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Isostructural phase transition in the GdPdAl single crystals
Journal of Alloys and Compounds 348 (2003) 65–71
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Isostructural phase transition in the GdPdAl single crystals ¨ b , E. Talik a , M. Skutecka a , J. Deniszczyk c J. Kusz a , *, H. Bohm a
Institute of Physics, University of Silesia, Uniwersytecka 4, 40 -007 Katowice, Poland b ¨ Gewissenschaften der Universitat ¨ , 55099 Mainz, Germany Institut f ur c Institute of Physics and Chemistry of Metals, University of Silesia, 40 -007 Katowice, Poland Received 22 May 2002; received in revised form 11 June 2002; accepted 11 June 2002
Abstract At 180 K, single crystals of the intermetallic ternary compound GdPdAl undergo an isostructural phase transition from the high temperature hexagonal ZrNiAl-type structure to the low temperature hexagonal structure. The lattice parameters for temperatures neighbouring the phase transition exhibit a hysteresis on heating and cooling which is indicative of a first-order phase transition. In order to understand this phase transition the crystal structure was determined on a single crystal for a few degrees below and above 180 K. Also X-ray photoelectron spectra were measured at 192 K and 173 K and compared with spectra simulated with the help of band structure calculations. 2002 Elsevier Science B.V. All rights reserved. Keywords: Rare earth compounds; Crystal structure; Phase transition; Photoelectron spectroscopy PACS: 71.20; 73.20
1. Introduction The stable crystal structures of the ternary intermetallic rare-earth aluminides have the hexagonal ZrNiAl-type and the orthorhombic TiNiSi-type structure. However, the heavy rare-earth RPdAl compounds were found to crystallize in both structures [1–4]. For example, a sample of TbPdAl annealed at 1050 8C for 120 h and rapidly quenched to room temperature crystallizes in the hexagonal ZrNiAl-type structure as a metastable high-temperature modification (HTM). The stable low temperature modification (LTM) which crystallizes in the orthorhombic TiNiSi-type structure was prepared by annealing as-cast material at 900 8C for 120 h. It is interesting that both the high (HTM) and low temperature modification (LTM) of TbPdAl undergo two ´ successive magnetic phase transitions with the same Neel ¨ temperatures [2]. Donni and co-workers [2] found that only the HTM phase showed a first-order isostructural phase transition from HTM I (at higher temperature) to HTM II *Corresponding author. Fax: 148-32-588-431. E-mail address: [email protected] (J. Kusz).
(at lower temperature) at 106 K (on heating) and at 91 K (on cooling), which can be seen as a jump in the hexagonal lattice parameters. A similar behaviour of the lattice parameters and of the electrical resistivity was observed for isostructural GdNiAl single crystals at 220 K [5,6]. When the sample was cooled down, a rapid jump in the hexagonal lattice parameters has been observed: a decrease in the parameter a and an increase in the parameter c. The structures in both HTM I ] and HTM II phases are of the ZrNiAl-type (P62m) and only rapid changes in the inter-atomic distances have been observed [6]. For GdNiAl, the X-ray diffraction patterns of powder samples obtained at low temperatures were all indexed on the basis of the hexagonal cell [5,6]. Recently, we observed the same rapid jump of the electrical resistivity and the lattice parameters on GdPdAl single crystals at about 180 K [1]. Also, the contraction of the lattice parameter a and a dilatation of the lattice parameter c were observed when the sample was cooled. But in contrast to GdNiAl, all powdered fragments of the crystal have also some peaks related to the orthorhombic TiNiSi structure. The single crystal structure was determined below and above 180 K. In order to understand
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this phase transition the X-ray photoelectron spectra were measured at 192 and 173 K and the spectra were simulated on the basis of theoretical electronic structure calculations.
2. Experimental GdPdAl single crystals were grown under an argon atmosphere by the Czochralski method from a levitated melt using high purity starting materials [1]. The compounds obtained were identified by X-ray powder diffraction. In all powdered fragments of the crystal, some peaks related to the orthorhombic TiNiSi structure were observed beside the peaks related to the hexagonal ZrNiAl structure [1]. For the single crystal X-ray analysis, small crystals of GdPdAl were isolated by mechanical fragmentation. Laue photographs of these crystals were taken in order to select
a crystal of good quality. In contrast to the powdered fragments of the crystals we found only crystals with the hexagonal ZrNiAl structure. Some of these single crystals were identified by electron microprobe analysis. A small single crystal (0.0830.1630.21 mm 3 ) of good quality was used to collect sets of diffraction data on a four-circle KM4 diffractometer with graphite-monochromatized Mo Ka radiation. For low temperature measurements a cool, dry nitrogen gas stream (Oxford Cryosystems equipment) was used. The temperature stability was better than 60.1 K. The lattice parameters a and c determined from 90 reflections are shown in Fig. 1. The data collection of intensities was performed at 300, 250, 220, 190, 150, 120 and 100 K. The intensities of two Bragg reflections were monitored every hour during the data collection. A semi-empirical psi-scan absorption correction was made because the absorption coefficient m is equal to 23 mm 21 . The structures were solved using the ] program SHELXL97 [11]. The space group P6m2 does not change below the phase transition. Details of the data collection for single crystals are presented in Table 1. The X-ray photoelectron spectra were obtained with the monochromatized Al Ka radiation using a Physical Electronics Spectrometer PHI 5700 / 660. The energy spectra of the electrons were analysed by a hemi-spherical mirror analyser with an energy resolution of about 0.3 eV. The Fermi level was referred to the gold 4f binding energy at 84 eV.
3. Results and discussion
3.1. Lattice parameter and crystal structure
Fig. 1. The variation of the lattice parameters a and c on heating and cooling.
