Squares of gold atoms and linear infinite chains of Cd atoms as building units in the intermetallic phases REAu₄Cd₂ (RE=La–Nd, Sm) with YbAl₄Mo₂-type structure

1 Introduction

The structures of intermetallic compounds can be described by the condensation of the different coordination polyhedra or via pronounced substructures of the individual components. This can nicely be illustrated for the YbAl₄Mo₂ type (Fig. 1) [1]. The molybdenum atoms form infinite linear chains which extend along [001] with Mo–Mo distances of 266 pm, indicating bonding interactions, since the distances are even slightly shorter than in bcc molybdenum (273 pm Mo–Mo) [2]. The same holds true for the aluminum substructure. Al₄ squares with Al–Al distances of 265 pm are condensed via Al–Al distances of 284 pm, both again shorter than in fcc aluminum (286 pm) [2]. Alternatively, one can describe the YbAl₄Mo₂ structure through polyhedra. The ytterbium atoms fill larger cages within the aluminum substructure, and these Yb@Al₁₂ polyhedra are condensed with the Mo@Al₈Mo₂ polyhedra via common edges.

Fig. 1:

The crystal structure of YbAl₄Mo₂ [1]. Ytterbium, molybdenum and aluminum atoms are drawn as medium grey, blue and magenta circles, respectively. The infinite molybdenum chains, the aluminum substructure and the Yb@Al₁₂ and Mo@Al₈Mo₂ polyhedra are emphasized.

So far, the Pearson data base [3] lists 62 entries for the YbAl₄Mo₂ type, space group I4/mmm, Pearson symbol tI14 and Wyckoff sequence hda. Besides the series of rare earth (RE) aluminum compounds REAl₄Mo₂ [1], [4], also the aluminum phases YbCu_5.1Al_0.9 [5], YbCu_5.12Al_0.88 [6] and UCu₅Al [7], [8] have been reported. Here the Cu atoms occupy the Al sites, while the Mo site is mixed occupied by Cu and Al. The higher congener gallium forms the series REGa₄Ti₂ [9], [10], [11], [12], [13], [14] and REGa₄V₂ [15], [16], [17], [18]. Especially HfGa₄V₂ and ScGa₄V₂ of the latter series have intensively been studied with respect to their superconducting properties and elastic anisotropy [17], [18].

The infinite chains in this structure type can also be formed by magnesium, zinc, cadmium, and indium atoms. The four series REAg_4+xMg_2−x [19], [20], [21], AAu_4+xZn_2−x (A=Ca, RE) [22], [23], AAu_4+xCd_2−x (A=Ca, Sr, RE) [24], and AAu_4+xIn_2−x (A=Sr, Eu) [25], [26], [27] are known. A common feature of all these phases is their ability to form solid solutions on the 4d Wyckoff sites, i.e. within the linear chains. So far, only few property studies have been performed. Compounds REAu₄Zn₂ with RE=Ce, Pr, Nd show Curie-Weiss behaviour without magnetic ordering down to 2.5 K [22]. The rare earth atoms thus show a stable trivalent ground state. This is different in EuAu₄Cd₂ [24], which, according to magnetic susceptibility data and ¹⁵¹Eu Mößbauer spectra, shows stable divalent europium and ferromagnetic ordering below T_C=16.3 K.

A further example is the intermetallic compound CeCu_4.7Mn_1.3 [28] with statistical Cu/Mn occupancy on the 4d site. CeCu_4.7Mn_1.3 can be considered as just one possible composition, and one can expect at least a small homogeneity range.

The different coloring variants [29], [30] listed above are summarized in Fig. 2. The distinctly different site occupancies lead to different valence electron counts and pronounced differences in chemical bonding. Most of these phases should consequently be called isopointal [31], [32] rather than isotypic.

Fig. 2:

Examples of coloring variants for YbAl₄Mo₂-type representatives (space group I4/mmm) and ordered superstructure variants in the klassengleiche subgroup P4/nmm.

