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New RNiSn4 compounds (R=rare earth): crystal structure of new LuNiSn4 type, magnetic and transport properties
Journal of Alloys and Compounds 296 (2000) 303–311
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New RNiSn 4 compounds (R5rare earth): crystal structure of new LuNiSn 4 type, magnetic and transport properties a a a b c, c R.V. Skolozdra , J.S. Mudryk , L.G. Akselrud , D. Fruchart , D. Gignoux *, J. Pierre , a c L.P. Romaka , D. Schmitt a
Department of Chemistry, I. Franko University, Kyryl and Mephodiy str. 8, 290005 Lviv, Ukraine b ´ , France Laboratoire de Cristallographie, CNRS, BP 166, 38042 Grenoble Cedex c ´ , CNRS, BP 166, 38042 Grenoble Cedex ´ 9, France Laboratoire Louis Neel Received 26 July 1999; accepted 29 July 1999
Abstract A series of new RNiSn 4 compounds (R5Gd–Tm, Lu) has been synthesized. The crystal structure of LuNiSn 4 has been determined. It is a new structure type, described as a commensurate modulated structure with space group Ammm /(ddd) and lattice parameters a 5 4.386 ˚ b 5 27.942 A ˚ and c 5 4.353 A. ˚ The other investigated compounds have the same structure. Magnetization was measured in the A, temperature range 1.5–300 K, and, except for the Dy compound, the resistivity was studied between 4 and 300 K. Moreover, the specific heat of the Er and Lu compounds was studied between 1.2 and 30 K. All compounds with magnetic rare earths order anti´ temperature, which ranges from 3 K (R5Tm) to 27 K (R5Gd). Below T N , metamagnetic transitions ferromagnetically below their Neel are observed. In the compound with Er, the specific heat reveals that, immediately below T N 58.8 K, there is a second transition at 8.5 K. The intermediate phase is likely a modulated structure. 2000 Elsevier Science S.A. All rights reserved. Keywords: Rare earth intermetallics; New crystallographic structure; Magnetic properties; Antiferromagnetic materials
1. Introduction Tin forms many ternary Sn-rich compounds with rare earths and transition metals (.50 at.% Sn) [1], namely the compounds: R 9 Ni 24 Sn 49 (R5Y, La–Sm–Tb, Gd 9 Ni 24 Sn 49 structure type (ST)) [2], RRh 2 Sn 4 (R5La–Sm, NdRh 2 Sn 4 ST) [3], R 7 Co 9 Sn 23 (R5Y, Tb–Er, Ho 7 Co 9 Sn 23 ST) [4], La 3 Co 2 Sn 7 [5] and R 3 Ni 2 Sn 7 [6] (R5La–Nd, La 3 Co 2 Sn 7 ST), and R 2 NiSn 6 (R5Ho, Er, Lu, Lu 2 NiSn 6 ST) [7]. The RM x Sn y phases (x ¯ 1.2–1.5, y ¯ 3.6–4.75) have the greatest number of representatives; they exist with all rare earth elements and with Fe, Co, Ru, Rh, Pd, Os, Ir, and Pt. These phases are indicated as I, II, III, V, and VII and are characterized by closely related structure types [8–13]. The phases of Er with Rh or Os, and of Tm with Os are characterized by the coexistence of superconductivity and magnetism [11]. The RM 12x Sn 12y (x # 0.76, y # 0.21, R5La–Sm, M5Mn, Fe, Co, Ni, Cu, CeNiSi 2 ST) compounds are also widespread. In contrast to other phases, they exhibit a homogeneity range [14–17]. Recently, we *Corresponding author. E-mail address: [email protected] (D. Gignoux)
obtained compounds of approximate composition RNiSn 4 , where R5Gd–Er, Lu. In this paper we report the results of the crystal structure determination and magnetic properties studied by magnetization, electrical resistivity and specific heat measurements.
2. Experimental The samples were prepared by fusion of the elements (purity 99.8, 99.98 and 99.99 wt.% for R, Ni and Sn, respectively) in an electric arc furnace under a purified argon atmosphere. The alloys were subsequently annealed at 770 K for 1 month and cold water quenched.The samples were checked using X-ray powder patterns (DRON-2.0 diffractometer, Fe Ka radiation) and a HCG4A powder diffractometer with Mo Ka radiation. Crystal structure determination for LuNiSn 4 was carried out on a single crystal using the Laue and rotation methods. The intensities were collected using a four-circle DARCH-1 diffractometer (Mo Ka radiation). Magnetization measurements were performed below room temperature using the extraction method under
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Fig. 1. Powder X-ray pattern of ErNiSn 4 (Cu Ka radiation).
applied fields up to 9 T. The electrical resistivity was measured using the classical ac current four-probe method in the temperature range 4–300 K, and the specific heat was determined using an ac technique between 1.2 and 30 K with an absolute error of ,3%.
