The Isothermal Section of the Phase Diagram of Dy-Sm-Ge Ternary System at 873 K

Abstract

The interaction of components in the Dy-Sm-Ge system at 873 K was investigated by means of x-ray phase and structural analyses, microstructural analysis and energy dispersive x-ray spectroscopy. The existence of the continuous solid solutions between the isostructural binary germanides of the Dy_1−xSm_xGe (CrB-type), Dy_5-xSm_xGe₄ (Sm₅Ge₄-type) and Dy_5-xSm_xGe₃ (Mn₅Si₃-type) were established. The limited solid solutions based on the binary germanides of the SmGe₂ (α-ThSi₂-type), DyGe₂ (TbGe₂-type) and Dy₁₁Ge₁₀ (Ho₁₁Ge₁₀-type) are formed. The solubility of Dy in SmGe₂ is 15 at.%, Sm in DyGe₂ and Dy₁₁Ge₁₀ − 10 at.%, Sm. Two ternary Sm_xDy_1−xGe_1.5 (x = 0.15-0.50) and Sm₂Dy₂Ge₇ compounds were found. Sm_xDy_1−xGe_1.5 crystallizes in AlB₂ structure type. The crystal structure of the new ternary compound of the Sm₂Dy₂Ge₇ (ordered superstructure to Nd₄Ge₇-type, Pearson symbol oS44, space group C222₁, a = 0.5942(1), b = 1.3823(4), c = 1.1801(3) nm, V = 0.9694 nm³) was investigated by means of x-ray single crystal diffraction. The germanium atoms form 3D anionic network the existence of which was confirmed by electronic structure calculations.

1 Introduction

Rare-earth intermetallics have been extensively studied in different fields and applications, including magnetic materials, thermoelectric, hydrogen storage materials and other.[1,2] The development of new materials on the base of rare-earth metals alloys requires systematic investigation of interactions between the components in binary, ternary and multicomponent systems, construction of their phase diagrams, and determination of crystal structure of the obtained phases.

In literature there are experimental data on ternary R-R’-Ge systems, where R and R’—rare earth metals cerium or yttrium subgroups. The most detailed were studied the sections between digermanides RGe₂-R’Ge₂.[3] On these sections the solid solutions as well as individual ternary phases are formed. The continuous solid solution for DyGe₂-TbGe₂ section was observed. In the DyGe₂-RGe₂ (were R = Er, Ho, Tm and Lu) sections forms the limited solid solutions. In the ternary systems with dysprosium the intermetallic compounds Dy_0.67Tm_0.33Ge_1.85,[4] Dy_0.5Ho_0.5Ge_1.75[5] and Dy_0.6Lu_0.4Ge₂[6] were observed. In the systems with samarium only one ternary compound of Sm_0.625Lu_0.375Ge_1.85[7] was studied.

In this contribution we report experimental results of the investigation of isothermal section at 873 K of phase diagram of the Dy-Sm-Ge ternary system in full concentration range.

2 Literature Data on Boundary Binary Diagrams

2.1 Sm-Ge System

The Sm-Ge phase diagram (Fig. 1a) was critically assessed by Gokhale and Abbaschian[8] based on experimental data of Eremenko et al.[9] Five binary compounds Sm₅Ge₃, Sm₅Ge₄, SmGe, SmGe_1.5, SmGe₂ forms in the Sm-Ge binary system. Sm₅Ge₃ phase melts congruently at 1973 K. The Sm₅Ge₄, SmGe and Sm₂Ge₃ (SmGe_1.5) forms peritectically.

Fig. 1

Phase diagram of Sm-Ge (taken from Ref 8), Dy-Ge[17] and Dy-Sm[30] binary systems

SmGe_1.5 (or Sm₂Ge₃) compound exists in three polymorphic modifications. The polymorphic transition α-SmGe_1.5 ↔ β-SmGe_1.5 occurs at 1018 K, and the β-SmGe_1.5 ↔ γ-SmGe_1.5 polymorphic transition is at 1358 К. The orthorhombic and hexagonal Sm₃Ge₅[10,11] phases are the α-SmGe_1.5 and β-SmGe_1.5 polymorphic modifications respectively.

The SmGe₂[12] compound according to the structural data has a composition of SmGe_1.63[9] and forms by peritectoid reaction.

