortex-lattice aerodynamic model of the ESAC is developed and is coupled with an aeroelastic finite-element model via an automated geometry modeler. This coupled model is used to compute static and dynamic aeroelastic solutions. The deflection information from the finite-element model and the vortex-lattice model is used to compute unsteady contributions to the aerodynamic force and moment coefficients. A coupled aeroelastic-longitudinal flight dynamic model is developed by coupling the finite-element model with the rigid-body flight dynamic model of the GTM.

Flexible Aicraft↗

Unravelling ultralow thermal conductivity in perovskite Cs2AgBiBr6: dominant wave-like phonon tunnelling and strong anharmonicity

Abstract Understanding the lattice dynamics and heat transport physics in the lead-free halide double perovskites remains an outstanding challenge due to their lattice dynamical instability and strong anharmonicity. In this work, we investigate the microscopic mechanisms of anharmonic lattice dynamics and thermal transport in lead-free halide double perovskite Cs 2 AgBiBr 6 from first principles. We combine self-consistent phonon calculations with bubble diagram correction and a unified theory of lattice thermal transport that considers both the particle-like phonon propagation and wave-like tunnelling of phonons. An ultra-low thermal conductivity at room temperature (~0.21 Wm −1 K −1 ) is predicted with weak temperature dependence( ~ T −0.34 ), in sharp contrast to the conventional ~T −1 dependence. Particularly, the vibrational properties of Cs 2 AgBiBr 6 are featured by strong anharmonicity and wave-like tunnelling of phonons. Anharmonic phonon renormalization from both the cubic and quartic anharmonicities are found essential in precisely predicting the phase transition temperature in Cs 2 AgBiBr 6 while the negative phonon energy shifts induced by cubic anharmonicity has a significant influence on particle-like phonon propagation. Further, the contribution of the wave-like tunnelling to the total thermal conductivity surpasses that of the particle-like propagation above around 310 K, indicating the breakdown of the phonon gas picture conventionally used in the Peierls-Boltzmann Transport Equation. Importantly, further including four-phonon scatterings is required in achieving the dominance of wave-like tunnelling, as compared to the dominant particle-like propagation channel when considering only three-phonon scatterings. Our work highlights the importance of lattice anharmonicity and wave-like tunnelling of phonons in the thermal transport in lead-free halide double perovskites.

Chemistry↗

Mechanical and Thermal Properties for Uranium and U–6Nb Alloy from First-Principles Theory

Elasticity, lattice dynamics, and thermal expansion for uranium and U–6Nb alloy (elastic moduli) are calculated from density functional theory that is extended to include orbital polarization (DFT+OP). Introducing 12.5 at.% of niobium, substitutionally, in uranium softens all the cii elastic moduli, resulting in a significantly softer shear modulus (G). Combined with a nearly invariant bulk modulus (B), the quotient B/G increases dramatically for U–6Nb, suggesting a more ductile material. Lattice dynamics from a harmonic model coupled with a DFT+OP electronic structure is applied for α uranium, and the obtained phonon density of states compares well with inelastic neutron-scattering measurements. The Debye temperature associated with the lattice dynamics falls within the range of experimentally observed Debye temperatures and it also validates our quasi-harmonic (QH) phonon model. The QH Debye–Grüneisen phonon method is combined with a DFT+OP electronic structure and used to explore the anisotropic thermal expansion in α uranium. The anomalous negative thermal expansion (contraction) of the b lattice parameter of the α-phase orthorhombic cell is relatively well reproduced from a free-energy model consisting of QH-phonon and DFT+OP electronic structure contributions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

High-Temperature Thermodynamics of Uranium from Ab Initio Modeling

We present high-temperature thermodynamic properties for uranium in its γ phase (γ-U) from first-principles, relativistic, and anharmonic theory. The results are compared to CALPHAD modeling. The ab initio electronic structure is obtained from density-functional theory (DFT) that includes spin–orbit coupling and an added self-consistent orbital-polarization (OP) mechanism for more accurate treatment of magnetism. The first-principles method is coupled to a lattice dynamics scheme that is used to model anharmonic lattice vibrations, namely, Self-Consistent Ab Initio Lattice Dynamics (SCAILD). The methodology can be summarized in the acronym DFT + OP + SCAILD. Upon thermal expansion, γ-U develops non-negligible magnetic moments that are included for the first time in thermodynamic theory. The all-electron DFT approach is shown to model γ-U better than the commonly used pseudopotential method. In addition to CALPHAD, DFT + OP + SCAILD thermodynamic properties are compared with other ab initio and semiempirical modeling and experiments. Our first-principles approach produces Gibbs free energy that is essentially identical to CALPHAD. The DFT + OP + SCAILD heat capacity is close to CALPHAD and most experimental data and is predicted to have a significant thermal dependence due to the electronic contribution.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Accurate quantification of lattice temperature dynamics from ultrafast electron diffraction of single-crystal films using dynamical scattering simulations

