Li doped Mg2Si p-type thermoelectric material: Theoretical and experimental study

Computational Materials Science xxx (2014) xxx–xxx

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Li doped Mg2Si p-type thermoelectric material: Theoretical and experimental study Andrzej Kolezynski a, Pawel Nieroda b,⇑, Krzysztof T. Wojciechowski b a Department of Silicate Chemistry and Macromolecular Compounds, Faculty of Materials Science and Ceramics, AGH University of Science and Technology, al. A. Mickiewicza 30, 30-059 Krakow, Poland b Department of Inorganic Chemistry, Faculty of Materials Science and Ceramics, AGH University of Science and Technology, al. A. Mickiewicza 30, 30-059 Krakow, Poland

a r t i c l e

i n f o

Article history: Received 29 August 2014 Received in revised form 7 November 2014 Accepted 11 November 2014 Available online xxxx Keywords: Magnesium silicide Full-Potential Linearized Augmented Plane Wave Method Thermoelectric properties p-type semiconductors Electronic structure

a b s t r a c t The aim of the study was to determine the influence of Li dopant on transport properties of Mg2Si by using computational methods and experimental study. The results of theoretical studies of electronic structure (Full Potential Linearized Augmented Plane Wave Method), electron density topology and bonding properties (Bader’s Quantum Theory of Atoms in Molecules topological analysis of total electron density) in Li-doped Mg2Si are presented. Detailed analysis of calculated band structures and densities of states shows that for two cases analyzed i.e.: Li substituting Si or Li located in interstitial region (4b Wyckoff position), the addition of lithium impurity leads to n-type conduction. On the other hand, if Li is located in Mg position, the samples have p-type conduction. A series of samples with the nominal compositions of Mg2xLixSi, (x = 0–0.3) were prepared using the Pulsed Electric Current Sintering Technique (PECS) method. Structural and phase composition analyses were carried out by X-ray diffraction. The investigations of the influence of Li dopant on the transport properties i.e.: electrical conductivity, the Seebeck coefficient and the thermal conductivity were carried out. Carrier concentration was measured using the Hall method. The positive value of the Seebeck coefficient indicates that all examined samples show p-type conductivity, which is consistent with the theoretical predictions. Ó 2014 Elsevier B.V. All rights reserved.

1. Introduction Magnesium silicide Mg2Si is one of the most promising thermoelectric materials, suitable for construction of thermoelectric generators TEG for middle range of temperatures (500–800 K). It is a non-toxic and inexpensive material in comparison to other, often used thermoelectric materials based on Te, Pb and Sb. The fundamental parameter characterizing the functional properties of thermoelectric materials is their dimensionless thermoelectric figure of merit ZT [1,2].

ZT ¼ a2 rk1 T where a – is the Seebeck coefficient, r – is the electrical conductivity, k – is the thermal conductivity, T – is the temperature. ⇑ Corresponding author. Tel.: +48 126175060. E-mail address: [email protected] (P. Nieroda).

ð1Þ

The value of the ZT parameter correlates positively with the efficiency of the thermoelectric devices like thermoelectric generators and heat pump [3–5]. Undoped Mg2Si does not have a high value of the ZT parameter (ZTmax = 0.04–0.06, T = 750–850 K [6–8]). However, this can be significantly enhanced by using of appropriate dopants, such as Sn, Ge, Sb and Bi, for example: ZTmax = 1.2, T = 700 K for Mg2Si0.6Sn0.4 [9]; ZTmax = 0.7–0.86, T = 823–862 for Mg2Si:Bi0.02 [10–12]; ZTmax = 0.56–0.62, T = 823–862 K for Mg2Si: Sb0.02 [7,8]; ZTmax = 1.4, T = 823 K for Mg2Si0.53Sn0.4Ge0.05Bi0.02 [13]. All of these materials are characterized by n-type conduction. For p-type materials that are currently known (impurities Ag, Ga), ZT parameter is usually several times lower compared to n-type materials (ZTmax = 0.11 for Mg2Si + 3% Ag [14]; ZTmax = 0.35 for Mg2Si0.6Ge0.4:Ga(0.8%) [15]). However, for the construction of thermoelectric modules, both type materials with good thermoelectric properties (high value of ZT parameter) are strongly desired. For this reason, the new impurities, resulting in acceptor character of conductivity in a given material are particularly sought. The aim of the study was to show the possibility of obtaining the p-type material by doping with lithium, introduced in a particular

