Interatomic Force Constants Research Articles

Theoretical investigation of the thermal conductivity of Ga2O3 polymorphs

Gallium oxide (Ga2O3) is a promising thermal preserving and heat-insulating material; understanding the thermal properties is important to improve its performance in technological applications. The thermal conductivities of Ga2O3 polymorphs labeled as α, β, δ, and ε are computed via the Boltzmann phonon transport equation (BTE) employing first-principles techniques. The lattice thermal conductivity tensor k of Ga2O3 for temperatures ranging from 50 K to 1000 K is derived using the second and third-order interatomic force constants (IFCs) for the potential based on a generalized gradient approximation (GGA), as well as the phonon dispersion relation, projected density of states (PDOS), and phonon group velocities. The results agree with the observed experimental values of rhombohedral polymorph β-Ga2O3 and with the previously calculated results of the other phases. At room temperature, the predicted thermal conductivity of the δ-Ga2O3 phase is 15.6 W/(m•K). By breaking down k into mode contributions, it is projected that the optical phonons contribute significantly to the lattice thermal conductivity because of a peculiar phonon dispersion relation.

Revisiting thermal transport in CuInTe2: Role of temperature-dependent anharmonicity and higher-order phonon–phonon interactions

The temperature-dependent phonon thermal transport in CuInTe2 is investigated by considering lattice thermal expansion, temperature-dependent anharmonicity, higher-order phonon–phonon interactions, and phonon renormalization with input from first-principles based density functional theory calculations. Incorporating these higher-order temperature-dependent effects reveals that the thermal conductivity varies with temperature as T−1.59 consistent with experimental measurements ranging from T−1.62 to T−1.78. Using the lowest-order theory or only temperature-dependent interatomic force constants or four-phonon scattering resulted in a wrong description of thermal transport physics.

Thermal properties of In2O3 and α-Ga2S3 compounds

We investigate the thermal conductivity of In₂O₃ and α-Ga₂S₃ lattices using simulations based on the Boltzmann phonon transport equation (BTE) and first-principles calculations. The study employs a real-space finite displacement method to determine the second- and third-order interatomic force constants (IFCs), which are critical for solving the BTE iteratively. Our findings indicate that In₂O₃ and α-Ga₂S₃ exhibit relatively low thermal conductivities compared to other wide-bandgap semiconductors. At room temperature (300 K), the calculated isotropic thermal conductivity of cubic In₂O₃ is 16.2 Wm−1K⁻1. For monoclinic α-Ga₂S₃, the three principal components of thermal conductivity are 17.0, 20.7, and 15.2 W m⁻1 K⁻1, depending on the crystallographic direction. This low thermal conductivity is primarily attributed to significant phonon scattering via three-phonon processes. Furthermore, we estimate the phonon mean free path (MFP) to be approximately 56 nm for In₂O₃ and between 198 and 231 nm for α-Ga₂S₃, varying with crystal orientation. These findings offer valuable insights into the thermal transport properties of In₂O₃ and α-Ga₂S₃, highlighting their potential for thermoelectric applications while delineating the constraints these properties impose on their use in electronic devices.

Composition-Dependent Phonon and Thermodynamic Characteristics of C-Based XxY1−xC (X, Y ≡ Si, Ge, Sn) Alloys

Novel zinc-blende (zb) group-IV binary XC and ternary XxY1−xC alloys (X, Y ≡ Si, Ge, and Sn) have recently gained scientific and technological interest as promising alternatives to silicon for high-temperature, high-power optoelectronics, gas sensing and photovoltaic applications. Despite numerous efforts made to simulate the structural, electronic, and dynamical properties of binary materials, no vibrational and/or thermodynamic studies exist for the ternary alloys. By adopting a realistic rigid-ion-model (RIM), we have reported methodical calculations to comprehend the lattice dynamics and thermodynamic traits of both binary and ternary compounds. With appropriate interatomic force constants (IFCs) of XC at ambient pressure, the study of phonon dispersions ωjq→ offered positive values of acoustic modes in the entire Brillouin zone (BZ)—implying their structural stability. For XxY1−xC, we have used Green’s function (GF) theory in the virtual crystal approximation to calculate composition x, dependent ωjq→ and one phonon density of states gω. With no additional IFCs, the RIM GF approach has provided complete ωjq→ in the crystallographic directions for both optical and acoustical phonon branches. In quasi-harmonic approximation, the theory predicted thermodynamic characteristics (e.g., Debye temperature ΘD(T) and specific heat Cv(T)) for XxY1−xC alloys. Unlike SiC, the GeC, SnC and GexSn1−xC materials have exhibited weak IFCs with low [high] values of ΘD(T) [Cv(T)]. We feel that the latter materials may not be suitable as fuel-cladding layers in nuclear reactors and high-temperature applications. However, the XC and XxY1−xC can still be used to design multi-quantum well or superlattice-based micro-/nano devices for different strategic and civilian application needs.

