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Crystal structure, electrical transport properties and electronic structure of the VFe1−xCuxSb solid solution
Journal of Alloys and Compounds 402 (2005) 30–35
Crystal structure, electrical transport properties and electronic structure of the VFe1−xCuxSb solid solution Yu. Stadnyk a,∗ , A. Horyn a , V. Sechovsky b , L. Romaka a , Ya. Mudryk a , J. Tobola c , T. Stopa c , S. Kaprzyk c , A. Kolomiets b a
Ivan Franko L’viv National University, Kyryl and Mephodiy Str. 6, 79005 L’viv, Ukraine b Charles University, Ke Karlovu 5, 121 16 Prague 2, Czech Republic c Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, 30-059 Krakow, Poland Received 28 March 2005; accepted 19 April 2005 Available online 7 July 2005
Abstract The electrical transport properties, crystal structure and electronic structure of the VFe1−x Cux Sb solid solution (0 ≤ x ≤ 0.2) were studied. The stability ranges of the limited solubility for these phases were established. All alloys of these solid solutions crystallize with the MgAgAs structure type, space group F43m and the stability range extends up to the VFe0.8 Cu0.2 Sb composition. All the samples in this series remained n-type in the temperature range from 4 to 400 K. They display metallic resistivity at high temperature, the resistivity passing through a shallow minimum as the temperature decreases. The Fermi level was determined to reside in a sharp d-DOS peak due to Cu located at the conduction band edge. A successive shift of the Fermi level from the gap (in pure VFeSb) to the conduction band (in Cu doped samples) well corresponds to the marked decrease of the electrical resistivity as measured in VFe1−x Cux Sb. The decrease of the electrical resistivity and thermopower is discussed in view of the Fermi surface change upon alloying VFeSb with Cu. The electronic structure of VFe0.8 Cu0.2 Sb in two allotropic phases was also calculated in order to shed light on the cubic-hexagonal transition and the solubility limit. © 2005 Elsevier B.V. All rights reserved. Keywords: Intermetallic compounds; Crystal structure; Electrical transport; Electronic structure
1. Introduction The first investigations on intermetallics with MgAgAs structure type as the materials for active elements in the power generators, for example, equiatomic MNiSn (M = Ti, Zr, Hf) compounds, have begun 10 years ago [1–5]. Numerous papers showed that pronounced improvement of the thermoelectric properties of MgAgAs phases may be achieved by doping these compounds with various elements [6–9]. The atoms in all crystallographic sites can be substituted by doping atoms, which have similar chemical properties and/or atomic size. For example, Sn is often substituted by Sb, Ni by Co or Mn, Ti (Zr) by Sc, etc. As a result the solid solutions ∗
Corresponding author. E-mail address: stadnyk [email protected] (Yu. Stadnyk).
0925-8388/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2005.04.186
are formed with quite large stability ranges [6,7,10,11]. The change of the physical properties in such solutions usually follows the change in composition providing good possibilities for obtaining thermoelectric materials with desired properties. The existence of the polymorphic transformation in the VFeSb was reported in [12–15]. DTA has shown a phase transition at 1042 K in this compound. Our recent investigation [16] showed that low-temperature modification of the VFeSb compound (MgAgAs-structure type, space group F 43m) and related multi-component substitution alloys based on this ternary phase may be considered as promising moderate temperature thermoelectric materials. Moreover, the recent band structure calculations on transition elements substituted VFeSb, performed by Korringa–Kohn–Rostoker method with the coherent potential approximation (KKR-
Yu. Stadnyk et al. / Journal of Alloys and Compounds 402 (2005) 30–35
31
CPA) [15], have shown particular effects of both chemical disorder and crystal defects on electronic structure and transport properties. In the present work we explored the crystal structure, electric transport properties and electronic structure of the VFe1−x Cux Sb (0 ≤ x ≤ 0.2) solid solution to improve the parameters of the basic material.
2. Experimental and theoretical details The samples were prepared by arc melting the pure elements under purified Ar atmosphere. The purity of V was 99.6%, Fe, Cu – 99.99% and Sb – 99.999%. The congealed melts were turned over and again remelted. Homogenization annealing was performed at 873 K for 950 h in evacuated and sealed vitreous silica tubes. The phase purity of our alloys was assessed via X-ray powder diffraction. Specific electric resistivity (ρ), measured using four-probe technique, and differential thermopower (S) in relation to the copper were examined at the 4–400 K temperature range. The X-ray powder diffraction data for the crystal structure refinement of the VFe1−x Cux Sb solid solution samples were collected at room temperature on a Siemens D500 X-ray powder diffractometer with Co K␣ radiation. The FullProf 98 program [17] was employed for the crystal structure refinement. The electronic structure calculations of VFe1−x Cux Sb (0 < x < 0.2) were performed using the self-consistent Korringa–Kohn–Rostoker (KKR) method with the coherent potential approximation (CPA) [18]. For the final crystal potentials, the total density of states (DOS), the sitedecomposed DOS and the l-decomposed DOS were deduced from our calculations. Moreover, the Fermi surface properties have been calculated for selected concentrations in order to elucidate the mechanism responsible for the semiconductor to metal crossover. Highly accurate total energy KKR-CPA computations have also been made in order to investigate the effect of Cu substitution in VFeSb on the lattice constant as well as on the site preference.
Fig. 1. X-ray powder diffraction pattern of the VFeSb sample (x = 0).
Fig. 2. X-ray powder diffraction pattern of the VFe0.9 Cu0.1 Sb sample (x = 0.1).
