Lattice Dynamics Calculations Research Articles

Anharmonic stabilization and lattice heat transport in rocksalt β-GeTe

Peierls-Boltzmann transport equation, coupled with third-order anharmonic lattice dynamics calculations, has been widely used to model lattice thermal conductivity (κl) in bulk crystals. However, its application to materials with structural phase transition at relatively high temperature is fundamentally challenged by the presence of lattice instabilities (imaginary phonon modes). Additionally, its accuracy suffers from the absence of higher-than-third-order phonon scattering processes, which are important near/above the Debye temperature. In this letter, we present an effective scheme that combines temperature-induced anharmonic phonon renormalization and four-phonon scattering to resolve these two theoretical challenges. We apply this scheme to investigate the lattice dynamics and thermal transport properties of GeTe, which undergoes a second-order ferroelectric phase transition from rhombohedral α-GeTe to rocksalt β-GeTe at about 700 K. Our results on the high-temperature phase β-GeTe at 800 K confirm the stabilization of β-GeTe by temperature effects. We find that considering only three-phonon scattering leads to significantly overestimated κl of 3.8 W/mK at 800 K, whereas including four-phonon scattering reduces κl to 1.7 W/mK, a value comparable with experiments. To explore the possibility to further suppress κl, we show that alloying β-GeTe with heavy cations such as Pb and Bi can effectively reduce κl to about 1.0 W/mK, whereas particle size needs to be around 10 nm through nanostructuring to achieve a comparable reduction in κl.

A theoretical investigation of structural, mechanical, electronic and thermoelectric properties of orthorhombic CH3NH3PbI3

The structural, mechanical, electronic and thermoelectric properties of the low temperature orthorhombic perovskite phase of CH3NH3PbI3 have been investigated using density functional theory (DFT). Elastic parameters bulk modulus B, Young’s modulus E, shear modulus G, Poisson’s ratio ν and anisotropy value A have been calculated by the Voigt–Reuss–Hill averaging scheme. Phonon dispersions of the structure were investigated using a finite displacement method. The relaxed system is dynamically stable, and the equilibrium elastic constants satisfy all the mechanical stability criteria for orthorhombic crystals, showing stability against the influence of external forces. The lattice thermal conductivity was calculated within the single-mode relaxation-time approximation of the Boltzmann equation from first-principles anharmonic lattice dynamics calculations. Our results show that lattice thermal conductivity is anisotropic, and the corresponding lattice thermal conductivity at 150 K was found to be 0.189, 0.138, and 0.530 Wm−1K−1 in the a, b, and c directions. Electronic structure calculations demonstrate that this compound has a DFT direct band gap at the gamma point of about 1.57 eV. The electronic transport properties have been calculated by solving the semiclassical Boltzmann transport equation on top of DFT calculations, within the constant relaxation time approximation. The Seebeck coefficient S is almost constant from 50 to 150 K. At temperatures 100 and 150 K, the maximal figure of merit is found to be 0.06 and 0.122 in the direction of the c-axis, respectively.

Lattice thermal conductivity and bandgap engineering of a three-dimensional [formula omitted]-hybridized Dirac carbon material: HS-C48

A sp2 hybridized three-dimensional Dirac carbon material, HS-C48, is predicted by means of first principles calculations. The evaluation of mechanical, thermodynamic and kinetic stabilities shows HS-C48 is a potential carbon allotrope to be prepared. By solving linearized phonon Boltzmann equation from first-principles anharmonic lattice dynamics calculations, we find that the lattice thermal conductivity of HS-C48 is anisotropic and quite low relative to sp2 hybridized graphene or nanotubes. Electronic structure calculation shows it is a metallic carbon with Dirac linear dispersion near Fermi level. By means of triaxial strain engineering, the bandgap of HS-C48 could be opened, especially when the positive strains εz is applied.

