- Email: [email protected]
Investigation on the thermoelectric properties of nanostructured Cr1−xTixSi2
Journal of Solid State Chemistry 199 (2013) 90–95
Contents lists available at SciVerse ScienceDirect
Journal of Solid State Chemistry journal homepage: www.elsevier.com/locate/jssc
Investigation on the thermoelectric properties of nanostructured Cr1x Tix Si2 S. Karuppaiah, M. Beaudhuin n, R. Viennois Institut Charles Gerhardt, Universite´ Montpellier II, UMR 5253 CNRS-UM2-ENSCM-UM1, 34095 Montpellier, France
a r t i c l e i n f o
a b s t r a c t
Article history: Received 6 September 2012 Received in revised form 30 November 2012 Accepted 2 December 2012 Available online 10 December 2012
CrSi2 material is outstanding because of its thermoelectric properties and also because of its many optimization routes. Indeed, its thermal conductivity at room temperature is about 9 W m 1 K 1 with a ZT of 0.25. In this paper we propose to decrease the thermal conductivity by nanostructuration and compensate the electron scattering by increasing the charge carrier concentration with Ti. The process which permitted to get nanocrystallite of about 14 nm is presented. After cold pressing and sintering the average crystallite size reaches 50 nm with a porosity of 70%. Nanostructuring and porosity to a lesser extent lead to a strong decrease of the thermal conductivity up to 0.97 0.15 W m 1 K 1 for pure CrSi2. A significant enhancement of the power factor from 1:25 mW cm1 K2 for pure nano-CrSi2 to 2:5 mW cm1 K2 for nano-Cr0.90Ti0.10Si2 was obtained. The stability of the different phases is also evaluated by comparing experiments with ab initio calculations. & 2012 Elsevier Inc. All rights reserved.
Keywords: Silicides Nano particles X-ray diffraction Thermoelectricity Ab initio
1. Introduction
performance of the material:
Interest in renewable energies has increased in recent years due to: the price increase of fossil and fissile resources combined with environmental concerns about global warming and air pollution; the improvement and the development of new materials permitting to reach a better efficiency and better competitivity. In this context the study of thermoelectric (TE) material for electricity power generation is booming. Waste recovery is one of the most astonishing application (industrial plants, exhaust pipes, boilers) of this kind of materials and take part of a sustainable development policy for energy. Currently, the best thermoelectric materials are telluride or antimonide based materials which highlight three problems: the thermal stability, the toxicity and the low abundance of Te and Sb. That is why it is important to focus our research on abundant and non-toxic materials like silicides based TE materials. Indeed, high figure of merit have been obtained with n-type semi-conducting alloys Mg2 Si1x Snx [1,2] which opens the way to promising figure of merit of this family of compounds. Especially the semiconducting alloy CrSi2 also possesses a low electrical resistivity, a high Seebeck coefficient and therefore a promising power factor, S2 s. Another interest lies in its high thermal conductivity which is about 9 W m 1 K 1 at room temperature [3] that could permit to further increase its Figure of Merit as will be seen below. If we look at the Figure of Merit, which describe the
ZT ¼
n
Corresponding author. Fax: þ33 467 144 290. E-mail address: [email protected] (M. Beaudhuin).
0022-4596/$ - see front matter & 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jssc.2012.12.004
S2 T
rk
ð1Þ
with S the Seebeck coefficient (V K 1), T the temperature (K), r the electrical resistivity (O m1 ) and k the thermal conductivity (W m 1 K 1). We observe that there are different ways to improve ZT, either by increasing S or by decreasing r and k. In case of CrSi2, the large thermal conductivity of the bulk materials could be decreased by phonon scattering by several different ways. Among others, nanostructuration is promising as it is an easy process to implement. No much work has been done on CrSi2 nor on the effect of crystallite size diminution. Some papers deal with the synthesis of CrSi2 by ball milling [3–5] but none on the effect of CrSi2 crystallite size reduction on the effective TE properties. However, it is important to remember that k and r are linked and a decrease of k will probably lead to an increase of r. Consequently, it is also necessary to control the charge carrier concentration in order to maintain a good electrical conductivity without being detrimental for the Seebeck coefficient. As we previously mentioned, the thermal conductivity can be decreased with grain size reduction at nanoscale, indeed phonon scattering increases as the mean free path between collisions is decreasing. However, this modification can also alter the electronic conductivity with increasing the interface defects which consequently creates new recombination sites. Few dopants have been investigated in the literature and it has been observed an increase of the Seebeck coefficient by doping on the Si site with Al or on the Cr site with V [6]. Investigation have been also pursued on Mn doping on the Cr site by Nishida and Sakata [7] which describes carefully the
S. Karuppaiah et al. / Journal of Solid State Chemistry 199 (2013) 90–95
semiconducting properties. It has been observed that a Mndoping as x ¼0.122 7 0.008 increase the maximum Seebeck coefficient by a factor 1.7. In this paper we investigate the influence of the grain size and the concentration of Ti on the TE properties. The experimental structure data will be also compared with simulation.
2. Experimental and computing details 2.1. Samples preparation Nanocrystalline CrSi2 powders were obtained by mechanical alloying of high purity Cr (99.995% Alfa Aesar) and Si (99.9999% Alfa Aesar) in stoichiometric ratio. The milling was carried out with a Fritsh ‘‘Pulverisette 7’’ planetary micromill. Speed of the supporting disc and of the grinding bowl was, respectively, fixed to 650 RPM and 1300 RPM for all the experiments corresponding to a ball acceleration about 147 m s 2. Silicon nitride container (45 ml) and five 15 mm balls were used as the milling media. A ball to powder ratio was fixed to 10:1 for all the experiments. Vessels were sealed under Argon atmosphere in order to avoid contamination during the milling. Powder samples were collected after 30, 60, 120, 300, 720 and 1440 min of milling for XRD, SEM and EDX analysis in order to adjust the milling time versus phase purity and grain size. Doping of CrSi2 was performed with Ti (99.95% Aldrich) well below its solubility limit of 70–78 at.% on chromium site [8]. The final milled powders were compacted by cold pressing at 8 tonnes cm 2 for 60 min with vacuum suction to prevent air entrapment inside the pellet. Then they were sintered at 1225 K under vacuum (2 10 3 mbar) for 2 h. This duration was chosen in order to limit grain coarsening. 2.2. Samples characterization 2.2.1. Structural and compositional characterization Phases evolution of the milled powders were analyzed with an X-Ray diffraction apparatus (Philips X’PERT, Cu-K radiation 1.5406 A˚ with an accelerated detector PW 3050/60 at 45 kV and 30 mA settings) after each milling, cold pressing and sintering. Peaks diffraction were analysed using Rietveld refinement with Fullprof software and crystallite size with Powdercell software. Compositional study was carried out using an Energy Dispersive Analysis of X-Ray (EDAX) with an Hitachi S4500 on powders and sintered pellets. 2.2.2. Thermoelectric characterization The Seebeck coefficient was measured under vacuum (1 10 3 mbar) with a home built apparatus with a working temperature ranging from 300 to 800 K. A temperature gradient of 5 K 70.1 K is applied between the hot side and cold side of the pellet, the voltage is measured from both alumel and chromel thermocouple with, respectively, corrected Seebeck coefficient of þ22 and 18 mV K1 . These coefficients are considered constant inside the working temperature range. Concerning electrical resistivity measurements they were carried out under vacuum with a home built apparatus using the Van Der Paw techniques from 300 to 800 K. The thermal conductivity was measured with a TPS 2500 S. Hot Disk Thermal Constants Analyzer apparatus at room temperature. 2.3. Ab initio calculations In order to determine the structural properties and stability of dopants in CrSi2, we have done ab initio relaxation computations of pure and doped CrSi2 using the pseudopotential based VASP