An interesting situation concerns those solid solutions where exactly half of the atoms of the linear chains are substituted. A splitting of the 4d site is possible through a klassengleiche symmetry reduction of index 2 to space group P4/nmm [33]. Two chemically different site occupancy variants have been discovered. In the solid solution LaAg_4+xMg_2−x [19], [20], ordered –Ag–Mg–Ag–Mg– chains occur in LaAg₅Mg while the intermediate-valent compound Ce₂RuZn₄ [34], [35], [36] shows –Ce^IV–Ru–Ce^IV–Ru– chains with short Ce^IV–Ru distances of 260 pm, while the other half of the cerium atoms has remained trivalent.

In the course of our phase analytical studies of the RE-T-Cd systems (T=electron-rich transition metal) [37], we have extended the REAu₄Cd₂ series including the trivalent rare earths La–Nd and Sm, for which there are also hints for the formation of solid solutions REAu_4+xCd_2−x, that have been studied exemplarily for cerium.

2 Experimental

2.2 X-ray diffraction

The polycrystalline products were characterized through Guinier patterns (Enraf-Nonius FR552 camera, imaging plate detector, Fuji film BAS-1800), which were recorded using CuKα₁ radiation and α-quartz (a=491.30, c=540.46 pm) as an internal standard. The tetragonal lattice parameters (Table 1) were deduced from least-squares refinements. Correct indexing was ensured by comparison with calculated patterns using the Lazy Pulverix routine [41]. As an example, we present the experimental and simulated CeAu₄Cd₂ powder diagram in Fig. 3.

Table 1:

Refined lattice parameters (Guinier powder data) of the intermetallic compounds REAu₄Cd₂ (RE=La–Nd, Sm) and the solid solution CeAu_4+xCd_2−x.

Compound	a (pm)	c (pm)	V (nm3)
LaAu4Cd2	716.73(8)	550.1(1)	0.2826
CeAu4Cd2	714.6(1)	551.9(1)	0.2818
CeAu4.2Cd1.8	714.35(7)	550.03(9)	0.2807
CeAu4.4Cd1.6	714.69(8)	547.9(2)	0.2799
CeAu4.6Cd1.4	714.58(6)	545.54(7)	0.2786
CeAu4.8Cd1.2	714.33(9)	544.20(7)	0.2777
CeAu5.0Cd1.0	714.25(8)	546.13(9)	0.2786
PrAu4Cd2	712.4(1)	549.5(2)	0.2789
NdAu4Cd2	711.8(1)	548.9(2)	0.2781
SmAu4Cd2	710.7(2)	547.0(2)	0.2763
EuAu4Cd2 [24]	717.0(1)	553.2(2)	0.2844

1. Standard deviations are given in parentheses.

Fig. 3:

Experimental and calculated Guinier powder pattern (CuKα₁ radiation) of CeAu₄Cd₂. The asterisk marks a reflection originating from the by-product AuCd with CsCl-type structure.

Single crystal fragments were isolated from the annealed CeAu₄Cd₂ and CeAu_4.2Cd_1.8 samples. The block-shaped splinters were glued to quartz fibres using beeswax and their quality was first tested on a Buerger camera (white Mo radiation). Complete intensity data sets were collected by use of a Stoe IPDS-II diffractometer (graphite-monochromatized MoKα radiation; oscillation mode). Numerical absorption corrections were applied to both data sets. Details of the data collections, the crystallographic parameters and the refinements are summarized in Table 2.

Table 2:

Crystallographic data and structure refinement of CeAu₄Cd₂ and CeAu_4.67(1)Cd_1.33(1); YbAl₄Mo₂ type, space group I4/mmm, Z=2.