First-order structural transition and pressure-induced lattice/phonon anomalies in Sr2IrO4

We investigate the crystal structure and lattice vibrations of Sr$_2$IrO$_4$ by a combined phonon Raman scattering and x-ray powder diffraction experiment under pressures up to $66$ GPa and room temperature. Density functional theory (DFT) and $ab$-initio lattice dynamics calculations were also carried out. A first-order structural phase transition associated with an $8$ % collapse of the $c$-axis is observed at high pressures, with phase coexistence being observed between $\sim 40$ and $55$ GPa. At lower pressures, lattice and phonon anomalies were observed, reflecting crossovers between isostructural competing states. A critical pressure of $P_1=17$ GPa is associated with: (i) a reduction of lattice volume compressibility and a change of behavior of the tetragonal $c/a$ ratio take place above $P_1$; (ii) a four-fold symmetry-breaking lattice strain associated with lattice disorder; (iii) disappearance of two Raman active modes (at $\sim 180$ and $\sim 260$ cm$^{-1}$); and (iv) development of an asymmetric Fano lineshape for the $\sim 390$ cm$^{-1}$ mode. DFT indicates that the phase above $P_1$ is most likely non-magnetic. Exploring the similarities between iridate and cuprate physics, we argue that these observations are consistent with the emergence of a rotational symmetry-breaking electronic instability at $P_1$, providing hints for the avoided metallization under pressure and supporting the hypothesis of possible competing orders that are detrimental to superconductivity in this family. Alternative scenarios for the transition at $P_1$ are also suggested and critically discussed. Additional phonon and lattice anomalies in the tetragonal phase are observed at $P_2=30$ and $P_3=40$ GPa, indicating further competing phases that are stabilized at high pressures.

Structure-Property Relations in Multiferroic [(CH3)2NH2] M(HCOO)3 ( M = Mn, Co, Ni).

We bring together magnetization, infrared spectroscopy, and lattice dynamics calculations to uncover the magnetic field-temperature ( B- T) phase diagrams and vibrational properties of the [(CH3)2NH2] M(HCOO)3 ( M = Mn2+, Co2+, Ni2+) family of multiferroics. While the magnetically driven transition to the fully saturated state in [(CH3)2NH2]Mn(HCOO)3 takes place at 15.3 T, substitution with Ni or Co drives the critical fields up toward 100 T, an unexpectedly high energy scale for these compounds. Analysis of the infrared spectrum of the Mn and Ni compounds across TC reveals doublet splitting of the formate bending mode which functions as an order parameter of the ferroelectric transition. By contrast, [(CH3)2NH2]Co(HCOO)3 reveals a surprising framework rigidity across the order-disorder transition due to modest distortions around the Co2+ centers. The transition to the ferroelectric state is thus driven by the dimethylammonium cation freezing and the resulting hydrogen bonding. Under applied field, the Mn (and most likely, the Ni) compounds engage the formate bending mode to facilitate the transition to their fully saturated magnetic states, whereas the Co complex adopts a different mechanism involving formate stretching distortions to lower the overall magnetic energy. Similar structure-property relations involving substitution of transition-metal centers and control of the flexible molecular architecture are likely to exist in other molecule-based multiferroics.

Experimental and theoretical study of Raman scattering spectra of ternary chalcogenides Tl4HgI6, Tl4HgBr6, and TlHgCl3

AbstractThe results of a comprehensive experimental and theoretical study of Raman scattering of Tl4HgI6, Tl4HgBr6, and TlHgCl3 ternary chalcogenides are presented. Phonon mode assignment to the specific lattice eigenmodes is achieved via comparison of experimental data with the results of first principle lattice dynamics calculations. Both experimental data and theoretical calculations allow to confirm that Tl4HgBr6 crystals belong to the non‐centrosymmetric space group P4nc, whereas Tl4HgI6 to the centrosymmetric space group P4/mnc.

