Revisiting Ce₃Pt₄Ge₆ – crystal structure and physical properties

Abstract

Structural reinvestigations of Ce₃Pt₄Ge₆ on high quality single crystals revealed additional reflections contradicting the previously reported structure featuring half occupied crystallographic sites for this compound. The structure could be solved and refined in the orthorhombic (3 + 1)D superspace group Cmcm(α,0,0)0s0 with α = 0.5a* and lattice parameters of a = 441.17(2), b = 2618.26(14) and c = 441.33(2) pm using the super space approach. The description of the modulated structure as commensurate case allows for an ordering of the Ce2/Ge3 atoms and the respective voids caused by the 50% occupation. The corresponding approximant can be described in the orthorhombic crystal system with space group Pnma and lattice parameters of a = 2618.26(14), b = 441.33(2) and c = 882.34(2) pm. Investigations of the magnetic properties revealed a magnetic moment of μ_eff = 2.48(1)μ_B/Ce atom and a Weiss constant of θ_p = −39(5) K, indicating stable trivalent cerium. No clear magnetic ordering was evident from the susceptibility measurements. Heat capacity investigations showed a λ-shaped anomaly at T = 2.1(1) K. Resistivity measurements show values corresponding to Ce₃Pt₄Ge₆ being a metal, however nearly temperature independent behavior is observed down to low temperatures. A shallow minimum and an abrupt drop suggest the title compound to be a Kondo material.

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Introduction

The isothermal section of the Ce–Pt–Ge phase diagram at 873 K has carefully been studied by Gribanov et al.¹ The phase analytical work, based on X-ray powder and single crystal diffraction as well as metallography in combination with electron microscopy revealed 12 ternary germanides. Most of the structures of these phases have been solved and preliminary physical property studies have been performed.^2–23 To give some examples, CePtGe^9,19 and CePt₂Ge₂¹⁰ order antiferromagnetically at T_N = 4 and 2.2 K, respectively. CePt₅Ge₃ is a low-dimensional magnetic material with an ordering temperature of 1.1 K.²¹

In the original work, the structures of CePtGe³ and Ce₃Pt₄Ge₆¹¹ were reported with mixed and partially occupied sites, respectively. Reinvestigation of the CePtGe structure^18,19 revealed weak superstructure reflections, originating from platinum–germanium ordering. The single crystal data clearly stated the orthorhombic YPdSi structure type. The Ce₃Pt₄Ge₆ structure¹¹ was refined in space group Bmmb (non-standard setting of Cmcm) with half-occupied Ce2 (4c) and Ge3 (8g) sites. Similar composition, but different space group symmetry was observed for the RE₃Pt₄Ge₆ representatives with the smaller rare earth (RE) elements.^24–26 The Y₃Pt₄Ge₆ structure²⁴ as well as the silicide Yb_∼3Pt_∼4Si_6−x (x = 0.3)²⁶ were described in the monoclinic space group P2₁/m and the germanides RE₃Pt₄Ge₆ (RE = Pr, Nd, Sm, Gd, Tb, Dy)²⁵ were reported with space group Pnma which allows for an ordering of all atomic sites. Reinvestigation of the Ce₃Pt₄Ge₆ structure by these authors gave hints for cerium–germanium ordering. Single crystals taken from a long-term annealed sample showed diffuse intensities.

We became interested in these order–disorder problems when solving the structure of a new monoclinic cerium–gold–germanide with an approximate composition Ce₃Au_∼5.5Ge_∼4.5²⁷ and presumably Y₃Pt₄Ge₆ structure. In the course of these systematic investigations we also synthesized new Ce₃Pt₄Ge₆ samples and obtained well shaped single crystals upon annealing arc-melted precursors in a water-cooled sample chamber of an induction furnace. Herein we report on crystal chemical data on the ordered phase and the magnetic properties of Ce₃Pt₄Ge₆. The order–disorder difficulty is discussed on the basis of a group–subgroup scheme.

