The system Nd–Fe–Sb: Phase equilibria, crystal structures and physical properties

Intermetallics 18 (2010) 2361e2376

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The system NdeFeeSb: Phase equilibria, crystal structures and physical properties Navida Nasir a, Andriy Grytsiv a, Peter Rogl a, *, Dariusz Kaczorowski b, Herta Silvia Effenberger c a

Institute of Physical Chemistry, University of Vienna, Währingerstrasse 42, A-1090 Wien, Austria Institute of Low Temperature and Structure Research, Polish Academy of Sciences, P.O. Box 1410, 50-950 Wrocław, Poland c Institute of Mineralogy and Crystallography, University of Vienna, Althanstrasse 14, A-1090 Wien, Austria b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 2 July 2010 Received in revised form 12 August 2010 Accepted 12 August 2010 Available online 24 September 2010

Phase equilibria within the isothermal section of the ternary system NdeFeeSb were derived at 800
C by using X-ray powder diffraction, light optical microscopy and electron probe microanalysis. Crystal structures of the ternary compounds Nd2Fe7xSb6y (s2-orthorhombic), Nd2Fe5xSb10y (s2-tetragonal) Nd3Fe3Sb7 (s3) and NdFeSb3 (s4) were determined by single crystal X-ray diffraction and by Rietveld Xray powder data refinement. The phase s2 was found to exhibit two modifications, orthorhombic (Nd2Fe7xSb6y-type, S.G. Immm, a ¼ 0.42632(6) nm, b ¼ 0.43098(7) nm, c ¼ 2.5823(3) nm) and tetragonal (La2Fe5xSb10y-type, S.G. I4/mmm, a ¼ 0.42897(2) nm, c ¼ 2.5693(4) nm). Tetragonal and orthorhombic modifications form a crystallographic groupesubgroup relation and are closely related to the Zr3Cu4Si6-type. Nd3Fe3Sb7 (s3) crystallizes with a unique structure type (S.G. P63/m, a ¼ 1.31808 (3) nm, c ¼ 0.41819(3) nm), which is isopointal to the Cu10Sb3-type. NdFeSb3 (s4) adopts the LaPdSb3type. Physical properties comprising magnetization, resistivity and specific heat were measured for RE2Fe5xSb10y (RE ¼ Ce, Nd), NdFeSb3 and Nd3Fe3Sb7. NdFeSb3 orders antiferromagnetically below 3.0 K due to the presence of magnetic moments on Nd sites. For the other compounds a more complex magnetic behaviour is observed at low temperatures that may be related to the contributions coming from both the rare earth and iron sublattices. Ó 2010 Elsevier Ltd. All rights reserved.

Keywords: A. Rare-earth intermetallics B. Crystal chemistry of intermetallics B. Phase diagrams B. Electrical resistance and other electrical properties B. Magnetic properties

1. Introduction Ternary rare earth (RE) transition metal antimonides are a class of compounds with a large diversity in structure and physical properties [1e5]. Although systems REeTeSb (T is a transition element) have been in the focus of many investigations [6e14], phase diagrams at temperatures higher than 600
C are scarce, and information on ternary compounds and their crystal structures is incomplete. The high thermoelectric efficiency of ternary and multicomponent skutterudites RET4Sb12 [15e17] has triggered intensive research on these Sb-rich compounds in general [18e21] and in layered structure antimonides with interesting magnetic properties e.g. RETSb3 [5,22e27]. As a logical continuation of our previous studies on phase equilibria in systems formed by rare earths with p2 elements (Si, Ge, Sn) and/or Sb [28], in this paper we focus on the system NdeFeeSb, on the phase relations at 800
C (particularly in the region with more than 40 at.% Sb), on the formation and crystal structure of ternary compounds and their isotypes with the homologous light rare earth elements (La, Ce, Pr, Nd). A first

* Corresponding author. Fax: þ43 1 42779524. E-mail address: [email protected] (P. Rogl). 0966-9795/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.intermet.2010.08.037

investigation of the system NdeFeeSb was performed by A. LeitheJasper in our institute as part of his PhD-thesis [6] revealing the phase relations at 800
C characterized by five ternary compounds: s1-Nd6Fe13Sb (Nd6Fe13Si-type [29]), and s2-NdFe2xSb2 (orthorhombic, a ¼ 0.42965(1), b ¼ 0.4276(2), c ¼ 2.5789(5) nm) s3Nd2Fe3xSb5 (hexagonal, a ¼ 1.31719(6), c ¼ 0.41785(8) nm; structure unknown), s4-NdFeSb3 (structure unknown) and s5-NdFe1xSb2 (ZrCuSi2-type [30]). At temperatures above 1000
C Leithe-Jasper [6] reported a high-temperature phase, NdFe3Sb2 (tetragonal, a ¼ 0.42879(7), c ¼ 2.5705(4) nm), as a tetragonal modification of orthorhombic s2-NdFe2xSb2. Whereas the crystal structures and physical properties of s1-Nd6Fe13Sb (Nd6Fe13Si-type) [29], and of s5NdFe1xSb2 (ZrCuSi2-type) [30] have been elucidated in detail, the structure solutions for the crystal structure of s2-NdFe3Sb2 (tetragonal, I4/mmm) and s2-NdFe2xSb2 (orthorhombic, Imm2) were not considered to be satisfactory (RF ¼ 0.086 and 0.081 respectively) and remained unpublished [6]. Compounds isotypic to the tetragonal structure were observed with La and Ce while compounds with Pr and Sm were found isostructural to the orthorhombic structure. A more recent investigation of the NdeFeeSb system by Zeng et al. [10] at 500
C showed a compound NdFe2.5Sb2 with unknown structure but did not reveal s3-Nd2Fe3xSb5 [6]. Therefore the aim of the present work is threefold: (i) to investigate phase relations in the Sb-

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rich part of the NdeFeeSb system (region FeeNdSbeSb) in a wider temperature range, (ii) to elucidate crystal structure and formation of ternary phases (s2, s3 and s4) including the light rare earth containing homologues, and (iii) to study their physical properties. 2. Experimental All samples, each of a total amount of ca. 1e1.5 g, were prepared in an electric arc furnace on a water-cooled copper hearth under Tigettered argon and with a non-consumable tungsten electrode. The purity of RE (Nd, La, Pr) was 99.5 mass%, of antimony and Fe was better than 99.9%. The alloys were remelted three times in order to ensure complete fusion and homogeneity. Weight losses were found to be 2e4 mass% and were compensated beforehand for the most volatile element Sb. The reguli were cut into 2 to 4 pieces in order to perform heat treatments at various temperatures. The individual pieces were sealed in evacuated quartz tubes and annealed at temperatures (500, 600, 700, 800, 900, 1000
C) for 7e14 days following quenching in water. X-ray powder diffraction (XRPD) data from as cast and annealed alloys were collected with a Guinier-Huber image plate system (CuKa1 or FeKa1; 8
< 2Q < 100
). Precise lattice parameters were calculated by least-squares fits to indexed 2Q-values employing Ge as internal standard (aGe ¼ 0.565791 nm). To determine the crystal structure of the ternary phases s2 (tetragonal and orthorhombic), and s3, single crystal fragments, suitable for X-ray structure determination, were broken from alloys with nominal compositions (i) La18Fe36Sb46 annealed at 1000
C (30 days), (ii) Nd19Fe39Sb42 annealed at 1000
C (30 days) and (iii) Nd22Fe27Sb51 annealed at 800
C (20 days) prior to quenching in cold water. Inspection on an AXS-GADDS texture goniometer assured high crystal quality, unit cell dimensions and Laue symmetry of the specimens prior to X-ray intensity data collection on a four-circle Nonius Kappa diffractometer equipped with a CCD area detector and employing graphite monochromatic MoKa radiation (l ¼ 0.071073 nm). Orientation matrix and unit cell

parameters were derived using the program DENZO [31]. No absorption correction was necessary because of the rather regular crystal shape and small dimensions of the investigated specimen. The structures were solved by direct/Patterson methods and refined with the SHELXL-97 and SHELXS-97 programs [32]. The as cast and annealed samples were polished using standard procedures and microstructures and compositions were examined by light optical microscopy (LOM) and scanning electron microscopy (SEM) via Electron Probe Micro-Analyses (EPMA) (i) on a Carl Zeiss EVO 40 equipped with a Pentafet Link EDX system and (ii) on a Zeiss Supra 55 VP equipped with an EDX system operated at 20 kV. Binary and ternary compounds NdSb2 and NdFeSb3 were used as EPMA standards. The differences between measured and nominal compositions were found to be <1 at.%. Magnetic measurements were performed in the temperature range 1.7e400 K in applied magnetic fields up to 50 kOe using a Quantum Design MPMS-5 SQUID magnetometer. The electrical resistivity was measured over the temperature interval 4.2e300 K employing a dc four-probe technique in a homemade setup. In the case of NdFeSb3 the resistivity measurements were extended down to 0.4 K using a standard ac technique implemented in a Quantum Design PPMS platform. Specific heat studies were carried out in the 0.35e300 K temperature range by a relaxation method employing a Quantum Design PPMS. 3. Results and discussion 3.1. Binary boundary systems Binary boundary systems NdeSb, FeeSb and FeeNd were accepted after [33e35] respectively. The monoclinic binary phase Nd9xSb21y (S.G. Cm) reported by Schmidt et al. [36] is not shown in any of the hitherto reported binary phase diagrams for the NdeSb system. It should be noted that this phase was not observed at any temperature in any sample investigated in the present work. Crystallographic data for the solid phases are summarized in Table 1.