3. Results and discussion
3.1. Crystal structure We first determined the crystal structure using the powder diffraction method on ErNiSn 4 (Fig. 1). Almost all reflections were well indexed in the orthorhombic system with parameters a 5 4.390(1), b 5 27.925(4) and c 5 ˚ However, different models showed a high 4.357(1) A. R-factor and the structure determination required X-ray diffraction experiments on a single crystal. These were performed on LuNiSn 4 , the only compound of the series that we succeeded in obtaining as a single crystal. As a result of the first stage of the X-ray study on the single crystal, an orthorhombic cell (Laue class mmm) ˚ with cell parameters a 5 8.77, b 5 55.48 and c 5 8.71 A was determined (a more detailed description of the structure determination will be presented in a separate paper). Regular h 1 k 5 2n, h 1 l 5 2n and k 1 l 5 2n extinctions testified to the benefit of F-centered space groups. However, determination of the structures with space groups F222, Fmm2 (Fm2 m, F2 mm) and Fmmm resulted in models of structures containing contradictions: for some
atomic positions a partial (50%) filling and physically ˚ interatomic distances were unjustified short (1–1.5 A) obtained. The presence of irregular extinctions complicated the refinement of the structure by the least-squares method, which was only possible to carry out by a block-diagonal method with step-by-step refinement of the coordinates of each atomic position separately. The magnitude of the disagreement factor, R 5 0.16, also testified to the low reliability of the structure. The dataset of the first stage of the X-ray analysis could possibly be interpreted as an elementary cell eight times smaller in volume and a 5 a9 /
Table 1 Main parameters of the refinement of the LuNiSn 4 modulated structure ˚ a (A) ˚ b (A) ˚ c (A) q ˚ 3) Cell volume (A Calculated density (g / cm 3 ) ˚ Radiation and wavelength (A) Mode of refinement Restrictions Weighting scheme Extinction formalism No. of measured reflections Reflections used for the refinement R(F ) R(F )(hkl000) R(F )(hklm1m2m3) Goodness of fit
4.386(1) 27.742(8) 4.353(1) 1/2 1/2 1/2 529.7(4) 8.883(7) Mo 0.71069 F(hklm1m2m3) F(hklm1m2m3) . 4.00sig(F ) 1 / [sig(F )2 1 0.01F(obs)2 ] Sheldrick 0.00006(3) 896 895 0.055 0.042 0.079 0.93
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Table 2 Modulation parameters for LuNiSn 4 Sn4 (0 0 0) Ux Uy Uz Sn5 (1 /2 0 1 /2) Ux Uy Uz
0.0036(9) 0.0000(1) 0.1223(4)
[sin(x4 1 x5 1 x6) 1 sin(2x4 1 x5 1 x6) 2 sin(x4 2 x5 1 x6) 1 sin(2x4 2 x5 1 x6)] [sin(x4 1 x5 1 x6) 2 sin(2x4 1 x5 1 x6) 1 sin(x4 2 x5 1 x6) 1 sin(2x4 2 x5 1 x6)] [sin(x4 1 x5 1 x6) 2 sin(2x4 1 x5 1 x6) 2 sin(x4 2 x5 1 x6) 2 sin(2x4 2 x5 1 x6)]
0.1228(4) 20.0007(2) 20.0071(9)
[sin(x4 1 x5 1 x6) 1 sin(2x4 1 x5 1 x6) 2 sin(x4 2 x5 1 x6) 1 sin(2x4 2 x5 1 x6)] [sin(x4 1 x5 1 x6) 2 sin(2x4 1 x5 1 x6) 2 sin(x4 2 x5 1 x6) 2 sin(2x4 2 x5 1 x6)] [sin(x4 1 x5 1 x6) 2 sin(2x4 1 x5 1 x6) 1 sin(x4 2 x5 1 x6) 1 sin(2x4 2 x5 1 x6)]
2, b 5 b9 / 2 and c 5 c9 / 2, and with a three-dimensional modulation vector q 5 [1 / 2,1 / 2,1 / 2] decomposed as 1 / 2 0 0; 0 1 / 2 0; 0 0 1 / 2. An average but smaller orthorhombic cell with a 5 ˚ is character4.386(1), b 5 27.742(8) and c 5 4.353(1) A ized by regular extinction with h 1 k 5 2n, which corresponds to possible space groups A222, Amm2 (Am2 m, A2 mm) and Ammm. Using a three-dimensional distribution of the Patterson function allowed us to construct a trial ‘‘average’’ model of the structure within the space group Ammm. All satellite reflections had values hkl111 (abs(m1) 5 abs(m2) 5 abs(m3) 5 1) characteristic of that kind of commensurate modulation. Refinement of the structure by the LS method was carried out with the help of a complex of CSD programs for Windows [21]. The programs realize a method of refinement based on the formalism proposed in Refs. [18,19]. The final parameters of the refinement are given in Table 1. Symmetry invariants for individual positions of the modulated structure with superspace group Ammm / (ddd)(1 /2 1 /2 1 /2), determining a kind of modulated wave, are obtained in the CSD program and are given in Table 2. The calculation of the structure factor for the commensurate modulated structure [18,19] included summation in t i
sections, which in this case had values 1 / 8 0 01h1 / 2 1 / 2 1 / 2j. Refinement of the modulation parameters shows that the essential deviations of atoms from average positions in a cell with space group Ammm is observed for atoms Sn4 and Sn5. The atomic coordinates of the ‘‘average’’ structure of LuNiSn 4 are listed in Table 3. The ‘‘average’’ LuNiSn 4 structure appears closely related to the Lu 2 NiSn 6 structure (SG Amm2, a 5 4.3552, ˚ which, in turn, is a derivative b 5 4.4039, c 5 22.044 A), structure of the GdSn 32x structure type [20]. The Lu 2 NiSn 6 structure consists of a linear combination of
Table 3 Atomic parameters of the ‘‘average’’ LuNiSn 4 structure (space group Ammm) Atom
Site
x
y
z
B (is / eq)
N
Lu Sn1 Sn2 Sn3 Sn4 Sn5 Ni
4i 4j 4j 4i 2a 2d 4j
0 1/2 1/2 0 0 1/2 1/2
0.69271(3) 0.21364(4) 0.60766(4) 0.60707(4) 0 0 0.04851(8)
0 0 0 1/2 0 1/2 0
0.62(2) 0.71(2) 0.75(2) 0.70(2) 0.66(4) 0.69(4) 0.54(3)
4 4 4 4 2 2 4
Fig. 2. Projection of the unit cell of the LuNiSn 4 (a) and Lu 2 NiSn 6 (b) structures.
