Pressure-induced phase transition and electrical properties of thermoelectric Al-doped Mg₂Si Free

Doped Magnesium silicide (Mg₂Si)-based alloys have been suggested as a candidate of a new generation of high performance and environmental friendly thermoelectric materials.^1–4 Compared with other lead-based thermoelectric materials, Mg₂Si-based alloys have the merits of being non-toxic, sustainable, and low cost. It is well known that the efficiency of thermoelectric materials may be increased through p- or n-type doping at ambient pressure.^5–9 A dopant can increase the carrier concentration and mobility of the conduction electrons. Doping with heavy atoms can affect the lattice vibrations and help to lower the thermal conductivity by increasing the phonon-phonon scatterings. Pressure can also be used to enhance the thermoelectric power factor. Recently, Mg₂Si nominally doped with 1% Al was compressed to 2–3 GPa, and the thermal power was found to increase significantly reaching a maximum value of 8 × 10⁻³ W/(K² m). In this case, the increase in the thermoelectric efficiency is associated with an increase of electrical conductivity, and it was suggested that the Al-doped sample became metallic between 5 and 12 GPa. A Raman spectroscopy study also hinted at two possible structural phase transitions at 5–7 GPa and 11–12 GPa.¹⁰ To date, the structure and the cause for the enhancement of the thermal power of the lightly Al-doped Mg₂Si are still not known. This is the focus of this investigation.

At ambient pressure and temperature, Mg₂Si has a cubic anti-fluorite structure (space group Fm-3m) and is a semiconductor with a small indirect band gap of 0.6 eV.¹¹ Using energy dispersive X-ray diffraction and silicone oil as the pressure medium, it was reported that Mg₂Si underwent a structural transition to an orthorhombic anti-cotunnite structure with space group Pnma at 7.5 GPa. Further compression led to a hexagonal Ni₂In-type P63/mmc structure at 21.3 GPa.^12,13 The high pressure structural phase transition behavior of pure Mg₂Si was re-investigated by Zhu et al. with an angle dispersive diffraction using NaCl as the pressure transmitting medium.¹⁴ A phase transition from the anti-fluorite structure to the monoclinic structure was reported at 11.1 GPa. No further phase transition was found up to 37.5 GPa.

The discrepancy between the two diffraction measurements is unsettling and raises the question on the true identity of compressed Mg₂Si and the role of the pressure transmission medium to the crystal structure. This is further complicated by experimental resistivity measurements of un-doped Mg₂Si, where three distinct regimes separated at 7, 12, and 22 GPa were observed, but Mg₂Si remained a semiconductor with the hint of eventual metallization at pressure exceeding 22 GPa.¹⁵ Since theoretical calculations have predicted that the high pressure anti-cotunnite and Ni₂In structures are metallic,^16,17 the resistivity measurements clearly show there is no insulator → metal transition below 7 GPa. As will be shown and discussed below, and contrary to earlier reports,^12,13 the present study reveals no structural phase transition in pure Mg₂Si up to 18 GPa. However, a structural phase transition was found in Al-doped Mg₂Si at 11 GPa.

Since the reflectivity is related to the dielectric function, frequency dependent optical conductivity can be extracted from the analysis. Static (dc) conductivities can be obtained by extrapolation to zero photon energy. In-situ high pressure far and mid-infrared reflectivity measurements have been performed on a nominal 1 at. % Al-doped Mg₂Si sample and compared to the results from bulk measurements.¹⁰ The general trend that the electrical conductivity increases with pressure is the same as that found in previous measurements. Data analysis is complemented with theoretical density functional band structure calculations, which reveal a partially filled mid-gap band due to localized electronic interactions between the Al dopant with the surrounding host atoms is responsible for the enhancement of the thermopower.

The objective of this paper is to investigate the high pressure structure and the relationship to the transport properties of Al-doped Mg₂Si. For comparison, we have also examined the structure of pure Mg₂Si. For this purpose, room-temperature high resolution synchrotron angle dispersive synchrotron X-ray diffraction experiments up to 14.7 GPa using helium as the quasi-hydrostatic pressure-transmitting medium. Compared to silicone oil and NaCl, helium has the advantage of remaining in the liquid state at higher pressure and, therefore, able to maintain the isotropic strain of the sample in the diamond anvil cell (DAC).

The layout of the paper is as follows. First, details on the experimental procedure will be described. Diffraction results on pure Mg₂Si will be then compared with earlier studies. New results on the structure and structural transformation of Al-doped Mg₂Si under pressure will then be presented. This is followed by a discussion on the electrical properties extracted from the analysis of far and mid-IR reflectivity spectra. Comparison of the electrical conductivity with the variation of theoretical electronic density of states (DOS) is then made. The paper concludes with a proposed mechanism for the increase in thermopower under pressure.