Table 1 Crystal structure data for relevant solid phases in the system NdeFeeSb. Phase

Pearson symbol

(Sb) (aFe) < 912
C Fe2xSb (x ¼ 0.73) NdSb aNdSb2 (<805
C) Nd4Sb3 Nd5Sb3 Nd2Sb Nd9xSb21y Nd2Fe17 s1-Nd6Fe13Sb NdFe3Sb2a s2-Nd2Fe5xSb10y (s2-tetragonal)e NdFe2xSb2b s2-Nd2Fe7xSb6y (s2-orthorhombic)e Nd2Fe3xSb5c s3-Nd3Fe3Sb7 NdFeSb3d s4-NdFeSb3 s5-NdFe1xSb2 s6-NdFe4Sb12 a b c d e

The The The The The

compound compound compound compound compound

hR2 cI2 hP6 cF8 oC24 cI28 hP16 tI12 mC(62e5.44) hR57 tI80 tI24 tI34 oI20 oI30 e hP26 oP60 oP40 tP8 cI34

Space group

R3m Im3m P63/mmc Fm3m Cmca I43m P63/mcm I4/mmm Cm R3m I4/mcm I4/mmm I4/mmm Imm2 Immm e P63/m Pbcm Pbcm P4/nmm Im3

Structure type

As W Ni2In NaCl LaSb2 Th3P4 Mn5Si3 La2Sb Nd9xSb21y Th2Zn17 Nd6Fe13Si NdFe3Sb2 La2Fe5xSb10y NdFe2Sb2 Nd2Fe7xSb6y e Nd3Fe3Sb7 CeNiSb3 LaPdSb3 ZrCuSi2 LaFe4P12

Lattice parameters, nm

Reference

a

b

c

0.43084 0.28665 0.4124 0.6321 0.6326 0.9370(8) 0.9199(8) 0.451 2.845(6) 0.85782 0.8090(1) 0.42879(7) 0.42897(2) 0.4296(1) 0.42632(6) 1.31719(6) 1.31808(3) 1.26828(2) 1.2677(3) 0.43514(6) 0.9130(1)

e e e e 0.6102 e e e 0.4247(8) b ¼ 95.42
e e e e 0.4276(2) 0.43098(7) e e 0.61666(2) 0.61613(7) e e

1.1274 e 0.5173 e 1.8086 e 0.6454(5) 1.761 1.3459(9) 1.24611 2.3192(6) 2.5705(4) 2.5693(4) 2.5789(5) 2.5823(3) 0.41785(8) 0.41819(3) 1.81867(4) 1.2132(4) 0.9652(1) e

[34] [45] [46] [45] [33] [45] [45] [45] [36] x ¼ 0.7; y ¼ 1.02 [46] [29] [6] This work x ¼ 1.48; y ¼ 5.12 [6], x ¼ 0 This work x ¼ 3.04; y ¼ 1.03 [6] This work [42] This work [30] x ¼ 0.4 [37]

“NdFe3Sb2“ reported by [6] corresponds to s2-Nd2Fe5xSb10y (s2-tetragonal) in the present work. “NdFe2xSb2“ reported by [6] corresponds to s2-Nd2Fe7xSb6y (s2-orthorhombic) in the present work. “Nd2Fe3xSb5“ reported by [6] corresponds to s3-Nd3Fe3Sb7 in the present work. NdFeSb3 with CeNiSb3 type reported by [42] was not confirmed but was observed with LaPdSb3-type in the present work. “NdFe2.5Sb2” with unknown structure observed by [10] at 500
C is likely to refer to the orthorhombic s2-phase.

N. Nasir et al. / Intermetallics 18 (2010) 2361e2376

Fig. 1. Isothermal section of NdeFeeSb system at 800
C. Empty circles represent alloys prepared in the present work. L represents a liquid phase (for details see text).

3.2. Phase equilibria in the NdeFeeSb system In order to define a proper temperature for the isothermal section, alloys, annealed at various temperatures (500, 600, 700, 800, 900, 1000, and 1100
C), were subjected to XRPD and LOM analyses,

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which revealed that the annealing temperature of 500
C is too low to achieve equilibrium condition: most of the alloys annealed at 500
C remained unchanged with respect to the as cast state. As above 800
C some of the alloys appeared completely melted, the optimal temperature for equilibration and for the formation of ternary compounds was defined as 800
C. The isothermal section derived at 800
C from EPMA and XRPD (Table 2) is presented in Fig. 1. Phase equilibria in the composition range FeeNdSbeNd are accepted after Leithe-Jasper [6]. All ternary phases reported previously, s1-Nd6Fe13Sb (Nd6Fe13Si-type) [6], s2-NdFe2xSb2 (orthorhombic) [6], NdFe3Sb2 (tetragonal) [6], wNdFe2.5Sb2 (unknown type [10], this phase is likely to correspond to orthorhombic s2NdFe2xSb2 of [6]), s3-Nd2Fe3xSb5 [6], s4-NdFeSb3 [6,10], s5NdFe1xSb2 (ZrCuSi2-type) [30] and s6-NdFe4Sb12 (LaFe4Sb12 type) [37] were observed in the present work. The crystal structures of s2 and s3 have been determined by single crystal x-ray diffraction in the present work (for details see Sections 3.3 and 3.4): as a result the proper structure formulae for s2 (tetragonal and orthorhombic) and s3 are now given as Nd2Fe5xSb10y (s2-tetragonal), Nd2Fe7xSb6y (s2-orthorhombic) and s3-Nd3Fe3Sb7, respectively. Microstructures of the selected as cast and annealed alloys documenting the phase equilibria are shown in Figs. 2 and 3. The as cast alloy with nominal composition Nd16Fe12Sb70 was multiphase with two different zones of crystallization. Fig. 2a and b show primary crystallization of NdSb2 with peritectic formation of s5, whilst Fig. 2c presents s5 as primary grains with subsequent crystallization of NdSb2 as secondary grains. The last liquid in both regions shows joint crystallization of s4, NdSb2, FeSb2 (Fig. 2aec). All phases were confirmed from XRPD. The alloy annealed at 800
C shows a completely different microstructure

Table 2 Three-phase equilibria and lattice parameters for NdeFeeSb (800
C). Phase equilibria

(L) þ Fe2xSb þ s4

(L) þ NdSb2 þ s4

NdSb2 þ s4 þ s5

s3 þ s4 þ s5 NdSb2 þ NdSb þ s5

NdSb þ s5 þ s2

(Fe) þ NdSb þ s2

(Fe) þ Fe2xSb þ s2

Fe2xSb þ s2 þ s3

s2 þ s3 þ s5 Fe2xSb þ s3 þ s4(solidus Temperature)

Phase

(Sb) Fe2xSb

s4

(Sb) NdSb2

s4

NdSb2

s4 s5 s3 s4 s5

NdSb2 NdSb

s5 NdSb

s5 s2-orthorh (Fe) NdSb s2-tetrag (Fe) Fe2xSb s2-orthorh Fe2xSb

s2 s3 s2 s3 s5

Fe2xSb

s3 s4

EPMA, at.%

Lattice Parameter, nm

Nd

Fe

Sb

a

b

c

e e e 1.8 32.9 20.2 33.9 20.5 28.4 23.1 e 27.9 e e e 49.7 e 18.2 0.1 48.5 18.0 e e 19.1 e 18.5 23.2 18.5 23.2 27.7 0.3 23.2 20.5

e e e 1.2 0.3 19.1 0.7 19.5 15.1 23.6 e 16.0 e e e 0.1 e 36.5 96.0 0.5 35.9 e 55.9 36.3 53.6 35.6 22.8 35.6 22.8 16.6 52.1 23.2 19.6

e e e 97.0 66.8 60.7 65.4 60.0 56.5 53.3 e 56.1 e e e 50.2 e 45.3 3.9 51.0 46.1 e 44.1 44.6 46.4 45.9 54.0 45.9 54.0 55.7 47.6 53.6 59.9

