Thermoelectric properties of ternary transition metal antimonides

Journal of Alloys and Compounds 296 (2000) 235–242

L

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Thermoelectric properties of ternary transition metal antimonides a,b c a, b ,† d G. Melnyk , E. Bauer , P. Rogl *, R. Skolozdra , E. Seidl a

b

¨ Physikalische Chemie der Universitat ¨ Wien, Wahringerstraße ¨ Institut f ur 42, A-1090 Wien, Austria Institute of Inorganic Chemistry, University of Lviv, Kyryla and Mefodiya Street 5, 290005 Lviv, Ukraine c ¨ Experimentalphysik, TU Wien, Wiedner Hauptstrasse 8 – 10 A-1040 Wien, Austria Institut f ur d ¨ ¨ , Schuttelstrasse ¨ Atominstitut der Osterreichischen Universitaten 115, A-1020 Wien, Austria Received 24 June 1999; accepted 24 June 1999

Abstract Novel compounds T 6 MBi 2 , where T5Zr, Hf; M5Fe, Co, Ni, were synthesised by arc melting elemental combinations. Isotypism of these compounds with the ordered Fe 2 P-type was established from Rietveld X-ray powder data. Physical properties (electrical resistivity and thermoelectric power) were investigated for a series of ternary transition metal compounds with stoichiometries such as TM 12x X and T 6 MX 2 , where T is an electropositive transition metal (Zr, Hf and Nb), M is a metal from the iron group (Fe, Co, Ni) and X is Sb or Bi. Resistivities reveal a general metallic behaviour except for ZrCoSb and NbFeSb which are characterized by variable range hopping conductivity in a substantial temperature region. Thermoelectric power of these materials does not exceed 100 mV K 21 .  2000 Elsevier Science S.A. All rights reserved. Keywords: Ternary transition metal antimonides and bismuthides; Rietveld refinement; Thermoelectric power; Seebeck coefficient; Electrical resistivity

1. Introduction Transition metal arsenides and antimonides with the filled scutterudite type (h 1 Co 4 As 12 ) have recently gained major interest with respect to their technologically promising properties for thermoelectric power generation [1]. Although many investigations in ternary antimonide systems concentrated on the phase equilibria, compound formation and their crystal structures [2–8], there is still a serious lack of profound knowledge particularly on the thermoelectric properties of these compounds as a function of composition. Rather little is at present known on the corresponding bismuth-containing systems. The authors have recently established phase equilibria in the ternary systems Nb–Fe–Sb [9] and Zr–Fe–Sb [10], revealing a series of ternary compounds such as NbFeSb (AlLiSitype), ZrFe 12x Sb (0.3,x,0.5; defect TiNiSi-type), Zr 6 Fe 12x Sb 21x (0,x,0.24; ordered Fe 2 P-type) and Zr 5 Fe 0.44 Sb 2.56 (W5 Si 3 -type). The compositions TMX and

*Corresponding author. Tel.: 143-1427752456; fax: 143-142779524. E-mail address: [email protected] (P. Rogl) † In memoriam.

T 6 MX 2 turned out to be adopted by a rather large group of combinations of various elements T, M, X, where T is an electropositive transition metal (Zr, Hf, Nb), M is a metal from the iron group (Fe, Co, Ni) and X is Sb or Bi. Whereas TMX compounds diversify further into a large variety of structure types partially also with defects on the M-sites, T 6 MX 2 compounds reveal small defects in the M-sites or show mutual exchange among M, X metals at a constant content of T, but all crystallize with the Fe 2 Ptype. Isotypism has been realized for Zr 6 CoAs 2 [4], Zr 6 FeSb 2 [8,10], (Zr, Hf) 6 Fe 12x Sb 21x [9], and for Hf 6 (Fe, ¨ Co, Ni) 12x Sb 21x [2]. From extended Debye–Huckel calculations Hf 6 NiSb 2 [2] and Zr 6 CoAs 2 [4] were concluded to behave metal-like. Magnetic susceptibility data, reported for a variety of TMX compounds, revealed Pauli-paramagnetism for Ti(Fe,Co,Ni,Ru)Sb, Nb(Fe,Ru,Rh)Sb, and for VNiSb [3]. Zr 5 FeSb 3 (filled Ti 5 Ga 4 -type) was mentioned in literature as a magnetically ordered compound [11]. Based on the lack of comprehensive data on physical properties, the present paper intends to provide basic information on the formation of novel bismuthides (Zr, Hf) 6 (Fe, Co, Ni)Bi 2 as well as on the thermoelectric properties of compounds TM 12x , X and (Zr, Hf) 6 (Fe, Co, Ni) 12x (Sb, Bi) 21x .