Anisotropic phonon properties in SiP2 monolayer: A first-principles study

Recently, the micromechanical exfoliation method has effectively separated the two-dimensional (2D) SiP2 flake, which exhibits superior performance in field-effect transistors and photodetectors. In this paper, first-principles calculations were utilized to investigate the phononic properties of a SiP2 monolayer, which would be significant to explain the thermal deformation of 2D SiP2-based devices. We found that the acoustic phonon branches of SiP2 monolayer demonstrate significant in-plane anisotropy. The anisotropic ratios for the group velocities are 2.41 and 1.66 for the longitudinal and transverse acoustic modes, respectively. Meanwhile, the anisotropic ratio of the negative thermal expansion coefficient only considering the contribution from acoustic phonons is 0.14, while this ratio is ∼0.279 occurs at 120 K when both acoustic and optical phonons are taken into account. For the Raman-active optical phonons, the largest Grüneisen constant of these Raman-active phonons reaches 22.76, while the largest anisotropic ratio of phonon frequency is up to 2.16. To interpret this significant in-plane anisotropy, we calculated the electron density distribution, crystal orbital Hamilton populations (COHP) and interatomic force constants (IFCs), and found the maximal IFC in the x-direction is 5.79 times greater than y-direction, suggesting it as a major origin of the phononic anisotropy.

Self-consistent phonon calculations and quartic anharmonic lattice thermal conductivity in 2D InS monolayer

Low lattice thermal conductivity (κl) is a crucial factor for higher figure-of merit and hence the efficiency of thermoelectric generators. There are several reports on intrinsically low κl values in two-dimensional (2D) van der Waals materials using density functional theory and molecular dynamics simulations. In general, phonon dispersions are studied at absolute zero temperature using the finite-displacement approach within harmonic approximations. In addition, the κlis calculated using the third-order cubic interatomic force constants (IFCs) by solving the Boltzmann transport equation for phonons. In these calculations, we use quartic IFCs to solve self-consistent phonon equations to obtain dynamical dispersion relations at a finite temperature of 300 K using finite-temperature Green’s function for Bosonic systems in 2D indium sulfide (InS) monolayer. The cubic and quartic IFCs are calculated using machine learning algorithms, namely, the ordinary least square fitting and the least absolute shrinkage and selection operator. It was found that there is a lowering of the renormalized anharmonic phonon frequencies in the dispersion relations at 300 K upon the inclusion of quartic IFCs and anharmonic terms in the case of the InS monolayer. Thus, the κlvalue is reduced to 0.6 W/mK as compared to 0.9 W/mK obtained using cubic IFCs.

Analysis of thermal diffuse scattering intensity of scandium oxide (Sc<sub>2</sub>O<sub>3</sub>)

