High-pressure phonon dispersion of copper by using the modified analytic embedded atom method

By using the Born-von Kfirmfin theory of lattice dynamics and the modified analytic embedded atom method, we reproduce the experimental results of the phonon dispersion in fcc metal Cu at zero pressure along three high symmetry directions and four oft-symmetry directions, and then simulate the phonon dispersion curves of Cu at high pressures of 50, 100, and 150 GPa. The results show that the shapes of dispersion curves at high pressures are very similar to that at zero pressure. All the vibration frequencies of Cu in all vibration branches at high pressures are larger than the results at zero pressure, and increase correspondingly as pressure reaches 50, 100, and 150 GPa sequentially. Moreover, on the basis of phonon dispersion, we calculate the values of specific heat of Cu at different pressures. The prediction of thermodynamic quantities lays a significant foundation for guiding and judging experiments of thermodynamic properties of solids under high pressures.

Phonon Confinement Effect in Two-dimensional Nanocrystallites of Monolayer MoS_2 to Probe Phonon Dispersion Trends Away from Brillouin-Zone Center

The fundamental momentum conservation requirement q - 0 for the Raman process is relaxed in the nanocrystal- lites （NCs）, and phonons away from the Brillouin-zone center will be involved in the Raman scattering, which is well-known as the phonon confinement effect in NCs. This usually gives a downshift and asymmetric broadening of the Raman peak in various NCs. Recently, the A1 mode of 1L MoS2 NCs is found to exhibit a blue shift and asymmetric broadening toward the high-frequency side [Chem. Soc. Rev. 44 （2015） 2757 and Phys. Rev. B 91 （2015） 195411]. In this work, we carefully check this issue by studying Raman spectra of lL MoS2 NCs prepared by the ion implantation technique in a wide range of ion-implanted dosage. The same confinement coefficient is used for both E＇ and A＇1 modes in 1L MoS2 NCs since the phonon uncertainty in an NC is mainly determined by its domain size. The asymmetrical broadening near the A＇1 and E＇ modes is attributed to the appearance of defect-activated phonons at the zone edge and the intrinsic asymmetrical broadening of the two modes, where the anisotropy of phonon dispersion curves along Г-K and Г- M is also considered. The photoluminescence spectra confirm the formation of small domain size of 1L MoS2 nanocrystallites in the ion-implanted 1L MoS2. This study provides not only an approach to quickly probe phonon dispersion trends of 2D materials away from Г by the Raman scattering of the corresponding NCs, but also a reference to completely understand the confinement effect of different modes in various nanomaterials.

Phonon Dispersion and Thermodynamics Properties of CaF_2 via Shell Model Molecular Dynamics Simulations

The phonon and thermodynamics properties of face-centered cubic CaF2 at high pressure and high temperature are investigated by using the shell model interatomic pair potential within General Utility Lattice Program （GULP）. The phonon dispersion curves and the corresponding density of state （PDOS） in this work are consistent with the experimental data and other theoretical results. The transverse optical （TO） and longitudinal optical （LO） mode splitting as well as heat capacity at constant volume Cv and entropy S versus pressure and temperature are also obtained.

Phonon dispersion on Ag(100)surface:A modified analytic embedded atom method study

Within the harmonic approximation, the analytic expression of the dynamical matrix is derived based on the modified analytic embedded atom method （MAEAM） and the dynamics theory of surface lattice. The surface phonon dispersions along three major symmetry directionsX,M, and X（v） are calculated for the clean Ag （100） surface by using our derived formulas. We then discuss the polarization and localization of surface modes at points X and by plotting the squared polarization vectors as a function of the layer index. The phonon frequencies of the surface modes calculated by MAEAM are compared with the available experimental and other theoretical data. It is found that the present results are generally in agreement with the referenced experimental or theoretical results, with a maximum deviation of 10.4%. The agreement shows that the modified analytic embedded atom method is a reasonable many-body potential model to quickly describe the surface lattice vibration. It also lays a significant foundation for studying the surface lattice vibration in other metals.

Phonon dispersion relations of crystalline solids based on LAMMPS package

The phonon dispersion relations of crystalline solids play an important role in determining the mechanical and thermal properties of materials.The phonon dispersion relation,as well as the vibrational density of states,is also often used as an indicator of variation of lattice thermal conductivity with the external stress,defects,etc.In this study,a simple and fast tool is proposed to acquire the phonon dispersion relation of crystalline solids based on the LAMMPS package.The theoretical details for the calculation of the phonon dispersion relation are derived mathematically and the computational flow chart is present.The tool is first used to calculate the phonon dispersion relation of graphene with two atoms in the unit cell.Then,the phonon dispersions corresponding to several potentials or force fields,which are commonly used in the LAMMPS package to modeling the graphene,are obtained to compare with that from the DFT calculation.They are further extended to evaluate the accuracy of the used potentials before the molecular dynamics simulation.The tool is also used to calculate the phonon dispersion relation of superlattice structures that contains more than one hundred of atoms in the unit cell,which predicts the phonon band gaps along the cross-plane direction.Since the phonon dispersion relation plays an important role in the physical properties of condensed matter,the proposed tool for the calculation of the phonon dispersion relation is of great significance for predicting and explaining the mechanical and thermal properties of crystalline solids.

Phonon dispersion relations and soft modes of 4 carbon nanotubes

The phonon dispersion relations of three kinds of 4 A carbon nanotubes are calculated by using the density functional perturbation theory. It is found that the frequencies of some phonon modes are very sensitive to the smearing width used in the calculations, and eventually become negative at low electronic temperature. Moreover, two kinds of soft modes are identified for the （5,0） tube which are quite different from those reported previously. Our results suggest that the （5,0） tube remains metallic at very low temperature, instead of the metallie-semiconducting transition claimed before.

Investigating Stability Properties for Transition Metal Carbonate Precursors Using Universal Cluster Expansion Technique(UNCLE)as Cathodes for Li-Ion Batteries

The universal cluster expansion technique was used in this study to determine the binary phase diagrams for the transition metal carbonate precursors MCO3(M:Mn,Ni,Co).The use of mixed cathode materials in lithium-ion batteries such as NMC(Ni,Mn and Co)formulations,is a strategic approach to optimize performance,enhance safety and address cost and environmental considerations in the rapidly evolving field of energy storage.This study focuses on the cost issue related to lithium ion batteries by investigating the manganese rich NMC since manganese is more abundant and cost-effective.We doped MnCO3 with nickel and doped MnCO3 with cobalt then ran cluster expansion calculations to generate binary phases.The binary phase diagrams generated indicated that doping MnCO3 with nickel favours the Mn-rich side,while doping MnCO3 with cobalt favours 50%Mn-rich and 50%Co-rich.We further extracted the most stable structures from both binary diagrams and determined their electronic,mechanical and vibrational stabilities using DFT(density functional theory)calculations within the LDA(local gradient approximation)with Hubbard parameter(U).The electronic properties revealed that both materials are semiconductors due to their narrow energy band gap obtained while the mechanical properties showed that structures are mechanically stable since their necessary conditions for trigonal and triclinic systems were satisfied.

Phase Transition and Phonon Spectrum of Zinc-Blende Structure ZnX (X=S, Se,Te)

Calculations have been performed to investigate the pressure-induced solid-solid phase transitions and the mechanical stability for three zinc-blende II-VI semiconductor compounds： ZnS, ZnSe, ZnTe by ab initio plane-wave pseudopotential density functional theory （DFT）. Using the generalized gradient approximation （GGA） for exchange and correlation in the scheme of Perdew-Wang 1991 （P Wgl ）, the ground state properties and equation of state are obtained, which are well consistent with the experimental data available and other calculations. On the basis of the forth-order Birch-Murnaghan equation of states, the transition pressures Pt are determined through the analysis of enthalpy variation with pressure. A linear-response approach is used to calculate the frequencies of the phonon dispersion. Finally, by the calculations of phonon frequencies, some thermodynamic properties such as the vibrational contribution to the Helmholtz free energy （F）, enthedpy （H）, entropy （S）, and the heat capacity （Cv ） are also successfully obtained.

