Effective four-phonon interactions

There are now three effective four-phonon interactions of the types... 

This work contributed in two major ways. First, the calculation shows that it is now possible for the first time to calculate from first principles phonon-phonon interaction parameters that are inaccessible from experiment. Second, since all the effective four-phonon terms (direct plus mediated processes up to are attractive for the k = 0 optical phonons in diamond, the formation of the two-phonon bound state is unlikely in this system. 

According to the band scheme of P-rhombohedral boron (Fig. 14), it is obvious that n-type conductivity requires the unoccupied states in the valence band range and the intrinsic electron trapping levels to be filled by electrons originating from donor levels, which must be positioned above the uppermost trapping level. Two states in the upper valence band originating from the Jahn-Teller effect in the icosahedron at the vertex of the unit cell and four states of intrinsic traps, which are generated by the electron-phonon interaction in the four B12 icosahedra in the unit cell, i.e., in total six sites, must be saturated by additional electrons to realize n-type behavior. 

From the comparison of the measured and calculated temperature dependences of the relaxation time (see Fig. 20), it follows that the inelastic phonon scattering is the most essential mechanism of the spin-lattice relaxation for Ge. It is evident that only at low temperatures T < 30K) some other mechanisms (the most probable one is the relaxation due to a small amount of paramagnetic impurities) become dominant. At T > 300/C some additional mechanism of relaxation may also exist. The interaction of the nuclear quadrupole moment with vibrations of the nearest four Ge atoms brings about the main contribution to the spin-lattice relaxation rate. The effective modulation of the EFG by the nearest bond charges is greatly reduced because of strong correlations between their displacements. As the main result of the present investigation of spin-lattice relaxation,... 

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