Rare earth-ruthenium-magnesium intermetallics

1 Introduction

The ternary systems rare earth metal (RE)-electron-rich transition metal (T)-magnesium exhibit a large number of RE_xT_yMg_z intermetallic compounds with a manifold of different structure types [1]. So far more than 200 ternary compounds have been reported [2]. Several of these compounds have simple compositions and crystallize with structure types that also occur for indides or stannides: RET₄Mg, RETMg, RE₄TMg, RETMg₂, and RE₂T₂Mg. Typical pairs of compounds [2] for these different compositions are NdNi₄In and NdNi₄Mg, LaPdIn and LaPdMg, Gd₄RhIn and Gd₄RhMg, LaPdIn₂ and LaPdMg₂, and Ce₂Pd₂Sn and Ce₂Pd₂Mg. These pairs nicely underline two important points: (i) the covalent character and individualism of magnesium (it does not behave like a typical alkaline earth element [1], [3]) and (ii) the In/Mg or Sn/Mg substitution leads to a reduction of the valence electron concentration and thus a change of the magnetic ground state.

Recent work on these RE_xT_yMg_z intermetallic compounds focused on the understanding of the phase formation and establishing complete isothermal sections of ternary systems, e.g. La-Co-Mg [4], Y-Cu-Mg [5] or La-Ag-Mg [6]. From the synthesis point of view especially the magnesium-rich phases are difficult to prepare since magnesium has a much lower boiling temperature than the rare earth and transition metals. An interesting example for such phases is NdNiMg₅ [7], [8], [9] with a pronounced magnesium substructure or the hydrogen sorption material Gd₁₃Ni₉Mg₇₈ [10].

The largest diversity of structure types has been observed for the RE-Ru-Mg ternary systems. Striking examples are CeRu₂Mg₅ [11] and Ce₂Ru₄Mg₁₇ [12], [13] which exhibit strong covalent Ce^~IV–Ru bonding, a consequence of almost tetravalent cerium. This peculiar bonding situation occurs in several Ce_xRu_yX_z (X=Mg, Cd, Al, Ga, In, Sn) compounds [14], [15] with complex structures. Besides the rare earth-rich series RE₄RuMg [16] and RE₂₃Ru₇Mg₄ [17] and the hexagonal compounds RE₃RuMg₇ [18], [19], a whole family of compounds RE₂RuMg₂ (RE=Dy, Ho, Er, Tm, Lu) [20], RE₂RuMg₃ (RE=Dy, Ho, Er, Tm, Lu) [21], RE₃Ru₂Mg (RE=Sc, Er, Lu) [21] and RE₂RuMg (RE=Sc, Y, Er, Tm, Lu) [22] with fully ordered bcc superstructures has recently been reported. Structurally closely related bcc cubes also occur in the structure of Nd_4.67Ru₃Mg_8.83 [23].

During or ongoing phase analytical studies in several RE-Ru-Mg systems we obtained a series of new compounds and determined their crystal structures. Herein we report on the new members RE_8+x Ru₆Mg_19−x (RE=Sm, Gd, Tb) with Nd_9.34Ru₆Mg_16.66 type structure, Y₂RuMg₂ and Tb₂RuMg₂ with Er₂RuMg₂ structure, Tm₃Ru₂Mg with a coloring variant of the Er₂RuMg₃ type and Tm₃Ru₂Mg₂ and Lu₃Ru₂Mg₂ which crystallize as ternary ordered variants of the Ti₃Cu₄ type [24], [25], [26]. The common structural motifs of all these phases are ordered cubes that derive from the bcc arrangement.

2 Experimental

2.3 Structure refinements

Isotypism of Sm_9.25Ru₆Mg_17.75, Gd_11.04Ru₆Mg_15.96 and Tb_10.66Ru₆Mg_16.34 with Nd_9.34Ru₆Mg_17.66 [23] was already obvious from the Guinier powder patterns. The three data sets showed body centred tetragonal lattices with high Laue symmetry. Similar to the prototype, space group I4/mmm was found to be correct. The atomic positions of the neodymium compound were taken as starting values and the structures were refined with the Jana2006 package (full-matrix least-squares on F_o²) [31]. Since the prototype showed positions with mixed occupancy, we refined the occupancy parameters of all sites in separate series of least-squares cycles. All crystals revealed similar RE/Mg mixing and these occupancies were refined as least-squares variables in the final cycles, leading to the compositions listed in Tables 2 and 3.