The electronic structures, Born effective charge tensors,and phonon properties of cubic, tetragonal,orthorhombic, and rhombohedral K_(0.5)Na_(0.5)NbO_3: A first-principles comparative study

The electronic structures, Born effective charges（BECs）, and full phonon dispersions of cubic, tetragonal, orthorhombic, and rhombohedral K0.5Na0.5Nb O3 are investigated by the first principles method based on density functional theory.The hybridized states of Nb 4d and O 2p states are observed in the valence band, showing the formation of a strong Nb–O covalent bond which should be responsible for the displacement of Nb and O atoms. The abnormally large BECs of Nb and O indicate the possibility of phase instability induced by the off-center displacement of Nb and O atoms. The phonon dispersions reveal that the ferroelectric instability of K0.5Na0.5Nb O3 is dominated by Nb and O displacements with significant Na characteristics. In addition to the ferroelectric instability, there is also rotational instability coming from the oxygen octahedra rotation around one axis. Moreover, the Γ phonon properties of orthorhombic KNb O3, Na Nb O3, and K0.5Na0.5Nb O3 are also studied in detail.

High Pressure Structural Instability and Thermal Properties of Rutile TiO2 from First-principles

We report a first-principles calculation to investigate the structural instability of rutile TiO2. The high pressure structural parameters are well reproduced. The calculated phonon disper-sion curves agree with experiments at zero pressure. Under compression, we capture a large softening around Γ point, which indicates the structural instability. From the high pressure elastic constants, we find that the rutile TiO2 is unstable when the applied pressure is larger than 17.7 GPa. Within the quasi-harmonic approximation, the thermal equation of state, thermal expansion oefficient, bulk modulus, and entropy are well reproduced. The thermal properties confirm the available experimental data and are extended to a wider pressure and temperature range.

Thermodynamic properties of 3C-SiC

In the present paper, we report on the results of various thermodynamic properties of 3C-SiC at high pressure and temperature using first principles calculations. We use the plane-wave pseudopotential density functional theory as im- plemented in Quantum ESPRESSO code for calculating various cohesive properties in ambient condition. Further, ionic motion at a finite temperature is taken into account using the quasiharmonic Debye model. The calculated thermody- namic properties, phonon dispersion curves, and phonon densities of states at different temperatures and structural phase transitions at high pressures are found to be in good agreement with experimental and other theoretical results.

An ab initio investigation of vibrational, thermodynamic, and optical properties of Sc_2AlC MAX compound

The structural vibrational, thermodynamical, and optical properties of potentially technologically important, weakly coupled MAX compound, Sc2 Al C are calculated using density functional theory(DFT). The structural properties of ScAlC are compared with the results reported earlier. The vibrational, thermodynamical, and optical properties are theoretically estimated for the first time. The phonon dispersion curve is calculated and the dynamical stability of this compound is investigated. The optical and acoustic modes are observed clearly. We calculate the Helmholtz free energy(F), internal energy(E), entropy(S), and specific heat capacity(Cv) from the phonon density of states. Various optical parameters are also calculated. The reflectance spectrum shows that this compound has the potential to be used as an efficient solar reflector.