Experimental

Synthesis

Ce₃Pt₄Ge₆ was synthesized from the elements using cerium ingots (Sigma-Aldrich), platinum sheets (Agosi AG), and germanium lumps (Chempur), all with stated purities better than 99.9%. Pieces of cerium were first arc-melted under an argon pressure of 800 mbar in a water cooled copper heart.²⁸ All starting materials were weighed in the ideal 3 : 4 : 6 ratio (Ce : Pt : Ge) and arc-melted under an argon pressure of 800 mbar. The obtained button was remelted and turned over several times to increase the homogeneity. In a subsequent step the ingot was heated to temperatures just below the melting point for 2 h in a high frequency furnace (Hüttinger Elektronik, Freiburg, Germany, Typ TIG 2.5/300).²⁹ Afterwards the sample was slowly cooled to room temperature. The sample shows metallic luster and is stable in air over months.

X-ray diffraction

The polycrystalline sample was characterized by a Guinier pattern (imaging plate detector, Fujifilm BAS-1800 scanner) with CuKα₁ radiation using α-quartz (a = 491.30, c = 540.46 pm, Riedel-de-Häen) as an internal standard.

Correct indexing of the diffraction lines was ensured through an intensity calculation. The lattice parameters were obtained through least-squares fits³⁰ with standard deviations smaller than ±0.1 pm for all axes.

Irregularly shaped crystals of Ce₃Pt₄Ge₆ were obtained by mechanical fragmentation of the annealed arc-melted button. These fragments were glued to thin quartz fibers using beeswax. The crystal quality was tested by Laue photographs on a Buerger camera (white molybdenum radiation, image plate technique, Fuji film, BAS-1800). Intensity data sets of a suitable crystal were collected at room temperature by use of a Stoe IPDS II diffractometer (graphite-monochromatized MoK_α radiation; oscillation mode). Numerical absorption correction was applied to the data set. All relevant crystallographic data and details of the data collections and evaluations are listed in Table 1.

Table 1 Crystallographic data and structure refinement for Ce₃Pt₄Ge₆

Empirical formula	Ce3Pt4Ge6
Superspace group	Cmcm(α,0,0)0s0
	α = 1/2 a*
Molar mass	1636.2 g mol^−1
Unit cell dimensions	a = 441.17(2) pm
	b = 2618.26(14) pm
	c = 441.33(2) pm
	V = 0.5098 nm^3
Calculated density	10.66 g cm^−3
Linear absorption coeff.	85.0 mm^−1
Transm. ratio (min/max)	0.096, 0.190
F(000)	1356
Crystal size/μm	30 × 30 × 35
Diffractometer	IPDS-II
Wavelength	MoKα (71.073 pm)
Detector distance	90 mm
Exposure time	8 min
Integr. param./A, B, EMS	9.9/1.5/0.012
θ range	2.4–30.7 °
Range in hklm	±6; ±37; ±6; ±1
Total no. reflections	23224
Independent reflections	1360 (Rint = 0.0519)
Reflections with I ≥ 3σ(I)	930 (Rσ = 0.0112)
Main + satellite	930 + 430
Data/parameters	1360/63
Goodness-of-fit	2.07
Final R indices [I ≥ 3σ(I)]	R M = 0.0186/wRM = 0.0451
	R S = 0.0751/wRS = 0.1480
R indices for all data	R M = 0.0227/wRM = 0.0459
	R S = 0.1243/wRS = 0.1557
Extinction scheme	Lorentzian isotropic^31
Extinction coefficient	222(12)
Largest diff. peak and hole/e Å^−3	8.71, −3.64

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Further details on the structure refinement are available from Fachinformationszentrum Karlsruhe, D-76344 Eggenstein-Leopoldshafen (Germany), E-mail: crysdata@fiz-karlsruhe.de, by quoting the Registry no. CSD 431566.

Physical property investigations

Magnetism. A polycrystalline piece of the annealed ingot was packed in kapton foil and attached to the sample holder rod of a Vibrating Sample Magnetometer (VSM) unit for measuring the magnetization M(T,H) in a Quantum Design Physical–Property–Measurement–System (PPMS). The sample was investigated in the temperature range of 2.0–300 K with magnetic flux densities up to 80 kOe.

Heat capacity. For the heat capacity measurements, one piece of the sample was fixed to a pre-calibrated heat capacity puck using Apiezon N grease and investigated in the temperature range of 1.9–300 K.

Electrical resistivity. An annealed button was embedded in a polymethyl-methacrylate (PMMA) matrix and after solidification of the polymer polished on one side until a cross section of at least 3 × 3 mm² was visible. The sample was subsequently removed from the polymer by dissolving the matrix in acetone. In a second step the ingot was embedded again in PMMA in a self-build mold which allows parallel polishing of the second side. The sample was polished until an approximately 1 mm thick specimen remained inside the polymer matrix. The disc shaped sample was removed by again dissolving the PMMA matrix. The resistivity measurement was carried out in the AC transport mode³² of a Quantum-Design Physical-Property-Measurement-System (PPMS). The ACT puck was modified by a van-der-Pauw press contact assembly purchased from Wimbush Science & Technology. The probes are spring contacts, gold plated over nickel; the distance between the pins was set to 2 mm. The resistivity was measured between 2–300 K with a data point every 0.1 K up to 10 K and a data point every 2 K up to 300 K. A maximum current of 10 mA was used; the AC frequency was set to 29 Hz with a measurement time of 1 s. The recorded data of channels 1 & 2 was converted according to the van-der-Pauw equation given in the Quantum Design Application Note 1076-304.

Results and discussion

Structure refinement

The obtained intensity data set of Ce₃Pt₄Ge₆ was initially indexed in analogy to the structure solution of Pr₃Pt₄Ge₆ in the orthorhombic space group Pnma (no. 62) with lattice parameters of a = 2625.4(8), b = 439.3(1) and c = 884.0(3) pm.²⁵ However both, the monoclinic unit cell (a = 882.8(2), b = 441.24(8), c = 1325.5(3) pm and β = 99.62(2) °) in analogy to Y₃Pt₄Ge₆²⁴ as well as an orthorhombic C-centered cell with space group Cmcm (a = 441.9(1), b = 2622.2(5), c = 442.2(1) pm) in analogy to the first report of Ce₃Pt₄Ge₆¹¹ could be found using the automated indexing features. Fig. 1 shows a selected h1l area of the reconstructed diffraction patterns indicating the cells found in literature as well as our interpretation. A careful investigation of the reconstructed diffraction patterns indicated systematically extinct reflections (red square) needed in order to justify the P-centered orthorhombic cell (Fig. 1, left). For the C-centered orthorhombic cell (denoted as Bbmm here) additional reflections along 1/2 c* are found in our diffraction experiments making this interpretation as 3D structure obsolete (Fig. 1, right).

Fig. 1 Sections of the (reconstructed) diffraction pattern of Ce₃Pt₄Ge₆. The different unit cells found in the literature are drawn to show the possible (mis)interpretations of the data. Also the monoclinic interpretation in superspace group P2₁/m(α,0,γ)00 with α = 1/4 a* and γ = 1/2 c* is shown.

Finally the description in the P-centered monoclinic cell lacks the interpretation of the additional reflections with 1/4 a* (green circles) and exhibits systematically absent reflection violations (red squares) for the interpretation as a primitive lattice (Fig. 1, top). A closer look at the reconstructed diffraction patterns reveals two possibilities to index all observed reflections. One possibility is to use the depicted Bbmm cell shown in Fig. 1 (right) along with a q-vector q = (0, 0, 1/2 c*), the other one is to use the depicted monoclinic cell with q = (1/4 a*, 0, 1/2 c*). Both possible cell settings have been integrated including all satellite reflections. The structure was subsequently solved by the program package Superflip,³³ included in the Jana2006 package, which was used for the refinement.^34,35 The corresponding superspace groups Cmcm(α,0,0)0s0 (SSG 63.1.13.2) and P2₁/m(α,0,γ)00 (SSG 11.1.2.1) have been identified. The notation of Stokes, Campbell and van Smaalen for the superspace groups was used.^36,37 Since both refinements gave identical residuals, the higher symmetry was chosen and will be described in the following. The symmetry operations for the orthorhombic superspace group are listed in Table 2.

