The temperature and magnetic field dependence of the specific heat cp(T,H) in the superconducting mixed state as well as the upper critical field Hc2(T) have been measured for polycrystalline Y_xLu_{1-x}Ni_2B_2C and Y(Ni_{1-y}Pt_y)_2B_2C samples. The linear-in-T electronic specific heat contribution gamma(H)T exhibits significant deviations from the usual linear-in-H law for all x and y the transition metal site (T) resulting in a disorder dependent negative curvature of gamma(H). The deviations from that linear behaviour of our unsubstituted samples are the largest reported so far for any superconductor. The H_c2(T) data point to the quasi-clean limit for (Y,Lu)-substitutions and to a transition to the quasi-dirty limit for (Ni,Pt)-substitutions. The gamma(H) dependence is discussed in the unitary d-wave as well as in the quasi-clean s-wave limits. From a consideration of gamma(H) data only, d-wave pairing cannot be ruled out.
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