Table 3:

Atomic coordinates and equivalent isotropic displacement parameters (pm²) of Sm_9.25Ru₆Mg_17.75, Gd_11.04Ru₆Mg_15.96, Tb_10.66Ru₆Mg_16.34 and Y₂RuMg₂.

Atom	Wyck.	x	y	z	Ueq
Sm9.25(2)Ru6Mg17.75(2)
Sm1	16m	0.19528(2)	x	0.10554(2)	138(1)
Ru1	8i	0.33082(7)	0	0	128(2)
Ru2	4e	0	0	0.18159(6)	159(2)
75.7(3)% Mg1+24.3(3)% Sm2	8j	0.2390(1)	1/2	0	159(4)
93.1(3)% Mg2+6.9(3)% Sm3	8g	0	1/2	0.1245(1)	164(7)
Mg3	16n	0	0.2473(2)	0.2636(1)	195(6)
Mg4	2a	0	0	0	111(10)
Mg5	4e	0	0	0.3759(3)	294(11)
Gd11.04(4)Ru6Mg15.96(4)
Gd1	16m	0.19161(4)	x	0.10679(3)	121(1)
Ru1	8i	0.3306(1)	0	0	109(3)
Ru2	4e	0	0	0.1809(1)	126(3)
54.1(5)% Gd2+45.9(5)% Mg1	8j	0.23623(1)	1/2	0	140(4)
78.2(5)% Mg2+21.8(5)% Gd3	8g	0	1/2	0.1255(1)	152(7)
Mg3	16n	0	0.2426(4)	0.2664(2)	164(10)
Mg4	2a	0	0	0	46(17)
Mg5	4e	0	0	0.3751(6)	320(20)
Tb10.66(2)Ru6Mg16.34(2)
Tb1	16m	0.19285(2)	x	0.1063(2)	126(1)
Ru1	8i	0.32922(5)	0	0	114(1)
Ru2	4e	0	0	0.17979(4)	137(1)
53.3(2)% Mg1+46.7(2)% Tb2	8j	0.23720(6)	1/2	0	140(2)
82.9(2)% Mg2+17.1(2)% Tb3	8g	0	1/2	0.12525(6)	143(3)
Mg3	16n	0	0.2447(2)	0.26509(9)	177(5)
89.4(5)% Mg4+10.6(5)% Tb4	2a	0	0	0	124(7)
Mg5	4e	0	0	0.3767(2)	298(9)
Y2 RuMg2
Y	4e	0	0	0.41859(6)	205(3)
Ru	2a	0	0	0	185(3)
Mg	4e	0	0	0.2011(2)	270(10)

The Y₂RuMg₂ crystal is tetragonal with a comparatively long c parameter. Similar to the whole family of magnesium intermetallics with bcc superstructures, also for Y₂RuMg₂ we observed lamellar crystal growth. Most crystals showed severe disorder in l direction. As an example we present the reconstructed hk0 and h0l layers of the investigated crystal in Fig. 1. Inspection of the data set revealed space group I4/mmm, in agreement with the prototype Er₂RuMg₂ [20]. The positions of Er₂RuMg₂ were taken as starting parameters and the structure was refined with anisotropic displacement parameters for all atoms. Refinement of the occupancy parameters gave no hint for deviation from the ideal composition. The final difference Fourier syntheses revealed no significant residual peaks. The refined atomic positions, displacement parameters, and interatomic distances are given in Tables 3–5 .

Fig. 1:

hk0 (left) and h0l (right) layers of the calculated reciprocal space of the investigated Y₂RuMg₂ single crystal.

Table 4:

Interatomic distances (pm) in the structure of Sm_9.25Ru₆Mg_17.75.

