A switch from homogeneous mixed-valent to trivalent cerium in the solid solutions CeNi_1–x Pd _x Zn

1 Introduction

Among the intermetallic cerium compounds, the families with the general compositions CeT ₂ X ₂ and CeTX (T = electron-rich transition metal; X = element of the 3rd, 4th or 5th main group) have intensively been studied with many hundred representatives listed in the Pearson data base. ¹ Most of the CeT ₂ X ₂ phases ^{2 , 3 , 4 , 5 , 6} crystallize with the ThCr₂Si₂ or CaBe₂Ge₂-type structures, while the equiatomic CeTX phases ^{2 , 7 , 8 , 9} in majority adopt the hexagonal ZrNiAl or the orthorhombic TiNiSi type. All of these types are so-called basic structure types for rare earth intermetallics.

The main interest in these cerium intermetallics focuses on the cerium valence and its influence on the magnetic and transport properties (correlated electron systems). Cerium can adopt two pure, different valence states: diamagnetic Ce⁴⁺ with closed-shell [Xe] configuration and paramagnetic Ce³⁺ with [Xe]4f ¹ configuration. In addition, depending on the element combination (i.e., in many cases on the electronegativity differences) and on the structure type, static or dynamic intermediate cerium valence can occur. These different electronic configurations lead to a manifold of physical properties like Kondo compounds, antiferromagnetic and ferromagnetic ordering, valence fluctuation, heavy fermion compounds, superconductivity or non-Fermi liquid systems. Especially the representatives with valence instabilities have attracted broad attention. Remarkable examples are CeNi₂Si₂, ^{10 , 11 , 12} CeRhSn ¹³ and CeRuSn. ^{14 , 15}

The magnetic properties of the CeT ₂ X ₂ and CeTX phases can effectively be manipulated by substitution on the cerium as well as on the T and X sites. Therefore, diverse solid solutions have thoroughly been studied. Some remarkable examples are: (i) the solid solutions Ce_1–x La _x Pd₂Si₂ ¹⁶ and Ce_1–x La _x TiGe ¹⁷ for studying the cerium spin dilution (decrease of the Néel temperature with increasing lanthanum content), (ii) changes of the valence electron count (VEC) in CeRh_2−x Ru _x Si₂ (switch from antiferromagnetic CeRu₂Si₂ to heavy fermion behavior (γ ≈ 600 mJ mol⁻¹ K⁻²) for the x = 0.8 and 1.0 samples) ¹⁸ and CeRh_1–x Pd _x In (change from an unstable 4f configuration in CeRhIn to localized 4f moments in CePdIn) ¹⁹ and (iii) substitution of the X component in CeRu₂Si_2−x Ge _x (transition from spin fluctuations in CeRh₂Si₂ to ferromagnetism in CeRu₂Ge₂) ²⁰ and CeAuGe_1–x Sn _x (switch from ferro- to antiferromagnetic ordering). ²¹

In the course of systematic studies of solid solutions for the CeTX phases, ^{21 , 22 , 23 , 24 , 25 , 26} we turned to the CeTZn phases. Representatives are known with Ni, ^{27 , 28 , 29 , 30} Cu, ^{31 , 32} Rh, ³³ Pd, ^{27 , 34 , 35} Pt ^{36 , 37 , 38 , 39} and Au. ²⁸ Besides the structure refinements, the CeTZn phases were thoroughly investigated with respect to their magnetic and transport properties. α-CePdZn (T _N = 1.3 K), β-CePdZn (T _N = 2.7 K), ^{30 , 35} CePtZn (T _N = 1.7 K) and CeAuZn (T _N = 1.7 K) ^{37 , 38 , 39} order antiferromagnetically at very low temperatures. In contrast, CeNiZn ²⁸ shows intermediate cerium valence while cerium in CeRhZn ³³ is almost tetravalent. Hydrogenation induces a valence change in CeNiZn towards a stable trivalent state; however, there is no magnetic ordering down to 1.8 K. ²⁹

Herein we report on the solid solutions CeNi_1−x Pd _x Zn in order to study the change from homogeneous mixed-valent CeNiZn to paramagnetic a-CePdZn.

