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Transport properties of intermetallic thulium compounds
Journal of Alloys and Compounds 305 (2000) 43–48
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Transport properties of intermetallic thulium compounds Thomas P. Braun*, Francis J. DiSalvo Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY 14853 -1301, USA Received 31 August 1999; accepted 21 December 1999
Abstract The Seebeck coefficient, electrical resistivity and magnetic susceptibility of TmAl 3 and TmPd 3 are reported. TmAl 3 melts peritectially and was prepared as a single phase sample for the first time. Like TmPd 3 it is a ‘normal’ metal as indicated by both electrical resistivity and magnetic susceptibility measurements. The room temperature thermopower of TmAl 3 is moderate (15 mV/ K) while that of TmPd 3 falls within the expected range for typical metals (25 mV/ K). Further properties are also reported for YbAl 3 , TmAl 2 and TmPd. From the magnetic susceptibility data it can be concluded that thulium adopts the normal trivalent state in all these compounds. 2000 Elsevier Science S.A. All rights reserved. Keywords: Thermopower; Thulium compounds; Intermetallic phases; Intermediate valence
1. Introduction The search for new thermoelectric materials has been revitalised in recent years [1–7]. Thermoelectric devices are designed to utilize the Peltier effect, either by developing an electric potential in a thermal gradient, or by cooling at the junction of two materials when an electrical current is flowing through it [8]. In addition to a general demand for improved performance of these materials, it has been proposed to apply these materials for thermoelectric cooling [9]. Besides various attempts to improve existing materials which are based on semiconductors like e.g. Sb 2 Te 3 / Bi 2 Te 3 alloys, some intermetallic phases containing rare earth elements have been recently studied in some detail [10]. These compounds show surprisingly high values of the Seebeck coefficient (‘thermopower’) if the rare earth atoms are in an intermediate valence state. The intermediate valence state has been investigated for various intermetallic compounds of cerium and ytterbium [11–17]. It manifests itself in a number of anomalies e.g. in the electrical resistivity or the magnetic susceptibility, and quite often also leads to relatively large values of the Seebeck coefficient. In this state a 4f electron is neither localized on the rare earth atom nor completely delocalized in the conduction band. Instead, the local f states form a many-body resonance at the Fermi level in the conduction
band. The thereby increased density of states at the Fermi energy is believed to account for the high values of the thermopower. So far mostly intermetallic compounds containing either cerium (e.g. CePd 3 [18]) or ytterbium (e.g. YbAl 3 [19,20]) have been investigated. In these cases the rare earth atom contains one f electron or hole, respectively. According to an exploratory theoretical study, the availability of more f electrons or holes might decrease the Seebeck coefficient although no splitting of the f-levels has been included in these calculations [2]. No experimental data are available yet to advance this discussion. We therefore decided to investigate the thermoelectric properties of the thulium analogues of the intermetallic compounds (CePd 3 , YbAl 3 and YbPd) with the highest Seebeck coefficients of all rare earth intermetallics. Thulium compounds seem to be an ideal candidate to study the effect of additional f holes on the transport properties. With a 4f 12 ground state configuration thulium possesses two f holes. Furthermore, some intermediate valence compounds of thulium are known (e.g. TmSe [21–24]), although these are not intermetallic phases.