I4/mcm), a = 0.6574(5) nm, c = 0.5621(8) nm (literature data: a = 0.6555(3), c = 0.5631(3) nm). Minor traces of these phases were observed in the samples with x = 0, 0.03, 0.05, 0.1. The presence of additional phases in the specimens, in particular of the phase with Ni2 In structure type, may be caused by insufficient homogenization time. The crystallographic characteristics of the alloys are presented in Table 1. It is worth to note that Cu differs from Fe by three electrons only. Sometimes, in case of sufficiently good X-ray powder patterns, it is possible to distinguish these atoms by
3. Results and discussion 3.1. Sample preparation and crystal structure analysis We synthesized for our investigation samples of the VFe1−x Cux Sb (0 ≤ x ≤0.5) compositions. No changes in crystal structure of the main phase were observed in the samples with VFe1−x Cux Sb composition, where x = 0, 0.03, 0.05, 0.1, 0.2 (Figs. 1 and 2). X-ray powder diffraction analysis shows that stability range of the solid solution extends up to the VFe0.8 Cu0.2 Sb composition. This specimen consists of a main phase (MgAgAs-type structure) and negligible amounts of an impurity phases (Fig. 3) identified as Ni2 In-type phase (space group P63 /mmc), a = 0.4163(1) nm, c = 0.5459(2) nm and a VSb2 phase (SG
Fig. 3. X-ray powder diffraction pattern of VFe0.8 Cu0.2 Sb sample. The numbers denote different phases identified by Rietveld refinement.
Yu. Stadnyk et al. / Journal of Alloys and Compounds 402 (2005) 30–35
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Table 1 Structural data (Rietveld refinements), for VFe1−x Cux Sb (x = 0, 0.03, 0.05, 0.1, 0.2) compounds Compound Structure type Space group a (nm) Reflections measured Number of variables RF = |F0 − Fc |/ F0 RI = |I0B − IcB |/ I0 B 1/2 2 [ wi |y0i − y wi |y0i |2 ] RwP = ci | / RP = |y0i − yci |/ |y0i | χ2 = (RwP /Re )2
VFeSb MgAgAs F 43m 0.58230(1) 30/2 17 0.039 0.064 0.026 0.020 5.47
VFe0.97 Cu0.03 Sb MgAgAs F 43m 0.58243(2) 30/2 16 0.034 0.054 0.025 0.017 15.6
VFe0.95 Cu0.05 Sb MgAgAs F 43m 0.58225(1) 30/2 17 0.030 0.050 0.025 0.020 4.51
VFe0.90 Cu0.10 Sb MgAgAs F 43m 0.58199(2) 30/2 17 0.032 0.049 0.028 0.021 4.90
VFe0.80 Cu0.20 Sb MgAgAs F 43m 0.58346(1) 30/2 21 0.029 0.051 0.024 0.018 3.37
Atom parameters V Biso (×102 nm2 ) Occ. Fea Biso (×102 nm2 ) Occ. Sb Biso (×102 nm2 ) Occ.
4a (0 0 0) 1.55(7) 1 4c (1/4 1/4 1/4) 1.06(5) 1 4d (3/4 3/4 3/4) 0.28(3) 1
4a (0 0 0) 1.51(1) 1 4c (1/4 1/4 1/4) 0.76(2) 0.93(1) 4d (3/4 3/4 3/4) 0.17(2) 1
4a (0 0 0) 0.76(3) 0.89(1) 4c (1/4 1/4 1/4) 0.18(2) 0.86(1) 4d (3/4 3/4 3/4) 0.07(2) 1
4a (0 0 0) 0.74(2) 0.90(1) 4c (1/4 1/4 1/4) 0.28(2) 0.85(1) 4d (3/4 3/4 3/4) 0.22(1) 1
4a (0 0 0) 1.43(6) 1 4c (1/4 1/4 1/4) 1.03(4) 0.97(1) 4d (3/4 3/4 3/4) 0.37(2) 1
a
Possibly mixed with Cu for samples (2–5).
Rietveld refinement, especially if they are located in different atomic positions. If Cu and Fe form a statistical mixture of atoms in one crystallographic site, it is almost impossible to quantify their amounts properly. Moreover, in our case some of the 4c (1/4 1/4 1/4) positions have a deficient occupation even assuming that only the iron atoms occupy this position. Thus, the determination of the amount of copper atoms in this position by Rietveld refinement does not make sense at all. In such a case the change of lattice parameters became the only indicator of solid solution formation in VFe1−x Cux Sb compounds. The calculated isotropic thermal displacement parameters for (Fe, Cu) atoms are, perhaps, slightly different from the “real” values because only the iron atoms were used during the calculations. The phases with x = 0.05, 0.1 have also an incomplete occupation in the 4a (0 0 0) position (vanadium atoms). It is important to note that a similar site deficiency was observed in such compounds earlier [1]. Because the proportion between Cu and Fe atoms cannot be established by Rietveld refinement, the starting composition were taken for the sample description.
Fig. 4. Electrical resistivity as function of temperature in the VFe1−x Cux Sb solid solution (1 – x = 0; 2 – x = 0.10; 3 – x = 0.05; 4 – x = 0.03).
3.2. Electric transport measurements The temperature dependences of the electrical resistivities for this series are shown in Fig. 4. All samples display metallic resistivity at high temperature and the latter passes through a shallow minimum as the temperature is decreased. Doping of the VFeSb compound with copper leads to a decrease of the resistivity of the solid solution alloys. The results are in agreement with previous work [16] on pure VFeSb and suggest that this material is a semimetal or dirty semiconductor. Fig. 5 shows the Seebeck coefficients as a function
Fig. 5. Differential thermopower as function of temperature in the VFe1−x Cux Sb solid solution (1 – x = 0.03; 2 – x = 0.10; 3 – x = 0.05; 4 – x = 0).