Table 2 Symmetry operations for the orthorhombic (3 + 1)D super space group Cmcm(α,0,0)0s0

x1	x2	x3	x4
−x1	−x2	x3 + 1/2	−x4
−x1	x2	−x3 + 1/2	−x4 + 1/2
x1	−x2	−x3	x4 + 1/2
−x1	−x2	−x3	−x4
x1	x2	−x3 + 1/2	x4
x1	−x2	x3 + 1/2	x4 + 1/2
−x1	x2	x3	−x4 + 1/2
x1 + 1/2	x2 + 1/2	x3	x4
−x1 + 1/2	−x2 + 1/2	x3 + 1/2	−x4
−x1 + 1/2	x2 + 1/2	−x3 + 1/2	−x4 + 1/2
x1 + 1/2	−x2 + 1/2	−x3	x4 + 1/2
−x1 + 1/2	−x2 + 1/2	−x3	−x4
x1 + 1/2	x2 + 1/2	−x3 + 1/2	x4
x1 + 1/2	−x2 + 1/2	x3 + 1/2	x4 + 1/2
−x1 + 1/2	x2 + 1/2	x3	−x4 + 1/2

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After refinement of the basic structure the satellites were added to the refinement and positional or occupational modulations for all atoms were applied. In addition, it was possible to refine modulated anisotropic atomic displacement parameters (ADP) for all atoms. The Fourier maps for all atoms showing significant modulations are depicted in Fig. 2. The space group allows for additional degrees of freedom, however some modulation components are very small (Table 3). While Ce1, Pt1, Pt2, Ge1 and Ge2 show positional modulations along x1/x4 and x3/x4, Ce2 and Ge3 exhibit occupational modulations along x3/x4. The occupational modulations were fitted using a crenel function; for the positional modulations simple harmonic functions were used. As a check for the correct composition, the occupancy parameters were refined in a separate series of least-squares cycles. All sites were fully occupied within three standard deviations. There was no indication of mixing on any site. The final difference electron-density synthesis was flat.

Fig. 2 Sections of the Fourier maps (based on F_obs) of the orthorhombic (3 + 1)D refinement with superspace group Cmcm(α,0,0)0s0 (α = 1/2 a*) of the commensurately modulated structure of Ce₃Pt₄Ge₆. Summation over 100 pm of the projected directions was conducted. Contour lines for all atoms correspond to a difference of 10 e Å⁻³, each.

Table 3 Atomic positions, Fourier coefficients of the modulation functions (sin) and equivalent isotropic displacement parameters (pm²) of Ce₃Pt₄Ge₆, superspace group Cmcm(α,0,0)0s0 with α = 1/2 a*. All atoms occupy Wyckoff positions 4c

Atom	Occ.	Wave	x	y	z	U eq
Ce1	1		0	0.34219(3)	1/4	96(2)
		sin	0.0174(3)	0	0
		cos	0	0.00002(5)	0
Ce2	0.5		1/2	0.47112(4)	1/4	94(3)
	x40 = 0.25	crenel	—	—	—
Pt1	1		1/2	0.06271(1)	1/4	77(1)
		sin	0.00094(17)	0	0
		cos	0	−0.00009(3)	0
Pt2	1		0	0.20433(1)	1/4	97(1)
		sin	−0.00671(19)	0	0
		cos	0	−0.00259(3)	0
Ge1	1		1/2	0.24984(5)	1/4	94(3)
		sin	0.0061(5)	0	0
		cos	0	−0.00197(9)	0
Ge2	0.5		0	0.11020(6)	1/4	146(4)
		sin	0.0003(5)	0	0
		cos	0	−0.00203(10)	0
Ge3	1		0.2039(3)	0.46437(6)	1/4	120(4)
	x40 = 0.6	crenel	—	—	—

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Due to the q-vector component α = 1/2 a*, the crystal structure can be refined as commensurate case in the corresponding orthorhombic superstructure with space group Pbnm and a doubled a axis. Standardization finally leads to space group Pnma and lattice parameters of a = 2618.26(14), b = 441.33(2) and c = 882.34(2) pm. This unit cell corresponds to the solution of the compounds in the RE₃Pt₄Ge₆ (RE = Pr–Dy) series,²⁵ however in our description all intensities were handled avoiding non-space group specific extinctions.

