Anharmonicity Of Lattice Vibrations Research Articles

Isotope-Induced Ferroelectric Phase Transition in Strontium Titanate Only by a Decrease in Zero-Point Vibration Frequency

The possibility of the ferroelectric phase transition in SrTi 18 O 3 only by decreasing the frequency of zero-point vibration due to the substitution of 18 O for 16 O is investigated by the self-consistent phonon approximation (SCPA) of an anharmonic lattice vibration system. The SC equation for the soft-mode frequency is shown to be described by only two parameters; the paraelectric Curie–Weiss temperature T 0 in SrTi 16 O 3 and the quantum factor T 1 inversely proportional to the square root of the effective mass M . The experimental finding that T c =0 in the mixed crystal SrTi( 18 O x 16 O 1- x ) 3 at x =0.33 is used to determine T 1 at this concentration and that at another x using only the ratio of M . The transition temperature T c in SrTi 18 O 3 is numerically calculated for comparison with the experimental value. Several factors determining T c are discussed on the basis of numerical results.

Charge-Density-Wave Instability in the Holstein Model with Quartic Anharmonic Phonons

The molecular-crystal model, that describes a one-dimensional electron gas interacting with quartic anharmonic lattice vibrations, offers great potentials in the mapping of a relatively wide range of low-dimensional fermion systems coupled to optical phonons onto quantum liquids with retarded interactions. Following a non-perturbative approach involving non-Gaussian partial functional integrations of lattice degrees of freedom, the exact expression of the phonon-mediated two-electron action for this model is derived. With the help of Hubbard-Stratonovich transformation the charge-density-wave instability is examined in the sequel, with particular emphasis on the effect of the quartic anharmonic phonons on the charge-density-wave transition temperature.

Static compressibility, thermal expansion and elastic anisotropy of [formula omitted] single crystals

The elastic anisotropy factor, isothermal compressibility, and thermal expansion of Zr 2SC single crystals are determined in the pressure range 0–50 GPa. With increasing temperature, its compressibility increases and Debye temperature decreases; with increasing pressure, the anisotropy factor, the c -axis and in-plane bulk moduli, longitudinal wave and transverse wave velocities increase, while the compressibility of Zr 2SC decreases. The results are interpreted in terms of the anharmonicity of lattice vibrations.

Theoretical Investigation of the Isotope-Induced Ferroelectric Phase Transition in Quantum Paraelectric Strontium Titanate

The isotope-induced ferroelectric phase transition is theoretically investigated in terms of a compact formula based on the self-consistent phonon approximation (SCA) on the anharmonic lattice vibration system. The T c − T 1 phase diagram, where T c and T 1 are the transition temperature T c and the quantum fluctuation parameter T 1, respectively, is numerically calculated to demonstrate the nonlinear dependence of T c on T 1 sensitive to the increase of the oxygen mass. Experimental results of the small transition entropy and the perfect softening are discussed from the viewpoint of the ideal displacive type phase transition.

Anharmonicity of lattice vibrations and transverse deformation of crystalline and vitreous solids

This paper reports on the additional data confirming the interrelation between the Gruneisen parameter and Poisson’s ratio in crystalline and vitreous solids. The assumption is made that the ratio between the velocities of longitudinal and transverse acoustic waves can depend on the anharmonicity of lattice vibrations.

Green's Function of Fully Anharmonic Lattice Vibration

Motivated by the discovery of superconductivity in β-pyrochlore oxides, we study property of rattling motion coupled with conduction electrons. We derive the general expression of the Green's function of fully anharmonic lattice vibration within the accuracy of the second order perturbation of electron–ion interaction by introducing self-energy, vertex-correction, and normalization factor for each transition. Using the expression, we discuss the characteristic properties of the spectral function in the entire range from weakly anharmonic potential to double-well case, and calculate NMR relaxation rate due to the two phonon Raman process.

Fragility and anharmonicity of lattice vibrations of glass-forming systems

The dependence of the fragility on the Gruneisen lattice parameter, which is a measure of the anharmonicity of lattice vibrations, is established for lead silicate and sodium borate glasses. An expression relating the fragility of glasses to the parameters of the Williams-Landell-Ferry equation is obtained. The calculation performed using this expression is in agreement with the results of the conventional determination of the fragility.

Melting temperature and anharmonicity of lattice vibrations in solids

A correlation between melting points and Gruneisen lattice constants was found for a number of glass-forming oxides. It was established that, at the melting point, the mean energy of the thermal motion of a kinetic unit equaled the ultimate strain work of the interatomic bond corresponding to the quasi-elastic force maximum.

Raman scattering study of ca-modified lead titanate

The paraelectric to ferroelectric phase transitions were studied by Raman scattering in Ca-doped lead titanate ceramics. The soft optic modes responsible for the ferroelectric phase transitions were clearly observed. The A(1)(1TO) mode, which softens toward T(c), contains four subpeaks. The frequencies of these subpeaks depend to a great extent on the Ca content and the temperature. These behaviors are discussed on the basis of the anharmonicity of lattice vibrations.

