Characterization lattice dynamics

One of the consequences of the suppression of the phase transition is the presence of a special critical point, Tc = 0 K. This point, called the quantum displacive limit, is characterized by special critical exponents. Its presence gives rise to classical quantum crossover phenomena. Quantum suppression and the response at and near this limit, Tc = 0 K, have been extensively studied on the basis of lattice dynamic models solved within the framework of both classical and quantum statistical mechanics. Figure 8 is a log-log plot of the 6 T) results for ST018 [15]. The expectation from theory is that in the quantum regime, y = 2 at 0.7 kbar, after which y should decrease. The results in Fig. 8 quantitatively show the expected behavior however, y is < 2 at 0.70 kbar. Despite the difference in the methods to suppress Tc in ST018, the results in Fig. 4a and Fig. 8 are quite similar. As shown in the results in Fig. 3b, uniaxial pressure also can be a critical parameter S for the evolution of ferroelectricity in STO. 

The dynamic RIS model developed for investigating local chain dynamics is further improved and applied to POE. A set of eigenvalues characterizes the dynamic behaviour of a given segment of N motional bonds, with v isomeric states available to each bond. The rates of transitions between isomeric states are assumed to be inversely proportional to solvent viscosity. Predictions are in satisfactory agreement with the isotropic correlation times and spin-lattice relaxation times from 13C and 1H NMR experiments for POE. 

June et al. (11) also performed MD calculations to characterize the dynamics of Xe in silicalite. A fixed lattice was assumed with potential parameters close to those used in previous MD studies. The potential between zeolite and guest was determined prior to the calculation over a three-dimensional grid spanning the asymmetric unit. From these grid points, the potential at any point in the lattice could be found by interpolation. Temperatures of 200, 300, and 400 K were imposed during the simulations, which ran for 1 ns. 

Ultraviolet Raman spectroscopy has emerged as a powerful technique for characterization of nanoscale materials, in particular, wide-bandgap semiconductors and dielectrics. The advantages of ultraviolet excitation for Raman measurements of ferroelectric thin films and heterostructures, such as reduced penetration depth and enhanced scattering intensity, are discussed. Recent results of application of ultraviolet Raman spectroscopy for studies of the lattice dynamics and phase transitions in nanoscale ferroelectric structures, such as superlattices based on BaTiOs, SrTiOs, and CaTiOs, as well as ultrathin films of BaTiOs and SrTi03 are reviewed. 

Conventional infrared spectra of powdery materials are very often used for studying solid hydrates in terms of sample characterization (fingerprints), phase transitions, and both structural and bonding features. For the latter objects mostly deuteration experiments are included. However, it must be born in mind that the band frequencies observed (except those of isotopically dilute samples (see Sect. 2.6)) are those of surface modes rather than due to bulk vibrations, i.e., the transverse optical phonon modes, and, hence, not favorably appropriate for molecular and lattice dynamic calculations. 

In 1912 Bom and von Karman [1, 2] proposed a model for the lattice dynamics of crystals which has become the standard description of vibrations in crystals. In it the atoms are depicted as bound together by harmonic springs, and their motion is treated collectively through traveling displacement waves, or lattice vibrations, rather than by individual displacements from their equilibrium lattice sites [3]. Each wave is characterized by its frequency, wavelength (or wavevector), amplitude and polarization. 

Period of the chain is equal to a. Let us suppose the linear relationship between the interaction force between the nearest neighbors and atomic displacement. Every internal motion of the lattice could be represented by the superposition of the mutually orthogonal waves as follows from the lattice dynamic theoiy (see e.g. Bom and Huang 1954 Leibfried 1955). Aiy lattice wave could be described by the wave vector K from the first Brillouin zone in the reciprocal space. Dispersion curve co K) has two separated branches (for 2 atoms in the primitive unit), which could be characterized as acoustic and optic phonons. If we suppose also the transversal waves (along with longimdinal ones), we can get three acoustic and three optical phonon branches. There is always one longitudinal (LA or LO) and two mutually perpendicular transversal (TA or TO) phonons. 

The molecules treated in this chapter are indeed large systems with complex chemical structures. Moreover, in going from the oligomers to the polymers it becomes necessary to consider the systems as one-dimensional crystals. The optical transitions (both vibrational and electronic) are determined by one-dimensional periodicity and translational symmetry. Collective motions (phonons) that extend throughout the chain need to be considered and are characterized by the wave vector k, and their frequencies show dispersion with k. Lattice dynamics in the harmonic approximation are well developed [12,13J, and vibrational frequency spectroscopy has reached full maturity and has been widely applied in polymer science [8,9,14]. 

Figure 2. A schematic of the free energy density of an aperiodic lattice as a function of the effective Einstein oscillator force constant a (a is also an inverse square of the locahzation length used as input in the density functional of the liquid). Specifically, the curves shown characterize the system near the dynamical transition at Ta, when a secondary, metastable minimum in F a) begins to appear as the temperature is lowered. Taken from Ref. [47] with permission.

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