Sm1:	2	Ru1	291.7	Mg1:	2	Ru1	275.0
	1	Ru2	292.5		2	Mg2	315.3
	1	Mg4	320.2		2	Mg5	329.8
	2	Mg3	339.2		4	Sm1	344.7
	2	Mg2	341.6		2	Mg1	346.7
	2	Mg1	344.7	Mg2:	2	Ru1	272.6
	2	Sm1	366.8		2	Mg3	309.7
	2	Mg3	372.8		2	Mg1	315.3
	1	Sm1	375.4		4	Sm1	341.6
Ru1:	2	Mg2	272.6		2	Mg3	342.8
	2	Mg1	275.0	Mg3:	1	Ru2	274.3
	4	Sm1	291.7		1	Mg5	306.3
	1	Mg4	310.7		1	Mg2	309.7
	1	Ru1	317.8		2	Mg3	328.5
Ru2:	4	Mg3	274.3		2	Mg3	339.1
	4	Sm1	292.5		2	Sm1	339.2
	1	Mg4	322.9		1	Mg2	342.8
					2	Sm1	372.8
				Mg4:	4	Ru1	310.7
					8	Sm1	320.2
					2	Ru2	322.9
				Mg5:	4	Mg3	306.3
					4	Mg1	329.8

1. Please note the minor Mg/Sm mixing for sites Mg1 and Mg2 (Table 3). Standard deviations are equal or smaller than 0.5 pm.

Table 5:

Interatomic distances (pm) of Y₂RuMg₂ and Lu₃Ru₂Mg₂ (using the Ti₃Cu₄ positional parameters).

Y2RuMg2				Lu3Ru2Mg2
Y:	4	Ru	293.6	Lu1:	8	Ru	301
	1	Y	328.7		4	Lu1	336
	4	Mg	342.9		2	Lu2	358
	4	Y	344.0	Lu2:	4	Ru	293
Ru:	8	Y	293.6		4	Mg	301
	4	Ru	344.0		4	Lu2	336
Mg:	4	Mg	313.3		1	Lu1	358
	4	Y	342.9	Ru:	4	Lu2	293
	4	Mg	344.0		4	Lu1	301
					4	Ru	336
				Mg:	4	Lu2	301
					4	Mg	336
					4	Mg	337

1. All distances within the first coordination spheres are listed. Standard deviations are all equal or less than 0.5 pm for Y₂RuMg₂ and 5 pm for Lu₃Ru₂Mg₂.

Further details of the crystal structure investigations may be obtained from FIZ Karlsruhe, 76344 Eggenstein-Leopoldshafen, Germany (fax: +49-7247-808-666; e-mail: crysdata@fiz-karlsruhe.de) on quoting the deposition numbers CSD-432824 (Sm_9.25Ru₆Mg_17.75), CSD-432825 (Gd_11.04Ru₆Mg_15.96), CSD-432823 (Tb_10.66Ru₆Mg_16.34), and CSD-432822 (Y₂RuMg₂).

3 Crystal chemistry

Eight new RE_xRu_yMg_z compounds have been synthesized and their structures were studied on the basis of X-ray powder and single crystal diffraction. The first family of compounds concerns Sm_9.25Ru₆Mg_17.75, Gd_11.04Ru₆Mg_15.96 and Tb_10.66Ru₆Mg_16.34 which crystallize with the tetragonal Nd_9.34Ru₆Mg_17.66 type structure [23], space group I4/mmm. The prototype structure has already been described in detail in the original work. Herein we exemplarily discuss the striking structural features of Sm_9.25Ru₆Mg_17.75. Although the unit cell is quite large, we observe simple coordination patterns. A cutout of the structure emphasizing these coordinations is presented in Fig. 2.

Fig. 2:

Cutout of the Sm_9.25Ru₆Mg_17.75 structure with atom designations. Samarium, ruthenium and magnesium atoms are drawn as grey, blue and magenta spheres, respectively. The 8+(4+2) bcc-like coordination of the Mg4 atoms is emphasized. Mg5 has a distorted square prismatic coordination while the smaller ruthenium atoms have square antiprismatic coordination. Mixed sites are emphasized by segments.

The magnesium atoms Mg4 and Mg5 both have slightly distorted square prismatic coordination; Mg4 by samarium atoms and Mg5 by magnesium atoms. The coordination around Mg4 is similar to CsCl type SmMg [32]. Distorted bcc magnesium cubes occur in many ternary magnesium-rich rare earth compounds. An overview is given in reference [21] along with a detailed discussion of the Er₂RuMg₃ structure. The smaller ruthenium atoms have square antiprismatic coordination by samarium and magnesium atoms. The condensation pattern in the Sm_9.25Ru₆Mg_17.75 structure is simple (Fig. 2). The square prisms and antiprisms are condensed via the square or rectangular faces. Fig. 3 shows a complete unit cell of Sm_9.25Ru₆Mg_17.75. The three prism types condense along the unit cell edges. Due to the body-centred lattice one observes the same network shifted by ½ ½ ½. For a detailed discussion of interatomic distances we refer to the original work on the neodymium compound [23].

