Specific heat of small vanadium particles in the normal and superconducting state

Abstract

The specific heat C of ultrafine vanadium particles of various diameters (2.9–13 nm) has been measured in the temperature interval 1.5–12 K and in magnetic fields up to 3.5 T. Both the vibrational and electronic contributions to C in the normal state are strongly enhanced as compared to the bulk behavior. For not too small particles (> ∼10nm), the vibrational specific heat can be interpreted in terms of the discrete phonon spectrum of free elastically vibrating small spheres while, at low temperatures, the vibrational specific heat of the smallest particles is predominantly due to Einstein modes which are attributed to low-frequency vibrations of weakly bound surface atoms. Level quantization does not appear to play a detectable role in the electronic specific heat of the normal state. Rather, the observed enhancement must be attributed to an increased electronic density of states at (100) surfaces of bcc metals or to electronic states of substoichiometric V-oxides. The transition range to superconductivity progressively broadens with decreasing particle size due to fluctuations. In this temperature range, the electronic specific heat behaves in qualitative agreement with theoretical predictions.