2. Results and discussion
2.1. Preparation *Corresponding author. E-mail address: [email protected] (T.P. Braun)
In previous studies TmAl 3 could never be prepared as a
0925-8388 / 00 / $ – see front matter 2000 Elsevier Science S.A. All rights reserved. PII: S0925-8388( 00 )00714-3
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T.P. Braun, F. J. DiSalvo / Journal of Alloys and Compounds 305 (2000) 43 – 48
single phase compound but only in conjunction with TmAl 2 . Except for an ‘estimated’ phase diagram no thermodynamic data are available for the system Tm–Al [25]. According to this phase diagram TmAl 3 is expected to decompose peritectially, although the temperature of this transition remains unknown. Our attempts to prepare TmAl 3 according to the reported procedures by arc melting only yielded mixtures of TmAl 3 and the higher melting compound TmAl 2 . To confirm the assumed peritectic decomposition of TmAl 3 we performed differential thermal analysis (DTA) scans on various samples. It proved essential to record the thermal profile of a pre-reacted sample, since the highly exothermic initial reaction of the pure metals otherwise dominates the DTA. Furthermore the experiment had to be performed in tantalum ampoules, reactions in quartz containers yielded irreversible DTAs and the products appeared to be oxidized. The thermal analysis of a prereacted sample (shown in Fig. 1) revealed a reversible endothermic reaction at |11008C which was attributed to the peritectic reaction TmAl 3 5TmAl 2 1Al. In order to prepare single phase samples of TmAl 3 it is therefore required to anneal stoichiometric mixtures of the elements in sealed Ta ampoules at temperatures below the decomposition temperature of |11008C. However, even if the temperature is constantly kept at only 10008C, the resulting product contains a significant amount of TmAl 2 . Indeed it has been found that, after annealing periods of several weeks, single phase samples of TmAl 2 could be obtained (vide infra). The amounts of aluminum that are ‘lost’ during annealing can be accounted for in two ways: either the vapour pressure of aluminum at these tempera-
tures is high enough to shift the equilibrium composition of the solid phase, or a solid state reaction with the container wall is taking place. As a result we detected a metallic deposit on the inside wall of the tantalum container that could not be analysed further. Single phase samples (as determined by X-ray powder diffractometry) of TmAl 3 could be finally prepared by the following two-step method: first a stoichiometric mixture of the elements is arc-melted. To avoid a substantial loss of thulium during this process, the elements are initially spatially separated and the arc used to selectively melt the aluminum. The aluminum melt is subsequently moved to the thulium, which quickly dissolves, into the melt. Typical weight losses during this step are generally lower than 1 wt.%. The inhomogeneous bead is then finely ground and pressed to pellets. The pellet is subsequently annealed in arc-welded tantalum ampoules (sealed in quartz ampoules for protection) for 2 days at 8508C. The X-ray powder diffractogram of TmAl 3 prepared by this method is shown in Fig. 2. No secondary phases can be detected and the refined lattice constant (Cu 3 Au-type) of 420.5(1) pm corresponds well with published values [25,26]. Single phase samples of YbAl 3 could also be prepared following the same procedure as in the case of TmAl 3 . In this case the weight loss during the initial arc-melting is slightly higher. Nevertheless we successfully used a sample of YbAl 3 prepared by this way as a reference for our thermopower measurements. The characteristic magnetization curve (vide infra) was reproduced to further characterize the sample. It appears that this preparation is a convenient alternative to the rather elaborate flux-growth /
Fig. 1. Differential thermal analysis of TmAl 3 .
T.P. Braun, F. J. DiSalvo / Journal of Alloys and Compounds 305 (2000) 43 – 48
45
Fig. 2. Powder diffractogram of single phase TmAl 3 . The simulated pattern is indicated as a bar graph.
hot-pressing method used to prepare specimens for previous thermopower measurements [20]. A sample of TmAl 2 was obtained during our initial annealing experiments. An arc-melted stoichiometric reaction mixture for the preparation of TmAl 3 was repeatedly ground and pressed into a pellet, which was annealed at 10008C for a total of 6 weeks. After this procedure, the sample consisted of a single phase TmAl 2 pellet. Both binary intermetallic phases of thulium and palladium can be easily obtained by arc-melting the respective stoichiometric mixtures of the elements [27]. Beads prepared in a special cast mold with two parallel sides (|4 mm apart, 7 mm deep and 28 mm long) have been subsequently annealed at 11008C (TmPd) and 9008C (TmPd 3 ), respectively, for 1 week. In all cases the purity of the phases was established by powder X-ray diffractometry.
2.2. Thermopower measurements The Seebeck coefficients of TmAl 3 , TmPd 3 and TmPd have been measured simultaneously with the respective thermal conductivities by a steady-state method using a custom built apparatus [28,29]. In this set-up the thermal conductivity and the Seebeck coefficient can be measured from ambient temperature to about 30 K. Suitable samples were cut from the annealed pellets or beads in a roughly rectangular shape with typical dimensions of 33335 mm. For the compounds containing palladium, we used indium
to solder the thermocouples, a copper heat sink and a heating resistor onto the samples. Since liquid indium does not bond well mechanically to TmAl 3 , we used silver epoxy to contact this sample. To ensure optimal thermal contact the thermocouples have been embedded in small holes (ø0.04 mm) drilled into the sample. YbAl 3 has been long known to exhibit a rather high thermopower. The Seebeck coefficient reaches an absolute maximum of approximately 290 mV/ K at around 2008C and declines only little up to 3008C [19]. Indeed, the so-called ‘thermoelectric power factor’ (the product of the square of the Seebeck coefficient and electrical conductivity) of this compound is reported to have the highest known value [20]. TmAl 3 on the other hand exhibits a rather modest Seebeck coefficient of only 15 mV/ K at room temperature. It also shows an interesting phase change at around 80 K, indicating a possible change of the dominant carrier type at lower temperatures. The data are shown in Fig. 3 (open circles). Obviously, the maximum value of 15 mV/ K does not render TmAl 3 a candidate material for thermoelectric applications. However, these data allow a comparison of the thermopowers within the isostructural triad TmAl 3 , YbAl 3 and LuAl 3 . We will come back to this aspect after reporting the remaining measurements. The temperature dependence of the Seebeck coefficient of TmPd 3 exhibits a maximum of 25 mV/ K at room temperature (see Fig. 3). This value is quite low and falls within the expected range for typical metals.
