Theoretical investigation of type II clathrate materials
Thermoelectric effects were discovered in the early 19th century. Seebeck (1821) discovered that a voltage appears when two different conductors are joined together and the junction is heated. The Peltier effect (1834) occurs when an electric current is passed through the junction between two conductors. The junction becomes heated or cooled according to the direction of current through it. These two effects combined constitute the thermoelectric phenomenon. Thermoelectric effect can have practical applications in the fields of alternate power generation (Seebeck effect) or as environment friendly refrigeration and cooling devices in modern electronics (Peltier effect). However, their performance would depend on the specific properties of the materials that are used to build those devices. A good thermoelectric material should have a high electrical conductivity like a metal, and low thermal conductivity, like a glass. One promising class of materials that fit the requirements for good thermolectrics is the semiconductor clathrates. Among the two major types of clathrate compounds, the type II clathrates has been relatively less investigated compared to the type I variety. The type II clathrates form a cage-like structure with 136 atoms in the cubic unit cell. The cages can accommodate weakly bound impurities or ï¿½guestsï¿½, usually Group I or Group II atoms. This unique structural characteristic lead to important electronic and vibrational properties which makes these materials potentially useful for various applications including thermoelectrics. This work is based on a theoretical study of the type II silicon (Si) and germanium (Ge) clathrates. It involves a systematic study of the structural, electronic and vibrational properties of several materials. The guest impurity atoms inside the clathrate cages modify the material electronic structure. Guest atom electrons occupy the host conduction band states, resulting in a Fermi Level shift into the conduction band of the ï¿½parentï¿½ framework, therefore making the materials metallic. This metallic character means that the electronic contribution to the total thermal conductivity could be large and hence such materials are not very useful as thermoelectrics. However, upon substitution of a few framework atoms by gallium (Ga) restores the semiconducting behavior of the partially filled materials. It indicates that the Ga atoms, with their s2p1 valence electronic configuration, accept electrons from the guest atoms and form covalent bonds with the neighboring Si atoms. The projected electronic density of the filled clathrates show the impurity derived s-orbital character of the states near the Fermi level. This feature may help to qualitatively explain the temperature-dependent Knight shift observed for the NMR-active nuclei in the filled clathrates. All the filled clathrates are predicted to have low frequency guest vibrational modes that are near the middle of the host acoustic band, which effectively compresses the acoustic mode band width. This could lead to an efficient scattering of the host acoustic phonons. Based on the harmonic oscillator model and the LDA-calculated frequencies, the effective force constants of the various guest atoms have been estimated. Those values have been used to predict the temperature-dependent isotropic mean square displacement amplitudes (Uiso) and the Einstein temperatures (ï¿½E) of the various guest atoms. The temperature dependence of the vibrational contribution to the free energy, the entropy and the specific heat capacity at constant volume (CV) of the empty Si136 and Ge136 clathrates have been predicted. All quantities were calculated using the harmonic approximation. The Si136 and Ge136 are structurally very different from their respective diamond structured phases. However, their entropies and specific heats bear close resemblance to their corresponding diamond phases.