http://dx.doi.org/10.1016/j.commatsci.2014.11.015 0927-0256/Ó 2014 Elsevier B.V. All rights reserved.

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A. Kolezynski et al. / Computational Materials Science xxx (2014) xxx–xxx

position in the Mg2Si structure by means of theoretical calculations of the electronic structure and topological properties of electron densities verified by subsequent experimental studies.

bonding in given molecule or crystal and allows to uniquely partition a space into adjacent volumes and thus to define the so called topological atoms and calculate unequivocal their net charges.

2. Material and methods

4. Results and discussion

Powders of Mg (extra pure-Fisher Scientific) and Si (99.9%, Alfa Aesar, 100 mesh) and Li ingot (99.9%, Alfa Aesar) were used for the synthesis. A series of samples with nominal composition Mg2xLixSi (x = 0, 0.05, 0.1, 0.2, 0.3) were prepared by a direct synthesis from above mentioned elements. The synthesis of pre-mixed powders was conducted in a graphite die of 10 mm diameter at a temperature of 833 K, in the PECS [16] device using Ar (99.999%) protective atmosphere. Then, each of the obtained samples was mechanically ground in an agate. Later the powders were densified in the PECS apparatus (T = 1023 K, p = 30 MPa, t = 15 min). The density was determined by hydrostatic Archimedes’ method with propan-2-ol as a medium. Relative densities for undoped samples were higher than 98.5%, whereas the density of the samples doped with lithium is higher than 95%. The resulting polycrystalline samples were examined using X-ray structural analysis (X-ray Diffractometer Empyrean PANalytical, Cu Ka1, k1 = 1.5406 Å, Cu Ka2, k2 = 1.5444 Å, 2H angle range from 20° to 137°). On the basis of the obtained X-ray patterns and by means of the Rietveld method (FullProf package, 2013 edition), the lattice parameters of the obtained materials were determined (Fig. 3). Electrical conductivity and Seebeck coefficient was measured in steady state conditions. Thermal conductivity was determined by laser flash method (LFA MicroFlash Netzsch 457 apparatus). The carrier concentration was measured by the Hall method (B = 0.705 T, DC method, j = 25 mA/mm2, scattering factor A = 1).

4.1. Electronic structure calculations

3. Computational details The electronic structure calculations for lithium doped magnesium silicide have been carried out using WIEN2k FP-LAPW (Full Potential Linearized Augmented Plane Wave Method) package [17], within Density Functional Theory (DFT) formalism [18–23]. The calculations has been done for pure Mg2Si crystal structure (space group 225, Fm3m, a = 6.391 Å [24]) and for three 2  2  2 superstructures in order to simulate approx. 1% of lithium doping, for various locations of Li atoms within the structure: (a) magnesium sub-lattice (Mg63LiSi32; sg no. 215, P43m, a = 12.782 Å), (b) silicon sub-lattice (Mg64Si31Li; sg no. 221, Pm3m, a = 12.782 Å) and (c) in interstitial region (Mg64Si32Li; sg no. 221, Pm3m, a = 12.782 Å). The following parameters have been chosen for calculation: 3000 k-points (14  14  14 mesh within the irreducible Brillouin zone) for pure magnesium silicide and 500 k-points (7  7  7 mesh) for 2  2  2 superstructures, cut-off parameter Rkmax = 7.5, GGA-PBE exchange–correlation potential [25], the values of muffin-tin radii (Ri) [a.u.]: Mg – 2.5, Si – 2.5, Li – 2.5 and the convergence criteria for SCF calculations set to DESCF  105 Ry for total energy and DqSCF  105 e for electron density topology analysis. The crystal structure parameters and fractional atomic coordinates used in DFT calculations are listed in Table 1. The calculated total SCF electron density distribution in crystal cell has been used as a basis for the calculations of the topological properties of bond critical points (within Bader’s Quantum Theory of Atoms in Molecules [26] formalism). As Bader et al. [27] have shown, the analysis of the gradient vector field, derived from the scalar electron density distribution provides us with the crucial information about properties of the electron density in topologically special points (so called critical points) for which gradient of the electron density rq(r) is equal to zero and thus about