91
code [9,10]. We have used the projected augmented wave (PAW) pseudopotential [10] and the Perdew Berke Ezernhof (PBE) exchange correlation functional [11]. In case of pure or slightly doped semiconductors, the integration method used was the Tetrahedron method [12] whereas the first order Methfessel– Paxton method was used in the case of metals [13]. In some cases, we have used both methods and have found results in good agreement. The Monkhorst Pack method was used for generating the k-points inside the irreducible Brillouin zone [14]. All calculations were done using a cut-off energy of 500 eV, a value sufficient to get a convergence in all cases we have examined here. For the reference materials (hexagonal chromium, diamond silicon, titanium) and for the transition metal disilicide, a fine 21 21 21 k-mesh was used. Very strict convergence criteria were used for the energy (dE¼10 9–10 10 eV/unit-cell) and the forces (dE ¼10 4–10 5 eV/A˙ 1). The formation energy were obtained by subtracting the energy of the reference elements in their ground state (i.e. in the antiferromagnetic ground state for the chromium) to the energy computed for the transition metal disilicide (with M ¼ Cr or Ti)
DEðMSi2 Þ ¼
EðMSi2 ÞEðMÞ2EðSiÞ 3
ð2Þ
In the case of the dopants, we have performed the calculations in an orthorhombic supercell with 72 atoms and using a 3 3 3 k-mesh. The same cut-off energy as above was used. In this case, due to the limitation of our calculation capabilities, the energy convergence criteria was limited to dE¼10 6 eV for the whole 72 atoms supercell. This was enough to get good results. The calculations were done for the pure compound Cr24Si48 and for the doped compound Cr23TiSi48. In this case, the energy per Ti atom is obtained as following
DEðTiÞ ¼
DEðCr23 TiSi48 ÞDEðCr24 Si48 Þ n
ð3Þ
where n ¼1/72 and DEðCr23 MSiÞ48 Þ and DEðCr24 Si48 Þ were obtained as in Eq. (2).
3. Results and discussion 3.1. Phase formation and grain size evolution—experimental and numerical approach In Fig. 1, the phase evolution of a mixture of Cr and Si is shown over milling time. After 2 h, the Silicon peak intensity is greatly reduced and this can be explained both by an extended solid solution of Cr in the Si lattice and by the brittle nature of Si [15]. This leads to a fast decrease of the Si particle size relative to Cr. Silicon X-ray amorphous phases are reported in the literature [3] and could explain the high intensity of the background at low angle. The milling was continued until the complete disappearance of Cr and Si phase. After 24 h, CrSi2 was obtained without remaining phase or pollution induced by the milling process (in the limit of detection of the instrument). All diffraction peaks can be matched to those of CrSi2 with the space group P6222. The unit cell of CrSi2 is found to be a ¼4.4317(3) A˙ and c ¼6.3655(2) A˙ which is in good agreement with the literature (a¼ 4.44283(1) A˙ and c¼6.36680(9) A˙ [16]). SEM and EDX analysis confirmed the homogeneity of the synthesized powders. All over the milling process, the particles are repeatedly flattened, cold welded, fractured and re-welded. The impact force plastically deforms the powder particles leading to work hardening and fracture. If fracture predominates, very fine particles form [17]. Their average crystallite size was calculated by the
92
S. Karuppaiah et al. / Journal of Solid State Chemistry 199 (2013) 90–95
Fig. 1. X-ray diffraction pattern of CrSi2 phase formation over milling time (30 min, 1 h, 2 h, 5 h, 12 h and 24 h). & Silicon, chromium, and n chromium disilicide.
Fig. 2. Grain size evolution of Cr–Si mixture over milling time.
Debye–Scherrer formula d¼
0:9l b cos y
ð4Þ
where d is the crystallite size, l the X-ray wavelength, b the full width at half maximum (FWHM) and y the Bragg’s angle. In Fig. 2,
Fig. 3. X-ray diffraction pattern of Cr1x Tix Si2 for x¼ 0, 0.06, 0.1, 0.15.
a fast decrease of the crystallite size from 270 nm after 30 min to 17 nm after 12 h is observed. With pursuing the milling, the crystallite size reaches 14 nm after 24 h. This nano-powder is then cold compacted and sintered in order to strengthen its mechanical properties. The crystallite size is then increased to 50 nm during the sintering. These conditions are a good compromise between mechanical strength and grain size and have been used for all the experiments presented in this paper. The titanium doping was performed for x¼0, 0.06, 0.10, 0.15% as a dopant on the Cr-site. The X-ray diffraction patterns are presented in Fig. 3. We observe a slight displacement of the peaks to the low angles which leads to a linear increase of the lattice parameters a from 4.4317(3) A˙ for x¼0 to 4.4897(9) A˙ for x ¼0.15 (see Table 1). The lattice parameters c is not influenced by the increasing doping. Consequently, the volume increases when the titanium is incorporated in CrSi2 and this is in good agreement with old literature results. Nowotny and coworkers in 1953 [18] and more recently Du and Schuster [8] found the same behavior in Cr1x Tix Si2 . This observation and the absence of secondary phases in the limit of the detection of both X-ray diffraction and EDXSEM experiments confirm that the titanium is well incorporated in our samples on the chromium site. In order to get further insight on this, we have done ab initio calculations of CrSi2 and TiSi2 in both the C40 and C54 structures. The C40 structure is the stable hexagonal structure existing for CrSi2 whereas the C54 structure is the stable face centered orthorhombic structure for
S. Karuppaiah et al. / Journal of Solid State Chemistry 199 (2013) 90–95
93
Table 1 Structural parameters and agreement factors of Cr1x Tix Si2 for x¼ 0, 0.06, 0.1, 0.15 as obtained from Rietveld refinement. CrSi2
Cr0:94 Ti0:06 Si2
˚ a (A) ˚ c (A)
4.4317(3)
4.4578(9)
6.3655(2)
6.3630(5)
Rp , Rwp , Rexp RBragg
1.99, 2.59, 1.43 3.76 3.28
2.78, 3.56, 3.38 2.47 1.10
Cr0:9 Ti0:1 Si2
Cr0:85 Ti0:15 Si2
˚ a (A) ˚ c (A)
4.4749(8)
4.4897(9)
6.3636(8)
6.3637(8)
Rp , Rwp , Rexp RBragg
1.71 2.19 1.98 2.45 1.23
2.70, 3.41, 3.47 2.130 0.968
w2
w2
Table 2 Structural parameters and formation energy of CrSi2, TiSi2 and Cr23TiSi48 obtained by ab initio calculations compared to experimental results from the literature. The formation energy Eform is given in kJ/mol at. CrSi2 (C40)
CrSi2 (C40)
˚ a (A)
4.40634
4.428–4.431 [19,16,8]
˚ c (A) xSi c/a
6.36494
6.364–6.368 [19,16,8]
V at (A˚ 3) Eform
0.1662 1.444 11.9
0.16578 [16] 1.438–1.459 [19,16,8] 11.95–12.01 [19,16,8]
34.77
25.8 7 4.4, 32.22, 40.17 [24,19,27,8]
TiSi2 (C40)
TiSi2 (C40)
˚ a (A)
4.73
4.7–4.71 [22,23]
˚ c (A) xSi c/a
6.5928
6.49–6.53 [22,23]
V at (A˚ 3) Eform
0.1622 1.394 14.19
0.1667 [22,23] 1.382–1.386 [22,23] 13.79–13.94 [22,23]
52.31
–
Cr23TiSi48 (C40)
CrSi2 (C54)
˚ a (A) ˚ b (A)
4.418
4.3935
4.418
7.6885
˚ c (A) xSi (C40) ySi (C54) c/a
6.3805
3
V at (A˚ ) Eform
0.1663 – 1.444 11.984
8.45 – 0.4578 1.394 14.19
38.69
31.3
TiSi2 (C54)
TiSi2 (C54)
˚ a (A)
4.806
4.81 [20]
˚ b (A) ˚ c (A)
8.265
8.2785 [20]
ySi V at (A˚ 3) Eform
8.5638
8.5652 [20]
0.4619 14.175
0.4615 [20] 14.21 [20]
53.66
53.5, 57 [21,24]
TiSi2. Therefore, it is expected to see a limited solubility of Ti in CrSi2. We report our results in Table 2. As can be seen, the structural parameters agree well with the experiment for CrSi2 and TiSi2 with C40 structure [8,16,19,20,22,23], and for TiSi2 with the C54 structure [21]. Note that the compound TiSi2 with the C54 structure can only be obtained using out of equilibrium deposition synthesis techniques of thin films such as radiofrequency sputtering [22,23]. Our results concerning the formation energy of these compounds agree much better in the case of TiSi2 with the C54 structure than in the case of CrSi2 with the C40 structure.