Collapse of Critical Nematic Fluctuations in FeSe under Pressure

We report the evolution of the electronic nematic susceptibility in FeSe via Raman scattering as a function of hydrostatic pressure up to 5.8GPa where the superconducting transition temperature T_{c} reaches its maximum. The critical nematic fluctuations observed at low pressure vanish above 1.6GPa, indicating they play a marginal role in the fourfold enhancement of T_{c} at higher pressures. The collapse of nematic fluctuations appears to be linked to a suppression of low energy electronic excitations which manifests itself by optical phonon anomalies at around 2GPa, in agreement with lattice dynamical and electronic structure calculations using local density approximation combined with dynamical mean field theory. Our results reveal two different regimes of nematicity in the phase diagram of FeSe under pressure: a d-wave Pomeranchuk instability of the Fermi surface at low pressure and a magnetic driven orthorhombic distortion at higher pressure.

Calculation of the optical phonons in ordered Ba2MgWO6 perovskite using short‐range force field model

AbstractBa2MgWO6 is a double perovskite tungstate presenting a cubic structure with cubic space group . This B‐site ordered system has potential applications as microwave ceramics in communication systems. Here, we present our results on the lattice dynamics calculations using short‐range force field model to describe both Raman (A1g ⊕ Eg ⊕ 2F2g) and infrared (4F1u) optical phonons at Γ‐point of the Brillouin zone in Ba2MgWO6 perovskite. Short‐range interactions were parameterized through four stretching and three bending force constants in light of the Wilson's GF‐matrix method. Satisfactory agreement between experimental and calculated vibrational data was found. We have used the potential energy distribution (PED) coefficients to determine the contribution of each force constant to the optical modes. The PED analysis elucidates that the W atom has a nonnegligible contribution in describing both A1g breathing and Last‐type (F1u) modes. Such a modeling provided insights into vibrational modes, enabling correlation between optical phonons, disorder effects, and physical properties for applications.

Reduced thermal conductivity of Si/Ge random layer nanowires: A comparative study against superlattice counterparts

Si/Ge nanowires are considered to be promising candidates as efficient thermoelectric materials due to their remarkable thermal insulating performance over bulk counterparts. In this study, thermal insulating performance of Si/Ge nanowires of randomly organized layer thickness, called random layer nanowires (RLNWs), is systematically investigated and compared against superlattice nanowires (SLNWs).The thermal conductivity (TC) of these structures is evaluated via non-equilibrium molecular dynamic simulations, and more informative insight is gained by normal mode decomposition and lattice dynamics calculations. It is demonstrated that the modes in random layer structures, in general, exhibit similar characteristics except the degree of localization to the corresponding superlattice counterparts by comparing the mode spectral energy densities, relaxation times, density of states, and participation ratios. For all physical and geometrical conditions investigated here, RLNWs show improved thermal insulating performance over corresponding SLNWs. More importantly, a RLNW of low mean layer thickness attains even lower TC than the corresponding Si/Ge alloy nanowire indicating the effectiveness of the random layer arrangements. An anomalous trend in TC of RLNWs (larger than the bulk counterpart) is observed at higher cross-sectional widths, and it is explained as a competing effect of phonon localization and wall scattering. Moreover, it is illustrated that the effectiveness of thermal insulating performance of RLNW depends on the fraction of coherent phonons that exist and how effectively those phonons are subject to localization under different cases.

Experimental and Theoretical Studies on α-In2Se3 at High Pressure.

α(R)-In2Se3 has been experimentally and theoretically studied under compression at room temperature by means of X-ray diffraction and Raman scattering measurements as well as by ab initio total-energy and lattice-dynamics calculations. Our study has confirmed the α ( R3 m) → β' ( C2/ m) → β ( R3̅ m) sequence of pressure-induced phase transitions and has allowed us to understand the mechanism of the monoclinic C2/ m to rhombohedral R3̅ m phase transition. The monoclinic C2/ m phase enhances its symmetry gradually until a complete transformation to the rhombohedral R3̅ m structure is attained above 10-12 GPa. The second-order character of this transition is the reason for the discordance in previous measurements. The comparison of Raman measurements and lattice-dynamics calculations has allowed us to tentatively assign most of the Raman-active modes of the three phases. The comparison of experimental results and simulations has helped to distinguish between the different phases of In2Se3 and resolve current controversies.