0.43090(8) 0.40635(2) 1.2677(3) 0.43097(4) 0.6224(1) 1.2673(2) 0.6235(2) 1.2675(3) 0.43503(3) 1.3185(1) 1.2681(2) 0.43535(5) 0.6227(2) 0.6355(3) 0.43509(4) 0.63378(4) 0.4346(5) 0.4302(1) e 0.6344(1) 0.42903(4) e 0.41259(6) 0.42726(9) 0.411(1) e 1.3185(2) e 1.3185(2) 0.4368(2) 0.40742(2) 1.31899(8) 1.2680(4)

e e 0.61613(7) e 0.6097(1) 0.61604(6) 0.6097(2) 0.61630(8) e e 0.61647(8) e 0.6111(2) e e e e 0.4286(1) e e e e e 0.4301(1) e e e e e e e e 0.61658(9)

1.1269(3) 0.51394(4) 1.2132(4) 1.1273(2) 1.8106(5) 1.2134(2) 1.8105(8) 1.2137(2) 0.9651(2) 0.41820(9) 1.2131(3) 0.9667(3) 1.814(1) e 0.9649(2) e 0.9710(6) 2.573(4) e e 2.5821(5) e 0.5172(2) 2.5843(5) 0.5149(3) e 0.41846(4) e 0.41846(4) 0.9648(9) 0.5145(2) 0.41814(4) 1.2131(3)

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Fig. 2. Microstructure of NdeFeeSb alloys: a), b) and c) Nd16Fe12Sb70 as cast; d) Nd16Fe12Sb70 800
C; e) Nd16Fe12Sb70 700
C; f) Nd22Fe27Sb51 800
C.

consisting of only three phases as can be seen from Fig. 2d which reveals big grains of s4 and NdSb2 inside a matrix that represents liquid state at 800
C. Morphology of the alloy annealed at 700
C represents the equilibrium, s6 (skutterudite)þs4þNdSb2 (Fig. 2e), which is different from that observed at 800
C (s4þNdSb2þ(L)). Solubility of Fe in NdSb2 at 800
C was found to be less than 1%. In an attempt to prepare a single-phase alloy NdFeSb3 weak unindexed reflections were observed in the X-ray profile of the alloy annealed at 800
C. The intensity of these reflections increased significantly in alloy Nd22Fe27Sb51. A single crystal selected from the latter alloy yields the ternary compound s3 (for details refer to Section 3.4). Microstructure of the alloy Nd22Fe27Sb51 annealed at 800
C (Fig. 2f) represents the triangle s3es2es5. Ternary phases s3 and s2 are also in equilibrium with Fe2xSb (see Figs. 1 and 3a). Equilibrium of s3 with s4 and Fe2xSb is shown in the micrograph of the alloy Nd19Fe25Sb56 annealed at 800
C (Fig. 3b). Due to very small difference in compositions, the SEM contrast between the s3 and s4 phases is very low (Fig. 3b), but compositions from EDX show a clear difference, which is also confirmed by X-ray analysis. Despite the presence of low melting Sb, kinetics in the system is quite slow and alloys with less than 50 at.% Sb were usually found to contain four to five phases after annealing at 800
C for 7e10 days. In order to clearly define phase equilibria, some alloys were repowderized and compacted

into tablets sealed in evacuated quartz tubes and additionally annealed at 800
C for 7e10 days. Microstructure of the as cast alloy Nd19Fe27Sb54 shows a ternary eutectic structure (E) consisting of s4, s5 and Fe2xSb (Fig. 3c) and with an overall eutectic composition Nd17.2Fe26.6Sb56.2 (marked as liquid (L) in Fig. 1). Most of the alloys in this composition range were found partially melted after annealing at 800
C indicating a eutectic temperature slightly below 800
C., Fig. 3d documents the equilibrium microstructure of s3 and s5 in the alloy with nominal composition Nd24Fe20Sb56. Microstructure of the alloy Nd20Fe35Sb45 after cyclic heat treatment (slow heating and cooling between 1075 and 1025
C) reveals very big grains of s2 with composition Nd18.0Fe37.6Sb44.3 with well-defined grain boundaries (Fig. 3e). The grains of s2 are separated by a very fine eutectic structure with composition Nd8.2Fe30.3Sb72.4 (Fig. 3f). However, no single crystal fragment suitable for X-ray single crystal investigations could be obtained from this sample. The phase equilibria associated with structural polymorphism in s2 (tetragonal and orthorhombic structure) appear to be very complicated. The as cast alloy Nd19Fe37Sb44 with primary crystallites of NdSb contains small amounts of s2 in orthorhombic modification crystallizing from the last liquid. After anneal at 900
C and 800
C NdSb disappears and s2 appears as tetragonal modification whilst the sample annealed at 700
C mainly consists

N. Nasir et al. / Intermetallics 18 (2010) 2361e2376

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Fig. 3. Microstructure of NdeFeeSb alloys: a) Nd21Fe26Sb53 (800
C); b) Nd19Fe25Sb56 (800
C); c) Nd19Fe27Sb54 (as cast); d) Nd23Fe20Sb57 (800
C); e) and f) Nd20Fe35Sb45 (after cycling between 1025 and 1075
C).

of orthorhombic s2. As the sample annealed at 500
C does not show any change in comparison with the as cast state, the sample first heat treated at 900
C (containing the tetragonal modification of s2) was subsequently annealed at 500
C: the tetragonal modification transformed to the orthorhombic modification. Another point to note is that high quenching rates are crucial to obtain the tetragonal modification. We furthermore cannot exclude the possibility of compositional polymorphism in addition to temperature polymorphism. Therefore it is presently very difficult to interpret the complex behaviour of polymorphism of the s2 phases. However, at 800
C both modifications are observed: the orthorhombic modification is in equilibrium with Fe2xSb and (aFe) whilst the tetragonal modification is observed in equilibrium with NdSb and (aFe). 3.3. Crystal structure of s2 An unknown x-ray spectrum was observed for the alloy with nominal composition Nd20Fe35Sb45 in as cast as well as in specimens annealed at 500, 800, 900 and 1000
C. EMPA analyses reveal a ternary composition wNd18.0Fe36.5Sb45.5. The ternary compounds in this composition range were reported as s2NdFe2xSb2 (orthorhombic) and NdFe3Sb2 (tetragonal) [6] and more recently as wNdFe2.5Sb2 (unknown structure) [10] in the

isothermal section at 500
C. Whilst in the systems LaeFeeSb and PreFeeSb at 500
C, the ternary compounds LaFe2Sb2 (a ¼ 0.45518 nm, b ¼ 0.77737 nm, c ¼ 0.84207 nm, b ¼ 128.39
) [11] and PrFe2Sb2 (a ¼ 0.60719 nm, b ¼ 0.60867 nm, c ¼ 1.33051 nm, b ¼ 103.1
) [12] were tentatively indexed as monoclinic phases with Ga2S3 prototype (S.G. Cc), we were unable to index or refine the observed XRPD (mentioned above) with the Ga2S3 structure type. However, the observed patterns were completely indexed on the basis of orthorhombic and tetragonal unit cells as reported by Leithe-Jasper [6] for s2-NdFe2xSb2 and NdFe3Sb2, respectively. In order to establish atom arrangements in these structures, attempts were made to select single crystal fragments. The single crystals selected from alloys annealed at 1000
C for about 7 days yielded only very small crystallites. Cyclic heat treatment (slow heating and cooling w10
C/h between 1075 and 1025
C) gave very big grains of the phase in equilibrium with liquid (Fig. 3e and f) but single crystal quality was poor. XRPD patterns show line splitting and a reduced intensity for some diffraction lines e.g. at 2Q w 42.1
as compared to the powder pattern of the alloy La18Fe36Sb45.5 which indicate a structural transformation. Single crystals were finally found from the alloys La18Fe36Sb46 and Nd19Fe39Sb42 annealed at 990
C for 30 days. Inspection on a GADDS instrument reveals tetragonal symmetry for the crystal selected from La18Fe36Sb46 (a w0.434, c w 2.63 nm) and orthorhombic symmetry