Electron microprobe analysis: Powder Mg₂Si with a purity of 99.5% was purchased from Alfa Products. Mg₂Si doped with nominal 1 at. % of Al was synthesized by spark plasma sintering technique. To quantitatively examine the chemical compositions of Al-doped Mg₂Si powder samples, elemental analysis was performed on a JEOL 8600 Superprobe electron microprobe analyzer operating at 15 kV and 50 nA. The beam diameter was 5 mm. Dwell time on the peak was 60 s. SPI metals were used as standards for each element. Random sites on a compressed powder sample were selected and analyzed to give an unbiased sampling of compositions.

High-pressure powder x-ray diffraction measurement: The ambient powder diffraction patterns for pure and 1% Al-doped Mg₂Si were measured at the CMCF beamline, Canadian Light Source (CLS). High-pressure X-ray diffraction experiments were performed at Sector 20, Advanced Photon Source (APS) at the Argonne National Laboratory, using synchrotron radiation (λ = 0.47685 Å). A DAC was used to generate the pressure. The powder sample was placed in the hole of a stainless steel gasket between the diamond anvils and then loaded with helium as the pressure transmitting medium. A ruby sphere was placed with the powder sample with the pressure determined from the peak shift of the ruby R₁ and R₂ fluorescence lines.¹⁸ The maximum pressure studied was 14.7 GPa for pure Mg₂Si and 16.6 GPa for Al-doped Mg₂Si. The diffraction patterns were analyzed using the JANA 2006 software package and the lattice parameters were determined by Le Bail fit.^19,20

High-pressure infrared reflectivity measurement: High-pressure infrared reflectance spectra on 1% Al-doped Mg₂Si sample were measured at the side-station of the U2A beamline at the National Synchrotron Radiation Facility, Brookhaven National Laboratory. The mid-infrared spectra were recorded on a Bruker Vertex 80v FTIR spectrometer and a Hyperion 2000 IR microscope attached with a liquid nitrogen cooled HgCdTe detector.

The far-infrared spectra were recorded by a vacuum liquid helium cooled bolometer detector. Powder sample of Al-doped Mg₂Si was prepared and loaded into a stainless steel gasket placed between two 300 μm culets of a Sintek mini type IIa diamond anvil cell. A stainless steel gasket was pre-indented in the diamond anvil cell, and a 100 μm hole was drilled in the center of the indentation to serve as a sample chamber. Prior to the loading of the sample, the reflected power intensities of air-diamond base (I_d) and air-diamond culet (I_c) interfaces were measured at each pressure point. This process allowed us to minimize the error due to the intensity difference between diamond culet and base. After loading the sample and closing the DAC, the power intensity reflected from the air-diamond base (I_d) was measured again, and subsequently, the power intensity reflected from the sample-diamond interface (I_sd) was measured.

The reflectivity of sample-diamond interface (R_sd) was calculated as R_sd = (I_sd/I_d) × (I_d/I_c) × (I_c/I₀), where I₀ is the power intensity reflected from gold foil. And I_c/I_o is a constant of 0.185. All the spectral data were collected at a resolution of 4 cm⁻¹ and accumulated for 512 scans. Once again, the fluorescence from a ruby crystal placed in the powder sample was used for pressure calibration.

Frequency dependent optical conductivity was obtained by Kramers−Kronig (K−K) analysis of the data obtained from normal incidence reflectivity measurements.²¹ The data were subsequently fitted using a variational K−K constrained dielectric function, as implemented in the RefFIT code.²² After the correction for the diamond contribution, the frequency dependent optical conductivity is derived from fitting to a Drude-Lorentz (DL) model, and the dc conductivity is obtained from the extrapolation to zero frequency.

Electronic structure calculations: First Principles electronic calculations were performed using density functional theory (DFT) within the Perdew-Burke-Ernzerh (PBE) of parameterization of the generalized gradient approximation (GGA) as implemented in the Vienna ab initio simulation package (VASP) code.^23–26 To obtain accurate band gap energy of pure Mg₂Si at ambient and high pressure, additional calculations were performed with the GW approximation (GWA), which utilized the one-particle Green's function and screened Coulomb interaction W to account for the effect of electrons to the electronic band structure.^27,28 For all calculations, the projector-augmented wave (PAW)^29,30 potentials constructed from the generalized PBE functional were used with 3s²3p¹, 3s²3p², and 2p⁶3s² as valence electrons for the Al, Si, and Mg atoms, respectively. A 4 × 4 × 4 k-points mesh was used for total density of states (TDOS) and projected density of states (PDOS) calculations. A 1 at. % Al doped Mg₂Si was constructed from a 2 × 2 × 2 supercell of the crystal where one of the Mg atoms is replaced with Al (i.e., Mg₆₃Si₃₂A_l).

