Improving the thermoelectric performance in Mg 3 + xSb 1 . 5 Bi 0 . 49 Te 0 . 01 by reducing excess Mg

The thermoelectric performance of Mg_(3+x)Sb_(1.5)Bi_(0.49)Te_(0.01) was improved by reducing the amount of excess Mg (x = 0.01-0.2). A 20% reduction in effective lattice thermal conductivity at 600 K was observed by decreasing the nominal xfrom 0.2 to 0.01 in Mg_(3+x)Sb_(1.5)Bi_(0.49)Te_(0.01), leading to a 20% improvement in the figure-of-merit zT. Since materials with different amounts of Mg have similar electronic properties, the enhancement is attributed primarily to the reduction in thermal conductivity. It is known that excess Mg is required to make n-type Mg_(3+x)Sb_(1.5)Bi_(0.49)Te_(0.01); however, too much excess Mg in the material increases the thermal conductivity and is therefore detrimental for the overall thermoelectric performance of the material.

Thermoelectric materials that can generate electricity directly from waste heat have attracted attention because of the large demand of higher fuel efficiency and environment-friendly technology. 1,2The maximum performance of thermoelectric materials is evaluated by its figure-of-merit zT = α 2 σ κ T , where α is the Seebeck coefficient, σ is the electrical conductivity, and T is the absolute temperature.κ is the total thermal conductivity which is the sum of the electronic κ e and lattice κ l contributions.][5] Mg 3 Sb 2 -based compounds have been investigated with the hope of achieving a high thermoelectric performance.Many trials were attempted to improve the thermoelectric performance of Mg 3 Sb 2 -based compounds such as Mg site substitution [6][7][8] or Sb site substitution [8][9][10][11] leading to zT ≈ 0.7.While higher thermoelectric performance in n-type is predicted from their band structure, 12,13 most of these Mg 3 Sb 2 -based thermoelectric materials were reported as highly doped p-type semiconductors because the formation of Mg cation vacancies prevents n-type materials to form.However, n-type Mg 3.2 Sb 1.5 Bi 0.49 Te 0.01 was discovered very recently with outstandingly high performance zT ≈ 1.3 at 600 K by adding excess Mg and Te doping, [14][15][16][17][18] attracting considerable interest for the high potential of n-type Mg 3 Sb 2 -based compounds.
The key factor to get n-type materials lies in the thermodynamic conditions where the materials are synthesized.For the Mg 3 Sb 2 case, there are two different thermodynamic states: Mg-excess and Sb-excess states (where matrix Mg 3 Sb 2 is equilibrated with elemental Mg or Sb, respectively).The n-type Mg 3 Sb 2 -compounds can only be obtained when it is in the Mg-excess state because the difference in the atomic chemical potential in the Mg excess state suppresses the formation of cation vacancies. 17,19Previously, as Mg interstitials were considered to have a role to make the material n-type, a substantial amount of nominal excess Mg (x = 0.2) in Mg 3+x Sb 1.5 Bi 0.49 Te 0.01 was added to ensure the n-type property. 14,16However, the thermodynamic explanation 17 suggested that such a large amount of excess Mg (x = 0.2) could be unnecessary to achieve n-type properties.In addition, the transport properties of materials might be affected by the amount of excess Mg due to the presence of impurity phases or defects as reported in Mg 2 (Si, Sn)-based materials. 20,21herefore, it is important to investigate the effect of excess Mg on the n-type Mg 3+x Sb 1.5 Bi 0.49 Te 0.01 properties.
One major challenge to control the amount of Mg in n-type Mg 3+x Sb 1.5 Bi 0.49 Te 0.01 exists in the synthesis process due to the high vapor pressure and high reactivity of elemental Mg.In practice, an excess of Mg in the nominal composition is required to compensate the Mg loss during synthesis to achieve n-type properties in Mg 3 Sb 2 .However, it is difficult to individually determine the exact quantity of Mg needed to compensate for the Mg loss and the remaining amount of elemental Mg in the final material because the amount of Mg loss depends on the synthesis process.In this study, we require only x = 0.01 excess Mg (nominally) in Mg 3+x Sb 1.5 Bi 0.49 Te 0.01 to ensure n-type properties.Beyond an excess Mg of x > 0.01 in our synthesis, we find that samples have increasingly higher thermal conductivity presumably due to impurities.We reveal that this excess elemental Mg above the minimal threshold is detrimental to the thermoelectric performance and that minimization of this excess Mg increases the thermoelectric performance of Mg 3+x Sb 1.5 Bi 0.49 Te 0.01 .
We note that, even for different excess Mg in the nominal composition, the composition of the main phase Mg 3 (Sb,Bi,Te) 2 is expected to be the same based on the Gibbs phase rule 17 (also see experimental evidence from Rietveld refinements in the supplementary material).
We synthesized Mg 3+x Sb 1.5 Bi 0.49 Te 0.01 with different values of nominal Mg (x = 0.01-0.2).Magnesium turnings (99.98%,Alfa Aesar), antimony shots (99.9999%,Alfa Aesar), bismuth granules (99.997%,Alfa Aesar), and tellurium lumps (99.999%,Alfa Aesar) were sealed into stainless-steel vials according to the nominal composition while inside the argon-filled glove box.Mechanically induced reaction was conducted by high energy-ball milling with a high-energy mill (SPEX 8000D) for two hours.The reacted powder was pressed by induction heating and rapid hot pressing for 1 h at 873 K and 45 MPa under argon gas flow to consolidate pellet samples. 22The Seebeck coefficient of each sample was measured with Chromel-Nb thermocouples in a two-probe configuration under high vacuum. 23The Hall coefficient and electric resistivity were measured simultaneously using a 4-point probe Van der Pauw technique with a 2 T magnetic field under high vacuum.Thermal diffusivity D was measured by using the flash method with Netzsch LFA 457 under a dynamic argon atmosphere.The thermal conductivity κ was calculated by κ = D × C p × d, where d is the density and C p is the heat capacity.Average values of the heat capacity reported in a previous study 14 were used.