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T.P. Braun, F. J. DiSalvo / Journal of Alloys and Compounds 305 (2000) 43 – 48
The device was evacuated and partially back filled with He for the temperature dependent measurements in a helium bath cryostat. The results for TmAl 3 and TmPd 3 are shown in Fig. 4. Both samples show a linear temperature dependence over the entire temperature range. The room temperature value for TmAl 3 is about 30 mV cm, for TmPd 3 we measured a value of around 50 mV cm. The extrapolated low temperature offset of the latter sample was about 20 mV cm, indicating a higher concentration of defects and / or impurities. The temperature dependent part of the resistivity however corresponds rather well to that of TmAl 3 .
2.4. Magnetic measurements
Fig. 3. Seebeck coefficients of TmAl 3 (circles) and TmPd 3 (squares).
TmPd shows an even smaller thermopower, its Seebeck coefficient gradually increasing to a maximum value of only 1 mV/ K.
2.3. Electrical measurements The electrical conductivities of TmAl 3 and TmPd 3 have been determined with a modified four-probe measurement in the temperature range from room temperature to about 30 K (5 K for TmPd 3 ). The samples have been cut into a flat rectangular shape of approximate dimensions 83432 mm. Copper wire current leads have been soldered on the short ends with indium, with two voltage leads attached with silver epoxy parallel to the former, |3 mm apart from each other. This whole set-up was glued to a copper block with epoxy cement and encapsulated in a brass container.
The magnetic susceptibilities of TmAl 3 , TmAl 2 , TmPd 3 , TmPd and YbAl 3 have been measured on a Quantum design SQUID magnetometer. Data were collected from room temperature to 5 K at intervals of 10 K. Typical fields were in the range of 1 to 2 T, samples sizes varying from about 100 to 500 mg. The data have been analyzed by two different methods. First a linear regression has been performed for the inverse molar susceptibilities versus the temperature according to the Curie–Weiss law: 1 /x 5 T /CM 2 u /CM . Only the values for temperatures above 50 K have been included in the data analysis to ensure the validity of the assumed linear dependence (the regressions yield Curie temperatures u substantially below that cut-off value — cf. Table 1). In a second non-linear regression a correction for the background susceptibility x0 has been introduced: x 5 x0 1 CM /(T 2 u ). This temperature independent susceptibility accounts for diamagnetic and Pauli paramagnetic contributions as well as for the typically very weak signal from the gel cap containers. The results are summarized in Table 1.
Fig. 4. Electrical resistivity of TmAl 3 (circles) and TmPd 3 (squares).
T.P. Braun, F. J. DiSalvo / Journal of Alloys and Compounds 305 (2000) 43 – 48 Table 1 Magnetic moments of all investigated compounds as extracted from the susceptibility measurements (see text) Compound
TmAl 3 TmAl 2 TmPd 3 TmPd YbAl 3
Linear regression
Non-linear regression
u (K)
u (K)
meff ( mB )
214.6 12.8 21.6 21.5 (Fig. 5)
7.33 7.76 7.12 6.67
214.0 15.0 10.4 26.9 Intermediate
meff ( mB ) 7.31 7.64 7.03 6.95 valent behaviour
Except for the case of YbAl 3 , all samples show typical Curie–Weiss behavior with magnetic moments corresponding to the calculated free-ion value for Tm 31 (7.56
47
mB ). The values do not change significantly if the temperature independent correction x0 is included or not. Thus it can be clearly established that none of the investigated thulium alloys exhibits intermediate valent behavior. A sample of YbAl 3 , prepared by our combination of arc melting and subsequent ‘low temperature’ annealing, showed the expected intermediate valent behavior in the form of a rather broad peak in the reciprocal susceptibility at around 50 K. A linear behavior of x 21 (as indicated by the dashed line in Fig. 5) is observed for temperatures above 150 K. A plot of the magnetic susceptibilities for TmAl 3 and YbAl 3 is given in Fig. 5. At low temperatures the magnetization curve of TmAl 3 deviates significantly from the linear Curie–Weiss fit. This
Fig. 5. Comparison of the magnetic susceptibilities of TmAl 3 (top) and YbAl 3 (bottom).
