DIAMONDS — LOGIE 367 



carried over to the solid where it is applied to the phonons. The 

 magnitude of L is determined by the scattering of phonons at the 

 bomidary of the crystal or by interaction with other phonons or by 

 scattering at imperfections in the lattice. If the forces between atoms 

 were purely harmonic, there would be no mechanism for collision 

 between the phonons, and the mean free path in a perfect crystal 

 would be limited solely by tlie size of the crystal. Because the thermal 

 conductivity is so high we conclude that there are few imi^erfections 

 in the crystal and further that the lattice vibrations are predominantly 

 harmonic. This has other consequences. 



By the statement that the oscillations are purely harmonic, we 

 mean two things : 



(1) That the forces are proportional to the displacement of the 

 nuclei; and 



(2) That all displacements of electric charges are proportional 

 to the displacement of the nuclei. 



Anharmonicity, that is lack of harmonicity, may accordingly be due 

 to two things. First, the proportionality between nuclear displace- 

 ments and restoring forces may not be satisfied. In this case we talk 

 about mechanical anharmonicity. Or deviations may exist from the 

 proportionality between nuclear displacements and the accompanying 

 changes in the dipole moment. In this case there exists an electrical 

 anharmonicity. Tlie diamond shows neither of tliese effects and this 

 has important consequences in the optical behavior of the crystal. 



Infrared absorption is another property of a solid which depends 

 on the vibration of the lattice. When light passes through a crystal 

 it may lose energy by settmg the atoms in motion, and strong absorp- 

 tion of the light occurs when its frequency is the same as the natural 

 frequency of the lattice. Besides this requirement, absorption will 

 occur only if the oscillations are not completely symmetrical m a 

 given unit cell of the lattice. If the center of gravity of the cell does 

 not change during an oscillation, then the opposite displacements of 

 the atoms in the cell give rise to opposite values of radiated electric 

 and magnetic fields, and the sum total of the field intensity in the 

 radiation is zero. In a recent paper by Burstein, Picus, and Sclar,^ 

 they point out that the diamond structure, consisting as it does of two 

 identical interpenetrating face-centered cubic lattices, one of which 

 is displaced relative to the other, will be mf rared mactive because of 

 the symmetrical considerations. 



The history of the experiments and theory on the infrared absorp- 

 tion by diamonds is not without its lighter moments. In 1907, Ein- 

 stein was the first to make a fairly reliable estimate of the vibration 



* "Optical and photo-conductive properties of SI and Ge." Photoconductivity Confer- 

 ence. New York, John Wiley, 1954. 