Fig. 4. Structure parameters and formation energy of CrSi2 and TiSi2 with structures C40 and C54 from ab initio calculations. These results are compared with structure parameters from experiments and simulations for the Cr1x Tix Si2 phases.
Indeed, as can be seen in Table 2, experimental results are relatively scattered for CrSi2, but according to Du et al. [27], the results from Topor and Kleppa [24] must be the most reliable. Our results are in good agreement with previous DFT work from Pankhurst et al. for CrSi2 [25] and Colinet et al. for TiSi2 [26]. As confirmed by the Pankhurst work [25], the DFT method overstimates the formation energy of the CrSi2 compounds. According to them, this could be due to underestimation of the energy of the pure chromium in its antiferromagnetic ground state. However, our DFT calculations reproduce the good qualitative trend, i.e. the formation energy of the TiSi2 compound with C54 structure is much more negative than that one of the CrSi2 compound with C40 structure. Note that La Via et al. [23] have tried to estimate the energy difference between the metastable C40 structure and the C54 structure for TiSi2 from energy total phase diagram and found about 2–3 kJ/mol at., a result that qualitatively agrees with our calculations (1.35 kJ/mol at.). From the above results, we are now trying to estimate the stability domains of the C40 and C54 structures in the solid solution Cr1x Tix Si2 . This is done in Fig. 4 where we have plotted the formation energy of the different phases and the volume variation with the titanium content, xTi . In order to estimate the stability of the different phases, we have just plotted a straight line between CrSi2 and TiSi2 with the C40 structure and we do the same thing in the case of the C54 structure. Doing like that, this is a very rough model as we do not make calculations for the intermediate titanium content. However, we find that the C40 phase has more negative formation energy and is therefore more stable for x o0:71, a result in good agreement with the experiments, giving the roughness of our model and the above comments. Indeed, if Nowotny found a titanium solubility in CrSi2 of about 90 percent at 1573 K [18], Du and Schusters found a lower solubility between 69 and 78 percent at 1073 K and 1273 K [8]. These last values compare well with our results which are for 0 K. In order to confirm the above results and because of the roughness of the used model, we have performed ab initio calculations on a 72 atoms orthorhombic supercell where 1 of the 24 chromium atoms was substituted by one titanium atom. We have also calculated the formation energy of the orthorhombic Cr24Si48 supercell for which we find the same value for the formation energy than for the CrSi2 in its hexagonal primitive cell. As can be seen in Table 2 and Fig. 4, the structure parameters of this Cr23TiSi48 alloys agree well with the Vegard law between CrSi2 and TiSi2 compounds with C40 structure, whereas the formation energy of this alloys is
94
S. Karuppaiah et al. / Journal of Solid State Chemistry 199 (2013) 90–95
decrease of the c/a ratio. This shows that too much titanium doping must become detrimental for the thermoelectric properties as this will close the energy bandgap.
below the formation energy expected from a simple mixing rule. More specifically, inserting titanium has decreased the energy of about 2.9 eV/Ti. This confirms that titanium can easily substitute to chromium in CrSi2. We also note the excellent agreement of our calculated structural parameters with the literature results and notably for the volume variation with titanium content. We note that the volume variation with titanium content we have found agrees well with the literature results and with our DFT calculations. However, in our samples, we find that most of the volume change is due to the increase of the a parameter whereas the c parameter does not change. As Du and Schusters observe a change of the c parameter for large titanium content (sample 25 in their paper) [8], we have to understand the origin of this disagreement. We remind that our samples have grain of nanometer size and this gives broader peaks in the X-ray patterns, as can be seen in Figs. 1 and 3. Our best explanation is therefore the following : as there is an overlap between the 003 and the 111 Bragg peaks at about 441, it could be difficult to estimate how the c parameter can change with the titanium doping. Therefore, in our case, if the change of the c parameter was underestimated in the refinement, this would mean that the change of the a parameter is overestimated. However, as the changes of these lattice parameters are small due to the small titanium content, the errors are more or less cancelled when the volume change with titanium content is determined. This would explain why the volume changes found in our samples agrees with literature and calculation results. We wish also to note that, in the literature, the c and a parameters are reported only for the compounds with the largest titanium content (about 70 percent of titanium content) [8]. Therefore, we cannot exclude the possibility of non-linear change of the lattice parameters with titanium content that could explain why the c parameter does not change for the low titanium content studied in our present paper. Now we discuss why the volume increases when Ti substitutes for the chromium in CrSi2. The simplest explanation is just because the radius of titanium atom is larger than the radius of the chromium atom (see [28]). Another important result confirmed by our ab initio calculations is the decrease of the c/a ratio between CrSi2 and TiSi2 that agrees well with the experiment (see Tables 1 and 2). This structural change is important as it can have an important impact on the electronic structure. Indeed, as shown long time ago by Mattheiss [29], the energy bandgap of CrSi2 is decreasing when the c/a ratio decreases. We therefore expect a closing of the energy bandgap not only because of titanium alloying but also because of the
The electrical resistivity and the Seebeck coefficient were measured for all the samples in function of the temperature and are given in Figs. 5 and 6. We observed that the electrical resistivity of nano-CrSi2 is about ten times higher than in bulk CrSi2 [6,30] whereas the thermopower remains the same. This larger value of the resistivity must have two combined origins: the small grains size and the low density (about 70%) which increase the charge carriers scattering. Although the value of the resistivity is much higher than in bulk CrSi2, we notice the existence of a maximum of r around 600 K as in the bulk samples [30]. This behaviour is due to a degenerated semiconducting nature, as already explained in the literature [7,31]. At high temperature, the conduction is of intrinsic type with the predominance of the acoustic phonon scattering, hence the negative dr=dT. At low temperature, we are in the extrinsic regime but the charge carrier scattering is more complicated than at high temperatures. Regarding on the thermal conductivity, measurements have been performed on both CrSi2 and Cr0.9Ti0.1Si2 samples at room temperature. We have, respectively, obtained the values of 0.970.15 W m 1 K 1 and 1.6470.15 W m 1 K 1. By comparing these value to the thermal conductivity of bulk CrSi2 polycrystals [30] or single-crystals [6], which is about 9 W m 1 K 1, there is a factor 10. Here again, both the nanostructuration and the porosity combine for decreasing so efficiently the thermal conductivity. Shaping of denser pellet is necessary in order to discriminate the contribution of the nanostructuration to the decrease of the thermal conductivity in order to have one better idea of the efficiency of the nanostructuration to reduce the thermal conductivity of CrSi2. At room temperature, if we consider the Loeb’s model [32] which describes the influence of the porosity on the thermal conductivity that can be expressed as kp ¼ ð1pÞk, with p the porosity. Many results on thermoelectric materials confirm this trend [33,34].Consequently we can assume that a porosity of 70% will lead to a decrease of the thermal conductivity about 30%. This value is much lower than the observed thermal conductivity reduction. With increasing Ti concentration, the values of the resistivity and thermopower decrease, suggesting that an efficient p-doping from titanium atoms takes place. The r decreases down to
Fig. 5. Electrical resistivity for CrSi2 and Cr1x Tix Si2 for x¼ 0.03, 0.06, 0.1, 0.15.