Empirical formula	CeAu4Cd2	CeAu4.67(1)Cd1.33(1)
Formula weight, g mol−1	1152.8	1209.4
Lattice parameters (single crystal data)
a, pm	714.65(11)	714.01(6)
c, pm	550.86(9)	544.65(5)
Cell volume, nm3	0.2813	0.2777
Calculated density, g cm−3	13.61	14.46
Crystal size, μm3	30×35×100	20×30×165
Transm. ratio (min/max)	0.154/0.054	0.164/0.037
Diffractometer type	IPDS-II (Stoe)	IPDS-II (Stoe)
Detector distance, mm	70	70
Exposure time, min	5	5
ω range/step width, deg	0–180/1.0	0–180/1.0
Integr. Param. A/B/EMS	14.0/–1.0/0.030	14.0/4.0/0.010
Abs. coefficient, mm−1	119.0	135.7
F(000), e	940	981
θ range, deg	4.03–33.43	4.04–33.22
hkl range	±10, ±11, ±8	±10, ±10, ±8
Total no. reflections	1701	1816
Independent reflections/Rint	179/0.0317	179/0.0262
Refl. with I>3 σ(I)/Rσ	162/0.0070	169/0.0048
Data/parameters	179/10	179/11
Goodness-of-fit on F2	2.50	1.82
R1/wR2 for I>3 σ(I)	0.0288/0.0623	0.0200/0.0435
R1/wR2 for all data	0.0320/0.0628	0.0217/0.0439
Extinction coefficient	520(30)	187(11)
Largest diff. peak/hole, e Å−3	3.77/–2.18	1.88/–1.79

2.5 Electron microscopy

CeAu₅Cd was investigated by using a Phillips CM-200 STEM transmission electron microscope (200 kV, point resolution 0.23 nm) equipped with a super twin objective lens and an EDAX EDX system. A small piece of sintered CeAu₅Cd was cooled down using liquid nitrogen in a steel mortar. The sample was carefully crushed into small particles to prevent mechanical damage of the crystals. The sample was suspended in ethanol, transferred to a carbon-coated copper grid (Plano) and investigated using a double-tilt low-background sample holder (Gatan). The chemical composition of the investigated crystal (Fig. 4) was measured by EDX analyses at several areas of the investigated crystal. Selected-area electron diffraction (SAED) patterns were simulated using the JEMS software package [43], [44].

Fig. 4:

TEM bright-field image of the investigated CeAu₅Cd crystal. The area used to obtain SAED patterns is emphasized by a white circle and visualized by an enlarged view.

3 Crystal chemistry

Our studies in the gold-rich parts of the RE-Au-Cd systems with the early rare earth elements revealed the YbAl₄Mo₂-type phases REAu₄Cd₂ with RE=La–Nd and Sm. The crystal chemical details of the YbAl₄Mo₂ type have repeatedly been discussed [13], [19], [20], [22]. In the following discussion we therefore mainly focus on the structural details that are directly associated with the formation of the solid solution CeAu_4+xCd_2−x.

Figure 5 shows a projection of the CeAu₄Cd₂ structure onto the xy plane. The gold atoms build a substructure with two different Au₁₂ cages. The larger cerium atoms fill the middle of one of these cages (Fig. 5, left), while pairs of cadmium atoms fill the second one (Fig. 5, middle). These Au₁₂ cages are condensed in c direction via common gold rectangles. This leads to infinite cadmium chains with Cd–Cd distances of 275 pm, which are even shorter than in hcp cadmium (6×298 and 6×329 pm) [2]. The rows of these condensed polyhedra are arranged in form of a tetragonal rod packing [45], [46], [47].

Fig. 5:

Projection of the CeAu₄Cd₂ structure along [001]. Cerium, gold and cadmium atoms are drawn as medium grey, blue and magenta circles, respectively. The coordination of the cerium respectively cadmium atoms is outlined at the left- and right-hand part of the unit cell along with two ordering models for alternating Au/Cd occupancy within the linear chains for the gold-rich compound CeAu₅Cd.