Crystal chemistry

The building blocks and motifs obtained by the refinement are the same compared to those presented in the previous descriptions in the orthorhombic space groups Cmcm,¹¹Pnma²⁵ and the monoclinic description of Y₃Pt₄Ge₆ in the space group P2₁/m.²⁴ However one previous work needed half-occupied sites for Ce and Ge atoms in order to describe the structure.¹¹ The other papers stated either the solution was achieved by “crystal chemical considerations”²⁴ or mentioned that the unit cell was chosen under “consideration of the very weak reflections causing a doubling of the a axis”.²⁵ These statements suggest that the diffraction patterns might have looked comparable to our investigations (vide supra), but were misinterpreted.

Using the motifs highlighted by Venturini et al. for Y₃Pt₄Ge₆, the structure can be described as an intergrowth between CaBe₂Ge₂- and YIrGe₂-type slabs. The latter forms pentagonal prisms built by Ir and Ge (here Pt and Ge), which are linked alternatively (up/down) to form layers that are connected further over the pentagonal faces to form a three-dimensional framework. The pentagonal prisms are occupied by the Y³⁺ cations, here Ce2. The CaBe₂Ge₂ arrangements consist of tetrahedral [GeBe_4/4] layers (here Pt and Ge), which are stacked along [100] and exhibit only Ge–Be bonds. The six-membered rings formed by the stacking of the layers are occupied by the Ca²⁺ cations, here Ce1. Due to the occupational modulation of the Ce2 and Ge3 atoms, the pentagonal prisms are allowed to order, facing either to the right or to the left along the a axis. In contrast to the description of Gribanov et al., no half occupied sites are needed in this description. The positional modulation can be easily understood since the orientation of the five membered rings influences the surrounding atoms of the remaining framework. The Pt1 atoms are the nearest neighbors of the five-membered rings, Ge2 is a part of the ring itself; therefore these atoms exhibit the strongest positional modulations along [100]. The remaining atoms follow the deformation of the framework, resulting in slightly lower amplitudes of the sin and cos functions (Table 3). In order to describe the crystal structure of Ce₃Pt₄Ge₆ a commensurate description can be used, which is obtained via a doubling of the a axis followed by a standardization. The detailed group–subgroup relations will be discussed in the following paragraph (vide infra). The resulting orthorhombic 3D-approximant (Pnma, a = 2618.26(14), b = 441.33(2) and c = 882.34(2) pm) describes the crystal structure without the need of half-occupied sites.

The crystallographic sites present in the modulated description split, resulting in three Ce, four Pt and six Ge sites. The structural elements described before are found as well in this model and are combined as shown in Fig. 3. In Fig. 4 the coordination polyhedra surrounding the Ce1/2 (left) and Ce3 (right) atoms are depicted. The refined anisotropic displacement parameters are listed in Table 4, interatomic distances in Table 5.

Fig. 3 Extended unit cell of the commensurate supercell structure (Pnma, a = 2618.26(14), b = 441.33(2) and c = 882.34(2) pm) of Ce₃Pt₄Ge₆. The YIrGe₂ and CaBe₂Ge₂ type parts are labelled. Ce atoms are depicted as blue, Pt atoms as black and Ge atoms as open white circles.

Fig. 4 Coordination environments surrounding the Ce1/2 (left) and Ce3 (right) atoms in the crystal structure of Ce₃Pt₄Ge₆. Ce atoms are depicted as blue, Pt atoms as black and Ge atoms as open white circles.

