The gold-rich intermetallic compounds REAu4Cd2 (RE = La–Nd, Sm) were synthesized from the elements in sealed tantalum ampoules. Their characterization by X-ray powder and single crystal data confirmed the tetragonal YbAl4Mo2 type, space group I4/mmm. The basic building units are Au4 squares (278 pm Au–Au in CeAu4Cd2) and infinite linear cadmium chains (275 pm Cd–Cd in CeAu4Cd2). We exemplarily studied the solid solution CeAu4+xCd2−x for x = 0–1 up to CeAu5Cd. Electron diffraction patterns on a CeAu5Cd sample confirm the single crystal data. They give no hint for complete gold-cadmium ordering. Temperature-dependent magnetic susceptibility measurements of CeAu4Cd2, CeAu5Cd, PrAu4Cd2 and NdAu4Cd2 show stable trivalent rare earth ions and give no hint for magnetic ordering above 3 K.
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) . The molybdenum atoms form infinite linear chains which extend along  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) . 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) . 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.
So far, the Pearson data base  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 , , also the aluminum phases YbCu5.1Al0.9 , YbCu5.12Al0.88  and UCu5Al ,  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 , , , , ,  and REGa4V2 , , , . Especially HfGa4V2 and ScGa4V2 of the latter series have intensively been studied with respect to their superconducting properties and elastic anisotropy , .
The infinite chains in this structure type can also be formed by magnesium, zinc, cadmium, and indium atoms. The four series REAg4+xMg2−x , , , AAu4+xZn2−x (A=Ca, RE) , , AAu4+xCd2−x (A=Ca, Sr, RE) , and AAu4+xIn2−x (A=Sr, Eu) , ,  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 . The rare earth atoms thus show a stable trivalent ground state. This is different in EuAu4Cd2 , which, according to magnetic susceptibility data and 151Eu Mößbauer spectra, shows stable divalent europium and ferromagnetic ordering below TC=16.3 K.
A further example is the intermetallic compound CeCu4.7Mn1.3  with statistical Cu/Mn occupancy on the 4d site. CeCu4.7Mn1.3 can be considered as just one possible composition, and one can expect at least a small homogeneity range.
The different coloring variants ,  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 ,  rather than isotypic.
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 . Two chemically different site occupancy variants have been discovered. In the solid solution LaAg4+xMg2−x , , ordered –Ag–Mg–Ag–Mg– chains occur in LaAg5Mg while the intermediate-valent compound Ce2RuZn4 , ,  shows –CeIV–Ru–CeIV–Ru– chains with short CeIV–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) , 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 REAu4+xCd2−x, that have been studied exemplarily for cerium.
Starting materials for the syntheses of the REAu4Cd2 samples with RE=La–Nd and Sm, were sublimed rare earth metal pieces (Smart Elements, 99.9%), gold drops or gold sheets (Agosi AG, 99.9%) and a cadmium rod (Sigma-Aldrich, 99.999%). The larger moisture sensitive rare earth pieces were cut under dry cyclohexane and stored in Schlenk tubes prior to the reactions. The three elements were then weighed in the ideal atomic ratios (approximate total masses of 250 mg) and arc-welded  in tantalum ampoules. The solid solution CeAu4+xCd2−x was studied exemplarily in x=0.2 steps up to x=1. Due to the low boiling temperature of cadmium (T=1038 K ), an excess of 3 weight-percent cadmium was used for each sample. This compensates approximately for the loss due to film formation at the top lid of the tubes after the annealing sequence.
The sealed tantalum ampoules were subsequently placed in a water-cooled sample chamber  of a high-frequency furnace (Hüttinger Elektronik, Freiburg, type TIG 1.5/300) and first rapidly heated to ca. 1473 K. This temperature was kept for 5 min, decreased to 923 K within 10 min and kept for another 4 h, followed by quenching. The temperature was controlled through a radiation pyrometer (Metis MS09, Sensortherm) with an accuracy of ±50 K.
The samples could mechanically be separated from the containers. No reaction with the ampoule material was evident. X-ray powder patterns of these inductively annealed samples showed significantly broadened reflections and by-products, inter alia binary AuCd with CsCl-type structure . In order to increase the crystallinity and the phase purity, all samples were subsequently ground to powders, cold-pressed to pellets and annealed in sealed silica tubes in a muffle furnace at 823 K. This annealing step is essential, as it leads to a significantly improved purity of the samples. The product phases are light grey/golden with some metallic lustre and stable in air.
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 . As an example, we present the experimental and simulated CeAu4Cd2 powder diagram in Fig. 3.
|Compound||a (pm)||c (pm)||V (nm3)|
Standard deviations are given in parentheses.
Single crystal fragments were isolated from the annealed CeAu4Cd2 and CeAu4.2Cd1.8 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.
|Formula weight, g mol−1||1152.8||1209.4|
|Lattice parameters (single crystal data)|
|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|
|θ range, deg||4.03–33.43||4.04–33.22|
|hkl range||±10, ±11, ±8||±10, ±10, ±8|
|Total no. reflections||1701||1816|
|Refl. with I>3 σ(I)/Rσ||162/0.0070||169/0.0048|
|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|
|Largest diff. peak/hole, e Å−3||3.77/–2.18||1.88/–1.79|
2.3 Structure refinements
The data sets of the crystals with nominal compositions CeAu4Cd2 and CeAu4.2Cd1.8 showed tetragonal body-centred unit cells with 4/mmm Laue symmetry and no further systematic extinctions. Space group I4/mmm was found to be correct, in agreement with previous results on isotypic CaAu4Cd2 . The atomic parameters of the calcium compound were taken as starting values and the structures were refined with full-matrix least-squares on Fo2 using the program Jana2006  with anisotropic displacement parameters for all atoms. Separate refinements of the occupancy parameters revealed full occupancies for CeAu4Cd2. The second crystal showed Au/Cd mixing on the 4d site. This mixed occupancy was refined as a least-squares variable in the final cycles and resulted in the composition CeAu4.67(1)Cd1.33(1) for the investigated crystal. The final difference Fourier syntheses revealed no significant residual peaks. The atomic positions, displacement parameters, and interatomic distances are given in Tables 3 and 4.
|0.67(1) Cd/0.33(1) Au2||4d||0||1/2||1/4||167(3)||136(4)||0||157(2)|
The equivalent isotropic displacement parameter Ueq is defined as Ueq=1/3 (U11+U22+U33) (pm2). U22=U11, U13=U23=0. Standard deviations are given in parentheses.