In ultrafast electron diffraction (UED) experiments, accurate retrieval of time-resolved structural parameters, such as atomic coordinates and thermal displacement parameters, requires an accurate scattering model. Unfortunately, kinematical models are often inaccurate even for relativistic electron probes, especially for dense, oriented single crystals where strong channeling and multiple scattering effects are present. This article introduces and demonstrates dynamical scattering models tailored for quantitative analysis of UED experiments performed on single-crystal films. As a case study, we examine ultrafast laser heating of single-crystal gold films. Comparison of kinematical and dynamical models reveals the strong effects of dynamical scattering within nm-scale films and their dependence on sample topography and probe kinetic energy. Applying to UED experiments on an 11 nm thick film using 750 keV electron probe pulses, the dynamical models provide a tenfold improvement over a comparable kinematical model in matching the measured UED patterns. Also, the retrieved lattice temperature rise is in very good agreement with predictions based on previously measured optical constants of gold, whereas fitting the Debye–Waller factor retrieves values that are more than three times lower. Altogether, these results show the importance of a dynamical scattering theory for quantitative analysis of UED and demonstrate models that can be practically applied to single-crystal materials and heterostructures.

36 MATERIALS SCIENCE↗

Thermodynamics of Plutonium Monocarbide from Anharmonic and Relativistic Theory

Thermodynamics of plutonium monocarbide is studied from first-principles theory that includes relativistic electronic structure and anharmonic lattice vibrations. Density-functional theory (DFT) is expanded to include orbital-orbital coupling in addition to the relativistic spin-orbit interaction for the electronic structure and it is combined with anharmonic, temperature dependent, lattice dynamics derived from the self-consistent ab initio lattice dynamics (SCAILD) method. The obtained thermodynamics are compared to results from simpler quasi-harmonic theory and experimental data. Formation enthalpy, specific heat, and Gibbs energy calculated from the anharmonic model are validated by direct comparison with a calculation of phase diagram (CALPHAD) assessment of PuC and sub-stochiometric PuC0.896. Overall, the theory reproduces CALPHAD results and measured data for PuC rather well, but the comparison is hampered by the sub-stoichiometric nature of plutonium monocarbide. It was found that a bare theoretical approach that ignores spin-orbit and orbital-orbital coupling (orbital polarization) of the plutonium 5f electrons promotes too soft phonons and Gibbs energies that are incompatible with that of the CALPHAD assessment of the experimental data. The investigation of PuC suggests that the electronic structure is accurately described by plutonium 5f electrons as “band like” and delocalized, but correlate through spin polarization, orbital polarization, and spin-orbit coupling, in analogy to previous findings for plutonium metal.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Enhancing Lattice Kinetic Schemes for Fluid Dynamics with Lattice-Equivariant Neural Networks

A new class of equivariant neural networks is presented, hereby dubbed lattice-equivariant neural networks (LENNs), designed to satisfy local symmetries of a lattice structure. The approach develops within a recently introduced framework aimed at learning neural network-based surrogate models’ lattice Boltzmann collision operators. Whenever neural networks are employed to model physical systems, respecting symmetries and equivariance properties has been shown to be key for accuracy, numerical stability, and performance. Here, hinging on ideas from group representation theory, trainable layers are defined whose algebraic structure is equivariant with respect to the symmetries of the lattice cell. In this work, the presented method naturally allows for efficient implementations, in terms of both memory usage and computational costs, supporting scalable training/testing for lattices in two spatial dimensions and higher (in which the size of symmetry group grows). The approach is validated and tested considering 2D and 3D flowing dynamics, both in laminar and turbulent regimes. It is compared with group-averaged-based symmetric networks and with plain, nonsymmetric, networks, showing how the presented approach unlocks the (a posteriori) accuracy and training stability of the former models and the train/inference speed of the latter networks. (LENNs are about one order of magnitude faster than group-averaged networks in 3D.) The work in this paper opens toward practical use of machine learning-augmented lattice Boltzmann CFD in real-world simulations.