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T.P. Braun, F. J. DiSalvo / Journal of Alloys and Compounds 305 (2000) 43 – 48
is also the case for the other intermetallic thulium compounds studied, TmAl 2 , TmPd 3 and TmPd.
3. Conclusions This study was motivated by our interest in intermediate valent intermetallic compounds of rare earth elements as potential materials for thermoelectric applications. We investigated four simple cubic alloys, TmAl 3 , TmAl 2 , TmPd 3 and TmPd, all of which have been known to exist, but whose electrical and magnetic properties have not been investigated previously. We succeeded in the preparation of single phase samples and measured their relevant properties. We found all four materials to be ‘simple’ metals containing trivalent thulium. It is interesting to compare the thermopowers within the series TmAl 3 , YbAl 3 and LuAl 3 . All three compounds are isostructural and differ only by the number of 4f electrons for the rare earth metal. With a closed subshell configuration 4f 14 for Lu 31 , there is no possibility for intermediate valent behavior. As expected, the reported thermopower is rather low (about 13 mV/ K at room temperature) [19]. YbAl 3 (4f 13 or one f hole) is known to be intermediate valent and its peak thermopower is an order of magnitude higher (around 290 mV/ K at room temperature) than that of LuAl 3 [19]. With a 4f 12 ground state (two f holes), we hoped that TmAl 3 could be intermediate valent. While this is clearly not the case, its Seebeck coefficient falls between the values of YbAl 3 and LuAl 3 .
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
[14] [15] [16] [17]
[18] [19] [20] [21]
Acknowledgements
[22]
Funding for this investigation was provided by ONR. This work made use of the Cornell Center for Materials Research facilities supported by NSF Funded Award [DMR-9632275. Some of the samples have been prepared by G. Glass in the course of an undergraduate summer research project. We would like to thank R. Eger (Max¨ Festkorperforschung, ¨ Planck-Institut fur Stuttgart) for performing the DTA experiments of TmAl 3 . Thanks are also due to an unknown reviewer for helpful comments that improved the readability of this paper.
[23] [24] [25] [26] [27] [28] [29]
G.D. Mahan, J.O. Sofo, Proc. Natl. Acad. Sci. USA 93 (1996) 7436. G.D. Mahan, Phys. Rev. B56 (1997) 11833. G.D. Mahan, B.C. Sales, J. Sharp, Phys. Today (1997) 42. B.C. Sales, Mater. Res. Bull. 23 (1998) 15. F.J. DiSalvo, Science 285 (1999) 703. D.M. Rowe, C.M. Bhandari, Modern Thermoelectrics, Reston, Reston, VA, 1983. C. Wood, Rep. Progr. Phys. 51 (1988) 459. J.C.A. Peltier, Ann. Chim. Phys. 56 (1834) 371. H.J. Goldsmid, Electronic Refrigeration, Pion, London, 1986. G.D. Mahan, in: Proceedings International Conference on Thermoelectrics ’97, IEEE, 1998, p. 21. E.E. Havinga, K.H.J. Buschow, H.J. van Daal, Solid State Commun. 13 (1973) 621. A. Iandelli, G.L. Olcese, A. Palenzona, J. Less-Common Metals 76 (1980) 317. R. Pott, W. Boksch, G. Leson, B. Politt, H. Schmidt, A. Freimuth, K. ¨ Keulerz, J. Langen, G. Neumann, F. Oster, J. Rohler, U. Walter, P. Weidner, D. Wohlleben, Phys. Rev. Lett. 54 (1985) 481. U. Walter, E. Holland-Moritz, Z. Fisk, Phys. Rev. B 43 (1991) 320. A.P. Murani, Phys. Rev. B 50 (1994) 9882. A. Hiess, J.X. Boucherle, F. Givord, P.C. Canfield, J. Alloys Comp. 224 (1995) 33. A. Hiess, J.X. Boucherle, F. Givord, J. Schweizer, E. LelievreBerna, F. Tasset, B. Gillon, P.C. Canfield, Physica B 234–236 (1997) 886. R.J. Gambino, W.D. Grobmann, A.M. Toxen, Appl. Phys. Lett. 22 (1973) 506. H.J. van Daal, P.B. van Aken, K.H.J. Buschow, Phys. Lett. 49A (1974) 246. D.M. Rowe, G. Min, V.L. Kuznetsov, Phil. Mag. Lett. 77 (1998) 105. P. Wachter, in: K.A. Gschneidner, L. Eyring (Eds.), Lanthanides / Actinides: Physics-II, Handbook on the Physics and Chemistry of Rare Earths, Vol. 19, North-Holland, Amsterdam, 1994, pp. 177– 382, Chapter 132. E. Kaldis, H. Spychinger, E. Jilek, J. Magn. Magn. Mater. 47–48 (1985) 478. H. Spychinger, E. Kaldis, B. Fritzler, J. Less-Common Metals 110 (1985) 61. C. Mondoloni, R. Suryanarayanan, M. Konczykowski, O. Gorochov, H. Bach, J. Magn. Magn. Mater. 63–64 (1987) 600. T.I. Jones, L.R. Norlock, R.R. Boucher, J. Less-Common Metals 5 (1963) 128. J.F. Cannon, H.T. Hall, J. Less-Common Metals 40 (1975) 313. W.E. Gardner, J. Penfold, T.F. Smith, I.R. Harris, J. Phys. F 2 (1972) 133. R.A. Gordon, Ph.D. thesis, Cornell University, 1995. C.D.W. Jones, Ph.D. thesis, Cornell University, 1999.