Detailed analysis of electronic structure calculated for Li-doped magnesium silicide shows (Fig. 1) that when lithium replaces silicon or locates in interstitial region, the overall structure exhibit ntype conduction. If, on the other hand, lithium is located in Mg sublattice, the resulting structure will exhibit p-type conduction. This difference in conductivity type can be easily explained by comparison of respective defect equations written down for each of three analyzed structures. In the case of Mg2yLiySi, the defect equation reads:

 y x y 0 ð2  yÞMg þ yLi þ Si ¼ ð2  yÞMgxMg þ yLiMg þ 1  SiSi þ V  4 4 Si y þ Si 4 One can easily see, that replacement of magnesium by lithium results in a formation of positively charged vacancies in silicon sub-lattice and removal of silicon excess in a form of separate phase (the latter was confirmed by XRD data – not included in this work due to paper size limits). Similar equations can be formulated for lithium located in silicon sub-lattice and in interstitial region:

Mg2 Sið1yÞ Liy : 2Mg þ ð1  yÞSi þ yLi   3 3 x  ¼ 2  y MgxMg þ ð1  yÞSiSi þ yLiSi þ yV 00Mg 2 2 3 þ yMg 2 Mg2 SiLiy : 2Mg þ Si þ yLi  y y y x  ¼ 2  MgxMg þ SiSi þ yLii þ V 00Mg þ Mg 2 2 2 In both cases the process of magnesium silicide doping with lithium would result in a formation of negatively charged vacancies in magnesium sub-lattice and appearance of separate MgO phase formed from excess of magnesium. 4.2. Electron density topology The total electron density distribution data obtained from FPLAPW SCF calculations has been used as a basis for Bader’s QTAiM topological analysis and the calculated net charges as well as volumes of topological atoms are presented in Table 2 (lithium and respective atoms bonded with lithium are in bold). Presented results indicate that substitution of magnesium by lithium leads to the smallest structure deviation – net charges and topological volumes calculated for silicon and magnesium atoms are very similar to those in pure magnesium silicide with root mean square error (r.m.s.e.) equal to 0.03 and 4.49 for net charge and volume, respectively. In the case of the structure with lithium located in a void the changes are also small, but here the environment of two atoms is influenced by lithium insertion, namely Si2 and Mg4 (r.m.s.e. equal to 0.05 and 4.68 for net charge and volume, respectively). The strongest structure deviation, as a result of Li doping, is in case of superstructure where lithium replaces silicon – here not only a charge of magnesium atom bonded with lithium, but also the volume of topological atom are strongly influenced (net charge equal to 1.032 vs 1.463 in pure Mg2Si and volume equal to 90.7 vs 55.4 in Mg2Si resulting in overall r.m.s.e. equal to 0.13 and 10.93

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A. Kolezynski et al. / Computational Materials Science xxx (2014) xxx–xxx Table 1 Fractional coordinates and Wyckoff positions for pure and Li-doped magnesium silicide crystal structures used in FP-LAPW DFT calculations. Structure and cell param. a/Å

