Reduction of the Yb valence in ${\text{YbAl}}_3$ nanoparticles

Measurements of specific heat, dc magnetic susceptibility, and Yb $L_{\text{II}}$ and $L_{\text{III}}$ x-ray absorption near-edge structure (XANES) and extended x-ray absorption fine structure (EXAFS) on ${\text{YbAl}}_3$ milled alloys are reported. X-ray diffraction patterns are consistent with a reduction in particle size down to 10 nm and an increase in the lattice strain up to 0.4% for 120 h of milling time. A decrease in the mean valence from 2.86 for the unmilled alloy to 2.70 for 120 h milled ${\text{YbAl}}_3$ is obtained from the analysis of XANES spectra. From the analysis of spectra in the EXAFS region, an increase in the mean-square disorder of neighbor distance with milling time is detected in good agreement with the results of x-ray diffraction. Size effects strongly influence the magnetic and thermal properties. The value for the maximum of the magnetic susceptibility decreases around 30% for 120 h milled alloy and an excess specific heat, with a peak around 40 K in the milled samples, is derived. These changes in the physical properties along the milled ${\text{YbAl}}_3$ alloys are associated with the reduction in particle size. Such a reduction leads to the existence of a large number of ${\text{Yb}}^{2+}$ atoms at the surface with respect to the bulk affecting the overall electronic state.

Figure 1

(Color online) X-ray diffraction patterns for the ${\text{YbAl}}_3$ milled alloys at 20, 70, and 120 h of grinding time. The spectra have been shifted up for clarity. The peak broadening is especially evident for the sample milled during 120 h.

Figure 2

(Color online) Particle size $\left(D\right)$ and strain $\left(\eta \right)$ as functions of the milling time for the ${\text{YbAl}}_3$ milled alloys. The decrease in size and increase in strain are features usually found in milled metallic systems. Continuous and dashed lines are guides for the eye.

Figure 3

(Color online) Temperature dependence of dc magnetic susceptibility $\chi \left(T\right)$ at $H=1\text{T}$. The maximum around 121 K for the unmilled alloy decreases slightly in the position but decreases strongly in absolute value with the increase in milling time. A low-temperature anomaly around $T=17\text{K}$ associated with coherence effects is clearly observed in the unmilled sample and is hardly present in the alloy milled for 20 h.

Figure 4

(Color online) Temperature dependence of the specific heat for unmilled and 20 h milled alloys. An excess of the specific heat is observed around 40 K and above 160 K for the milled sample. The dashed line is the specific heat of ${\text{LuAl}}_3$. A maximum in $c_{\text{mag}}$ of the unmilled alloy appears around 100 K.

Figure 5

(Color online) (a) Magnetic contribution to the specific heat vs temperature curves calculated for the series of ${\text{YbAl}}_3$ milled alloys [$c_{\text{mag}}\left(\text{milled}\right)=\omega c_{mag}\left(\text{bulk}\right)$, where $\omega$ is the fraction of the Yb atoms in the valence state of the bulk]. (b) Excess specific heat for the ${\text{YbAl}}_3$ milled alloys. A peak around 40 K and a slope above 160 K (increasing with the milling time) are observed (see text).

Figure 6

(Color online) Yb ${\text{L}}_{\text{III}}$ normalized x-ray absorption $\left({\mu }_{\text{Norm}}\right)$ vs relative photon energy $E-E_0$ ($E_0=8946.5\text{eV}$ is the energy of the maximum of the first derivative of the spectrum of the reference ${\text{Yb}}_2{\text{O}}_3$ sample) for the unmilled, 20, 70, and 120 h milled ${\text{YbAl}}_3$ and ${\text{Yb}}_2{\text{O}}_3$ reference sample. A change in the ${\text{Yb}}^{2+}$ contribution is clearly observed (marked with an arrow) and is also shown in detail in the inset.

Figure 7

(Color online) Fourier filtered EXAFS functions $\chi \left(k\right)$ $k$ weighted and their fits (solid lines) as a function of photoelectron wave vector $k$ for unmilled and 20, 70, and 120 h milled ${\text{YbAl}}_3$ alloys. The fits were restricted to first shell in the range $k=2–12{\text{Å}}^{-1}$ with $r=1.1–3.2\text{Å}$ using a Hanning window function. For the unmilled sample the experimental data are also shown.

Figure 8

(Color online) Amplitude of the $k$-weighted Fourier transform in $r$ space taken at $L_{\text{III}}$ edge for unmilled, 20, 70, and 120 h milled ${\text{YbAl}}_3$ alloys. $\text{Yb-}{L}_{\text{III}}$-edge data are transformed from $k=2–12{\text{Å}}^{-1}$ using a Hanning window function. The main peak correspond to the contribution of the first shell of nearest neighbors (12 Al atoms).

Figure 9

(Color online) Lattice strain $\left(\eta \right)$ and Debye-Waller factor $\left({\sigma }^2\right)$ in the unmilled, 20, 70 and 120 h milled alloys as a function of the milling time. The lines are guides for the eye.

Figure 10

(Color online) Milling time dependence of the valence $\nu$ (a), the value of the magnetic susceptibility at maximum $\left({\chi }_{\text{max}}\right)$ (b), Slope of the high-temperature excess contribution to the specific heat $\left(SL\right)$ (c), the size of the particles $\left(D\right)$ (d). The grain size of the unmilled alloy can only be suggested (marked with an arrow). Errors in $D$ are smaller than the square symbol.