An effective temperature approach for molecular dynamics simulations of quantum solids

We examine two standard methods to incorporate quantum effects in classical molecular dynamics simulations of quantum solids. It is shown that thermal harmonic quantum correction fails to generate a reliable structure of solid neon, while augmenting the classical equations of motion with a quantum Langevin force is no longer appropriate for heavier noble gases. An alternative approach is proposed which accounts as simply as possible for the characteristic frequency and the anharmonicity of lattice vibrations. Simulations carried out within this approach in the canonical ensemble show that normal solid-like structure could be achieved while lattice symmetry is preserved.

Dielectric Loss Spectrum of Ceramic MgTiO3 Investigated by AC Impedance and Microwave Resonator Measurements

MgTiO3 ceramic was selected as a model material of the microwave dielectric ceramics for the investigation of the dielectric loss spectrum. Conductivity spectra in the low‐frequency range 1–106 Hz at elevated temperatures and the dielectric loss spectrum in the microwave range 6–14 GHz at room temperature were characterized by AC impedance spectroscopy and the microwave resonator method, respectively. The experimental data were analyzed by using Jonscher's universal power law, the Arrhenius equation as well as the classic dispersion theory. Consequently, a dielectric loss spectrum (tg δ∼f plot) at room temperature in a wide frequency range was obtained. Based on the loss spectrum, the dielectric loss can be classified into three mechanisms in MgTiO3 ceramic (each dominates the loss in different frequency ranges): DC conductance (in DC field), AC conductance (<107 Hz), and anharmonicity of lattice vibration (in GHz range). The influence of defects on the microwave dielectric loss possibly is because of atom defects via damage of the perfection of lattice and modification of the anharmonic force in lattice, while the electronic defects trapped on the atomic defects affect the DC and AC losses.

Elastic Anisotropy, Isothermal Compressibility, and Gruneisen Parameter of GaS Single Crystals

The elastic anisotropy factor, isothermal compressibility, and Gruneisen parameters of GaS single crystals are determined in the range 80–410 K. With increasing temperature, the anisotropy factor and volume compressibility of GaS increase, while its Gruneisen parameters decrease. The results are interpreted in terms of the anharmonicity of lattice vibrations.

Atomistic Study of Fracture of Crystalline Materials by Lattice Green's Function Method: Effects of Anharmonicity of Lattice Vibration

Atomistic Study of Fracture of Crystalline Materials by Lattice Green's Function Method: Effects of Anharmonicity of Lattice Vibration

Structure, thermal, and transport properties of the clathratesSr8Zn8Ge38,Sr8Ga16Ge30, andBa8Ga16Si30

The structural parameters, thermal properties, and transport properties of three type I clathrates, namely ${\mathrm{Sr}}_{8}{\mathrm{Zn}}_{8}{\mathrm{Ge}}_{38}$, ${\mathrm{Sr}}_{8}{\mathrm{Ga}}_{16}{\mathrm{Ge}}_{30}$, and ${\mathrm{Ba}}_{8}{\mathrm{Ga}}_{16}{\mathrm{Si}}_{30}$, have been determined at or below room temperature. The structural parameters of these clathrates were determined by powder neutron diffraction. Their lattice thermal expansion is two to four times greater than that of the diamond phases of silicon and germanium, consistent with more anharmonic lattice vibrations. From the temperature dependence of the isotropic atomic displacement parameters, the estimated rattling frequencies of guests in the large cages of these clathrates are in the range $50--60\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$. The heat capacities of these three clathrate materials increase smoothly with increasing temperatures and approach the Dulong--Petit value around room temperature. The Gr\"uneisen parameter of these materials is constant between $100$ and $300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ but increases below $100\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, due to the dominance of the low-frequency guest-rattling modes. The room-temperature electrical resistivity and the Seebeck coefficient show that these materials are metallic. The temperature profile of the thermal conductivities and calculated phonon mean free paths of these materials show glasslike behavior, although they are crystalline materials, indicating strong resonant scattering of heat-carrying acoustic phonons via the rattling of the guests in the clathrate cages.

Atomistic Study of Fracture of Crystalline Materials by Lattice Green's Function Method: Effects of Anharmonicity of Lattice Vibration

Using the lattice Green's function approach which includes the temperature dependence of the materials parameters, we study the both cleavage and dislocation emission processes in the fracture of crystalline materials. Firstly, we calculate the Green's function for the defective lattice, with dislocation and crack, by solving the Dyson equation. After the lattice Green's functions have been determined, the relaxation problem for the reconstituted bonds in the cohesive zone is solved. The external force F with tensile and shear components is applied, as a pair of forces, to the atoms at the center of the crack. In this lattice Green's function calculation the temperature effects resulting from the anharmonicity of lattice vibrations are included by introducing the thermal lattice expansion, temperature dependent force constant matrix and temperature dependent non-linear cohesive forces at the crack tip region. We compare the cleavage and dislocation emission processes at the absolute zero temperature with ...