Table 4 Anisotropic displacement parameters (pm²) for Ce₃Pt₄Ge₆, superspace group Cmcm(α,0,0)0s0 with α = 1/2 a*. U₁₃ = U₂₃ = 0

Atom	U 11	U 22	U 33	U 12
Ce1	101(3)	93(3)	94(3)	0
Ce2	89(4)	98(4)	96(5)	0
Pt1	66(2)	93(2)	73(2)	0
Pt2	87(2)	109(2)	94(2)	0
Ge1	79(5)	122(6)	81(6)	0
Ge2	80(5)	96(6)	262(8)	0
Ge3	116(6)	147(6)	97(7)	−28(5)

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Table 5 Interatomic distances of the 3D supercell of Ce₃Pt₄Ge₆ (Pnma)

Ce1	2	Ge4	251.66(1)	Ce2	2	Pt3	249.77(1)	Ce3	2	Pt2	237.84(1)	Pt1	1	Ce3	239.61(1)	Pt2	2	Ce3	237.84(1)
	2	Pt4	254.45(1)		2	Ge3	255.40(1)		1	Pt1	239.61(1)		1	Ge3	251.14(1)		2	Ge6	248.77(1)
	1	Ge1	325.20(1)		1	Ge1	327.63(1)		2	Ge5	307.05(1)		1	Ge4	255.34(1)		1	Ge3	251.13(1)
	1	Ge2	327.05(1)		1	Ge2	329.60(1)		1	Ge5	311.04(1)		2	Ge5	265.86(1)		1	Ge4	255.33(1)
	1	Ge6	343.50(2)		1	Ge5	333.86(2)		2	Ge3	375.68(1)		1	Ge6	272.66(1)		1	Ge5	288.73(1)
	1	Pt3	365.87(2)		1	Pt4	356.18(2)		2	Ge4	379.92(1)		2	Pt2	395.62(2)		2	Ge5	387.29(1)
	2	Ge2	394.54(1)		2	Ge2	392.41(1)										2	Pt1	395.62(2)
	2	Ge1	396.19(1)		2	Ge1	393.96(1)										2	Ce2	395.99(1)
	2	Pt2	396.25(1)		2	Pt2	395.99(1)										2	Ce1	396.25(1)
Pt3	1	Ge3	245.44(1)	Pt4	1	Ge4	247.52(1)	Ge1	2	Ge2	220.70(1)	Ge2	2	Ge1	220.70(1)	Ge3	1	Pt3	245.44(1)
	2	Ce2	249.77(1)		1	Ge2	249.99(1)		1	Pt4	250.38(1)		1	Pt4	249.99(1)		1	Pt2	251.13(1)
	1	Ge2	251.38(1)		1	Ge1	250.38(1)		1	Pt3	251.43(1)		1	Pt3	251.38(1)		1	Pt1	251.14(1)
	1	Ge1	251.43(1)		2	Ce1	254.45(1)		1	Ce1	325.20(1)		1	Ce1	327.05(1)		2	Ce2	255.40(1)
	2	Pt4	325.42(1)		2	Pt3	325.42(1)		1	Ce2	327.63(1)		1	Ce2	329.60(1)		2	Ge5	305.67(1)
	2	Ge1	337.29(1)		2	Ge1	331.25(1)		2	Pt4	331.25(1)		2	Pt4	331.48(1)		2	Ce3	375.68(1)
	2	Ge2	337.35(1)		2	Ge2	331.48(1)		2	Pt3	337.29(1)		2	Pt3	337.35(1)		1	Ge5	388.62(2)
	1	Ce1	365.87(2)		1	Ce2	356.18(2)		2	Ce2	393.96(1)		2	Ce2	392.41(1)
									2	Ce1	396.19(1)		2	Ce1	394.54(1)
Ge4	1	Pt4	247.52(1)	Ge5	2	Pt1	265.86(1)	Ge6	2	Pt2	248.77(1)
	2	Ce1	251.66(1)		1	Pt2	288.73(1)		1	Pt1	272.66(1)
	1	Pt2	255.33(1)		2	Ge3	305.67(1)		2	Ge4	324.63(1)
	1	Pt1	255.34(1)		2	Ce3	307.05(1)		1	Ce1	343.50(2)
	2	Ge6	324.63(1)		1	Ce3	311.04(1)		2	Ge5	363.54(1)
	2	Ce3	379.92(1)		1	Ce2	333.86(2)		2	Ge6	389.56(1)
					2	Ge5	340.39(1)
					2	Ge6	363.54(1)
					2	Pt2	387.29(1)
					1	Ge3	388.62(2)