We find that the figure-of-merit is 1.2 times higher at 600 K in the sample with reduced nominal x (Mg 3+x Sb 1.5 Bi 0.49 Te 0.01 ) due to the reduction in thermal conductivity.Figure 1 is the comparison of transport properties of the n-type Mg 3+x Sb 1.5 Bi 0.49 Te 0.01 measured up to 700 K.All samples have largely similar values of Seebeck coefficient showing behavior typical of degenerate semiconductors.Negative values of Seebeck coefficient indicate that n-type behavior was obtained in Mg 3+x Sb 1.5 Bi 0.49 Te 0.01 even with small amounts of nominal Mg (x = 0.01).This supports the idea that being in the Mg-excess state is the necessary condition to get n-type Mg 3+x Sb 1.5 Bi 0.49 Te 0.01 . 17lthough small variations in the carrier concentration are found depending on the amount of excess Mg as shown in Fig. S1 of the supplementary material, those are two orders of magnitude smaller than what is expected from the changes in nominal Mg content.Such changes may be potentially attributed to Te loss during the synthesis (e.g., Te loss during the ball milling) or minor sample inhomogeneity preventing the material from reaching thermodynamic equilibrium (the limit in which the main phase composition is strictly fixed by the Gibbs phase rule).
On the contrary, the total thermal conductivity significantly decreases as a smaller amount of excess Mg is used to change the nominal composition toward the minimal threshold for APL Mater.6, 016106 ( 2018 While the electronic properties remain similar, the total thermal conductivity becomes smaller as less Mg (nominal composition) is used which leads to a higher zT value.The error bars indicate the following: for the Seebeck coefficient, the estimated range of underestimation due to the twoprobe configuration 26 combined with observed sample variation; for the thermal conductivity, thickness uncertainty combined with instrument accuracy which is to be compared with sample-to-sample variation; for conductivity, thickness uncertainty combined with probe error estimation 27 and sample variation.
n-type behavior.The 20% reduction in total thermal conductivity at 600 K from x = 0.2 to x = 0.01 is significantly larger than either the uncertainty of the measurement (4% combined from uncertainties of the diffusivity, thickness, and density measurements but excluding heat capacity which was fixed for all samples) or the sample-to-sample variations (maximum case shown from the two x = 0.2 samples prepared identically).Since the reduction in thermal conductivity due to a decreased amount of nominal excess Mg is much more significant than the changes in electrical properties, the improvement of the zT value from ≈1.2 to 1.4 at 600 K after reducing the nominal amount of Mg from 3.2 to 3.01 is mostly attributed to the reduction in thermal conductivity.This result demonstrates how controlling the amount of nominal Mg is crucial to improve the thermoelectric performance.A similar reduction in thermal conductivity was observed when a secondary dopant was substituted on the Mg site (Mg 3.2x Nb x Sb 1.5 Bi 0.49 Te 0.01 and Mg 3.1 T 0.1 Sb 1.5 Bi 0.49 Te 0.01 ). 16,24Such reduction in thermal conductivity could be explained with the change of excess Mg because the addition of a secondary dopant accompanied a reduction in the nominal Mg content.
The effective lattice thermal conductivity also decreases with the reduction of the nominal amount of excess Mg.As shown in Fig. 2(a), the effective lattice thermal conductivity of the sample with the least amount of nominal Mg (Mg 3.01 Sb 1.5 Bi 0.49 Te 0.01 ) is 0.52 W/m K at 600 K while that of the largest amount of nominal Mg (Mg 3.2 Sb 1.5 Bi 0.49 Te 0.01 ) is 0.66 W/m K at 600 K.In Mg 3 Sb 2 , the lattice thermal conductivity decreases with temperature due to Umklapp scattering and saturates around 600 K.We compare the >600 K lattice thermal conductivities to the high temperature glassy limit of lattice thermal conductivity κ min , 3 obtained with the following equation: where V is the average volume per atom and v T and v L are the transverse and longitudinal speed of sound, respectively.With speed of sound measurements at room temperature, the calculation gives similar values of κ min ≈ 0.49 W/m K for both compositions (Table I), which is similar to the >600 K effective lattice thermal conductivity observed in Mg 3.01 Sb 1.5 Bi 0.49 Te 0.01 [Fig.2(a)].It is seen that the sample with excess of Mg content above the minimal threshold (x > 0.01) does not reach the glassy limit at >600 K.The increase in the effective lattice thermal conductivity with the increasing amount of nominal Mg content above the threshold could be partially explained by assuming the presence of elemental Mg impurities in high excess samples.A small elemental Mg XRD peak would sometimes be observed by X-ray diffraction measurements in some of the samples.Segregation of elemental Mg as a secondary phase would increase the thermal conductivity from an effective medium theory point-of-view since elemental Mg has a much higher thermal conductivity; 25 in the effective medium theory for small volume fractions of an impurity phase, the change in the overall thermal conductivity is proportional to the volume fraction of the secondary phase, consistent with the trend shown in Fig. 2(b).We note that similar trends are also found in Mg 2 (Si,Sn)-based materials. 20,21owever, the effective medium theory does not fully explain the experimental results; we do not find a significant correlation between the excess Mg content and the electrical conductivity, which, according to effective medium theory, would be expected to scale similarly as seen in the thermal conductivity if the impurity phase is much more conductive.One could suspect the formation of an electrically insulating impurity phase rather than elemental Mg (or an insulating surface such as an oxide layer on the impurity).However, none of our samples showed any diffraction peaks associated with oxides such as MgO.Microscopy (using either secondary electrons or back scattered electrons) or wave-dispersive spectroscopy did not show any noticeable differences as well.Deviation from the classical effective medium theory is possible when interfacial effects are significant; however, the simplest case where additional interfaces contribute to thermal resistance does not explain the decreased conductivity with the reduced excess Mg.
In summary, a 20% reduction in effective lattice thermal conductivity was observed by reducing the excess Mg content x from 0.2 to 0.01 in Mg 3+x Sb 1.5 Bi 0.49 Te 0.01 leading to a 20% improvement in the figure-of-merit zT at 600 K.For the best thermoelectric performance, one should minimize the excess Mg content in the material while still maintaining a composition above the minimal threshold for n-type behavior.