Fig. 6. Seebeck coefficient for CrSi2 and Cr1x Tix Si2 for x¼ 0.03, 0.06, 0.1, 0.15.
3.2. Thermoelectric properties
S. Karuppaiah et al. / Journal of Solid State Chemistry 199 (2013) 90–95
95
best Ti-doped sample compared to the pure CrSi2. Consequently, Ti dopant is promising for improving the TE properties of CrSi2.
Acknowledgment The authors would like to acknowledge the ‘‘Programme Interdisciplinaire Energie’’ from the CNRS for his kind support that makes available to us more calculation capabilities. References
Fig. 7. Power factor for CrSi2 and Cr1x Tix Si2 for x¼ 0.03, 0.06, 0.1, 0.15.
4 mO cm with 15% Ti doping. The same behavior is observed with the seebeck coefficient. Up to 6% Ti doping, S is slightly similar but for a concentration higher than 10% the Seebeck coefficient is greatly reduced. The maximum observed in the resistivity of the pure CrSi2 disappears from 6% Ti doping, whereas the maximum in the thermopower disappears at larger Ti content. For the two samples with the largest Ti content, we observe a negative slope for the resistivity on the whole temperature range. This behavior is surprising as we would expect a metallic behavior as the Ti doping is increased. At the present time, we have no clear explanation for this behavior. Now, if we look at the power factor (Fig. 7) we see that the optimum is obtained for 10% Ti doping. If we compare it with the power factor of CrSi2 it is increased by a factor 2 at 800 K. The titanium is therefore an efficient dopant for improving thermoelectric properties of CrSi2 in the high temperature range.
4. Conclusion We have successfully obtained nano-CrSi2 Ti-doped pellets without residual phases. The experimental results were compared with simulation and are in good agreement despite the use of rough models. We observed that nanostructuration at 50 nm with 70% density permits to decrease the thermal conductivity and increase the electrical resistivity by a factor 10. After doping with Ti, the electrical resistivity is strongly reduced by a factor 3 at 600 K leading to a rise of the power factor of 100 percent in the
[1] V.K. Zaitsev, M.I. Fedorov, I.S. Eremin, E.A. Gurieva, Thermoelectrics Handbook: Macro to Nano-Structured Materials, CRC press, New York, 2005. [2] X.J. Tan, W. Liu, H.J. Liu, J. Shi, X.F. Tang, C. Uher, Phys. Rev. B 85 (2012) 2052121. [3] T. Dasgupta, A.M. Umarji, J. Alloys Compd. 461 (2008) 292–297. [4] M. Morris, D. Morris, J. Mater. Sci. 26 (1991) 4687–4696. [5] D.L. Zhang, J. Mater. Sci. 31 (1996) 895–899. [6] Z.J. Pan, L.T. Zhang, J.S. Wu, Script. Mater. 56 (2007) 245–248. [7] I. Nishida, T. Sakata, J. Phys. Chem. Solids 39 (1978) 499–505. [8] Y. Du, J.C. Schuster, Scand. J. Metall. 31 (2002) 25–33. [9] G. Kresse, J. Furthmueller, Phys. Rev. B 54 (1996) 11169–11186. [10] G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758–1775. [11] J. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865–3868. [12] P.E. Blochl, Phys. Rev. B 50 (1994) 17953–17979. [13] M. Methfessel, A.T. Paxton, Phys. Rev. B 40 (1989) 3616–3621. [14] J.H. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188–5192. [15] B. Fernandes, G. Rodrigues, G.C. Coelho, A.S. Ramos, Mater. Sci. Eng. A 405 (2005) 135–139. [16] K. Tanaka, K. Nawata, H. Inui, M. Yamaguchi, M. Koiwa, Mater. Res. Soc. Symp. Proc. 646 (2001) N4.3.1–N4.3.5. [17] J. Lua, H. Yang, B. Liu, J. Han, G. Zou, Mater. Chem. Phys. 59 (1999) 101–106. [18] H. Nowotny, H. Schroth, R. Kieffer, F. Benesorvsky, Monatsh. Chem. 84 (1953) 579–584. [19] H. Lange, Phys. Status Solidi (b) 201 (1997) 3–65. [20] F. Weitzer, P. Rogl, H. Nol, J. Alloys Compd. 350 (2003) 155–159. [21] R.J. Kematick, C.E. Myers, Chem. Mater. 8 (1996) 287–291. [22] K. Li, S.Y. Chen, Z.X. Shen, Appl. Phys. Lett. 78 (2001) 3989–3991. [23] F. La Via, F. Mammoliti, G. Corallo, M.G. Grimaldi, D.B. Migas, L. Miglio, Appl. Phys. Lett. 78 (2001) 1864–1866. [24] L. Topor, O.J. Kleppa, Metall. Trans. A 17A (1986) 1217–1221. [25] D.A. Pankhurst, D. Nguyen-Mahn, D.G. Pettifor, Phys. Rev. B 69 (2004) 0751131–0751139. [26] C. Colinet, W. Wolf, R. Podloucky, A. Pasturel, Appl. Phys. Lett. 87 (2005) 0419101–0419103. [27] Y. Du, J.C. Schuster, J. Phase Equilibr. 21 (2000) 281–286. [28] See /http://www.webelements.comS. [29] L.F. Mattheiss, Phys. Rev. B 45 (1992) 3252–3259. [30] T. Dasgupta, J. Etourneau, B. Chevalier, S.F. Matar, A.M. Umarji, J. Appl. Phys. 103 (2008) 113516. [31] I. Nishida, J. Mater. Sci. 7 (1972) 1119–1124. [32] A.L. Loeb, J. Am. Ceram. Soc. 37 (1954) 96–99. [33] G.S. Nolas, J.L. Cohn, G.A. Slack, Phys. Rev. B 58 (1998) 164–170, and ref. therein. [34] J.W. Sharp, E.C. Jones, R.K. Williams, P.M. Martin, B.C. Sales, J. Appl. Phys. 78 (1995) 1013–1019.
