Vacancy motion in rare-earth-deficient $R_{1-x}{\mathrm{Ni}}_2$ Laves phases observed by perturbed angular correlation spectroscopy

Rare-earth-deficient $R_{1-x}{\mathrm{Ni}}_2$ Laves phases, which reportedly crystallize in a $C15$ superstructure with ordered $R$ vacancies, have been investigated by perturbed angular correlation $\left(\mathrm{PAC}\right)$ measurements of electric quadrupole interactions at the site of the probe nucleus ${}^{111}\mathrm{Cd}$. Although ${}^{111}\mathrm{Cd}$ resides on the cubic $R$ site, a strong axially symmetric quadrupole interaction $\left(\mathrm{QI}\right)$ with frequencies ${\nu }_q\approx 265–275\mathrm{MHz}$ has been found in the paramagnetic phases of $R_{1-x}{\mathrm{Ni}}_2$ with $R=\mathrm{Pr},\mathrm{Nd},\mathrm{Sm},\mathrm{Gd}$. This interaction is not observed for the heavy $R$ constituents $R=\mathrm{Tb},\mathrm{Dy},\mathrm{Ho},\mathrm{Er}$. The fraction of probe nuclei subject to the $\mathrm{QI}$ in $R_{1-x}{\mathrm{Ni}}_2$, $R=\mathrm{Pr},\mathrm{Nd},\mathrm{Sm},\mathrm{Gd}$, decreases from $100\%$ at low temperatures to zero at $T>300\mathrm{K}$ and $500\mathrm{K}$ for $R=\mathrm{Sm},\mathrm{Gd}$ and $R=\mathrm{Pr},\mathrm{Nd}$, respectively. At $T=100\mathrm{K}$ the $\mathrm{QI}$ is static within the $\mathrm{PAC}$ time window, but at $T=200\mathrm{K}$ fluctuations with correlation times ${\tau }_C<{10}^{-6}\mathrm{s}$, have been detected. These observations can be explained consistently by two assumptions: (i) the mother isotope ${}^{111}\mathrm{In}$ of the $\mathrm{PAC}$ probe ${}^{111}\mathrm{Cd}$ constitutes an attractive potential for vacancies and (ii) the $R$ vacancies in $R_{1-x}{\mathrm{Ni}}_2$ are highly mobile at temperatures $T<300\mathrm{K}$, which is incompatible with a static vacancy superstructure. The measurements indicate a decrease of the vacancy-probe binding energy from the light to the heavy $R$ constituents of $R_{1-x}{\mathrm{Ni}}_2$. For $R=\mathrm{Pr},\mathrm{Nd},\mathrm{Sm},\mathrm{Gd}$ the binding energy is in the range $0.15–0.40\mathrm{eV}$. The activation energy $E_A$ for vacancy jumps near the probe derived from the temperature dependence of the nuclear spin relaxation at $200\mathrm{K}⩽T⩽300\mathrm{K}$ is small. The values observed in different samples cover a range of $0.1\mathrm{eV}⩽E_A⩽0.23\mathrm{eV}$. The trial frequency $w_0$ of these jumps appears to be correlated to the activation energy: $\ln w_0\left(\mathrm{MHz}\right)\approx 58E_A\left(\mathrm{eV}\right)$. At high temperatures $T>500\mathrm{K}$ nuclear spin relaxation related to vacancy hopping is observed in nearly all $R_{1-x}{\mathrm{Ni}}_2$. Auxiliary ${}^{111}\mathrm{Cd}$ $\mathrm{PAC}$ measurements have been carried in ${\mathrm{Sc}}_{0.95}{\mathrm{Ni}}_2$, ${\mathrm{ScNi}}_2$, ${\mathrm{ScNi}}_{0.97}$, ${\mathrm{Gd}}_2{\mathrm{Ni}}_{17}$, ${\mathrm{GdNi}}_5$, ${\mathrm{GdNi}}_3$, and $\mathrm{GdNi}$.

Figure 1

$\mathrm{PAC}$ spectra of ${}^{111}\mathrm{Cd}$ in ${\mathrm{PrNi}}_2$ between $100\mathrm{K}$ and $600\mathrm{K}$.

Figure 2

$\mathrm{PAC}$ spectra of ${}^{111}\mathrm{Cd}$ in ${\mathrm{GdNi}}_2$ between $100\mathrm{K}$ and $600\mathrm{K}$.

Figure 3

The temperature dependence of the fraction of ${}^{111}\mathrm{Cd}$ probe nuclei in $R{\mathrm{Ni}}_2$ with $R=\mathrm{Pr},\mathrm{Nd},\mathrm{Sm},\mathrm{Gd}$ subject to an axially symmetric $\mathrm{QI}$ with frequency ${\nu }_q=260–270\mathrm{MHz}$.

Figure 4

Arrhenius plot of the relaxation parameter ${\lambda }_2$ describing the attenuation of the periodic modulation of the spectra of ${}^{111}\mathrm{Cd}:R{\mathrm{Ni}}_2$ between $200\mathrm{K}$ and $300\mathrm{K}$.

Figure 5

The temperature dependence of the intensity of the superstructure lines (422), (511), (531), and (442) in the x-ray diffraction spectrum of ${\mathrm{Sm}}_{0.95}{\mathrm{Ni}}_2$ compared to the intensity of the (440) and (622) reflections of the cubic Laves phase.

Figure 6

The preexponential factor ${\lambda }_2^0$ of the Arrhenius relation ${\lambda }_2={\lambda }_2^0\exp (-E_A∕k_{B}T)$ vs the activation energy $E_A$ of different compounds $R{\mathrm{Ni}}_2$.

Figure 7

The relaxation parameter ${\lambda }_2$ of some ${}^{111}\mathrm{Cd}:R{\mathrm{Ni}}_2$ compounds at $T>450\mathrm{K}$.

Figure 8

$\mathrm{PAC}$ spectra of ${}^{111}\mathrm{Cd}$ in ${\mathrm{Tb}}_{0.98}{\mathrm{Ni}}_2$ between $4.2\mathrm{K}$ and $900\mathrm{K}$.

Figure 9

$\mathrm{PAC}$ spectra of ${}^{111}\mathrm{Cd}$ in ${\mathrm{SmNi}}_2$ doped with $3\text{at.}\%$ of stable indium.

Figure 10

The temperature dependence of the fraction of ${}^{111}\mathrm{Cd}$ probe nuclei subject an axially symmetric $\mathrm{QI}$ in ${\mathrm{SmNi}}_2$ at different concentrations of stable indium.

Figure 11

The relaxation parameter ${\lambda }_2$ of ${\mathrm{SmNi}}_2$ between $200\mathrm{K}$ and $300\mathrm{K}$ at different concentrations of stable indium.

Figure 12

$\mathrm{PAC}$ spectra of ${}^{111}\mathrm{Cd}$ in the paramagnetic phases of ${\mathrm{Gd}}_2{\mathrm{Ni}}_{17}$, ${\mathrm{GdNi}}_5$, ${\mathrm{GdNi}}_3$, and $\mathrm{GdNi}$.