The described earlier Sm₄Ge₇[13,14] and SmGe₅[15] compounds which are not observed on phase diagram, probably, are metastable phases. Crystals of Sm₄Ge₇ was prepared by Zhang et al.[14] using the flux method, flux In (99.99 wt.%), heated to 1373 K at a rate of 300 K h⁻¹, heated at 1373 K for 1.5-3 h, cooled to 673 K over 20 h and structurally investigated by both x-ray and electron diffraction. This structure belongs to superstructure of RGe_2−x with the α-ThSi₂ or α-GdSi₂ types at x = 1/4. The orthorhombic structure is realized through the long-range order of vacant Ge positions. The high-pressure phase SmGe₅[15] synthesized by heating of pure elements at 1123 K and 10 GPa. New germanide Sm₂Ge₉ was received by thermal decomposition of high-pressure phase SmGe₅[16]

Crystallographic characteristics of all known Sm-Ge binary compounds are presented in Table 1.

Table 1 Literature data for binary phases of the Sm-Ge system

2.2 Dy-Ge System

The Dy-Ge phase diagram (Fig. 1b) is redrawn from Eremenko et al.[17] Seven binary compounds: Dy₅Ge₃, Dy₅Ge₄, DyGe, DyGe_1.59 (Dy₂Ge₃), Dy₃Ge₅, DyGe_1.85 and DyGe₃ forms in this system.[18,19,20,21,22,23,24,25,26] The DyGe₃, DyGe_1.85, DyGe_1.59, DyGe and Dy₅Ge₄ phases are formed by peritectic reactions.

The polymorphic transitions α-DyGe_1.59 ↔ β-DyGe_1.61 and β-DyGe_1.61 ↔ γ-DyGe_1.5 at 1160 К and 1573 К are observed respectively. The reaction of formation of the Dy₃Ge₅ is peritectoid.

The Dy₅Ge₃ germanide melts congruently at 2100 К and has a has an insignificant ~2 at.% homogeneity region.

During the investigation of polymorphism in the binary rare-earth metal germanides the new hexagonal phase of Dy₃Ge₅ was observed at 120 K by Tobash et al.[27]

The DyGe_1.90, Dy₃Ge₄ (T = 20 K)[28] and Dy₁₁Ge₁₀[21] compounds for which crystal structures were studied, but are not displayed on the diagram.

New cubic phase DyGe_2.85 crystallized in the cubic AuCu₃ structure type was synthesized at a pressure of 8 GPa and described by Tsvyashchenko et al.[29]

Crystallographic characteristics of known Dy-Ge binary compounds are presented in Table 2.

Table 2 Literature data for binary phases of the Dy-Ge system

2.3 Dy-Sm System

The Dy-Sm phase diagram (Fig. 1b) is redrawn from Okamoto.[30] Dysprosium exists in two allotropic modifications: α-Dy (Mg-type) and β-Dy (W-type). The transformation α-Dy ↔ β-Dy occurs at 1654 K. Samarium exists in three allotropic modifications: α-Sm (Sm-type), β-Sm (Mg-type) and γ-Sm (W-type). The transformation of α-Sm to β-Sm occurs at 1007 K and the following transformation of β-Sm ↔ γ-Sm is at 1195 K.

Based on the high-temperature modifications β-Dy and γ-Sm and low-temperature modifications α-Dy and β-Sm forms continuous series of solid solutions (β-Dy/γ-Sm and α-Dy/β-Sm). Based on low-temperature modifications of α-Sm limited solid solution is formed, and the homogeneity region of which extends from 15 to 25 at.% Dy at room temperature.

3 Experimental Details

Samarium, dysprosium and germanium, all with a nominal purity greater than 99.9 wt.%, were used as starting materials. The 64 samples a total mass of each about 2 g were prepared by arc melting of pure metals in a high-purity argon atmosphere. The mass losses after the melting were less than 1 wt.%. After the melting the samples were sealed in evacuated quartz ampoules and annealed at 873 K during 720 h. After annealing the ampoules with the samples were quenched in cold water.

Phase analysis of the samples was carried out with the use of powder x-ray diffraction (XRD) (DRON-4.0M and STOE STADI P diffractometers with Fe- and Cu-Kα radiation, respectively). The obtained powder diffraction data were analyzed by Rietveld method using Fullprof software.[31] Wavelength Dispersive Spectrometry (WDS) and CAMECA SX-100 Electron Probe Micro Analyser (EPMA) and REMMA-102-02 scanning microscope were used to measure the number of phases and their qualitative and quantitative chemical compositions some alloys.