For GdPdAl the lattice parameters a and c for temperatures neighbouring the phase transition (180 K) exhibit a hysteresis on heating and cooling (Fig. 1). This hysteresis is indicative of a first-order phase transition. The rapid change in the lattice parameters is due to the temperatureinduced transition from the hexagonal ZrNiAl structure (HTM I) to the hexagonal ZrNiAl structure (HTM II). A contraction of the lattice parameter a (decrease of 0.7%) and a dilatation of the lattice parameter c (increase of 1.3%) were observed when the sample was cooled down. For comparison, the decrease in the lattice parameter a is 1.0 and 0.6% and the increase in the c lattice parameter is 1.9 and 1.0%, respectively for TbPdAl and GdNiAl [2,6]. The decrease in the volume is small, being 0.7, 0.2 and 0.2%, respectively for GdPdAl, TbPdAl and GdNiAl. For a first-order phase transition, which occurs through the mechanism of nucleation and growth, one would expect a change in symmetry. However, the data clearly show that the structure remains hexagonal with the same space group. It should also be mentioned that in all powdered
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Table 1 ] Details of data collection, refinement and structural parameters for GdPdAl for the HTM I (T .180 K) and HTM II phase in space group P62m, z53 Temperature (K) ˚ Cell parameter a (A) ˚ Cell parameter c (A) Axial factor c /a ˚ 3) Volume (A Range of data collection
Scan mode No. of measured reflections Space group No. of unique reflections R(int) R(sigma) Number of variables Extinction ( g310 3 ) Atom parameters Gd in 3g, [x,0,0]; x ˚ 3) Ueq (A Al in 3f, [x,0,0]; x ˚ 3) Ueq (A Pd1 in 1b, [0,0,1 / 2] Ueq (A3 ) Pd2 in 2c, [1 / 3,2 / 3,0] ˚ 3) Ueq (A R1 wR 2 Goodness-of-fit
100 7.1007(8) 4.1157(10) 0.5796 179.71 u #508 0#h#13 213#k#15 0#h#8 v -2u 1865
120 7.1041(8) 4.1157(10) 0.5793 179.88 u #508 0#h#13 213#k#15 0#h#8 v -2u 1862
150 7.1106(8) 4.1115(10) 0.5782 180.03 u #508 0#h#13 213#k#15 0#h#8 v -2u 1859
190 7.1737(11) 4.0527(7) 0.5649 180.62 u #508 0#h#13 213#k#15 0#h#8 v -2u 1857
220 7.1810(8) 4.0475(10) 0.5636 180.75 u #508 0#h#13 213#k#15 0#h#8 v -2u 1858
250 7.1883(11) 4.0456(7) 0.5628 181.04 u #508 0#h#13 213#k#15 0#h#8 v -2u 1858
300 7.1992(8) 4.0398(9) 0.5611 181.33 u #508 0#h#13 213#k#15 0#h#8 v -2u 1932
] P62m 664
] P62m 663
] P62m 662
] P62m 661
] P62m 662
] P62m 662
] P62m 686
0.050 0.034 14 0.024(2)
0.049 0.032 14 0.025(2)
0.050 0.034 14 0.021(2)
0.047 0.033 14 0.025(2)
0.048 0.033 14 0.027(2)
0.048 0.033 14 0.027(2)
0.046 0.032 14 0.028(2)
0.58242(5) 0.00708(7) 0.2346(4) 0.00853(4) 0.00071(1)
0.58246(5) 0.00708(7) 0.2344(4) 0.0085(4) 0.0071(1)
0.58245(5) 0.00817(8) 0.2348(4) 0.0087(3) 0.0083(1)
0.58274(6) 0.00946(8) 0.2362(4) 0.0104(4) 0.0100(1)
0.58275(6) 0.01035(8) 0.2363(4) 0.0117(4) 0.0111(2)
0.58280(6) 0.01100(8) 0.2363(4) 0.0128(4) 0.0121(1)
0.58281(5) 0.01227(8) 0.2369(4) 0.0141(4) 0.0135(2)
0.0078(1)
0.0078(1)
0.0089(1)
0.0102(1)
0.0113(1)
0.0122(1)
0.0138(1)
0.029 0.070 1.28
0.029 0.070 1.28
0.029 0.072 1.29
0.029 0.074 1.29
0.029 0.074 1.28
0.029 0.071 1.21
0.030 0.071 1.20
Ueq 5 kUu l, equivalent isotropic temperature factor; R 1 5 S(uFo u 2 uFc u)2 / S(uFo u)2 , discrepancy factor; wR 2 5 (S(w(F 2o 2 F 2c )2 ) / S(w(Fo )2 )1 / 2 ; w 5 1 / (s 2 (F o2 ) 1 (a P)2 ) where P 5 (2F c2 1 max(F o2 , 0)) / 3.
fragments of the GdPdAl crystal, some peaks related to the orthorhombic TiNiSi structure were also observed beside the peaks related to the hexagonal ZrNiAl structure, as was reported previously [1]. The structure determinations carried out on a single crystal below and above 180 K should reveal the structural changes at the transition, and in particular, they should reveal the change in the bond lengths. The discrepancy factors R 1 for all unique reflections are 2.93, 2.93, 2.98, 2.87, 3.04, 2.91 and 3.05% for 100, 120, 150, 190, 220, 250 and 300 K, respectively. The structural parameters of the phases above (HTM I) and below the phase transition (HTM II) are shown in Table 1. The projection of the structure along the hexagonal c-axis is shown in Fig. 2. The structure consists of two layers perpendicular to the c-axis. One layer (z50) contains Al- and Pd2-atoms, the other one Gd- and Pd1-atoms. In Fig. 3, these layers are depicted separately. The Al-atoms form trigonal prisms with Pd1 in the centre, the Gd-atoms form trigonal prisms with Pd2 in the centre. In Fig. 2, only the intra-layer bonds between the layers are shown, whereas the inter-layer bonds are depicted in Fig. 3. At the phase transition, the Gd- and Al-atoms move, whereas the Pd1- and Pd2-atoms remain fixed on their special positions (Table 1). This
results in a shortening of the bonds for Gd–Gd, for Gd–Pd1 and for Al–Al upon cooling (Table 2). The movement of the Al-atoms and the shortening of the Gd–Pd1 bonds are indicated by arrows in Fig. 3. Whereas the c lattice parameter expands on cooling (Fig. 1), the Al–Pd1 bond in the trigonal prism with Pd1 in the centre
Fig. 2. The projection along the c-axis of the structure of GdPdAl (four unit cells); only intra-layer bonds are shown.
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Fig. 3. The two layers of the structure of GdPdAl (four unit cells) at level z50.5 (a) and z50 (b); only inter-layer bonds are shown. The arrows indicate the movement of the Al-atoms and the shortening of the bonds upon cooling (strongly exaggerated).
remains almost constant, because the expansion of the prism is compensated by the contraction of the Al 3 -group within the plane. The same argument is true for the Gd–Pd2 bond. Although the trigonal prism of Gd with Pd2 in the centre expands in the c direction, the Gd–Pd2 bond remains constant because the plane Gd 3 -group contracts. The contraction of the planar groups within the plane leads to a decrease in the lattice parameter a. An overview of the change in the bond lengths at the phase transition is given in Fig. 4. On the other hand, there is neither a hexagonal nor a ] trigonal space group (besides P62m) which meets the crystal chemical requirements of the structure. The other alternative to hexagonal would be an orthorhombic deformation (e.g. Pm2m) and a subsequent threefold twinning. This appears not to be very likely, since we were ] able to refine the structure in P62m with an R-value of less than 3.00% (Table 1). Therefore we must assume that there is no change in space group at the transition and the phase transition must be called isostructural. Similar ¨ results have been reported so far by Donni et al. [2] for TbPdAl.
Fig. 4. The variation of the bond lengths at the phase transition of GdPdAl.
J. Kusz et al. / Journal of Alloys and Compounds 348 (2003) 65–71
3.2. Electronic structure The spectral measurements were carried out at a temperature of 192 K within the HTM I phase just before the isostructural transition and at 173 K within the HTM II phase just after the transition (Fig. 5a). The XPS results of the electronic structure at room temperature have recently been published [1]. The XPS valence band spectrum within the HTM I phase (thick line) exhibits a flat character (Fig. 5b). Several measurements within the HTM II phase exhibit a narrow peak at the Fermi level. This is accompanied by an insignificant depletion of the full narrow Pd 4d states. Both spectra were normalized to Gd 4f. The peak Pd 4d is slightly lower after the transition (Fig. 5a). This might explain the enhancement of the effective magnetic moment (8.35 mB in HTM II) compared to the magnetic moment of 7.94 mB in HTM I. The reason for such behaviour may be a stronger hybridization of the full Pd 4d states with the almost empty Gd 5d and Al 3p states. This correlates well with the shortening of the bond length within the layers.
3.3. Theoretical calculation The electronic structure of GdPdAl was calculated using the tight-binding linear muffin-tin orbital method in the atomic sphere approximation (TB-LMTO-ASA) [7]. The
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local spin-density approximation (LSDA) of the exchangecorrelation potential was used in the von Barth-Hedin [8] form (cited e.g. in Ref. [9]). To account for the strong correlation interaction in the narrow bands (Pd-4d and Gd-4f) occurring in the investigated compound the nonlocal correction of Langreth–Mehl–Hu [10] was applied. The calculations were scalar relativistic neglecting the spin–orbit interaction. The calculations were restricted to the magnetic solutions. The starting electronic configurations of the constituent atoms were taken as follows: Gd-[Xe]4f 7 5d 1 6s 2 6p 0 , Pd-[Kr]4d 10 5s 0 5p 0 and Al2 1 0 [Ne]3s 3p 3d . The states of the 4d 10 closed shell of Pd were included in the group of the core states. The ASA-based methods demand partitioning of the unit cell space into the Wigner–Seitz (W-S) spheres filling up the unit cell volume. The calculations were performed for different sets of W-S radii. The results like the positions and widths of bands as well as the local magnetic moment distributions and magnitudes were found to not depend sensitively on the choice of the W-S radii. In all cases, the linear overlap (s 1 2 s 2 ) /d 12 of the W-S spheres did not exceed 18% and no empty spheres were considered. To reduce the effect of the overlapping spheres the standard combined correction [7] was used in the calculations. The crystallographic data were taken from our experiment. The high temperature (HTM I) phase and the low temperature one (HTM II) were assumed to have the same crystal
Fig. 5. XPS spectra of GdPdAl at 192 and 173 K (a) Pd 4d states, the insert shows a simulated XPS spectrum based on the calculated partial densities of states, (b) the valence band spectrum.
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space group. According to the conclusions drawn from the crystallographic investigations, the HTM II and HTM I phase were distinguished by the lattice parameters and relative positions of the constituent atoms. The self-consistent calculations were performed using 341 k-points in the irreducible Brillouin zone (IBZ). The density of states (DOS) was calculated by means of the tetrahedron integration in the reciprocal space. Analysis of the calculated total energies have shown that the HTM I phase is energetically less favourable. The energy difference per constituent atom is roughly 280 K (24.5 meV) and is close to the temperature of the phase transition observed in this compound. Fig. 6 summarises the results for the band structure of the GdPdAl in both the HTM II and the HTM I phase. The DOS in both phases is very similar and is composed of clearly separated parts. In the energy range of 9–5 eV below the Fermi energy, the 4s states of Al form a band separated by a gap from the rest of the bands. The band is only weakly hybridized with the low lying d-states of Pd. The narrow band located just above the gap is built up by the 4d states of Pd. The width of the Pd-4d band complex though relatively small is several times larger than the Gd-4f bands. In the energies from 23 eV to above the Fermi level, the DOS of GdPdAl is made up of s, p, and d states of all constituent atoms. The relatively wide band centred at the Fermi energy is
separated from the complex of the Pd-4d band by a deep valley which is partially filled by the narrow band to make up for hybridized s, p and d states of all atoms. The presence of this valley may account for the occurrence of a plateau (in HTM I) or for a small peak followed by a shallow dip (in HTM II) visible just below the Fermi energy in the XPS spectra. For both the HTM II and HTM I crystal structures of GdPdAl the calculations also yield almost the same magnetic results. The magnitude of the local magnetic moment of Gd is close to that calculated in hcp-Gd [12], but the contribution of the 5d states is much less (0.15 mB ) than that in hcp-Gd. The Pd and Al atoms were found to be almost nonmagnetic. The XPS spectra were simulated on the basis of the calculated partial densities of states (PDOS). The data for the plots were prepared by convolution of the PDOS by Lorentz functions (with half-width of 0.35 eV) and multiplication by the corresponding cross-sections taken from Ref. [13]. With respect to the valence band part of the XPS spectra the simulated lines agree qualitatively well with the experimental ones (Fig. 5a). The simulation method is more sensitive to the details of the electronic density of states. The dip in the experimental spectrum, like that visible in the XPS spectrum of the HTM II phase of GdPdAl at 1.5 eV of binding energy (BE), should be more pronounced in the simulated spectra. Both the HTM II and
Fig. 6. The total spd-DOS of GdPdAl for: (a) HTM II phase and (b) HTM I phase with separated atomic and orbital contributions. Vertical lines show the position of ´F .