2 Experimental

2.2 X-ray diffraction

The basic sample characterization proceeded through X-ray powder diffraction. The samples were carefully ground to fine powders under a protective layer of dry (sodium wire) cyclohexane and then placed on a thin X-ray amorphous tape (Scotch^® Magic™ tape 810) that was fixed to a brass sample holder used for the Guinier camera: Enraf-Nonius FR552 camera, Fujifilm image plate system, BAS-1800 analyzer. The camera was equipped with a source of CuKα₁ radiation, and α-quartz (a = 491.30, c = 540.46 pm) was used as an internal standard. The hexagonal lattice parameters (Table 1) were obtained from least-squares refinements of the experimental 2θ values. Correct indexing of the patterns was ensured by comparison of the experimental patterns with calculated ones using the Lazy Pulverix routine. ⁴² The course of the cell volumes is presented in Figure 1. Within the solid solution we observe almost Vegard-type behavior between CeNiZn ^{27 , 28 , 29 , 30} and α-CePdZn. ^{27 , 34 , 35} The discontinuities are discussed in the crystal chemical chapter (vide infra).

Table 1:

Refined lattice parameters for the compounds of the solid solution CeNi_1−x Pd _x Zn based on Guinier powder data. Standard deviations are given in parentheses.

Compound	a/pm	c/pm	V/nm3	Reference
CeNiZn	713.3(3)	388.7(1)	0.1713	28
CeNiZna	714.17(7)	388.36(10)	0.1716	28
CeNiZn	713.6(1)	388.57(8)	0.1714	This work
CeNi0.95Pd0.05Zn	715.1(3)	389.9(2)	0.1727	This work
CeNi0.9Pd0.1Zn	717.3(3)	390.5(1)	0.1740	This work
CeNi0.85Pd0.15Zn	719.7(3)	392.6(2)	0.1761	This work
CeNi0.8Pd0.2Zn	721.3(3)	392.8(1)	0.1770	This work
CeNi0.75Pd0.25Zn	722.5(3)	393.3(1)	0.1778	This work
CeNi0.7Pd0.3Zn	724.7(3)	395.1(1)	0.1797	This work
CeNi0.65Pd0.35Zn	727.2(4)	396.4(1)	0.1815	This work
CeNi0.6Pd0.4Zn	727.8(1)	396.88(7)	0.1821	This work
CeNi0.59(1)Pd0.41Zna	727.61(8)	396.75(4)	0.1819	This work
CeNi0.5Pd0.5Zn	729.9(4)	397.7(2)	0.1835	This work
CeNi0.4Pd0.6Zn	733.2(2)	399.11(8)	0.1858	This work
CeNi0.3Pd0.7Zn	734.5(4)	399.8(1)	0.1868	This work
CeNi0.2Pd0.8Zn	736.5(2)	400.8(1)	0.1883	This work
CeNi0.1Pd0.9Zn	738.3(4)	400.8(2)	0.1892	This work
α-CePdZn	740.7(2)	402.1(1)	0.1911	This work
α-CePdZna	739.76(7)	401.71(10)	0.1904	35
α-CePdZn	740.4(1)	402.18(5)	0.1909	35

1. ^aSingle-crystal data.

Figure 1:

Course of the cell volume (Table 1) of the solid solutions CeNi_1–x Pd _x Zn. Single crystal data is marked by red dots. The straight lines serve as a guide to the eye.

Single crystals were selected under an optical microscope from a carefully crushed sample with the starting composition CeNi_0.7Pd_0.3Zn. The crystals were fastened to quartz fibers using beeswax. Their quality was tested by Laue photographs on a Buerger camera (white molybdenum radiation, image plate technique, Fujifilm, BAS-1800). A complete data set was collected at room temperature on a STOE IPDS-II diffractometer (graphite-monochromatized MoKα radiation; oscillation mode). A numerical absorption correction was applied. Details about the data collection and the structure refinement are listed in Table 2.