Room-temperature high resolution synchrotron angle dispersive X-ray diffraction patterns of pure Mg₂Si were measured up to 14.7 GPa (Figure 1) using helium as the pressure medium. It was shown in a recent report comparing argon and silicone oil as the pressure transmission medium.^31,32 The linewidth of diffraction pattern in silicone oil is substantially broadened above 10 GPa. Compared to silicone oil and NaCl, helium has the advantage of remaining in the liquid state at higher pressure and, therefore, able to maintain the isotropic strain of the sample in the DAC. Furthermore, the diffraction patterns will be interfered by the diffraction lines of NaCl. It is unlikely the helium will occupy the empty sites in Mg₂Si. Since Mg₂Si is built from a FCC Si lattice with Mg in the octahedral sites, the only possible site that helium atoms may diffuse into is the tetrahedral site. However, the powder diffraction pattern of pure Mg₂Si was measured independently without a medium. The cubic unit cell parameter determined at ambient pressure agrees well with the results obtained in the DAC extrapolated to zero pressure with helium as the medium. In addition, the lattice constant and volume fitted with the 3rd order Birch-Murnaghan equation of state (red lines) are also in reasonable agreement with results of theoretical calculations (Figure 2). Therefore, there is no evidence that the helium can incorporate in the crystal lattice.

It is important to point out that we observed no impurity peaks that can be attributed to MgO. The lattice constants were determined from full profile Le Bail fit to the diffraction peaks between 7° to 18° using the JANA 2006 software package. All the X-ray diffraction patterns can be indexed readily to the ambient pressure cubic anti-fluorite (CaF₂) structure with space group Fm-3m. The Miller indices (hkl) of the Bragg peaks are identified as (111), (200), (220), (311), (222), and (400) reflections with increasing scattering angles. No structural phase transition was found up to 14.7 GPa, the highest pressure studied. All diffraction patterns display the same profile except shifts of the Bragg peaks to higher angles with increasing pressure. The derived lattice parameters and unit cell volumes as a function of pressure were reported in Figures 2(a) and 2(b), respectively. The pressure coefficient for the cubic lattice determined from the experiment is −0.045 Å/GPa. The lattice parameters are in good accord with previous results by Zhu et al. and Hao et al. within the overlapping pressure region up to 7.5 GPa.¹³ 

To examine the electronic property of Mg₂Si at high pressure, theoretical density functional calculations with the PBE function were performed at 0, 4, 8, and 11 GPa (Figure 3). The calculated band structures were corrected for electron correlation effect as GW-correction.⁴⁰ Obviously, Mg₂Si is a semiconductor with the small band gap over this pressure range. The GW band gaps are 0.62, 0.46, 0.41, and 0.30 eV at 0, 4, 8, and 11 GPa, respectively. The theoretical results agree with the resistivity measurements that show Mg₂Si is an insulator at least up to 22 GPa. Together with the electrical measurements, structural transitions to the high pressure anti-cotunnite and Ni₂In phases at 7 and 11 GPa can be ruled out.

Experimental angle dispersive synchrotron radiation X-ray diffraction patterns of 1% Al-doped Mg₂Si were measured as a function of pressure up to 16.6 GPa (Figure 4). Again crystal lattice parameters were extracted from full profile of the diffraction patterns. At 0.9 GPa, diffraction peaks located at 7.5°, 8.7°, 12.3°, 14.5°, 15.1°, and 17.5° are indexed to (111), (200), (220), (311), (222), and (400) reflections of the cubic anti-fluorite structure of Mg₂Si. Below 10.5 GPa, the diffraction patterns of 1% Al-doped Mg₂Si are similar to pristine Mg₂Si. At low pressure, a small amount of Al dopant is not expected to affect the crystal lattice of the host significantly.

The unit cell of Al-doped Mg₂Si is slightly larger than the pure Mg₂Si below 2 GPa. This suggests the Al dopants should occupy the Mg sites in the crystal structure. Therefore, under ambient conditions and low Al-doping concentration, Mg₂Si is expected to be an n-type semiconductor. This assignment is in agreement with the negative value of Hall coefficient reported.¹⁰ The cubic structure is maintained up to 10.5 GPa. Interestingly, the derived pressure coefficient for the cubic lattice of 0.023 Å/GPa is substantially smaller than in the pure sample. This observation indicates that even at 1% doping the Al-Mg₂Si crystal lattice is more resilient to compression. Figures 5(a) and 5(b) show the pressure dependence of the lattice parameters and the unit cell volumes (Figure 5). At ambient pressure, the cell parameter of the cubic anti-fluorite structure (Fm-3m) of 6.2878(9) Å is reduced to 6.0261(11) Å at 10.5 GPa. Concomitantly, the cell volume per formula unit decreased from 62.15(12) ų to 54.71(12) ų. It is interesting to note that the ambient pressure lattice constant obtained here with high resolution synchrotron radiation is noticeably shorter than the earlier report of 6.396(1) Å.¹⁰ As will be discussed below (vide supra), this difference may have important implications on the transport properties. The experimental results conclusively indicated the anti-fluorite structure (Fm-3m) of Al-doped Mg₂Si is stable up to 10.5 GPa.