The gold substructure shows Au–Au distances of 278 and 297 pm, close to the Au–Au distances in fcc gold (288 pm [2]). The cadmium chains bind to the gold substructure via Au–Cd contacts with 293 pm Au–Cd, significantly longer than the sum of the covalent radii [39] for Au+Cd of 275 pm, indicating weaker Au–Cd bonding.

Keeping the Pauling electronegativities [39] in mind (1.12 for Ce, 2.54 for Au and 1.69 for Cd), we can ascribe auride character to CeAu₄Cd₂, similar to isotypic CaAu₄Cd₂ [24]. A Bader charge analysis of the latter compound revealed +1.98 for Ca, +0.43 for Cd and –0.71 for Au. The other gold-containing YbAl₄Mo₂-type phases show the same electronic fingerprint.

Detailed phase analytical work revealed the formation of extended solid solutions for several of the YbAl₄Mo₂-type phases, resulting from continuous substitution of the chain atoms on Wyckoff position 4d by the transition metal [19], [20], [21], [22], [23], [24], [25], [26], [27]. This is also the case for CeAu₄Cd₂ reported herein. We observe the complete solid solution CeAu_4+xCd_2−x up to x=1. The lattice parameters of the CeAu_4+xCd_2−x samples are summarized in Table 1 and plotted as a function of the x value in Fig. 6. The lattice parameter a is approximately unaffected by the substitution while c decreases with increasing gold content, since cadmium atoms (covalent radius of 141 pm [39]) are substituted by smaller gold atoms (covalent radius 134 pm [39]). Whereas the decrease of c is almost linear for the solid solution EuAu_4+xCd_2−x [24] up to EuAu₅Cd, for the x=1 sample of the solid solution CeAu_4+xCd_2−x we observe a small recovery for the c parameter, as it has also been observed within the solid solution LaAg_4+xMg_2−x [19], where it has been associated with superstructure formation. In an ordered model for x=1 (i.e. LaAg₅Mg or CeAu₅Cd) one observes alternating chains –Ag–Mg–Ag–Mg– or –Au–Cd–Au–Cd– extending in c direction. The complete ordering leads to a symmetry reduction. A single crystal structure refinement of LaAg₅Mg [20] clearly manifested space group P4/nmm, a klassengleiche subgroup of index 2 of I4/mmm. The splitting of the 4d site into two two-fold sites allows for the –Ag–Mg–Ag–Mg– ordering [19]. The corresponding group-subgroup scheme for the pair LaAg₄Mg₂ (I4/mmm)/LaAg₅Mg (P4/nmm) has been described in detail in [19], [20]. It is similar to the pair CeAu₄Cd₂ (I4/mmm)/Ce₂RuZn₄ (P4/nmm) [22]. Ce₂RuZn₄ is a static mixed-valence cerium compound with an ordering of Ce^IV and Ru on the linear chain. In view of the completely different bonding pattern, LaAg₅Mg and Ce₂RuZn₄ are only isopointal [31], [32].

Fig. 6:

Course of the lattice parameters a and c of the solid solution CeAu_4+xCd_2−x. 1:1 Gold-cadmium ordering within the chains is possible around x=1 (blue shaded region). For details see text.

Thus, the occurrence of primitive (superstructure) reflections indicates the ordering within the chains. The CeAu_4.67(1)Cd_1.33(1) crystal still shows a body-centered lattice without evidence for Au/Cd long-range ordering. Unfortunately, the annealed CeAu₅Cd sample prepared in this work was essentially polycrystalline and it was not possible to select sufficiently large crystals for a diffraction study. Therefore, we have analyzed the Guinier powder pattern (Fig. 7) in more detail. Besides the experimental pattern we present three different calculated powder patterns, all with the same lattice parameters: (i) the subcell structure of CeAu₄Cd₂ in space group I4/mmm, (ii) the subcell structure of CeAu₅Cd in space group I4/mmm with a statistical 50% Au and 50% Cd occupancy on Wyckoff site 4d, and (iii) the fully ordered model for CeAu₅Cd in the primitive subgroup P4/nmm.