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N. Nasir et al. / Intermetallics 18 (2010) 2361e2376

for the crystal selected from sample Nd19Fe39Sb42 (a w 0.42 nm, b w 0.43 nm, c w 2.58 nm). 3.3.1. Crystal structure of tetragonal s2-La2Fe5xSb10y; x ¼ 1.12; y ¼ 5.08 Single crystal X-ray intensity data confirm a body centred tetragonal unit cell with a ¼ 0.43410 nm, c ¼ 2.63070 nm. The observed systematic extinctions suggest space groups I4/mmm, I4m2, I42m, I4mm, I422, I4/m, I4, I4. Initial atomic positions for the highest symmetry I4/mmm were found from a three dimensional Patterson map. Although the residual value approaches RF ¼ 0.045 a residual electron density of about 8 e/Å3 was left close to the Wyckoff position 2b (0, 0, ½) occupied by Sb. Structure solution in space group I4 (lowest symmetry) also terminated with same electron density near the Wyckoff position 2b, however, a test for higher symmetry prompted space group I4/mmm. The difference Fourier map around the site 2b (0, 0, ½,) (Fig. 4a and b) revealed that the electron density for this site is not spherical but indicates an off-centre atom position (Fig. 4b). Therefore the site 2b was split into 2 sites 4e and 8j for which partial occupancies were refined to 0.168(3) and 0.145(4) respectively and result in a final RF value of 0.025 and residual electron densities 3.15 e/2.81 e/Å3. Interestingly the sum of the occupancies of site 4e and 8j

Fig. 5. Extended view of crystal structures of La2Fe5xSb10y (x ¼ 1.12; y ¼ 5.08) and Nd2Fe7xSb6y (x ¼ 3.04; y ¼ 1.03).

corresponds to w100% of the occupancy in the 2b site. The effect of these two sites which appear as a cluster (Fig. 5) is reflected in the anisotropy of neighbouring Fe2 at the 8g site. It seems that the split of these sites is originated by a partial occupancy of the Fe2atoms. A difference Fourier map for the site 8g (Fig. 6), however, reveals simple anisotropy. All crystallographic data and interatomic distances are given in Table 3. Although overall interatomic distances agree well with the sum of the atomic radii of the elements, the very short interatomic distances encountered (Table 3b) correspond to the sites with partial occupancies. The resulting formula La2Fe5xSb10y (x ¼ 1.12, y ¼ 5.08; La18.5Fe35.9Sb45.5 in at.%) agrees well with the EMPA results of La18.4Fe36.3Sb45.3 and the structural model complies very well with the observed XRPD pattern. Although the present structural model for La2Fe5xSb10y confirms the main features of the structure model developed by Leithe-Jasper [6] for “NdFe3Sb2” the main differences concern (i) the split of the 2b site (Fe atoms in the model by Leithe-Jasper [6]) into 4e and 8j (Sb atoms) and (ii) the defect Fe-site 8g resulting in a different formula. The XRPD patterns of the almost single phase alloys Ce20Fe35Sb45 and Nd18.5Fe36Sb45.5 (both quenched from 1000
C) refined successfully (Table 3) employing this structural model and thereby confirm isotypism of these compounds with the structure of La2Fe5xSb10y.

Fig. 4. Crystal structure of La2Fe5xSb10y. Fourier map for electron density at 2b (Sb3 and Sb4); a) three dimensional view; b) projection in xey plane.

3.3.2. Crystal structure of orthorhombic s2 (Nd2Fe7xSb6y; x ¼ 3.04, y ¼ 1.03) X-ray intensity data collected for a crystal selected from the sample with nominal composition Nd19Fe39Sb42 confirm orthorhombic symmetry (a ¼ 0.42670 nm, b ¼ 0.43100 nm, c ¼ 2.58560 nm) and a body centred Bravias lattice. Extinction conditions suggest space groups Immm, Imm2, I2mm, Im2m, Imm2, I222, I212121. The structure was successfully solved in the highest symmetry space group Immm using direct methods, whilst structure refinement for NdFe2xSb2 by [6] was performed in space group

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with the presence of both modifications. It should be noted that, although the structure formulae look quite different, the two structure modifications, s2-tetragonal (Nd2Fe5xSb10y, x ¼ 1.12, y ¼ 5.08; Nd18.5Fe36Sb45.5 in at.%) and s2-orthorhombic (Nd2Fe7xSb6y, x ¼ 3.04, y ¼ 1.03; Nd18.3Fe36.2Sb45.5 in at.%), adopt practically the same composition in the phase diagram and both without a significantly large homogeneous region.

Fig. 6. Crystal structure of La2Fe5xSb10y. Fourier map for electron density at 8g (Fe2); a) three dimensional view; b) projection in xey plane.

Imm2. As a huge anisotropy (U11:U22 ¼ 1:8) was observed for Fe3 atoms at the 4j site, a difference Fourier map for the electron density (Fig. 7) was made for this site, which suggested a split of the site whilst the difference Fourier map for the Fe2 atom yields normal anisotropy. Therefore the 4j site was replaced by the 8l site (0, y, z), which on refinement reveals a partial occupancy of 0.404. The final least-squares cycle gives RF ¼ 0.032 at a residual electron density of 2.58/2.80 e/Å3. Refinement of the occupancies reveals partial occupation for the site 4i (occ. ¼ 0.486) occupied by Sb3 and 4j occupied by Fe2 (occ. ¼ 0.672) resulting in a formula Nd2Fe7xSb6y (x ¼ 3.04, y ¼ 1.03; Nd18.3Fe36.2Sb45.5 in at.%), which agrees very well with the microprobe analysis Nd18.0Fe35.9Sb46. All crystallographic data and interatomic distances are given in Table 4a,b. Partial occupancy of the three sites is reflected from very short interatomic distances (Table 4b). The structural model fits very well with the XRPD pattern. The transformation from tetragonal to orthorhombic symmetry is obvious from a reduction in intensity and the broadening or splitting of peaks in the XRPD patterns of samples quenched from different temperatures (Fig. 8). Reflections (200) (105) and (107) in the tetragonal space group split into orthorhombic reflections (200) and (020), (015) and (105), (017) and (107) respectively. Broadening of peaks observed in most of the XRPD patterns can be associated

3.3.3. Structural relations between the s2 modifications The crystal structures of La2Fe5xSb10y (s2-tetragonal), and Nd2Fe7xSb6y (s2-orthorhombic) are shown in Fig. 5. Both structures are closely related to each other forming almost identical coordination polyhedra (Fig. 9). Rare earth atoms are at the centres of Archimedean antiprisms with 8 surrounding Sb atoms. Similar archimedean polyhedra are formed around Sb1, which has four rare earth and four Fe neighbours. Sb2 is in a tetrahedral environment of rare earth atoms while Fe1 has a coordination sphere of 10 atoms (see Fig. 9). Tetragonal and orthorhombic structures can be related via a groupesubgroup relation in the Bärnighausen formalism [38,39] as a ‘translationengleiche’ symmetry reduction of index 2 (Fig. 10). Ideally, the 8g site in I4/mmm (occupied by Fe2) should split into two 4j sites but actually a distortion is observed for one 4j site which was replaced by a partially occupied 8l site as discussed above. If we consider the ideal Wyckoff sequence ge3da (sites 2a, 4d, 4e, 4e, 4e, 8g), La2Fe5xSb10y seems to be isotypic with the Zr3Cu4Si6type [40] with exactly the same arrangement of atoms in the unit cell as in La2Fe5xSb10y (except for Sb4 in the 8j site). Structures of s2 whether tetragonal or orthorhombic like Zr3Cu4Si6 can be considered as intergrowth of slabs of the ZrCuSi2-type and cubic facecentred Fe (Fig.11). There are many structure types with space group I4/mmm e.g. U2Cu4As5, Pd3Ti0.667Pb0.33, Eu2Pt7AlP3, Ce2NiGa10 which are closely related to these structures and are interpreted as composed of slabs of BaAl4 and CaF2 (see e.g. Ref. [41]). It seems that in both compounds La2Fe5xSb10y and Nd2Fe7xSb6y the presence of rare earths results in a distortion of the ideal position of electron density. Isotypism with La2Fe5xSb10y is observed also for Ce2Fe5xSb10y, whereas the Pr- and Nd-compounds exhibit both the orthorhombic and tetragonal modifications. The plot of lattice parameters and volume vs. rare earths shows the lanthanide contraction as was also observed by Leithe-Jasper [6] (Fig. 12). From the variation of lattice parameters one can expect a partial Ceþ4 state for Ce2Fe5xSb10y. Lattice parameters for isotypic compounds are presented in Table 5. 3.4. Crystal structure of s3-Nd3Fe3Sb7 XRPD analysis of the alloy with nominal composition Nd22Fe27Sb51 annealed at 800
C reveals a set of unindexed reflections which were not present in the XRPD patterns of the as cast alloys or in samples annealed at 500
C and 900
. These reflections were indexed by programme TREOR on the basis of a hexagonal cell (a z 1.32 nm and c z 0.42 nm), which was different from any of the known phases around, pointing to a ternary compound with hitherto unknown crystal structure, which in previous investigations by Leithe-Jasper [6] was labelled as s3-Nd2Fe3xSb5 (hexagonal, a ¼ 1.317 nm, c ¼ 0.418 nm). However, due to small grain size it was difficult to isolate a single crystal fragment from the alloy annealed at 800
C for 7 days, therefore the sample was kept at annealing temperature for 30 days followed by quenching in cold water. XRSC measurements of a proper single crystal fragment confirm a new ternary compound with hexagonal symmetry and lattice parameters a z 1.32 nm and c z 0.42 nm. The observed systematic extinctions indicated three