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Table 2 Structural and electro-kinetic parameters of the VFe1−x Cux Sb alloys Composition
Lattice parameter, a (nm)
S (V/K)
ρ ( m)
S2 /ρ (W/(K2 cm))
VFeSb VFe0.97 Cu0.03 Sb VFe0.95 Cu0.05 Sb VFe0.90 Cu0.10 Sb VFe0.80 Cu0.20 Sb
0.58230(1) 0.58243(2) 0.58225(1) 0.58199(2) 0.58346(1)
−203.1 −112.9 −174.8 −139.1 −122.2
17.9 6.4 8.5 10.4 15.5
22.9 19.4 35.9 19.3 9.6
of temperature for the VFe1−x Cux Sb (x = 0, 0.03, 0.05, 0.10) solid solution. All the samples in this series remained n-type at all temperatures with a similar temperature dependence of the resistivity and only changes of its magnitude. Electric transport properties of the VFe0.8 Cu0.2 Sb specimen have only been measured at room temperature. The values of the power factor (S2 /ρ), being an estimate of the efficiency for metallic thermoelectric generators, are given for the VFe1−x Cux Sb solid solution alloys in Table 2. It is worth noting that the doping of the equatomic VFeSb compound by small amounts of copper (∼5 mol.%) results in an increase of the power factor. 3.3. Electronic structure calculations A simple rule, based on chemical bonding analysis and valence electron count (VEC), makes it possible to predict the occurrence of a band gap at the Fermi level in half-Heusler ordered systems with VEC = 18. Many band structure calculations, using different computational methods seem to fully support this phenomenological interpretation. Hence, VFeSb was also expected to exhibit semiconducting properties due to VEC = 18. On the other hand, present as well as previous electric transport measurements [14,15,19] have shown a metallic-like character of the resistivity curve at low temperatures whereas a semiconducting-like behavior was found at high temperatures (with a maximum of ρ(T) near 700 K [15]). The aforementioned electrical resistivity behaviors combined with the large thermopower measured in VFeSb suggest to classify this compound as a dirty semiconductor. One possible explanation of the complex transport properties of pure and doped FeVSb are crystal defects that apparently occur in the investigated samples. Indeed, the previous KKR-CPA computations [15] have shown that both vacancies and excess Sb atoms on the Fe sublattice behave as a hole donors. Consequently, the Fermi level is pushed from the energy gap, as in perfect VFeSb, into the conduction valence band edge if such defects appear. This result may tentatively explain why experimentally VFeSb does not fully exhibit semi-conducting properties and why the sign of the Seebeck coefficient is negative. Bearing in mind the above-mentioned remarks we present in Fig. 6 the density of states in VFe1−x Cux Sb for x = 0.0, 0.01, 0.05 and 0.10. The energy gap between valence and conduction bands (of the order of 0.5 eV) arises from strong hybridization of d-states from the transition metal atoms (Fe, lying mostly below the gap and V, lying mostly above the energy gap) and p-states of Sb [14,15]. Doping with Cu shifts
the Fermi level into the conduction band edge with strongly increasing DOS. Note, that the Fermi level variations versus Cu substitution (with respect to the energy gap) should not change substantially if the crystal defects (a vacancy or an Sb excess on the Fe sublattice) appear, since they also tend to locate the Fermi level in the conduction band. Interestingly, one can notice a sharp d-states peak attributed to Cu that occurs at the conduction band edge (Fig. 6). It is a rather uncommon situation if Cu electronic states strongly contribute to the density of states near EF (main Cu d-states are usually located well below the Fermi energy). Such electronic structure behaviors found in VFe1−x Cux Sb indicate that Cu substitution into the VFeSb compound (three electrons added per one Cu atom) does not shift the Fermi level in a simple rigid way. Contrary, in view of our results alloying (in particular at low Cu content) significantly modifies the Fermi surface shape and related transport properties (electron group velocities, lifetimes and effective masses of electrons). Fig. 7 illustrates the concentration dependence of the Fermi surface cross-sections in VFe1−x Cux Sb as computed along the kx –ky plane. The total and site-decomposed density of states at EF in VFe1−x Cux Sb calculated for 0 < x < 0.2 is presented in Fig. 8, where one can roughly observe that N(EF ) strongly increases with x. At very low Cu contents the Cu d-states (per atom)
Fig. 6. KKR-CPA density of states in VFe1−x Cux Sb (x = 0, 0.01, 0.05 and 0.10). Total DOS and Cu-DOS are plotted by dashed and solid lines, respectively. EF is marked by vertical dotted line.
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Yu. Stadnyk et al. / Journal of Alloys and Compounds 402 (2005) 30–35
Fig. 7. Variations of density of states at the Fermi level in half-Heusler VFe1−x Cux Sb. Total and all site contributions are plotted. Lines were added as a guide to eyes.
dominate over the other site contributions, whereas the V d-states become more important at EF for higher Cu concentrations. Such a rapid enhancement of N(EF ) with Cu concentration is energetically unfavorable, since the band energy contribution substantially increases the total energy of the system. This may lead to magnetic or structural instability. Noteworthy, the DOS value computed on V reaches the well-known Stoner limit for x Cu close to 0.2, which corresponds to the experimentally detected limit of stability for the cubic phase and should turn the system into a magnetic state. Spin-polarized KKR-CPA calculations of cubic VFe0.8 Cu0.2 Sb resulted in a ferrimagnetic ground state due to magnetic moments computed both on the V (0.8µB ) and the Fe (−0.3µB ) atoms. Our experimental observations suggest that a different mechanism, competitive to the appearance of
Fig. 8. The KKR-CPA Fermi surface cross-sections along the kx –ky plane in VFe1−x Cux Sb.
