The theory of the vibrations and the Raman spectrum of the diamond lattice

Abstract

The crystal structure of diamond was first determined by Bragg in 1913 from X-ray photographs; the carbon atoms are arranged at the apices and median points of interlinked tetrahedra. Born (1914) derived expressions for the three elastic constants of diamond in terms of two force constants related to the valency bonds between neighbouring atoms. But, at that time, the only experimental data available were the compressibility and the Debye characteristic temperature 0, and precise determination of the valence force constants was not possible. Meanwhile, investigation of the optical properties of diamond had produced evidence for the existence of two distinct types, one with an absorption band at 8 [i in the infra-red, the other transparent at this point. Robertson, Fox & Martin (1934) took up this problem and found that absorption in the infra-red is associated with absorption in the ultra-violet; diamonds transparent at 8y transmit much farther into the ultra-violet. Both types of diamond have Bragg’s tetrahedral structure, the same refractive index, specific gravity, dielectric constant and electron diffraction. Their infra-red spectra are identical up to 7y, and the frequency shift of the principal Raman line is the same. The derivation of the elastic constants was again considered by Nagendra Nath (1934). He extended the theory to include central forces between second neighbours in the lattice. He also suggested that the frequency shift of the principal Raman line corresponds to the relative vibration of the two carbon atoms in the unit cell, along the line joining their nuclei. Raman and his collaborators have recently (1941) put forward a new theory of lattice dynamics according to which the vibrational spectrum of a crystal consists of a few discrete lines. This is in direct contradiction to the quasi-continuous vibrational spectrum predicted by classical or quantum mechanics. On this new theory there are eight fundamental frequencies of vibration for diamond; the values of these frequencies are deduced from the observed specific heat, ultra-violet absorption and Raman spectrum, which, it is claimed, cannot be explained by ‘orthodox’ lattice dynamics. Raman (1944) has suggested that there are, not two, but four types of diamond, two with tetrahedral symmetry and two with octahedral symmetry depending on the electronic configurations, but X-ray analysis gives no indication of this and the attempts of his school to explain the observed infra-red spectra on the basis of their new lattice theory have been, up to now, unsuccessful.