Thermoelectric properties of Zintl compound Ca_1−xNa_xMg₂Bi_1.98 Free

The thermoelectric effect is currently a widely discussed topic as one of the alternative green approaches for electrical power generation. Thermoelectric energy conversion technology can be used to convert waste heat into electricity, which can help in alleviating the energy crisis.^1–6 Unfortunately, the application of thermoelectric materials has been limited, mainly because of their low efficiency.⁶ This property can be quantified by the dimensionless figure of merit (ZT), defined as $ZT=(S2σ/κ)T$⁠, where S, σ, κ, and T are the Seebeck coefficient, electrical conductivity, thermal conductivity, and absolute temperature, respectively.³ The numerator S²σ is known as power factor PF. An ideal thermoelectric material must have a power factor PF as high as possible and thermal conductivity κ as low as possible.

Generally, the effective strategies of bulk nanostructuring, nanoscale secondary phase, complex crystal structure, and solid solution are desirable for low thermal conductivity, which significantly increases the ZTs.^7–9 However, for practical use, high power factor is as important as efficiency when the capacity of the heat source is huge (such as solar heat), or the cost of the heat source is not a concern (such as waste heat from automobiles, steel industry, etc.).¹⁰ The output power density is mainly determined by the power factor in addition to the heat source temperature and geometry via the following formula:

where ω, T_h, T_c, and L represent the output power density, hot side temperature, cold side temperature, and length of thermoelectric legs, respectively. The enhancements for power factor have been found possible through modification of carrier concentration, resonant state, band convergence, and energy barrier filtering.^11,12

The low efficiency, unavailability, and in some cases toxicity of good thermoelectric materials prevent thermoelectric generators from widely being applied in converting waste heat into electricity to make a real impact on environment.⁶ Typically, the best thermoelectric materials are still Bi₂Te₃^13,14 and Pb-Te-based materials,¹⁵ which contain heavy elements such as lead and tellurium that are toxic and not earth abundant. In the ongoing search for promising materials, the availability and cost of the raw elements need to be seriously considered. For example, Zintl compounds, based on antimony and alkali and alkaline earth metals, such as Zn₄Sb₃,¹⁶ Mg₃Sb₂,¹⁷ and Ca_xYb_1−xZn₂Sb₂,¹⁸ are potentially good candidates due to their environmentally friendliness and earth-abundance. Generally, good thermoelectric performance is found in doped semiconductors, so it is important to be able to control the carrier concentration in Zintl compounds via doping, such as Na doping in Ca₅Al₂Sb₂,¹⁹ Ca₃AlSb₃,²⁰ Mg₃Sb₂,¹⁷ etc.

Besides the popular Sb-based Zintl phase, the Bi-based Zintl phase CaMg₂Bi₂ has recently attracted some attention.^21,22 Using the ball milling and hot pressing method, we have achieved a competitive ZT value of ∼0.8 in CaMg₂Bi₂.²³ Further investigation demonstrated a 1% Bi deficiency (CaMg₂Bi_1.98) resulted in phase pure Zintl phase with a peak ZT of ∼0.9. However, the carrier concentration of CaMg₂Bi_1.98 is relatively low (in the order of 10¹⁸cm⁻³), and it is important to increase the carrier concentration through doping. Here, we explore the effect of doping Na into Ca on the thermoelectric transport properties in Ca_1−xNa_xMg₂Bi_1.98. Upon Na doping, the carrier concentration increased by more than one order of magnitude, contributing to reduced resistivity and a much higher average power factor.

Calcium (Ca, Sigma Aldrich, 99.9%, pieces), sodium (Na, Sigma Aldrich, 99.9%, cubes), magnesium (Mg, Sigma Aldrich, 99.9%, pieces), and bismuth (Bi, Sigma Aldrich, 99.999%, chunks) were weighed according to the stoichiometry of Ca_1−xNa_xMg₂Bi_1.98 with x = 0, 0.0025, 0.005, and 0.0075, and sealed directly in the stainless steel jar with stainless steel balls inside an argon-filled glove box. The sealed jar was taken out for mechanical alloying by a high energy ball mill (SPEX 8000D) for 12 h. The final nanopowder was then loaded into a graphite die with an inner diameter of 12.7 mm, and consolidated by alternating current (AC) hot pressing at ∼933 K for 2 min. After cooling down, the desired phase was achieved. Ball milling process using stainless jar and balls does not have a significant Fe or other metal contamination problem in preparing high performance thermoelectric bulk materials,¹³ which has been confirmed repeatedly in many other materials.^10,14,24 The final hot pressed samples were cut in both directions and polished to the required dimensions for characterizations.

