Engineering defects are an important tool to improve the properties of a semiconductor, particularly a thermoelectric material. 1 Mg 3 Sb 2 is a new thermoelectric material in which understanding and engineering its point defects was crucial to unlocking its potential as a good thermoelectric material. 2 Mg 3 Sb 2 was computationally suggested to be a good n-type thermoelectric material in 2013 (ref. 3) due to its high n-type valley degeneracy. While experimentalists were equipped with this information, they struggled to dope the material n-type due to persistent Mg vacancies on the Mg-1 octahedral cite, which would counteract any extrinsic n-type doping that was attempted. 2 Once this killer Mg vacancy defect was appreciated, experimentalists were able to counteract the killer defect by adding extra Mg to their samples to suppress the Mg vacancy formation and allow for extrinsic dopants to add electrons to the material. [4][5][6][7][8][9] Mg vacancies still readily form when samples are heated to temperatures above 400 C, 10 due to the preferential sublimation of Mg from the sample. 11 Mg 3 Sb 2 can be thought of as a special case of the layered CaAl 2 Si 2 (AB 2 X 2 ) Zintl phase crystal structure in which the A and B sites are both composed of Mg, which we'll refer to as Mg (1) and Mg(2) respectively. 12 The Mg(2) site is tetrahedrally coordinated with Sb and forms the B 2 X 2 layer. The Mg(1) site forms the intralayer site and is octahedrally coordinated with Sb atoms. Though Mg 3 Sb 2 can be visualized through the layered CaAl 2 Si 2 structure, Zhang et al. carefully showed the "layered" term may not be appropriate. This is because the Mg(1) and Mg(2) sites have similar Bader charge and bond strength with Sb, making the calculated material properties isotropic. 12 While the term layered may not be apt for Mg 3 Sb 2 , the similar size and charges on Mg(1) and Mg(2) might play a role in why the material's electronic properties are unique within this crystal structure. Zhang et al. rst pointed out that the conduction band minimum states of Mg 3 Sb 2 are made out of Mg(1) s and Mg(2) s and p states. 9 Sun et al., took this a step further and showed that the highly degenerate U* band (N v ¼ 6) was made up of covalent interactions between the Mg(1) and Mg(2) atoms. 13 This interaction can be demonstrated from rst principles electronic structure and crystal orbital Hamilton population (COHP) calculations (see Fig. 1). The conduction band minima at the non high-symmetry U*-point lies in the G-A-L-M plane (see 2D Fermi-Energy contour plot in Fig. 2b). The k-resolved COHP for the conduction band in this 2D plane reveals Mg(1)s-Mg(2)s as the dominant interaction in the vicinity of U*-point. These conduction band states exhibit a signicant bonding interaction between 3s levels of Mg (1) and Mg(2) as indicated by the negative values COHP values (see blue regions in Fig. 2) for states close to U*. Sun went on to show that changing the octahedral site to another atom such as Yb or Ca computationally resulted in a more ionic interaction between the octahedral atom and the Mg 2 Sb 2 layer. In these XMg 2 Sb 2 compounds the conduction band minimum is moved to the higher symmetry M point (N v ¼ 3), which has less band degeneracy. 3,13,14 Mg 3 Sb 2 can form solid solutions with other compounds of the same crystal structure, with solubilities varying to differing degrees. Mg 3 Bi 2 is commonly alloyed with Mg 3 Sb 2 and is used to lower the material's lattice thermal conductivity and increase its weighted mobility. 15,16 Besides studies with Bi, Sun et al. calculated the valley degeneracy of Mg 3 Sb 2 , could be increased by alloying Yb or Ca onto the octahedral Mg site, moving the conduction band at U* up slightly in energy to be aligned with the band at M. 13 Beyond this computational alloying study, there have been numerous papers published both computationally 17,18 and experimentally 9,19-21 testing the impact of different doping techniques. The main focus of which is the dopant's dopability (i.e. the maximum soluble amount of a dopant which donates charge carriers). However, in many of these dopant and alloying papers the type of states that make up the conduction band character is oen overlooked. Disrupting these states can lead to additional short ranged potential scattering 22,23 or alloy scattering, 24 decreasing the materials performance.
Herein we investigate the properties of Mg 3.125Àx Yb x Sb 1.5 Bi .5 -Te 0.01 and show a decrease in the mobility of the material as more Yb is added from disrupting the Mg(1)-Mg(2) interaction that make up the conduction band. Additionally, we show that this reduction can be well explained via an alloy scattering model. Finally, we show that while a sample's mobility is decreased, Yb alloying does benet a sample's high temperature stability.