Contents lists available at SciVerse ScienceDirect
Journal of Solid State Chemistry journal homepage: www.elsevier.com/locate/jssc
Investigation on the thermoelectric properties of nanostructured Cr1x Tix Si2 S. Karuppaiah, M. Beaudhuin n, R. Viennois Institut Charles Gerhardt, Universite´ Montpellier II, UMR 5253 CNRS-UM2-ENSCM-UM1, 34095 Montpellier, France
a r t i c l e i n f o
a b s t r a c t
Article history: Received 6 September 2012 Received in revised form 30 November 2012 Accepted 2 December 2012 Available online 10 December 2012
CrSi2 material is outstanding because of its thermoelectric properties and also because of its many optimization routes. Indeed, its thermal conductivity at room temperature is about 9 W m 1 K 1 with a ZT of 0.25. In this paper we propose to decrease the thermal conductivity by nanostructuration and compensate the electron scattering by increasing the charge carrier concentration with Ti. The process which permitted to get nanocrystallite of about 14 nm is presented. After cold pressing and sintering the average crystallite size reaches 50 nm with a porosity of 70%. Nanostructuring and porosity to a lesser extent lead to a strong decrease of the thermal conductivity up to 0.97 0.15 W m 1 K 1 for pure CrSi2. A significant enhancement of the power factor from 1:25 mW cm1 K2 for pure nano-CrSi2 to 2:5 mW cm1 K2 for nano-Cr0.90Ti0.10Si2 was obtained. The stability of the different phases is also evaluated by comparing experiments with ab initio calculations. & 2012 Elsevier Inc. All rights reserved.
Keywords: Silicides Nano particles X-ray diffraction Thermoelectricity Ab initio
1. Introduction
performance of the material:
Interest in renewable energies has increased in recent years due to: the price increase of fossil and fissile resources combined with environmental concerns about global warming and air pollution; the improvement and the development of new materials permitting to reach a better efficiency and better competitivity. In this context the study of thermoelectric (TE) material for electricity power generation is booming. Waste recovery is one of the most astonishing application (industrial plants, exhaust pipes, boilers) of this kind of materials and take part of a sustainable development policy for energy. Currently, the best thermoelectric materials are telluride or antimonide based materials which highlight three problems: the thermal stability, the toxicity and the low abundance of Te and Sb. That is why it is important to focus our research on abundant and non-toxic materials like silicides based TE materials. Indeed, high figure of merit have been obtained with n-type semi-conducting alloys Mg2 Si1x Snx [1,2] which opens the way to promising figure of merit of this family of compounds. Especially the semiconducting alloy CrSi2 also possesses a low electrical resistivity, a high Seebeck coefficient and therefore a promising power factor, S2 s. Another interest lies in its high thermal conductivity which is about 9 W m 1 K 1 at room temperature [3] that could permit to further increase its Figure of Merit as will be seen below. If we look at the Figure of Merit, which describe the
ZT ¼
n
Corresponding author. Fax: þ33 467 144 290. E-mail address: [email protected] (M. Beaudhuin).
0022-4596/$ - see front matter & 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jssc.2012.12.004
S2 T
rk
ð1Þ
with S the Seebeck coefficient (V K 1), T the temperature (K), r the electrical resistivity (O m1 ) and k the thermal conductivity (W m 1 K 1). We observe that there are different ways to improve ZT, either by increasing S or by decreasing r and k. In case of CrSi2, the large thermal conductivity of the bulk materials could be decreased by phonon scattering by several different ways. Among others, nanostructuration is promising as it is an easy process to implement. No much work has been done on CrSi2 nor on the effect of crystallite size diminution. Some papers deal with the synthesis of CrSi2 by ball milling [3–5] but none on the effect of CrSi2 crystallite size reduction on the effective TE properties. However, it is important to remember that k and r are linked and a decrease of k will probably lead to an increase of r. Consequently, it is also necessary to control the charge carrier concentration in order to maintain a good electrical conductivity without being detrimental for the Seebeck coefficient. As we previously mentioned, the thermal conductivity can be decreased with grain size reduction at nanoscale, indeed phonon scattering increases as the mean free path between collisions is decreasing. However, this modification can also alter the electronic conductivity with increasing the interface defects which consequently creates new recombination sites. Few dopants have been investigated in the literature and it has been observed an increase of the Seebeck coefficient by doping on the Si site with Al or on the Cr site with V [6]. Investigation have been also pursued on Mn doping on the Cr site by Nishida and Sakata [7] which describes carefully the
S. Karuppaiah et al. / Journal of Solid State Chemistry 199 (2013) 90–95
semiconducting properties. It has been observed that a Mndoping as x ¼0.122 7 0.008 increase the maximum Seebeck coefficient by a factor 1.7. In this paper we investigate the influence of the grain size and the concentration of Ti on the TE properties. The experimental structure data will be also compared with simulation.
2. Experimental and computing details 2.1. Samples preparation Nanocrystalline CrSi2 powders were obtained by mechanical alloying of high purity Cr (99.995% Alfa Aesar) and Si (99.9999% Alfa Aesar) in stoichiometric ratio. The milling was carried out with a Fritsh ‘‘Pulverisette 7’’ planetary micromill. Speed of the supporting disc and of the grinding bowl was, respectively, fixed to 650 RPM and 1300 RPM for all the experiments corresponding to a ball acceleration about 147 m s 2. Silicon nitride container (45 ml) and five 15 mm balls were used as the milling media. A ball to powder ratio was fixed to 10:1 for all the experiments. Vessels were sealed under Argon atmosphere in order to avoid contamination during the milling. Powder samples were collected after 30, 60, 120, 300, 720 and 1440 min of milling for XRD, SEM and EDX analysis in order to adjust the milling time versus phase purity and grain size. Doping of CrSi2 was performed with Ti (99.95% Aldrich) well below its solubility limit of 70–78 at.% on chromium site [8]. The final milled powders were compacted by cold pressing at 8 tonnes cm 2 for 60 min with vacuum suction to prevent air entrapment inside the pellet. Then they were sintered at 1225 K under vacuum (2 10 3 mbar) for 2 h. This duration was chosen in order to limit grain coarsening. 2.2. Samples characterization 2.2.1. Structural and compositional characterization Phases evolution of the milled powders were analyzed with an X-Ray diffraction apparatus (Philips X’PERT, Cu-K radiation 1.5406 A˚ with an accelerated detector PW 3050/60 at 45 kV and 30 mA settings) after each milling, cold pressing and sintering. Peaks diffraction were analysed using Rietveld refinement with Fullprof software and crystallite size with Powdercell software. Compositional study was carried out using an Energy Dispersive Analysis of X-Ray (EDAX) with an Hitachi S4500 on powders and sintered pellets. 2.2.2. Thermoelectric characterization The Seebeck coefficient was measured under vacuum (1 10 3 mbar) with a home built apparatus with a working temperature ranging from 300 to 800 K. A temperature gradient of 5 K 70.1 K is applied between the hot side and cold side of the pellet, the voltage is measured from both alumel and chromel thermocouple with, respectively, corrected Seebeck coefficient of þ22 and 18 mV K1 . These coefficients are considered constant inside the working temperature range. Concerning electrical resistivity measurements they were carried out under vacuum with a home built apparatus using the Van Der Paw techniques from 300 to 800 K. The thermal conductivity was measured with a TPS 2500 S. Hot Disk Thermal Constants Analyzer apparatus at room temperature. 2.3. Ab initio calculations In order to determine the structural properties and stability of dopants in CrSi2, we have done ab initio relaxation computations of pure and doped CrSi2 using the pseudopotential based VASP