magnetism, drives the total energy decrease and a cubic-tohexagonal transition takes place. Fig. 9 presents a comparison of the density of states in the limiting solid solution phase VFe0.8 Cu0.2 Sb, computated for both allotropic forms. In the hexagonal phase, the electronic spectrum is continuous (indicating metallic state) and the Fermi level is found in the minimum between the two DOS peaks, whereas in the cubic one EF is located on the strongly increasing slope of DOS. From Fig. 9 one can also notice that the hybridization between the d-states in the vicinity of the Fermi level, being attributed essentially to Fe and V, is much weaker in the cubic phase than in the hexagonal one. This electronic structure behavior reveals that adding electrons into the cubic system (replacing Fe by Cu) tends to shift the Fermi level into non-bonding electronic states, which can tentatively explain the solubility limit of copper
Fig. 9. The KKR-CPA density of states in cubic (MgAgAs-type) and hexagonal (Ni2 In-type) phases of VFe0.8 Cu0.2 Sb. Total (thick solid), Fe (dotted), V (dot-dashed), Cu (thin solid) and Sb (dashed) contributions are plotted. The Fermi level (EF ) is at zero.
Yu. Stadnyk et al. / Journal of Alloys and Compounds 402 (2005) 30–35
in the half-Heusler V(Fe–Cu)Sb system. Conversely, observing site-decomposed density of states in the hexagonal phase, one can notice that electronic states lying around EF have presumably bonding character due to strong overlap of transition metal d-states. In order to obtain a more qualitative description of the electron transport phenomena occurring in the half-Heusler V(Fe–Cu)Sb system, preliminary KKR-CPA calculations have been undertaken, according to the concept of Butler et al. [20], to derive transport coefficients from the electronic bands with complex energy. After self-consistency on electronic charges and effective crystal potentials, we deduced group velocities and life-times of electrons from real and imaginary parts of E(k), respectively. In the next step electrical conductivity and thermopower were computed using well-known formulas [20]. Although some trends observed on experimental curves in V(Fe–Cu)Sb system with alloy composition (residual resistivity ρ and thermopower slopes S/T extrapolated to T = 0 K) are well reproduced from our preliminary KKR-CPA results, the quantitative agreement was not fully satisfying. It seems that electron transport behaviors in half-Heusler V(Fe–Cu)Sb are very sensitive to crystal defects that occur in real samples. Thus, they should be taken into account in further calculations in order to allow for critical comparison between experiment and theory. Moreover, the question concerning the crystallographic phase transition in the half-Heusler V(Fe–Cu)Sb system (close to x = 0.2) should be addressed in a comparative analysis from the total energy KKR-CPA calculations.
4. Conclusions The VFe1−x Cux Sb solid solution formed by substitution of Cu for Fe in the VFeSb ternary compound has a cubic crystal structure of the MgAgAs structure type with VFe0.8 Cu0.2 Sb representing the limiting composition. All samples of the VFe1−x Cux Sb solid solution show a metallic-like resistivity at high temperatures which passes through a shallow minimum with decreasing temperature and all samples retain n-type conductivity at all temperatures. A sharp Cu d-states peak occurring at the conduction band edge seems to be responsible for the high and negative Seebeck coefficient experimentally observed in VFe1−x Cux Sb at low Cu contents. A successive shift of the Fermi level from the gap (in pure VFeSb) to the conduction band (in Cu doped
35
samples) well corresponds to the marked decrease of electrical resistivity as measured in VFe1−x Cux Sb. The strong increase of N(EF ) with Cu substitution is energetically unfavorable for the system and should turn the system to either magnetic state or to a different crystal structure with lower formation energy. This electronic structure behavior corroborates with the cubic-to-hexagonal transition observed for x > 0.2.
