Structural and vibrational properties of the 6H diamond: First-principles study

The 6H diamond is the first successfully synthesized diamond polytype, which are not found in nature. We have performed the investigations on structural properties and vibrational properties of the 6H diamond with a first-principles method and we also have identified the vibration normal modes of the 6H diamond with group theory. The structural properties of the 6H diamond are quite similar to the cubic diamond (3C diamond) and the lonsdaleite (2H diamond) as expected. The vibrational properties of the 6H diamond are more complicated than the 3C and 2H diamonds. At Γ point of the first Brillouin zone of the 6H diamond, there are 15 Raman active modes with nine different frequencies, and six IR active modes with four different frequencies. However, there are no IR active modes in the 3C and 2H diamonds. Therefore, the IR active modes of the 6H diamond can provide the indication modes for distinguishing the 6H diamond from the 2H and 3C diamonds. For Raman active modes, the frequencies of the E_1g² and E_2g² modes of the 6H diamond are much smaller than the Raman frequencies of the 2H and 3C diamonds; consequently, it also can contribute to distinguishing the 6H diamond from the 2H and 3C diamonds. The frequencies of two Raman active modes of the 6H diamond-the A_1g² mode and the E_1g¹ mode-agree very well with the experimental results.