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Table 3a X-ray single crystal data for La2Fe5xSb10y and Rietveld refinement for XRPD profiles of the isotypic compounds with Ce and Nd (s2-tetragonal); structure data standardized with program Structure Tidy [41]. Anisotropic displacement parameters Uij and isotropic temperature factor Biso in [102 nm2]. Parameter/compound

La2Fe5xSb10y (x ¼ 1.12; y ¼ 5.08)

Ce2Fe5xSb10y (x ¼ 1.16; y ¼ 5.08)

Nd2Fe5xSb10y (x ¼ 1.48; y ¼ 5.12)

X-ray technique used Prototype Space group a; c (nm), Ge standard; Z Reflections in refinement Q range Total number of frames Number of variables RF 2 ¼ SjF2o  F2c j/SF2o RF ¼ SjFo  Fcj/SFo RI ¼ SjIo e Icj/SIo RP ¼ Sjyoi  ycij/Sjyoij RwP ¼ [Swijyoi  ycij2/Swijyoij2]½ Re ¼ [(N  P þ C)/Swiy2oi)]½ c2 ¼ (RwP/Re)2 Mosaicity Extinction Residual density e/Å3; max; min

XRSC (MoKa) La2Fe5xSb10y I4/mmm 0.43374(3); 2.6272(7); 2 353  4s(Fo) of 379 2  2Q  70 515; 10 sets; 250 s/frame 22 0.0250 e RInt ¼ 0.0355 e wR2 ¼ 0.071 e GOF ¼ 1.163 <4.5 0.0013(2) 3.15; 2.81

XRPD (CuKa) La2Fe5xSb10y I4/mmm 0.43098(3); 2.5994(6); 2 123 8  2Q  100 e 24 e 0.0594 0.0770 0.025 0.0360 0.0075 23.1 e e e

XRPD (CuKa) La2Fe5xSb10y I4/mmm 0.42897(2); 2.5693(4); 2 122 8  2Q  100 e 24 e 0.0743 0.0846 0.0202 0.0285 0.0108 6.93 e e e

Atom parameters RE in 4e (0, 0, z); z; Occ. U11 ¼ U22; U33; Ueq. or Biso Fe1 in 2a (0, 0, 0); Occ. U11 ¼ U22; U33; Ueq. or Biso Fe2 in 8g (0, ½, z); z; Occ. U11; U22; U33 Ueq. or Biso Sb1 in 4e (0, 0, z); z; Occ. U11 ¼ U22; U33; Ueq. or Biso Sb2 in 4d (0, ½, ¼); Occ. U11 ¼ U22; U33; Ueq. or Biso Sb3 in 4e (0, 0, z); z; Occ. U11 or Biso Sb4 in 8j (x, ½, 0); x; Occ. U11 or Biso

0.34739(3); 1.01(2) 0.0107(2); 0.0129(7); 0.0115(2) 1.01(2) 0.0167(7); 0.0124(9); 0.0152(5) 0.04970(7); 0.719(7) 0.065(2); 0.0102(9); 0.0104(7) 0.284(7) 0.10786(3); 1.01(2) 0.0115(2); 0.0135(8); 0.0122(2) 1.01(2) 0.0118(2); 0.0122(3); 0.0120(2) 0.4851(5); 0.168(3) 0.029(2) 0.417(2); 0.145(4) 0.029(2)

0.34786(6); 1.01(2) 0.55(6) 1.02(2) 1.57(9) 0.0517(2); 0.71(4) e 1.18(9) 0.10980(6); 1.01(2) 0.64(5) 1.01(2) 0.69(5) 0.4763(7): 0.10(1) 0.56(5) 0.424(2); 0.18(9) 0.35(5)

0.34745(4); 1.01(2) 1.09(4) 1.01(2) 1.42(7) 0.0540(2); 0.63(4) e 1.94(7) 0.11071(4); 1.01(2) 1.01(3) 1.01(2) 1.01(3) 0.4774(4); 0.12(5) 1.01(3) 0.432(2); 0.16(8) 1.01(3)

e e e e e

e e e e e

Principal mean square atomic displacements U La 0.0130; Fe1 0.0167; Fe2 0.0647; Sb1 0.0136; Sb2 0.0122;

0.0107; 0.0167; 0.0104; 0.0115; 0.0119;

0.0107 0.0124 0.0102 0.0115 0.0119

Table 3b Interatomic distances [nm] for La2Fe5xSb10y (x ¼ 1.12; y ¼ 5.08); Standard deviation 0.0004 nm. Sb2 Sb1 Fe1

La

4 4 4 4 8 8 2 8 8 4 4

Sb2 La Fe2 La Fe2 Sb4 Sb1 Sb3 Sb4 Sb1 Sb2

0.3070 0.3359 0.2656 0.3288 0.2540 0.2827a 0.2837 0.3094a 0.3334a 0.3288 0.3358

Fe2

Sb3

1 2 2 2 4 1 2 2 2 4 1

Sb3 Sb4 Sb3 Fe1 Sb4 Fe2 Sb1 Sb3 Sb4 Sb4 Sb3

0.3623a 0.2233 0.2356 0.2534 0.2559 0.2615 0.2656 0.2756 0.2848 0.0531b 0.0782b

Sb4

4 4 4 1 2 2 1 6 2 2 2

Fe2 Fe2 Fe1 La Sb4 Sb3 Sb4 Fe2 Fe1 Fe2 Fe1

0.2356 0.2756 0.3094 0.3623 0.0509 0.0531b 0.0719b 0.2233 0.2827 0.2848 0.3334

a Atoms are not shown in Fig. 9 due to long distance or partial occupancy of the site. b Short distances correspond to partial occupancies of the sites.

possible space groups, P6322, P63/m, P63. The crystal structure was successfully solved via direct methods in space group P63/m. The final least square cycle reveals residual electron densities as low as 3.195/1.46 e/Å3 corresponding to RF 2 ¼ 0.0178. Structural details are given in Table 6a and b. The formula resulting from the

refinement is Nd3Fe3Sb7 (Nd23.1Fe23.1Sb53.8 at.%), which is in good agreement with EMPA (Nd23.2Fe22.8Sb54.0). The structure of Nd3Fe3Sb7 is given in Fig. 13 and shows full atom order. Wyckoff sequence of the atom positions is h4c, which at first glance gives the impression of isotypism with the Cu10Sb3-type (Au10In3). However, s3 can only be regarded as isopointal to Cu10Sb3 because even with similar Wyckoff positions changes in x, y parameters result in a different arrangement of Sb atoms forming walls as can be seen from Fig. 14. In contrast to Cu10Sb3 there are twodimensional channels of Sb with alternating short and long bonds (Fig. 13) typical for the structures of many of the antimonides [2,28]. The crystal structure of s3 can be considered as composed of three unique structural units: (i) centred triangular prisms of RE atoms, (ii) interconnected octahedra of Fe atoms running parallel to [001] (Fig. 13) forming a column of Fe atom clusters along the 6-fold rotation axis, and (iii) Sb ribbons which are running in between (i) and (ii) (Fig. 13). Similar infinite parallel columns exist in the structures of Cu10Sb3 and Ni3Sn-type (S.G. P63/mmc) and are formed by triangular prisms (i) that are shifted against each other by c/2 (central atom at z ¼ ¼ and 3/4 , Fig. 14). Octahedral clusters (ii), which are linked to triangles in Ni3Sn, are completely isolated in Cu10Sb3 and s3.