Novel structures and mechanical properties of Zr_(2)N:Ab initio description under high pressures

With the formation of structural vacancies,zirconium nitrides(key materials for cutting coatings,super wearresistance,and thermal barrier coatings) display a variety of compositions and phases featuring both cation and nitrogen enrichment.This study presents a systematic exploration of the stable crystal structures of zirconium heminitride combining the evolutionary algorithm method and ab initio density functional theory calculations at pressures of 0 GPa,30 GPa,60 GPa,90 GPa,120 GPa,150 GPa,and 200 GPa.In addition to the previously proposed phases P42/mnm-,Pnnn-,and Cmcm-Zr2 N,five new high-pressure Zr_(2)N phases of PA/nmm,IA/mcm,P2_(1)/m,P3 m1,and C2/m are discovered.An enthalpy study of these candidate configurations reveals various structural phase transformations of Zr2 N under pressure.By calculating the elastic constants and phonon dispersion,the mechanical and dynamical stabilities of all predicted structures are examined at ambient and high pressures.To understand the structure-property relationships,the mechanical properties of all Zr_(2)N compounds are investigated,including the elastic moduli,Vickers hardness,and directional dependence of Young’s modulus.The Cmncm-Zr2 N phase is found to belong to the brittle materials and has the highest Vickers hardness(12.9 GPa) among all candidate phases,while the I4/mcm-Zr2 N phase is the most ductile and has the lowest Vickers hardness(2.1 GPa).Furthermore,the electronic mechanism underlying the diverse mechanical behaviors of Zr2 N structures is discussed by analyzing the partial density of states.

Phonon engineering significantly reducing thermal conductivity of thermoelectric materials: a review

Lattice thermal conductivity, κL, is a fundamental parameter for evaluating the performance of thermoelectric materials. However, the predicted value of κL based on the Debye dispersion model is often overestimated compared with the experimentally determined value.Many researchers have attempted to modify the theoretical model and have sought more reliable results. In this review,the recent progress in the study of phonon dispersion models is summarized and we propose that the lattice thermal conductivity can be most accurately determined by using the modified sinusoidal phonon dispersion model.Moreover, experimental methods that have the potential to reduce a thermoelectric material's κLare reviewed, for example, methods that generate standing waves or anharmonic lattice vibrations. A high concentration of standing waves and anharmonic lattice vibrations can effectively suppress excessive κL. Finally, this review presents the challenges of sinusoidal phonon dispersion when applied to real materials, which are often complicated and therefore time-consuming, especially when dealing with material defects.

First principles study and comparison of vibrational and thermodynamic properties of XBi(X=In,Ga,B,Al)

In the present work, vibrational and thermodynamic properties of XBi（X = B, Al, Ga, In） compounds are compared and investigated. The calculation is carried out using density functional theory（DFT） within the generalized gradient approximation（GGA） in a plane wave basis, with ultrasoft pseudopotentials. The lattice dynamical properties are calculated using density functional perturbation theory（DFPT） as implemented in Quantum ESPRESSO（QE） code. Thermodynamic properties involving phonon density of states（DOS） and specific heat at constant volume are investigated using quasiharmonic approximation（QHA） package within QE. The phonon dispersion diagrams for InBi, GaBi, BBi, and AlBi indicate that there is no imaginary phonon frequency in the entire Brillouin zone, which proves the dynamical stability of these materials. BBi has the highest thermal conductivity and InBi has the lowest thermal conductivity. AlBi has the largest and GaBi has the smallest reststrahlen band which somehow suggests the polar property of XBi materials. The phonon gaps for InBi, GaBi, BBi and AlBi are about 160 cm^-1, 150 cm^-1, 300 cm^-1, and 150 cm^-1, respectively. For all compounds,the three acoustic modes near the gamma point have a linear behavior. C_V is a function of T-3 at low temperatures while for higher temperatures it asymptotically tends to a constant as expected.