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Fig. 3. Thermal variation of the reciprocal susceptibility of RNiSn 4 compounds with R5Gd, Tb, Dy. The inset shows the low temperature behavior in more detail.
fragments of the ZrGa 2 (containing fragments of AlB 2 ) and CaF 2 structure types, alternating along the y-axis (Lu 2 NiSn 6 52LuSn 2 1NiSn 2 ). The Lu 2 NiSn 6 unit cell contains two fragments of the ZrGa 2 (232LuSn 2 ) type and two fragments of the CaF 2 (2NiSn 2 ) type, with the NiSn 2 fragments separating the LuNiSn 2 fragments. The ‘‘average’’ LuNiSn 4 structure also consists of fragments of
ZrGa 2 , which are also separated by fragments of the CaF 2 type, however the last fragments are doubled in relation to the NiSn 2 fragments of the Lu 2 NiSn 6 structure. Thus, the LuNiSn 4 unit cell contains two fragments of the ZrGa 2 (232LuSn 2 ) type and two double fragments of the CaF 2 (2Ni 2 Sn 4 ) type (4LuNiSn 4 5232LuSn 2 12Ni 2 Sn 4 ). The projections of both structures are shown in Fig. 2.
Fig. 4. Thermal variation of the reciprocal susceptibility of RNiSn 4 compounds with R5Ho, Er, Tm. The inset shows the low temperature behavior in more detail.
R.V. Skolozdra et al. / Journal of Alloys and Compounds 296 (2000) 303 – 311
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Table 4 Crystallographic and magnetic characteristics of RNiSn 4 compounds R
˚ a (A)
˚ b (A)
˚ c (A)
up (K)
Gd Tb Dy Ho Er Tm Lu a
4.410(1) 4.403(1) 4.397(1) 4.395(1) 4.390(1) 4.395(1) 4.386(1)
28.325(3) 28.179(3) 28.100(2) 28.011(3) 27.925(4) 27.892(9) 27.742(8)
4.369(1) 4.363(1) 4.362(1) 4.359(1) 4.357(1) 4.363(2) 4.353(1)
247 224 217 213 25 29
a
meff (m B )
T N (K)
8.4 10.0 11.00 10.9 9.6 7.7 Pauli paramagnet
26.8(5) 28.6(5) 11.2(5) 11.6(5) 8.8(1) 3.2(5)
Parameters from single crystal data.
The ‘‘average’’ LuNiSn 4 structure is a new representative of a homologous series of structures with the common formula mRX 2 3nX9X 2 , based on a combination of fragments of the ZrGa 2 and CaF 2 structure types. This series belongs to a group of non-uniform linear structures containing fragments of the AlB 2 structure type. X-ray powder patterns of RNiSn 4 alloys show that isotypic compounds are formed with R5Gd–Tm. The reflections are well indexed in the orthorhombic system with the unit cell parameters corresponding to those of LuNiSn 4 , except for several weak reflections.
3.2. Magnetic properties LuNiSn 4 is a Pauli paramagnet, the susceptibility of which weakly depends on temperature. All the other ´ temcompounds order antiferromagnetically at their Neel perature (insets of Figs. 3 and 4 and Table 4). Above T N the magnetic susceptibilities follow the Curie–Weiss law
(Figs. 3 and 4). The deduced effective moments and paramagnetic Curie temperatures are reported in Table 4. The effective moments are generally slightly larger than those of the corresponding free R31 ions. This may originate from the weak polarization of the conduction band by the rare earth atoms. Magnetization curves obtained at 2 K for the compounds with Gd and Tb are reported in Figs. 5 and 6. Although hardly visible, both compounds exhibit metamagnetic processes, amplified by the Arrott plots (M 2 vs. H /M) shown in the insets. Note that, for TbNiSn 4 , two metamagnetic transitions are present. For the other compounds the metamagnetic processes are much more pronounced, in particular at low temperature, as shown in Fig. 7. The difference between the Gd and Tb compounds on the one hand and the other compounds on the other suggests that the magnetic structures are incommensurate in the former, whereas they would be commensurate in the latter. This assumption is enhanced by the fact that the cusp of the thermal variation
Fig. 5. Field dependence of the magnetization of GdNiSn 4 at 2 K. The inset shows the Arrott plot (M 2 vs. H /M) at the same temperature.
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Fig. 6. Field dependence of the magnetization of TbNiSn 4 at 2 K. The inset shows the Arrott plot (M 2 vs. H /M) at the same temperature.