Single crystal diffraction data were collected by Xcalibur™3 CCD diffractometer with graphite-monochromated Mo-Kα radiation. Scans were taken in the ω mode, the analytical absorption corrections were made by CrysalisRed[32] The crystal structure was solved by direct methods and refined using the SHELX-97 program package.[33,34]

The electronic structures of the ternary compound was calculated using the tight-binding linear muffin-tin orbital (TB-LMTO) method in the atomic spheres approximation (TB-LMTO-ASA[35,36,37]) using the experimental crystallographic data reported here. The exchange and correlation were interpreted in the local density approximation.[38] All the figures and graphics concerning electron structure calculations were generated using wxDragon.[39]

4 Results and Discussion

4.1 Isothermal Section at 873 K of the Dy-Sm-Ge System

The isothermal section of the Dy-Sm-Ge system at 873 K was constructed by XRD and SEM-EPMA methods based on the phase analysis of 13 binary and 51 ternary alloys (Fig. 2a, b). This isothermal section in the full concentration region consists of 11 three-phase, 23 two-phase and 13 single-phase regions. From Fig. 3(a)-(h), it can be seen that in the germanium-rich region at 870 K the stable phases are the Dy₂Sm₂Ge₇ ternary compound, solid solutions phases based on SmGe₂, DyGe_1.9 and DyGe₃ binary compounds. Formation of other binary phases known from the literature (metastable) or solid solutions based on these phases are not observed. The binary SmGe_2-x phase with α-ThSi₂ structure type has homogeneity region from SmGe₂ to SmGe_1.67, although in the literature[9,12] for these compositions were indicated different structural types (α-ThSi₂ and AlB₂ respectively). From the SmGe_1.6 to SmGe_1.5 (α-SmGe_1.5) realized hexagonal Sm₃Ge₅ structure type.

Fig. 2

Gross compositions of the analyzed Dy-Sm-Ge alloys (a) and isothermal section at 873 K (b)

Fig. 3

Micrographs of selected samples from the Ge-rich region of Dy-Sm-Ge system: (a) Dy₂₀Sm₅Ge₇₅ (light grey phase—Dy_1−xSm_xGe_1.9, composition from EPMA Dy_24.6(4)Sm_9.2(4)Ge_66.2(5); grey phase—Dy_xSm_1−xGe₃, Dy_20.1(3)Sm_4.8(3)Ge_75.1(4); dark phase—Ge); (b) Dy₁₀Sm₁₀Ge₈₀ (grey phase—Dy₂Sm₂Ge₇, Dy_17.5(2)Sm_18.1(2)Ge_64.4(3); dark phase—Ge); (c) Dy₁₈Sm₁₀Ge₇₂ (light grey phase—Dy_1−xSm_xGe_1.9, Dy_23.1(3)Sm_10.6(3)Ge_66.3(4); grey phase—Dy₂Sm₂Ge₇, Dy_17.7(2)Sm_18.1(2)Ge_64.2(3); dark phase—Ge); (d) Dy₁₀Sm₁₈Ge₇₂ (light grey phase—Dy_xSm_1−xGe₂, Dy_10.1(3)Sm_23.6(3)Ge_66.3(4) grey phase—Dy₂Sm₂Ge₇, Dy_17.6(3)Sm_18.2(3)Ge_64.2(4); dark phase—Ge); (e) Dy₂₄Sm₁₀Ge₆₆ (grey phase—Dy_1−xSm_xGe_1.9, Dy_23.7(3)Sm_10.1(3)Ge_66.2(4); single dark spots—Ge); (f) Dy₁₇Sm₁₇Ge₆₆ (grey phase—Dy₂Sm₂Ge₇, Dy_17.7(2)Sm_18.2(2)Ge_64.1(3); single dark spots—Ge); (g) Dy₁₀Sm₂₄Ge₆₆ (grey phase—Sm_1−xDy_xGe₂, Dy_10.7(2)Sm_22.9(3)Ge_66.4(4); single dark spots—Ge)

The following three-phase regions were detected:

Dy_1−xSm_xGe_1.9+ Dy_1−xSm_xGe₃+Ge, Dy_1−xSm_xGe_1.9+ Dy₂Sm₂Ge₇+Ge,

Dy_1−xSm_xGe₂+ Dy₂Sm₂Ge₇+Ge, Dy_1−xSm_xGe_1.9+ Dy₂Sm₂Ge₇+Sm_xDy_1−xGe_1.5,

Dy_xSm_1−xGe₂+ Dy₂Sm₂Ge₇+Dy_1−xSm_xGe_1.5, Sm_1−xDy_xGe₂+Dy_1−xSm_xGe+Dy_1−xSm_xGe_1.5,

Dy_5-xSm_xGe₄+Dy_1−xSm_xGe+Dy_11−xSm_xGe₁₀, Dy_1−xSm_xGe_1.9+Dy_1−xSm_xGe_1.5+Dy₃Ge₅,

Dy_1−xSm_xGe_1.5+DyGe_1.59+Dy₃Ge₅, Sm_xDy_1−xGe_1.5+DyGe_1.59+ Dy_1−xSm_xGe,

Dy_xSm_1−xGe₂+SmGe_1.5+Dy_1−xSm_xGe. The micrographs of selected three-phase samples are shown Fig. 4(a-f).

Fig. 4

Micrographs of selected three-phase samples from Dy-Sm-Ge system: (a) Dy₂₁Sm₁₇Ge₆₂ (light grey phase—Dy_1−xSm_xGe_1.5, composition from EPMA Dy_22.6(4)Sm_17.2(4)Ge_60.2(4); grey phase—Dy_1−xSm_xGe_1.9, Dy_24.6(4)Sm_9.2(4)Ge_66.2(5); dark grey phase—Dy₂Sm₂Ge₇, Dy_17.4(2)Sm_18.1(2)Ge_64.5(4); Ge); (b) Dy₁₇Sm₂₁Ge₆₂ (light grey phase—Dy_1−xSm_xGe_1.5, Dy_23.1(4)Sm_16.8(4)Ge_60.1(4); grey phase—Dy₂Sm₂Ge₇, Dy_17.4(2)Sm_18.4(2)Ge_64.2(4); Ge); dark grey phase—Dy_xSm_1−xGe₂, Dy_11.6(4)Sm_22.1(4)Ge_66.3(5); (c) Dy₂₀Sm₂₆Ge₅₄ (light grey phase—Dy_1−xSm_xGe, Dy_13.0(3)Sm_43.6(3)Ge_33.4(5); grey phase—Dy_1−xSm_xGe_1.5, Dy_20.2(4)Sm_19.6(4)Ge_60.2(4); dark grey phase—Dy_xSm_1−xGe₂, Dy_11.1(4)Sm_22.6(4)Ge_66.3(5); (d) Dy₅Sm₅₅Ge₄₀ (dark grey phase—Dy_xSm_1−xGe₂, Dy_11.1(4)Sm_22.6(4)Ge_66.3(5); grey phase—SmGe_1.5, Sm_39.6(3)Ge_60.4(4) bright phase—Dy_1−xSm_xGe, Dy_8.1(3)Sm_58.5(3)Ge_33.4(5); (e) Dy₃₃Sm₅Ge₆₂ (light grey phase—DyGe_1.59, Dy_38.7(3)Ge_61.3(4); grey phase—Dy_1−xSm_xGe_1.5, Dy_31.1(4)Sm_8.8(4)Ge_60.1(4); dark grey phase—Dy₃Ge₅, Dy_37.6(3)Ge_62.4(5); (f) Dy₃₂Sm₂₀Ge₄₈ (light grey phase—Dy_5-xSm_xGe₄, Dy_33.2(2)Sm_22.3(2)Ge_44.5(3); grey phase—Dy_11−xSm_xGe₁₀, Dy_43.1(4)Sm_9.4(4)Ge_47.5(5); dark grey phase—Dy_1−xSm_xGe, Dy_17.0(3)Sm_49.6(3)Ge_33.4(5))

The single-phase regions consist new ternary compounds of Dy₂Sm₂Ge₇ and Dy_1−xSm_xGe_1.5, limited solid solutions based on binary compounds: Dy_1−xSm_xGe₃, Dy_1−xSm_xGe_1.9, Dy_xSm_1−xGe₂, Dy_11−xSm_xGe₁₀ and continuous solid solutions: Dy_1−xSm_xGe, Dy_5-xSm_xGe₄ and Dy_5-xSm_xGe₃. A solid solutions between the isostructural binary compounds of Sm-Ge and Dy-Ge systems are unlimited. All solid solution forms by mutual substitution of Dy and Sm. The solubility of Sm in DyGe₃ is less than 5 at.% Sm. At 873 K we are not confirmed the existence of Dy₃Ge₅ compound, which was presented on the Dy-Ge phase diagram (Fig. 1b)[15], instead, we confirmed the existence of Dy₁₁Ge₁₀ phase which earlier was studied by Tharp et al.[18], but is absent in Fig. 1(b).