97 MATHEMATICS AND COMPUTING↗

Ultrafast Suppression of the Ferroelectric Instability in KTaO 3

We use an x-ray free-electron laser to study the lattice dynamics following photoexcitation with ultrafast near-UV light (wavelength 266 nm, 50 fs pulse duration) of the incipient ferroelectric potassium tantalate, KT a O 3 . By probing the lattice dynamics corresponding to multiple Brillouin zones through the x-ray diffuse scattering with pulses from the Linac Coherent Light Source (LCLS) (wavelength 1.3 Å and < 10 fs pulse duration), we observe changes in the diffuse intensity associated with a hardening of the transverse acoustic phonon branches along Γ to X and Γ to M. Using force constants from density functional theory, we fit the quasiequilibrium intensity and obtain the instantaneous lattice temperature and density of photoexcited charge carriers. Additionally, the density functional theory calculations demonstrate that photoexcitation transfers charge from oxygen 2p derived π-bonding orbitals to Ta 5d derived antibonding orbitals, further suppressing the ferroelectric instability and increasing the stability of the cubic, paraelectric structure.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Quantum theory of laser-stimulated desorption

A quantum theory of laser-stimulated desorption (LSDE) is presented and critically analyzed. It is shown how LSDE depends on laser-pulse characteristics and surface-lattice dynamics. Predictions of the theory for a Debye model of the lattice dynamics are compared to recent experimental results.

Slutsky, M. S.↗

The Debye-Waller factor of disordered solids: The case for amorphous silicon

This paper presents a first-principles study of the Debye-Waller factor and the Debye temperature for amorphous silicon (α-Si) from lattice-dynamical calculations and direct molecular-dynamics simulations using density-functional theory (DFT). The effects of temperature and structural disorder on the intensity of the diffraction maxima and the vibrational mean-square displacement (MSD) of Si atoms are studied in the harmonic approximation, with particular emphasis on the bond-length disorder, the presence of coordination defects, and microvoids in α-Si networks. It has been observed that the MSDs associated with tetrahedrally bonded Si atoms are considerably lower than their dangling-bond counterparts—originating from isolated and vacancy-induced clustered defects—and those on the surface of microvoids, leading to an asymmetric non-Gaussian tail in the distribution of atomic displacements. An examination of the effect of anharmonicity on the MSD at high temperatures using direct ab initio molecular-dynamics simulations (without the harmonic approximation) suggests that the vibrational motion in α-Si is practically unaffected by anharmonic effects at temperatures below 400 K, as far as the present DFT calculations are concerned. The Debye temperature of α-Si is found to be in the range of 488–541 K from specific-heat and MSD calculations using first-principles lattice-dynamical calculations in the harmonic approximation, which matches closely with the experimental value of 487–528 K obtained from specific-heat measurements of α-Si at low temperatures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Evaluation of Thermal Scattering Law for U 3 Si 2 Using Temperature-Dependent Phonon Density of States

The thermal scattering law for uranium silicide, a candidate material for high-density nuclear fuel, was evaluated from the temperature-dependent phonon density of states obtained using the quasi-harmonic approximation. For uranium silicide model systems of various volumes near the equilibrium volume, Hellmann-Feynman forces were calculated by performing ab initio lattice dynamics simulations based on density functional theory. Subsequently, the quasi-harmonic approximation was applied by interpolating the results of the harmonic approximation for each volume system. As a sensitivity test, the phonon density of states was calculated for the structures with temperature-dependent volumes at 298 K and 1000 K, obtained by the quasi-harmonic approximation, and the corresponding thermal neutron scattering cross section was evaluated. The temperature-dependent volume and heat capacity of uranium silicide obtained by the quasi-harmonic approximation showed reasonable agreement with experimental data while lattice thermal expansion showed deviation from experimental observations. Thermal scattering cross sections evaluated from 0 K and temperature-dependent phonon density of states exhibited differences of up to 4.1% at 1000 K. This study examines the impact of temperature on the thermal scattering law, employing ab initio lattice dynamics simulations through the quasi-harmonic approximation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Observation of Extraordinary Vibration Scatterings Induced by Strong Anharmonicity in Lead‐Free Halide Double Perovskites