References [1] Yu. Stadnyk, Ph.D. Thesis, University of Lviv, 1993. [2] R.V. Skolozdra, Stannides of Transition Metals and Rare Earths, L’viv, Svit, 1993, 200 pp. (in Ukrainian). [3] F.G. Aliev, N.B. Brandt, V.V. Kozyrkov, V.V. Moshchalkov, R.V. Skolozdra, Yu.V. Stadnyk, Phizika Nizkih Temperature 12 (1987) 498. [4] F.G. Aliev, N.B. Brandt, V.V. Kozyrkov, V.V. Moshchalkov, R.V. Skolozdra, Yu.V. Stadnyk, V.K. Pecharski, Pisma v JETF 45 (11) (1987) 535. [5] F.G. Aliev, A.I. Belogorohov, N.B. Brandt, V.V. Kozyrkov, R.V. Skolozdra, Yu.V. Stadnyk, Pis’ma v JETF 47 (3) (1988) 151. [6] A.O. Avetisian, O.M. Goriachev, S.V. Kalchenko, R.V. Skolozdra, Yu.V. Stadnyk, Ukr. Phys. J. 36 (1991) 773. [7] Yu. Stadnyk, Yu. Gorelenko, A. Tkachuk, A. Goryn, V. Davydov, O. Bodak, J. Alloys Comp. 329 (2001) 37. [8] Y. Kawaharada, K. Kurosaki, H. Muta, M. Uno, S. Yamanaka, J. Alloys Comp. 384 (2004) 303. [9] Y. Kawaharada, K. Kurosaki, H. Muta, M. Uno, S. Yamanaka, J. Alloys Comp. 384 (2004) 308. [10] R.V. Skolozdra, J. Pierre, J. Tobola, L.P. Romaka, Yu.V. Stadnyk, J. Thermoelectr. 4 (1999) 28. [11] A. Horyn’, O. Bodak, L. Romaka, Yu. Gorelenko, A. Tkachuk, V. Davydov, Yu. Stadnyk, J. Alloys Comp. 363 (2004) 10. [12] P. Villars, L.D. Calvert, Pearsons Handbook of Crystallographic Data for Intermetallic Phases, ASM, Materials Park, OH, USA, 1997. [13] R.V. Skolozdra, A.L. Ganzyuk, Yu.K. Gorelenko, P.Yu. Zavaliy, Abstracts VIth Workshop Conference on Crystal Chemistry of Inorganic and Coordination Compounds, L’viv, Ukraine, 1992, p. 222. [14] K. Kaczmarska, J. Pierre, J. Beille, J. Tobola, R.V. Skolozdra, G.A. Melnyk, J. Magn. Magn. Mater. 187 (1998) 210–220. [15] L. Jodin, J. Tobola, P. Pecheur, H. Scherrer, S. Kaprzyk, Phys. Rev. B 70 (2004) 184207. [16] Yu. Stadnyk, L. Romaka, Yu. Gorelenko, A. Tkachuk, Yu. Pierre, Proceedings of the ICT’2001, Beijing, China, 2001, pp. 251–253. [17] J. Rodriguez-Carvajal, XV Congress of the International Union of Crystallography, Toulouse, France, 1990 (abstracts). [18] A. Bansil, S. Kaprzyk, P.E. Mijnarends, J. Tobola, Phys. Rev. B 60 (1999) 13396. [19] D. Young, P. Kalifah, R.J. Cava, A.P. Ramirez, J. Appl. Phys. 87 (2000) 317. [20] W.H. Butler, G.M. Stocks, Phys. Rev. B 29 (1984) 4217.
Crystal structure, electrical transport properties and electronic structure of the VFe1−xCuxSb solid solution Yu. Stadnyk a,∗ , A. Horyn a , V. Sechovsky b , L. Romaka a , Ya. Mudryk a , J. Tobola c , T. Stopa c , S. Kaprzyk c , A. Kolomiets b a
Ivan Franko L’viv National University, Kyryl and Mephodiy Str. 6, 79005 L’viv, Ukraine b Charles University, Ke Karlovu 5, 121 16 Prague 2, Czech Republic c Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, 30-059 Krakow, Poland Received 28 March 2005; accepted 19 April 2005 Available online 7 July 2005
Abstract The electrical transport properties, crystal structure and electronic structure of the VFe1−x Cux Sb solid solution (0 ≤ x ≤ 0.2) were studied. The stability ranges of the limited solubility for these phases were established. All alloys of these solid solutions crystallize with the MgAgAs structure type, space group F43m and the stability range extends up to the VFe0.8 Cu0.2 Sb composition. All the samples in this series remained n-type in the temperature range from 4 to 400 K. They display metallic resistivity at high temperature, the resistivity passing through a shallow minimum as the temperature decreases. The Fermi level was determined to reside in a sharp d-DOS peak due to Cu located at the conduction band edge. A successive shift of the Fermi level from the gap (in pure VFeSb) to the conduction band (in Cu doped samples) well corresponds to the marked decrease of the electrical resistivity as measured in VFe1−x Cux Sb. The decrease of the electrical resistivity and thermopower is discussed in view of the Fermi surface change upon alloying VFeSb with Cu. The electronic structure of VFe0.8 Cu0.2 Sb in two allotropic phases was also calculated in order to shed light on the cubic-hexagonal transition and the solubility limit. © 2005 Elsevier B.V. All rights reserved. Keywords: Intermetallic compounds; Crystal structure; Electrical transport; Electronic structure
1. Introduction The first investigations on intermetallics with MgAgAs structure type as the materials for active elements in the power generators, for example, equiatomic MNiSn (M = Ti, Zr, Hf) compounds, have begun 10 years ago [1–5]. Numerous papers showed that pronounced improvement of the thermoelectric properties of MgAgAs phases may be achieved by doping these compounds with various elements [6–9]. The atoms in all crystallographic sites can be substituted by doping atoms, which have similar chemical properties and/or atomic size. For example, Sn is often substituted by Sb, Ni by Co or Mn, Ti (Zr) by Sc, etc. As a result the solid solutions ∗
Corresponding author. E-mail address: stadnyk [email protected] (Yu. Stadnyk).
0925-8388/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2005.04.186
are formed with quite large stability ranges [6,7,10,11]. The change of the physical properties in such solutions usually follows the change in composition providing good possibilities for obtaining thermoelectric materials with desired properties. The existence of the polymorphic transformation in the VFeSb was reported in [12–15]. DTA has shown a phase transition at 1042 K in this compound. Our recent investigation [16] showed that low-temperature modification of the VFeSb compound (MgAgAs-structure type, space group F 43m) and related multi-component substitution alloys based on this ternary phase may be considered as promising moderate temperature thermoelectric materials. Moreover, the recent band structure calculations on transition elements substituted VFeSb, performed by Korringa–Kohn–Rostoker method with the coherent potential approximation (KKR-
Yu. Stadnyk et al. / Journal of Alloys and Compounds 402 (2005) 30–35
31
CPA) [15], have shown particular effects of both chemical disorder and crystal defects on electronic structure and transport properties. In the present work we explored the crystal structure, electric transport properties and electronic structure of the VFe1−x Cux Sb (0 ≤ x ≤ 0.2) solid solution to improve the parameters of the basic material.