Programmable repulsive potential for tight-binding from Chen-Möbius inversion theorem

An accurate total energy calculation is essential in materials computation.To date,many tight-binding(TB)approaches based on parameterized hopping can produce electronic structures comparable to those obtained using first-principles calculations.However,TB approaches still have limited applicability for determining material properties derived from the total energy.That is,the predictive power of the TB total energy is impaired by an inaccurate evaluation of the repulsive energy.The complexity associated with the parametrization of TB repulsive potentials is the weak link in this evaluation.In this study,we propose a new method for obtaining the pairwise TB repulsive potential for crystalline materials by employing the Chen-Möbius inversion theorem.We show that the TB-based phonon dispersions,calculated using the resulting repulsive potential,compare well with those obtained by first-principles calculations for various systems,including covalent and ionic bulk materials and twodimensional materials.The present approach only requires the first-principles total energy and TB electronic band energy as input and does not involve any parameters.This striking feature enables us to generate repulsive potentials programmatically.

Phonon dynamics of glassy copper alloys

The well recognized model potential is used to investigate the phonon properties for five glassy Copper alloys viz.Cu_(57)Zr_(43),Cu_(60)W_(40),Cu_(33)Y_(67),Cu_(43)Ti_(57) and Cu_(66)Ti_(34).The thermodynamic and elastic properties are also computed from the elastic limits of the phonon dispersion curves(PDC).Three theoretical approaches given by Hubbard-Beeby(HB),Takeno-Goda(TG)and Bhatia-Singh(BS)are used in the present study to compute the PDC.Five local field correction functions proposed by Hartree(H),Taylor(T),Ichimaru-Utsumi(IU),Farid et al.(F)and Sarkar et al.(S)are employed to see the effect of exchange and correlation in the aforesaid properties.

Graphene-based thermal modulators

The quest for materials and devices that are capable of controlling heat flux continues to fuel research on thermal controlling devices. In this letter, using molecular dynamics simulations, we demonstrate that a partially clamped singlelayer graphene can serve as a thermal modulator. The mismatch in phonon dispersion between the unclamped and clamped graphene sections results in phonon interface scattering, and the strength of interface scattering is tunable by controlling the clamp-graphene distance via applying the external pressure. Owing to the ultra-thin structure of graphene and its highly sensitive phonon dispersion to external physical interaction, the modulation efficiency--which is defined as the ratio of the highest to lowest heat flux-can reach as high as 150% at a moderate pressure of 50 GPa. This modulation efficiency can be further enhanced by arranging a number of clamps in series along the direction of the heat flux.

Vibrational dynamics of Fe-based glassy alloys

The well recognized model potential is used to investigate the vibrational properties of four Fe-based binary glassy alloys viz.Fe_(90)Zr_(10),Fe_(80)B_(20),Fe_(83)B_(17) and Fe_(80)P_(20).The thermodynamic and elastic properties are also computed from the elastic limits of the phonon dispersion curves(PDC).Three theoretical approaches given by Hubbard-Beeby(HB),Takeno-Goda(TG)and Bhatia-Singh(BS)are used in the present study to compute the PDC.Six local field correction functions proposed by Hartree(H),Taylor(T),Ichimaru-Utsumi(IU),Farid et al.(F)and Sarkar et al.(S)and Sarkar et al.’s local field factor(SLFF)based excgange and correlation function are employed to see the effect of exchange and correlation in the aforesaid properties.

Vibrational Properties of Vacancy in Na and K Using MEAM Potential

The modified embedded atom method(MEAM)with the universal form of embedding function and a modified energy term along with the pair potential has been employed to determine the potentials for alkali metals:Na,K,by fitting to the Cauchy pressure(C_(12)−C_(44))/2,shear constants Gv=(C_(11)−C_(12)+3C_(44))/5 and C_(44),the cohesive energy and the vacancy formation energy.The obtained potentials are used to calculate the phonon dispersions of these metals.Using these calculated phonons we evaluate the local density of states of neighbours of vacancy using Green’s function method.The local density of states of neighbours of vacancy has been used to calculate mean square displacements of these atoms and formation entropy of vacancy.The calculated mean square displacements of both 1st and 2nd neighbours of vacancy are found to be lower than that of host atom.The calculated phonon dispersions agree well with the experimental phonon dispersion curves and the calculated results of vacancy formation entropy compare well with the other available results.