J. Kusz et al. / Journal of Alloys and Compounds 348 (2003) 65–71
HTM I simulated XPS spectra in the energy range up to 3 eV of BE are very similar in contrast to the measured ones. The change in the shape of the XPS spectrum just below the Fermi energy observed on decreasing the temperature may have different origins. The shallow dip in the spectrum of the HTM II phase which replaces the plateau for the HTM I phase may indicate the formation of a relatively wide and deep valley or even a gap in the DOS structure centred at approximately 2 eV below the Fermi energy. A similar effect can result from the occurrence of the narrow, high peak in the DOS located just below the Fermi level. No such changes were found in the results of the band structure calculations. It is well known that the ab initio methods of the electronic structure calculations provide the ground state (T50 K) energy bands and other properties of the investigated substances. Based on the results of the electronic structure calculations it is justified to claim that the static picture (T50 K) of the electronic structure does not change from HTM I to HTM II phase of GdPdAl. In this view the changes in the XPS spectra observed experimentally might be related to thermodynamic effects like spin fluctuation.
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ESR measurements give evidence for the phase transition from HTM II to HTM I [1]. To understand the origin of the phase transition we measured the X-ray photoelectron spectra above and below the phase transition and both spectra were normalised to the Gd 4f peak. It turns out that the Pd 4d peak after the transition became slightly lower which might explain the enhancement of the effective magnetic moment behind and below the phase transition. The XPS valence band spectrum within the HTM I phase exhibits a flat plateau whereas within the HTM II phase it exhibits a narrow peak at the Fermi level. This is accompanied by an insignificant depletion of the occupied narrow Pd 4d band. The analysis of the calculated total energies have shown that the HTM I phase is energetically less favourable than HTM II phase. The theoretical XPS spectra simulated on the basis of the calculated partial densities of states (PDOS) and normalised to the intensity of the Gd 4f peak agree qualitatively well with the experimental data. In particular the reduction of the Pd-4d intensity observed in the HTM II phase is reproduced correctly. The simulated XPS spectra in the energy range up to 3 eV of BE in both phases are very similar, in contrast to the measured ones.
4. Conclusions References The X-ray experiments provide clear evidence for the occurrence of an isostructural phase transition in GdPdAl at 180 K. The same kind of phase transition has been observed for another ZrNiAl-type structure, namely for TbPdAl [2] and GdNiAl [6]. A hysteresis of 5 K between heating and cooling is indicative of a first-order phase transition. The main differences between the HTM II and the HTM I phase are differences in the inter-atomic distances. On decreasing the temperature, both Gd and Al atoms within each layer move closer to each other and also closer to the Pd atoms whereas the distance between the layers is increased. This leads to a decrease in the lattice parameter a and to an increase in the c lattice parameter. ¨ Donni et al. [2] report that for TbPdAl, it is possible that the phase transition is connected with a change in the oxidation state of the Pd1 and / or Pd2 atoms and that the driving force is the conduction electrons. For GdPdAl, the temperature dependence of the magnetic susceptibility exhibits a change in the slope at the temperature of the phase transition. This is accompanied by an increase in the effective magnetic moment meff from 7.94 mB to 8.35 mB when the sample is cooled down [1]. Also electrical and
¨ [1] E. Talik, M. Skutecka, J. Kusz, H. Bohm, T. Mydlarz, A. Winiarski, J. Alloys Comp. 325 (2001) 42. ¨ [2] A. Donni, H. Kitazawa, P. Fischer, F. Fauth, J. Alloys Comp. 289 (1999) 11. [3] F. Hulliger, J. Alloys Comp. 218 (1995) 44. [4] A.E. Dwight, J. Less-Common Met. 102 (1984) L9. [5] F. Merlo, S. Cirafici, F. Canepa, J. Less-Common Met. 266 (1998) 22. ¨ [6] J. Jarosz, E. Talik, T. Mydlarz, J. Kusz, H. Bohm, A. Winiarski, J. Magn. Magn. Mater. 208 (2000) 169. [7] O.K. Andersen, O. Jepsen, Phys. Rev. Lett. 53 (1984) 2571; ¨ O.K. Andersen, O. Jepsen, D. Glotzel, in: F. Bassani, F. Fumi, M.P. Tosi (Eds.), Highlights of Condensed Matter Theory, North-Holland, Amsterdam, 1985, p. 59; O. Jepsen, O.K. Andersen, Solid State Commun. 9 (1971) 1763. [8] V. von Barth, L. Hedin, J. Phys. C Solid State Phys. 5 (1972) 1629. [9] J. Deniszczyk, W. Borgiel, J. Phys. Condens. Matter. 9 (1997) 2187. [10] D.C. Langreth, M.J. Mehl, Phys. Rev. B 28 (1981) 1809; C.D. Hu, D.C. Langreth, Phys. Scripta 32 (1985) 391. [11] G.M. Sheldrick, Program for the Refinement of Crystal Structure, ¨ University of Gotingen, Germany, 1997. [12] G. Skorek, J. Deniszczyk, J. Szade, B. Tyszka, J. Phys. Condens. Matter. 13 (2001) 6397. [13] J. Yeh, I. Lindau, At. Data Nucl. Data Tables 32 (1985) 1.