Atoms in crystals will generate thermal diffuse scattering during thermal vibration. Thermal diffuse scattering analysis has great potential applications in condensed matter physics and material science research. Scandium oxide (Sc<sub>2</sub>O<sub>3</sub>) has unique physical and chemical properties, which make it have high research and application value. In this work, X-ray diffraction experiment is performed on Sc<sub>2</sub>O<sub>3</sub> at room temperature of 26℃. The thermal diffuse scattering intensity exhibits a clear vibrational shape. The full diffraction back-based intensity equation of Sc<sub>2</sub>O<sub>3</sub> is expanded, and the theoretical value of the thermal diffuse scattering intensity is calculated until the full diffraction back-based intensity spectrum of the 14th nearest atom (<i>r</i> = 0.3816nm) is calculated. By fitting the theoretical value to the experimental value, we can see the inter-atomic thermal vibration correlation effect <i>μ</i> values corresponding to the nearest neighbor atom to the 7th nearest neighbor atom, the values of distance <i>r</i> from the nearest neighbor atom to the 7th nearest neighbor atom are 0.2067, 0.2148, 0.2161, 0.2671, 0.2945, 0.3229 and 0.3265nm, respectively, corresponding to their inter-atomic thermal vibration correlation effect <i>μ</i> values of 0.64, 0.63, 0.62, 0.61, 0.60, 0.58 and 0.57. Research result shows that the intensity of thermal diffuse scattering in Sc<sub>2</sub>O<sub>3</sub> is closely related to the atomic thermal vibration, the most significant influence on the vibration shape of thermal diffuse scattering intensity is the thermal vibration correlation effect between the 7th nearest atom Sc<sub>1</sub>-Sc<sub>2</sub>. Inter-atomic thermal vibration correlation effect <i>μ</i> values will provide important parameters for studying the mechanical and thermal properties of materials, laying the foundation for the next-step calculating specific heat and interatomic force constant, and thus playing a crucial role in the use and development of materials.

Higher-order anharmonicity and strain impact on the lattice thermal conductivity of monolayer InTe

In this work, we calculated the lattice thermal conductivity of monolayer InTe by means of phonon Boltzmann transport theory with first-principles calculated inter-atomic force constants. The higher-order phonon anharmonicity was found to play a strong impact on thermal transport in InTe. With the involvement of the phonon–phonon scattering process up to the fourth-order, the in-plane lattice thermal conductivity of monolayer InTe is 5.1 W m−1 K−1 at room temperature, which is 35% of that considering only third-order force constants. Furthermore, strain was found to be an effective way to manipulate the thermal transport in InTe, which reduces to one half when applying 5% in-plane tensile strain. The strain adjustment is due to the decreases in the phonon group velocity as well as the increase in the phonon scattering rates. These findings can enrich thermal transport properties of group-III monochalcogenides and benefit the material design of thermoelectrics and thermal management electronic devices.

Extreme sensitivity of higher-order interatomic force constants and thermal conductivity to the energy surface roughness of exchange-correlation functionals

In this Letter, we report that the fourth-order interatomic force constants (4th-IFCs) are significantly sensitive to the energy surface roughness of exchange-correlation (XC) functionals in density functional theory calculations. This sensitivity, which is insignificant for the second- (2nd-) and third-order (3rd-) IFCs, varies for different functionals in different materials and can cause misprediction of thermal conductivity by several times of magnitude. As a result, when calculating the 4th-IFCs using the finite difference method, the atomic displacement needs to be taken large enough to overcome the energy surface roughness, in order to accurately predict phonon lifetime and thermal conductivity. We demonstrate this phenomenon on a benchmark material (Si), a high-thermal conductivity material (BAs), and a low thermal conductivity material (NaCl). For Si, we find that the LDA, PBE, and PBEsol XC functionals are all smooth to the 2nd- and 3rd-IFCs but all rough to the 4th-IFCs. This roughness can lead to a prediction of nearly one order of magnitude lower thermal conductivity. For BAs, all three functionals are smooth to the 2nd- and 3rd-IFCs, and only the PBEsol XC functional is rough for the 4th-IFCs, which leads to a 40% underestimation of thermal conductivity. For NaCl, all functionals are smooth to the 2nd- and 3rd-IFCs but rough to the 4th-IFCs, leading to a 70% underprediction of thermal conductivity at room temperature. With these observations, we provide general guidance on the calculation of 4th-IFCs for an accurate thermal conductivity prediction.

Temperature-dependent interatomic force constants and phonon coherent resonance contribution in quaternary non-centrosymmetric chalcogenides BaAg2SnSe4

