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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Onset of anharmonicity and thermal conductivity in SnSe

The anharmonicity in SnSe is investigated through the analysis of moments of 119Sn nuclear resonant inelastic x-ray scattering and ab initio molecular dynamics calculations. Experimental evidences show that the anharmonic behavior started around 300 K, substantially lower than the usually suggested structural transition at 800 K. Both theory and experiments reveal substantial lifetime broadening and frequency renormalization of the optical phonons. Additionally, thermal conductivities calculated from the temporal energy moment using the Einstein diffusion equation are in good agreement with previous experiments. The abrupt increase of the thermal power near 800 K is driven by an electronic factor and not by the enhanced anharmonicity due to structural change.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

First-Principles Phonon Quasiparticle Theory Applied to a Strongly Anharmonic Halide Perovskite

Understanding and predicting lattice dynamics in strongly anharmonic crystals is one of the long-standing challenges in condensed matter physics. Here we propose a first-principles method that gives accurate quasiparticle (QP) peaks of the phonon spectrum with strong anharmonic broadening. On top of the conventional first-order self-consistent phonon (SC1) dynamical matrix, the proposed method incorporates frequency renormalization effects by the bubble self-energy within the QP approximation. We apply the developed methodology to the strongly anharmonic α-CsPbBr 3 that displays phonon instability within the harmonic approximation in the whole Brillouin zone. While the SC1 theory significantly underestimates the cubic-to-tetragonal phase transition temperature (T c ) by more than 50%, we show that our approach yields T c = 404–423 K, in excellent agreement with the experimental value of 403 K. Furthermore, we also demonstrate that an accurate determination of QP peaks is paramount for quantitative prediction and elucidation of phonon linewidth.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

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↗
DOE OSTI2022

Anharmonic Cation–Anion Coupling Dynamics Assisted Lithium‐Ion Diffusion in Sulfide Solid Electrolytes

Abstract Sulfide‐based lithium superionic conductors often show higher Li‐ion conductivity than other types of electrolyte materials. This work unveils a unique Li‐ion conductive behavior in these materials through the perspective of anharmonic coupling assisted Li‐ion diffusion. Li hopping events can happen simultaneously with various types of lattice dynamics, while only a statistically important synchronization of motions may indicate coupling. This method enables a direct evaluation of the coupling strength between these motions, which more fundamentally decides if a specific type of lattice motion is really anharmonically coupled to the Li hopping event and whether the coupling can facilitate the Li diffusion. By a new ab initio computational approach, this work unveils a unique phenomenon in prototype sulfide electrolytes in comparison with typical halide ones, that Li‐ion conduction can be boosted by the anharmonic coupling of low‐frequency Li phonon modes with high‐frequency anion stretching or flexing phonon modes, rather than the low‐frequency rotational modes. The coupling pushes Li ions toward the diffusion channels for reduced diffusion barriers. The result from the lower temperature range (≈0–300 K) of simulation can also be more relevant to the application of solid‐state batteries.

Chemistry↗
DOE OSTI2025

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↗
DOE OSTI2022

Origin of ultralow phonon transport and strong anharmonicity in lead-free halide perovskites

All-inorganic lead-free halide double perovskites offer a promising avenue toward non-toxic, stable optoelectronic materials, properties that are missing in their prominent lead-containing counterparts. Their large thermopowers and high carrier mobilities also make them promising for thermoelectric applications. Here, in this work, we present a first-principles study of the lattice vibrations and thermal transport behaviors of Cs 2 SnI 6 and γ-CsSnI 3 , two prototypical compounds in this materials class. We show that conventional static zero temperature density functional theory (DFT) calculations severely underestimate the lattice thermal conductivities (κ l ) of these compounds, indicating the importance of dynamical effects. By calculating anharmonic renormalized phonon dispersions, we show that some optic phonons significantly harden with increasing temperature (T), which reduces the scattering of heat carrying phonons and enhances calculated κ l values when compared with standard zero temperature DFT. Furthermore, we demonstrate that coherence contributions to κ l , arising from wave like phonon tunneling, are important in both compounds. Overall, calculated κ l with temperature-dependent interatomic force constants, built from particle and coherence contributions, are in good agreement with available measured data, for both magnitude and temperature dependence. Large anharmonicity combined with low phonon group velocities yield ultralow values, with room temperature values of 0.26 W/m-K and 0.72 W/m-K predicted for Cs 2 SnI 6 and γ-CsSnI 3 , respectively. We further show that the lattice dynamics of these compounds are highly anharmonic, largely mediated by rotation of the SnI6 octahedra and localized modes originating from Cs rattling motion. These thermal characteristics combined with their previously computed excellent electronic properties make these perovskites promising candidates for optoelectronic and room temperature thermoelectric applications.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Anharmonic phonon dispersion in polyethylene

