Band structure calculations 3-phase

The roots of the CALPHAD approach lie with van Laar (1908), who applied Gibbs energy concepts to phase equilibria at the turn of the century. However, he did not have the necessary numerical input to convert his algebraic expressions into phase diagrams that referred to real systems. This situation basically remained unchanged for the next 50 years, especially as an alternative more physical approach based on band-structure calculations appeared likely to rationalise many hitherto puzzling features of phase diagrams (Hume-Rotheiy et al. 1940). 

Detailed comparison between band structure calculations and experiments has been possible only for Th and to a less extent a-U. It is doubtful that such a level of sophistication will be reached for the low temperature, low symmetry, phases of Np and Pu metals. 

As early as 1943, Sommer (101) reported the existence of a stoichiometric compound CsAu, exhibiting nonmetallic properties. Later reports (53, 102, 103,123) confirmed its existence and described the crystal structure, as well as the electrical and optical properties of this compound. The lattice constant of its CsCl-type structure is reported (103) to be 4.263 0.001 A. Band structure calculations are consistent with observed experimental results that the material is a semiconductor with a band gap of 2.6 eV (102). The phase diagram of the Cs-Au system shows the existence of a discrete CsAu phase (32) of melting point 590°C and a very narrow range of homogeneity (42). 

The data in Table 3.16 may be used to estimate the band gap energy for unstrained wurtzite-structure MgO of E = 6.9 eV and for rocksalt-structure ZnO of Ee — 7.6 eV, with stronger bowing for the rocksalt-structure than for the wurtzite-structure occurrence of the alloys. Theoretical band-structure calculations for ZnO revealed the high-pressure rocksalt-structure phase as... 

With the discovery of superconductivity (Tc = 15.5 K) in the Y-Ni-B-C system [6, 80], a new class of quaternary borocarbide superconductors has emerged. Superconductivity has been observed in several rare earth (Lu, Tm, Er and Ho) nickel borocarbides[80], and with transition metals such as Pd and Pt. The superconducting phase having the composition of YNi2B2C, crystallizes [81] in a tetragonal structure with alternating Y-C and Ni2B2 layers. Band structure calculations [82] indicate that these materials, unlike cuprate superconductors, are three-dimensional metals. 

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[. 

In this section, after introducing some crystal structures, a selection of band structures calculated for different phases of the ET salts will be presented in Sect. 2.3.2. The band structures for some special materials will be presented in Chap. 4 together with the experimentally determined FS. In Sect. 2.3.3 an introduction to the superconducting properties of the 2D materials will be given. 

The main difference between the (3" structure compared to the / phase is the direction of the strong intermolecular interactions. Due to the smaller anion size the interaction directions are at 0°, 30°, and 60°, respectively, instead of face-to-face (90°) overlaps [335]. The more complicated interstack interaction results in a more anisotropic band structure with ID and 2D energy bands. There exists considerable disagreement between different band-structure calculations which might be caused by small differences in the transfer integral values [332, 335, 336]. One calculated FS based on the room temperature lattice parameters is shown in Fig. 4.27a [335]. Small 2D pockets occur around X and two ID open sheets run perpendicular to the a direction. In contrast, the calculation of [332] (not shown) revealed a rather large closed orbit around the F point. 

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