4.2 Limited Solid Solutions

Limited solid solution from the SmGe₂—DyGe_1.9 section. The SEM/EPMA and XRD phase analysis of alloys (Fig. 3, and Fig. S1) from the isoconcentrate Sm₃₄Ge₆₆—Dy₃₄Ge₆₆ shows that the SmGe₂ (α-ThSi₂- type) solve up to 15 at.% Dy and DyGe_1.9 (TbGe₂- type) solve up to 10 at.% Sm. Between these limited solutions, the formation of a new ternary phase of Dy₂Sm₂Ge₇ was found (Fig. 3c-e). The lattice parameters for alloys from the homogeneity range of Sm_1−xDy_xGe₂ solid solution were determined and refined by powder diffraction data (Table 3 and Fig. 5a). The lattice parameters show an decreasing trend with increasing Dy content and the relative changes of the unit cell volume of Sm_1−xDy_xGe₂/SmGe₂ with the increase of Dy content is presented in Fig. 5(a).

Table 3 Composition of alloys and unit cell parameters of Dy_xSm_1−xGe₂ (α-ThSi₂- type) and Dy_11−xSm_xGe₁₀ (Ho₁₁Ge₁₀- type) limited solid solutions

Fig. 5

The relative changes of the unit cell volume of Sm_1−xDy_xGe₂/SmGe₂ with the increase of Dy content (a), Dy_1−xSm_xGe_1.9/DyGe_1.9 (b) and Dy_11−xSm_xGe₁₀/Dy₁₁Ge₁₀ (c) with the increase of Sm content

According to SEM/EPMA and XRD phase analysis data (Fig. 3b, and Fig. S2) the DyGe_1.9 (TbGe₂- type) solve up to 10 at.% Sm. The lattice parameters for alloys from the homogeneity range of Dy_1−xSm_xGe_1.9, (x = 0-0.30) solid solution were determined and refined by powder diffraction data are presented in Table 4). The lattice parameters increase with increasing Sm content. The relative changes of the unit cell volume of Dy_1−xSm_xGe_1.9/DyGe_1.9 Dy_11−xSm_xGe₁₀/Dy₁₁Ge₁₀ (d) with the increase of Sm content is shown in Fig. 5(b).

Table 4 Composition of alloys and unit cell parameters of Dy_1−xSm_xGe_1.9 (TbGe₂- type) limited solid solution

Dy_11−xSm_xGe₁₀, (x = 0-2.1) limited solid solution. The x-ray diffraction patterns of the studied Dy_11-xSm_xGe₁₀, (x = 0 and 2.1) alloys were similar to each other and they corresponded to single phase material with the tetragonal Ho₁₁Ge₁₀-type of crystal structure. The alloy with x =  3.1 is no single phase and in addition to the tetragonal phase, contains additional hexagonal Dy_xSm_5-xGe₃ and orthorhombic Dy_xSm_1−xGe phases. In Table 3 the appropriate unit cell parameters and calculated unit cell volumes are presented. Careful analysis of the values of the lattice parameters and the unit cell volumes indicates insignificant increase of these parameters with partial substitution of Dy by Sm atoms up to 10 at.% (Fig. 5c). Rietveld refinement of the crystal structure of this solid solution for the alloy with x = 2.1 (Fig. 6) showed that the substitution of Dy by Sm occurs in two crystallographic positions 8h and 4e. At the final, all parameters were refined up to R_B  =  8.27, R_F  =  6.93, R_p  =  5.12, R_wp  =  6.84 and χ²  =  1.47.