Fig. 7:

The experimental Guinier powder pattern (CuKα₁ radiation) of CeAu₅Cd (top) along with different simulated powder patterns. Relevant reflections indicating Au/Cd ordering are highlighted by red and green arrows. For details see text.

The substantial population of the chain with gold atoms leads to an increase of the intensity of the 110 reflection at 2θ=17.55° (green arrow in Fig. 7). However, the weak superstructure reflections (red arrows in Fig. 7) that occur in the fully ordered P4/nmm model are not visible in our experimental powder pattern. As emphasized at the right-hand part of Fig. 4, adjacent fully ordered (!) chains can be shifted by half the c axis, avoiding long-range ordering between the chains. We have thus studied our compound CeAu₅Cd by electron diffraction (vide infra) in order to get more detailed information on the gold/cadmium ordering within and between the chains.

Finally we need to mention that Au/Cd ordering within the chains is also possible in other subgroups. A first possibility is a translationengleiche symmetry reduction to space group I4̅m2. Refinement of the CeAu_4.67(1)Cd_1.33(1) data in this space group revealed the same degree of Au/Cd mixing on both twofold sites and 50/50 twin domains, indicating that I4̅m2 is not the correct space group for the investigated crystal. Besides P4/nmm, also P4₂/mmc is a klassengleiche subgroup. In view of the missing primitive reflections, also space group P4₂/mmc is not correct. An orthorhombic subgroup along with twinning would also be possible; however, our single crystal data gave no hint for this alternative. Keeping the precise single crystal data of LaAg₅Mg [20] and Ce₂RuZn₄ [34], [35], [36] and the close structural relationship of magnesium and cadmium intermetallics [37], [48] in mind, the subgroup P4/nmm is the most probable one for the ordering within the chains.

4 Electron-microscopic characterization of CeAu₅Mg

Since superstructure reflections cannot be expected to be detectable in powder X-ray diffraction patterns due to their low relative intensity, the differentiation of the possible space group symmetries I4/mmm (YbAl₄Mo₂ type) and P4/nmm (LaAg₅Mg type) was performed by analysis of SAED patterns (Figs. 8–10). The correct space group could be determined by SAED diagrams along [013], [012] and [1̅23] for which systematic extinction according to I centering was observed suggesting mixed Au/Cd occupancy on the 4d site. Investigation of several crystals confirmed this observation. Additionally, results of a TEM-EDX analysis of the investigated crystal are in excellent agreement with the expected composition of CeAu₅Cd (Ce: 14±1 at%, Au: 71±1 at%, Cd: 15±1 at%, 5 points measured).

Fig. 8:

Experimental (middle) and simulated SAED patterns of the investigated CeAu₅Cd crystal obtained along different zone axes. The simulations with kinematic intensities were generated on the basis of the structure models in space groups P4/nmm (top, LaAg₅Mg type) and I4/mmm (bottom, YbAl₄Mo₂ type), respectively. Systematic extinction of reflections according to an I centered lattice are observed for the diffraction patterns along [013], [012] and [1̅23]. Diffuse intensity in the SAED patterns is due to poor crystal quality and pronounced intergrowth.

Fig. 9:

Comparison of the experimental SEAD pattern recorded along [013] and simulated ones (left: I4/mmm; right: P4/nmm). Systematic extinction is observed for reflections (depicted in red) fulfilling h+k+l≠2n, compatible with I centering.

Fig. 10:

Goniometer positions of the obtained SAED patterns along with experimental (black font) and calculated (red font) tilt angles between the zone axes.