0925-8388 / 00 / $ – see front matter  2000 Elsevier Science S.A. All rights reserved. PII: S0925-8388( 99 )00537-X

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G. Melnyk et al. / Journal of Alloys and Compounds 296 (2000) 235 – 242

2. Experimental Binary and ternary alloy samples, each with a total weight of 1 g, were synthesized by arc-melting proper amounts of the constituent elements under high purity argon on a water-cooled copper hearth. The starting materials were used as ingots of antimony and bismuth (99.9 mass% from Johnson-Matthey, UK), of niobium and tantalum in form of rods (99.9%, Alfa Ventron, Karlsruhe, Germany) and of vanArkel-zirconium and hafnium (99.98% Zr, 99.8% Hf). Iron group metals were in the form of rods (Co, Ni) or platelets (Fe), which were surface cleaned in dilute HNO 3 prior to use (99.9%, all from Alfa-Ventron). The samples were repeatedly remelted under low electric current. The weight losses due to vaporization of Sb, Bi were generally less than 2 mass% and were compensated for beforehand. The alloys were then sealed in evacuated quartz tubes and annealed for 170–250 h at 600 or at 8008C. After heat treatment, the samples were quenched by submerging the silica tubes in cold water. All compounds T 6 MX 2 proved to be moisture sensitive and precautions needed to be taken to avoid extensive handling of the specimens in air (see below). Samples for microprobe analysis (EMPA) were cut with a diamond saw and polished metallographically with water-free lubricants and diamond suspension. Quantitative composition analyses were performed on a CAMEBAX SX50 wavelength dispersive spectrograph comparing the Ka, La emissions of the three elements in the alloys with those from Zr, Fe, Sb elemental standards and applying a deconvolution and ZAF correction procedure [12]. The experimental parameters employed were: acceleration voltage of 15 kV, sample current of 15 nA and spectrometer crystals such as PET for Zr La and Sb La, and LiF for the Fe Ka radiation. Precise lattice parameters and standard deviations were obtained by a least-squares refinement of room temperature Guinier–Huber X-ray (Cu Ka 1 ) powder data employing an internal standard of 99.9999 mass% pure Ge (a Ge 5 0.5657906 nm). For quantitative refinement of the atom positions X-ray intensities were recorded from flat specimens mounted in a Siemens D5000 automatic powder diffractometer (Cu Ka). During exposure samples were short-term moisture protected by an X-ray amorphous sprayed-on thin film of varnish. Full matrix-full profile Rietveld refinements were performed with the FULLPROF program [13]. The electrical resistivity of bar-shaped samples was measured using a four probe d.c. method in the temperature range from 4.2 K to room temperature. Pieces with a length of about 5 mm were used for differential thermopower measurements. The absolute thermopower Sx (T ) was calculated using the following equation: VPb /x Sx (T ) 5 SPb (T ) 2 ]] DT

where Spb (T ) is the absolute thermopower of lead whose values are taken from the literature [14]. (VPb /x) is the thermal-induced voltage across the sample, depending on the temperature difference DT.