The particle-in-cell model for ab initio thermodynamics: implications for the elastic anisotropy of the Earth’s inner core

We assess the quantitative accuracy of the particle-in-cell (PIC) approximation used in recent ab initio predictions of the thermodynamic properties of hexagonal-close-packed (hcp) iron at the conditions of the Earth’s inner core. The assessment is made by comparing PIC predictions for a range of thermodynamic properties with the results of more exact calculations that avoid the PIC approximation. It is shown that PIC gives very accurate results for some properties, but that it gives an unreliable treatment of anharmonic lattice vibrations. In addition, our assessment does not support recent PIC-based predictions that the hexagonal c/ a ratio increases strongly with increasing temperature, and we point out that this casts doubt on a proposed re-interpretation of the elastic anisotropy of the inner core.

Application of statistical moment method to thermodynamic quantities of metals and alloys

The thermodynamic quantities of metals and alloys are studied using the moment method in the quantum statistical mechanics, going beyond the harmonic approximation, and fully taking into account the anharmonicity of lattice vibrations. Including the power moments of the atomic displacements up to the fourth order, the free energy, specific heats C v and C p, mean square relative displacements and thermal lattice expansion coefficients are given explicitly in terms of the second and fourth order vibrational coupling constants. The effects of anharmonicity of lattice vibration on the long range order (LRO) parameter and order-disorder transitions of the binary alloys are investigated in detail. The changes in the root mean square atomic displacements upon the order-disorder phase transition are evaluated and compared with the available experimental results. We also discuss the melting transitions of metals and alloys within the framework of the present statistical moment method, and estimate the melting temperatures through the limiting temperature of the crystalline stability.

Anharmonicity of lattice vibrations induced by charged nickel impurities in II–VI semiconductors

The lattice vibrations induced by nickel impurities with a negative charge relative to the lattice in ZnSe: Ni, ZnO: Ni, ZnS: Ni, and CdS: Ni semiconductors are investigated using very sensitive field-induced vibronic spectroscopy. This technique is based on the interaction of lattice vibrations with impurity excitons and the effect of an ac electric field on these excitons. The phonon replicas of the zero-phonon line (ZPL) of impurity excitons (including intense peaks of combination replicas up to the eighth order) in the experimental spectra of the system under investigation are observed for the first time. These spectra make it possible to analyze the interaction between different vibrations. The experimental results are interpreted in terms of model calculations of the vibrations in a lattice with a charged impurity center and vibrations in a monoatomic chain with a strong anharmonicity. It is demonstrated that charged impurity centers initiate new lattice vibrations, namely, extrinsic anharmonic modes with a considerable third-or fourth-order anharmonicity.

Calculation of thermodynamic quantities of metals and alloys by the statistical moment method

The thermodynamic properties of metals and alloys are studied using the moment method in the statistical dynamics, which allows us to take into account the anharmonicity of thermal lattice vibrations and size mismatch of constituent atoms, going beyond the quasi-harmonic approximation. Within the fourth-order moment approximation, the free energy and equilibrium lattice spacing of the binary alloys are given explicitly in terms of the effective pair potentials and the second- and fourth-order vibrational constants. The long-range order (LRO) parameter η and order-disorder transition temperatures (ODTs) Tc of binary alloys are obtained by solving the explicit transcendental equations. The numerical calculations of thermodynamic quantities for Cu3Au and β-CuZn alloys show that the inclusion of the anharmonicity of lattice vibration plays an essentially important role in determining the phase stabilities of metals and alloys.

Heat capacities of icosahedral and hexagonal phases of Zn–Mg–Y system

Heat capacity measurements have been performed in the temperature range 4–300K for an icosahedral phase of Zn–Mg–Y alloy (Zn55Mg35Y10) and the related crystalline phases, a hexagonal phase (Zn65.2Mg27.9Y6.9) and the Laves phase of MgZn2, to study the feature of lattice vibrations in quasicrystals. A single quasicrystal of Zn56.8Mg34.6Y8.7 was also investigated for comparison. The vibrational density of states is delineated in terms of the temperature dependence of the apparent Debye temperature (ΘD) on a reduced basis using the limiting value at high temperature (Θ∞). A deeper minimum (ΘD/Θ∞∼0.82) is observed at substantially lower temperatures (T/Θ∞∼0.055) in the quasicrystals than in the crystals, which suggests significant enhancement of the density of states at the corresponding energies. The fact is compatible to that obtained previously for Al–Cu–Ru, Al–Pd–Re and Al–Pd–Mn systems. The presence of some defects or inhomogeneity in quasicrystals might be responsible for the anharmonic lattice vibrations.