Tunable thermal expansion behavior in the intermetallic YbGaGe

We investigate the effects of carbon and boron doping on the thermal expansion of the hexagonal $(P{6}_3∕mmc)$ intermetallic YbGaGe. X-ray powder diffraction was used to measure the lattice constants on pure and doped (C or B at nominal levels of 0.5%) samples from $T\sim 10\mathrm{K}\text{to}T\sim 300\mathrm{K}$. Also measured were resistivity, specific heat, and magnetic susceptibility. While the pure YbGaGe samples exhibit positive thermal volume expansion, $\left(V_{300\mathrm{K}}\text{−}{V}_{10\mathrm{K}}\right)∕V_{300\mathrm{K}}=0.94$, the volume expansion in the lightly C- or B-doped samples changes slope and tends toward zero-volume expansion. Such a strong response to light doping suggests that the underlying mechanism for the reported zero-volume expansion is substitutional disorder, and not the previously proposed valence fluctuations.

Figure 1

Unit cell of YbGaGe structure. The structure consists of puckered $\mathrm{Ga}\text{−}\mathrm{Ge}$ planes sandwiched between Yb planes.

Figure 2

Profile fit to the synchrotron x-ray powder diffraction pattern observed for the yttria-grown, stoichiometric sample at $10\mathrm{K}$. The sets of tick marks below the data indicate the positions of the allowed reflections. The lower curves represent the differences to the observed profiles on the same scale.

Figure 3

Temperature dependence of the unit-cell volume and edge lengths are plotted (a) for the yttria-grown, stoichiometric sample; and (b) the B-doped, alumina-grown sample. The curves are from a polynomial fit and are meant to be guides to the eye.

Figure 4

(Color) Temperature dependence of the normalized unit-cell volumes ($V∕V_{10\mathrm{K}}$ or $V∕V_{20\mathrm{K}}$ for all samples. Lines are polynomial fits and serve as guides to the eye).

Figure 5

(Color) Normalized resistance measurements of single crystalline YbGaGe prepared in alumina or yttria crucibles with different cooling rates (a). The effect of C or B doping of YbGaGe is shown as the $R\left(T\right)∕R\left(300\mathrm{K}\right)$ values and reflect the amount of disorder in the lattice. Magnetic-susceptibility measurements $(M∕H)$ at $H=1\mathrm{T}$ of stoichiometric YbGaGe, and a sample that was quenched, is shown in the inset (b). In the quenched sample, at low temperature, there is antiferromagnetic ordering of the ${\mathrm{Yb}}^{+3}$ moments.

Figure 6

(Color) Magnetic specific heat $\left(C_{\mathrm{mag}}\right)$ was obtained by subtracting $C_{\text{phonon}}+C_{\text{electron}}$ for the same YbGaGe quenched sample shown in the inset of Fig. 1b. To quantify the ${\mathrm{Yb}}^{3+}$ moments present, an extrapolation to $T=0\mathrm{K}$ assumed $C_{\mathrm{mag}}={\beta }_3{T}^3$ (antiferromagnetic spin waves), with ${\beta }_3$ evaluated from a fit to the lower six data points. For the high-temperature tail an extrapolation was made using the empirical expression $C_{\mathrm{mag}}∕T=D_4∕T^5+D_3∕T^4+D_2∕T^3$ and evaluating the parameters by fitting data between $\sim 4$ and $6\mathrm{K}$. Integration of $C_{\mathrm{mag}}∕T$ from $T=0$ to ∞ gives a magnetic change in entropy of $\Delta S_{\mathrm{mag}}=180\mathrm{mJ}{\mathrm{K}}^{-1}{\mathrm{mol}}^{-1}$ compared to $\mathrm{R}\ln 2=5736\mathrm{mJ}{\mathrm{K}}^{-1}{\mathrm{mol}}^{-1}$ for one mole of ${\mathrm{Yb}}^{+3}$, which translates to $3\mathrm{mol}\%$ ${\mathrm{Yb}}^{3+}$.