Table 2:

Crystal data and structure refinement parameters for CeNi_0.59(1)Pd_0.41Zn of the solid solution CeNi_1−x Pd _x Zn, ZrNiAl type, space group P 6 ‾ 2m, Z = 3.

Empirical formula	CeNi0.59(1)Pd0.41Zn
Formula weight/g mol−1	283.7
Lattice parameters (single-crystal data)
a/pm	727.61(8)
c/pm	396.75(4)
Cell volume/nm3	0.1819
Calculated density/g cm−3	7.77
Crystal size/µm3	20 × 30 × 70
Transmission (min; max)	0.312; 0.618
Absorption coefficient/mm−1	35.4
Detector distance/mm	70
Exposure time/min	15
ω range; increment/deg	0–180; 1
Integration param. (A; B; EMS)	14.0; −1.0; 0.030
F(000)/e	370
θ range/deg	3.23–33.31
Range in hkl	±11; ±10; ±6
Total no. reflections	2,201
Independent reflections; R int	297; 0.0333
Reflections with I ≥ 3σ(I); R σ	285; 0.0116
Data; parameters	297; 17
Goodness-of-fit on F 2	1.07
R1; wR2 for I ≥ 3σ(I)	0.0141; 0.0292
R1; wR2 for all data	0.0162; 0.0301
Flack parameter	−0.01(5)
Extinction coefficient	159(12)
Largest diff. peak; hole/e Å−3	+0.66; −0.66

3 Crystal chemistry

The ternary intermetallic zinc compounds CeNiZn ^{27 , 28 , 29 , 30} and α-CePdZn ^{27 , 34 , 35} crystallize with the ZrNiAl-type structure, ^{52 , 53 , 54} space group P6‾2m. They form a continuous set of solid solutions CeNi_1−x Pd _x Zn. Although both phases crystallize with the same structure type, they have a different magnetic ground state. The cerium atoms in CeNiZn are in a homogeneous mixed-valent state, ^{28 , 29} while α-CePdZn ^{27 , 34 , 35} shows a stable [Xe]4f ¹ state, i.e., trivalent cerium. The cell volumes of the two boarder phases are thus governed by (i) the cerium valence (smaller intermediate-valent vs larger trivalent cerium) and (ii) the covalent radii ⁵⁵ of 115 pm for nickel and 128 pm for palladium.

The course of the unit cell parameters within the solid solutions CeNi_1−x Pd _x Zn is evident from Table 1. We observe an almost continuous increase of the a (3.8 %) and c (3.5 %) lattice parameter from CeNiZn to α-CePdZn. The x dependence of the cell volume is shown in Figure 1. From α-CePdZn to CeNi_0.65Pd_0.35Zn we observe an almost linear decrease of the cell volume. The decrease is also linear from CeNi_0.75Pd_0.25Zn to CeNiZn, however, with a larger slope. These different ranges are directly related to the physical properties (vide infra), i.e., the trivalent regime from α-CePdZn to CeNi_0.65Pd_0.35Zn and the intermediate-valent one from CeNi_0.75Pd_0.25Zn to CeNiZn. Comparable cell volume dependencies have been observed for the isotypic solid solutions CeNi_1–x Pd _x In ⁵⁶ and CeRh_1–x Pd _x In. ¹⁹

A projection of the CeNi_0.59(1)Pd_0.41Zn structure is shown in Figure 2. The basic building units are two types of trigonal prisms that are filled by the transition metal (T) atoms. Both T sites show nickel/palladium mixing with a slightly higher nickel content on Wyckoff position 1a. The T1 site (1a, Ni_0.66(2)Pd_0.34) has trigonal-prismatic zinc coordination and the rectangular faces of the prisms are capped by three cerium atoms, leading to coordination number 9. Also, the T2 site (2d, Ni_0.56(1)Pd_0.44) is trigonal-prismatically coordinated. Here, the prism is built by cerium atoms and capped by zinc atoms. The projection shows the connectivity pattern of the two prismatic types. The T2@Ce₆ prisms are condensed via common edges, forming six-membered rings. These rings are condensed via the triangular faces in c direction, forming tubes that extend in c direction. These tubes are filled by strands of face-sharing T1@Zn₆ prisms. The two prism types are shifted with respect to each other by half the translation period c, thus enabling the capping of the rectangular prism sites.