Fig. 3:

The crystal structure of Sm_9.25Ru₆Mg_17.75, emphasizing the condensation of square prisms and antiprisms. Samarium, ruthenium and magnesium atoms are drawn as grey, blue and magenta spheres, respectively. Mixed sites are emphasized by segments.

The four compounds all show RE/Mg mixing on two, respectively three sites and the structure refinements led to the compositions Sm_9.25Ru₆Mg_17.75, Gd_11.04Ru₆Mg_15.96 and Tb_10.66Ru₆Mg_16.34 for the investigated crystals. In general one can write the formula RE_8+x Ru₆Mg_19−x for the solid solution. The maximum x value was observed for the gadolinium compound.

The second family of compounds of the present investigation concerns simple bcc superstructures that derive from complete RE-Ru-Mg ordering and stacking of three, five, or seven distorted cubes in c direction. In contrast to the Nd_9.34Ru₆Mg_17.66 type compounds discussed above, ruthenium is always in a square prismatic rare earth coordination (CsCl derivative) in these bcc superstructures.

The smallest unit cell (shortest c parameter) has been observed for Tm₃Ru₂Mg which is isotypic with Sc₃Ru₂Mg [21]. The cell parameters of Tm₃Ru₂Mg nicely fit in between those of Er₃Ru₂Mg and Lu₃Ru₂Mg. A projection of the Tm₃Ru₂Mg unit cell is presented in Fig. 4. It consists of a simple stacking of almost regular TmRu cubes and significantly elongated square prisms TmMg. The RE₃Ru₂Mg phases are a coloring variant of the Er₂RuMg₃ type. Due to the different occupation of the Wyckoff sites and the concomitant changes in chemical bonding, these compounds are rather isopointal than isotypic.

Fig. 4:

Projection of the Tm₃Ru₂Mg, Ti₃Cu₄ and Lu₃Ru₂Mg₂ structures along the a axis. Thulium (lutetium, titanium), ruthenium (copper) and magnesium atoms are drawn as medium grey, blue and magenta circles, respectively. The crystallographically independent thulium, titanium, copper, and lutetium atoms are emphasized.

Y₂RuMg₂ and Tb₂RuMg₂ are isotypic with Er₂RuMg₂ [20]. The Y₂RuMg₂ structure has been refined from single crystal diffractometer data. It consists of a stacking sequence of five ordered bcc cubes. The Y₂RuMg₂ unit cell is presented in Fig. 4. The ruthenium atoms have square-prismatic yttrium coordination (294 pm Ru–Y). These YRu units condense in ab direction and the layers are separated by layers of condensed (edge-sharing) Mg₄ tetrahedra (313–344 pm Mg–Mg), a rare structural motif in intermetallic crystal chemistry. The tetrahedral magnesium layer corresponds to half a layer of bcc cubes. The series of RE₂RuMg₂ phases is a ternary ordered version of the Os₂Al₃ type [33], however, in view of the bonding differences, with a much larger c/a ratio of the tetragonal cells.

All members of this structural series (RE₂RuMg₂, RE₂RuMg₃, RE₃Ru₂Mg and RE₂RuMg) have a striking feature in the X-ray powder pattern. At low 2 θ angles one observes a front reflection which corresponds to 002 for the body-centred variants and 001 for the primitive ones. Our recent phase analytical studies revealed [20], [21], [22] that some samples showed up to five of these front reflections at the same time (i.e. those samples contained five different phases and were definitely not in equilibrium). Not all of these front reflections could be assigned to the known ordering variants. First we observe that the RE₃RuMg₇ phases [18], [19] with a totally different crystal structure also show such a front reflection. The d spacing of the remaining front reflection, first observed for a sample of the starting composition 3Tm : 2Ru : 2Mg, indicated a stacking of seven bcc subcells. Such a structure would contain 14 atoms in the tetragonal unit cell. A search for the Pearson symbol tI14 in the Pearson data base [2] revealed the Ti₃Cu₄ type [24], [25], [26] as the only member with such an atomic arrangement. The ternary ordered version of our sample would then be Tm₃Ru₂Mg₂. Indexing of the observed Guinier powder pattern fully confirmed this assumption. The experimental and simulated powder pattern of Lu₃Ru₂Mg₂ is presented in Fig. 5.