Phonon heat transfer by thermoelectric modules undoubtedly plays a pivotal role for the future waste heat recovery and utilization. BaAg2SnSe4, a prototypical glasslike compound among quaternary non-centrosymmetric chalcogenides, demonstrates remarkable thermoelectric performance due to its exceptionally low lattice thermal conductivity (κL). Even with a comprehensive grasp of the underlying cause behind ultra-low κL and the subsequent heightened thermoelectric conversion efficiency, the temperature-dependent lattice dynamics and glass-like attributes governing κL continue to pose unresolved questions. In this study, we investigate the phonon thermal transport properties of quaternary BaAg2SnSe4 by incorporating the influence of phonon coherent resonance, thereby departing from the conventional Peierls's framework. Based on the temperature dependence of the interatomic force constants and coherences’ contribution to total lattice thermal conductivity (κL(C)), we intriguingly observe that the particle-like driven lattice thermal conductivity (κL(P)) and κL(C) have the quite significant and dominant role for describing ultralow phonon transport behaviors in the middle-high-temperature regions. Specially, enhanced phonon anharmonicity coupled with excited coherent phonons due to increasing temperature yields two close values, with 700 K values of 0.16 and 0.13 W/mK predicted for BaAg2SnSe4, respectively, accelerating its application in thermoelectric field. Furthermore, we also find that the off-diagonal terms of heat flux operators in κL exist distinction for different phonons, with zero contribution modes exhibiting temperature-independent phonon coherence effect. Temperature response of the force constants tensors and coherent resonance proposed in our work can be employed as a powerful tool, which would substantially be expected to inspire a broad revisiting phonon transport study in various device applications, including advanced thermal barrier coatings and superior thermoelectrics.

Glass-like Transport Dominates Ultralow Lattice Thermal Conductivity in Modular Crystalline Bi4O4SeCl2.

Crystalline Bi4O4SeCl2 exhibits record-low 0.1 W/mK lattice thermal conductivity (κL), but the underlying transport mechanism is not yet understood. Using a theoretical framework which incorporates first-principles anharmonic lattice dynamics into a unified heat transport theory, we compute both the particle-like and glass-like components of κL in crystalline and pellet Bi4O4SeCl2 forms. The model includes intrinsic three- and four-phonon scattering processes and extrinsic defect and extended defect scattering contributing to the phonon lifetime, as well as temperature-dependent interatomic force constants linked to phonon frequency shifts and anharmonicity. Bi4O4SeCl2 displays strongly anisotropic complex crystal behavior with dominant glass-like transport along the cross-plane direction. The uncovered origin of κL underscores an intrinsic approach for designing extremely low κL materials.

Anisotropic Mechanical Properties of Orthorhombic SiP2 Monolayer: A First-Principles Study.

In recent years, the two-dimensional (2D) orthorhombic SiP2 flake has been peeled off successfully by micromechanical exfoliation and it exhibits an excellent performance in photodetection. In this paper, we investigated the mechanical properties and the origin of its anisotropy in an orthorhombic SiP2 monolayer through first-principles calculations, which can provide a theoretical basis for utilizing and tailoring the physical properties of a 2D orthorhombic SiP2 in the future. We found that the Young's modulus is up to 113.36 N/m along the a direction, while the smallest value is only 17.46 N/m in the b direction. The in-plane anisotropic ratio is calculated as 6.49, while a similar anisotropic ratio (~6.55) can also be observed in Poisson's ratio. Meanwhile, the in-plane anisotropic ratio for the fracture stress of the orthorhombic SiP2 monolayer is up to 9.2. These in-plane anisotropic ratios are much larger than in black phosphorus, ReS2, and biphenylene. To explain the origin of strong in-plane anisotropy, the interatomic force constants were obtained using the finite-displacement method. It was found that the maximum of interatomic force constant along the a direction is 5.79 times of that in the b direction, which should be considered as the main origin of the in-plane anisotropy in the orthorhombic SiP2 monolayer. In addition, we also found some negative Poisson's ratios in certain specific orientations, allowing the orthorhombic SiP2 monolayer to be applied in next-generation nanomechanics and nanoelectronics.

Intrinsically Low Thermal Conductivity in the Most Lithium-Rich Binary Stannide Crystalline Li5Sn.

Using ab initio lattice dynamics and a unified heat transport theory, we compute the lattice thermal conductivity (κL) of Li5Sn, a newly synthesized crystalline material for Li-ion batteries. The weak bonding in the Li-rich environment leads to significant softening of the optical phonon modes, temperature-induced hardening, and strong anharmonicity. This complexity is captured in the particle-like and glass-like components of κL by accounting for the temperature-dependent interatomic force constants acting on the renormalized phonon frequencies and three- and four-phonon scatterings contributing to the phonon lifetime. We predict very low room-temperature κL values of 0.857, 0.599, and 0.961 W/mK for the experimental Cmcm phase and 0.996, 0.908, and 1.385 W/mK for the theoretically predicted Immm phase along the main crystallographic directions. Both phases display complex crystal behavior with glass-like transport exceeding 20% above room-temperature and an unusual κL temperature dependence. Our results can be used to inform system-level thermal models of Li-ion batteries.