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The annealing temperature and the cooling rate are important parameters for the growth of high quality crystals. The structural details of Ce₃Pt₄Ge₆ are comparable to the recently reported stannide Ce₃Pt₄Sn₆.³⁸ The stannide crystals showed smeared out reflections and disorder.

Group–subgroup relations

As mentioned before, the crystal structure of Ce₃Pt₄Ge₆ can be derived from the published orthorhombic cell with space group Cmcm.¹¹ The title compound, however, clearly shows additional reflections which were interpreted as satellite reflections, pointing towards an also C-centered orthorhombic (3 + 1)D superspace group. The according superspace group associated to the 3D space group is shown on the top left in Fig. 5. Due to α = 0.5 of the q-vector, the structure can be described as commensurately modulated. Therefore a description as approximant by a projection onto 3D space can be used. The corresponding 3D space group for this description is Pbnm. This is achieved by a transition of index a4 where a is introduced synonymously for approximant.³⁹

Fig. 5 Relation of the (3 + 1)D and 3D space groups of the modulated structure of Ce₃Pt₄Ge₆. Group–supgroup scheme in the Bärnighausen formalism^40–43 for the subcell of Ce₃Pt₄Ge₆ (*occupancy parameter listed as 50% in the literature²⁴) and the supercell. The indices for the klassengleiche (k) symmetry reduction as well as the evolution of the atomic parameters are given. The index a is introduced for the formation of the approximant of the modulated structure.³⁹ The last line gives the atomic coordinates for Gd₃Pt₄Ge₆, published by Mewis in space group Pnma.²⁵

Here two transitions are involved, a doubling of the a axis along with a loss of the centering and an origin shift of (1/4, 1/4, 0). The a4 transition is paralleled by two k2 transitions in 3D space. First a symmetry reduction from Cmcm to Pbcm by a klassengleiche transition of index 2 takes place, which is accompanied by an origin shift of (1/4, 1/4, 0). In the second step again a klassengleiche transition of index 2 takes place, allowing the doubling of the a axis. The final step is used to reach the standard setting of Pbnm, the orthorhombic space group Pnma. The group–supgroup scheme in the Bärnighausen formalism^40–43 is shown in Fig. 5. The observed disorder and diffuse superstructure reflections of³⁸ have their origin most likely in the occurrence of anti phase boundaries triggered by the klassengleiche transitions.

Magnetic properties

The magnetic properties of Ce₃Pt₄Ge₆ were determined via susceptibility and magnetization experiments. Fig. 6 (top) shows the temperature dependence of the magnetic and inverse magnetic susceptibility (χ and χ⁻¹ data) measured at 10 kOe. A fit of the χ⁻¹ data in the region above 50 K using the Curie–Weiss law, revealed an effective magnetic moment of μ_eff = 2.48(1)μ_B/Ce atom and a Weiss constant of θ_p = −39(5) K. The effective magnetic moment matches well with the theoretical value of 2.54μ_B for a free Ce³⁺-ion indicating a stable trivalent ground state. The obvious negative value of the Weiss constant can be attributed to antiferromagnetic interactions in the paramagnetic regime, however crystal electric field splitting is a common feature in cerium intermetallics^44–46 and also responsible for the curvatures in the low temperature region.

Fig. 6 Magnetic properties of Ce₃Pt₄Ge₆: (top) Temperature dependence of the magnetic susceptibility χ and its reciprocal χ⁻¹ measured with a magnetic field strength of 10 kOe; (middle) magnetic susceptibility in zero-field (ZFC) and field-cooled (FC) mode at 100 Oe; (bottom) magnetization isotherms at 3, 10, and 50 K.