3. Results and discussion

3.1. Compound formation and structural chemistry 3.1.1. The compounds of ( Zr, Hf )Fe12 x Sb, Nb12 x Ta x CoSb, NbCoSb12 x Bi x and HfNiSb Crystallographic information on the ternary compounds TM 12x X is summarized in Table 1 and compares well with data from literature. Accordingly compounds with the AlLiSi-type such as ZrCoSb, HfCoSb, NbFeSb and NbCoSb form at stoichiometric compositions. Rietveld refinements revealed no deviation from the formula TMX with full occupation of all atom sites and no significant deviation from full atom order (AlLiSi-type). Replacement of T and X atoms by heavy metals such as Ta for T and Bi for X, however, did not result in the formation of extended solid solutions Nb 12x Tax FeSb or NbFeSb 12x Bix . In both cases, unit cell dimensions stayed practically constant and alloys turned multiphase even for values of x as small as 0.2. In contrast to the stoichiometric AlLiSi-type compounds all compounds with the TiNiSi-type revealed significant deviation from full stoichiometry showing defects on the M-sites. The homogeneity region for ZrFe 12x Sb was recently determined by the present authors in the 6008C isothermal section for 0.3,x,0.5 [10]. A similar situation is encountered in our isotypic alloys HfFe 12x Sb and HfNi 12x Sb with x around 0.4. 3.1.2. Rietveld refinement of the crystal structure of isotypic ( Zr, Hf )6 ( Fe, Co, Ni)12 x ( Sb, Bi)21 x (ordered Fe2 P-type) A detailed compilation of our results (full matrix, full profile Rietveld refinements) and literature data on structure types and lattice parameters of the ternary compounds and phases synthesized are given in Table 2a,b. Crystal symmetry and atom site distribution is confirmed for the compound Zr 6 Fe 12x Sb 21x (ordered Fe 2 P-type [2], earlier listed as Zr 6 CoAl 2 -type [8]). Refinements for all the single-phase compounds prepared at the stoichiometric composition M 6 TX 2 with M5Zr, Hf T5Fe, Co, Ni and X5Sb, Bi were consistent with the fully ordered hexagonal Fe 2 P-type. There were no deviations from full occupancy although small solubility ranges may exist as for instance observed for Zr 6 Fe 12x Sb 21x in the 8008C isothermal section (0,x,0.24) [10]. The data presented in Table 2a,b were standardised with respect to proper crystallographic setting of unit cell and atom positions using the program routine Typix [15]. The compounds T 6 M 1 X 2 were synthesised for the first time. Due to incomplete reaction kinetics or slight deviations

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237

Table 1 Crystallographic and thermoelectric properties for alloys T 6 MX 2 and TMX a Phase

Heat treatment

Struct. type

Space group

Lattice parameters (nm)

Physical properties QD [K] R [mV cm K 21 ]

a

b

c

0.775150(4) 0.76707(7) 0.775187(6) 0.766825(4) 0.773314(3) 0.763951(6)

– – – – – –

0.366335(2) 0.36204(8) 0.365814(1) 0.361482(2) 0.368035(2) 0.364096(3)

95 88.5 199 105.6 192.7 142

Zr 6 FeSb 2 Hf 6 FeSb 2 Zr 6 CoSb 2 Hf 6 CoSb 2 Zr 6 NiSb 2 Hf 6 NiSb 2

8008C / 250 h 8008C / 250 h 8008C / 250 h 8008C / 250 h 8008C / 250 h 8008C / 250 h

Fe 2 P Fe 2 P Fe 2 P Fe 2 P Fe 2 P Fe 2 P

¯ m P62 ¯ m P62 ¯ m P62 ¯ m P62 ¯ m P62 ¯ m P62

Zr 6 FeBi 2 Hf 6 FeBi 2 Zr 6 CoBi 2 Hf 6 CoBi 2 Zr 6 NiBi 2 Hf 6 NiBi 2

8008C / 250 h 8008C / 250 h 8008C / 250 h 8008C / 250 h 8008C / 250 h 8008C / 250 h

Fe 2 P Fe 2 P Fe 2 P Fe 2 P Fe 2 P Fe 2 P

¯ m P62 ¯ m P62 ¯ m P62 ¯ m P62 ¯ m P62 ¯ m P62

0.78562(8) 0.77808(16) 0.784965(4) 0.77773(8) 0.78281(4) 0.75707(10)

– – – – – –

0.36914(7) 0.36465(17) 0.370001(2) 0.36225(8) 0.37287(7) 0.36543(6)