An Unusual Phase Transition Driven by Vibrational Entropy Changes in a Hybrid Organic–Inorganic Perovskite

The driving forces for the phase transitions of ABX3 hybrid organic-inorganic perovskites have been limited to the octahedral tilting, order-disorder, and displacement. Now, a complex structural phase transition has been explored in a HOIP, [CH3 NH3 ][Mn(N3 )3 ], based on structural characterizations and ab initio lattice dynamics calculations. This unusual first-order phase transition between two ordered phases at about 265 K is primarily driven by changes in the collective atomic vibrations of the whole lattice, along with concurrent molecular displacements and an unusual octahedral tilting. A significant entropy difference (4.35 J K-1 mol-1 ) is observed between the low- and high-temperature structures induced by such atomic vibrations, which plays a main role in driving the transition. This finding offers an alternative pathway for designing new ferroic phase transitions and related physical properties in HOIPs and other hybrid crystals.

An Unusual Phase Transition Driven by Vibrational Entropy Changes in a Hybrid Organic–Inorganic Perovskite

AbstractThe driving forces for the phase transitions of ABX3 hybrid organic–inorganic perovskites have been limited to the octahedral tilting, order–disorder, and displacement. Now, a complex structural phase transition has been explored in a HOIP, [CH3NH3][Mn(N3)3], based on structural characterizations and ab initio lattice dynamics calculations. This unusual first‐order phase transition between two ordered phases at about 265 K is primarily driven by changes in the collective atomic vibrations of the whole lattice, along with concurrent molecular displacements and an unusual octahedral tilting. A significant entropy difference (4.35 J K−1 mol−1) is observed between the low‐ and high‐temperature structures induced by such atomic vibrations, which plays a main role in driving the transition. This finding offers an alternative pathway for designing new ferroic phase transitions and related physical properties in HOIPs and other hybrid crystals.

Localization of vibrational modes leads to reduced thermal conductivity of amorphous heterostructures

We investigate the vibrational heat transfer mechanisms in amorphous Stillinger-Weber silicon and germanium-based alloys and heterostructures via equilibrium and nonequilibrium molecular dynamics simulations along with lattice dynamics calculations. We find that similar to crystalline alloys, amorphous alloys demonstrate large size effects in thermal conductivity, while layering the constituent materials into superlattice structures leads to length-independent thermal conductivities. The thermal conductivity of an amorphous ${\mathrm{Si}}_{x}{\mathrm{Ge}}_{1\ensuremath{-}x}$ alloy reduces by as much as $\ensuremath{\sim}53%$ compared to the thermal conductivity of amorphous silicon; compared to the larger reduction in crystalline phases due to alloying, we show that compositional disorder rather than structural disorder has a larger impact on the thermal conductivity reduction. Our thermal conductivity predictions for a-Si/a-Ge superlattices suggest that the alloy limit in amorphous SiGe-based structures can be surpassed with interface densities above $\ensuremath{\sim}0.35\phantom{\rule{4pt}{0ex}}{\mathrm{nm}}^{\ensuremath{-}1}$. We attribute the larger reduction in thermal conductivity of layered Si/Ge heterostructures to greater localization of modes at and around the cutoff frequency of the softer layer as demonstrated via lattice dynamics calculations and diffusivities of individual eigenmodes calculated according to the Allen-Feldman theory [P. B. Allen and J. L. Feldman, Phys. Rev. B 48, 12581 (1993)] for our amorphous SiGe-based alloys and superlattice structures.