The density functional theory (DFT) calculation 25 in this study were performed using Vienna ab initio simulation package (VASP). 26 We have used Perdew-Burke-Ernzerhof (PBE) formulation of the exchange correlation energy functional derived under a gradient-generalized approximation (GGA). 27 Plane-wave basis sets truncated at a constant energy cutoff of 390 eV were used, as were G-centered k-point meshes with a density of $8000 k-points per reciprocal atom (KPPRA). All structures were relaxed with respect to cell vectors and their internal degrees of freedom until forces on all atoms were less than 0.1 eV nm À1 . The k-resolved crystal orbital Hamilton populations (COHPs) calculations were performed using the version 3.2.0 of the LOBSTER soware. [28][29][30]
Samples of Mg 3.125Àx Yb x Sb 1.4925 Bi 0.4975 Te 0.01 (x ¼ 0, 0.075, 0.25, 0.4) were prepared via a high-energy ball mill using stoichemetric ratios of Mg turning (99.95% Alpha Aesar), Yb chunk (99.5% Alpha Aesar), Sb shot (99.999% 5N Plus), Bi shot (99.999% 5N Plus), Te shot (99.999% 5N Plus). Excess Mg was used in all samples in order to suppress the formation of electron killing Mg vacancies. Starting elements were loaded into a steel ball milling vial in an argon dry glove box. Samples were then milled for 2 90 minute periods using a SPEX Sample Prep 800 Series Mixer/Mill. The powder from this milling process was consolidated using an induction heated rapid hotpress 31 under a owing argon atmosphere within a 1/2 inch diameter high-density graphite die (POCO) into pellets approximately 1.5 mm in thickness. Samples were pressed at 800 C for 20 minutes at 45 MPa. Resulting samples were found to have densities exceeding 95% theoretical densities.
X-ray diffraction was performed on polished pellets using a STOE STADI MP with pure Cu Ka1 radiation in reection geometry, followed by scanning electron microscopy with a Hitachi S-3400N-II. Densities of samples were measured geometrically and then conrmed with the Archimedes Principle. Resistivity and Hall coefficients were measured concurrently using a van der Pauw technique with pressure-assisted molybdenum contacts equipped with a 2T magnet. 32 Thermal diffusivity measurements were taken with a Netzsch LFA 457 under purged owing argon, and the thermal conductivity was calculated using heat capacity from Agne et al. 33 Seebeck coef-cient were measured under dynamic high vacuum with a homebuilt system using Chromel-Nb thermocouples. 34 All samples were investigated in pellet form with Seebeck and thermal diffusivity measured out of plane and resistivity and Hall coefficient being measured in the in-plane direction. The thermal stability of materials studied were measured via the change in Hall carrier concentration as a function of time at elevated temperatures. 10
X-Ray Diffraction patterns for samples created of Mg 3 Sb 2 alloyed with Bi and Yb and doped with Te are shown in Fig. S1 of the ESI. † From XRD we can identify no visible impurity phases. Fig. 3 shows the lattice parameters obtained from diffraction pattern of samples, with the dashed line showing the lattice parameters expected assuming a weighted average contribution from the four compounds that make up the solid solution. Both a and c rise linearly with increased Yb content up to x ¼ 0.25, where beyond this composition the solubility of Yb into the structure has likely been exceeded. This is reected by the x ¼ 0.4 sample's lattice parameters deviating slightly from the predicted line. In addition to this evidence, energy dispersive spectroscopy (EDS) of the x ¼ 0.4 and x ¼ 0.25 samples (Fig. S3 and S4 in ESI †) shows no secondary phases precipitating out of the matrix, and a matrix composition that is within error of the respective samples' nominal compositions. Based on this data we can assume a solid solution is obtained at least until composition x ¼ 0.25.
Table 1 shows how the Hall carrier concentration (dened as simply 1/R H , the Hall resistance) of Te doped Mg 3 Sb 1.5 Bi 0.5 is reduced as Yb is alloyed in. Additionally, Table 1 shows the Hall mobility and experimental density of states effective mass calculated from the Hall carrier concentration and Seebeck coefficient 39 for the samples that are unaffected by bipolar conduction. The x ¼ 0.2 and x ¼ 0.4 samples clearly show bipolar effects in both Seebeck and electrical conductivity so the actual free electron concentration is likely to be less than the measured n H ) There is barely an increase in effective mass observed to support the claim that adding Yb produces additional conducting states, however a benet of these states to the materials' weighted mobility (Fig. 5) is not seen.
