Theory Of Lattice Dynamics Research Articles

Mode-coupling theory of lattice dynamics for classical and quantum crystals

The dynamical properties of nuclei, carried by the concept of phonon quasiparticles , are central to the field of condensed matter. While the harmonic approximation can reproduce a number of properties observed in real crystals, the inclusion of anharmonicity in lattice dynamics is essential to accurately predict properties such as heat transport or thermal expansion. For highly anharmonic systems, non-perturbative approaches are needed, which result in renormalized theories of lattice dynamics. In this article, we apply the Mori–Zwanzig projector formalism to derive an exact generalized Langevin equation describing the quantum dynamics of nuclei in a crystal. By projecting this equation on quasiparticles in reciprocal space, and with results from linear response theory, we obtain a formulation of vibrational spectra that fully accounts for the anharmonicity. Using a mode-coupling approach, we construct a systematic perturbative expansion in which each new order is built to minimize the following ones. With a truncation to the lowest order, we show how to obtain a set of self-consistent equations that can describe the lineshapes of quasiparticles. The only inputs needed for the resulting set of equations are the static Kubo correlation functions, which can be computed using (fully quantum) path-integral molecular dynamics or approximated with (classical or ab initio) molecular dynamics. We illustrate the theory with an application on fcc 4He, an archetypal quantum crystal with very strong anharmonicity.

Lattice dynamics study of gold nanotube

We have developed an analytical analysis based on lattice dynamics theory to study phonon dispersion relation for gold nanotube. This paper gives an overview of the methodology for calculating of phonon dispersion of gold nanotube using an example of small gold nanosheet. The dynamical matrix for the gold nanosheet was calculated using the force constants derived from Gupta Potential (GP). A better understanding of properties of gold nanotube is useful for its quick characterisation for possible applications in bio sensing, imaging etc. This work may be helpful in formulating algebra for calculating the phonon dispersion of gold nanotube and can be further used for calculating properties such as specific heat, thermal conductivity etc. at low computational cost in comparison with first principle calculations.

Ab initio lattice thermal conductivity of (Mg,Fe)O ferropericlase at the Earth’s lower mantle pressure and temperature

The effects of iron (Fe) incorporation on the lattice thermal conductivity () of MgO are investigated under the Earth’s lower mantle pressure (P) and temperature (T) condition (P > ∼20 GPa, T > ∼2000 K) based on the density-functional theory combined with the anharmonic lattice dynamics theory. The of ferropericlase (FP) is determined combining the internally consistent LDA + U method and self-consistent approach to solve the phonon Boltzmann transport equation. The calculated are well fitted to the extended Slack model which is proposed in this study to represent in a wide volume and T range. Results demonstrate that the of MgO decreases strongly by Fe incorporation. This strong negative effect is found due to decreases in phonon group velocity and lifetime. Consequently, the of MgO at the core-mantle boundary condition (P∼ 136 GPa, T ∼ 4000 K) is substantially reduced from ∼40 to ∼10 W m−1 K−1 by the incorporation of Fe (12.5 mol%). The effect of Fe incorporation on the of MgO is found to be insensitive to P and T, and at high T, the of FP obeys a well-established T inverse relation unlike the experimental observations.

Theoretical study of entropy-induced friction in graphene

The exceptional properties of graphene and other two-dimensional (2D) materials have endowed them with enormous potentials as fundamental elements in future microscale devices. With the dimension reduction in 2D materials, new friction behavior emerges: the friction is dominated by the contact edges rather than the contact areas. This edge-dominated behavior has an essentially entropic origin. Herein we develop an analytical model to describe this entropy-originated friction in graphene based on lattice dynamics theory. This edge-dominated friction is attributed to a translation effect of the surface interaction on the local vibration modes. By considering the potential stiffness on the vibration modes, the analytical model enables us to investigate the dependence of friction on sliding speed, normal load, and stiffness of the supporting surface. The analytical model is found to give accurate prediction close to those given by molecular dynamics simulations. These findings confirm that the analytical model can capture the underlying physics of graphene interlayer friction effectively. Though graphene is investigated herein, the analytical model will have general applications in characterizing the tribological behavior of other single-atom-thick 2D materials since they possess similar phononic properties as graphene.