Standard deviations are equal or smaller than 0.1 pm. All distances of the first coordination spheres are listed. Note that the M site shows a mixed occupancy of 67(1)% Cd and 33(1)% Au.
CCDC 1953900 (CeAu4Cd2) and 1953960 (CeAu4.67Cd1.33) contain the supplementary crystallographic data for this paper. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif.
2.4 EDX data
The crystals of CeAu4Cd2 and CeAu4.67(1)Cd1.33(1) studied on the single crystal diffractometer were analyzed by EDX in variable pressure mode (60 Pa) using a Zeiss EVO® MA10 scanning electron microscope with CeO2, Au and Cd as standards. Each crystal was analyzed at 10 points. The averaged values of 13±2 at% Ce: 58±2 at% Au: 29±2 at% Cd for the CeAu4Cd2 (14.3: 57.1:28.6) and 14±2 at% Ce: 66±2 at% Au: 20±2 at% Cd for the CeAu4.67Cd1.33 (14.3:66.7:19.0) crystal confirmed the X-ray data. No impurity elements (especially with respect to the tantalum of the containers) were observed.
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 , .
2.6 Physical property studies
Polycrystalline powders of CeAu4Cd2, PrAu4Cd2, NdAu4Cd2 as well as CeAu5Cd were packed in polyethylene (PE) capsules and attached to the sample holder rod of a Vibrating Sample Magnetometer unit (VSM) for measuring the magnetization M(T,H) in a Quantum Design Physical Property Measurement System (PPMS). The samples were investigated in the temperature range of 2.5–300 K and with applied magnetic fields up to 80 kOe (1 kOe=7.96×104 A m−1).
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 , , , . In the following discussion we therefore mainly focus on the structural details that are directly associated with the formation of the solid solution CeAu4+xCd2−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) . The rows of these condensed polyhedra are arranged in form of a tetragonal rod packing , , .
The gold substructure shows Au–Au distances of 278 and 297 pm, close to the Au–Au distances in fcc gold (288 pm ). 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  for Au+Cd of 275 pm, indicating weaker Au–Cd bonding.
Keeping the Pauling electronegativities  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 . 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 , , , , , , , , . This is also the case for CeAu4Cd2 reported herein. We observe the complete solid solution CeAu4+xCd2−x up to x=1. The lattice parameters of the CeAu4+xCd2−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 ) are substituted by smaller gold atoms (covalent radius 134 pm ). Whereas the decrease of c is almost linear for the solid solution EuAu4+xCd2−x  up to EuAu5Cd, for the x=1 sample of the solid solution CeAu4+xCd2−x we observe a small recovery for the c parameter, as it has also been observed within the solid solution LaAg4+xMg2−x , 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  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 . The corresponding group-subgroup scheme for the pair LaAg4Mg2 (I4/mmm)/LaAg5Mg (P4/nmm) has been described in detail in , . It is similar to the pair CeAu4Cd2 (I4/mmm)/Ce2RuZn4 (P4/nmm) . Ce2RuZn4 is a static mixed-valence cerium compound with an ordering of CeIV and Ru on the linear chain. In view of the completely different bonding pattern, LaAg5Mg and Ce2RuZn4 are only isopointal , .
Thus, the occurrence of primitive (superstructure) reflections indicates the ordering within the chains. The CeAu4.67(1)Cd1.33(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.
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 CeAu4.67(1)Cd1.33(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  and Ce2RuZn4 , ,  and the close structural relationship of magnesium and cadmium intermetallics ,  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 ,  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).
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 μeff=2.49(1) μB per Ce atom for CeAu4Cd2 and μeff=2.54(1) μB per Ce atom for CeAu5Cd. The effective magnetic moments match the theoretical value for a free Ce3+ ion (μtheo=2.54 μB). The Weiss constants are θp=+8.0(5) K (CeAu4Cd2) and θp=−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 μsat=1.20(2) μB per Ce atom (CeAu4Cd2) and μsat=1.04(2) μB per Ce atom (CeAu5Cd), which is drastically below the expected saturation magnetization of 2.14 μB per Ce atom according to gJ×J, however in line with that of several other intermetallic cerium compounds , .
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 (μeff(PrAu4Cd2)=3.75(1) μB; μcalc(Pr3+)=3.58 μB; μeff(NdAu4Cd2)=3.55(1) μB; μcalc(Nd3+)=3.62 μB). The Weiss constants (θP(PrAu4Cd2)=−1.5(1) K; θP(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 μsat(PrAu4Cd2)=1.96(1) μB and μsat(NdAu4Cd2)=1.88(1) μB, which are below the theoretical values of μsat,calc(Pr3+)=3.20 μB and μsat,calc(Nd3+)=3.27 μB, a consequence of anisotropy and the polycrystalline character of the samples.
Dedicated to: Professor Arndt Simon on the occasion of his 80th birthday.
We thank Dipl.-Ing. U. Ch. Rodewald for the single crystal data collections.
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