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Transport properties of intermetallic thulium compounds Thomas P. Braun*, Francis J. DiSalvo Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY 14853 -1301, USA Received 31 August 1999; accepted 21 December 1999
Abstract The Seebeck coefficient, electrical resistivity and magnetic susceptibility of TmAl 3 and TmPd 3 are reported. TmAl 3 melts peritectially and was prepared as a single phase sample for the first time. Like TmPd 3 it is a ‘normal’ metal as indicated by both electrical resistivity and magnetic susceptibility measurements. The room temperature thermopower of TmAl 3 is moderate (15 mV/ K) while that of TmPd 3 falls within the expected range for typical metals (25 mV/ K). Further properties are also reported for YbAl 3 , TmAl 2 and TmPd. From the magnetic susceptibility data it can be concluded that thulium adopts the normal trivalent state in all these compounds. 2000 Elsevier Science S.A. All rights reserved. Keywords: Thermopower; Thulium compounds; Intermetallic phases; Intermediate valence
1. Introduction The search for new thermoelectric materials has been revitalised in recent years [1–7]. Thermoelectric devices are designed to utilize the Peltier effect, either by developing an electric potential in a thermal gradient, or by cooling at the junction of two materials when an electrical current is flowing through it [8]. In addition to a general demand for improved performance of these materials, it has been proposed to apply these materials for thermoelectric cooling [9]. Besides various attempts to improve existing materials which are based on semiconductors like e.g. Sb 2 Te 3 / Bi 2 Te 3 alloys, some intermetallic phases containing rare earth elements have been recently studied in some detail [10]. These compounds show surprisingly high values of the Seebeck coefficient (‘thermopower’) if the rare earth atoms are in an intermediate valence state. The intermediate valence state has been investigated for various intermetallic compounds of cerium and ytterbium [11–17]. It manifests itself in a number of anomalies e.g. in the electrical resistivity or the magnetic susceptibility, and quite often also leads to relatively large values of the Seebeck coefficient. In this state a 4f electron is neither localized on the rare earth atom nor completely delocalized in the conduction band. Instead, the local f states form a many-body resonance at the Fermi level in the conduction
band. The thereby increased density of states at the Fermi energy is believed to account for the high values of the thermopower. So far mostly intermetallic compounds containing either cerium (e.g. CePd 3 [18]) or ytterbium (e.g. YbAl 3 [19,20]) have been investigated. In these cases the rare earth atom contains one f electron or hole, respectively. According to an exploratory theoretical study, the availability of more f electrons or holes might decrease the Seebeck coefficient although no splitting of the f-levels has been included in these calculations [2]. No experimental data are available yet to advance this discussion. We therefore decided to investigate the thermoelectric properties of the thulium analogues of the intermetallic compounds (CePd 3 , YbAl 3 and YbPd) with the highest Seebeck coefficients of all rare earth intermetallics. Thulium compounds seem to be an ideal candidate to study the effect of additional f holes on the transport properties. With a 4f 12 ground state configuration thulium possesses two f holes. Furthermore, some intermediate valence compounds of thulium are known (e.g. TmSe [21–24]), although these are not intermetallic phases.