Quantum theory of light-driven coherent lattice dynamics

The exposure to intense electromagnetic radiation can induce distortions and symmetry breaking in the crystal structure of solids, providing a route for the all-optical control of their properties. In this manuscript, we formulate a unified theoretical approach to describe the coherent lattice dynamics in presence of external driving fields, electron-phonon and phonon-phonon interactions, and quantum nuclear effects. The main mechanisms for the excitation of coherent phonons - including infrared absorption, displacive excitation, inelastic stimulated Raman scattering, and ionic Raman scattering - can be seamlessly accounted for. We apply this formalism to a model consisting of two coupled phonon modes, where we illustrate the influence of quantum nuclei on structural distortions induced by ionic Raman scattering. Besides validating the widely-employed classical models for the coherent lattice dynamics, our work provides a versatile approach to methodically explore the emergence of quantum nuclear effects in the structural response of crystal lattice to strong fields.

First principles study of the lattice thermal conductivity of alkaline earth oxides

Lattice thermal conductivity (κlatt) is an important physical parameter for understanding the thermal transport and dynamics evolution. Here, we calculate κlatt of alkaline earth metal oxides (MOs, M = Be, Mg, Ca, Sr, Ba) by first principles calculations combined with lattice dynamics theory. Our results indicate that the magnitudes of κlatt of MOs at ambient conditions are closely related to the atomic masses of metal atoms, that is, the lighter atomic masses of metals in MOs possess the larger κlatt, which is consistent with the order of alkaline earth metals in Periodic Table. Under high pressure, κlatt of MOs show linearly increase as a function of pressure; meanwhile, the pressure dependence of κlatt is relatively larger for MOs with lighter atomic masses. The calculations show that the structural phase transitions of MOs lead to obvious reductions in κlatt due to the giant variations in scattering rates. By contrast, the effect of phase transition on elastic property and wave velocities are weak, which implies the variation of group velocities are faintly effect on κlatt.

Investigation on the Phonon Focusing, Polaritons and Reflection of Gan with Lattice Dynamics Theory

Investigation on the Phonon Focusing, Polaritons and Reflection of Gan with Lattice Dynamics Theory

Lattice-based J integral for a steadily moving dislocation

According to continuum theory and the conservation theorem, the J integral represents the net translational force acting on a defect and, specifically, it is equivalent to the Peach–Koehler force for dislocation. In this study, we newly derive the J integral to quantify driving force on a uniformly moving dislocation with considering its core-induced dynamic behaviors. Using both molecular dynamics simulation and lattice dynamics theory based on atomic chain model, we prove that radiation drag and self-stress asymmetry during the dislocation motion, which are generated by lattice discreteness, make the newly derived J integral depend on the distance from the dislocation core, which is lumped into resistance to the dislocation motion. Finally, we show that the J integral converges to the Peach–Koehler force as the resistance term disappears for a stationary dislocation.

Experimental and Theoretical Contribution to the Phase Equilibria in the Ternary CaO-Al2O3-B2O3 System

The phase equilibria in the lime rich part of the CaO-Al2O3-B2O3 ternary system were investigated by thermodynamic modeling and key experiments. Three ternary compounds, CaAl2B2O7 (CAB), Ca2Al2B2O8 (C2AB) and Ca2Al2B6O14 (C2AB3), are reported in the literature and their thermodynamic properties were calculated using Density Functional Theory and lattice dynamics theory. Partial isothermal sections of the lime rich part of the CaO-Al2O3-B2O3 ternary system were investigated at 950 and 1020 °C using solid state reactions and x-ray diffraction on 14 selected samples. The observed results confirm the available experimental data from the literature. Based on thermal analysis using differential scanning calorimetry, the Ca3Al2O6-CaB2O4 and CaAl2O4-CaB2O4 T-x sections as well as a tentative partial liquid surface of the lime rich part were constructed.

