Superconducting properties of ${\mathrm{Y}}_x{\mathrm{Lu}}_{1-x}{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}$ and ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{B}}_2{\mathrm{N}}_{3-\delta }:$ A comparison between experiment and Eliashberg theory

Specific heat and resistivity measurements were performed on polycrystalline samples of the solid-solution ${\mathrm{Y}}_x{\mathrm{Lu}}_{1-x}{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}$ in order to determine thermodynamic properties such as the specific-heat difference $\Delta C,$ the thermodynamic critical field $H_c\mathrm{}\left(T\right),$ as well as the upper critical field $H_{c2\mathrm{}}\mathrm{}\left(T\right).$ These properties were analyzed within the Eliashberg theory including anisotropy effects, yielding electron-phonon coupling anisotropy parameters $〈a_{\mathbf{k}}^2〉$ ranging between $0.02$ and $0.03$ for the whole series, and Fermi velocity anisotropy parameters of $〈b_{\mathbf{k}}^2〉=0.245\mathrm{}–\mathrm{0.3.}$ Excellent agreement between theory and experiment was achieved for these parameters, the Sommerfeld constant $\gamma$ and model phonon spectra determined from specific heat measurements. An analysis of the previously investigated boronitride ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{B}}_2{\mathrm{N}}_{3-\delta }$ for comparison revealed the electron-phonon anisotropy to be of great significance in describing its thermodynamic properties and the calculations yielded $〈a_{\mathbf{k}}^2〉\simeq 0.08$ and $〈b_{\mathbf{k}}^2〉\simeq \mathrm{0.245.}$ The $T_c$ behavior within the series ${\mathrm{Y}}_x{\mathrm{Lu}}_{1-x}{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}$ is discussed in terms of the density of states at the Fermi level $N\left(0\right).$