2. Results and discussion
2.1. Preparation *Corresponding author. E-mail address: [email protected] (T.P. Braun)
In previous studies TmAl 3 could never be prepared as a
0925-8388 / 00 / $ – see front matter 2000 Elsevier Science S.A. All rights reserved. PII: S0925-8388( 00 )00714-3
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T.P. Braun, F. J. DiSalvo / Journal of Alloys and Compounds 305 (2000) 43 – 48
single phase compound but only in conjunction with TmAl 2 . Except for an ‘estimated’ phase diagram no thermodynamic data are available for the system Tm–Al [25]. According to this phase diagram TmAl 3 is expected to decompose peritectially, although the temperature of this transition remains unknown. Our attempts to prepare TmAl 3 according to the reported procedures by arc melting only yielded mixtures of TmAl 3 and the higher melting compound TmAl 2 . To confirm the assumed peritectic decomposition of TmAl 3 we performed differential thermal analysis (DTA) scans on various samples. It proved essential to record the thermal profile of a pre-reacted sample, since the highly exothermic initial reaction of the pure metals otherwise dominates the DTA. Furthermore the experiment had to be performed in tantalum ampoules, reactions in quartz containers yielded irreversible DTAs and the products appeared to be oxidized. The thermal analysis of a prereacted sample (shown in Fig. 1) revealed a reversible endothermic reaction at |11008C which was attributed to the peritectic reaction TmAl 3 5TmAl 2 1Al. In order to prepare single phase samples of TmAl 3 it is therefore required to anneal stoichiometric mixtures of the elements in sealed Ta ampoules at temperatures below the decomposition temperature of |11008C. However, even if the temperature is constantly kept at only 10008C, the resulting product contains a significant amount of TmAl 2 . Indeed it has been found that, after annealing periods of several weeks, single phase samples of TmAl 2 could be obtained (vide infra). The amounts of aluminum that are ‘lost’ during annealing can be accounted for in two ways: either the vapour pressure of aluminum at these tempera-
tures is high enough to shift the equilibrium composition of the solid phase, or a solid state reaction with the container wall is taking place. As a result we detected a metallic deposit on the inside wall of the tantalum container that could not be analysed further. Single phase samples (as determined by X-ray powder diffractometry) of TmAl 3 could be finally prepared by the following two-step method: first a stoichiometric mixture of the elements is arc-melted. To avoid a substantial loss of thulium during this process, the elements are initially spatially separated and the arc used to selectively melt the aluminum. The aluminum melt is subsequently moved to the thulium, which quickly dissolves, into the melt. Typical weight losses during this step are generally lower than 1 wt.%. The inhomogeneous bead is then finely ground and pressed to pellets. The pellet is subsequently annealed in arc-welded tantalum ampoules (sealed in quartz ampoules for protection) for 2 days at 8508C. The X-ray powder diffractogram of TmAl 3 prepared by this method is shown in Fig. 2. No secondary phases can be detected and the refined lattice constant (Cu 3 Au-type) of 420.5(1) pm corresponds well with published values [25,26]. Single phase samples of YbAl 3 could also be prepared following the same procedure as in the case of TmAl 3 . In this case the weight loss during the initial arc-melting is slightly higher. Nevertheless we successfully used a sample of YbAl 3 prepared by this way as a reference for our thermopower measurements. The characteristic magnetization curve (vide infra) was reproduced to further characterize the sample. It appears that this preparation is a convenient alternative to the rather elaborate flux-growth /
Fig. 1. Differential thermal analysis of TmAl 3 .