Fig. 7. Field dependence of the magnetization of RNiSn 4 compounds with R5Dy, Ho, Er, Tm at different temperatures.
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309
Fig. 8. Thermal variation of the electrical resistivity of RNiSn 4 compounds with R5Gd, Er, Tm.
of the susceptibility is less pronounced in compounds with Gd and Tb than in the others (see insets of Figs. 3 and 4).
3.3. Electrical resistivity The electrical resistivity was measured between 4 and 300 K for all samples except DyNiSn 4 (Figs. 8 and 9). The ¨ resistivity of LuNiSn 4 follows the Gruneisen law with a T 4 variation at low temperature and a Debye temperature
uD 5 220630 K. No anomaly is observed for the com´ temperature being less than 4 K, pound with Tm, the Neel the lowest measurement temperature. For the other compounds (R5Gd, Tb, Ho and Er) a change of slope is observed at T N . There is good agreement between the values of T N determined from magnetization and resistivity measurements. As reported, the slope of the resistivity just below T N becomes larger as the number of energy levels involved at this temperature becomes smaller [22,23]. Moreover, this slope is smaller for an incommensurate
Fig. 9. Thermal variation of the electrical resistivity of RNiSn 4 compounds with R5Tb, Ho, Lu.
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Fig. 10. Thermal variation of the total heat capacity of LuNiSn 4 and ErNiSn 4 below 15 K. The inset shows details around T N .
structure than for a commensurate structure with equal moments. From a qualitative point of view we can infer that, in compounds with Gd and Tb, more energy levels are involved than in compounds with Ho and Er. This is expected with Gd where no crystal field effects occur and
where the degeneracy at T N is 8. On the contrary, with Ho and Er crystal field effects likely lead to a splitting of the ground state multiplet much larger than T N so that the number of levels involved at T N is small (typically around 2).
Fig. 11. Thermal variation of the magnetic heat capacity of ErNiSn 4 . The inset shows the deduced magnetic entropy.
R.V. Skolozdra et al. / Journal of Alloys and Compounds 296 (2000) 303 – 311
3.4. Specific heat The total heat capacity of ErNiSn 4 and that of the corresponding non-magnetic compound LuNiSn 4 was measured between 1.2 and 30 K. The values are reported up to 15 K in Fig. 10. For LuNiSn 4 , fitting the low temperature variation leads to a small electronic coefficient g ¯ 2 mJ / K 2 -mol and a Debye temperature uD 5 265 K (note that the Debye temperatures deduced from resistivity and specific heat measurements are expected to have the same order of magnitude, but cannot be compared directly as they are determined in different temperature ranges). For the magnetic compound, two distinct transitions are observed at 8.8 and 8.5 K (see inset of Fig. 10). If the former ´ temperature, the latter has is obviously related to the Neel to be associated with a change in magnetic structure. From the narrowness of the high temperature phase, it is suggested that the corresponding magnetic structure is very likely a modulated magnetic structure [24]. However, this phase is stable in a temperature range that is too small to lead to a perceptible effect on the resistivity anomaly at T N (see above). Subtracting the Lu variation from the Er one allows us to appreciate the magnetic contribution to the heat capacity of ErNiSn 4 (Fig. 11). A broad Schottky anomaly can then be seen, centered around 20 K. From the value of the entropy immediately above T N and at 35 K (inset of Fig. 11), it can be deduced that several (at least three) doublets are involved in this broad anomaly, located around 40–60 K above the doublet ground state. This latter conclusion agrees with that deduced from the low temperature resistivity measurements.
References
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[1] R.V. Skolozdra, Stannides of rare earth and transition metals, in: K.A. GschneidnerJr., L. Eyring (Eds.), Handbook on the Physics and
