Question

Why do isotopically pure crystals show a higher thermal conductivity than mixed isotope crystals? How is the influence of isotopes on the electrical conductivity?

Answer 1

1) Thermal conductivity is generally due to the phonon vibrations of the atoms in the crystal structure. In an isotopically pure crystal, phonon vibrations are in phase. However, in a mixed isotope crystal, the phonon vibrations are generally out of phase. This is one reason why isotopically pure crystals show higher thermal conductivity.

2) Mixed isotope crystal is anisotropic in its crystal structure, and when anisotropy is present, the direction of heat flow may not be the same as the direction of the thermal gradient.

Even considering the phonon frequency for the simplest case, 1d lattice,

$\omega \alpha 1/M$ , $\omega$ -> phonon vibration frequency M-> atomic mass

Here we see that $\omega \alpha (1/M_{1} + 1/M_{2})$ M₁ & M₂ -> for mixed isotopes