Figure 2:

The crystal structure of CeNi_0.59(1)Pd_0.41Zn. Cerium and zinc atoms are drawn as medium grey and magenta circles; the mixed occupied sites are drawn as segments in blue (nickel) and green (palladium). (a) Projection along the c axis with emphasis on the trigonal-prismatic building units. The two prism types are shifted by c/2 with respect to each other as is emphasized by thin and thick lines. (b) and (c) Coordination of the two crystallographically independent Ni/Pd mixed sites. Relevant interatomic distances (/ pm) and the site symmetries are indicated.

Table 4 lists the interatomic distances in CeNiZn, CeNi_0.59(1)Pd_0.41Zn and a-CePdZn. Similar to the continuous increase of the unit cell volume (Table 1) within the solid solutions, the interatomic distances follow the same trend. For further crystal chemical details on ZrNiAl-type CeTX phases we refer to our previous review article. ⁷

We now turn to the cerium substructures of CeNiZn, CeNi_0.59(1)Pd_0.41Zn and α-CePdZn. Within the ab plane, each cerium atom has four shorter Ce–Ce distances to the neighboring triangles and two slightly longer ones along the c axis. All these Ce–Ce distances are distinctly longer than the Hill limit ^{57 , 58} of ca. 340 pm, which discriminates between superconducting and magnetically ordered (f electron localization) intermetallic cerium compounds. In his original work, ⁵⁷ Hill relied this limit only on 19 compounds and this was extended in the work of Koelling ⁵⁹ to 33 compounds. In a recent work, Miyahara et al. ⁵⁸ studied more than 700 intermetallic cerium compounds with respect to their Ce–Ce distances and magnetic ordering temperatures. It turned out that the shortest average Ce–Ce distance amounts to approximately 416.1 pm. Intermediate-valent cerium compounds occur in the entire range from 300 to 450 pm; however, as expected, with an accumulation towards the shorter distances, where increased hybridization between the 4f cerium electrons and the Ni/Pd d electrons is observed. Thus, the Ce–Ce distances alone are not the decisive criterion for formation of an intermediate-valent cerium intermetallic compound. The members of the present solid solutions fit approximately in the middle of the Miyahara plot.

4 Magnetic properties

Magnetic susceptibility measurements were performed on all samples. The motivation of this investigation was to study the valence transition from intermediate-valent CeNiZn to trivalent α-CePdZn as a function of the nickel content within the solid solutions CeNi_1−x Pd _x Zn. A common feature of the results of all susceptibility measurements was the absence of long-range magnetic order down to 2 K.

In the following we discuss the course of the susceptibility behavior with increasing nickel content. For α-CePdZn and small amounts of nickel within the CeNi_1−x Pd _x Zn samples, a nearly linear increase of χ ⁻¹ with increasing temperature can be observed (Figure 3, bottom). A higher nickel content raises the absolute values of χ ⁻¹ and causes a higher deviation of the linear progression at low temperatures. Up to the sample composition CeNi_0.65Pd_0.35Zn, the linear part of the inverse susceptibilities could be fitted with a modified Curie-Weiss law (Figure 3, bottom). The resulting fitting parameters are listed in Table 5. The susceptibility behavior of the new α-CePdZn sample is similar to the literature data. ³⁵ The addition of nickel to the solid solution CeNi_1−x Pd _x Zn up to the composition CeNi_0.65Pd_0.35Zn does not alter the cerium valence, since the effective magnetic moment stays almost constant in these samples. The experimental magnetic moments are close to the free ion value of 2.54 µ_B for Ce³⁺. ⁶⁰ In the same range we observe a decrease of the paramagnetic Curie temperature (Table 5).