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Chemistry of Rare Earths, Vol. 24, North-Holland, Amsterdam, 1997, p. 199. L.G. Akselrud, L.P. Komarovskaya, R.V. Skolozdra, Dokl. Akad. Nauk Ukr. SSR, Ser. B 3 (1983) 33. M. Meot-Meyer, G. Venturini, B. Malaman, B. Roques, Mater. Res. Bull. 20 (1985) 13. R.V. Skolozdra, O.E. Koretskaya, L.G. Akselrud, Ukr. Fiz. Zh. 31 (1982) 1537. ¨ ¨ W. Dorrscheidt, H. Schafer, J. Less-Common Met. 70 (1986) 1. R.V. Skolozdra, I.V. Yasnitskaya, L.G. Akselrud, L.P. Komarovskaya, Ukr. Fiz. Zh. 32 (1987) 729. R.V. Skolozdra, L.G. Akselrud, O.E. Koretskaya, L.P. Komarovskaya, Dokl. Akad. Nauk Ukr. SSR, Ser. B 12 (1985) 36. G.P. Espinoza, Mater. Res. Bull. 15 (1980) 791. A.S. Cooper, Mater. Res. Bull. 15 (1980) 799. G.P. Espinoza, A.S. Cooper, H. Bartz, J.P. Remeika, Mater. Res. Bull. 15 (1980) 1635. G.P. Espinoza, A.S. Cooper, H. Bartz, Mater. Res. Bull. 17 (1982) 963. J.L. Hodeau, J. Chenavas, M. Marezio, J.P. Remeika, Solid State Commun. 36 (1980) 839. J.L. Hodeau, M. Marezio, J.P. Remeika, Acta Crystallogr. B 40 (1984) 26. R.V. Skolozdra, Yu.K. Gorelenko, E.E. Terletskaya, V.D. Tkachuk, Fiz. Met. Metalloved. 66 (1988) 864. R.V. Skolozdra, S.A. Sadykov, L.P. Komarovskaya, O.K. Kuvandikov, Fiz. Met. Metalloved. 65 (1988) 527. L.P. Komarovskaya, S.A. Sadykov, R.V. Skolozdra, Ukr. Fiz. Zh. 33 (1988) 1249. F.K. Weitzer, K. Hiebl, P. Rogl, Solid State Commun. 82 (1992) 353. A. Yamamoto, Acta Crystallogr. A 38 (1982) 87. F. Parisi, Acta Crystallogr. A 50 (1994) 574. R.V. Skolozdra, L.G. Akselrud, O.E. Koretskaja, L.P. Komarovskaja, Dokl. Akad. Nauk Ukr. SSR, Ser. B N12 (1985) 36. L.G. Akselrud, Yu. Grin, V.K. Pecharsky, P.Yu. Zavalij, B.D. Baumgartner, E. Wolfel, Trans. Tech. Pub. Pt 1 (1993) 335. T. van Peski-Tinbergen, A.J. Dekker, Physica 29 (1963) 917. S. Auffret, J. Pierre, B. Lambert-Andron, R. Madar, E. Houssay, D. Schmitt, E. Siaud, Physica B 173 (1991) 265. D. Gignoux, D. Schmitt, in: K.A. GschneidnerJr., L. Eyring (Eds.), Handbook on the Physics and Chemistry of Rare Earths, Vol. 20, Elsevier, Amsterdam, 1995, p. 293, Chapt. 138.
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New RNiSn 4 compounds (R5rare earth): crystal structure of new LuNiSn 4 type, magnetic and transport properties a a a b c, c R.V. Skolozdra , J.S. Mudryk , L.G. Akselrud , D. Fruchart , D. Gignoux *, J. Pierre , a c L.P. Romaka , D. Schmitt a
Department of Chemistry, I. Franko University, Kyryl and Mephodiy str. 8, 290005 Lviv, Ukraine b ´ , France Laboratoire de Cristallographie, CNRS, BP 166, 38042 Grenoble Cedex c ´ , CNRS, BP 166, 38042 Grenoble Cedex ´ 9, France Laboratoire Louis Neel Received 26 July 1999; accepted 29 July 1999
Abstract A series of new RNiSn 4 compounds (R5Gd–Tm, Lu) has been synthesized. The crystal structure of LuNiSn 4 has been determined. It is a new structure type, described as a commensurate modulated structure with space group Ammm /(ddd) and lattice parameters a 5 4.386 ˚ b 5 27.942 A ˚ and c 5 4.353 A. ˚ The other investigated compounds have the same structure. Magnetization was measured in the A, temperature range 1.5–300 K, and, except for the Dy compound, the resistivity was studied between 4 and 300 K. Moreover, the specific heat of the Er and Lu compounds was studied between 1.2 and 30 K. All compounds with magnetic rare earths order anti´ temperature, which ranges from 3 K (R5Tm) to 27 K (R5Gd). Below T N , metamagnetic transitions ferromagnetically below their Neel are observed. In the compound with Er, the specific heat reveals that, immediately below T N 58.8 K, there is a second transition at 8.5 K. The intermediate phase is likely a modulated structure. 2000 Elsevier Science S.A. All rights reserved. Keywords: Rare earth intermetallics; New crystallographic structure; Magnetic properties; Antiferromagnetic materials
1. Introduction Tin forms many ternary Sn-rich compounds with rare earths and transition metals (.50 at.% Sn) [1], namely the compounds: R 9 Ni 24 Sn 49 (R5Y, La–Sm–Tb, Gd 9 Ni 24 Sn 49 structure type (ST)) [2], RRh 2 Sn 4 (R5La–Sm, NdRh 2 Sn 4 ST) [3], R 7 Co 9 Sn 23 (R5Y, Tb–Er, Ho 7 Co 9 Sn 23 ST) [4], La 3 Co 2 Sn 7 [5] and R 3 Ni 2 Sn 7 [6] (R5La–Nd, La 3 Co 2 Sn 7 ST), and R 2 NiSn 6 (R5Ho, Er, Lu, Lu 2 NiSn 6 ST) [7]. The RM x Sn y phases (x ¯ 1.2–1.5, y ¯ 3.6–4.75) have the greatest number of representatives; they exist with all rare earth elements and with Fe, Co, Ru, Rh, Pd, Os, Ir, and Pt. These phases are indicated as I, II, III, V, and VII and are characterized by closely related structure types [8–13]. The phases of Er with Rh or Os, and of Tm with Os are characterized by the coexistence of superconductivity and magnetism [11]. The RM 12x Sn 12y (x # 0.76, y # 0.21, R5La–Sm, M5Mn, Fe, Co, Ni, Cu, CeNiSi 2 ST) compounds are also widespread. In contrast to other phases, they exhibit a homogeneity range [14–17]. Recently, we *Corresponding author. E-mail address: [email protected] (D. Gignoux)
obtained compounds of approximate composition RNiSn 4 , where R5Gd–Er, Lu. In this paper we report the results of the crystal structure determination and magnetic properties studied by magnetization, electrical resistivity and specific heat measurements.