Fig. 6

Observed (circles), calculated (line) and difference (bottom line) x-ray powder diffraction patterns for Dy_11−xSm_xGe₁₀ at x = 2.1 (R_p = 5.12, R_wp = 6.84, R_Bragg = 10.01, R_f = 9.35). Vertical bars indicate the Bragg positions

4.3 Continuous Solid Solutions

Three series Dy_1−xSm_xGe, Dy_5-xSm_xGe₃ and Dy_5-xSm_xGe₄ of continuous solid solutions at the 873 K in the Dy-Sm-Ge system are observed. The SEM micrographs of selected samples from homogeneity regions of continuous solid solutions show their almost single phase state (Fig. S3).

Dy_1−xSm_xGe, (x = 0-1) continuous solid solution. Both equiatomic binary DyGe and SmGe compounds crystallises in a orthorhombic CrB—type in which the 4c crystallographic site occupy atoms of rare earth metals. Between these binary compound four ternary alloys were prepared and studied by SEM, EPMA (Fig. S3a-c) and XRD (Fig. S4) method of analysis. Almost linear changes in the unit cell parameters and volume are observed in fully concentration range of this solid solution (Table 5) The relative changes of the unit cell volume of Dy_1−xSm_xGe/DyGe with the increase of Sm content is presented in Fig. 7(a).

Table 5 Composition of alloys and unit cell parameters of Dy_1−xSm_xGe (CrB-type) and Dy_5-xSm_xGe₄ (Sm₅Ge₄-type) continuous solid solutions

Fig. 7

The relative changes of the unit cell volume of Dy_1−xSm_xGe/DyGe (a), Dy_5-xSm_xGe₃/Dy₅Ge₃ (b), Dy_5-xSm_xGe₄/ Dy₅Ge₄ (c) with the increase of Sm content

Dy_5-xSm_xGe₃, (x = 0-5) continuous solid solution. The Dy_5-xSm_xGe₃ (x = 0-5) continuous solid solution was detected by SEM, EPMA (Fig. 8d-f) and XRD (Fig. S5) methods on the Dy₅Ge₃—Sm₅Ge₃ section. All samples consist hexagonal phase with Mn₅Si₃ structure type. This solid solution is formed by mutual substitution of rare earth metals (Sm and Dy). The lattice parameters for alloys from the homogeneity range of this solid solution were determined and refined by powder diffraction data (Table 6). The relative changes of the unit cell volume of Dy_5-xSm_xGe₃/Dy₅Ge₃ obtained in this work show a tendency to increase cell volume with increasing Sm content (Fig. 7b).

Fig. 8

Observed (circles), calculated (line) and difference (bottom line) x-ray powder diffraction patterns for Dy_5-xSm_xGe₄ at x=3.2 (R_p = 3.62, R_wp = 5.30, R_Bragg = 7.31, R_f = 6.74). Vertical bars indicate the Bragg positions

Table 6 Composition of alloys and unit cell parameters of Dy_5-xSm_xGe₃ (Mn₅Si₃-type) continuous solid solution

Dy_5-xSm_xGe₄, (x = 0-5) continuous solid solution. Six alloys from the Dy₅Ge₄—Sm₅Ge₄ section were prepared and analysed by SEM/EPMA (Fig. S3j-i) and XRD (Fig. 7c) methods. Both binary phases crystallises in orthorhombic Sm₅Ge₄-type. The x-ray powder diffraction patterns obtained for all the investigated alloy samples were completely indexed on the basis of the Sm₅Ge₄-type structure by the assuming a statistical distribution of the Dy and Sm atoms on the both 8d and 4c sites. The Rietveld analysis (Fig. 8) performed for the alloy of the Dy₂₀Sm_35.5Ge_44.5 composition has shown that the distribution of its constituent atoms of rare earth metals in all sites are an statistical mixed. The structural parameters were refined up to R_B  =  6.43, R_F  =  5.92, R_p  =  2.34, R_wp  =  3.07 and χ²  =  0.33. The lattice parameters for alloys from the homogeneity range of this solid solution are presented in Table 5 and Fig. 7(c) presents the relative changes of the unit cell volume of Dy_5-xSm_xGe₄/Dy₅Ge₄ with the increase of Sm content.

