Lattice anharmonicity

Laser-plasma accelerator, 150 Laser-driven acceleration, 140 Lattice anharmonicity, 32 Leader, 110 Lewenstein model, 66 Lightning, 109 LINAC, 172... 

Ethylene was one of the first systems subjected to detailed vibrational analysis using HOCM modified to account for lattice anharmonicity. Agreement with experiment is excellent (Fig. 5.5). The differences in the VPIE s of the equivalent isotopomers cis- trans-, and gem-dideuteroethylene (Fig. 5.6) are of considerable interest since they neatly demonstrate the close connection between molecular structure and isotope chemistry. The IE s are mainly a consequence of hindered rotation in the liquid (moments of inertia for cis-, trans-, and gem-C2D2H2 are slightly... 

Ferroelectricity is a highly collective phenomenon involving the long-range internal electric field, and occurs only when the size of the system is large enough. Yet local physics does play a major role, as is evidenced by the relevance of the lattice anharmonicity that develops a local double-well potential. 

Extrinsic dielectric loss in the microwave Ereqnency range is related to microstructure, secondary phases, and processing conditions. Intrinsic loss, however, represents the minimnm loss related to the lattice anharmonicity that can be expected for a particnlar material composition and crystal structure. It plays a... 

It is generally agreed that thermally induced vibrations of atoms in solids play a major role in melting [2.144]. The simple vibrational model of Linde-mann predicts a lattice instability when the root-mean-square amplitude of the thermal vibrations reaches a certain fraction / of the next neighbor distances. However, the Lindemann constant/varies considerably for different substances because lattice anharmonicity and soft modes are not considered, thus limiting the predictive power of such a law. Furthermore, Born proposed the collapse of the crystal lattice to occur when one of the effective elastic shear moduli vanishes [2.138], Experimentally, it is found instead that the shear modulus as a function of dilatation is not reduced to zero at Tm and would vanish at temperatures far above Tm for a wide range of different substances [2.145]... 

The IR active mode V5 corresponds to the well known sharp band in the FIR spectrum of PE with maximum at 73 cm" . The mode originates from translational vibrations of the lattice, this agrees with the IR dichroism [13] and deuteration studies [14]. Increasing the temj rature shifts the band toward lower wave numbers, from 81 to 68 cm" between 12 and about 400 K [15]. The application of external pressure leads to a fi-equency shift in the opposite direction. This result makes it possible to discuss lattice anharmonicity and Grueneisen parameters [16]. 

The above analyses is based on the thermodynamical theory, while G. Rupprecht et al. and Johnson also diseussed the origin of such field-dependent behavior according to the ion oscillating in a lattice anharmonic potential in perovskites [3,42]. It has been concluded that the anharmonic restoring forces on the Ti ion when it is displaced from its equilibrium position, is responsible for the dielectrie tuning in BST and STO. G. Rupprecht et al. also evaluated the nonlinear constant of A(= in Eq. 6. Their theoretical results indicated... 

According to the above discussions, the dielectric tunable properties of perovskites are highly associated with the phase transition of ferroelectrics, crystal texture, and lattice anharmonic interactions. These accordingly provide us approaches to enhance the tunable properties of perovskites thin films. 

The observation of the departure from cubic symmetry above Tm co-incident with the appearance of the central peak scattering serves to resolve the conflict between dynamic and lattice strain models. The departure from cubic symmetry may be attributed to a shift in the atomic equilibrium position associated with the soft-mode anharmonicity. In such a picture, the central peak then becomes the precusor to a Bragg reflection for the new structure. 

It is clear that nonconfigurational factors are of great importance in the formation of solid and liquid metal solutions. Leaving aside the problem of magnetic contributions, the vibrational contributions are not understood in such a way that they may be embodied in a statistical treatment of metallic solutions. It would be helpful to have measurements both of ACP and A a. (where a is the thermal expansion coefficient) for the solution process as a function of temperature in order to have an idea of the relative importance of changes in the harmonic and the anharmonic terms in the potential energy of the lattice. 

T. Riste, Anharmonic Lattices, Structural Transitions and Melting, Noordhoff, Leiden, 1974. 

We note first that not all amorphous substances actually exhibit a negative a in the experimentally probed temperature range. In such cases, it is likely that the contraction coming from those interactions in these materials is simply weaker than the regular, anharmonic lattice thermal expansion. Other contributions to the Griineisen parameter will be discussed later as well. 

In the Heitler-London approximation, with allowance made only for biquadratic anharmonic coupling between collectivized high-frequency and low-frequency modes of a lattice of adsorbed molecules (admolecular lattice), the total Hamiltonian (4.3.1) can be written as a sum of harmonic and anharmonic contributions ... 

The heat capacity models described so far were all based on a harmonic oscillator approximation. This implies that the volume of the simple crystals considered does not vary with temperature and Cy m is derived as a function of temperature for a crystal having a fixed volume. Anharmonic lattice vibrations give rise to a finite isobaric thermal expansivity. These vibrations contribute both directly and indirectly to the total heat capacity directly since the anharmonic vibrations themselves contribute, and indirectly since the volume of a real crystal increases with increasing temperature, changing all frequencies. The constant volume heat capacity derived from experimental heat capacity data is different from that for a fixed volume. The difference in heat capacity at constant volume for a crystal that is allowed to relax at each temperature and the heat capacity at constant volume for a crystal where the volume is fixed to correspond to that at the Debye temperature represents a considerable part of Cp m - Cv m. This is shown for Mo and W [6] in Figure 8.15. 

Contents Lattice Dynamics. - Symmetry. - Inter-molecular Potentials. - Anharmonic Interactions. - Two-Phonon Spectra of Molecular Crystals. -Infrared and Raman Intensities in Molecular Crystals. 

Our development has assumed temperature independent force constants. In real liquids, however, there is a small temperature dependence of frequencies and force constants due to anharmonicities, lattice expansion, etc. The incorporation of these effects into the theory is treated in later sections. 

MSN.50. 1. Prigogine, F. Henin, and C. George, Entropy and quasiparticle description of anharmonic lattices, Physica 32, 1873-1900 (1966). 

MSN.158.1. Prigogine and T. Petrosky, Extension of classical dynamics—the case of anharmonic lattices, in Ivanenko Memorial Volume in Gravity, Particles and Space-Time, P. Pronin and G. Sardanshvili, eds.. World Scientific, Singapore, 1996. 

One result of studying nonlinear optical phenomena is, for instance, the determination of this susceptibility tensor, which supplies information about the anharmonicity of the potential between atoms in a crystal lattice. A simple electrodynamic model which relates the anharmonic motion of the bond charge to the higher-order nonlinear susceptibilities has been proposed by Levine The application of his theory to calculations of the nonlinearities in a-quarz yields excellent agreement with experimental data. 

Displacive ferroeiectrics where a discrete symmetry group is broken at Tc and the ferroelectric transition can be described as the result of an instability of the anharmonic crystal lattice against soft polar lattice vibration (e.g., BaTiOs). 

Whereas the first microscopic theory of BaTiOs [1,2] was based on order-disorder behavior, later on BaTiOs was considered as a classical example of displacive soft-mode transitions [3,4] which can be described by anharmonic lattice dynamics [5] (Fig. 1). BaTiOs shows three transitions at around 408 K it undergoes a paraelectric to ferroelectric transition from the cubic Pm3m to the tetragonal P4mm structure at 278 K it becomes orthorhombic, C2mm and at 183 K a transition into the rhombohedral low-temperature Rm3 phase occurs. 

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