2. Experimental and theoretical details The samples were prepared by arc melting the pure elements under purified Ar atmosphere. The purity of V was 99.6%, Fe, Cu – 99.99% and Sb – 99.999%. The congealed melts were turned over and again remelted. Homogenization annealing was performed at 873 K for 950 h in evacuated and sealed vitreous silica tubes. The phase purity of our alloys was assessed via X-ray powder diffraction. Specific electric resistivity (ρ), measured using four-probe technique, and differential thermopower (S) in relation to the copper were examined at the 4–400 K temperature range. The X-ray powder diffraction data for the crystal structure refinement of the VFe1−x Cux Sb solid solution samples were collected at room temperature on a Siemens D500 X-ray powder diffractometer with Co K␣ radiation. The FullProf 98 program [17] was employed for the crystal structure refinement. The electronic structure calculations of VFe1−x Cux Sb (0 < x < 0.2) were performed using the self-consistent Korringa–Kohn–Rostoker (KKR) method with the coherent potential approximation (CPA) [18]. For the final crystal potentials, the total density of states (DOS), the sitedecomposed DOS and the l-decomposed DOS were deduced from our calculations. Moreover, the Fermi surface properties have been calculated for selected concentrations in order to elucidate the mechanism responsible for the semiconductor to metal crossover. Highly accurate total energy KKR-CPA computations have also been made in order to investigate the effect of Cu substitution in VFeSb on the lattice constant as well as on the site preference.
Fig. 1. X-ray powder diffraction pattern of the VFeSb sample (x = 0).
Fig. 2. X-ray powder diffraction pattern of the VFe0.9 Cu0.1 Sb sample (x = 0.1).
I4/mcm), a = 0.6574(5) nm, c = 0.5621(8) nm (literature data: a = 0.6555(3), c = 0.5631(3) nm). Minor traces of these phases were observed in the samples with x = 0, 0.03, 0.05, 0.1. The presence of additional phases in the specimens, in particular of the phase with Ni2 In structure type, may be caused by insufficient homogenization time. The crystallographic characteristics of the alloys are presented in Table 1. It is worth to note that Cu differs from Fe by three electrons only. Sometimes, in case of sufficiently good X-ray powder patterns, it is possible to distinguish these atoms by
3. Results and discussion 3.1. Sample preparation and crystal structure analysis We synthesized for our investigation samples of the VFe1−x Cux Sb (0 ≤ x ≤0.5) compositions. No changes in crystal structure of the main phase were observed in the samples with VFe1−x Cux Sb composition, where x = 0, 0.03, 0.05, 0.1, 0.2 (Figs. 1 and 2). X-ray powder diffraction analysis shows that stability range of the solid solution extends up to the VFe0.8 Cu0.2 Sb composition. This specimen consists of a main phase (MgAgAs-type structure) and negligible amounts of an impurity phases (Fig. 3) identified as Ni2 In-type phase (space group P63 /mmc), a = 0.4163(1) nm, c = 0.5459(2) nm and a VSb2 phase (SG
Fig. 3. X-ray powder diffraction pattern of VFe0.8 Cu0.2 Sb sample. The numbers denote different phases identified by Rietveld refinement.
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Table 1 Structural data (Rietveld refinements), for VFe1−x Cux Sb (x = 0, 0.03, 0.05, 0.1, 0.2) compounds Compound Structure type Space group a (nm) Reflections measured Number of variables RF = |F0 − Fc |/ F0 RI = |I0B − IcB |/ I0 B 1/2 2 [ wi |y0i − y wi |y0i |2 ] RwP = ci | / RP = |y0i − yci |/ |y0i | χ2 = (RwP /Re )2
VFeSb MgAgAs F 43m 0.58230(1) 30/2 17 0.039 0.064 0.026 0.020 5.47
VFe0.97 Cu0.03 Sb MgAgAs F 43m 0.58243(2) 30/2 16 0.034 0.054 0.025 0.017 15.6
VFe0.95 Cu0.05 Sb MgAgAs F 43m 0.58225(1) 30/2 17 0.030 0.050 0.025 0.020 4.51
VFe0.90 Cu0.10 Sb MgAgAs F 43m 0.58199(2) 30/2 17 0.032 0.049 0.028 0.021 4.90
VFe0.80 Cu0.20 Sb MgAgAs F 43m 0.58346(1) 30/2 21 0.029 0.051 0.024 0.018 3.37
Atom parameters V Biso (×102 nm2 ) Occ. Fea Biso (×102 nm2 ) Occ. Sb Biso (×102 nm2 ) Occ.
4a (0 0 0) 1.55(7) 1 4c (1/4 1/4 1/4) 1.06(5) 1 4d (3/4 3/4 3/4) 0.28(3) 1
4a (0 0 0) 1.51(1) 1 4c (1/4 1/4 1/4) 0.76(2) 0.93(1) 4d (3/4 3/4 3/4) 0.17(2) 1
4a (0 0 0) 0.76(3) 0.89(1) 4c (1/4 1/4 1/4) 0.18(2) 0.86(1) 4d (3/4 3/4 3/4) 0.07(2) 1
4a (0 0 0) 0.74(2) 0.90(1) 4c (1/4 1/4 1/4) 0.28(2) 0.85(1) 4d (3/4 3/4 3/4) 0.22(1) 1
4a (0 0 0) 1.43(6) 1 4c (1/4 1/4 1/4) 1.03(4) 0.97(1) 4d (3/4 3/4 3/4) 0.37(2) 1
a
Possibly mixed with Cu for samples (2–5).