To obtain more information about the magnetic ground state, a low-field measurement was performed in a zero-field- and field-cooled mode (ZFC/FC) which is shown in the middle graph of Fig. 6. No anomaly indicating clear magnetic ordering could be detected in this measurement, however in the low temperature region saturation effects can be observed, while the derivative dχ/dT shows a double feature at 2.5(1) K and 3.0(1) K (Fig. 6, inset). No bifurcation between the ZFC and FC curve is visible.

The bottom graph in Fig. 6 displays the magnetization isotherms of Ce₃Pt₄Ge₆ measured at 3, 10, and 50 K. The isotherms at 10 and 50 K both display a linear field dependency of the magnetization as expected for a paramagnetic material. With respect to the 10 K isotherm less saturation effects are visible at 50 K. At 3 K a curvature of the magnetization isotherm can be observed with weak saturation effects towards higher fields. The magnetic moment at 3 K and 80 kOe is 0.61(5)μ_B/Ce atom which is significantly below the expected saturation magnetization of 2.14μ_B/Ce according to g_J × J. Magnetic susceptibility measurements reported in the literature¹ found no ordering phenomena and a reduced magnetic moment of μ_eff = 2.19μ_B between 40 and 140 K and a moment of μ_eff = 1.86μ_B above 150 K. Between 140 and 150 K an anomaly is observed which is in agreement with their resistivity measurements (vide supra). A magnetization isotherm at 5.5 K shows a small hysteresis. Both, the reduced moment and the anomaly between 140–150 K, are in contrast to our investigations. However the authors report their sample to be “predominantly single phase”, which might be an explanation for the missing features in our investigations.

Heat capacity

In order to check for magnetic phase transitions by a second method, heat capacity measurements were conducted in the temperature region between 1.9 and 300 K. Fig. 7 (top) depicts the full temperature scale, the inset displays the low temperature region between 1.9 and 15 K. Here a clear λ-shaped anomaly can be observed with a maximum at T = 2.1(1) K indicating a magnetic phase transition. This anomaly is in good agreement with the change of the slope of the ZFC/FC curve and its derivative.

Fig. 7 Physical properties of Ce₃Pt₄Ge₆: (top) Heat capacity measurement in the temperature range of 1.9–300 K, the inset shows the low temperature region between 1.9–15 K, indicating a λ-shaped anomaly; (bottom) temperature dependent electrical resistivity ρ.

Electrical resistivity

Fig. 7 (bottom) shows the electrical resistivity of Ce₃Pt₄Ge₆ between 2 K and 300 K. Down to about 75 K, the resistivity shows a nearly temperature independent behaviour. However a shallow minimum around 200 K is clearly visible. Below 75 K, the resistivity increases with a broad maximum centred at 50 K. When going to lower temperatures, a significant drop is observed. This behaviour is indicative of Kondo lattice systems. The upturn in the resistivity can be explained by the screening of the conduction electrons at the localized 4f¹ electron from the Ce³⁺ ions.

Conclusions

We have resynthesized Ce₃Pt₄Ge₆ and reinvestigated its crystal structure. A commensurate modulated structure has been found. The structure can be solved and refined in the orthorhombic superspace group Cmcm(α,0,0)0s0 with α = 1/2 a*. The superspace group correlates with the orthorhombic description of Pr₃Pt₄Ge₆ with space group Pnma, however the latter exhibits non space group specific extinction conditions. Magnetic investigations indicate that the cerium atoms are in the +3 oxidation state. Heat capacity measurements show a λ-anomaly at T = 2.1(1) K. Resistivity measurements confirmed the metallic nature, the temperature dependent behavior exhibits a broad maximum centered around 50 K followed by an abrupt drop below, suggesting Kondo behavior for the title compound.

Acknowledgements

This work was supported by the Deutsche Forschungs-gemeinschaft. O. N. is indebted to the NRW Forschungsschule Molecules and Materials – A common Design Principle for a PhD stipend.

Notes and references

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Footnote

† Dedicated to Professor Mercouri G. Kanatzidis on the occasion of his 60^th birthday.

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