Reduced Lattice Thermal Conductivity in Bi-doped Mg 2 Si 0.4 Sn 0.6

Reduced Lattice Thermal Conductivity in Bi-doped Mg 2 Si 0.4 Sn 0.6 Peng Gao 1, Xu Lu 2, Isil Berkun 3, Robert D. Schmidt 1, Eldon D. Case 1 and Timothy P. Hogan 1,3 1. Department of Chemical Engineering and Materials Science, Michigan State University, East Lansing, MI, 48824, USA 2. Department of Physics and Astronomy, Michigan State University, East Lansing, MI, 48824, USA 3. Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI, 48824, USA Abstract This letter reports the thermoelectric properties of Bi-doped Mg 2 Si 0.4 Sn 0.6 thermoelectric materials. It was found that the ZTs of this material could be greatly enhanced by Bidoping. Analyses on the transport properties showed that the power factors of the material were enhanced while the lattice thermal conductivities were reduced by Bidoping. The reduction of the lattice thermal conductivity was likely caused by the interstitial Bi impurities. A peak ZT 1.55 at 773 K was obtained. Introduction Thermoelectric power generation could convert waste heat to electricity and improve energy efficiency in places such as power plants, automobiles and nuclear generators. 1 The thermoelectric efficiency is determined by the figure of merit of a material ZT = S2 σ κ T (1) where S is Seebeck coefficient, σ is the electrical conductivity and κ is the thermal conductivity. The efficiency of heat to electricity conversion is directly related to ZT such that a high ZT is needed for good thermoelectric performance. As those materials properties are dependent on each other, the denominator (thermal conductivity κ) could not be minimized without suppressing the numerator (power factor S 2 σ), or vice versa. Finding a balance between these material parameters is one common way to optimize ZT and it is usually done by adjusting the carrier concentration of the material. 2-5 Introducing new scattering mechanisms that only affect κ or S has also been proven to successfully increase ZT. 6,7 In this work we present a possible route to increase ZT by decreasing the lattice thermal conductivity while maintaining the high power factor in the Mg 2 Si 0.4 Sn 0.6 solid solution, which is one of the most promising candidate materials for mid-temperature thermoelectric power generation application. Experimental Samples of Mg 2.08 Si 0.4-x Sn 0.6 Bi x (x = 0, 0.005, 0.010, 0.015, 0.020 and 0.030) were synthesized using the flux synthesis method. 8,9 A p-type sample of Mg 2.005 Si 0.4 Sn 0.6 Ag 0.075 was also made to investigate hole conduction in these materials. Excess Mg was used to compensate for the loss of Mg during synthesis. The naturally cooled cast ingot was ground into powders with particle size less than 53 μm and Page 1 of 6

densified using a Pulsed Electrical Current Sintering (PECS) system at 973 K and 30 MPa for 15 min in a 304 stainless-steel die. A Rigaku MiniFlex x-ray diffractometer with a Cu K α radiation source was used to identify the crystallographic phase of the synthesized materials. The room temperature densities (ρ 0 ) of the pellets were measured by the Archimedes method. The thermal diffusivity D and the specific heat C P of the samples were measured using a Netzsch LFA 457 system. The thermal conductivity (κ) was then calculated as κ = DC P ρ 0 [1 + α(t T RT )] 3 (2) where a linear thermal expansion coefficient of 2.0 10-5 was used. 9 The temperature-dependent electrical conductivity and Seebeck coefficient were measured using a ULVAC ZEM-3 system and the temperature-dependent carrier concentration and Hall mobility were measured using a laboratory-built Hall measurement system using a Hallbar configuration. 10 Results and Discussion The XRD spectra for all the samples follow the pattern for anti-fluorite structured crystals (Figure 1). All characteristic peaks lie between the peaks for single phase Mg 2 Si and Mg 2 Sn, indicating the formation of the single phase Mg 2 Si-Mg 2 Sn solid solution. Figure 1. XRD spectra for Mg 2.08 Si 0.4-x Sn 0.6 Bi x samples. The temperature dependent S and σ are shown in Figure 2a and 2b. The undoped specimen (x = 0.000) showed typical intrinsic semiconductor behavior as σ monotonically increased with increasing temperature. The absolute value of S started decreasing at about 450 K. The Mg 2 Si 0.4 Sn 0.6 solid solution has a small band gap of about 0.44 ev at room temperature. 11 This was in good agreement with the value obtained from 2S max T max which gives E g = 0.45 ev. 12 The roll-over of S at high temperatures was due to the increased bipolar conduction at higher temperatures. For the Bi-doped samples, the values of σ were greater than those of the undoped specimen. The Bi doping increased the room temperature carrier concentration by an order of magnitude (Figure 2c). The roll-over temperatures for S systematically increased with increased Bi doping. In the heavily doped samples, higher holes concentrations were needed for the bipolar conduction to become significant, which could only be obtained at elevated temperatures. Page 2 of 6