2. Experimental The samples were prepared by fusion of the elements (purity 99.8, 99.98 and 99.99 wt.% for R, Ni and Sn, respectively) in an electric arc furnace under a purified argon atmosphere. The alloys were subsequently annealed at 770 K for 1 month and cold water quenched.The samples were checked using X-ray powder patterns (DRON-2.0 diffractometer, Fe Ka radiation) and a HCG4A powder diffractometer with Mo Ka radiation. Crystal structure determination for LuNiSn 4 was carried out on a single crystal using the Laue and rotation methods. The intensities were collected using a four-circle DARCH-1 diffractometer (Mo Ka radiation). Magnetization measurements were performed below room temperature using the extraction method under
0925-8388 / 00 / $ – see front matter 2000 Elsevier Science S.A. All rights reserved. PII: S0925-8388( 99 )00548-4
304
R.V. Skolozdra et al. / Journal of Alloys and Compounds 296 (2000) 303 – 311
Fig. 1. Powder X-ray pattern of ErNiSn 4 (Cu Ka radiation).
applied fields up to 9 T. The electrical resistivity was measured using the classical ac current four-probe method in the temperature range 4–300 K, and the specific heat was determined using an ac technique between 1.2 and 30 K with an absolute error of ,3%.
3. Results and discussion
3.1. Crystal structure We first determined the crystal structure using the powder diffraction method on ErNiSn 4 (Fig. 1). Almost all reflections were well indexed in the orthorhombic system with parameters a 5 4.390(1), b 5 27.925(4) and c 5 ˚ However, different models showed a high 4.357(1) A. R-factor and the structure determination required X-ray diffraction experiments on a single crystal. These were performed on LuNiSn 4 , the only compound of the series that we succeeded in obtaining as a single crystal. As a result of the first stage of the X-ray study on the single crystal, an orthorhombic cell (Laue class mmm) ˚ with cell parameters a 5 8.77, b 5 55.48 and c 5 8.71 A was determined (a more detailed description of the structure determination will be presented in a separate paper). Regular h 1 k 5 2n, h 1 l 5 2n and k 1 l 5 2n extinctions testified to the benefit of F-centered space groups. However, determination of the structures with space groups F222, Fmm2 (Fm2 m, F2 mm) and Fmmm resulted in models of structures containing contradictions: for some
atomic positions a partial (50%) filling and physically ˚ interatomic distances were unjustified short (1–1.5 A) obtained. The presence of irregular extinctions complicated the refinement of the structure by the least-squares method, which was only possible to carry out by a block-diagonal method with step-by-step refinement of the coordinates of each atomic position separately. The magnitude of the disagreement factor, R 5 0.16, also testified to the low reliability of the structure. The dataset of the first stage of the X-ray analysis could possibly be interpreted as an elementary cell eight times smaller in volume and a 5 a9 /
Table 1 Main parameters of the refinement of the LuNiSn 4 modulated structure ˚ a (A) ˚ b (A) ˚ c (A) q ˚ 3) Cell volume (A Calculated density (g / cm 3 ) ˚ Radiation and wavelength (A) Mode of refinement Restrictions Weighting scheme Extinction formalism No. of measured reflections Reflections used for the refinement R(F ) R(F )(hkl000) R(F )(hklm1m2m3) Goodness of fit
4.386(1) 27.742(8) 4.353(1) 1/2 1/2 1/2 529.7(4) 8.883(7) Mo 0.71069 F(hklm1m2m3) F(hklm1m2m3) . 4.00sig(F ) 1 / [sig(F )2 1 0.01F(obs)2 ] Sheldrick 0.00006(3) 896 895 0.055 0.042 0.079 0.93
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305
Table 2 Modulation parameters for LuNiSn 4 Sn4 (0 0 0) Ux Uy Uz Sn5 (1 /2 0 1 /2) Ux Uy Uz
0.0036(9) 0.0000(1) 0.1223(4)
[sin(x4 1 x5 1 x6) 1 sin(2x4 1 x5 1 x6) 2 sin(x4 2 x5 1 x6) 1 sin(2x4 2 x5 1 x6)] [sin(x4 1 x5 1 x6) 2 sin(2x4 1 x5 1 x6) 1 sin(x4 2 x5 1 x6) 1 sin(2x4 2 x5 1 x6)] [sin(x4 1 x5 1 x6) 2 sin(2x4 1 x5 1 x6) 2 sin(x4 2 x5 1 x6) 2 sin(2x4 2 x5 1 x6)]
0.1228(4) 20.0007(2) 20.0071(9)
[sin(x4 1 x5 1 x6) 1 sin(2x4 1 x5 1 x6) 2 sin(x4 2 x5 1 x6) 1 sin(2x4 2 x5 1 x6)] [sin(x4 1 x5 1 x6) 2 sin(2x4 1 x5 1 x6) 2 sin(x4 2 x5 1 x6) 2 sin(2x4 2 x5 1 x6)] [sin(x4 1 x5 1 x6) 2 sin(2x4 1 x5 1 x6) 1 sin(x4 2 x5 1 x6) 1 sin(2x4 2 x5 1 x6)]