The second-order Green's function method for anharmonic crystals has been applied to an infinite, periodic chain of polyethylene taking into account up to quartic force constants. The frequency-independent approximation to the Dyson self-energy gives rise to numerous divergent resonances, which are fortuitous. Instead, solving the Dyson equation self-consistently with a frequency-dependent self-energy resists divergences from resonances or zero-frequency acoustic vibrations. Here, the calculated anharmonic phonon dispersion, which nonetheless displays many true resonances, and anharmonic phonon density of states furnish hitherto unknown details that explain smaller features of observed vibrational spectra.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Adsorbate Partition Functions via Phase Space Integration: Quantifying the Effect of Translational Anharmonicity on Thermodynamic Properties

A new method for computing anharmonic thermophysical properties for adsorbates on metal surfaces is presented. Classical Monte Carlo phase space integration is performed to calculate the partition function for the motion of a hydrogen atom on Cu(111). Here, a minima-preserving neural network potential energy surface is used within the integration routine. Two different sampling schema for generating the training data are presented, and two different density functionals are used. The results are benchmarked against direct state counting results by using discrete variable representation. The phase space integration results are in excellent quantitative agreement with the benchmark results. Additionally, both the discrete variable representation and the phase space integration results confirm that the motion of H on Cu(111) is highly anharmonic. The results were applied to calculate the free energy of dissociative adsorption of H 2 and the resulting Langmuir isotherms at 400, 800, and 1200 K in a partial pressure range of 0–1 bar. It shows that the anharmonic effects lead to significantly higher predicted surface site fractions of hydrogen.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

High-throughput computational framework for high-order anharmonic thermal transport in cubic and tetragonal crystals

Accurate first-principles prediction of lattice thermal conductivity (κL) remains challenging in identifying materials with extreme thermal behavior. While the harmonic approximation with three-phonon scattering (HA + 3ph) is now routine, reliable κL prediction often requires higher-order anharmonic effects, including self-consistent phonon renormalization, three- and four-phonon scattering, and off-diagonal heat flux (SCPH + 3, 4ph + OD). We present a state-of-the-art high-throughput workflow that unifies these effects and apply it to 773 cubic and tetragonal crystals spanning diverse chemistries and structures. From 562 dynamically stable compounds, we assess the hierarchical impacts of higher-order anharmonicity. For around 60% of materials, HA + 3ph predictions closely match those from SCPH + 3, 4ph + OD. SCPH generally increases κ L , by over 8 times in extreme cases, whereas four-phonon scattering universally suppresses κ L , sometimes to 15% of the HA + 3ph value. Off-diagonal contributions are negligible in high-κ L systems but can rival diagonal terms in highly anharmonic low-κ L compounds. We highlight four case studies, Rb 2 TlAlH 6 , Cu 3 VSe 4 , CuBr, and KTlCl 4 , that exhibit distinct extreme behaviors. This work delivers not only a robust workflow for high-fidelity κL dataset but also a quantitative framework to determine when higher-order effects are essential. The hierarchy of κ L results, from the HA + 3ph to SCPH + 3, 4ph + OD level, offers a scalable, interpretable route to discovering next-generation extreme thermal materials.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Database and deep-learning scalability of anharmonic phonon properties by automated brute-force first-principles calculations

Understanding the anharmonic phonon properties of crystal compounds—such as phonon lifetimes and thermal conductivities—is essential for investigating and optimizing their thermal transport behaviors. These properties also impact optical, electronic, and magnetic characteristics through interactions between phonons and other quasiparticles and fields. In this study, we develop an automated first-principles workflow to calculate anharmonic phonon properties and build a comprehensive database encompassing more than 6500 inorganic compounds. Utilizing this dataset, we train a graph neural network model to predict thermal conductivity values and spectra from structural parameters, demonstrating a scaling law in which prediction accuracy improves with increasing training data size. High-throughput screening with the model enables the identification of materials exhibiting extreme thermal conductivities—both high and low. The resulting database offers valuable insights into the anharmonic behavior of phonons, thereby accelerating the design and development of advanced functional materials.