Non-BG – 167.2 – – –

NbFeSb NbFeSb ZrCoSb ZrCoSb HfCoSb HfCoSb HfNiSb HfNi 12x Sb NbCoSb NbCoSb ZrFe 12x Sb ZrFe 12x Sb HfFe 12x Sb HfFe 12x Sb HfFe 12x Sb Zr 5 Fe x Sb 31y Zr 5 Fe x Sb 31y Zr 5 Fe 0.44 Sb 2.56 Zr 5 Fe 0.45 Sb 2.55 Nb 12x Ta x FeSb NbFeSb 12x Bi x

8008C / 250 h 8008C / 250 h 8008C / 250 h 6008C / 1 w 8008C / 250 h 6008C / 1 w 8008C / 250 h As cast 8008C / 250 h 8008C / 250 h 8008C / 250 h 8008C / 250 h 8008C / 250 h 8008C / 250 h 8008C / 250 h 8008C / 250 h

AlLiSi AlLiSi AlLiSi AlLiSi AlLiSi AlLiSi AlLiSi TiNiSi AlLiSi AlLiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi Ti 5 Ga 4 Ti 5 Ga 4 W5 Si 3 W5 Si 3 AlLiSi AlLiSi

¯ m F43 ¯ m F43 ¯ m F43 ¯ m F43 ¯ m F43 ¯ m F43 ¯ m F43 Pnma ¯ m F43 ¯ m F43 Pnma Pnma Pnma Pnma Pnma P63 /mcm P63 /mcm I4 /mcm I4 /mcm ¯ m F43 ¯ m F43

0.59500(7) 0.5952(2) 0.60677(3) 0.6068 0.60381(4) 0.6040 0.60089(7) 0.66391(25) 0.59004(3) 0.5896(2) 0.68202(28) 0.680784(6) 0.67379(40) 0.67346(10) 0.67410(26) 0.853642(7) 0.8551(1) 1.108752(4) 1.1066(1) 0.59444(2) 0.59505(2)

– – – – – – – 0.41455(06) – – 0.41774(11) 0.419117(3) 0.41447(06) 0.41425(03) 0.41380(07) – – – – – –

– – – – – – – 0.73729(34) – – 0.73924(51) 0.741008(6) 0.73754(22) 0.73662(17) 0.73624(39) 0.582482(3) 0.5853(1) 0.554765(2) 0.5535(1) – –

Isolating behaviour

a

8008C / 250 h 8008C / 250 h 8008C / 250 h

Comments

71 96.2 195.6 200 75.5 207

302.3

[3] Isolating behaviour [20] 190.5

9076 [20]

– – Non-BG Non-BG – – – 210

x50.5

58.2

[3] x50.5 x50.3 x50.5 x50.4 x50.3 x50.63, y50.21 x51, y50 [11]

Non-BG [8] Isolating behaviour

¨ BG, modified Bloch–Gruneisen relation.

from stoichiometry, the alloys Hf 6 Fe 1 Bi 2 and Hf 6 Ni 1 Bi 2 were not obtained in single phase condition revealing some amounts of secondary impurity phases (see Tables 1 and 2), although there is no doubt about the formation and the isotypism with the Fe 2 P-type. Fig. 1a displays the crystal structure of Zr 6 Fe 1 Sb 2 in a three-dimensional view of a ball (atom) and stick (bond) model with detailed insight in the interatomic bonding situation reflected by interatomic distances within the first neighbour shell in Table 2a,b. In the fully ordered arrangement, M-atoms are at the centres of triangular prisms formed by T atoms, T 6 M. Pnicogen atoms reside within larger triangular T-metal tubes with tetrakaidekahedral coordination T 6 1X 3 and form infinite strings parallel to the c-axis. Alternatively one may view the crystal structure as an array of triangular columns of T 1 -atoms (each triangular prism centered by an iron group atom) within a hexagonal array of triangular columns of T 2 -atoms (each triangular prism centered by a pnicogen atom). The tetrakaidekahedral coordination of the pnicogen

atoms naturally arrives from the shift of the two sets of infinite columns against each other by a vector of c / 2 (see Fig. 1b).