4.4 Ternary Compounds

4.4.1 Dy₂Sm₂Ge₇ Ternary Compound

During a study of alloys from the Sm₃₄Ge₆₆—Dy₃₄Ge₆₆ concentration section the formation of a new ternary phase of Dy₂Sm₂Ge₇ was found. The powder diffraction pattern indicated that the Dy₁₇Sm₁₄Ge₆₆ alloy consists as main phase of the Dy₂Sm₂Ge₇ and small amounts of Ge (Fig. 9a). The irregular form single crystal was extracted from this alloy after its defragmentation (Fig. 9b) and diffraction pattern is presented in Fig. 9(c). The crystal structure of Dy₂Sm₂Ge₇ was investigated by single crystal experiments and was successfully solved by direct methods using SHELX-97 package programs. This compound may be viewed as the ordered superstructure to Nd₄Ge₇-type.[14] The orthorhombic unit cell with C222₁ space group of this intermetallic compound contains 44 atoms occupying 7 different Wyckoff sites. In the Nd₄Ge₇-type the all neodymium atoms occupy the 4a, 4b and 8c sites, instead, in the Dy₂Sm₂Ge₇ ternary phase, the first two sites occupy the atoms of dysprosium, and the third site is occupied by the atoms of samarium. This distribution of atoms gives the nominal composition of Sm_18.2Dy_18.2Ge_63.6, which is very consistent with the composition Sm_18.2(2)Dy_17,7(2)Ge_64,1(3) received from EPMA data. The crystal data and refined atomic parameters for Dy₂Sm₂Ge₇ are listed in Tables 7 and 8 respectively. The structural parameters from single crystal was confirmed by Rietveld refinements of powder data (R_p  =  4.99, R_wp  =  6.36, R_B  =  8.11, R_F  =  9.73 and χ²  =  1.15). The projection of the unit cell and coordination polyhedra of the atoms is shown in Fig. 10. The distorted equatorial four-capped trigonal prisms [RGe₁₀] are typical for all rare-earth atoms. The germanium atoms are enclosed in to tricapped trigonal prisms. The germanium atoms form 3D network (Fig. 11a) and atoms of rare-earth metals form filled and empty trigonal prisms which a linked by lateral faces (Fig. 11b). The electronic structure calculations by TB-LMTO-ASA confirm the existence of 3D network and the isosurfaces of electron localization function (ELF) around the Ge atoms at the 0.70 level is presented in Fig. 12(a).

Fig. 9

Observed (circles), calculated (line) and difference (bottom line) x-ray powder diffraction patterns for Dy₂Sm₂Ge₇ (R_p = 4.99, R_wp = 6.36, R_B = 8.11, R_F = 9.73) (a). Image of single crystal (b) and diffraction pattern of Dy₂Sm₂Ge₇ single crystal (c)

Table 7 Crystal data and structure refinement

Table 8 Fractional atomic coordinates and thermal displacement parameters (Ų) for Dy₂Sm₂Ge₇

Fig. 10

Unit cell and coordination polyhedra of atoms in the Dy₂Sm₂Ge₇

Fig. 11

The germanium atomic 3D network (a) and kind of linking of the filled and empty trigonal prisms (b)

Fig. 12

The isosurfaces of the ELF around the atoms (a) and total and partial DOS (b) in the Dy₂Sm₂Ge₇ structure

The distribution of electron localization function around Ge atoms and crystal chemical analysis suggest that 3D network from germanium atoms form negatively charged n[Ge₇]^4m- polyanions, which are compensated by positively charged 2nDy^m+ and 2nSm^m+ polycations. It should be noted, that for intermetallics there are known examples of compounds with polyanions, here are some of the previously investigated: LiGe, (n[Ge₆]^4- polyanion),[40] Li₄Ge₂B (n[B₃Ge₆]^m-),[41] Li₉Al₄Sn₅ (n[Al₄Sn₅]^m-),[42] TmNi_1−xLi_xSn₂ (n[Sn]^m-)[43] and La₄Mg₅Ge₆ (n[Mg₅Ge₆]^δ−).[44]

The description of chemical bonding used by us to some extent was based on the Zintl-Klemm concept according to which structure consists of a polyanion with cations located between the anionic lattice. In the typical Zintl phases the anion-cation interaction prevails, and they have low conductivity, or semiconductivity. This causes an insignificant density of states or a pseudo-gap at the Fermi level. The Dy₂Sm₂Ge₇ structure, like other similar phases well-known from literature, has a predominant metallic bonding, and cation-anion interaction is an additional interaction based on partial charges.

The total and partial density of states (DOS) for the Dy₂Sm₂Ge₇ is shown in Fig. 12(b). The higher density of electronic states at the Fermi level confirm the metallic behaviour. The feature of this structure is a very intense peaks from the overlapping of the f orbitals of Dy and Sm with p orbital of Ge in the valence band nearly Fermi level.