Theoretical methods for calculations of optical phonons in BiOBr: Analysis and correction of propagated errors

AbstractTheoretical and experimental methods were employed to investigate the vibrational modes of BiOBr. Wavenumber prediction and assignments of the infrared and Raman modes were performed using density functional theory and lattice dynamics calculations. The theoretical models were directly compared with the experimental results of particles fabricated using the microwave‐assisted hydrothermal method and results reported in literature. The simulation results of the structure parameters, band gap, and vibrational modes are in agreement with the corresponding experimental values. The proposed models and calculations provided detailed insights into the vibrational modes and enabled to determine propagated assignment errors in results reported in the literature.

Lattice dynamical probe of phase transformations in niobium oxyfluoride Nb2O2F3

Raman scattering spectroscopy is used to monitor the transition of reduced niobium oxyfluoride ${\mathrm{Nb}}_{2}{\mathrm{O}}_{2}{\mathrm{F}}_{3}$ single crystals from their high-temperature monoclinic (I2/a) phase into the low-temperature triclinic ($P\overline{1}$) phase at ${T}_{c}\phantom{\rule{4pt}{0ex}}\ensuremath{\approx}90\phantom{\rule{4.pt}{0ex}}\text{K}$ due to charge disproportionation of (${\mathrm{Nb}\text{\ensuremath{-}}\mathrm{Nb})}^{7+}$ dimers and creation of crystallographically nonequivalent dimers with long and short Nb-Nb bonds. The group-theoretic analysis of lattice vibrations is performed, and the assignment of observed phonon lines to the specific lattice eigenmodes of the two phases is achieved based on a comparison with the results of density functional lattice dynamics calculations. Nb-Nb dimers are found to possess stretching vibrational frequencies as high as 382 ${\mathrm{cm}}^{\ensuremath{-}1}$. Strikingly, the kinetics of the monoclinic-to-triclinic structural transformation and the volume fraction of corresponding phases below ${T}_{c}$ are shown to strongly depend upon the sample cooling rate. Fast cooling results in a ``freezing'' of the high-temperature monoclinic phase and allows us to observe a spin-ordered state below ${\mathrm{T}}_{N}\ensuremath{\approx}$ 49 K.

Anisotropic thermal conductivity in carbon honeycomb

Carbon honeycomb, a new kind of 3D carbon allotrope experimentally synthesized recently, has received much attention for its fascinating applications in electronic device and energy storage. In the present work, we perform equilibrium molecular dynamics (EMD) to study the thermal transport properties of carbon honeycombs with different chirality. It is found that the thermal conductivity along the honeycomb axis () is three times larger than that normal to the axis (), which shows strong anisotropy reflecting their geometric anisotropy. Lattice dynamics calculations reveal that this anisotropy stems from the orientation-dependent phonon group velocities. Moreover, when ambient temperature () increases from 200 K to 800 K, the dependence of is observed due to the enhanced Umklapp scattering. The detailed phonon spectra analyses indicate phonon group velocities are insensitive to the variation of ambient temperature, and the temperature dependence of the relaxation times of low-frequency phonons (<20 THz) follows behavior. Our results have a certain guiding significance to develop carbon honeycomb for effective thermal channeling devices.

Lattice dynamics of ASb2O6 ( A=Cu , Co) with trirutile structure

Raman spectroscopy experiments on single crystals of CuSb2O6 and CoSb2O6 quasi-one-dimensional antiferromagnets with trirutile crystal structure were performed, with a focus on the first material. The observed Raman-active phonon modes and previously reported infrared-active modes were identified with the aid of ab-initio lattice dynamics calculations. The structural transition between monoclinic beta-CuSb2O6 and tetragonal alpha-CuSb2O6 phases at Ts=400 K is manifested in our spectra by a "repulsion" of two accidentally quasi-degenerate symmetric modes below Ts, caused by a phonon mixing effect that is only operative in the monoclinic beta-CuSb2O6 phase due to symmetry restrictions. Also, two specific phonons, associated with CuO6 octahedra rotation and with a Jahn-Teller elongation mode, soften and broaden appreciably as T -> Ts. A crossover from a displacive to an order-disorder transition at Ts is inferred.