3.2. Physical properties In order to characterise the physical behaviour of the investigated ternary compounds, in particular with respect to possible thermoelectric applications, resistivity and thermoelectric power measurements were performed from 4 K up to room temperature. Results for the temperaturedependent electrical resistivity are shown in Figs. 2 and 3 and for the thermoelectric power in Figs. 4 and 5. Compounds T 6 MX 2 are characterised by a generally metallic behaviour with the residual resistivity r0 ranging from about 40–500 mV cm, classifying this group of ternary compounds as dirty metals. At somewhat elevated temperatures r (T ) of all the investigated compounds exhibits a rather strong curvature except for Zr 6 CoSb 2 and

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238

Table 2a Structural data of compounds T 6 MSb 2 a Parameter / compound

Zr 6 FeSb 2

Hf 6 FeSb 2

Zr 6 CoSb 2

Hf 6 CoSb 2

Zr 6 NiSb 2

Hf 6 NiSb 2

a (nm) c (nm) V (nm 3 ) rx (Mg m 23 ) 2Q range Reflections measured Number of variables R F 5 S uF0 2 Fc u /S F0 R I 5 S uI0B 2 IcB u /S I0B 2 R wP 5 [S w i uy 0i 2 y ci u / 2 1/2 S w i uy 0i u ] R P 5 S uy 0i 2 y ci u /S uy 0i u 2 1/2 R e 5 [(N 2 P 1 C) /(S w i y 0i )] 2 2 x 5 (R wP /R e )

0.775150(4) 0.366335(2) 0.190625(3) 7.3747(1) 15–110 132 22 0.048 0.065

0.767203(5) 0.361382(3) 0.184212(4) 12.3512(4) 15–110 130 22 0.062 0.074

0.775187(6) 0.365814(1) 0.190372(3) 7.4114(1) 15–110 132 22 0.052 0.069

0.766825(4) 0.361486(2) 0.184083(3) 12.3876(2) 15–110 130 22 0.048 0.067

0.773314(3) 0.368035(2) 0.190604(3) 7.4005(1) 20–110 132 22 0.068 0.080

0.763951(6) 0.364096(3) 0.184025(4) 12.3895(3) 15–110 130 17 0.059 0.067

0.192 0.125 0.055 12.19

0.126 0.092 0.047 7.19

0.167 0.118 0.053 9.93

0.135 0.103 0.038 12.62

0.109 0.084 0.057 3.66

0.104 0.080 0.052 4.00

0.6002(4) 1.88(5) 1.00

0.5962(5) 1.9(1) 1.00

0.6011(3) 1.54(6) 1.00

0.5962(3) 1.03(7) 1.00

0.5999(4) 1.77(6) 1.00

0.2432(3) 1.91(4) 1.00

0.2428(5) 2.2(1) 1.00

0.2422(3) 1.23(6) 1.00

0.2427(3) 1.03(7) 1.00

0.2434(3) 2.11(7) 1.00

1.67(3) 1.00

2.1(2) 1.00

2.6(3) 1.00

1.0(2) 1.00

1.7(3) 1.00

1.73(4) 1.00

2.2(1) 1.00

1.48(9) 1.00

1.03(7) 1.00

2.0(1) 1.00

0.2961 0.3224 0.3293 0.2592 0.2968 0.3217 0.3224 0.3293 0.2592 0.2961 0.2968

0.2987 0.3286 0.3295 0.2628 0.2990 0.3251 0.3286 0.3295 0.2628 0.2987 0.2990

0.2960 0.3230 0.3276 0.2602 0.2951 0.3221 0.3230 0.3276 0.2602 0.2951 0.2960

Atom parameters, T 1 , T 2 5Zr or Hf; M5Fe, Co or Ni. T 1 in 3f(x, 0, 1 / 2) x 0.5961(4) Beq (Biso )10 2 (nm 2 ) 1.75(9) Occupation 1.00 T 2 in 3g (x, 0, 0) x 0.2432(4) Beq (Biso )10 2 (nm 2 ) 1.9(1) Occupation 1.00 M in 1b (0, 0, 1 / 2) Beq (Biso )10 2 (nm 2 ) 1.7(2) Occupation 1.00 Sb in 2c (1 / 3, 2 / 3, 0) Beq (Biso )10 2 (nm 2 ) 1.88(9) Occupation 1.00 Distances (nm) within T1 4 Sb 4 T2 2 T2 T2 2M 2 Sb 2 T2 4 T1 2 T1 M 6 T2 Sb 6 T1 3 T2