Atom

x

y

Z

Wyckoff position

Atom

x

y

z

Wyckoff position

Mg2Si 6.391

Mg Si

0.250 0.000

0.250 0.000

0.250 0.000

8c 4a

Mg63LiSi32 12.782

Mg1 Mg2 Mg3 Mg4 Mg5 Mg6 Mg7 Mg8

0.000 0.500 0.000 0.000 0.250 0.250 0.500 0.250

0.000 0.500 0.500 0.000 0.750 0.750 0.250 0.250

0.250 0.250 0.750 0.500 0.750 0.250 0.250 0.000

6f 6g 12h 3d 4e 4e 12i 12i

Mg9 Mg10 Si1 Si2 Si3 Si4 Li

0.500 0.500 0.875 0.875 0.375 0.375 0.000

0.000 0.500 0.875 0.875 0.875 0.375 0.000

0.500 0.500 0.875 0.375 0.375 0.375 0.000

3c 1b 4e 12i 12i 4e 1a

Mg63LiSi32 12.782

Mg1 Mg2 Mg3 Mg4 Li

0.625 0.875 0.625 0.125 0.000

0.625 0.875 0.625 0.125 0.000

0.875 0.375 0.375 0.125 0.000

24m 24m 8g 8g 1a

Si1 Si2 Si3 Si4 Si5

0.500 0.000 0.000 0.750 0.750

0.500 0.500 0.000 0.750 0.000

0.500 0.500 0.500 0.500 0.750

1b 3c 3d 12j 12i

Mg64Si31Li 12.782

Mg1 Mg2 Mg3 Mg4 Li

0.375 0.875 0.875 0.875 0.000

0.375 0.375 0.375 0.875 0.000

0.375 0.375 0.125 0.875 0.000

8g 24m 24m 8g 1a

Si1 Si2 Si3 Si4

0.250 0.250 0.250 0.250

0.250 0.000 0.500 0.500

0.250 0.000 0.000 0.500

8g 6e 12h 6f

Fig. 1. Density of states for (a) Mg2Si, (b) Mg64Si32Li, (c) Mg63LiSi32 and (d) Mg64Si31Li.

for net charge and volume, respectively). This suggests that location of lithium atom in silicon sub-lattice is highly unlikely from thermodynamic point of view, since it will require significantly higher amount of energy in comparison with the remaining two cases (Li replacing magnesium and Li in a void) which are much more probable, with somewhat higher probability of the former of these two, due to smaller structure modification resulting from lithium doping. 4.3. Structural analysis Fig. 2 presents the diffraction patterns for the undoped Mg2Si and Mg2xLixSi samples. Analysis of the XRD patterns for undoped

Mg2Si show the presence of only one phase with very small amount of MgO. The samples after doping contain, besides main Mg2Si phase, also MgO and free Si. The amount of free silicon clearly increases with the nominal content of the dopant, which is in good agreement with the proposed defect equation for the case in which Mg atoms are substituted by Li atoms in the Mg2Si structure (which, according to the results of topological analysis of total electron density is the most probable one). In addition, the slight increase of MgO amount with the increase of nominal content of dopant was observed. This effect can be related to partial occupation of interstitial position by the lithium atoms (which cannot be ruled out, but according to topological analysis results is much less probable than the substitution of Mg by Li atoms).

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A. Kolezynski et al. / Computational Materials Science xxx (2014) xxx–xxx

Table 2 Topological properties of electron density. Vx – atomic volume of a topological atom (a. u. 3); q – net charge (e). q

Vx

2.927

329.7

Mg63LiSi32 (8c) Li 0.850 Si1 2.880 Si2 2.944 Si3 2.942 Si4 2.897 Mg1 1.476 Mg2 1.482 Mg3 1.485