Ab Initio Molecular Dynamics and Lattice Dynamics-Based Force Field for Modeling Hexagonal Boron Nitride in Mechanical and Interfacial Applications.

Hexagonal boron nitride (hBN) is an up-and-coming two-dimensional material, with applications in electronic devices, tribology, and separation membranes. Herein, we utilize density-functional-theory-based ab initio molecular dynamics (MD) simulations and lattice dynamics calculations to develop a classical force field (FF) for modeling hBN. The FF predicts the crystal structure, elastic constants, and phonon dispersion relation of hBN with good accuracy and exhibits remarkable agreement with the interlayer binding energy predicted by random phase approximation calculations. We demonstrate the importance of including Coulombic interactions but excluding 1-4 intrasheet interactions to obtain the correct phonon dispersion relation. We find that improper dihedrals do not modify the bulk mechanical properties and the extent of thermal vibrations in hBN, although they impact its flexural rigidity. Combining the FF with the accurate TIP4P/Ice water model yields excellent agreement with interaction energies predicted by quantum Monte Carlo calculations. Our FF should enable an accurate description of hBN interfaces in classical MD simulations.

First-principles calculations of lattice dynamics and thermodynamic properties for Yb14MnSb11

Systematic first-principles calculations were performed to study the lattice dynamics of Yb14MnSb11 and hence to obtain a wide range of its thermodynamic properties at high temperatures. The calculated results were analyzed in terms of the lattice contribution and the electronic contribution, together with a comparison with a collection of experimental thermochemical data. At 0 K, the electronic density of states showed the typical feature of a p-type semiconductor—a small amount of unoccupied electronic states exclusively made of the major spin by a range of ∼0.6 eV above the Fermi energy. It showed that the Mn atom had a ferromagnetic spin moment of ∼4 μB. As a semiconductor, it was found that the electronic contribution to the heat capacity was substantial, with an electronic heat capacity coefficient of ∼0.0006 J/mole-atom/K2.

Lattice dynamics, elasticity and magnetic abnormality in ordered crystalline alloys Fe3Pt at high pressures

The ordered crystalline Invar alloy Fe3Pt is in a special magnetic critical state, under which the lattice dynamic stability of the system is extremely sensitive to external pressures. We studied the pressure dependence of enthalpy and magnetism of Fe3Pt in different crystalline alloys by using the first-principles projector augmented-wave method based on the density functional theory. Results show that the P4/mbm structure is the ground state structure and is more stable relative to other structures at pressures below 18.54 GPa. The total magnetic moments of L12, I4/mmm and DO22 structures decrease rapidly with pressure and oscillate near the ferromagnetic collapse critical pressure. At the pressure of 43 GPa, the ferrimagnetic property in DO22 structure becomes apparently strengthened and its volume increases rapidly. The lattice dynamics calculation for L12 structures at high pressures shows that the spontaneous magnetization of the system in ferromagnetic states induces the softening of the transverse acoustic phonon TA1 (M), and there exists a strong spontaneous volume magnetostriction at pressures below 26.95 GPa. Especially, the lattice dynamics stability is sensitive to pressure, in the pressure range between the ferromagnetic collapse critical pressure (41.9 GPa) and the magnetism completely disappearing pressure (57.25 GPa), and near the pressure of phase transition from L12 to P4/mbm structure (27.27 GPa). Moreover, the instability of magnetic structure leads to a prominent elastic modulus oscillation, and the spin polarizability of electrons near the Fermi level is very sensitive to pressures in that the pressure range. The pressure induces the stability of the phonon spectra of the system at pressures above 57.25 GPa.