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Isostructural phase transition in the GdPdAl single crystals ¨ b , E. Talik a , M. Skutecka a , J. Deniszczyk c J. Kusz a , *, H. Bohm a
Institute of Physics, University of Silesia, Uniwersytecka 4, 40 -007 Katowice, Poland b ¨ Gewissenschaften der Universitat ¨ , 55099 Mainz, Germany Institut f ur c Institute of Physics and Chemistry of Metals, University of Silesia, 40 -007 Katowice, Poland Received 22 May 2002; received in revised form 11 June 2002; accepted 11 June 2002
Abstract At 180 K, single crystals of the intermetallic ternary compound GdPdAl undergo an isostructural phase transition from the high temperature hexagonal ZrNiAl-type structure to the low temperature hexagonal structure. The lattice parameters for temperatures neighbouring the phase transition exhibit a hysteresis on heating and cooling which is indicative of a first-order phase transition. In order to understand this phase transition the crystal structure was determined on a single crystal for a few degrees below and above 180 K. Also X-ray photoelectron spectra were measured at 192 K and 173 K and compared with spectra simulated with the help of band structure calculations. 2002 Elsevier Science B.V. All rights reserved. Keywords: Rare earth compounds; Crystal structure; Phase transition; Photoelectron spectroscopy PACS: 71.20; 73.20
1. Introduction The stable crystal structures of the ternary intermetallic rare-earth aluminides have the hexagonal ZrNiAl-type and the orthorhombic TiNiSi-type structure. However, the heavy rare-earth RPdAl compounds were found to crystallize in both structures [1–4]. For example, a sample of TbPdAl annealed at 1050 8C for 120 h and rapidly quenched to room temperature crystallizes in the hexagonal ZrNiAl-type structure as a metastable high-temperature modification (HTM). The stable low temperature modification (LTM) which crystallizes in the orthorhombic TiNiSi-type structure was prepared by annealing as-cast material at 900 8C for 120 h. It is interesting that both the high (HTM) and low temperature modification (LTM) of TbPdAl undergo two ´ successive magnetic phase transitions with the same Neel ¨ temperatures [2]. Donni and co-workers [2] found that only the HTM phase showed a first-order isostructural phase transition from HTM I (at higher temperature) to HTM II *Corresponding author. Fax: 148-32-588-431. E-mail address: [email protected] (J. Kusz).
(at lower temperature) at 106 K (on heating) and at 91 K (on cooling), which can be seen as a jump in the hexagonal lattice parameters. A similar behaviour of the lattice parameters and of the electrical resistivity was observed for isostructural GdNiAl single crystals at 220 K [5,6]. When the sample was cooled down, a rapid jump in the hexagonal lattice parameters has been observed: a decrease in the parameter a and an increase in the parameter c. The structures in both HTM I ] and HTM II phases are of the ZrNiAl-type (P62m) and only rapid changes in the inter-atomic distances have been observed [6]. For GdNiAl, the X-ray diffraction patterns of powder samples obtained at low temperatures were all indexed on the basis of the hexagonal cell [5,6]. Recently, we observed the same rapid jump of the electrical resistivity and the lattice parameters on GdPdAl single crystals at about 180 K [1]. Also, the contraction of the lattice parameter a and a dilatation of the lattice parameter c were observed when the sample was cooled. But in contrast to GdNiAl, all powdered fragments of the crystal have also some peaks related to the orthorhombic TiNiSi structure. The single crystal structure was determined below and above 180 K. In order to understand
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J. Kusz et al. / Journal of Alloys and Compounds 348 (2003) 65–71
this phase transition the X-ray photoelectron spectra were measured at 192 and 173 K and the spectra were simulated on the basis of theoretical electronic structure calculations.
2. Experimental GdPdAl single crystals were grown under an argon atmosphere by the Czochralski method from a levitated melt using high purity starting materials [1]. The compounds obtained were identified by X-ray powder diffraction. In all powdered fragments of the crystal, some peaks related to the orthorhombic TiNiSi structure were observed beside the peaks related to the hexagonal ZrNiAl structure [1]. For the single crystal X-ray analysis, small crystals of GdPdAl were isolated by mechanical fragmentation. Laue photographs of these crystals were taken in order to select
a crystal of good quality. In contrast to the powdered fragments of the crystals we found only crystals with the hexagonal ZrNiAl structure. Some of these single crystals were identified by electron microprobe analysis. A small single crystal (0.0830.1630.21 mm 3 ) of good quality was used to collect sets of diffraction data on a four-circle KM4 diffractometer with graphite-monochromatized Mo Ka radiation. For low temperature measurements a cool, dry nitrogen gas stream (Oxford Cryosystems equipment) was used. The temperature stability was better than 60.1 K. The lattice parameters a and c determined from 90 reflections are shown in Fig. 1. The data collection of intensities was performed at 300, 250, 220, 190, 150, 120 and 100 K. The intensities of two Bragg reflections were monitored every hour during the data collection. A semi-empirical psi-scan absorption correction was made because the absorption coefficient m is equal to 23 mm 21 . The structures were solved using the ] program SHELXL97 [11]. The space group P6m2 does not change below the phase transition. Details of the data collection for single crystals are presented in Table 1. The X-ray photoelectron spectra were obtained with the monochromatized Al Ka radiation using a Physical Electronics Spectrometer PHI 5700 / 660. The energy spectra of the electrons were analysed by a hemi-spherical mirror analyser with an energy resolution of about 0.3 eV. The Fermi level was referred to the gold 4f binding energy at 84 eV.
3. Results and discussion
3.1. Lattice parameter and crystal structure
Fig. 1. The variation of the lattice parameters a and c on heating and cooling.