Fig. 5:

Experimental and calculated powder pattern (CuK_α1 radiation) of Lu₃Ru₂Mg₂. Asterisks mark additional reflections that result from a tiny (unknown) impurity phase.

In subsequent synthetic work we tried to grow single crystals of Tm₃Ru₂Mg₂ and in parallel also of the heavier congener Lu₃Ru₂Mg₂. Although we obtained almost pure powder patterns, the quality of the single crystals was poor. The stacking of seven bcc subcells always led to extremely lammelar crystal growth and severe disorder in c direction, more pronounced than observed for the Y₂RuMg₂ crystal (Fig. 1). The single crystal data clearly confirmed the ordered Ti₃Cu₄ type for Tm₃Ru₂Mg₂ and Lu₃Ru₂Mg₂, however, the refinements suffered from high residuals. Therefore, in Table 6 we only present the positional parameter assigment of Lu₃Ru₂Mg₂ based on the Ti₃Cu₄ type.

The unit cell of Lu₃Ru₂Mg₂ is presented in Fig. 6 along with the Y₂RuMg₂ structure. The two structures differ by an additional CsCl unit in Lu₃Ru₂Mg₂, leading to double layers which are separated by layers of condensed, edge-sharing Mg₄ tetrahedra. The range of Mg–Mg distances (336–337 pm) is similar to Y₂RuMg₂. The LuRu slab (301 pm Lu–Ru) is comparable to binary LuRu (288 pm Lu–Ru) with CsCl type structure [34].

Fig. 6:

The crystal structures of Y₂RuMg₂ and Lu₃Ru₂Mg₂ (refined lattice parameters of Lu₃Ru₂Mg₂ and positional parameters of Ti₃Cu₄). The layers of condensed Ru@Y₈ (Ru@Lu₈) cubes and Mg₄ tetrahedra are emphasized.

The structure of Lu₃Ru₂Mg₂ is related to the bcc tungsten type via a group-subgroup scheme which is presented in the Bärnighausen formalism [35], [36], [37] in Fig. 7. In the first step the space group symmetry is lowered via a translationengleiche transition of index 3 (t3) to I4/mmm which corresponds to the structure of protactinium (compressed bcc variant). The second step is an isomorphic transition of index 7 (i7) to I4/mmm, leading to the new structure type. Thus Lu₃Ru₂Mg₂ nicely fits into the larger family of bcc superstructures [38], [39].

Fig. 7:

Group-subgroup scheme in the Bärnighausen formalism [35–37] for the structures of bcc-W, Pa and Lu₃Ru₂Mg₂. The indices of the translationengleiche (t) and the isomomorphic (i) symmetry reductions, the unit cell transformations and the evolution of the atomic parameters are given. The experimental positional parameters were taken from the prototype Ti₃Cu₄.

The crystal chemical behavior of ruthenium in the large family of RE_xT_yMg_z intermetallic compounds is unique. Future studies will now focus on the osmium-based ternary systems in order to manifest whether geometric or electronic factors dominate formation of a certain structure type. The high melting point (and consequently the low reactivity) of osmium might be a hindrance.

4 Magnetic properties

The molar susceptibility χ of Y₂RuMg₂ and Lu₃Ru₂Mg₂ (only these two phases have been obtained in sufficiently pure form) in the temperature range of 3–300 K measured with an external field of 10 kOe is depicted in Fig. 8. The susceptibility of both compounds is almost independent of temperature down to 75 K. The increase in the susceptibility at low temperatures can be attributed to trace amounts of paramagnetic impurities. The magnetic behavior of both compounds is dominated by the Pauli contribution of the conduction electrons. The 300 K susceptibility values are χ_{(300 K)}=3.6(2)×10⁻⁴ emu mol⁻¹ for Y₂RuMg₂ and χ_{(300 K)}=2.6(2)×10⁻⁴ emu mol⁻¹ for Lu₃Ru₂Mg₂.

Fig. 8:

Temperature dependence of the magnetic susceptibility of Y₂RuMg₂ and Lu₃Ru₂Mg₂ from 3 to 300 K measured at a magnetic field strength of 10 kOe.