91
code [9,10]. We have used the projected augmented wave (PAW) pseudopotential [10] and the Perdew Berke Ezernhof (PBE) exchange correlation functional [11]. In case of pure or slightly doped semiconductors, the integration method used was the Tetrahedron method [12] whereas the first order Methfessel– Paxton method was used in the case of metals [13]. In some cases, we have used both methods and have found results in good agreement. The Monkhorst Pack method was used for generating the k-points inside the irreducible Brillouin zone [14]. All calculations were done using a cut-off energy of 500 eV, a value sufficient to get a convergence in all cases we have examined here. For the reference materials (hexagonal chromium, diamond silicon, titanium) and for the transition metal disilicide, a fine 21 21 21 k-mesh was used. Very strict convergence criteria were used for the energy (dE¼10 9–10 10 eV/unit-cell) and the forces (dE ¼10 4–10 5 eV/A˙ 1). The formation energy were obtained by subtracting the energy of the reference elements in their ground state (i.e. in the antiferromagnetic ground state for the chromium) to the energy computed for the transition metal disilicide (with M ¼ Cr or Ti)
DEðMSi2 Þ ¼
EðMSi2 ÞEðMÞ2EðSiÞ 3
ð2Þ
In the case of the dopants, we have performed the calculations in an orthorhombic supercell with 72 atoms and using a 3 3 3 k-mesh. The same cut-off energy as above was used. In this case, due to the limitation of our calculation capabilities, the energy convergence criteria was limited to dE¼10 6 eV for the whole 72 atoms supercell. This was enough to get good results. The calculations were done for the pure compound Cr24Si48 and for the doped compound Cr23TiSi48. In this case, the energy per Ti atom is obtained as following
DEðTiÞ ¼
DEðCr23 TiSi48 ÞDEðCr24 Si48 Þ n
ð3Þ
where n ¼1/72 and DEðCr23 MSiÞ48 Þ and DEðCr24 Si48 Þ were obtained as in Eq. (2).
3. Results and discussion 3.1. Phase formation and grain size evolution—experimental and numerical approach In Fig. 1, the phase evolution of a mixture of Cr and Si is shown over milling time. After 2 h, the Silicon peak intensity is greatly reduced and this can be explained both by an extended solid solution of Cr in the Si lattice and by the brittle nature of Si [15]. This leads to a fast decrease of the Si particle size relative to Cr. Silicon X-ray amorphous phases are reported in the literature [3] and could explain the high intensity of the background at low angle. The milling was continued until the complete disappearance of Cr and Si phase. After 24 h, CrSi2 was obtained without remaining phase or pollution induced by the milling process (in the limit of detection of the instrument). All diffraction peaks can be matched to those of CrSi2 with the space group P6222. The unit cell of CrSi2 is found to be a ¼4.4317(3) A˙ and c ¼6.3655(2) A˙ which is in good agreement with the literature (a¼ 4.44283(1) A˙ and c¼6.36680(9) A˙ [16]). SEM and EDX analysis confirmed the homogeneity of the synthesized powders. All over the milling process, the particles are repeatedly flattened, cold welded, fractured and re-welded. The impact force plastically deforms the powder particles leading to work hardening and fracture. If fracture predominates, very fine particles form [17]. Their average crystallite size was calculated by the
92
S. Karuppaiah et al. / Journal of Solid State Chemistry 199 (2013) 90–95
Fig. 1. X-ray diffraction pattern of CrSi2 phase formation over milling time (30 min, 1 h, 2 h, 5 h, 12 h and 24 h). & Silicon, chromium, and n chromium disilicide.
Fig. 2. Grain size evolution of Cr–Si mixture over milling time.
Debye–Scherrer formula d¼
0:9l b cos y
ð4Þ
where d is the crystallite size, l the X-ray wavelength, b the full width at half maximum (FWHM) and y the Bragg’s angle. In Fig. 2,
Fig. 3. X-ray diffraction pattern of Cr1x Tix Si2 for x¼ 0, 0.06, 0.1, 0.15.
a fast decrease of the crystallite size from 270 nm after 30 min to 17 nm after 12 h is observed. With pursuing the milling, the crystallite size reaches 14 nm after 24 h. This nano-powder is then cold compacted and sintered in order to strengthen its mechanical properties. The crystallite size is then increased to 50 nm during the sintering. These conditions are a good compromise between mechanical strength and grain size and have been used for all the experiments presented in this paper. The titanium doping was performed for x¼0, 0.06, 0.10, 0.15% as a dopant on the Cr-site. The X-ray diffraction patterns are presented in Fig. 3. We observe a slight displacement of the peaks to the low angles which leads to a linear increase of the lattice parameters a from 4.4317(3) A˙ for x¼0 to 4.4897(9) A˙ for x ¼0.15 (see Table 1). The lattice parameters c is not influenced by the increasing doping. Consequently, the volume increases when the titanium is incorporated in CrSi2 and this is in good agreement with old literature results. Nowotny and coworkers in 1953 [18] and more recently Du and Schuster [8] found the same behavior in Cr1x Tix Si2 . This observation and the absence of secondary phases in the limit of the detection of both X-ray diffraction and EDXSEM experiments confirm that the titanium is well incorporated in our samples on the chromium site. In order to get further insight on this, we have done ab initio calculations of CrSi2 and TiSi2 in both the C40 and C54 structures. The C40 structure is the stable hexagonal structure existing for CrSi2 whereas the C54 structure is the stable face centered orthorhombic structure for
S. Karuppaiah et al. / Journal of Solid State Chemistry 199 (2013) 90–95
93
Table 1 Structural parameters and agreement factors of Cr1x Tix Si2 for x¼ 0, 0.06, 0.1, 0.15 as obtained from Rietveld refinement. CrSi2
Cr0:94 Ti0:06 Si2
˚ a (A) ˚ c (A)
4.4317(3)
4.4578(9)
6.3655(2)
6.3630(5)
Rp , Rwp , Rexp RBragg
1.99, 2.59, 1.43 3.76 3.28
2.78, 3.56, 3.38 2.47 1.10
Cr0:9 Ti0:1 Si2
Cr0:85 Ti0:15 Si2
˚ a (A) ˚ c (A)
4.4749(8)
4.4897(9)
6.3636(8)
6.3637(8)
Rp , Rwp , Rexp RBragg
1.71 2.19 1.98 2.45 1.23
2.70, 3.41, 3.47 2.130 0.968
w2
w2
Table 2 Structural parameters and formation energy of CrSi2, TiSi2 and Cr23TiSi48 obtained by ab initio calculations compared to experimental results from the literature. The formation energy Eform is given in kJ/mol at. CrSi2 (C40)
CrSi2 (C40)
˚ a (A)
4.40634
4.428–4.431 [19,16,8]
˚ c (A) xSi c/a
6.36494
6.364–6.368 [19,16,8]
V at (A˚ 3) Eform
0.1662 1.444 11.9
0.16578 [16] 1.438–1.459 [19,16,8] 11.95–12.01 [19,16,8]
34.77
25.8 7 4.4, 32.22, 40.17 [24,19,27,8]
TiSi2 (C40)
TiSi2 (C40)
˚ a (A)
4.73
4.7–4.71 [22,23]
˚ c (A) xSi c/a
6.5928
6.49–6.53 [22,23]
V at (A˚ 3) Eform
0.1622 1.394 14.19
0.1667 [22,23] 1.382–1.386 [22,23] 13.79–13.94 [22,23]
52.31
–
Cr23TiSi48 (C40)
CrSi2 (C54)
˚ a (A) ˚ b (A)
4.418
4.3935
4.418
7.6885
˚ c (A) xSi (C40) ySi (C54) c/a
6.3805
3
V at (A˚ ) Eform
0.1663 – 1.444 11.984
8.45 – 0.4578 1.394 14.19
38.69
31.3
TiSi2 (C54)
TiSi2 (C54)
˚ a (A)
4.806
4.81 [20]
˚ b (A) ˚ c (A)
8.265
8.2785 [20]
ySi V at (A˚ 3) Eform
8.5638
8.5652 [20]
0.4619 14.175
0.4615 [20] 14.21 [20]
53.66
53.5, 57 [21,24]
TiSi2. Therefore, it is expected to see a limited solubility of Ti in CrSi2. We report our results in Table 2. As can be seen, the structural parameters agree well with the experiment for CrSi2 and TiSi2 with C40 structure [8,16,19,20,22,23], and for TiSi2 with the C54 structure [21]. Note that the compound TiSi2 with the C54 structure can only be obtained using out of equilibrium deposition synthesis techniques of thin films such as radiofrequency sputtering [22,23]. Our results concerning the formation energy of these compounds agree much better in the case of TiSi2 with the C54 structure than in the case of CrSi2 with the C40 structure.
