II. EXPERIMENTAL

The sample of Tb₃CuAl₃Ge₂ was prepared by arc melting of Al (99.8%), Cu (99.99%), Tb (99.5%), and Ge (99.99%) in a water-cooled copper hearth with a non-consumable tungsten electrode under argon atmosphere. The sample of Tb₃CuAl₃Ge₂ was turned over and remelted three times to ensure sample homogeneity. The weight loss of the sample was less than 1 wt%. The obtained ingot of Tb₃CuAl₃Ge₂ was annealed in an evacuated quartz tube at 800 °C for 480 h, and then cooled down slowly at a rate of 10 °C h⁻¹ to room temperature. The specimen of Tb₃CuAl₃Ge₂ for XRD measurements was ground in an agate mortar and pestle to a particle size of less than 10 μm. Powder sample of Tb₃CuAl₃Ge₂ was loaded to an Al-holder and gently pressed. Two sets of the powder XRD patterns, with or without Si (99.9999%) added as an internal standard, were collected at room temperature on a Rigaku D/Max 2500 V diffractometer (with CuKα radiation and a graphite monochromator). The scan ranged from 10° to 110°2θ with a step size of 0.02° and a counting time of 2 s per step. The Jade 6 software package (Materials Data, Inc., 2002) was used to analyze the data. The XRD pattern of the Tb₃CuAl₃Ge₂ specimen with high-purity Si internal standard was used to obtain the observed peak positions 2θ _obs for indexing, whereas the XRD pattern without Si internal standard was used to pick out the observed intensity of each peak, I _obs. The 2θ _obs values of the peaks were determined by the Savitzky–Golay second derivative method after background subtracting, Kα ₂ stripping and Si internal standard calibration using PDF 027-1402 (ICDD, Reference Kabekkodu2011) with λ = 1.540 56 Å.

III. RESULTS AND DISCUSSION

A. Crystal structure

The powder XRD pattern of Tb₃CuAl₃Ge₂, shown in Figure 1, was successfully indexed using the Jade 6 program in a hexagonal unit cell with the lattice parameters a = 7.0041(2) Å and c = 4.1775(1) Å. No conditions for reflections of the Tb₃CuAl₃Ge₂ pattern pointed to five possible space groups: P6/mmm (no. 191), P-62m (no.189), P-6m2 (no. 187), P6mmm (no. 183), and P622 (no. 177) (Hahn, Reference Hahn1992). By comparing the crystallographic characteristics of the Tb₃CuAl₃Ge₂ compound with those presented in the structural type database it was found that Tb₃CuAl₃Ge₂ and Y₃NiAl₃Ge₂ (Zhao and Parthe, Reference Zhao and Parthe1990) have the same structure type. So the space group P-62m (no. 189) and the atomic position parameters of Y₃NiAl₃Ge₂ were taken as the starting values to refine the structural parameters of Tb₃CuAl₃Ge₂. The Tb sites correspond to the Y sites and the Cu to the Ni sites in Y₃NiAl₃Ge₂. The structural refinement of Tb₃CuAl₃Ge₂ was then performed using the DBWS9807a program (Young et al., Reference Young, Larson and Paiva-Santos2000). The pseudo-Voigt function was used for the simulation of the peak shapes. The indexing results for Tb₃CuAl₃Ge₂ were taken as the starting lattice parameters. A total of 23 parameters of the Tb₃CuAl₃Ge₂ compound were refined, including peak shape parameters, scale factor, cell parameters, atomic coordinates, isotropic displacement parameters, full-width at half-maximum (FWHM) parameters, and preferred orientation parameter. The background of the XRD data of Tb₃CuAl₃Ge₂ was refined with a polynomial. The final Rietveld refinement led to agreement factors of: R _p = 6.43%, R _wp = 8.65%, and R _B = 4.81%, and R _F = 4.09%, respectively. The details of the Rietveld Refinement of Tb₃CuAl₃Ge₂ are summarized in Table I, and the atomic positions and thermal displacement factors for Tb₃CuAl₃Ge₂ are presented in Table II. The observed, calculated, and residual powder XRD patterns of Tb₃CuAl₃Ge₂ are shown in Figure 2 and the crystal structure of Tb₃CuAl₃Ge₂ is given in Figure 3. The selected atomic distances are listed in Table III.

Figure 1.

Powder XRD pattern of Al₃CuGe₂Tb₃.

Figure 2.

The observed, calculated, and residuals powder XRD patterns of Tb₃CuAl₃Ge₂.

Figure 3.

(Color online) The crystal structure of Tb₃CuAl₃Ge₂.

Table I.

Rietveld refinement data of Tb₃CuAl₃Ge₂.

$${R_{\rm P}}=\displaystyle{{\sum {\left\vert {{Y_i}\lpar {\rm obs}\rpar - {Y_i}\lpar {\rm calc}\rpar } \right\vert } } \over {\sum {{Y_i}\lpar {\rm obs}\rpar } }}\comma \; {R_{{\rm WP}}}={\left\{{\displaystyle{{\sum {{\omega _i}{{\left[{{Y_i}\lpar {\rm obs}\rpar - {Y_i}\lpar {\rm calc}\rpar } \right]}^2}} } \over {\sum {{\omega _i}{{\left[{{Y_i}\lpar {\rm obs}\rpar } \right]}^2}} }}} \right\}^{1/2}}$$

$${R_{\rm B}}=\displaystyle{{\sum {\left\vert {{I_{\rm H}}\lpar {\rm obs}\rpar - {I_{\rm H}}\lpar {\rm calc}\rpar } \right\vert } } \over {\sum {{I_{\rm H}}\lpar {\rm obs}\rpar } }}\comma \; {R_{\rm F}}=\displaystyle{{\sum {\left\vert {{{\lsqb {I_{\rm H}}\lpar {\rm obs}\rpar \rsqb }^{1/2}} - {{\lsqb {I_{\rm H}}\lpar {\rm calc}\rpar \rsqb }^{1/2}}} \right\vert } } \over {\sum {{{\lpar {I_{\rm H}}\lpar {\rm obs}\rpar \rpar }^{1/2}}} }}$$

Table II.

Atomic coordinates and thermal parameters for Tb₃CuAl₃Ge₂.

Table III.

Selected interatomic distances (nm) for Tb₃CuAl₃Ge₂.

B. X-ray powder diffraction data

The Tb₃CuAl₃Ge₂ compound is in a hexagonal unit cell with parameters a = 7.0041(2) Å, c = 4.1775(1) Å, and unit-cell volume V = 177.48 ų. The figure of merit for the indexing F _N (Smith and Snyder, Reference Smith and Snyder1979) is F ₃₀ = 120.9 (0.0073, 34). The powder XRD data for Tb₃CuAl₃Ge₂ are listed in Table IV.

Table IV.

Powder diffraction data for Tb₃CuAl₃Ge₂ (CuKα ₁,with λ = 1.540 56 Å).