Rietveld refinement, especially if they are located in different atomic positions. If Cu and Fe form a statistical mixture of atoms in one crystallographic site, it is almost impossible to quantify their amounts properly. Moreover, in our case some of the 4c (1/4 1/4 1/4) positions have a deficient occupation even assuming that only the iron atoms occupy this position. Thus, the determination of the amount of copper atoms in this position by Rietveld refinement does not make sense at all. In such a case the change of lattice parameters became the only indicator of solid solution formation in VFe1−x Cux Sb compounds. The calculated isotropic thermal displacement parameters for (Fe, Cu) atoms are, perhaps, slightly different from the “real” values because only the iron atoms were used during the calculations. The phases with x = 0.05, 0.1 have also an incomplete occupation in the 4a (0 0 0) position (vanadium atoms). It is important to note that a similar site deficiency was observed in such compounds earlier [1]. Because the proportion between Cu and Fe atoms cannot be established by Rietveld refinement, the starting composition were taken for the sample description.
Fig. 4. Electrical resistivity as function of temperature in the VFe1−x Cux Sb solid solution (1 – x = 0; 2 – x = 0.10; 3 – x = 0.05; 4 – x = 0.03).
3.2. Electric transport measurements The temperature dependences of the electrical resistivities for this series are shown in Fig. 4. All samples display metallic resistivity at high temperature and the latter passes through a shallow minimum as the temperature is decreased. Doping of the VFeSb compound with copper leads to a decrease of the resistivity of the solid solution alloys. The results are in agreement with previous work [16] on pure VFeSb and suggest that this material is a semimetal or dirty semiconductor. Fig. 5 shows the Seebeck coefficients as a function
Fig. 5. Differential thermopower as function of temperature in the VFe1−x Cux Sb solid solution (1 – x = 0.03; 2 – x = 0.10; 3 – x = 0.05; 4 – x = 0).
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Table 2 Structural and electro-kinetic parameters of the VFe1−x Cux Sb alloys Composition
Lattice parameter, a (nm)
S (V/K)
ρ ( m)
S2 /ρ (W/(K2 cm))
VFeSb VFe0.97 Cu0.03 Sb VFe0.95 Cu0.05 Sb VFe0.90 Cu0.10 Sb VFe0.80 Cu0.20 Sb
0.58230(1) 0.58243(2) 0.58225(1) 0.58199(2) 0.58346(1)
−203.1 −112.9 −174.8 −139.1 −122.2
17.9 6.4 8.5 10.4 15.5
22.9 19.4 35.9 19.3 9.6
of temperature for the VFe1−x Cux Sb (x = 0, 0.03, 0.05, 0.10) solid solution. All the samples in this series remained n-type at all temperatures with a similar temperature dependence of the resistivity and only changes of its magnitude. Electric transport properties of the VFe0.8 Cu0.2 Sb specimen have only been measured at room temperature. The values of the power factor (S2 /ρ), being an estimate of the efficiency for metallic thermoelectric generators, are given for the VFe1−x Cux Sb solid solution alloys in Table 2. It is worth noting that the doping of the equatomic VFeSb compound by small amounts of copper (∼5 mol.%) results in an increase of the power factor. 3.3. Electronic structure calculations A simple rule, based on chemical bonding analysis and valence electron count (VEC), makes it possible to predict the occurrence of a band gap at the Fermi level in half-Heusler ordered systems with VEC = 18. Many band structure calculations, using different computational methods seem to fully support this phenomenological interpretation. Hence, VFeSb was also expected to exhibit semiconducting properties due to VEC = 18. On the other hand, present as well as previous electric transport measurements [14,15,19] have shown a metallic-like character of the resistivity curve at low temperatures whereas a semiconducting-like behavior was found at high temperatures (with a maximum of ρ(T) near 700 K [15]). The aforementioned electrical resistivity behaviors combined with the large thermopower measured in VFeSb suggest to classify this compound as a dirty semiconductor. One possible explanation of the complex transport properties of pure and doped FeVSb are crystal defects that apparently occur in the investigated samples. Indeed, the previous KKR-CPA computations [15] have shown that both vacancies and excess Sb atoms on the Fe sublattice behave as a hole donors. Consequently, the Fermi level is pushed from the energy gap, as in perfect VFeSb, into the conduction valence band edge if such defects appear. This result may tentatively explain why experimentally VFeSb does not fully exhibit semi-conducting properties and why the sign of the Seebeck coefficient is negative. Bearing in mind the above-mentioned remarks we present in Fig. 6 the density of states in VFe1−x Cux Sb for x = 0.0, 0.01, 0.05 and 0.10. The energy gap between valence and conduction bands (of the order of 0.5 eV) arises from strong hybridization of d-states from the transition metal atoms (Fe, lying mostly below the gap and V, lying mostly above the energy gap) and p-states of Sb [14,15]. Doping with Cu shifts
the Fermi level into the conduction band edge with strongly increasing DOS. Note, that the Fermi level variations versus Cu substitution (with respect to the energy gap) should not change substantially if the crystal defects (a vacancy or an Sb excess on the Fe sublattice) appear, since they also tend to locate the Fermi level in the conduction band. Interestingly, one can notice a sharp d-states peak attributed to Cu that occurs at the conduction band edge (Fig. 6). It is a rather uncommon situation if Cu electronic states strongly contribute to the density of states near EF (main Cu d-states are usually located well below the Fermi energy). Such electronic structure behaviors found in VFe1−x Cux Sb indicate that Cu substitution into the VFeSb compound (three electrons added per one Cu atom) does not shift the Fermi level in a simple rigid way. Contrary, in view of our results alloying (in particular at low Cu content) significantly modifies the Fermi surface shape and related transport properties (electron group velocities, lifetimes and effective masses of electrons). Fig. 7 illustrates the concentration dependence of the Fermi surface cross-sections in VFe1−x Cux Sb as computed along the kx –ky plane. The total and site-decomposed density of states at EF in VFe1−x Cux Sb calculated for 0 < x < 0.2 is presented in Fig. 8, where one can roughly observe that N(EF ) strongly increases with x. At very low Cu contents the Cu d-states (per atom)
Fig. 6. KKR-CPA density of states in VFe1−x Cux Sb (x = 0, 0.01, 0.05 and 0.10). Total DOS and Cu-DOS are plotted by dashed and solid lines, respectively. EF is marked by vertical dotted line.