2, b 5 b9 / 2 and c 5 c9 / 2, and with a three-dimensional modulation vector q 5 [1 / 2,1 / 2,1 / 2] decomposed as 1 / 2 0 0; 0 1 / 2 0; 0 0 1 / 2. An average but smaller orthorhombic cell with a 5 ˚ is character4.386(1), b 5 27.742(8) and c 5 4.353(1) A ized by regular extinction with h 1 k 5 2n, which corresponds to possible space groups A222, Amm2 (Am2 m, A2 mm) and Ammm. Using a three-dimensional distribution of the Patterson function allowed us to construct a trial ‘‘average’’ model of the structure within the space group Ammm. All satellite reflections had values hkl111 (abs(m1) 5 abs(m2) 5 abs(m3) 5 1) characteristic of that kind of commensurate modulation. Refinement of the structure by the LS method was carried out with the help of a complex of CSD programs for Windows [21]. The programs realize a method of refinement based on the formalism proposed in Refs. [18,19]. The final parameters of the refinement are given in Table 1. Symmetry invariants for individual positions of the modulated structure with superspace group Ammm / (ddd)(1 /2 1 /2 1 /2), determining a kind of modulated wave, are obtained in the CSD program and are given in Table 2. The calculation of the structure factor for the commensurate modulated structure [18,19] included summation in t i
sections, which in this case had values 1 / 8 0 01h1 / 2 1 / 2 1 / 2j. Refinement of the modulation parameters shows that the essential deviations of atoms from average positions in a cell with space group Ammm is observed for atoms Sn4 and Sn5. The atomic coordinates of the ‘‘average’’ structure of LuNiSn 4 are listed in Table 3. The ‘‘average’’ LuNiSn 4 structure appears closely related to the Lu 2 NiSn 6 structure (SG Amm2, a 5 4.3552, ˚ which, in turn, is a derivative b 5 4.4039, c 5 22.044 A), structure of the GdSn 32x structure type [20]. The Lu 2 NiSn 6 structure consists of a linear combination of
Table 3 Atomic parameters of the ‘‘average’’ LuNiSn 4 structure (space group Ammm) Atom
Site
x
y
z
B (is / eq)
N
Lu Sn1 Sn2 Sn3 Sn4 Sn5 Ni
4i 4j 4j 4i 2a 2d 4j
0 1/2 1/2 0 0 1/2 1/2
0.69271(3) 0.21364(4) 0.60766(4) 0.60707(4) 0 0 0.04851(8)
0 0 0 1/2 0 1/2 0
0.62(2) 0.71(2) 0.75(2) 0.70(2) 0.66(4) 0.69(4) 0.54(3)
4 4 4 4 2 2 4
Fig. 2. Projection of the unit cell of the LuNiSn 4 (a) and Lu 2 NiSn 6 (b) structures.
306
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Fig. 3. Thermal variation of the reciprocal susceptibility of RNiSn 4 compounds with R5Gd, Tb, Dy. The inset shows the low temperature behavior in more detail.
fragments of the ZrGa 2 (containing fragments of AlB 2 ) and CaF 2 structure types, alternating along the y-axis (Lu 2 NiSn 6 52LuSn 2 1NiSn 2 ). The Lu 2 NiSn 6 unit cell contains two fragments of the ZrGa 2 (232LuSn 2 ) type and two fragments of the CaF 2 (2NiSn 2 ) type, with the NiSn 2 fragments separating the LuNiSn 2 fragments. The ‘‘average’’ LuNiSn 4 structure also consists of fragments of
ZrGa 2 , which are also separated by fragments of the CaF 2 type, however the last fragments are doubled in relation to the NiSn 2 fragments of the Lu 2 NiSn 6 structure. Thus, the LuNiSn 4 unit cell contains two fragments of the ZrGa 2 (232LuSn 2 ) type and two double fragments of the CaF 2 (2Ni 2 Sn 4 ) type (4LuNiSn 4 5232LuSn 2 12Ni 2 Sn 4 ). The projections of both structures are shown in Fig. 2.
Fig. 4. Thermal variation of the reciprocal susceptibility of RNiSn 4 compounds with R5Ho, Er, Tm. The inset shows the low temperature behavior in more detail.
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307
Table 4 Crystallographic and magnetic characteristics of RNiSn 4 compounds R
˚ a (A)
˚ b (A)
˚ c (A)
up (K)
Gd Tb Dy Ho Er Tm Lu a
4.410(1) 4.403(1) 4.397(1) 4.395(1) 4.390(1) 4.395(1) 4.386(1)
28.325(3) 28.179(3) 28.100(2) 28.011(3) 27.925(4) 27.892(9) 27.742(8)
4.369(1) 4.363(1) 4.362(1) 4.359(1) 4.357(1) 4.363(2) 4.353(1)
247 224 217 213 25 29
a
meff (m B )
T N (K)
8.4 10.0 11.00 10.9 9.6 7.7 Pauli paramagnet
26.8(5) 28.6(5) 11.2(5) 11.6(5) 8.8(1) 3.2(5)
Parameters from single crystal data.
The ‘‘average’’ LuNiSn 4 structure is a new representative of a homologous series of structures with the common formula mRX 2 3nX9X 2 , based on a combination of fragments of the ZrGa 2 and CaF 2 structure types. This series belongs to a group of non-uniform linear structures containing fragments of the AlB 2 structure type. X-ray powder patterns of RNiSn 4 alloys show that isotypic compounds are formed with R5Gd–Tm. The reflections are well indexed in the orthorhombic system with the unit cell parameters corresponding to those of LuNiSn 4 , except for several weak reflections.