)FIG. 1 .
FIG. 1. Transport properties of Mg 3+x Sb 1.5 Bi 0.49 Te 0.01 (x = 0.01-0.2) as a function of temperature: (a) Seebeck coefficient; (b) total thermal conductivity; (c) electrical conductivity; (d) figure-of-merit.While the electronic properties remain similar, the total thermal conductivity becomes smaller as less Mg (nominal composition) is used which leads to a higher zT value.The error bars indicate the following: for the Seebeck coefficient, the estimated range of underestimation due to the twoprobe configuration26 combined with observed sample variation; for the thermal conductivity, thickness uncertainty combined with instrument accuracy which is to be compared with sample-to-sample variation; for conductivity, thickness uncertainty combined with probe error estimation27 and sample variation.

016106- 4 Imasato
FIG. 2. (a) The effective lattice thermal conductivity of Mg 3+x Sb 1.5 Bi 0.49 Te 0.01 (x = 0.01-0.2) as a function of temperature.(b) The trend in effective lattice thermal conductivity and nominal x (Excess Mg) in n-type Mg 3+x Sb 1.5 Bi 0.49 Te 0.01 at 600 K and 450 K.The linear fits to the data are guides to the eyes.The effective lattice thermal conductivity decreases as less excess Mg is used to change the nominal composition toward the minimal threshold required for n-type.

TABLE I .
Longitudinal v L and transverse v T speed of sounds at room temperature.Although Mg 3.2 Sb 1.5 Bi 0.49 Te 0.01 shows a slightly higher speed of sound, the calculated values of the glassy limit of the lattice thermal conductivity κ min for both compositions are similar.See supplementary material for data on density, lattice constant, Hall carrier concentration, and thermal diffusivity.