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Yu. Stadnyk et al. / Journal of Alloys and Compounds 402 (2005) 30–35
Fig. 7. Variations of density of states at the Fermi level in half-Heusler VFe1−x Cux Sb. Total and all site contributions are plotted. Lines were added as a guide to eyes.
dominate over the other site contributions, whereas the V d-states become more important at EF for higher Cu concentrations. Such a rapid enhancement of N(EF ) with Cu concentration is energetically unfavorable, since the band energy contribution substantially increases the total energy of the system. This may lead to magnetic or structural instability. Noteworthy, the DOS value computed on V reaches the well-known Stoner limit for x Cu close to 0.2, which corresponds to the experimentally detected limit of stability for the cubic phase and should turn the system into a magnetic state. Spin-polarized KKR-CPA calculations of cubic VFe0.8 Cu0.2 Sb resulted in a ferrimagnetic ground state due to magnetic moments computed both on the V (0.8µB ) and the Fe (−0.3µB ) atoms. Our experimental observations suggest that a different mechanism, competitive to the appearance of
Fig. 8. The KKR-CPA Fermi surface cross-sections along the kx –ky plane in VFe1−x Cux Sb.
magnetism, drives the total energy decrease and a cubic-tohexagonal transition takes place. Fig. 9 presents a comparison of the density of states in the limiting solid solution phase VFe0.8 Cu0.2 Sb, computated for both allotropic forms. In the hexagonal phase, the electronic spectrum is continuous (indicating metallic state) and the Fermi level is found in the minimum between the two DOS peaks, whereas in the cubic one EF is located on the strongly increasing slope of DOS. From Fig. 9 one can also notice that the hybridization between the d-states in the vicinity of the Fermi level, being attributed essentially to Fe and V, is much weaker in the cubic phase than in the hexagonal one. This electronic structure behavior reveals that adding electrons into the cubic system (replacing Fe by Cu) tends to shift the Fermi level into non-bonding electronic states, which can tentatively explain the solubility limit of copper
Fig. 9. The KKR-CPA density of states in cubic (MgAgAs-type) and hexagonal (Ni2 In-type) phases of VFe0.8 Cu0.2 Sb. Total (thick solid), Fe (dotted), V (dot-dashed), Cu (thin solid) and Sb (dashed) contributions are plotted. The Fermi level (EF ) is at zero.
Yu. Stadnyk et al. / Journal of Alloys and Compounds 402 (2005) 30–35
in the half-Heusler V(Fe–Cu)Sb system. Conversely, observing site-decomposed density of states in the hexagonal phase, one can notice that electronic states lying around EF have presumably bonding character due to strong overlap of transition metal d-states. In order to obtain a more qualitative description of the electron transport phenomena occurring in the half-Heusler V(Fe–Cu)Sb system, preliminary KKR-CPA calculations have been undertaken, according to the concept of Butler et al. [20], to derive transport coefficients from the electronic bands with complex energy. After self-consistency on electronic charges and effective crystal potentials, we deduced group velocities and life-times of electrons from real and imaginary parts of E(k), respectively. In the next step electrical conductivity and thermopower were computed using well-known formulas [20]. Although some trends observed on experimental curves in V(Fe–Cu)Sb system with alloy composition (residual resistivity ρ and thermopower slopes S/T extrapolated to T = 0 K) are well reproduced from our preliminary KKR-CPA results, the quantitative agreement was not fully satisfying. It seems that electron transport behaviors in half-Heusler V(Fe–Cu)Sb are very sensitive to crystal defects that occur in real samples. Thus, they should be taken into account in further calculations in order to allow for critical comparison between experiment and theory. Moreover, the question concerning the crystallographic phase transition in the half-Heusler V(Fe–Cu)Sb system (close to x = 0.2) should be addressed in a comparative analysis from the total energy KKR-CPA calculations.
4. Conclusions The VFe1−x Cux Sb solid solution formed by substitution of Cu for Fe in the VFeSb ternary compound has a cubic crystal structure of the MgAgAs structure type with VFe0.8 Cu0.2 Sb representing the limiting composition. All samples of the VFe1−x Cux Sb solid solution show a metallic-like resistivity at high temperatures which passes through a shallow minimum with decreasing temperature and all samples retain n-type conductivity at all temperatures. A sharp Cu d-states peak occurring at the conduction band edge seems to be responsible for the high and negative Seebeck coefficient experimentally observed in VFe1−x Cux Sb at low Cu contents. A successive shift of the Fermi level from the gap (in pure VFeSb) to the conduction band (in Cu doped
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samples) well corresponds to the marked decrease of electrical resistivity as measured in VFe1−x Cux Sb. The strong increase of N(EF ) with Cu substitution is energetically unfavorable for the system and should turn the system to either magnetic state or to a different crystal structure with lower formation energy. This electronic structure behavior corroborates with the cubic-to-hexagonal transition observed for x > 0.2.
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