Lattice Thermal Conductivity of MgSiO3 Postperovskite Under the Lowermost Mantle Conditions From Ab Initio Anharmonic Lattice Dynamics

AbstractThe lattice thermal conductivity (κlat) of MgSiO3 postperovskite (Mg‐PPv) under the lowermost mantle pressure (P) and temperature (T) conditions was calculated using density functional theory combining anharmonic lattice dynamics theory. The κlat of Mg‐PPv was found to be ~50% higher than that of MgSiO3 bridgmanite (Mg‐Brg) owing to the larger phonon group velocity and lifetime. The lateral variation in the core‐mantle boundary heat flux (qCMB) can be enhanced by the Brg‐PPv phase transition. We also found that the κlat along the c axis of Mg‐PPv is close to the conductivity of isotropic aggregate. This suggests that the effect of anisotropy in the κlat on qCMB would be minor if the transversely isotropic aggregate with the c axis vertical alignment, a potential source of seismic anisotropy in the D″ layer, is developed.

Theoretical Study of Alkali-Metal Hydrides at High Pressures: A Case of NaH Supported by Inelastic Neutron Scattering (INS) Experiments at 1 and 2 GPa.

Pressure-induced effects in alkali hydrides are investigated using a plane-wave density functional theory method. For the first time, we have measured the inelastic neutrons scattering (INS) spectra of NaH at pressures 1 and 2 GPa and used it to validate INS simulated from the first-principles calculations using both local density approximation (LDA) and the generalized gradient approximation (GGA). We found that LDA describes lattice dynamics better compared to the GGA. Thermodynamic properties such as lattice parameters, bulk modulus, and their derivatives are calculated using full lattice dynamics theory within the quasi-harmonic approximation (QHA) for all alkali hydrides. Anharmonic effects are investigated for NaH from the molecular dynamics trajectories and are negligible at given temperature and pressures. We have shown that the phase-change pressures obtained from the equal Gibbs free-energy conditions for two phases compare well with the available experimental data and is the accurate phase-change criterion. This study corroborates INS as an important complementary tool in benchmarking first-principles calculations.

Application of Wavelet Transform to the study of Lattice Dynamics of two-dimensional Nanostructures

Abstract Theory of vibration of atoms that is the theory of lattice dynamics now forms an important part of study in Nanotechnology as these vibrations determine thermal and mechanical characteristics of a material and also govern phenomena like diffuse scattering of X-rays, neutron scattering, spin-lattice relaxation, etc. Lattice Dynamical analysis is helpful in the design and engineering of Nanomaterial and nanostructures for phononic and acoustic applications. Unlike current techniques that are based on Fourier analysis that gives results for frequency distribution along the wave vector, the wavelet transform can be used to determine how the energy of a simulated system is distributed in time, space, and among wave numbers, simultaneously. This is important in the study of interfacial phonon (quanta of crystal vibration) conductance, where the time the phonon packet interacts with the interface is preserved in the transformation. Wavelet transform is a unique tool for probing localized phonon physics at Nano scales. Two- dimensional Nanostructures like Graphene and hexagonal Boron Nitride has unique thermal properties which make them suited for a variety of applications. Wavelet Transform is applied to the lattice dynamics of a two- dimensional lattice and phonon transport is studied for industrially important materials like Graphene and its variations.

Theory of spin and lattice wave dynamics excited by focused laser pulses

We develop a theory of spin wave dynamics excited by ultrafast focused laser pulses in a magnetic film. We take into account both the volume and surface spin wave modes in the presence of applied, dipolar and magnetic anisotropy fields and include the dependence on laser spot exposure size and magnetic damping. We show that the sound waves generated by local heating by an ultrafast focused laser pulse can excite a wide spectrum of spin waves (on top of a dominant magnon–phonon contribution). Good agreement with recent experiments supports the validity of the model.