4.4.2 Dy_1−xSm_xGe_1.5 (x = 0.15-0.50) Ternary Phase

The samples of the compositions Dy₄₀Ge₆₀, Dy₃₅Sm₅Ge₆₀, Dy₃₀Sm₁₀Ge₆₀, Dy₂₀Sm₂₀Ge₆₀ and Dy₁₀Sm₃₀Ge₆₀ were prepared and investigated by the XRD powder method (Fig. S6a). The extent of homogeneity region of Dy_1−xSm_xGe_1.5, (x = 0.15-0.50) ternary phase was determined by the change in lattice parameters. The change in lattice parameters with varying concentrations of Sm are presented in Table 9. From the data of Table 9 it is obvious that replacement of Dy atoms by Sm atoms increases the unit cell volume of Dy_1−xSm_xGe_1.5.

Table 9 Composition of alloys and unit cell parameters of Dy_1−xSm_xGe_1.5 (AlB₂-type) ternary phase

Rietveld matrix full-profile structure refinements confirm well the powder patterns calculated on the basis of defected AlB₂ structure model (Fig. S6b). The 1a site fully occupied by statistical mixture of Dy and Sm atoms and the germanium atoms partially occupy the 2d site. For the Dy_1−xSm_xGe_1.5 (x = 0.25) ternary phase after last cycle refinement the residual factors are: Rp  =  6.57, Rwp  =  8.93, R_B  =  8.37, R_f  =  8.87, and χ²  =  1.54.

The Dy_1−xSm_xGe_1.5 is a ternary compound with wide homogeneity of region, and can be interpreted as a residue of a high-temperature solid solution based on high temperature phase γ-DyGe_1.5. It is known that germanium-rich phases exhibit structural instability and, depending on the conditions and methods of synthesis, the purity of metals, some phases may not form, and some, on the contrary, can stabilize (the formation of metastable phases). Also, the addition of a third component to binary germanides can lead to the stabilization of structures that are typical for metastable phases (as in the case of Sm₄Ge₇ and Dy₂Sm₂Ge₇), or also stabilization of structures that are typical for high-temperature phases (as in the case of DyGe_1.5 and Dy_1−xSm_xGe_1.5). Similar cases are known in the literature, for example, in system Sm-Ni-Ge[45] and Sm-Rh-Ge,[46] the ternary phases SmNi_0.5Ge_1.5 and SmRh_0.6Ge_1.4 with the AlB₂ structure type also formed at 600°C, although high temperature phase SmGe_1.5 (AlB₂-type structure) exist above 1085°C). It should be noted that the formation of superstructures to binary phases, as well as the decreasing of the temperature of formation of high-temperature phases at the addition of the third component, were found in other systems which do not contain germanium, such as La-Ni-Zn,[47] Mn-Al-Li[48] etc.

5 Summary

The isothermal section of phase diagram of the Dy-Sm-Ge system was studied in the full concentration range by means of x-ray phase and structural analyses, microstructural analysis and energy dispersive x-ray spectroscopy. Phase relations of this system were determined at 873 K by characterizing of 56 alloys. The features of this system are the formation of continuous solid solutions: Dy_1−xSm_xGe (x = 0-1), Dy_5-xSm_xGe₃ (x = 0-5) and Dy_5-xSm_xGe₄, (x = 0-5), and limited solid solutions: Dy_1−xSm_xGe_1.9, (x = 0-0.30), Dy_xSm_1−xGe₂ (x = 0-0.45) and Dy_11−xSm_xGe₁₀, (x = 0-2.1). All solid solutions are formed by the mutual substitution of atoms of rare earth metals.

Two ternary Dy_1−xSm_xGe_1.5 (x = 0.15-0.50) and Sm₂Dy₂Ge₇ compounds were found. The crystal structure of Sm₂Dy₂Ge₇ was investigated by means of x-ray single crystal diffraction: Pearson symbol oS44, space group C222₁, a  =  0.5942(1), b  =  1.3823(4), c  =  1.1801(3) nm, V  =  0.9694 nm³. This compound is ordered superstructure to Nd₄Ge₇-type. The electronic structure was calculated by the tight-binding linear muffin-tin orbital atomic spheres approximation method. The electron localization function is higher around the Ge atoms, which form an n[Ge₇]^4m- polyanion.