5 Magnetic properties

CeAu₄Cd₂, CeAu₅Cd, PrAu₄Cd₂ and NdAu₄Cd₂ were investigated by magnetic susceptibility measurements at an applied external field of 10 kOe using a zero-field-cooled routine. The χ and χ⁻¹ data of the cerium compounds is exemplarily shown in Figs. 11 and 12 , top panel. A fit of the χ⁻¹ data in the region above T=50 K using the modified Curie-Weiss law revealed effective magnetic moments of μ_eff=2.49(1) μ_B per Ce atom for CeAu₄Cd₂ and μ_eff=2.54(1) μ_B per Ce atom for CeAu₅Cd. The effective magnetic moments match the theoretical value for a free Ce³⁺ ion (μ_theo=2.54 μ_B). The Weiss constants are θ_p=+8.0(5) K (CeAu₄Cd₂) and θ_p=−8.4(5) K (CeAu₅Cd), suggesting ferromagnetic interactions in the paramagnetic temperature region in the case of CeAu₄Cd₂, while antiferromagnetic interactions are deduced for CeAu₅Cd. The temperature independent contributions are χ₀(CeAu₄Cd₂)=−4.44(5)×10⁻⁴ emu mol⁻¹ and χ₀(CeAu₅Cd)=−1.25(3)×10⁻⁴ emu mol⁻¹. To obtain more information about possible ordering phenomena, low-field measurements were performed in zero-field and field-cooled mode (ZFC/FC), the data is shown in the bottom panels of Figs. 11 and 12. No bifurcation between the ZFC and FC curve and no magnetic ordering was observed down to 3.0 K. The insets in Figs. 11 and 12 (bottom panels) display the magnetization isotherms measured at T=3, 10, and 50 K. The 10 and 50 K isotherms display a linear field dependency of the magnetization, as expected for a paramagnetic material. The 3 K isotherm exhibits curvatures along with the onset of saturation at high fields. The magnetizations at 3 K and 80 kOe reach μ_sat=1.20(2) μ_B per Ce atom (CeAu₄Cd₂) and μ_sat=1.04(2) μ_B per Ce atom (CeAu₅Cd), which is drastically below the expected saturation magnetization of 2.14 μ_B per Ce atom according to g_J×J, however in line with that of several other intermetallic cerium compounds [49], [50].

Fig. 11:

Magnetic properties of CeAu₄Cd₂: (top) temperature dependence of the magnetic susceptibility χ and its reciprocal χ⁻¹ measured with an applied magnetic field of 10 kOe; (bottom) magnetic susceptibility in zero-field (ZFC) and field-cooled (FC) mode at 100 Oe; (inset) magnetization isotherms recorded at T=3, 10, and 50 K.

Fig. 12:

Magnetic properties of CeAu₅Cd: (top) temperature dependence of the magnetic susceptibility χ and its reciprocal χ⁻¹ measured with an applied magnetic field of 10 kOe; (bottom) magnetic susceptibility in zero-field (ZFC) and field-cooled (FC) mode at 100 Oe; (inset) magnetization isotherms recorded at T=3, 10, and 50 K.

Also PrAu₄Cd₂ and NdAu₄Cd₂ exhibit no magnetic ordering down to T=2.5 K. The effective magnetic moments are in line with the calculated ones, indicating purely trivalent oxidation states (μ_eff(PrAu₄Cd₂)=3.75(1) μ_B; μ_calc(Pr³⁺)=3.58 μ_B; μ_eff(NdAu₄Cd₂)=3.55(1) μ_B; μ_calc(Nd³⁺)=3.62 μ_B). The Weiss constants (θ_P(PrAu₄Cd₂)=−1.5(1) K; θ_P(NdAu₄Cd₂)=−1.1(1) K) are small but negative, indicating antiferromagnetic interactions in the paramagnetic temperature regime. Finally, the magnetizations at T=3 K and 80 kOe are μ_sat(PrAu₄Cd₂)=1.96(1) μ_B and μ_sat(NdAu₄Cd₂)=1.88(1) μ_B, which are below the theoretical values of μ_sat,calc(Pr³⁺)=3.20 μ_B and μ_sat,calc(Nd³⁺)=3.27 μ_B, a consequence of anisotropy and the polycrystalline character of the samples.