Elastic band theory

Many of the problems with elastic band theory are rooted in this definition and their effect... 

A computational design procedure of a thermoelectric power device using Functionally Graded Materials (FGM) is presented. A model of thermoelectric materials is presented for transport properties of heavily doped semiconductors, electron and phonon transport coefficients are calculated using band theory. And, a procedure of an elastic thermal stress analysis is presented on a functionally graded thermoelectric device by two-dimensional finite element technique. First, temperature distributions are calculated by two-dimensional non-linear finite element method based on expressions of thermoelectric phenomenon. Next, using temperature distributions, thermal stress distributions are computed by two-dimensional elastic finite element analysis. 

Althou, in principle, the general theory is superior to the band theory, the appropriate techniques for its application are not yet developed sufficiently well and a unified approach to a quantitative description of the structures and the physical properties of crystals is still lacking. The less generally valid band theory can at present give clearer and more convincing explanations of changes in the physical properties of crystals caused by variations in the temperature, pressure, magnetic and electric fields intensities, impurity concentrations, etc. However, many problems encoimtered in the study of chemical bonds in crystals cannot be considered within the framework of the standard band theory. They include, for example, determination of the elastic, thermal, and thermodynamic properties of solids, as well as the structure and properties of liquid and amorphous semiconductors. 

The measured activation energy was close to that predicted by first-principles theory using the nudged-elastic-band method. The measured diffusivity of nickel was higher than previously published values at temperatures below 1150C, and orders of magnitude higher when extrapolated to room temperature. 

In atomic scale simulations, there is often a clear separation of timescales. The rate of rare events, e.g., chemical reactions, in a system coupled to a heat bath can be estimated by evaluating the free energy barriers for the transitions. Transition State Theory (TST) [9] is the foundation for this approach. Due to the large difference in time scale between atomic vibrations and typical thermally induced processes such as chemical reactions or diffusion, this would require immense computational power to directly simulate dynamical trajectories for a sufficient period of time to include these rare events. Identification of transition states is often the critical step in assessing rates of chemical reactions and path techniques like the nudged elastic band method is often used to identify these states [10-12,109]. 

Figure 5. HREELS cross-section curves (peak height normalized to the elastic peak intensity) for the excitation of selected molecular vibrational bands of polyimide. The dielectric theory predicts a E 1 behaviour.

Density functional theory is used for band structure calculations of hydrogen storage materials. This method has been applied to a variety of hydrides such as ABs [77-79], AB [77], transition metals [53, 80], Laves phases [81], and complex hydrides [82[. Theoretical investigation is not only useful for the prediction of the heat of formation but it could also assess the elastic and mechanical properties of these materials, properties which are usually difficult to measure in the case of hydrides [78[. 

Timgsten has been of keen theoretical interest for electron band-structure calculations [1.14-1.25], not only because of its important technical use but also because it exhibits many interesting properties. Density functional theory [1.11], based on the at initio (nonempirical) principle, was used to determine the electronic part of the total energy of the metal and its cohesive energy on a strict quantitative level. It provides information on structural and elastic properties of the metal, such as the lattice parameter, the equilibrium volume, the bulk modulus, and the elastic constants. Investigations have been performed for both the stable (bcc) as well as hypothetical lattice configurations (fee, hep, tetragonal distortion). 

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