the first nearest-neighbor coordination, standard deviation ,0.0005 nm CN510 0.2986 0.2960 0.2985 0.3288 0.3230 0.3286 0.3292 0.3281 0.3294 CN512 0.2628 0.2597 0.2625 0.2995 0.2964 0.2997 0.3265 0.3232 0.3260 0.3288 0.3230 0.3286 0.3292 0.3281 0.3294 CN56 0.2628 0.2597 0.2625 CN59 0.2986 0.2960 0.2985 0.2995 0.2964 0.2997

¨ Zr 6 NiSb 2 . This allows the Bloch–Gruneisen relation to be applicable for both the latter compounds. Accordingly the evaluated electron–phonon coupling constants R are 195.6 and 75.5 mV cm K 21 for Zr 6 CoSb 2 and Zr 6 NiSb 2 whilst the Debye temperatures QD amount to 199 and 192.7 K, respectively (see Table 1). To account also for the other compounds, a Mott–Jones term has to be added (k T 3 ), which considers scattering of conduction electrons on a narrow feature of the electronic density of states near the Fermi energy. Such structures are supposed to emerge from d-states of the elements involved. From least-squares

¨ fits of the thus modified Bloch–Gruneisen relation to the experimental data, the material-specific parameters R and QD are found, which are all listed in Table 1. When analysing the remaining Zr-compounds (Fig. 3a), the temperature-dependent behaviour of the various compounds cannot be accounted for in terms of simple electron–phonon interaction mechanisms, because unrealistic low values of the Debye temperature are revealed, except for Zr 5 Fe 0.63 Sb 3.21 (QD 5210 K). It is supposed that in these cases magnetic scattering processes substantially contribute to the overall r (T ) behaviour.

G. Melnyk et al. / Journal of Alloys and Compounds 296 (2000) 235 – 242

239

Table 2b Structural data of compounds T 6 MBi 2 a Parameter / compound

Zr 6 FeBi 2

Zr 6 CoBi 2

Hf 6 CoBi 2

Zr 6 NiBi 2

a (nm) c (nm) V (nm 3 ) rx (Mg m 23 ) 2Q range Reflections measured Number of variables R F 5 S uF0 2 Fc u /S F0 R I 5 S uI0B 2 IcB u /S I0B R wP 5 [S w i uy 0i 2 y ci u 2 /S w i uy 0i u 2 ] 1 / 2 R P 5 S uy 0i 2 y ci u /S uy 0i u R e 5 [(N 2 P 1 C) /(S w i y 20i )] 1 / 2 x 2 5 (R wP /R e )2

0.785672(3) 0.369637(1) 0.197601(2) 8.5804(1) 15–110 138 22 0.039 0.052 0.161 0.116 0.048 11.25

0.784965(4) 0.370001 (2) 0.197440(1) 8.6133(1) 15–110 138 22 0.063 0.088 0.173 0.135 0.063 7.54

0.777823(3) 0.362562(2) 0.189965(3) 13.5289(2) 15–110 132 22 0.068 0.085 0.154 0.132 0.057 7.30

0.782687(4) 0.372053(3) 0.197384(4) 8.6138(2) 15–110 136 22 0.072 0.091 0.183 0.156 0.067 7.46