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Table 4a X-ray single crystal data for Nd2Fe7xSb6y (s2-orthorhombic); standardized with program Structure Tidy [41]. Radiation: MoKa; 2Q range (
) ¼ 22Q  70; u-scans, scan width 2
; Total number of frames and sets: 564 and 11; 140 s/frame; Anisotropic displacement parameters in [102 nm2].

Fig. 7. Crystal structure of Nd2Fe7xSb6y. Fourier map for electron density at 8l (Fe3); a) three dimensional view; b) Projection in yez plane.

From EMPA a homogeneity range corresponding to a Fe/Sb substitution of w1e1.5 at.% is observed for s3. However, lattice parameters and Rietveld refinement do not give any hint towards a solid solution. s3 was not observed in as cast samples annealed directly at 500
C or cooled at a rate of w2
/min from 900
C to 500
C. But if the sample, which has been annealed at 800
C containing this phase, was kept at 500
C for 30 days, the phase was still present. It seems from our observation that s3 remains stable at 700
C, 600
C and 500
C. The decomposition temperature of s3 lies somewhere between 820 and 900
C, as the alloy annealed at 900
C does not contain this phase whilst the alloy annealed at 850
C contains this phase but only in small amounts. Annealing at 800
C of the same alloy increases the amount of s3. Therefore due to improper choice of annealing temperature, this phase was not caught by Zeng et al. [10]. s3 is found to exist in equilibrium with three other ternary compounds s2, s4 and s5 (details in Section 3.2).

Parameter/compound

Nd2Fe7xSb6y (x ¼ 3.04, y ¼ 1.03)

Prototype Space group a; c [nm], Ge standard Z Reflections in refinement Number of variables Mosaicity RF 2 ¼ SjF2o  F2c j/SF2o RInt wR2 GOF Extinction Residual density e/Å3; max; min

Nd2Fe7ySb6y Immm 0.42632(6); 0.43098(7); 2.5823(3) 2 592  4s(Fo) of 646 34 <4.5 0.0324 0.0486 0.0898 1.131 0.0009(3) 2.58; 2.80

Atom parameters Nd in 4i (0, 0, z); z; Occ. U11; U22; U33; Ueq. Fe1 in 2c (½, ½, 0); Occ. U11; U22; U33; Ueq. Fe2 in 4j (½, 0, z); Occ. U11; U22; U33; Ueq. Fe3 in 8l (0, y, z) y; z; Occ. U11; U22; U33; Ueq. Sb1 in 4i (0, 0, z); z; Occ. U11; U22; U33; Ueq. Sb2 in 4j (½, 0, z); Occ. U11; U22; U33; Ueq. Sb3 in 4i (0, 0, z); z; Occ. U11; U22; U33; Ueq.

0.15348(2); 1.01(2) 0.0175(3); 0.0178(5); 0.0144(2); 0.0166(2) 1.01(2) 0.0207(9); 0.023(1); 0.0146(8); 0.0196(4) 0.0513(1); 0.672(9) 0.062(2); 0.021(1); 0.0133(1); 0.0320(9) 0.4432(7); 0.05186(9); 0.404(5) 0.015(1); 0.029(2); 0.0135(9); 0.0192(9) 0.38842(2); 1.01(2) 0.0175(3); 0.0180(6); 0.0135(2); 0.0163(2) 0.25023(2); 1.02(2) 0.0180(3); 0.0181(6); 0.0130(3); 0.0164(2) 0.01678(7); 0.486(4) 0.042(1); 0.0324(9); 0.0199(6); 0.0316(5)

Principal mean square atomic displacements U Nd 0.0178; 0.0175; Fe1 0.0235; 0.0207; Fe2 0.0619; 0.0209; Fe3 0.0288; 0.0154; Sb1 0.0180; 0.0175; Sb2 0.0181; 0.0180; Sb3 0.0425; 0.0324;

0.0144 0.0146 0.0133 0.0135 0.0135 0.0130 0.0199

type [43]. Rietveld refinement of NdFeSb3 annealed at 800
C (4 days) and 500
C (30 days), did not confirm the structure model presented by [42]. However, the observed XRPD pattern was successfully fitted as isotypic to the LaPdSb3-type [5] and corresponding Rietveld refinement data are given in Table 7.

Table 4b Interatomic distances [nm] for Nd2Fe7xSb6y, x ¼ 3.04, y ¼ 1.03 (s2-orthorhombic); standard deviation 0.0004. Nd

Sb1

3.5. Crystal structure of s4-NdFeSb3

Sb2

The crystal structure of NdFeSb3 was recently determined from Rietveld refinement of X-ray powder data [42] and was described as isotypic to CeNiSb3 [22]. Quite recently the crystal structure of REFeSb3 (RE ¼ Pr, Nd, Sm, Gd and Tb) was mentioned as LaPdSb3-

Fe1

a

4 2 2 4 2 1 4 4 2 2 4 8 2

Sb1 Sb2 Sb2 Fe3 Fe2 Fe1 Nd Sb2 Nd Nd Fe2 Fe3 Sb1

0.3220 0.3288 0.3293 0.2645 0.2660 0.2885 0.3220 0.3032 0.3288 0.3293 0.2530 0.2532 0.2885

Sb3

Fe2

8 1 2 2 2 2 2 2 4 1 2 2 1

Sb3 Sb3 Fe3 Fe2 Fe3 Fe3 Fe2 Fe3 Fe1 Nd Sb3 Fe1 Fe2

0.3063 0.0868a 0.2115 0.2313 0.2565 0.2607 0.2766 0.2984 0.3063 0.3535 0.2313 0.2530 0.2653

Fe3

2 2 4 1 1 2 1 1 2 1 1 2 1

Sb1 Sb3 Fe3 Fe3 Sb3 Fe1 Sb3 Sb3 Sb1 Fe3 Fe3 Fe2 Sb3

Short distances correspond to the partial occupancy of the site.

0.2659 0.2766 0.2864 0.0489a 0.2115 0.2532 0.2565 0.2607 0.2645 0.2682 0.2726 0.2864 0.2984

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3.6. Magnetic and transport properties The temperature dependence of the inverse molar magnetic susceptibility of NdFeSb3 is shown in Fig. 15a. Above about 50 K, the susceptibility follows a modified CurieeWeiss (MCW) law with the paramagnetic Curie temperature qp ¼ 9.9(2) K, the effective magnetic moment meff ¼ 3.68(5) mB, and the temperature-independent term c0 ¼ 5.56(2)  104 emu/mol. The experimentally determined effective magnetic moment is very close to the free Ndþ3 ion value of 3.62(4) mB, which shows that Fe atoms do not impart any magnetic influence to the magnetic properties of NdFeSb3. As is apparent from the upper inset to Fig. 15a, NdFeSb3 orders antiferromagnetically below TN ¼ 3.0(1) K. The isothermal magnetization at 1.71 K measured as a function of the magnetic field strength is typical for an antiferromagnetic ground state (see the lower inset to Fig. 15a). Remarkably, a metamagnetic-like transition is observed near 15 kOe. The resistivity data for NdFeSb3 are presented in Fig. 16a. The magnitude and shape of the resistivity curve is typical for rare earth intermetallics. The antiferromagnetic phase transition at 3.0 K manifests itself as a distinct kink in r(T) (see the inset to Fig. 15a). Below 1 K the resistivity curve exhibits a downward curvature that may hint at another phase transition, which could be associated with some spin reorientation. In the paramagnetic region, above about 70 K, the r(T) curve may be represented by the so-called Bloch-Grüneisen-Mott (BGM) expression [44]




rðTÞ ¼ r0 þ Fig. 8. XRPD patterns of RE2Fe5xSb10y (RE ¼ La, Ce, Nd) and Nd2Fe7xSb6y (alloys quenched from 990  10
C): a) tetragonal; b) orthorhombic þ tetragonal c) orthorhombic.

