Lattice dynamical theory

Polarized Raman spectra from the alkali fluorides LiF, NaF and CsF habe been observed with argon laser excitations by Evans and Fitchen 09). These spectra are of interest as an extreme test of lattice dynamics theories and polarizability models. 

Vibrations in a real crystal are described by the lattice dynamical theory, discussed in section 2.1, rather than by the atomic oscillator model. Each harmonic phonon mode with branch index k and wavevector q then has, analogous to Eq. 

Yamada Y, Tsuneyuki S, Matsui Y (1992) Presstrre-induced phase transitiorrs in rutile-type ciystals. In Y Syono, MH Manghnani (eds) High Pressttie Research Application to Earth and Planetary Sciences. Geophys Monogr Ser 67 441-446, Am Geophys Union, Washington DC Yamamoto A (1974) Lattice-dynamical theory of structmal phase transition in quartz. J Phys Soc Japan... 

The thermal Green s function, or phonon propagator, that is used in lattice dynamics theory is defined as... 

Since it became clear from various observations that the librational motions of the molecules, even in the ordered a and y phases of nitrogen at low temperature, have too large amplitudes to be described correctly by (quasi-) harmonic models, we have resorted to the alternative lattice dynamics theories that were described in Section IV. Most of these theories have been developed for large-amplitude rotational oscillations, hindered or even free rotations, and remain valid when the molecular orientations become more and more localized. 

In summary, using the electron—lattice dynamics theory, we have been able to explore the details of the intrachain polaron motion. In particular, we have shown that the velocity of the polaron can exceed the sound velocity of the system. This is achieved by the decoupling of acoustic phonons from the polaron. With this knowledge about the intrachain behavior of the polaron dynamics, we will now go on to discuss the interchain transport of polarons. 

The first attempt to establish an atomic theory of piezoelectricity is corrsidered to be the work of Lord Kelvin. Using Debye s theory of electrical polarization Schrodinger attempted to determine the order of magnitude of the piezoelectric constants of tourmaline and quartz. However the first to succeed was Bom in 1920 in his book Lattice-dynamical theory . An atomic model for the qualitative explanation of piezoelectric polarization of quartz was discovered by the method of X-ray analysis by Bragg and Gibbs in 1925. 

The thermal properties of a lattice are generally affected by the anharmonicity of the potential between atoms and are described using lattice dynamic theories. 

Figure 9. The full curves are the MD S(Q,to) data for longitudinal phonons propagating along the c-axis of hep solid (l-N,. Curves labeled QH and SCHA refer to lattice dynamical theories C19). The unit of energy is 16.5 cm , 0.50 THz,...

Born M and Huang K 1954 Dynamical Theory of Crystal Lattices (Oxford Clarendon)... 

M, Born and K. Huang, Dynamical Theory of Crystal Lattices Oxford University Press, 1954, pp. 166-177, 402 07,... 

M. Bom and K. Huang, Dynamical theory of Crystal Lattices, Oxford University Press, New York, 1954. 

Jourjine [jour85] generalizes Euclidean lattice field theory on a d-dimensional lattice to a cell complex. He uses homology theory to replace points by cells of various dimensions and fields by functions on cells, the cochains, in hopes of developing a formalism that treats space-time as a dynamical variable and describes the change in the dimension of space-time as a phase transition (see figure 12.19). 

Elastomers are solids, even if they are soft. Their atoms have distinct mean positions, which enables one to use the well-established theory of solids to make some statements about their properties in the linear portion of the stress-strain relation. For example, in the theory of solids the Debye or macroscopic theory is made compatible with lattice dynamics by equating the spectral density of states calculated from either theory in the long wavelength limit. The relation between the two macroscopic parameters, Young s modulus and Poisson s ratio, and the microscopic parameters, atomic mass and force constant, is established by this procedure. The only differences between this theory and the one which may be applied to elastomers is that (i) the elastomer does not have crystallographic symmetry, and (ii) dissipation terms must be included in the equations of motion. 

H. BOttger, Principles of the Theory of Lattice Dynamics (Academie-Verlag, Berlin, 1983). 149, 176 ... 

Born, M. and Huang, K., Dynamical Theory of the Crystal Lattice, Clarendon Oxford (1954). 

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. 

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. 

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