F r = x r 1 1 + e 0 x η dx (7) Figure 2. a)electrical conductivities, b)seebeck coefficients, c)carrier concentration and d)thermal conductivities for Mg 2.08 Si 0.4-x Sn 0.6 Bi x samples. The thermal conductivities κ are shown in Figure 2d. For all the samples κ decreased with increasing temperature until the bipolar conduction became significant, similar to the roll-over observed in S. As the Bi content increased, the room temperature κ increased. The total thermal conductivities consists of three components κ = κ l + κ e + κ bp (3) where κ l, κ e and κ bp are the lattice, electronic and bipolar thermal conductivities, respectively. A single-parabolic-band model was employed to extract the three components explicitly based on experimental results. 5 First, κ e is related to the electrical conductivity by the Wiedemann-Franz law L = ( k B q ) 2 κ e = LσT (4) { (λ + 7 2 ) F λ+5/2(η) (λ + 7 δ 2 } (5) 2 ) F λ+1/2(η) δ = (λ + 5 2 ) F λ+3/2(η) (λ + 3 2 ) F λ+1/2(η) (6) where L is the Lorenz number, q is the electron charge and η is the reduced Fermi level measured from the bottom of the conduction band. There is no direct measure of η. An iterative method was used to find η based on the experimental Seebeck coefficient data as S = μ nns n + μ p ps p μ n n + μ p p (8) S n = k B q [(λ + 5/2)F λ+3/2(η) η] (9) (λ + 3/2)F λ+1/2 (η) S p = k B q (5 2 + λ η p) (10) η + η p = E g k B T n = 1 2π 2 (2m n k B T ħ 2 ) 3/2 p = 1 2π 2 (2m p k B T ħ 2 ) (11) F 1/2 (η) (12) 3/2 e η (13) where S n (S p ), n (p) and µ n (µ p ) are the Seebeck coefficients, carrier concentration and mobility for electrons (holes). As stated previously, the bipolar conduction could be significant at elavated temperatures because of the small band gap. The density of states effective mass m n * ( m p * ) and the band gap values were taken from the literature where the values have been experimentally or theoretically verified. 11,13 The mobilities for electrons and holes were obtained by the high temperature Hall measurement (Figure 3). Since all of the Bi-doped sample are heavily degenerate n-type Page 3 of 6