Identification of Material Dimensionality Based on Force Constant Analysis.

Identification of low-dimensional structural units from the bulk atomic structure is a widely used approach for discovering new low-dimensional materials with new properties and applications. Such analysis is usually based solely on bond-length heuristics, whereas an analysis based on bond strengths would be physically more justified. Here, we study dimensionality classification based on the interatomic force constants of a structure with different approaches for selecting the bonded atoms. The implemented approaches are applied to the existing database of first-principles calculated force constants with a large variety of materials, and the results are analyzed by comparing them to those of several bond-length-based classification methods. Depending on the approach, they can either reproduce results from bond-length-based methods or provide complementary information. As an example of the latter, we managed to identify new non-van der Waals two-dimensional material candidates.

Suppression of intervalley scattering and enhanced phonon anharmonic interactions in 2D Bi2TeSe2: Crystal-field symmetry and band convergence

The electron-phonon (el-ph) and phonon-phonon interactions play a key role in determining electronic and thermal transport properties, respectively, in promising two-dimensional (2D) semiconductor devices. In this study, we investigated el-ph interactions using Wannier-Fourier interpolation method and renormalized phonon scattering considering finite-temperature effects in Bi2TeSe2 monolayer. The results show that the optical phonon modes dominate the carrier scattering, where level repulsion induced by crystal field splitting and spin-orbit coupling (SOC) effect effectively suppresses intervalley scattering, leading to high hole mobility. Moreover, the strong anharmonicity in Bi2TeSe2 monolayer results in the temperature-dependent softening of its optical phonons, along with a corresponding variation in interatomic force constants (IFCs). As a result, the lattice thermal conductivity is remarkably low and exhibits weak temperature dependence. Finally, the predicted dimensionless thermoelectric figure of merit exceeds unity in the range of 200–800 K, indicating the potential of Bi2TeSe2 monolayer for thermoelectric applications. This work provides new insights into the elimination of intervalley scattering by crystal field splitting and SOC effects, and paves the way for the evaluation of thermoelectric properties of materials with complex scattering mechanisms and strong anharmonicity.

Two-channel thermal transport and scattering channel of high-temperature phase SnSe using temperature-dependent effective potential

To resolve the imaginary phonon frequency of high-temperature phase SnSe (853 K) caused by ground-state theory, the temperature-dependent effective potential (TDEP) method is used to evaluate the temperature-dependent interatomic force constants (IFCs). Based on the Boltzmann transport equation, both two-channel transport and scattering channel are studied using the temperature-dependent IFCs. Considering three-phonon and four-phonon scattering, the particle-like thermal conductivity along the xx axis, yy axis, and zz axis is 0.66, 0.34, and 0.61 W/mK, respectively. For glass-like thermal conductivity, the value along the xx axis, yy axis, zz axis are 0.0777, 0.0316, and 0.0791 W/mK, respectively. For the three-phonon scattering channel, the scattering channels of X + O/A→O and X→O+O/A play a major role. For four-phonon scattering channel, the major scattering channels are X + O+A→O, X + A+A→O, X + O-O/A→A, X + A-O→A, X-O/A-O/A→O, X-O-A→A. By utilizing the crystal orbital Hamilton population (COHP) analysis, the low lattice thermal conductivity is attributed to the weak chemical bonds from anti-bonding orbitals between Se4p and Sn5s states. This work provides new insight into the physical mechanisms for thermal transport of high-temperature phase SnSe with strong anharmonic effects.