Ohnishi, Masato [University of Tokyo (Japan); Inst↗
DOE OSTI2020

Density functional study of relaxation of adsorbate vibration modes: Dominance of anharmonic interaction

Formulation and density functional workflow for calculating the lifetime of vibrational modes of molecular adsorbates on solid surfaces due to vibration–phonon coupling are presented. The anharmonic coupling is invoked to give the correct description of the origin of temperature dependence. Using pyrrolidine (C 4 H 9 N) absorbed on the Cu(001) surface as a concrete example, here we show that the anharmonic coupling can be one to two orders more significant than the harmonic interaction for the broadening of vibrational spectra, especially as temperature increases. These results challenge the common assumption that the anharmonic interaction is weak and call for attention of considering its effect in quantum relaxation and related problems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Prediction and observation of intermodulation sidebands from anharmonic phonons in NaBr

A quantum Langevin model, like models from optomechanics, was developed for phonons. It predicts intermodulation phonon sidebands (IPSs) in anharmonic crystals. Ab initio calculations of anharmonic phonons in rock-salt NaBr showed these spectral features as many-body effects. Modern inelastic neutron scattering measurements on a crystal of NaBr at 300 K revealed diffuse intensity at high phonon energy from a predicted upper IPS. The transverse optical (TO) part of the new features originates from phonon intermodulation between the transverse acoustic (TA) and TO phonons. The longitudinal optical spectral features originate from three-phonon coupling between the TA modes and the TO lattice modes. The partner lower IPS proves to be an intrinsic localized mode. Interactions with the thermal bath broaden and redistribute the spectral weight of the IPS pair. These sidebands are a probe of the anharmonicity and quantum noise of phonons in NaBr and suggest novel interactions between photons and phonons.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Elucidating the atomistic origin of anharmonicity in tetragonal CH3NH3PbI3 with Raman scattering

Halide perovskite (HP) semiconductors exhibit unique strong coupling between the electronic and structural dynamics. In this work, we use Raman polarization-orientation (PO) measurements and ab initio molecular dynamics (AIMD) to investigate the origin and temperature evolution of the strong structural anharmonicity throughout the tetragonal phase of CH 3 NH 3 PbI 3 . Raman PO measurements reveal a soft modelike spectral feature. This mode shows an unusual continuous increase in damping with temperature which is indicative of an anharmonic potential surface. The analysis of AIMD trajectories identifies two major sources of anharmonicity: the orientational unlocking of the [CH 3 NH 3 ] + ions and large-amplitude octahedral tilting that continuously increases with temperature. Our work suggests that the standard phonon picture cannot describe the structural dynamics of tetragonal CH 3 NH 3 PbI 3 .

36 MATERIALS SCIENCE↗
DOE OSTI2023

Correlated anharmonicity and dynamic disorder control carrier transport in halide perovskites

Halide pervoskites are an important class of semiconducting materials that hold great promise for optoelectronic applications. In this work we investigate the relationship between vibrational anharmonicity and dynamic disorder in this class of solids. Via a multiscale model parametrized from first-principles calculations, we demonstrate that the non-Gaussian lattice motion in halide perovskites is microscopically connected to the dynamic disorder of overlap fluctuations among electronic states. This connection allows us to rationalize the emergent differences in temperature-dependent mobilities of prototypical MAPbI 3 and MAPbBr 3 compounds across structural phase transitions, in agreement with experimental findings. In conclusion, our analysis suggests that the details of vibrational anharmonicity and dynamic disorder can complement known predictors of electronic conductivity and can provide structure-property guidelines for the tuning of carrier transport characteristics in anharmonic semiconductors.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Anharmonic Exciton‐Phonon Coupling in Metal‐Organic Chalcogenides Hybrid Quantum Wells

Abstract In contrast to inorganic quantum wells, hybrid quantum wells (HQWs) based on metal‐organic semiconductors are characterized by relatively soft lattices, in which excitonic states can strongly couple to lattice phonons. Therefore, understanding the lattice's impact on exciton dynamics is essential for harnessing the optoelectronic potential of HQWs. Beyond 2D metal halide perovskites, layered metal‐organic chalcogenides (MOCs), which are an air‐stable, underexplored material class hosting room‐temperature excitons, can be exploited as photodetectors, light emitting devices, and ultrafast photoswitches. Here, the role of phonons in the optical transitions of the prototypical MOC [AgSePh] ∞ is elucidated. Impulsive stimulated Raman scattering (ISRS) allows the detection of coherent exciton oscillations driven by Fröhlich interaction with low‐energy optical phonons. Steady state absorption and Raman spectroscopies reveal a strong exciton‐phonon coupling (Huang‐Rhys parameter ≈1.7) and its anharmonicity, manifested as a nontrivial temperature‐dependent Stokes shift. The ab initio calculations support these observations, hinting at an anharmonic behavior of the low‐energy phonons <200 cm −1 . These results untangle complex exciton‐phonon interactions in MOCs, establishing an ideal testbed for room‐temperature many‐body phenomena.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Lone-Electron-Pair Micelles Strengthen Bond Anharmonicity in MnPb16Sb14S38 Complex Sulfosalt Leading to Ultra-Low Thermal Conductivity

