K₇B₇Si₃₉, a Borosilicide with the Clathrate I Structure

Abstract

Including boron: K7B7Si39 (see structure; large spheres: K, small spheres: Si, B) is the first clathrate I compound with boron atoms. With 9.952(1) Å, the borosilicide exhibits the smallest lattice parameter among all intermetallic clathrate I compounds. The composition is in agreement with the Zintl rule.

Energetic Stability and Thermoelectric Property of Alkali-Metal-Encapsulated Type-I Silicon-Clathrate from First-Principles Calculation

“…23) A constant carrier relaxation time approximation was assumed so that the Seebeck coefficient could be obtained independent of the carrier relaxation time, while the electrical conductivity and electronic thermal conductivity could be obtained as carrier-relaxation-timedependent quantities. Carrier doping was treated as a shift in the Fermi level on the basis of the band structure of the X 8 Y 8 Si 38 . Such a treatment is called a "rigid-band approximation".…”

“…However, as the band structure is expected to severely change in heavy doping, the rigid-band approximation would fail when Fermi-level is located more than 0.1 eV into the band edge. 24) We also checked the applicability of rigid-band approximation to the present Si-clathrate system, from the analysis on band structures of one electron and/or hole doped Si 46 and K 8 Ga 8 Si 38 . It was confirmed that changes of band structure could be characterized only by shifting the Fermi level, which was moved about 0.1 eV inside bands.…”

“…In Fig. 7, the dotted line indicates the formation energy of K 8 B 8 Si 38 . Because a nearly identical composition, K 7 B 7 Si 39 , was synthesized, 38) formation energy of K 8 B 8 Si 38 can be regarded as a criterion whether composition is formable as a clathrate or not.…”

“…7, the dotted line indicates the formation energy of K 8 B 8 Si 38 . Because a nearly identical composition, K 7 B 7 Si 39 , was synthesized, 38) formation energy of K 8 B 8 Si 38 can be regarded as a criterion whether composition is formable as a clathrate or not. Therefore, X 8 Y 8 Si 38 (X = K, Rb and Cs, Y = Al and Ga) was selected for further transport analysis because their formation energies were well lower than that of K 8 B 8 Si 38 .…”

“…All alkali metals could be encapsulated as the guest element into a Si 46 cage, and either Al or Ga was suitable for a substitutional atom. From the formation energy, possible clathrate compositions were selected as K 8 38 . The thermoelectric properties of these compositions were calculated as functions of temperature and carrier density, using the Boltzmann transport equation and the calculated band energy.…”