T.P. Braun, F. J. DiSalvo / Journal of Alloys and Compounds 305 (2000) 43 – 48
45
Fig. 2. Powder diffractogram of single phase TmAl 3 . The simulated pattern is indicated as a bar graph.
hot-pressing method used to prepare specimens for previous thermopower measurements [20]. A sample of TmAl 2 was obtained during our initial annealing experiments. An arc-melted stoichiometric reaction mixture for the preparation of TmAl 3 was repeatedly ground and pressed into a pellet, which was annealed at 10008C for a total of 6 weeks. After this procedure, the sample consisted of a single phase TmAl 2 pellet. Both binary intermetallic phases of thulium and palladium can be easily obtained by arc-melting the respective stoichiometric mixtures of the elements [27]. Beads prepared in a special cast mold with two parallel sides (|4 mm apart, 7 mm deep and 28 mm long) have been subsequently annealed at 11008C (TmPd) and 9008C (TmPd 3 ), respectively, for 1 week. In all cases the purity of the phases was established by powder X-ray diffractometry.
2.2. Thermopower measurements The Seebeck coefficients of TmAl 3 , TmPd 3 and TmPd have been measured simultaneously with the respective thermal conductivities by a steady-state method using a custom built apparatus [28,29]. In this set-up the thermal conductivity and the Seebeck coefficient can be measured from ambient temperature to about 30 K. Suitable samples were cut from the annealed pellets or beads in a roughly rectangular shape with typical dimensions of 33335 mm. For the compounds containing palladium, we used indium
to solder the thermocouples, a copper heat sink and a heating resistor onto the samples. Since liquid indium does not bond well mechanically to TmAl 3 , we used silver epoxy to contact this sample. To ensure optimal thermal contact the thermocouples have been embedded in small holes (ø0.04 mm) drilled into the sample. YbAl 3 has been long known to exhibit a rather high thermopower. The Seebeck coefficient reaches an absolute maximum of approximately 290 mV/ K at around 2008C and declines only little up to 3008C [19]. Indeed, the so-called ‘thermoelectric power factor’ (the product of the square of the Seebeck coefficient and electrical conductivity) of this compound is reported to have the highest known value [20]. TmAl 3 on the other hand exhibits a rather modest Seebeck coefficient of only 15 mV/ K at room temperature. It also shows an interesting phase change at around 80 K, indicating a possible change of the dominant carrier type at lower temperatures. The data are shown in Fig. 3 (open circles). Obviously, the maximum value of 15 mV/ K does not render TmAl 3 a candidate material for thermoelectric applications. However, these data allow a comparison of the thermopowers within the isostructural triad TmAl 3 , YbAl 3 and LuAl 3 . We will come back to this aspect after reporting the remaining measurements. The temperature dependence of the Seebeck coefficient of TmPd 3 exhibits a maximum of 25 mV/ K at room temperature (see Fig. 3). This value is quite low and falls within the expected range for typical metals.
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T.P. Braun, F. J. DiSalvo / Journal of Alloys and Compounds 305 (2000) 43 – 48
The device was evacuated and partially back filled with He for the temperature dependent measurements in a helium bath cryostat. The results for TmAl 3 and TmPd 3 are shown in Fig. 4. Both samples show a linear temperature dependence over the entire temperature range. The room temperature value for TmAl 3 is about 30 mV cm, for TmPd 3 we measured a value of around 50 mV cm. The extrapolated low temperature offset of the latter sample was about 20 mV cm, indicating a higher concentration of defects and / or impurities. The temperature dependent part of the resistivity however corresponds rather well to that of TmAl 3 .
2.4. Magnetic measurements
Fig. 3. Seebeck coefficients of TmAl 3 (circles) and TmPd 3 (squares).
TmPd shows an even smaller thermopower, its Seebeck coefficient gradually increasing to a maximum value of only 1 mV/ K.
2.3. Electrical measurements The electrical conductivities of TmAl 3 and TmPd 3 have been determined with a modified four-probe measurement in the temperature range from room temperature to about 30 K (5 K for TmPd 3 ). The samples have been cut into a flat rectangular shape of approximate dimensions 83432 mm. Copper wire current leads have been soldered on the short ends with indium, with two voltage leads attached with silver epoxy parallel to the former, |3 mm apart from each other. This whole set-up was glued to a copper block with epoxy cement and encapsulated in a brass container.