3.2. Magnetic properties LuNiSn 4 is a Pauli paramagnet, the susceptibility of which weakly depends on temperature. All the other ´ temcompounds order antiferromagnetically at their Neel perature (insets of Figs. 3 and 4 and Table 4). Above T N the magnetic susceptibilities follow the Curie–Weiss law
(Figs. 3 and 4). The deduced effective moments and paramagnetic Curie temperatures are reported in Table 4. The effective moments are generally slightly larger than those of the corresponding free R31 ions. This may originate from the weak polarization of the conduction band by the rare earth atoms. Magnetization curves obtained at 2 K for the compounds with Gd and Tb are reported in Figs. 5 and 6. Although hardly visible, both compounds exhibit metamagnetic processes, amplified by the Arrott plots (M 2 vs. H /M) shown in the insets. Note that, for TbNiSn 4 , two metamagnetic transitions are present. For the other compounds the metamagnetic processes are much more pronounced, in particular at low temperature, as shown in Fig. 7. The difference between the Gd and Tb compounds on the one hand and the other compounds on the other suggests that the magnetic structures are incommensurate in the former, whereas they would be commensurate in the latter. This assumption is enhanced by the fact that the cusp of the thermal variation
Fig. 5. Field dependence of the magnetization of GdNiSn 4 at 2 K. The inset shows the Arrott plot (M 2 vs. H /M) at the same temperature.
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Fig. 6. Field dependence of the magnetization of TbNiSn 4 at 2 K. The inset shows the Arrott plot (M 2 vs. H /M) at the same temperature.
Fig. 7. Field dependence of the magnetization of RNiSn 4 compounds with R5Dy, Ho, Er, Tm at different temperatures.
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309
Fig. 8. Thermal variation of the electrical resistivity of RNiSn 4 compounds with R5Gd, Er, Tm.
of the susceptibility is less pronounced in compounds with Gd and Tb than in the others (see insets of Figs. 3 and 4).
3.3. Electrical resistivity The electrical resistivity was measured between 4 and 300 K for all samples except DyNiSn 4 (Figs. 8 and 9). The ¨ resistivity of LuNiSn 4 follows the Gruneisen law with a T 4 variation at low temperature and a Debye temperature
uD 5 220630 K. No anomaly is observed for the com´ temperature being less than 4 K, pound with Tm, the Neel the lowest measurement temperature. For the other compounds (R5Gd, Tb, Ho and Er) a change of slope is observed at T N . There is good agreement between the values of T N determined from magnetization and resistivity measurements. As reported, the slope of the resistivity just below T N becomes larger as the number of energy levels involved at this temperature becomes smaller [22,23]. Moreover, this slope is smaller for an incommensurate
Fig. 9. Thermal variation of the electrical resistivity of RNiSn 4 compounds with R5Tb, Ho, Lu.
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Fig. 10. Thermal variation of the total heat capacity of LuNiSn 4 and ErNiSn 4 below 15 K. The inset shows details around T N .
structure than for a commensurate structure with equal moments. From a qualitative point of view we can infer that, in compounds with Gd and Tb, more energy levels are involved than in compounds with Ho and Er. This is expected with Gd where no crystal field effects occur and
where the degeneracy at T N is 8. On the contrary, with Ho and Er crystal field effects likely lead to a splitting of the ground state multiplet much larger than T N so that the number of levels involved at T N is small (typically around 2).
Fig. 11. Thermal variation of the magnetic heat capacity of ErNiSn 4 . The inset shows the deduced magnetic entropy.
R.V. Skolozdra et al. / Journal of Alloys and Compounds 296 (2000) 303 – 311
3.4. Specific heat The total heat capacity of ErNiSn 4 and that of the corresponding non-magnetic compound LuNiSn 4 was measured between 1.2 and 30 K. The values are reported up to 15 K in Fig. 10. For LuNiSn 4 , fitting the low temperature variation leads to a small electronic coefficient g ¯ 2 mJ / K 2 -mol and a Debye temperature uD 5 265 K (note that the Debye temperatures deduced from resistivity and specific heat measurements are expected to have the same order of magnitude, but cannot be compared directly as they are determined in different temperature ranges). For the magnetic compound, two distinct transitions are observed at 8.8 and 8.5 K (see inset of Fig. 10). If the former ´ temperature, the latter has is obviously related to the Neel to be associated with a change in magnetic structure. From the narrowness of the high temperature phase, it is suggested that the corresponding magnetic structure is very likely a modulated magnetic structure [24]. However, this phase is stable in a temperature range that is too small to lead to a perceptible effect on the resistivity anomaly at T N (see above). Subtracting the Lu variation from the Er one allows us to appreciate the magnetic contribution to the heat capacity of ErNiSn 4 (Fig. 11). A broad Schottky anomaly can then be seen, centered around 20 K. From the value of the entropy immediately above T N and at 35 K (inset of Fig. 11), it can be deduced that several (at least three) doublets are involved in this broad anomaly, located around 40–60 K above the doublet ground state. This latter conclusion agrees with that deduced from the low temperature resistivity measurements.
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