For GdPdAl the lattice parameters a and c for temperatures neighbouring the phase transition (180 K) exhibit a hysteresis on heating and cooling (Fig. 1). This hysteresis is indicative of a first-order phase transition. The rapid change in the lattice parameters is due to the temperatureinduced transition from the hexagonal ZrNiAl structure (HTM I) to the hexagonal ZrNiAl structure (HTM II). A contraction of the lattice parameter a (decrease of 0.7%) and a dilatation of the lattice parameter c (increase of 1.3%) were observed when the sample was cooled down. For comparison, the decrease in the lattice parameter a is 1.0 and 0.6% and the increase in the c lattice parameter is 1.9 and 1.0%, respectively for TbPdAl and GdNiAl [2,6]. The decrease in the volume is small, being 0.7, 0.2 and 0.2%, respectively for GdPdAl, TbPdAl and GdNiAl. For a first-order phase transition, which occurs through the mechanism of nucleation and growth, one would expect a change in symmetry. However, the data clearly show that the structure remains hexagonal with the same space group. It should also be mentioned that in all powdered
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Table 1 ] Details of data collection, refinement and structural parameters for GdPdAl for the HTM I (T .180 K) and HTM II phase in space group P62m, z53 Temperature (K) ˚ Cell parameter a (A) ˚ Cell parameter c (A) Axial factor c /a ˚ 3) Volume (A Range of data collection
Scan mode No. of measured reflections Space group No. of unique reflections R(int) R(sigma) Number of variables Extinction ( g310 3 ) Atom parameters Gd in 3g, [x,0,0]; x ˚ 3) Ueq (A Al in 3f, [x,0,0]; x ˚ 3) Ueq (A Pd1 in 1b, [0,0,1 / 2] Ueq (A3 ) Pd2 in 2c, [1 / 3,2 / 3,0] ˚ 3) Ueq (A R1 wR 2 Goodness-of-fit
100 7.1007(8) 4.1157(10) 0.5796 179.71 u #508 0#h#13 213#k#15 0#h#8 v -2u 1865
120 7.1041(8) 4.1157(10) 0.5793 179.88 u #508 0#h#13 213#k#15 0#h#8 v -2u 1862
150 7.1106(8) 4.1115(10) 0.5782 180.03 u #508 0#h#13 213#k#15 0#h#8 v -2u 1859
190 7.1737(11) 4.0527(7) 0.5649 180.62 u #508 0#h#13 213#k#15 0#h#8 v -2u 1857
220 7.1810(8) 4.0475(10) 0.5636 180.75 u #508 0#h#13 213#k#15 0#h#8 v -2u 1858
250 7.1883(11) 4.0456(7) 0.5628 181.04 u #508 0#h#13 213#k#15 0#h#8 v -2u 1858
300 7.1992(8) 4.0398(9) 0.5611 181.33 u #508 0#h#13 213#k#15 0#h#8 v -2u 1932
] P62m 664
] P62m 663
] P62m 662
] P62m 661
] P62m 662
] P62m 662
] P62m 686
0.050 0.034 14 0.024(2)
0.049 0.032 14 0.025(2)
0.050 0.034 14 0.021(2)
0.047 0.033 14 0.025(2)
0.048 0.033 14 0.027(2)
0.048 0.033 14 0.027(2)
0.046 0.032 14 0.028(2)
0.58242(5) 0.00708(7) 0.2346(4) 0.00853(4) 0.00071(1)
0.58246(5) 0.00708(7) 0.2344(4) 0.0085(4) 0.0071(1)
0.58245(5) 0.00817(8) 0.2348(4) 0.0087(3) 0.0083(1)
0.58274(6) 0.00946(8) 0.2362(4) 0.0104(4) 0.0100(1)
0.58275(6) 0.01035(8) 0.2363(4) 0.0117(4) 0.0111(2)
0.58280(6) 0.01100(8) 0.2363(4) 0.0128(4) 0.0121(1)
0.58281(5) 0.01227(8) 0.2369(4) 0.0141(4) 0.0135(2)
0.0078(1)
0.0078(1)
0.0089(1)
0.0102(1)
0.0113(1)
0.0122(1)
0.0138(1)
0.029 0.070 1.28
0.029 0.070 1.28
0.029 0.072 1.29
0.029 0.074 1.29
0.029 0.074 1.28
0.029 0.071 1.21
0.030 0.071 1.20
Ueq 5 kUu l, equivalent isotropic temperature factor; R 1 5 S(uFo u 2 uFc u)2 / S(uFo u)2 , discrepancy factor; wR 2 5 (S(w(F 2o 2 F 2c )2 ) / S(w(Fo )2 )1 / 2 ; w 5 1 / (s 2 (F o2 ) 1 (a P)2 ) where P 5 (2F c2 1 max(F o2 , 0)) / 3.
fragments of the GdPdAl crystal, some peaks related to the orthorhombic TiNiSi structure were also observed beside the peaks related to the hexagonal ZrNiAl structure, as was reported previously [1]. The structure determinations carried out on a single crystal below and above 180 K should reveal the structural changes at the transition, and in particular, they should reveal the change in the bond lengths. The discrepancy factors R 1 for all unique reflections are 2.93, 2.93, 2.98, 2.87, 3.04, 2.91 and 3.05% for 100, 120, 150, 190, 220, 250 and 300 K, respectively. The structural parameters of the phases above (HTM I) and below the phase transition (HTM II) are shown in Table 1. The projection of the structure along the hexagonal c-axis is shown in Fig. 2. The structure consists of two layers perpendicular to the c-axis. One layer (z50) contains Al- and Pd2-atoms, the other one Gd- and Pd1-atoms. In Fig. 3, these layers are depicted separately. The Al-atoms form trigonal prisms with Pd1 in the centre, the Gd-atoms form trigonal prisms with Pd2 in the centre. In Fig. 2, only the intra-layer bonds between the layers are shown, whereas the inter-layer bonds are depicted in Fig. 3. At the phase transition, the Gd- and Al-atoms move, whereas the Pd1- and Pd2-atoms remain fixed on their special positions (Table 1). This
results in a shortening of the bonds for Gd–Gd, for Gd–Pd1 and for Al–Al upon cooling (Table 2). The movement of the Al-atoms and the shortening of the Gd–Pd1 bonds are indicated by arrows in Fig. 3. Whereas the c lattice parameter expands on cooling (Fig. 1), the Al–Pd1 bond in the trigonal prism with Pd1 in the centre
Fig. 2. The projection along the c-axis of the structure of GdPdAl (four unit cells); only intra-layer bonds are shown.