The magnetic susceptibilities of TmAl 3 , TmAl 2 , TmPd 3 , TmPd and YbAl 3 have been measured on a Quantum design SQUID magnetometer. Data were collected from room temperature to 5 K at intervals of 10 K. Typical fields were in the range of 1 to 2 T, samples sizes varying from about 100 to 500 mg. The data have been analyzed by two different methods. First a linear regression has been performed for the inverse molar susceptibilities versus the temperature according to the Curie–Weiss law: 1 /x 5 T /CM 2 u /CM . Only the values for temperatures above 50 K have been included in the data analysis to ensure the validity of the assumed linear dependence (the regressions yield Curie temperatures u substantially below that cut-off value — cf. Table 1). In a second non-linear regression a correction for the background susceptibility x0 has been introduced: x 5 x0 1 CM /(T 2 u ). This temperature independent susceptibility accounts for diamagnetic and Pauli paramagnetic contributions as well as for the typically very weak signal from the gel cap containers. The results are summarized in Table 1.
Fig. 4. Electrical resistivity of TmAl 3 (circles) and TmPd 3 (squares).
T.P. Braun, F. J. DiSalvo / Journal of Alloys and Compounds 305 (2000) 43 – 48 Table 1 Magnetic moments of all investigated compounds as extracted from the susceptibility measurements (see text) Compound
TmAl 3 TmAl 2 TmPd 3 TmPd YbAl 3
Linear regression
Non-linear regression
u (K)
u (K)
meff ( mB )
214.6 12.8 21.6 21.5 (Fig. 5)
7.33 7.76 7.12 6.67
214.0 15.0 10.4 26.9 Intermediate
meff ( mB ) 7.31 7.64 7.03 6.95 valent behaviour
Except for the case of YbAl 3 , all samples show typical Curie–Weiss behavior with magnetic moments corresponding to the calculated free-ion value for Tm 31 (7.56
47
mB ). The values do not change significantly if the temperature independent correction x0 is included or not. Thus it can be clearly established that none of the investigated thulium alloys exhibits intermediate valent behavior. A sample of YbAl 3 , prepared by our combination of arc melting and subsequent ‘low temperature’ annealing, showed the expected intermediate valent behavior in the form of a rather broad peak in the reciprocal susceptibility at around 50 K. A linear behavior of x 21 (as indicated by the dashed line in Fig. 5) is observed for temperatures above 150 K. A plot of the magnetic susceptibilities for TmAl 3 and YbAl 3 is given in Fig. 5. At low temperatures the magnetization curve of TmAl 3 deviates significantly from the linear Curie–Weiss fit. This
Fig. 5. Comparison of the magnetic susceptibilities of TmAl 3 (top) and YbAl 3 (bottom).
48
T.P. Braun, F. J. DiSalvo / Journal of Alloys and Compounds 305 (2000) 43 – 48
is also the case for the other intermetallic thulium compounds studied, TmAl 2 , TmPd 3 and TmPd.
3. Conclusions This study was motivated by our interest in intermediate valent intermetallic compounds of rare earth elements as potential materials for thermoelectric applications. We investigated four simple cubic alloys, TmAl 3 , TmAl 2 , TmPd 3 and TmPd, all of which have been known to exist, but whose electrical and magnetic properties have not been investigated previously. We succeeded in the preparation of single phase samples and measured their relevant properties. We found all four materials to be ‘simple’ metals containing trivalent thulium. It is interesting to compare the thermopowers within the series TmAl 3 , YbAl 3 and LuAl 3 . All three compounds are isostructural and differ only by the number of 4f electrons for the rare earth metal. With a closed subshell configuration 4f 14 for Lu 31 , there is no possibility for intermediate valent behavior. As expected, the reported thermopower is rather low (about 13 mV/ K at room temperature) [19]. YbAl 3 (4f 13 or one f hole) is known to be intermediate valent and its peak thermopower is an order of magnitude higher (around 290 mV/ K at room temperature) than that of LuAl 3 [19]. With a 4f 12 ground state (two f holes), we hoped that TmAl 3 could be intermediate valent. While this is clearly not the case, its Seebeck coefficient falls between the values of YbAl 3 and LuAl 3 .
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
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Acknowledgements
[22]
Funding for this investigation was provided by ONR. This work made use of the Cornell Center for Materials Research facilities supported by NSF Funded Award [DMR-9632275. Some of the samples have been prepared by G. Glass in the course of an undergraduate summer research project. We would like to thank R. Eger (Max¨ Festkorperforschung, ¨ Planck-Institut fur Stuttgart) for performing the DTA experiments of TmAl 3 . Thanks are also due to an unknown reviewer for helpful comments that improved the readability of this paper.
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