Fig. 4. Structure parameters and formation energy of CrSi2 and TiSi2 with structures C40 and C54 from ab initio calculations. These results are compared with structure parameters from experiments and simulations for the Cr1x Tix Si2 phases.
Indeed, as can be seen in Table 2, experimental results are relatively scattered for CrSi2, but according to Du et al. [27], the results from Topor and Kleppa [24] must be the most reliable. Our results are in good agreement with previous DFT work from Pankhurst et al. for CrSi2 [25] and Colinet et al. for TiSi2 [26]. As confirmed by the Pankhurst work [25], the DFT method overstimates the formation energy of the CrSi2 compounds. According to them, this could be due to underestimation of the energy of the pure chromium in its antiferromagnetic ground state. However, our DFT calculations reproduce the good qualitative trend, i.e. the formation energy of the TiSi2 compound with C54 structure is much more negative than that one of the CrSi2 compound with C40 structure. Note that La Via et al. [23] have tried to estimate the energy difference between the metastable C40 structure and the C54 structure for TiSi2 from energy total phase diagram and found about 2–3 kJ/mol at., a result that qualitatively agrees with our calculations (1.35 kJ/mol at.). From the above results, we are now trying to estimate the stability domains of the C40 and C54 structures in the solid solution Cr1x Tix Si2 . This is done in Fig. 4 where we have plotted the formation energy of the different phases and the volume variation with the titanium content, xTi . In order to estimate the stability of the different phases, we have just plotted a straight line between CrSi2 and TiSi2 with the C40 structure and we do the same thing in the case of the C54 structure. Doing like that, this is a very rough model as we do not make calculations for the intermediate titanium content. However, we find that the C40 phase has more negative formation energy and is therefore more stable for x o0:71, a result in good agreement with the experiments, giving the roughness of our model and the above comments. Indeed, if Nowotny found a titanium solubility in CrSi2 of about 90 percent at 1573 K [18], Du and Schusters found a lower solubility between 69 and 78 percent at 1073 K and 1273 K [8]. These last values compare well with our results which are for 0 K. In order to confirm the above results and because of the roughness of the used model, we have performed ab initio calculations on a 72 atoms orthorhombic supercell where 1 of the 24 chromium atoms was substituted by one titanium atom. We have also calculated the formation energy of the orthorhombic Cr24Si48 supercell for which we find the same value for the formation energy than for the CrSi2 in its hexagonal primitive cell. As can be seen in Table 2 and Fig. 4, the structure parameters of this Cr23TiSi48 alloys agree well with the Vegard law between CrSi2 and TiSi2 compounds with C40 structure, whereas the formation energy of this alloys is
94
S. Karuppaiah et al. / Journal of Solid State Chemistry 199 (2013) 90–95
decrease of the c/a ratio. This shows that too much titanium doping must become detrimental for the thermoelectric properties as this will close the energy bandgap.
below the formation energy expected from a simple mixing rule. More specifically, inserting titanium has decreased the energy of about 2.9 eV/Ti. This confirms that titanium can easily substitute to chromium in CrSi2. We also note the excellent agreement of our calculated structural parameters with the literature results and notably for the volume variation with titanium content. We note that the volume variation with titanium content we have found agrees well with the literature results and with our DFT calculations. However, in our samples, we find that most of the volume change is due to the increase of the a parameter whereas the c parameter does not change. As Du and Schusters observe a change of the c parameter for large titanium content (sample 25 in their paper) [8], we have to understand the origin of this disagreement. We remind that our samples have grain of nanometer size and this gives broader peaks in the X-ray patterns, as can be seen in Figs. 1 and 3. Our best explanation is therefore the following : as there is an overlap between the 003 and the 111 Bragg peaks at about 441, it could be difficult to estimate how the c parameter can change with the titanium doping. Therefore, in our case, if the change of the c parameter was underestimated in the refinement, this would mean that the change of the a parameter is overestimated. However, as the changes of these lattice parameters are small due to the small titanium content, the errors are more or less cancelled when the volume change with titanium content is determined. This would explain why the volume changes found in our samples agrees with literature and calculation results. We wish also to note that, in the literature, the c and a parameters are reported only for the compounds with the largest titanium content (about 70 percent of titanium content) [8]. Therefore, we cannot exclude the possibility of non-linear change of the lattice parameters with titanium content that could explain why the c parameter does not change for the low titanium content studied in our present paper. Now we discuss why the volume increases when Ti substitutes for the chromium in CrSi2. The simplest explanation is just because the radius of titanium atom is larger than the radius of the chromium atom (see [28]). Another important result confirmed by our ab initio calculations is the decrease of the c/a ratio between CrSi2 and TiSi2 that agrees well with the experiment (see Tables 1 and 2). This structural change is important as it can have an important impact on the electronic structure. Indeed, as shown long time ago by Mattheiss [29], the energy bandgap of CrSi2 is decreasing when the c/a ratio decreases. We therefore expect a closing of the energy bandgap not only because of titanium alloying but also because of the
The electrical resistivity and the Seebeck coefficient were measured for all the samples in function of the temperature and are given in Figs. 5 and 6. We observed that the electrical resistivity of nano-CrSi2 is about ten times higher than in bulk CrSi2 [6,30] whereas the thermopower remains the same. This larger value of the resistivity must have two combined origins: the small grains size and the low density (about 70%) which increase the charge carriers scattering. Although the value of the resistivity is much higher than in bulk CrSi2, we notice the existence of a maximum of r around 600 K as in the bulk samples [30]. This behaviour is due to a degenerated semiconducting nature, as already explained in the literature [7,31]. At high temperature, the conduction is of intrinsic type with the predominance of the acoustic phonon scattering, hence the negative dr=dT. At low temperature, we are in the extrinsic regime but the charge carrier scattering is more complicated than at high temperatures. Regarding on the thermal conductivity, measurements have been performed on both CrSi2 and Cr0.9Ti0.1Si2 samples at room temperature. We have, respectively, obtained the values of 0.970.15 W m 1 K 1 and 1.6470.15 W m 1 K 1. By comparing these value to the thermal conductivity of bulk CrSi2 polycrystals [30] or single-crystals [6], which is about 9 W m 1 K 1, there is a factor 10. Here again, both the nanostructuration and the porosity combine for decreasing so efficiently the thermal conductivity. Shaping of denser pellet is necessary in order to discriminate the contribution of the nanostructuration to the decrease of the thermal conductivity in order to have one better idea of the efficiency of the nanostructuration to reduce the thermal conductivity of CrSi2. At room temperature, if we consider the Loeb’s model [32] which describes the influence of the porosity on the thermal conductivity that can be expressed as kp ¼ ð1pÞk, with p the porosity. Many results on thermoelectric materials confirm this trend [33,34].Consequently we can assume that a porosity of 70% will lead to a decrease of the thermal conductivity about 30%. This value is much lower than the observed thermal conductivity reduction. With increasing Ti concentration, the values of the resistivity and thermopower decrease, suggesting that an efficient p-doping from titanium atoms takes place. The r decreases down to
Fig. 5. Electrical resistivity for CrSi2 and Cr1x Tix Si2 for x¼ 0.03, 0.06, 0.1, 0.15.
