Superconducting isotope effect in ZrB12

Abstract The Zr isotope effect appears to be much stronger in ZrB12 than in elemental Zr (the B isotope effect in ZrB12 is known to be small). The superconductivity of ZrB12 is apparently caused by optical phonon modes associated with the internal motion of Zr atoms inside boron cages.

ZrB12 belongs to an interesting group of superconductors in which transition metal atoms are embedded in a light atom matrix of high Debye temperature.The small boron isotope effect on the superconducting transition temperature of ZrB12 (~ =d log Tc/d log m = -0.09+0.05, m = mass of boron isotope) [1] shows either that the acoustic phonon modes which determine the high Debye temperature (OD= 945 K) [2] are not responsible for the relatively high superconducting transition temperature (T c = 5.9 K), or that Coulomb repulsion effects between the electrons are strong enough to strongly reduce the isotope effect which one might expect on the basis of the BCS theory.The latter situation is believed to occur, for example, in elemental Zr and Ru.The Zr isotope effect in ZrB12 is therefore of interest for understanding the superconductivity of these curous compounds.
Zr isotopes 90, 91, 92 and 94 were obtained from Oak Ridge National Laboratories in the form of 10 mil sheet.The T c values for these isotopes did not agree with those published.The isotopes were purified by heating several minutes under He in an arc-furnace.
ZrB12 was then pre- There is no correlation between the T c of the Zr isotope starting material and that of the corresponding ZrB12.This makes us confident that the isotope effect observed is not due to any impurities present.Only Sc, Y, rare earths and actinides are expected to be at all soluble in ZrB12 , and the spectrographic analyses supplied with the Zr isotopes show these not present.Fig. 1. is a (base 10) log T c versus log M plot, where M is the Zr atomic weight appropriate for the isotopic abundance of Zr in each specimen.We prepared three specimens of ZrB12 for each Zr isotope, and the points in the figure give the average value of the midpoint of the transitions for each isotope, the error bars indicating the spread of mid-points observed.Only one specimen of ZrB12 with natural abundance of Zr was measured, the transition width for this being 40 mdeg.
The slope of the straight line in the figure gives c~ = -0.32+ 0.02, somewhat larger, but comparable, to c~ = -0.23 for Mo in MoBe22 [3].It is interesting that the isotope effect in elemental Zr is zero [4].Our result contrasts with Engelhardt's on the isotope effect of Mo in Mo2B [5]: Zr in ZrB12 behaves very differently from elemental Zr, while the behavior of Mo in MoBe22 and Mo2B does not differ much from that of elemental Mo.
The fact that a large ~(Zr) exists in ZrB12 shows that Coulomb repulsion effects are not responsible for the small c~(B).Then it is clear that if acoustic phonon modes are responsible for the superconductivity, one would expect a value for c~(B) which is much larger than that observed.We conclude that in ZrB12 the superconductivity is caused by the optical phonon modes associated with the internal motion of Zr atoms inside their boron cages.

Fig. 1 .
Fig. 1.Logarithm of T c of ZrB12 versus logarithm of Zr isotopic mass in ZrB12.Our measured T c for natural abundance Zr in ZrB12 is 5.94OK.