Fig. 9. Atomic environment of La, Sb1, Sb2 and Fe1 in the crystal structure of La2Fe5xSb10y (x ¼ 1.12; y ¼ 5.08). For interatomic distances see Table 3b.

rN 0



 þ 4RT

T

QD

4 QZD =T 0

x5 dx
  KT 3 ; ðex  1Þ 1  ex

where (r0 þ rN 0 ) stands for the sum of the residual resistivity due to static defects in the crystal lattice and the spin-disorder resistivity due to the presence of disordered magnetic moments, respectively. The second term describes the phonon contribution to the total resistivity (QD is the Debye temperature), and the third term represents sed interband scattering processes. Fitting the BGM model to the experimental data of NdFeSb3 one obtains the values: r0 þ rN 0 ¼ 139.2(8) mUcm, QD ¼ 193.6(9) K, R ¼ 0.42(1) mUcm/K and K ¼ 1.23(3)  106 mUcm/K3. Below ca. 70 K, the experimental r(T) curve markedly deviates from the BGM fit, likely due to crystal field contribution to the electrical resistivity that makes the rN 0 term being temperature dependent. The specific heat of NdFeSb3 varies as a function of temperature in a usual sigmoid-shape manner (Fig. 17). A small hump in C(T) centred around 7.0 K is probably due to crystal field effects (Fig. 17b). At higher temperatures, the C/T vs. T2 curve exhibits a straight-line behaviour, observed up to 24 K. From this region one may extrapolate an enhanced Sommerfeld coefficient of about 400 mJ/(mol K2) (see the inset to Fig. 17). The antiferromagnetic transition, as inferred from the magnetization and resistivity data, is clearly corroborated by a pronounced lambda-shaped peak at TN ¼ 3.0 K. The magnetic data obtained for tetragonal Nd2Fe5xSb10y (s2) and isotypic Ce2Fe5xSb10y are presented in Fig. 15b and c, respectively. For both compounds the magnetic susceptibility exhibits a plateau below 30 K and then shows an upturn below about 5 K (see the upper insets). The isothermal magnetization taken at 1.71 K is almost linear with the magnetic field strength (cf. the lower insets) and shows no hysteresis effect. For both compounds, above 50 K the magnetic susceptibility exhibits a modified CurieeWeiss behaviour. The least-squares fit of the MCW law to the experimental data yielded the following values: meff ¼ 9.6(1) mB, qp ¼ 48.1(3) K and c0 ¼ 7.0(5)  103 emu/mol for

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Fig. 10. Groupesubgroup relation for La2Fe5xSb10y (x ¼ 1.12; y ¼ 5.08) and Nd2Fe7xSb6y (x ¼ 3.04; y ¼ 1.03) in Bärnighausen formalism [38,39]. Fe3:4j in Nd2Fe7xSb6y was replaced by Fe3:8l and Sb4:4e and 4j in Nd2Fe7xSb6y are vacant sites (see text).

the Nd-based compound, and meff ¼ 8.6(1) mB, qp ¼ 78.9(4) K and c0 ¼ 5.2(5)  103 emu/mol for the Ce-based phase. As the soderived effective magnetic moments are much larger than the values for the respective free REþ3 ions, some magnetic contribution due to the Fe sublattice becomes obvious. Assuming that the magnetic moments on the Nd ions contribute to the total meff the RusselleSaunders value of 3.63 mB, one obtains a value mFe ¼ 4.2 mB

for the Fe-contribution in Nd2Fe7xSb6y. This magnetic moment is slightly smaller than the theoretical spin-only value of 4.97 mB for an Fe2þ ion. If in Ce2Fe5xSb10y the Fe sublattice contributes the same moment as in the Nd-based counterpart, then the effective magnetic moment associated with Ce ions is 1.7 mB, i.e. it is distinctly smaller than that expected for trivalent cerium (2.54 mB).

Fig. 11. Structural relations among La2Fe5xSb10y, Nd2Fe7xSb6y, Zr3Cu4Si6 and ZrCuSi2.

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N. Nasir et al. / Intermetallics 18 (2010) 2361e2376 Table 6a X-Ray single crystal data for Nd3Fe3Sb7 (s3) standardized with program Structure Tidy [41]. Radiation: MoKa; 2Q range (
): 2  2Q  70; u-scans, scan width 2
; 595 frames; 280 s/frame. Anisotropic displacement parameters in [102 nm2]. Parameter/compound

Nd3Fe3Sb7

Prototype Space group Composition, EMPA at.% Composition from refinement at.% a; c [nm], Ge standard Z Reflections in refinement Number of variables Mosaicity RInt RF 2 ¼ SjF2o  F2c j/SF2o wR2 GOF Extinction Residual density e/Å3; max; min

Nd3Fe3Sb7 P63/m Nd22.5Fe24.3Sb53.1 Nd23.1Fe23.1Sb53.8 1.31808(3); 0.41819(3) 2 983  4s(Fo) of 1029 28 <4.5 0.029 0.018 0.046 1.225 0.0014 3.19; 1.46

Atom parameters Nd1 in 6h (x, y, ¼); x, y U11; U22; U33 U12; Ueq Occ. Fe1 in 6h (x, y, ¼); x, y; Occ. U11; U22; U33 U12; Ueq Sb1 in 2c (1/3, 2/3, ¼); Occ. U11 ¼ U22; U33 U12; Ueq Sb2 in 6h (x, y, ¼); x, y; Occ. U11; U22; U33 U12; Ueq Sb3 in 6h (x, y, ¼); x, y; Occ. U11; U22; U33 U12; Ueq

0.46133(2), 0.18310(2) 0.0113(1), 0.0098(1), 0.0103(1) 0.00571(7); 0.01023(7) 0.998(3) 0.13082(6), 0.07664(6); 1.00(1) 0.0148(3), 0.0123(2), 0.0104(3) 0.0075(2); 0.0121(1) 1.012(6) 0.0116(1), 0.0092(2), 0.00581(6); 0.01081(9) 0.08317(3), 0.27640(3); 0.994(4) 0.0133(1), 0.0115(1), 0.0118(1) 0.00349(9); 0.01340(7) 0.58845(2), 0.02317(2); 1.011(4) 0.0117(1), 0.0098(1), 0.0135(1) 0.00477(9); 0.01196(7)

Principal mean square atomic displacements U Nd1 0.0113, 0.0103, 0.0091 Sb1 0.0116, 0.0116, 0.0092 Sb2 0.0180, 0.0118, 0.0104 Sb3 0.0135, 0.0126, 0.0098 Fe1 0.0148, 0.0113, 0.0103 Fig. 12. Lattice parameters vs. rare earths for RE2Fe5xSb10y (RE ¼ La, Ce, Pr, Nd; tetragonal) and RE2Fe7xSb6y (RE ¼ Pr, Nd, Sm; orthorhombic).

temperatures. As displayed in Fig. 16c, above about 70 K, r(T) may be approximated by the formula The latter finding is in line with the indication from the lattice parameters towards a Ce4þ state. From these arguments one may expect that Ce ions in Ce2Fe5xSb10y have an unstable 4f shell. The latter conjecture finds further support in the behaviour of the electrical resistivity of the compound (Fig. 16c), which is reminiscent of the properties of Ce intermetallics governed by Kondo effect. Apparently, the resistivity of Ce2Fe5xSb10y exhibits a maximum near 30 K followed by a negative slope at higher

Table 5 Lattice parameters for isotypic compounds RE2Fe5xSb10y and RE2Fe7xSb6y (RE ¼ La, Ce, Pr, Nd). Compound

La2Fe5xSb10y Ce2Fe5xSb10y Pr2Fe5xSb10y Nd2Fe5xSb10y Pr2Fe7xSb6y Nd2Fe7xSb6y

Prototype

La2Fe5xSb10y La2Fe5xSb10y La2Fe5xSb10y La2Fe5xSb10y Nd2Fe7xSb6y Nd2Fe7xSb6y

Space group

Lattice parameters, nm a

b

c

I4/mmm I4/mmm I4/mmm I4/mmm Immm Immm

0.43374(3) 0.43098(3) 0.42989(4) 0.42897(2) 0.42808(6) 0.42632(6)

e e e e 0.43164(5) 0.43098(7)

2.6272(7) 2.5994(6) 2.5939(4) 2.5693(4) 2.5956(3) 2.5823(3)






rðTÞ ¼ r0 þ rN 0 þ cph T þ cK lnT where the second term stands for the phonon contribution to the total resistivity, while the third term represents the spin-flip Kondo scattering of conduction electrons on localised magnetic moments. The parameters derived from the least-squares fit are as follows: r0 þ rN 0 ¼ 241.0(2) mUcm, cph ¼ 0.037(4) mUcm/K and cK ¼ 13.0

Table 6b Interatomic distances [nm] for Nd3Fe3Sb7 (s3); standard deviation 0.0004. Nd1-

Sb2-

1 2 2 2 1 1 2 4

Sb4 Sb2 Sb4 Sb3 Sb4 Sb3 Nd1 Nd1

0.3205 0.3208 0.3231 0.3269 0.3288 0.3526 0.3208 0.3208

Sb3-

Sb4-

1 2 1 2 2 1 2

Fe5 Fe5 Fe5 Nd1 Sb4 Nd1 Sb4

0.2620 0.2737 0.3001 0.3269 0.3322 0.3526 0.2964

Fe5-

1 2 1 4 2 1 2

Nd1 Nd1 Nd1 Fe5 Fe5 Sb3 Sb3

0.3205 0.3231 0.3288 0.2578 0.2603 0.2620 0.2737

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Table 7 X-Ray powder diffraction data for NdFeSb3 (s4); structure data standardized with program Structure Tidy [41]. Temperature factors in [102 nm2]).