Lattice thermal conductivity of two-dimensional CrB4 and MoB4 monolayers against Slack’s guideline

Two-dimensional (2D) CrB4 and MoB4 monolayers are typical graphene-like materials with excellent electrical transport properties and high structural stability. Yet, their thermal transport properties are unknown. By first-principles calculations and solving the Boltzmann transport equation iteratively, we report low lattice thermal conductivity (κl) of CrB4 and MoB4 monolayers. At room temperature, κl of CrB4 and MoB4 monolayers are 31.19 and 96.59 W/mK, respectively. This trend is against the well-known Slack’s guideline that the same type of materials with greater atomic mass generally have lower κl. The cause of this anomaly is analyzed from the first-principles harmonic and anharmonic parameters. It is surprising that no obvious correlation is observed between three-phonon scattering rates and mode Grüneisen parameters, despite their common determination by third-order interatomic force constants and one-to-one mode correspondence. The applicability of Grüneisen parameters to searching for novel materials with low κl is discussed from a theoretical viewpoint.

Revisiting thermal transport in single-layer graphene: On the applicability of thermal snapshot interatomic force constant extraction methodology for layered materials

The thermal conductivities of single-/bi-layer graphene and bulk-graphite are obtained using the Boltzmann transport equation (BTE) framework by accounting for three-phonon and four-phonon scatterings. For single-layer graphene, the thermal conductivity and interatomic force constants obtained using temperature-independent finite-difference, and temperature-dependent molecular dynamics-based approaches agree with each other. The use of the thermal snapshot approach to get temperature-dependent force constants results in a non-physical description of interatomic distances for single-layer graphene. The predicted thermal conductivity at room temperature using finite-difference based force constants is 800 W/m K, which is a severe under-prediction of experimentally measured values. For bi-layer graphene and bulk graphite, the thermal snapshot methodology is applicable and thermal conductivity changes by 25% and 5% with temperature-dependent force constants. The effect of four-phonon scattering is less than 10% on the predicted thermal conductivity of bi-layer graphene and graphite, and the obtained thermal conductivities using thermal snapshot methodology are in agreement with the literature. The limitation in the prediction of thermal conductivity of single-layer graphene via the BTE approach stems from non-accountability of temperature-dependence in finite-difference based force constants and non-physical description of interatomic bonds in thermal snapshot based force constants extraction for planar 2-atoms unitcell of single layer graphene.

Full optimization of quasiharmonic free energy with an anharmonic lattice model: Application to thermal expansion and pyroelectricity of wurtzite GaN and ZnO

We present a theory and a calculation scheme of structural optimization at finite temperatures within the quasiharmonic approximation (QHA). The theory is based on an efficient scheme of updating the interatomic force constants (IFCs) with the change of crystal structures, which we call the IFC renormalization. The cell shape and the atomic coordinates are treated equally and simultaneously optimized. We apply the theory to the thermal expansion and the pyroelectricity of wurtzite GaN and ZnO, which accurately reproduces the experimentally observed behaviors. Furthermore, we point out a general scheme to obtain correct $T$ dependence at the lowest order in constrained optimizations that reduce the number of effective degrees of freedom, which is helpful to perform efficient QHA calculations with little sacrificing of accuracy. We show that the scheme works properly for GaN and ZnO by comparing with the optimization of all the degrees of freedom.

Anharmonic Terms of the Potential Energy Surface: A Group Theoretical Approach

In the framework of density functional theory (DFT) simulations of molecules and materials, anharmonic terms of the potential energy surface are commonly computed numerically, with an associated cost that rapidly increases with the size of the system. Recently, an efficient approach to calculate cubic and quartic interatomic force constants in the basis of normal modes [Theor. Chem. Acc., 120, 23 (2008)] was implemented in the Crystal program [J. Chem. Theory Comput., 15, 3755-3765 (2019)]. By applying group theory, we are able to further reduce the associated computational cost, as the exploitation of point symmetry can significantly reduce the number of distinct atomically displaced nuclear configurations to be explicitly explored for energy and forces calculations. Our strategy stems from Wigner's theorem and the fact that normal modes are bases of the irreducible representations (irreps) of the point group. The proposed group theoretical approach is implemented in the Crystal program and its efficiency assessed on six test case systems: four molecules (methane, CH4; tetrahedrane, C4H4; cyclo-exasulfur, S6; cubane, C8H8), and two three-dimensional crystals (Magnesium oxide, MgO; and a prototypical Zinc-imidazolate framework, ZIF-8). The speedup imparted by this approach is consistently very large in all high-symmetry molecular and periodic systems, peaking at 76% for MgO.