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Chapter 10
Three Words to Experimenters
should be twice as large.
10.3 The Effect of Isotopic Substitution on the
Condensation of Zero-Point Oscillations
The attention of experimentalists could be attracted to the isotope effect in
superconductors, which served as a starting point of the B-BCS theory. In the 50’s, it had
been experimentally established that there is a dependence of the critical temperature of
superconductors due to the mass of the isotope. As the effect depends on the ionic mass,
this is considered to be due to the fact that it is based on the vibrational (phonon) process.
The isotope effect for a number of I-type superconductors - Zn, Sn, In, Hg, P b - can
be described by the relationship:
√
Mi T c = const, (10.4)
where M i is the mass of the isotope, T c is the critical temperature. The isotope effect in
other superconductors can either be described by other dependencies, or is absent
altogether.
In recent decades, however, the effects associated with the replacement of isotopes in
the metal lattice have been studied in detail. It was shown that the zero-point oscillations
of ions in the lattice of many metals are non-harmonic. Therefore, the isotopic substitution
can directly affect the lattice parameters, the density of the lattice and the density of the
electron gas in the metal, on its Fermi energy and on other properties of the electronic
subsystem.
The direct study of the effect of isotopic substitution on the lattice parameters of
superconducting metals has not been carried out.
The results of measurements made on Ge, Si, diamond and light metals, such as Li
[50], [49] (researchers prefer to study crystals, where the isotope effects are large, and it is
easier to carry out appropriate measurements), show that there is square-root dependence
of the force constants on the isotope mass, which was required by Eq.(10.4). The same
dependence of the force constants on the mass of the isotope has been found in tin [51].
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