Fig. 13. Crystal structure of Nd3Fe3Sb7.

(3) mUcm. The enhanced value of the latter coefficient implies a fairly large density of states at the Fermi level, and significant mass enhancement due to interactions of Ce 4f electronic states with conduction electron states. Further studies on the intriguing electrical transport phenomena in Ce2Fe5xSb10y are presently underway and will be reported in a separate article. In contrast to the Ce-based compound, the electrical resistivity of Nd2Fe5xSb10y shows a regular metallic behaviour (Fig. 16b). In the entire temperature range studied, the r(T) curve may be described within the BGM approach. Fitting the BGM model to the experimental data of Nd2Fe5xSb10y one derives the values: r0 þ rN 0 ¼ 197.1(3) mUcm, QD ¼ 167.9(6) K, R ¼ 0.066(2) mUcm/K and K ¼ 6.0(1)  108 mUcm/K3. As the BGM formalism neglects crystal field interactions that likely affect r(T) of Nd2Fe5xSb10y at low temperatures, the above values should be considered as rough estimations only.

Parameter/compound

NdFeSb3

Prototype Space group Composition, EMPA at.% Composition, refinement at.% a; b; c [nm], Ge standard Reflections in refinement 2Q-range Number of variables RF ¼ SjFo  Fcj/SFo RI ¼ SjIo  Icj/SIo RwP ¼ [Swijyoi  ycij2/Swijyoij2]½ RP ¼ Sjyoi  ycij/Sjyoij Re ¼ [(N  P þ C)/Swiy2oi)]½ c2 ¼ (RwP/Re)2

LaPdSb3 Pbcm Nd20.0Fe19.9Sb60.1 Nd20Fe20Sb60 1.2681(4); 0.61659(7); 1.2133(3) 596 8  2Q  100 44 0.053 0.060 0.028 0.021 0.074 14.5

Atom parameters Nd1 in 4c (x, ¼, 0); x Occ.; Biso Nd2 in 4d (x, y, 3/4 ); x, y Occ.; Biso Fe in 8e (x, y, z); x, y, z Occ.; Biso Sb1 in 4c (x, ¼, 0); x Occ.; Biso Sb2 in 4d (x, y, 3/4 ); x, y Occ.; Biso Sb3 in 8e (x, y, z); x, y, z Occ.; Biso Sb4 in 4c (x, ¼, 0); x Occ.; Biso Sb5 in 4d (x, y, 3/4 ); x, y Occ.; Biso

0.6995(2) 1.01(2); 0.74(7) 0.3077(2), 0.2733(5) 1.0(2); 0.86(8) 0.1032(4), 0.0343(9), 0.8579(4) 1.0(2); 1.9(1) 0.9716(2) 1.0(2); 1.31(6) 0.7794(3), 0.2685(7) 1.01(2); 1.3(1) 0.5032(2), 0.5124(4), 0.8768(2) 1.0(2); 0.50(4) 0.2226(3) 1.0(2); 0.61(9) 0.9382(2), 0.8965(4) 1.0(2); 1.01(8)

As documented in Fig. 15d, the magnetic behaviour of Nd3Fe3Sb7 is fairly complex. The compound orders magnetically at about 360 K, likely with a ferri- or ferromagnetic arrangement of both neodymium and iron magnetic moments. This magnetic state becomes unstable around 50 K, and at lower temperatures the magnetization curves measured in zero field cooling (ZFC) and field cooling (FC) regimes display very unusual behaviour. In order to clarify these complex features, neutron diffraction studies are indispensable. The electrical resistivity of Nd3Fe3Sb7 has metallic character (Fig. 16d). Because the compound is in the magnetically ordered state up to the upper temperature limit of the measurements performed, no attempts to analyse r(T) in terms of particular contributions were made. At the hypothetical phase transition at about 50 K the resistivity curve shows a clear kink, which brings about a pronounced anomaly in the temperature derivative of the resistivity (see the inset to Fig. 16d).

Fig. 14. Comparison of structures of Nd3Fe3Sb7 with Cu10Sb3 and Ni3Sn.

Fig. 15. Temperature dependencies of the inverse magnetic susceptibility of a) NdFeSb3 b) Nd2Fe5xSb10y and c) Ce2Fe5xSb10y. The solid lines represent the modified CurieeWeiss fits discussed in the text. The upper insets show the low temperature susceptibility measured in the field of 1 kOe, while the lower insets display the magnetization isotherms taken at 1.71 K with increasing (full symbols) and decreasing (open symbols) magnetic field. d) The magnetization vs. temperature measured for Nd3Fe3Sb7 in a magnetic field of 0.1 kOe upon cooling the specimen in zero (ZFC) and applied field (FC).

Fig. 16. Temperature variation of the electrical resistivities of a) NdFeSb3, b) Nd2Fe5xSb10y, c) Ce2Fe5xSb10y and d) Nd3Fe3Sb7. The inset to a) displays the low temperature part of the electrical resistivity. The inset to b) shows the temperature derivative of the electrical resistivity in the low temperature range. The solid lines in a) and b) are the BlochGrüneisen-Mott fits discussed in the text. The solid line in c) is a Kondo fit (see the text).

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Fig. 17. a) Temperature dependence of the specific heat of NdFeSb3. The inset presents C/T vs. T2. The solid line represents the fit discussed in the text. b) Temperature variation of the C/T ratio at low temperatures on a logarithmic scale.

4. Conclusions Systematic investigations using XRDP, XRSC, LOM and EPMA were made in the NdeFeeSb system and an isothermal section at 800
C was constructed. Five ternary compounds take part in the phase equilibria at 800
C of which the ternary compounds, Nd6Fe13Sb (s1) and NdFe1xSb2 (s5), already known in literature, were confirmed in the present work, whilst the crystal structures for three ternary compounds La2Fe5xSb10y, Nd2Fe7xSb6y (s2), Nd3Fe3Sb7 (s3), and NdFeSb3 (s4) were established in the present investigations. The crystal structure of s2, s3 were determined by single crystal X-ray diffraction. Two different modifications were confirmed for s2: tetragonal is La2Fe5xSb10y-type (S.G. I4/mmm, a ¼ 0.42897(2), c ¼ 2.5693(4)) and orthorhombic is Nd2Fe7xSb6ytype (S.G. Immm, a ¼ 0.42632(6), b ¼ 0.43098(7), c ¼ 2.5823(3)). Ce2Fe5xSb10y was found isotypic to the tetragonal La2Fe5xSb10y-type, while compounds with Pr and Nd were found to adopt both modifications. La2Fe5xSb10y-type is similar to the Zr3Cu4Si6-type with one additional Wyckoff position. Structural relations between the orthorhombic and tetragonal modification and with other structure types were described. s3-Nd3Fe3Sb7 was found to crystallize with a unique structure type (S.G. P63/m, a ¼ 1.31808(3)nm, c ¼ 0.41819(3) nm) and is isopointal to the Cu10Sb3-type. Similarities among the structures of s3-Nd3Fe3Sb7, Cu10Sb3 and Ni3Sn were discussed in detail. The structure of s4NdFeSb3 was solved by Rietveld refinement of the X-ray powder pattern and was found isotypic to LaPdSb3, which is the b-modification of the RECrSb3 type with a doubled c-parameter. NdFeSb3 orders antiferromagnetically below w3.0 K, as manifested in all the bulk characteristics of the compound: temperature variations of the magnetic susceptibility, the specific heat and the electrical resistivity. The latter data hint at another ordereorder phase transition at about 1 K. In this compound the magnetic features are associated exclusively with Nd ions. In contrast, in all the other ternaries studied, likely also the Fe sublattices significantly contribute to the overall magnetic behaviour. As a result, Nd2Fe5xSb10y, Ce2Fe10xSb6y and Nd3Fe3Sb7 exhibit very complex physical properties that call for further studies with the use of other experimental techniques, especially neutron diffraction. Acknowledgments The research reported herein was supported by the Higher Education Commission of Pakistan (HEC) under the scholarship scheme “PhD in Natural & Basic Sciences from Austria”. The work

was also supported by the Austrian-Polish Scientific-Technical Exchange Program under project PL 06/2009. We are thankful to Dr. S. Puchegger for help in EPMA measurements.

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