28.6 342.4 334.2 332.9 328.5 55.5 53.6 53.2

Mg2Si Si

q

Vx

Mg

1.463

55.4

Mg4 Mg5 Mg6 Mg7 Mg8 Mg9 Mg10

1.488 1.484 1.486 1.482 1.484 1.483 1.487

53.1 53.7 53.2 53.5 53.4 53.1 53.7

q

Vx

q

Vx

Mg64Si31Li Si1 Si2 Si3 Si4 Si5

(4a) 2.900 2.889 2.954 2.962 2.961

327.6 328.0 333.8 335.7 335.0

Li Mg1 Mg2 Mg3 Mg4

0.741 1.485 1.486 1.491 1.032

28.3 53.1 53.3 53.1 90.7

Mg64Si32Li Li Si1 Si2 Si3 Si4

(4b) 0.819 2.975 3.013 2.956 3.0059

26.1 334.6 325.6 334.0 339.1559

Mg1 Mg2 Mg3 Mg4

1.492 1.486 1.486 1.478

52.9 53.2 53.3 51.9

Table 3 Thermoelectric properties of Li-doped Mg2Si at 330 K. x 0.0 0.05 0.1 0.2 0.3

0.6364

a [nm]

2

0 .0 y=

0.6356

04

3 0 .6 x+

52

R

=0

0.05

0.10

0.15

9.0  10 1.7  1018 7.1  1017 5.0  1017 8.0  1016

r (Sm1)

a (mVK1)

k (Wm1K1)

57 38 12 19 22

456 429 498 571 654

6.0 4.7 4.2 3.7 3.2

.9 8

5. Conclusions

0.6352 0.00

16

theoretical predictions. The Seebeck coefficient increases with the nominal content of Li impurities from 429 to 654 lVK1 for 0.05 6 x 6 0.3 while carrier concentration decreases (which is quite unusual behavior). Electrical conductivity has similar values to the undoped material and the thermal conductivity decreases from 6 Wm1K1 (x = 0) to 3.2 Wm1K1 (x = 0.3 at 330 K). The mentioned effect of Seebeck coefficient increase and concurrent carrier concentration decrease with increasing impurities amount was not studied here in detail (this lies outside the scope of this paper and will be a subject of the future work, as well as the temperature dependence of the ZT parameter in relation to doping agent amount).

Fig. 2. X-ray diffraction patterns for Mg2xLixSi samples.

0.6360

n (cm3)

0.20

0.25

0.30

x Fig. 3. Lattice constant dependence on amount of Li dopant.

On the basis of the experimental XRD data, the lattice parameters were determined by means of the Rietveld refinement method (Fig. 3). The lattice constant increases linearly with the increase of the nominal content of the Li dopant, which confirm the presence of Li atoms in the Mg2Si structure (but not where exactly it is located).

The calculated densities of states show, that only in the case when Li atoms are located in Mg position, the Fermi level is located inside the valence band and thus Li dopants should lead to p-type conductivity. Simultaneously, the topological analysis of total electron density and calculated deviations of respective structures resulting from doping (volumes and net charges of topological atoms) indicate, that the most probable location of Li dopant is in magnesium sub-lattice, but one cannot rule out the interstitial position, which is only slightly less probable. In order to confirm theoretical predictions, the synthesis of the samples having the general formula Mg2xLixSi has been carried out. For each sample doped with lithium, a positive sign of thermoelectric power has been determined. This result is a sign of the formation of p-type semiconductor, which is in good accordance with the theoretical calculations and suggests that the Li most probably substitutes Mg position in magnesium silicide compound.

Acknowledgements 4.4. Thermoelectric properties The Seebeck coefficient of the stoichiometric Mg2Si sample (x = 0) is equal 456 lVK1 at 330 K while all examined samples show p-type conductivity (Table 3), which is consistent with the

This research was supported in part by PL-Grid Infrastructure and in part the calculations have been carried out using resources provided by Wroclaw Centre for Networking and Supercomputing (http://wcss.pl), Grant No. 297.

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