Fig. 6. Seebeck coefficient for CrSi2 and Cr1x Tix Si2 for x¼ 0.03, 0.06, 0.1, 0.15.
3.2. Thermoelectric properties
S. Karuppaiah et al. / Journal of Solid State Chemistry 199 (2013) 90–95
95
best Ti-doped sample compared to the pure CrSi2. Consequently, Ti dopant is promising for improving the TE properties of CrSi2.
Acknowledgment The authors would like to acknowledge the ‘‘Programme Interdisciplinaire Energie’’ from the CNRS for his kind support that makes available to us more calculation capabilities. References
Fig. 7. Power factor for CrSi2 and Cr1x Tix Si2 for x¼ 0.03, 0.06, 0.1, 0.15.
4 mO cm with 15% Ti doping. The same behavior is observed with the seebeck coefficient. Up to 6% Ti doping, S is slightly similar but for a concentration higher than 10% the Seebeck coefficient is greatly reduced. The maximum observed in the resistivity of the pure CrSi2 disappears from 6% Ti doping, whereas the maximum in the thermopower disappears at larger Ti content. For the two samples with the largest Ti content, we observe a negative slope for the resistivity on the whole temperature range. This behavior is surprising as we would expect a metallic behavior as the Ti doping is increased. At the present time, we have no clear explanation for this behavior. Now, if we look at the power factor (Fig. 7) we see that the optimum is obtained for 10% Ti doping. If we compare it with the power factor of CrSi2 it is increased by a factor 2 at 800 K. The titanium is therefore an efficient dopant for improving thermoelectric properties of CrSi2 in the high temperature range.
4. Conclusion We have successfully obtained nano-CrSi2 Ti-doped pellets without residual phases. The experimental results were compared with simulation and are in good agreement despite the use of rough models. We observed that nanostructuration at 50 nm with 70% density permits to decrease the thermal conductivity and increase the electrical resistivity by a factor 10. After doping with Ti, the electrical resistivity is strongly reduced by a factor 3 at 600 K leading to a rise of the power factor of 100 percent in the
[1] V.K. Zaitsev, M.I. Fedorov, I.S. Eremin, E.A. Gurieva, Thermoelectrics Handbook: Macro to Nano-Structured Materials, CRC press, New York, 2005. [2] X.J. Tan, W. Liu, H.J. Liu, J. Shi, X.F. Tang, C. Uher, Phys. Rev. B 85 (2012) 2052121. [3] T. Dasgupta, A.M. Umarji, J. Alloys Compd. 461 (2008) 292–297. [4] M. Morris, D. Morris, J. Mater. Sci. 26 (1991) 4687–4696. [5] D.L. Zhang, J. Mater. Sci. 31 (1996) 895–899. [6] Z.J. Pan, L.T. Zhang, J.S. Wu, Script. Mater. 56 (2007) 245–248. [7] I. Nishida, T. Sakata, J. Phys. Chem. Solids 39 (1978) 499–505. [8] Y. Du, J.C. Schuster, Scand. J. Metall. 31 (2002) 25–33. [9] G. Kresse, J. Furthmueller, Phys. Rev. B 54 (1996) 11169–11186. [10] G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758–1775. [11] J. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865–3868. [12] P.E. Blochl, Phys. Rev. B 50 (1994) 17953–17979. [13] M. Methfessel, A.T. Paxton, Phys. Rev. B 40 (1989) 3616–3621. [14] J.H. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188–5192. [15] B. Fernandes, G. Rodrigues, G.C. Coelho, A.S. Ramos, Mater. Sci. Eng. A 405 (2005) 135–139. [16] K. Tanaka, K. Nawata, H. Inui, M. Yamaguchi, M. Koiwa, Mater. Res. Soc. Symp. Proc. 646 (2001) N4.3.1–N4.3.5. [17] J. Lua, H. Yang, B. Liu, J. Han, G. Zou, Mater. Chem. Phys. 59 (1999) 101–106. [18] H. Nowotny, H. Schroth, R. Kieffer, F. Benesorvsky, Monatsh. Chem. 84 (1953) 579–584. [19] H. Lange, Phys. Status Solidi (b) 201 (1997) 3–65. [20] F. Weitzer, P. Rogl, H. Nol, J. Alloys Compd. 350 (2003) 155–159. [21] R.J. Kematick, C.E. Myers, Chem. Mater. 8 (1996) 287–291. [22] K. Li, S.Y. Chen, Z.X. Shen, Appl. Phys. Lett. 78 (2001) 3989–3991. [23] F. La Via, F. Mammoliti, G. Corallo, M.G. Grimaldi, D.B. Migas, L. Miglio, Appl. Phys. Lett. 78 (2001) 1864–1866. [24] L. Topor, O.J. Kleppa, Metall. Trans. A 17A (1986) 1217–1221. [25] D.A. Pankhurst, D. Nguyen-Mahn, D.G. Pettifor, Phys. Rev. B 69 (2004) 0751131–0751139. [26] C. Colinet, W. Wolf, R. Podloucky, A. Pasturel, Appl. Phys. Lett. 87 (2005) 0419101–0419103. [27] Y. Du, J.C. Schuster, J. Phase Equilibr. 21 (2000) 281–286. [28] See /http://www.webelements.comS. [29] L.F. Mattheiss, Phys. Rev. B 45 (1992) 3252–3259. [30] T. Dasgupta, J. Etourneau, B. Chevalier, S.F. Matar, A.M. Umarji, J. Appl. Phys. 103 (2008) 113516. [31] I. Nishida, J. Mater. Sci. 7 (1972) 1119–1124. [32] A.L. Loeb, J. Am. Ceram. Soc. 37 (1954) 96–99. [33] G.S. Nolas, J.L. Cohn, G.A. Slack, Phys. Rev. B 58 (1998) 164–170, and ref. therein. [34] J.W. Sharp, E.C. Jones, R.K. Williams, P.M. Martin, B.C. Sales, J. Appl. Phys. 78 (1995) 1013–1019.