X-ray diffraction (XRD) spectra were collected on a PANalytical multipurpose diffractometer with an X'celerator detector (PANalytical X'Pert Pro). The microstructures, examined on a freshly broken surface, were investigated by a scanning electron microscope (SEM, JEOL 6330F). The electrical resistivity (ρ) and Seebeck coefficient (S) were simultaneously measured on a commercial system (ZEM-3, ULVAC) using a four-point direct current switching method and the static temperature difference method. The thermal conductivity was determined by measuring the thermal diffusivity (D) on a laser flash apparatus (LFA 457, NETZSCH), specific heat (C_P) on a DSC (404 C, NETZSCH), and volumetric density (ρ_D) by the Archimedes method. The carrier concentration was obtained by Hall effect measurement (van der Pauw method) at room temperature using a modified sample puck in a Physical Properties Measurement System (PPMS D060, Quantum Design).

Fig. 1(a) shows the X-ray diffraction (XRD) patterns of Ca_1−xNa_xMg₂Bi_1.98 (x = 0, 0.0025, 0.005, and 0.0075). Na doped Ca_1−xNa_xMg₂Bi_1.98 show the same XRD patterns as the pure phase without noticeable peak position shift. All diffraction peaks are indexed with the reported CaAl₂Si₂ structure-type (trigonal, No. 164, P-3m1). The change in lattice parameters is negligible with Na doping, attributed to the very small amount of dopant. By applying the Zintl concept, the structure of CaMg₂Bi_1.98 can be described as an anionic building block (Mg₂Bi₂)²⁻ with divalent cations Ca²⁺ located between the chains to provide electrons. Na and Ca belong to alkali and alkaline earth metals, respectively, and show similar behaviors by donating electrons to the more electronegative anions (Mg₂Bi₂)²⁻ and form covalent bonds. Increasing Na content effectively increases the carrier concentrations (discussed later). It can be concluded that Na is incorporated into the lattice in Ca_1−xNa_xMg₂Bi_1.98. The SEM image of the optimized Ca_0.995Na_0.005Mg₂Bi_1.98 sample is displayed in Fig. 1(b), from which we can see that the sample is densely packed and the grain size varies from 100 to 500 nm.

To determine the effect of Na doping at the Ca site on the thermoelectric properties of Ca_1−xYb_xMg₂Bi_1.98, electrical resistivity, Seebeck coefficient, and power factor were first measured. Fig. 2(a) illustrates the electrical resistivity as a function of temperature up to 873 K. The electrical resistivity of the Na doped samples is much smaller than that of the un-doped one, indicating that Na is a very effective hole donor. At room temperature, the resistivity of sample with x = 0.0075 is around 9.2 μΩ m, which is about 15 times smaller compared to 131 μΩ m for the un-doped sample. The Hall carrier concentration at 300 K is shown in Table I. Obviously, the carrier concentration has increased by more than one order of magnitude from 3.46 × 10¹⁸cm⁻³ to 4.4 × 10¹⁹cm⁻³. With increasing Na content, Hall mobility experienced little change. Moreover, the relation for the resistivity dependence of temperature follows ρ vs. T^1.5, indicating that the carrier transport mechanism is dominated by acoustic phonon scattering before intrinsic excitation. For x = 0.75 at. %, it is observed that the resistivity exhibits a metal-like behavior, indicating that the doping level is high enough to suppress the intrinsic excitation.

Fig. 2(b) represents the temperature dependent Seebeck coefficient of all the Na doped samples. The positive Seebeck coefficient indicates a p-type electrical transport behavior. Doping of Na into Ca sites decreases the Seebeck coefficient, and the decrease becomes smaller with the increase in Na content from 0.0025 to 0.0075. Meanwhile, all the samples exhibit peak values of the Seebeck coefficient, the typical characteristics of bipolar effect due to the very small bandgap.^21,25 With more Na concentration, the temperature corresponding to peak Seebeck coefficient increases, indicating that the increased majority carrier concentration suppresses the bipolar effect.

Fig. 2(c) shows the power factor calculated from the measured electrical resistivity and Seebeck coefficient of Ca_1−xNa_xMg₂Bi_1.98 samples. With increasing Na concentration from x = 0 to 0.0075, the power factor monotonically increases over the entire temperature range, especially at low temperatures. The power factor increases from 5 μW cm⁻¹ K⁻² for x = 0 to 12 μW cm⁻¹ K⁻² for x = 0.0075 at 300 K. Unlike the un-doped sample, all the Na doped samples maintain high power factors over all temperatures.