Figure 3:

Inverse magnetic susceptibility of several samples of the solid solution CeNi_1–x Pd _x Zn in the temperature range of 2–300 K. The white lines in the upper plot show the fit using the ICF model. The circles are shown in larger sizes in order to guide the eye. The bottom plot shows the samples with trivalent cerium. CeNi_0.75Pd_0.25Zn and CeNi_0.7Pd_0.3Zn are shown in both plots because they represent the breaking point between ICF and Curie-Weiss behavior.

The samples of compositions CeNi_0.75Pd_0.25Zn and CeNi_0.7Pd_0.3Zn do not give reasonable results that follow the Curie-Weiss law. They are in the intermediate range of composition, where the cerium atoms switch from trivalent to homogeneous mixed-valent, and probably exhibit a more complex magnetic domain structure.

With a further increase of the nickel content, we observe a drastic variation in χ ⁻¹ (Figure 3, top). The deviation at low temperature becomes larger and the slope at higher temperatures becomes smaller, reaching a plateau. For CeNiZn, χ ⁻¹ even slightly decreases again, comparable to the results of original work. ²⁸ This behavior does not follow the Curie-Weiss law, since the temperature-induced valence change from trivalent to intermediate-valent cerium must also be considered. This is done using the ICF (inter-configuration fluctuation) model developed by Sales and Wohlleben. ⁶¹ The underlying formulæ are documented in the original work and have also been applied for the intermediate-valent cerium-based solid solutions CeRh_1−x Ru _x Sn, ²³ CeRu_1−x Ni _x Al, ⁶² CeRu_1−x Ni _x Sn ²⁵ and CeRh_1−x Pd _x Sn. ²⁶ For further details we refer to these publications.

The susceptibility data of the CeNi_0.8Pd_0.2Zn, CeNi_0.85Pd_0.15Zn and CeNiZn samples were fitted with the Sales-Wohlleben model. The fitted functions are shown as white lines in the plot of the temperature dependence of the reciprocal magnetic susceptibility in the upper part of Figure 3 (top) and the fitting parameters are summarized in Table 6. The amount of stable trivalent cerium in CeNiZn had to be fixed in the fitting procedure in order to prevent too large correlations. The CeNi_0.9Pd_0.1Zn and CeNi_0.95Pd_0.05Zn samples slightly deviated from the expected course of χ ⁻¹, probably due to clustering of different magnetic domains. From the Sales-Wohlleben fits, the temperature-dependent Ce valency could be calculated (Figure 4). With decreasing nickel content, the cerium valence tends towards the trivalent state.

Figure 4:

Temperature-dependent valency of cerium in the compounds CeNiZn (black), CeNi_0.85Pd_0.15Zn (violet) and CeNi_0.8Pd_0.2Zn (green).

Finally, we point to the magnetization behavior of the CeNi_1−x Pd _x Zn samples. The 2 K magnetization isotherms are summarized in Figure 5. The value of the saturation magnetization (the numerical values are listed in Table 5) decreases with increasing nickel content as expected for the change from a paramagnetic trivalent to a homogeneous mixed-valence system. The obtained saturation magnetizations are all distinctly lower than the theoretical value of 2.14 µ_B per Ce atom according to g × J. ⁶⁰

Figure 5:

2 K magnetization isotherms of samples of the solid solutions CeNi_1–x Pd _x Zn between 0 and 90 kOe. The color codes of the different samples are the same as in Figure 3.

Summing up, all samples of the solid solutions CeNi_1−x Pd _x Zn crystallize with the hexagonal ZrNiAl-type structure with one crystallographic cerium site. The magnetic susceptibility data show a change from a 4f ¹ configuration for Curie-Weiss-paramagnetic α-CePdZn to a homogeneous mixed valence ^{63 , 64 , 65} in CeNiZn. Thus, the cerium atoms in the homogeneous mixed-valence regime transfer higher electron density to the [Ni_1−x Pd _x ] ^δ− substructure.