Features of the Percolation Scheme of Vibrational Spectrum Reconstruction in the Ga1 – xAl x P Alloy

Specific features of the properties of Ga–P lattice vibrations have been investigated using the percolation model of a mixed Ga1 – xAl x P crystal (alloy) with zero lattice mismatch between binary components of the alloy. In contrast to other two-mode alloy systems, in Ga1 – xAl x P a percolation splitting of δ ~ 13 cm–1 is observed for the low-frequency mode of GaP-like vibrations. An additional GaP mode (one of the percolation doublet components) split from the fundamental mode is observed for the GaP-rich alloy, which coincides in frequency with the gap corresponding to the zero density of one-phonon states of the GaP crystal. The vibrational spectrum of impurity Al in the GaP crystal has been calculated using the theory of crystal lattice dynamics. Upon substitution of lighter Al for the Ga atom, the calculated spectrum includes, along with the local mode, a singularity near the gap with the zero density of phonon states of the GaP crystal, which coincides with the mode observed experimentally at a frequency of 378 cm–1 in the Ga1 – xAl x P (x < 0.4) alloy.

Strain effects on rotational property in nanoscale rotation system

This paper presents a study of strain effects on nanoscale rotation system consists of double-walls carbon nanotube and graphene. It is found that the strain effects can be a real-time controlling method for nano actuator system. The strain effects on rotational property as well as the effect mechanism is studied systematically through molecular dynamics simulations, and it obtains valuable conclusions for engineering application of rotational property management of nanoscale rotation system. It founds that the strain effects tune the rotational property by influencing the intertube supporting effect and friction effect of double-walls carbon nanotube, which are two critical factors of rotational performance. The mechanism of strain effects on rotational property is investigated in theoretical level based on analytical model established through lattice dynamics theory. This work suggests great potentials of strain effects for nanoscale real-time control, and provides new ideas for design and application of real-time controllable nanoscale rotation system.

Особенности перколяционной схемы перестройки колебательного спектра сплава с составом для Ga-=SUB=-1-x-=/SUB=-Al-=SUB=-x-=/SUB=-P

AbstractSpecific features of the properties of Ga–P lattice vibrations have been investigated using the percolation model of a mixed Ga_1 – x Al_ x P crystal (alloy) with zero lattice mismatch between binary components of the alloy. In contrast to other two-mode alloy systems, in Ga_1 – x Al_ x P a percolation splitting of δ ~ 13 cm^–1 is observed for the low-frequency mode of GaP-like vibrations. An additional GaP mode (one of the percolation doublet components) split from the fundamental mode is observed for the GaP-rich alloy, which coincides in frequency with the gap corresponding to the zero density of one-phonon states of the GaP crystal. The vibrational spectrum of impurity Al in the GaP crystal has been calculated using the theory of crystal lattice dynamics. Upon substitution of lighter Al for the Ga atom, the calculated spectrum includes, along with the local mode, a singularity near the gap with the zero density of phonon states of the GaP crystal, which coincides with the mode observed experimentally at a frequency of 378 cm^–1 in the Ga_1 – x Al_ x P ( x &lt; 0.4) alloy.

Nonmonotonic dependence of polymer-glass mechanical response on chain bending stiffness.

We investigate the mechanical properties of amorphous polymers by means of coarse-grained simulations and nonaffine lattice dynamics theory. A small increase of polymer chain bending stiffness leads first to softening of the material, while hardening happens only upon further strengthening of the backbones. This nonmonotonic variation of the storage modulus G^{'} with bending stiffness is caused by a competition between additional resistance to deformation offered by stiffer backbones and decreased density of the material due to a necessary decrease in monomer-monomer coordination. This counterintuitive finding suggests that the strength of polymer glasses may in some circumstances be enhanced by softening the bending of constituent chains.