Abstract Lead‐free halide double perovskites provide a promising solution for the long‐standing issues of lead‐containing halide perovskites, i.e., the toxicity of Pb and the low stability under ambient conditions and high‐intensity illumination. Their light‐to‐electricity or thermal‐to‐electricity conversion is strongly determined by the dynamics of the corresponding lattice vibrations. Here, the measurement of lattice dynamics is presented in a prototypical lead‐free halide double perovskite(Cs 2 NaInCl 6 ). The quantitative measurements and first‐principles calculations show that the scatterings among lattice vibrations at room temperature are at the timescale of ≈1 ps, which stems from the extraordinarily strong anharmonicity in Cs 2 NaInCl 6 . Further the degree of anharmonicity of each type of atom is quantitatively characterized in the Cs 2 NaInCl 6 single crystal, which stems from the interatomic forces, and demonstrate that this strong anharmonicity is synergistically contributed by the bond hierarchy, the tilting of the NaCl 6 and InCl 6 octahedral units, and the rattling of Cs + ions. Consequently, the crystalline Cs 2 NaInCl 6 possesses an ultralow thermal conductivity of ≈0.43 W mK −1 at room temperature, and a weak temperature dependence ofT −0.41 . These findings uncovered the underlying mechanisms behind the dynamics of lattice vibrations in double perovskites, which can largely benefit the design of optoelectronics and thermoelectrics based on halide double perovskites.

Chemistry↗

Site-Selective Modification of Lanthanum Oxychloride to Modulate Halide-Ion Conduction

Design principles for solid-state halide-ion conduction remain poorly defined despite the increasing importance of halide ions as charge carriers in a variety of energy storage and electrochemical computing technologies. Here, we employ a siteselective modification strategy in which aliovalent cations are preferentially introduced at the La 3+ crystallographic site of LaOCl in the 2c Wyckoff position, enabling controlled generation of chloride vacancies and modification of lattice dynamics to enhance chloride-ion conductivity. Aliovalent substitution of La 3+ with Mg 2+ , Ca 2+ , and Sr 2+ generates charge-compensating Cl vacancies while preserving the matlockite crystal structure. X-ray excited optical luminescence measurements with Dy 3+ as a reporter chromophore evidence vacancy-derived midgap electronic states and an extended energy range of radiation-less Auger electron emission corresponding to substantial modification of electronic structure and local electrostatic potentials. Ca alloying at 8−10 at. % increases the chloride-ion conductivity by three- to 4 orders of magnitude as compared to unalloyed LaOCl, whereas comparable amounts of Sr- and Mg-alloying in LaOCl imbue less pronounced conductivity enhancements. Temperature-dependent Raman spectroscopy measurements reveal that Ca- and Sr-alloying substantially soften the La−Cl sublattice and yield a more compliant crystal lattice that can deform to accommodate Cl-ion migration. Structure solutions derived from Rietveld refinements to powder Xray diffraction reveal larger O−La−Cl bond-angle deviations and enhanced out-of-plane cation displacements for Ca- and Sr-alloyed compositions as compared to Mg-alloyed LaOCl. Such local distortions enhance chloride-ion mobility by reshaping and flattening vacancy migration energy landscapes and by modulating lattice dynamics governing anion conduction. We further illustrate that coalloying of Ca with Mg and Sr induces a nonmonotonic conductivity−defect stoichiometry relationship that can be rationalized based on cooperative interactions. Together, these results establish site-selective aliovalent alloying of LaOCl as an effective route to halide-ion solid electrolytes and provide broadly generalizable design principles for site-selective modification to induce vacancy formation and lattice softening to engender facile anion transport

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Trimeron-phonon coupling in magnetite

Using density functional theory, we study the lattice dynamical properties of magnetite (Fe 3 O 4 ) in the high-temperature cubic and low-temperature monoclinic phases. The calculated phonon dispersion curves and density of states are compared with the available experimental data obtained by inelastic neutron, inelastic x-ray, and nuclear inelastic scattering. We find a very good agreement between the theoretical and experimental results for the monoclinic Cc structure revealing the strong coupling between the charge-orbital (trimeron) order and specific phonon modes. For the cubic phase, clear discrepancies arise due to fluctuation effects, which are not included in the calculation method. Despite this shortcoming, we argue that the main spectral features can be understood assuming that the strong trimeron-phonon coupling is extended above the Verwey transition, with lattice dynamics influenced by the short-range order instead of the average cubic structure. Our results indicate the validity of trimerons (and trimeron-phonon coupling) to explain the physics of magnetite much beyond their original formulation.

36 MATERIALS SCIENCE↗

Nonthermal Bonding Origin of a Novel Photoexcited Lattice Instability in SnSe

Lattice dynamics measurements are often crucial tools for understanding how materials transform between different structures. Here, we report time-resolved x-ray scattering-based measurements of the nonequilibrium lattice dynamics in SnSe, a monochalcogenide reported to host a novel photoinduced lattice instability. By fitting interatomic force models to the fluence dependent excited-state dispersion, we determine the nonthermal origin of the lattice instability to be dominated by changes of interatomic interactions along a bilayer-connecting bond, rather than of an intralayer bonding network that is of primary importance to the lattice instability in thermal equilibrium.

36 MATERIALS SCIENCE↗