The phonon and thermodynamic properties of the divalent alkaline-earth hexaborides, M B6 (M=Ca, Sr, Ba), and the reference elements α-B, fcc-Ca, fcc-Sr, and bcc-Ba are investigated on the basis of first-principles projector augmented wave method together with the quasiharmonic phonon calculations. The calculated phonon dispersion relations by using the supercell approach are in good agreements with those obtained by the inelastic neutron scattering, Raman scattering, and infrared absorption. The experimentally revealed anomalous behaviors of phonon dispersions in the alkaline-earth metals are correctly predicted; i.e., for both fcc-Ca and fcc-Sr, the frequency of the lower transverse [ξ ξ 0] branch exhibits slightly positive dispersion, and for bcc-Ba the frequency of the longitudinal branch along the [ξ 0 0] direction is lower than that of the transverse branch. These anomalous phenomena can be traced back to the effect of d electron. The predicted phonon dispersion relations among Ca B6, Sr B6, and Ba B6 show similar features except that the frequencies decrease from Ca B6, Sr B6, to Ba B6 due to the influence of mass. It is also found that the low frequency T1u modes of Ca B6, Sr B6, and Ba B6 have large LO/TO splitting (greater than 5 THz). To that end, the finite temperature thermodynamic properties (entropy, enthalpy, and Gibbs energy) of M B6 (M=Ca, Sr, Ba) and elements B, Ca, Sr, and Ba are calculated; herein, both the electronic and phonon contributions are considered. This work indicates that the difference of the enthalpies of formation of Ca B6, Sr B6, and Ba B6 is small (less than 4 kJ mol instead of the measured 30 kJ mol), which agrees with the facts that they possess the similar phonon dispersion relations, melting temperatures, bulk moduli, and Debye temperatures.
|Original language||English (US)|
|Journal||Physical Review B - Condensed Matter and Materials Physics|
|State||Published - Jan 25 2007|
All Science Journal Classification (ASJC) codes
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics