Experimental confirmation of the isotopic volume effect in superconducting molybdenum by means of energy-dispersive x-ray diffration at low temperatures

Abstract

Differences in the lattice constants of Mo-100 and Mo-92 have been measured by x-ray diffraction, in order to search directly for the volume effect of isotopes in a superconductor. No significant difference in the lattice constanta(Mo-100)−a(Mo-92) could be detected at 290 K, while the differences −0.0014±0.0008 and −0.0029±0.0009 Å were detected at 85.3 and 4.31 K, respectively. These values, and their temperature dependence, are considered to be theoretically reasonable. The exponent α in the isotope effect defined by T_c∝M^-α is represented thermodynamically by α=−(∂ lnT _c /∂ lnM)−(∂ lnT _c /∂ lnV)(d lnV/d lnM). From the results, d lnV/d lnM is found to be −0.033±0.009 at 4.31 K. Then, the second term representing the isotopic volume effect is estimated to be about 0.09, with ∂ lnT _c /∂ lnV≃2.81. The observed value of α is 0.33, so that the contribution of the second term, 0.09, is 27% of the value of α. It becomes quite clear that the isotopic volume effect in superconducting Mo should not be neglected.