Piezoelectricity in two-dimensional materials: Comparative study between lattice dynamics andab initiocalculations

Elastic constant C_{11} and piezoelectric stress constant e_{1,11} of two-dimensional (2D) dielectric materials comprising h-BN, 2H MoS2 and other transition metal dichalcogenides (TMDCs) and -dioxides (TMDOs) are calculated using lattice dynamical theory. The results are compared with corresponding quantities obtained by ab-initio calculations. We identify the difference between clamped-ion and relaxed-ion contributions with the dependence on inner strains which are due to the relative displacements of the ions in the unit cell. Lattice dynamics allows to express the inner strains contributions in terms of microscopic quantities such as effective ionic charges and optoacoustical couplings, which allows us to clarify differences in the piezoelectric behavior between h- BN versus MoS2. Trends in the different microscopic quantities as functions of atomic composition are discussed.

Structural, lattice dynamics and thermodynamic properties of Sr2VO4 from first principles

The structural, lattice dynamics and thermodynamic properties of Sr2VO4 are systematically explored from ab initio density functional theory. In order to describe correlated phenomena among the localized V 3d electrons, DFT + U method have been used. The Born effective charges, and vibrational properties are calculated based on lattice dynamics theory. The calculated phonon wave numbers of infrared normal mode are found to be in consistency with experimental values available present. By comparing with the experimental data, we get more reasonable mode assignments. Additionally, some thermodynamic properties, e.g., Helmholtz free energy, entropy, and heat capacity, are also analyzed based on quasi-harmonic approximation. Comparison of the calculated specific heat at constant pressure P = 0 GPa with previous experimental data can further confirm the anomalous peak around 100 K due to the orbital ordering transition. The rapid increase of thermal expansion coefficient around the crystal growth temperature, 1000–1300 K, may be one reason of resulting in the difficulty of synthesizing the bulk single crystal phase.

First-principles calculations of crystal and electronic structures and thermodynamic stabilities of La–Ni–H, La–Ni–Al–H and La–Ni–Al–Mn–H hydrogen storage compounds

First-principles density functional theory (DFT) and lattice dynamical theory (LDT) calculations have been used to investigate the crystal and electronic structures and thermodynamic stabilities of La–Ni–H, La–Ni–Al–H and La–Ni–Al–Mn–H hydrogen storage compounds. We find that all these compounds studied are dynamically stable. For LaNi3.8Al1.2−xMnxH (x = 0.2, 0.4, 0.6) hydrides, Al only substitutes Ni at 3g0 site, H occupies 12n tetrahedral site. The structural optimizations indicate that Mn prefers to substitute Ni at 3g1 site. Mn substitutions for Ni and Al decrease their stabilities. A detailed analysis of bonding interactions reveals that the covalent bonds of H with one Ni or Mn at 3g1 site and two Ni at 2c site are mainly responsible for the stabilities of these compounds. We also present a comprehensive investigation of phonon spectra and vibrational thermodynamics of LaNi5−xAlxH (x = 0, 0.25, 0.5, 0.75 and 1) and LaNi3.8Al1.2−xMnxH (x = 0.2, 0.4 and 0.6). We find that all phonon vibrations have contribution to their vibrational enthalpies; in contrast, the low-frequency phonon vibrations mainly dominate their vibrational entropies. The calculated accuracy of low-frequency phonon vibrations is closely related to crystal symmetry, supercell size and atomic distribution in selected supercell. Generally, calculated enthalpies are more accurate than calculated entropies with respect to their experimental values. We present in the current research a first-principles method to predict the variation of enthalpy with hydrogen content at hydrogenation or dehydrogenation plateau and then to identify the so-called plateau enthalpy of each La–Ni based hydrogen storage alloy. By using this method, we find that the partial substitutions of Ni by Al decrease the so-called plateau enthalpy but impair the hydrogen storage capacity obviously, while Mn and Al substitutions for Ni not only decrease the so-called plateau enthalpy but also extend the plateau length.