0.6049(4) 1.07(7) 1.00

0.5964(5) 1.54(9) 1.00

0.6083(3) 0.96(8) 1.00

0.6026(6) 1.07(8) 1.00

0.2390(4) 1.08(7) 1.00

0.2425(4) 1.03(9) 1.00

0.2362(6) 0.92(7) 1.00

0.2399(5) 1.26(7) 1.00

1.01(5) 1.00

0.98(9) 1.00

1.06(5) 1.00

0.87(6) 1.00

1.03(4) 1.00

1.36(6) 1.00

1.11(8) 1.00

0.98(7) 1.00

Distances (nm) within the first nearest-neighbor coordination T1 4 Bi CN510 0.3040 4 T2 0.3279 2 T2 0.3312 T2 2M CN512 0.2635 2 Sb 0.3058 2 T2 0.3252 4 T1 0.3279 2 T1 0.3312 M 6 T2 CN56 0.2635 Bi 6 T1 CN59 0.3040 3 T2 0.3058

0.3022 0.3324 0.3338 0.2654 0.3036 0.3297 0.3324 0.3338 0.2654 0.3022 0.3036

0.3006 0.3216 0.3242 0.2581 0.3042 0.3182 0.3216 0.3242 0.2581 0.3006 0.3042

0.3035 0.3289 0.3394 0.2643 0.3041 0.3252 0.3289 0.3394 0.2643 0.3035 0.3041

Atom parameters, T 1 , T 2 5Zr or Hf; M5Fe, Co or Ni T 1 in 3f (x, 0, 1 / 2) x Beq (Biso )10 2 (nm 2 ) Occupation T 2 in 3g (x, 0, 0) x Beq (Biso )10 2 (nm 2 ) Occupation M in 1b (0, 0, 1 / 2) Beq (Biso )10 2 (nm 2 ) Occupation Bi in 2c (1 / 3, 2 / 3, 0) Beq (Biso )10 2 (nm 2 ) Occupation

a

¯ m, centre at 62¯ m; Z51. Structure type is ordered Fe 2 P; space group is P62

The temperature-dependent resistivity of the 1:1:1 compounds (ZrCoSb, NbFeSb, HfCoSb and Nb 0.8 Tao 0.2 FeSb) is displayed in Fig. 3b in a normalised presentation. Both metallic and non-metallic behaviour is encountered. In order to account for r (T ) of ZrCoSb and NbFeSb we tried to use the resistivity dependence described by a simple activation behaviour represented by

S D

Egap r 5 r0 exp ]] . 2k B T However, in both cases, neither at high, nor at low temperatures, this model is able to explain the experimental features. It is well known [16,17] that compounds with large values of the resistivity can exhibit localisation

effects due to disorder. Thus, a new type of a transport process may appear: variable range hopping, assisted by thermally excited phonons. The conductivity (s 51 /r ) is then given [17] by

H S D J.

T0 s 5 s exp – ] T

1/4

A least squares fit of this model to the data reveals excellent agreement over the rather extended temperature range from 4 to 200 K for ZrCoSb and from 4 to 40 K for NbFeSb. The characteristic temperature T 0 is found in the former case to be 18 660 K and in the latter 87 K, where the constant T 0 is a measure for the localisation length j and the electronic density of states. Such a general hopping type of conductivity does not

240

G. Melnyk et al. / Journal of Alloys and Compounds 296 (2000) 235 – 242

Fig. 1. The crystal structure of Zr 6 FeSb 2 (ordered Fe 2 P-type) in three-dimensional view; (a) bonding among atoms in a ball and stick model. The unit cell is outlined with thin lines; (b) the nearest neighbour coordination around M- and X-atoms is shown in form of two systems of triangular prism columns (for details see text).

comply with the temperature dependence Nb 0.8 Ta 0.2 FeSb. Rather a behaviour with

of

HS D J

T0 s 5 s0 exp – ] T

Fig. 2. Temperature-dependent resistivity r of hZr, Hfj 6 hFe, Co, NijSb 2 .

