Observation of phonon anomalies inNbCxN1−xalloys

We have measured the specific heat of various $\mathrm{Nb}{\mathrm{C}}_x{\mathrm{N}}_{1-x}$ pseudobinary alloys in the temperature range $1.5<T<\mathrm{}90\mathrm{}$ K. For a better determination of the electronic specific heat $\gamma$ and the Debye temperature ${\Theta }_D$ ($T\to 0$), the measurements have been partially performed in a magnetic field of 70 kG which suppressed the superconducting transition to $T_c<10.5\mathrm{}$ K. All observed quantities show reversals of trends near $x\approx 0.25$. By differential analysis of our data we determine an anomalous soft-mode regime in the transverse-acoustic part of the phonon density of states, which is shifted from 216 K (4.5 THz) in NbC to 116 K (2.4 THz) in Nb${\mathrm{C}}_{0.2}$ ${\mathrm{N}}_{0.8}$. Simultaneously, the values for ${\Theta }_D (T\to 0)$ and ${\Theta }_D$ ($T=70\mathrm{}$ K) are lowered from 495 and 366 K in Nb${\mathrm{C}}_{0.93}$ to 322 and 298 K in Nb${\mathrm{C}}_{0.2}$ ${\mathrm{N}}_{0.8}$, respectively. These results indicate that the anomaly in the TA phonons of NbC is not further enhanced, but that all TA-phonon frequencies are lowered in similar fashion. In contrast, the LA-phonon energies seem to decrease only a little. Using McMillan's theory, the increase in $T_c$ from NbC to Nb${\mathrm{C}}_{0.2}$ ${\mathrm{N}}_{0.8}$ is attributed to the overall softening of the acoustic phonons.