Fig. 2(d) shows the total thermal conductivity as a function of temperature for the Ca_1−xNa_xMg₂Bi_1.98 samples. The densities (ρ_D) of all the samples Ca_1−xNa_xMg₂Bi_1.98 with x = 0, 0.0025, 0.005, and 0.0075 measured by Archimedes method are 5.48, 5.50, 5.52, and 5.49 g cm⁻³, respectively. All samples are densely packed, demonstrated by the SEM images taken on the freshly fractured surface. Specific heat (C_p) and the diffusivity (D), shown in supplementary Figure S1,²⁶ are used to calculate the total thermal conductivity (κ) of all the samples by using $κ=DρDCP$⁠. The total thermal conductivity gradually increases with increasing Na doping concentration, mainly due to the enhanced contribution of electronic thermal conductivity κ_e, estimated using the Wiedemann−Franz relationship (⁠$κe=LT/ρ$⁠), where L is the Lorenz number, based on a single parabolic band model. By directly subtracting the electronic contribution from the total thermal conductivity, the lattice thermal conductivities (κ_L) were obtained and are shown in Fig. 2(e). It is well known that the total thermal conductivity comprises three parts, including lattice thermal conductivity, electronic thermal conductivity, and bipolar thermal conductivity (⁠$κtotal=κL+κe+κbipol$⁠). In order to investigate the effect of Na substitution on the κ_L, the lattice thermal conductivity before the occurrence of intrinsic excitation (∼550 K) are used to make the comparison. It is apparent that all samples exhibit almost the same value before 550 K, which means doping with Na at such a low concentration does not result in a significant scattering of the phonons.

The figure-of-merit ZT versus temperature and Na content x is plotted in Fig. 2(f). With increasing temperature, ZT increases continuously. The Na doped samples have better ZT values when the temperature is below 750 K, mainly due to the improved power factor. The optimized composition is Ca_0.995Na_0.005Mg₂Bi_1.98, which possesses the highest ZT over all temperatures and reaches a peak ZT of ∼0.9 at 873 K.

Since ZT only indicates the ratio of electrical to thermal characteristics at each instantaneous temperature, it cannot indicate the practical efficiency of a TE material at a large temperature gradient between the cold and hot sides. Instead of using the peak ZT, Kim et al. recently took another big step and proposed the engineering figure of merit (ZT)_eng as a function of thermal boundary conditions, i.e., the temperatures of hot side T_h and cold side T_c to reliably predict the possible efficiency and output power density.²⁷ Figs. 3(a) and 3(b) show the calculated (PF)_eng and ω_max and dependence of the hot side temperature up to 773 K while the cold side temperature is kept at 323 K. It is clear that both (PF)_eng and ω_max increase more than 100% with Na doping concentration from x = 0 to 0.0075. Specifically, the un-doped sample exhibits a (PF)_eng∼ 0.36 W m⁻¹ K⁻¹ and ω_max ∼ 2.5 W cm⁻² but the 0.0075 Na doped sample exhibits a (PF)_eng ∼ 0.77 W m⁻¹ K⁻¹ and ω_max ∼ 5.3 W cm⁻². Figs. 3(c) and 3(d) present the hot side temperature dependence of (ZT)_eng and efficiency, respectively. The calculated (ZT)_eng increases from 0.23 for x = 0 to 0.4 for the optimized sample with x = 0.005, which makes the possible efficiency increase from 4.9% for x = 0 to 7.8% for x = 0.005 at T_h = 873 K.

In order to investigate the anisotropy of the thermoelectric properties, thick un-doped CaMg₂Bi_1.98 samples were prepared. Fig. 4(a) shows the very similar X-ray diffraction patterns from both planes perpendicular and parallel to the hot press direction, which might attribute to the uniform polycrystalline grains observed in the SEM image. Figs. 4(b)–4(f) show the thermoelectric properties of CaMg₂Bi_1.98 measured in two different directions. The electrical resistivity and Seebeck coefficient measured perpendicular to the press direction is about 10% higher than parallel direction, indicating there is minor grain orientation. However, there is not much difference between the power factors measured from the two directions. Further due to the similar thermal conductivities in Fig. 4(e), the ZT values in two directions are basically the same within the experimental errors ∼10%–12%. Therefore, the similar thermoelectric properties along the parallel and perpendicular to hot press direction shows that CaMg₂Bi_1.98 has little anisotropy.

The exploration of complex Zintl compounds continues to reveal good thermoelectric properties. Good thermoelectric properties are achieved in Bi-based Zintl compound Ca_1−xNa_xMg₂Bi_1.98 by doping Na into Ca to increase the carrier concentration and power factor. The optimized Ca_0.995Na_0.005Mg₂Bi_1.98 sample achieves better average ZT, output power density, and efficiency. This work highlights the potential of Na doped Ca_1−xNa_xMg₂Bi_1.98 for potential waste heat recovery application for middle temperatures.

The work performed at University of Houston is funded by DOE under Contract No. DE-SC0010831/DE-FG02-13ER46917 (sample synthesis and characterizations) and also supported by the National Natural Science Foundation of China (No. 51471061).