1/2

is encountered [18], which allows for strong interaction between electrons. A least-squares fit yields then T 0 541.7 K. Metals with poor conductivity are in general good candidates to provide enhanced values of the thermoelectric power. This is, to a first approximation, due to the fact that the low number of free carriers causes a large value of the coefficient of the thermoelectric power. However, as can be seen from Fig. 4, the Seebeck coefficient S(T ) is rather small, ranging at room temperature from about 24 mV K 21 (Zr 6 FeSb 2 ) to about 7 mV K 21 (Hf 6 CoSb 2 ), with a rather smooth temperature dependence. As can be

G. Melnyk et al. / Journal of Alloys and Compounds 296 (2000) 235 – 242

241

Fig. 3. Temperature-dependent resistivity r : (a) for various Zr-containing antimonides; (b) normalized resistivity for hZr, HfjCoSb and NbFeSb.

temperature values Z.T of about ¯1. In order to have such a value of ZT one should find a Seebeck coefficient in a new material of at least 160 mV K 21 [19].

expected from the isolating behaviour of the resistivity, NbFeSb and ZrFeSb are characterized by substantially larger values of the Seebeck coefficient (Figs. 3 and 4). In order to obtain a large value of the figure of merit Z, which describes the efficiency of a particular material with respect to thermoelectric applications, both the Seebeck coefficient should be as large as possible whereas the electrical resistivity should be small [Z5(S 2 /rl), with l being the coefficient of the thermal conductivity]. Materials which are used either for thermoelectric energy conversion or for cooling devices are characterised by room

Acknowledgements

Fig. 4. Temperature-dependent Seebeck coefficient S for various compounds T 6 MX 2 .

Fig. 5. Temperature-dependent Seebeck coefficient S for various compounds TM 12x X.

This research was supported by the Austrian FWF under grants S5604 / S5605 and P12899. The authors are thankful to M. Bohn from CNRS-URA 1278, IFREMER for his expertised XMA measurements.

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References [1] B.C. Sales, D. Mandrus, R.K. Williams, Science 272 (1996) 1325– 1328. [2] H. Kleinke, J Alloys Comp. 270 (1998) 136–141. [3] C.B.H. Evers, C.G. Richter, K. Hartjes, W. Jeitschko, J. Alloys Comp. 252 (1997) 93–97. [4] H. Kleinke, J. Alloys Comp. 252 (1997) L29–L31. [5] O. Sologub, P. Rogl, O. Bodak, J. Phase Equilibria 17 (5) (1996) 399–402. [6] O. Sologub, P. Rogl, O. Bodak, J. Phase Equilibria 16 (1) (1995) 61–64. [7] A. Leithe-Jasper, Diploma-Thesis, Univ. Vienna (1991). [8] Y.U. Kwon, S.C. Sevov, J.D. Corbett, Chem. Mater. 2 (1990) 550–556. [9] G. Melnyk, A. Leithe-Jasper, P. Rogl, R. Skolozdra, J. Phase Equilibria 20 (2) (1999) 113–118. [10] G. Melnyk, A. Leithe-Jasper, P. Rogl, R. Skolozdra, J. Phase Equilibria 20 (5) (1999) 497–507. [11] E. Garcia, H.C. Ku, R.N. Shelton, J.D. Corbett, Solid State Commun. 65 (7) (1988) 757–760.

[12] L. Pouchon, F. Pichoir, J. Mikrosc. Spectrosc. Electron. 10 (1985) 279–305. [13] J. Rodriguez-Carvajal, ‘FULLPROF: A Program for Rietveld Refinement and Pattern Matching Analysis’, Abstracts of the Satellite Meeting on Powder Diffraction of the XV Congr. Intl. Union of Crystallogr., Talence, France, p. 127. [14] J. Christian, Phys. Rev. 15 (1958) 312. ´ L. Gelato, B. Chabot, M. Penzo, K. Cenzual, R. [15] E. Parthe, Gladyshevskii, Typix-standardized data and crystal chemical characterization of inorganic structure types, in: 8th ed., Table E52; as a part of the Gmelin Handbook of Inorganic and Organometallic Chemistry, Vol. 1, Springer Verlag, 1994, p. 233. [16] P.W. Anderson, Phys. Rev. 109 (1958) 1492. [17] N.F. Mott, Phil. Mag. 19 (1969) 835. [18] A. Efros, B.I. Shklovskii, J. Phys. C8 (1975) L49. [19] D.J. Singh, I.I. Mazin, Phys. Rev. B 56 (4) (1997) R1650–R1653. [20] R. Marazza, R. Ferro, G. Rambaldi, J. Less-Common Met. 39 (1975) 341–345.