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Fig. 3. The two layers of the structure of GdPdAl (four unit cells) at level z50.5 (a) and z50 (b); only inter-layer bonds are shown. The arrows indicate the movement of the Al-atoms and the shortening of the bonds upon cooling (strongly exaggerated).
remains almost constant, because the expansion of the prism is compensated by the contraction of the Al 3 -group within the plane. The same argument is true for the Gd–Pd2 bond. Although the trigonal prism of Gd with Pd2 in the centre expands in the c direction, the Gd–Pd2 bond remains constant because the plane Gd 3 -group contracts. The contraction of the planar groups within the plane leads to a decrease in the lattice parameter a. An overview of the change in the bond lengths at the phase transition is given in Fig. 4. On the other hand, there is neither a hexagonal nor a ] trigonal space group (besides P62m) which meets the crystal chemical requirements of the structure. The other alternative to hexagonal would be an orthorhombic deformation (e.g. Pm2m) and a subsequent threefold twinning. This appears not to be very likely, since we were ] able to refine the structure in P62m with an R-value of less than 3.00% (Table 1). Therefore we must assume that there is no change in space group at the transition and the phase transition must be called isostructural. Similar ¨ results have been reported so far by Donni et al. [2] for TbPdAl.
Fig. 4. The variation of the bond lengths at the phase transition of GdPdAl.
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3.2. Electronic structure The spectral measurements were carried out at a temperature of 192 K within the HTM I phase just before the isostructural transition and at 173 K within the HTM II phase just after the transition (Fig. 5a). The XPS results of the electronic structure at room temperature have recently been published [1]. The XPS valence band spectrum within the HTM I phase (thick line) exhibits a flat character (Fig. 5b). Several measurements within the HTM II phase exhibit a narrow peak at the Fermi level. This is accompanied by an insignificant depletion of the full narrow Pd 4d states. Both spectra were normalized to Gd 4f. The peak Pd 4d is slightly lower after the transition (Fig. 5a). This might explain the enhancement of the effective magnetic moment (8.35 mB in HTM II) compared to the magnetic moment of 7.94 mB in HTM I. The reason for such behaviour may be a stronger hybridization of the full Pd 4d states with the almost empty Gd 5d and Al 3p states. This correlates well with the shortening of the bond length within the layers.
3.3. Theoretical calculation The electronic structure of GdPdAl was calculated using the tight-binding linear muffin-tin orbital method in the atomic sphere approximation (TB-LMTO-ASA) [7]. The
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local spin-density approximation (LSDA) of the exchangecorrelation potential was used in the von Barth-Hedin [8] form (cited e.g. in Ref. [9]). To account for the strong correlation interaction in the narrow bands (Pd-4d and Gd-4f) occurring in the investigated compound the nonlocal correction of Langreth–Mehl–Hu [10] was applied. The calculations were scalar relativistic neglecting the spin–orbit interaction. The calculations were restricted to the magnetic solutions. The starting electronic configurations of the constituent atoms were taken as follows: Gd-[Xe]4f 7 5d 1 6s 2 6p 0 , Pd-[Kr]4d 10 5s 0 5p 0 and Al2 1 0 [Ne]3s 3p 3d . The states of the 4d 10 closed shell of Pd were included in the group of the core states. The ASA-based methods demand partitioning of the unit cell space into the Wigner–Seitz (W-S) spheres filling up the unit cell volume. The calculations were performed for different sets of W-S radii. The results like the positions and widths of bands as well as the local magnetic moment distributions and magnitudes were found to not depend sensitively on the choice of the W-S radii. In all cases, the linear overlap (s 1 2 s 2 ) /d 12 of the W-S spheres did not exceed 18% and no empty spheres were considered. To reduce the effect of the overlapping spheres the standard combined correction [7] was used in the calculations. The crystallographic data were taken from our experiment. The high temperature (HTM I) phase and the low temperature one (HTM II) were assumed to have the same crystal
Fig. 5. XPS spectra of GdPdAl at 192 and 173 K (a) Pd 4d states, the insert shows a simulated XPS spectrum based on the calculated partial densities of states, (b) the valence band spectrum.
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space group. According to the conclusions drawn from the crystallographic investigations, the HTM II and HTM I phase were distinguished by the lattice parameters and relative positions of the constituent atoms. The self-consistent calculations were performed using 341 k-points in the irreducible Brillouin zone (IBZ). The density of states (DOS) was calculated by means of the tetrahedron integration in the reciprocal space. Analysis of the calculated total energies have shown that the HTM I phase is energetically less favourable. The energy difference per constituent atom is roughly 280 K (24.5 meV) and is close to the temperature of the phase transition observed in this compound. Fig. 6 summarises the results for the band structure of the GdPdAl in both the HTM II and the HTM I phase. The DOS in both phases is very similar and is composed of clearly separated parts. In the energy range of 9–5 eV below the Fermi energy, the 4s states of Al form a band separated by a gap from the rest of the bands. The band is only weakly hybridized with the low lying d-states of Pd. The narrow band located just above the gap is built up by the 4d states of Pd. The width of the Pd-4d band complex though relatively small is several times larger than the Gd-4f bands. In the energies from 23 eV to above the Fermi level, the DOS of GdPdAl is made up of s, p, and d states of all constituent atoms. The relatively wide band centred at the Fermi energy is
separated from the complex of the Pd-4d band by a deep valley which is partially filled by the narrow band to make up for hybridized s, p and d states of all atoms. The presence of this valley may account for the occurrence of a plateau (in HTM I) or for a small peak followed by a shallow dip (in HTM II) visible just below the Fermi energy in the XPS spectra. For both the HTM II and HTM I crystal structures of GdPdAl the calculations also yield almost the same magnetic results. The magnitude of the local magnetic moment of Gd is close to that calculated in hcp-Gd [12], but the contribution of the 5d states is much less (0.15 mB ) than that in hcp-Gd. The Pd and Al atoms were found to be almost nonmagnetic. The XPS spectra were simulated on the basis of the calculated partial densities of states (PDOS). The data for the plots were prepared by convolution of the PDOS by Lorentz functions (with half-width of 0.35 eV) and multiplication by the corresponding cross-sections taken from Ref. [13]. With respect to the valence band part of the XPS spectra the simulated lines agree qualitatively well with the experimental ones (Fig. 5a). The simulation method is more sensitive to the details of the electronic density of states. The dip in the experimental spectrum, like that visible in the XPS spectrum of the HTM II phase of GdPdAl at 1.5 eV of binding energy (BE), should be more pronounced in the simulated spectra. Both the HTM II and
Fig. 6. The total spd-DOS of GdPdAl for: (a) HTM II phase and (b) HTM I phase with separated atomic and orbital contributions. Vertical lines show the position of ´F .