semiconductors, accurate Fermi-Dirac integrals were used in the calculation for electrons and the Boltzmann approximation could be applied to simplify the formulas for holes. Figure 3. High temperature hall mobilities for the n-type and p-type samples. Using the results from Equation (8-13), the bipolar thermal conductivity was calculated as κ bp = μ nn μ p p μ n n + u p p (S n S p ) 2 T (14) The lattice thermal conductivity was obtained from Equation (3). As seen in Figure 4a the κ e increases as Bi content increases which resulted from the increase σ. The κ bp are small at low temperatures but start to increase nearly exponationally at high temperatures. Figure 4b shows that κ l decreases as the doping concentration increases. Figure 4. a)electronic (line+symbol), bipolar (symbol) and b) lattice thermal conductivities for the Mg 2.08 Si 0.4-x Sn 0.6 Bi x samples. To verify the reliability of the κ l derived in this method, the pure lattice thermal conductivity of the undoped sample was also estimated using Slack s formula 14 κ l = A M θ 3 V 1/3 γ 2 n V 2/3 T (15) Page 4 of 6 γ = 3βBV m C V (16) where A is a collection of physical constants and a value of 3.1 10-7 s -3 K -3 was used in our calculation, 14-16 M is the average mass of the atoms in the crystal, V is the average volume occupied by an atom, n V is the number of atoms per primitive cell, β is the volume thermal expansion coefficient, B is the bulk modulus, V m is the molar volume and C V ( C P ) is the isochoric specific heat per mole. The Debye temperature θ and the Grüneisen parameter γ were calculated based on the mechanical properties measured in our previous work on the undoped sample. 9 The κ l was estimated by Equation (15) (solid line in Figure 4b) and showed good agreement with the result derived from Equations (1 14) (scatters in Figure 4b). Figure 4b shows a reduction in the lattice thermal conductivity could be achieved by introducing Bi impurity atoms to the Mg 2 Si 0.4 Sn 0.6 matrix. The most heavily doped sample (x = 0.030) had a κ l ~13% lower than the κ l for the undoped sample at room temperature. The influence of impurities on the intrinsic lattice thermal conductivity has been studied by Ioffe in various semiconductors and an empirical formula has been proposed as 17-19 κ 0 κ l = 1 + χ N D N 0 l 0 a (17) where κ 0 is the lattice thermal conductivity for the pristine crystal and κ l is that for the doped crystal. N D is the impurity concentration, N 0 is the number of atoms per unit volume, l 0 is the mean free path of phonons in the materials, a is the lattice constant and χ is a parameter determined by the effective scattering area of the impurity atoms. Intersitial impurities would result in χ >

1 and substitutional impurities would make χ < 1. Figure 5. Dependence of κ 0 /κ l on the Bi content. The κ l of the samples under different temperatures in our work were fit to Equation (17), as shown in Figure 5. We did not find accurate reported values for l 0 in Mg 2 Si 0.4 Sn 0.6, but a range of 10 ~ 100 Å for l 0 in Mg 2 Si has been reported. 20 If l 0 of 10 ~ 100 Å was used, the calculated χ was in the range of 2.0 ~ 51. Noting that the lattice thermal conductivities of Mg 2 Si 0.4 Sn 0.6 are much lower than that of Mg 2 Si due to the formation of solid solution, 21 a smaller l 0 should be expected in Mg 2 Si 0.4 Sn 0.6. Thus, the real values of χ should be close to the high end of the range 2.0 ~ 51, which is expected to be much greater than 1. This indicates that there is at least a portion of the Bi atoms occupied the interstitial sites. The interstitial Bi atoms acted as strong phonon scattering centers and reduced the lattice thermal conductivities. One thing to note here is that Equation (17) is an empirical equation so the existence of the interstitial Bi atoms needs to be confirmed by further studies. It was observed that in the lattice of GaSb χ = 7 for Te atoms and χ = 3 for Se atoms. While for isovalent impurities such as Si in Ge, Sn in Si and Se in PbTe, χ = 1 held well. Bi is not an isovalent impurity compared with Si or Sn, so the behavior of Bi in Mg2(Si,Sn) might be closer to Te in GaSb. One possible explanation for origin of the off-site Bi atoms might be the solubility limit of Bi in the Mg 2 (Si,Sn) materials. 5 While the lattice thermal conductivity is reduced, increasing the Bi content showed no detrimental effect on the power factors (Figure 6a). This should be attributed to the low alloy scattering and deformation scattering potentials to electrons in the Mg 2 (Si,Sn) solid solutions. 22 In Figure 3, the mobilities were not significantly altered by the Bi-doping. As a result, all Bidoped samples showed peak ZT > 1 and increasing with increasing Bi content. A maximum ZT ~ 1.55 was obtained at 773 K for x = 0.030. Based on the current results it is likely that the peak ZT could be pushed to a higher value for x > 0.030. Figure 6. a) Power factors and b) ZTs for the samples. Conclusion The thermoelectric properties of Mg 2.08 Si 0.4-x Sn 0.6 Bi x have been studied in this work. The lattice thermal conductivities of the samples were extracted from total thermal conductivities using a single parabolic band model with bipolar conduction considered. Increasing Bi content could reduce the lattice thermal conductivity by up to 13% while the power factors were kept at high levels. The samples with x = 0.030 had the highest peak ZT of ~ 1.55 at 773K. Further studies of higher Bi-doping content are of interest. Acknowledgement Page 5 of 6

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