Designing crystalline solids in which intrinsic extremely low lattice thermal conductivity mainly arises from its unique bonding nature rather than structure complexity and/or atomic disorder could promote thermal energy manipulation and utilization for applications ranging from thermoelectric energy conversion to thermal barrier coatings. Here, we report an extremely low lattice thermal conductivity of ~0.34 W m-1 K-1 at 300 K in the new complex sulfosalt MnPb16Sb14S38. We attribute the ultra-low lattice thermal conductivity to a synergistic combination of scattering mechanisms involving (1) strong bond anharmonicity in various structural building units, owing to the presence of stereoactive lone-electron-pair (LEP) micelles, and (2) phonon scattering at the interfaces between building units of increasing size and complexity. Remarkably, low-temperature heat capacity measurement revealed a Cp value of 0.206 J g-1 K-1 at T > 300 K, which is 22% lower than the Dulong-Petit value (0.274 J g-1 K-1). Further analysis of the Cp data and sound velocity (ν = 1834 m/s) measurement yielded Debye temperature values of 161 K and 187 K, respectively. Here, the resulting Grüneisen parameter, γ = 1.65, further supports strong bond anharmonicity as the dominant mechanism responsible for the observed extremely low lattice thermal conductivity.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Configuration Space Integration for Adsorbate Partition Functions: The Effect of Anharmonicity on the Thermophysical Properties of CO–Pt(111) and CH 3 OH–Cu(111)

A method for computing anharmonic thermophysical properties for adsorbates on metal surfaces has been extended to include libration, or frustrated rotation. Classical phase space integration is used with Monte Carlo sampling of the configuration space to obtain the partition function of CO on Pt(111) and CH 3 OH on Cu(111). A minima-preserving neural network potential energy surrogate is used within the integration routines. Direct state counting using discrete variable representation is used to benchmark the results. We find that the phase space integration approach is in excellent agreement with the direct state counting results. Comparison with standard models such as the harmonic oscillator indicates that anharmonicity contributes significantly to the thermodynamic properties of CH 3 OH on Cu(111). We find that there is also a considerable difference between the harmonic oscillator and phase space integration for CO on Pt(111), although the discrepancy can largely be attributed to the presence of multiple binding sites within the unit cell. We demonstrate that a multisite harmonic oscillator model might be sufficient for CO-Pt(111). A more thorough description of the potential energy surface, which can be achieved with phase space integration, is necessary for weakly bound adsorbates such as CH 3 OH. In conclusion, the thermophysical properties were used to calculate free energies of adsorption on the respective metals, and subsequently the equilibrium constants and Langmuir isotherms in relevant temperature ranges. The results show that the choice of model to obtain partition functions greatly affects the resulting surface coverages in kinetic models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Finite-temperature many-body perturbation theory for anharmonic vibrations: Recursions, algebraic reduction, second-quantized reduction, diagrammatic rules, linked-diagram theorem, finite-temperature self-consistent field, and general-order algorithm

A unified theory is presented for finite-temperature many-body perturbation expansions of the anharmonic vibrational contributions to thermodynamic functions, i.e., the free energy, internal energy, and entropy. The theory is diagrammatically size-consistent at any order, as ensured by the linked-diagram theorem proved in this study, and, thus, applicable to molecular gases and solids on an equal footing. It is also a basis-set-free formalism, just like its underlying Bose–Einstein theory, capable of summing anharmonic effects over an infinite number of states analytically. It is formulated by the Rayleigh–Schrödinger-style recursions, generating sum-over-states formulas for the perturbation series, which unambiguously converges at the finite-temperature vibrational full-configuration-interaction limits. Two strategies are introduced to reduce these sum-over-states formulas into compact sum-over-modes analytical formulas. One is a purely algebraic method that factorizes each many-mode thermal average into a product of one-mode thermal averages, which are then evaluated by the thermal Born–Huang rules. Canonical forms of these rules are proposed, dramatically expediting the reduction process. The other is finite-temperature normal-ordered second quantization, which is fully developed in this study, including a proof of thermal Wick’s theorem and the derivation of a normal-ordered vibrational Hamiltonian at finite temperature. The latter naturally defines a finite-temperature extension of size-extensive vibrational self-consistent field theory. These reduced formulas can be represented graphically as Feynman diagrams with resolvent lines, which include anomalous and renormalization diagrams. Two order-by-order and one general-order algorithms of computing these perturbation corrections are implemented and applied up to the eighth order. The results show no signs of Kohn–Luttinger-type nonconvergence.

74 ATOMIC AND MOLECULAR PHYSICS↗