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HTM I simulated XPS spectra in the energy range up to 3 eV of BE are very similar in contrast to the measured ones. The change in the shape of the XPS spectrum just below the Fermi energy observed on decreasing the temperature may have different origins. The shallow dip in the spectrum of the HTM II phase which replaces the plateau for the HTM I phase may indicate the formation of a relatively wide and deep valley or even a gap in the DOS structure centred at approximately 2 eV below the Fermi energy. A similar effect can result from the occurrence of the narrow, high peak in the DOS located just below the Fermi level. No such changes were found in the results of the band structure calculations. It is well known that the ab initio methods of the electronic structure calculations provide the ground state (T50 K) energy bands and other properties of the investigated substances. Based on the results of the electronic structure calculations it is justified to claim that the static picture (T50 K) of the electronic structure does not change from HTM I to HTM II phase of GdPdAl. In this view the changes in the XPS spectra observed experimentally might be related to thermodynamic effects like spin fluctuation.
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ESR measurements give evidence for the phase transition from HTM II to HTM I [1]. To understand the origin of the phase transition we measured the X-ray photoelectron spectra above and below the phase transition and both spectra were normalised to the Gd 4f peak. It turns out that the Pd 4d peak after the transition became slightly lower which might explain the enhancement of the effective magnetic moment behind and below the phase transition. The XPS valence band spectrum within the HTM I phase exhibits a flat plateau whereas within the HTM II phase it exhibits a narrow peak at the Fermi level. This is accompanied by an insignificant depletion of the occupied narrow Pd 4d band. The analysis of the calculated total energies have shown that the HTM I phase is energetically less favourable than HTM II phase. The theoretical XPS spectra simulated on the basis of the calculated partial densities of states (PDOS) and normalised to the intensity of the Gd 4f peak agree qualitatively well with the experimental data. In particular the reduction of the Pd-4d intensity observed in the HTM II phase is reproduced correctly. The simulated XPS spectra in the energy range up to 3 eV of BE in both phases are very similar, in contrast to the measured ones.
4. Conclusions References The X-ray experiments provide clear evidence for the occurrence of an isostructural phase transition in GdPdAl at 180 K. The same kind of phase transition has been observed for another ZrNiAl-type structure, namely for TbPdAl [2] and GdNiAl [6]. A hysteresis of 5 K between heating and cooling is indicative of a first-order phase transition. The main differences between the HTM II and the HTM I phase are differences in the inter-atomic distances. On decreasing the temperature, both Gd and Al atoms within each layer move closer to each other and also closer to the Pd atoms whereas the distance between the layers is increased. This leads to a decrease in the lattice parameter a and to an increase in the c lattice parameter. ¨ Donni et al. [2] report that for TbPdAl, it is possible that the phase transition is connected with a change in the oxidation state of the Pd1 and / or Pd2 atoms and that the driving force is the conduction electrons. For GdPdAl, the temperature dependence of the magnetic susceptibility exhibits a change in the slope at the temperature of the phase transition. This is accompanied by an increase in the effective magnetic moment meff from 7.94 mB to 8.35 mB when the sample is cooled down [1]. Also electrical and
¨ [1] E. Talik, M. Skutecka, J. Kusz, H. Bohm, T. Mydlarz, A. Winiarski, J. Alloys Comp. 325 (2001) 42. ¨ [2] A. Donni, H. Kitazawa, P. Fischer, F. Fauth, J. Alloys Comp. 289 (1999) 11. [3] F. Hulliger, J. Alloys Comp. 218 (1995) 44. [4] A.E. Dwight, J. Less-Common Met. 102 (1984) L9. [5] F. Merlo, S. Cirafici, F. Canepa, J. Less-Common Met. 266 (1998) 22. ¨ [6] J. Jarosz, E. Talik, T. Mydlarz, J. Kusz, H. Bohm, A. Winiarski, J. Magn. Magn. Mater. 208 (2000) 169. [7] O.K. Andersen, O. Jepsen, Phys. Rev. Lett. 53 (1984) 2571; ¨ O.K. Andersen, O. Jepsen, D. Glotzel, in: F. Bassani, F. Fumi, M.P. Tosi (Eds.), Highlights of Condensed Matter Theory, North-Holland, Amsterdam, 1985, p. 59; O. Jepsen, O.K. Andersen, Solid State Commun. 9 (1971) 1763. [8] V. von Barth, L. Hedin, J. Phys. C Solid State Phys. 5 (1972) 1629. [9] J. Deniszczyk, W. Borgiel, J. Phys. Condens. Matter. 9 (1997) 2187. [10] D.C. Langreth, M.J. Mehl, Phys. Rev. B 28 (1981) 1809; C.D. Hu, D.C. Langreth, Phys. Scripta 32 (1985) 391. [11] G.M. Sheldrick, Program for the Refinement of Crystal Structure, ¨ University of Gotingen, Germany, 1997. [12] G. Skorek, J. Deniszczyk, J. Szade, B. Tyszka, J. Phys. Condens. Matter. 13 (2001) 6397. [13] J. Yeh, I. Lindau, At. Data Nucl. Data Tables 32 (1985) 1.