Thermoelectric transport studied (Fig. 4) follows a trend that is expected given the decreasing carrier concentration with Yb content. The Seebeck coefficient increases as Yb is alloyed is due to the reduction of carrier concentration, and the conductivity decreases. The thermal conductivity decreases with the addition of Yb, which is due in part to the reduction in the electronic portion of thermal conductivity. Additionally this decreasing trend can be attributed to a reduction in the lattice portion of thermal conductivity (Fig. S2 †) as Yb is added due to a reduction in speed of sound computationally predicted 13 as well as alloy scattering of phonons. [40][41][42][43][44] This journal is © The Royal Society of Chemistry 2020
To compare transport in the samples we extracted the weighted mobility from a sample's Seebeck and conductivity data following. 39,45 Weighted mobility makes up the numerator of a materials quality factor and can be used to obtain a material's the peak power factor with changing carrier concentration. 22 As Yb is alloyed into the material we see a resulting decrease in its weighted mobility that follows the trend expected due to alloy scattering. As pointed out by Sun et al. 13 the Mg(1)-Mg(2) interaction is important in the electronic states at the conduction band minimum in Mg 3 Sb 2 . This explains why disrupting the Mg1 sites by replacing Mg with Yb has a large detrimental effect. This reduction in mobility is not seen 15,16 with alloying Bi on the anion site, which is expected because anions do not contribute much to the conduction band states.
To study the reduction in mobility in samples, an alloy scattering model is employed, which Wang et al. used to study the PbTe-PbSe alloy. 24 In this model we assume the total relaxation time of an electron is given by Matthiessen's rule such that:
or equivalently
where the scattering time from an alloy takes the form:
in which U is the volume per atom, x is the concentration faction of the alloying atom, m * b is the density of states mass for a single band, and U is the alloy scattering potential.
While the initial compound is already an alloy of Mg 3 Sb 2 and Mg 3 Bi 2 , we can separate Yb's contribution to alloy scattering by taking the 25% Mg 3 Bi 2 as giving a "pure" weighted mobility. The reduction in weighted mobility due to alloy scattering therefore takes the form: where m * DOS is the density of states effective mass, m * I is the inertial effective mass and N v is the degeneracy of the band(s) involved in transport. Using a N v ¼ 6 given by the degeneracy of the CB1 pocket, and using Zhang et al.'s calculated inertial masses isotropically averaged to 0.3m e (ref. 46) we nd an alloy scattering potential of 2.2 eV gives a curve matching the experimental data at a range of different temperatures (Fig. 5).
The reduction of carrier concentration as Yb is alloyed into the crystal is likely from cation site vacancies in the crystal, which have the effect of lowering the Te dopability in the alloy. Pomrehn et al. showed in AZn 2 Sb 2 (A ¼ Ca, Sr, Eu, Yb) as the A site was changed the vacancy formation energy of the A site also changed, with YbZn 2 Sb 2 being the most susceptible to the formation of vacancies. 47 While the compound studied here contained Mg instead of Zn, the experimental data suggests a similar effect might exist as Yb is alloyed into Mg 3 Sb 2 .
While the mobility of Mg 3 Sb 2 was decreased with alloying Yb, long term Hall tests (Fig. 6) show adding Yb appears to increase its high temperature stability. We speculate this change is due to a reduction of the diffusivity of Mg within the material aer adding the larger Yb atom as it is also observed in a La-doping study. 10 Regardless of cause, this observed increased stability provides a possible route for Mg 3 Sb 2 compounds to be used at higher temperatures.
The zT of the samples (Fig. 7) follows the same trend as weighted mobility with the zT decreasing with increasing Yb alloying. Yb alloying does decrease the lattice thermal conductivities of the samples studied, which is good for thermoelectric performance. However this decrease is not substantial enough to overcome the decrease in mobility from disrupting the Mg(1)-Mg(2) interaction.
In conclusion, alloying Yb on to the cation site of Mg 3.05 -Sb 1.4925 Bi 0.4975 Te 0.01 results in a reduction of the materials mobility due to alloy scattering. Alloying on the cation site appears to be detrimental not only because the conduction band is normally dominated by cations 23 but also because Yb disrupts the Mg(1)-Mg(2) interaction that is responsible for locating the conduction band minimum at the high valley degeneracy point U*. Although we see a reduction of zT with Yb alloy, the high temperature stability of the material increases with its addition.
When we compare anion site alloying with cation site alloying the importance of the Mg(1)-Mg(2) interaction becomes even more clear. Both cation site alloying with Yb and anion site alloying with Bi decreases thermal conductivity, and both alloying cases are predicted to create a band convergence effect should improve the weighted mobility. However the cation-site disorder disrupts the Mg(1)-Mg(2) interaction much more strongly than the anion-site disorder. Thus alloying on the anion site, which is less effected by the additional scattering, can benet from the lower thermal conductivity and band convergence, producing higher zT.
This journal is © The Royal Society of Chemistry 2020