Above 11.9 GPa, three new diffraction peaks marked by arrows in Figure 4 have emerged, indicating a change in the crystal structure. The new peaks at 10.7°, 11.4°, and 13.5° can be indexed to an orthorhombic anti-cotunnite (Pnma) structure with a = 5.8282(20) Å, b = 4.6313(12) Å, and c = 6.6059(23) Å. The strong diffraction peaks at 7.5°, 8.7°, and 12.3° can still be assigned to the cubic anti-fluorite structure (Fm-3m), indicating that the orthorhombic anti-cotunnite (Pnma) structure co-exists with the cubic anti-fluorite structure (Fm-3m) at this pressure. The amount of the cubic structure decreased with increasing pressure and eventually vanished at 16.6 GPa. Concomitantly, the diffraction peaks around 10.7°, 11.4°, and 13.5°, corresponding to orthorhombic anti-cotunnite (Pnma) structure, increased gradually and became dominant. Therefore, the diffraction results show unambiguously a structural phase transition of Al-doped Mg₂Si had occurred around 11.9 GPa and was completed at 16.6 GPa. This structural transformation is accompanied by a large volume reduction of almost 23%. The experimental equation of state (volume vs. pressure) shown in Figure 5 indicates that the anti-cotunnite phase is more compressible than the cubic structure.

In the previous high energy dispersive X-ray diffraction study of pure Mg₂Si using silicone oil as the pressure medium, the same Fm-3m to Pnma transition was observed at 7.5 GPa where the volume collapsed from the cubic structure of 56.3 ų/f.u to Pnma of 49.4 ų/f.u, a reduction of 12.3%.¹³ The transition in Al-doped Mg₂Si was observed at a higher pressure of 10 GPa, and the volume reduced by 18% from the cubic phase of 55 ų/f.u to Pnma 45 ų/f.u. Therefore, the volume changes are comparable.

The behavior of pressure-induced structural phase transition for Al-doped Mg₂Si is different from pristine Mg₂Si which shows no structural transition up to 14.7 GPa. The phase transformation is related to the Al dopant in the crystal structure. A larger atomic size of Al compared to Mg expanded the cubic crystal lattice at low pressure, resulting in a smaller pressure coefficient (vide supra). We speculate this mismatch in the atomic size helps to promote the structural transformation at high pressure.

The measured reflectivities from ambient to 14 GPa are shown in Figure 6. Even at ambient pressure, the IR reflectivity shows a Drude-like behavior at a low frequency implying a metallic-like behaviour. In Mg₂Si, the valence bands are completely filled, the electrons provided by the Al dopants must occupy the conduction band. By definition, the partial occupation of the conduction band is a metal. A practical definition for a metal is that the electrical conductivity should decrease with temperature. Previous experiment¹⁰ shows that the electrical conductivity of Al-doped Mg₂Si indeed decreases with temperature, an indication of a metallic-like behaviour. We recognize that doped Mg₂Si are often referred as a semiconductor. However, we believe it is just a matter of semantic. This point is highlighted from a comparison of the reflectivity of pure and Al-doped Mg₂Si at zero pressure (Figure 7). In comparison to the flat and featureless reflectivity, typical of a semiconductor of pure Mg₂Si, the extrapolated reflectivity at zero frequency of the doped sample is almost 0.4. On closer examination (inset of Fig. 6), it is observed that the reflectivity rose gradually from ambient pressure to about 10.5 GPa. From 8.5 to 10.5 GPa, there is a noticeable jump in the reflectivity from 0.32 to 0.58. Beyond this pressure, the reflectivities increase rapidly and reach 0.75 at 600 cm⁻¹ at 14.1 GPa. This is to be compared with reflectivity close to unity at zero frequency for a good metal, such as copper or aluminum. Qualitatively, the observed trend in the reflectivity parallels that of the bulk measurements reported previously.¹⁰ It was reported that the electrical resistivity decreases (conductivity increases) almost by one order of magnitude from 0 to 1 GPa but became more gradual from 1 to 8 GPa. However, the rapid drop (rise) in the electrical resistivity (conductivity) at low pressure reported earlier by quasi-4-probe method¹⁰ was not so obvious in the infrared reflectivity measurements.

The frequency dependent conductivity (optical conductivity) can be obtained by performing a K−K analysis of the reflectivity data using the RefFIT code.²² The procedure is as follows: the optical conductivity obtained from a variational K-K transformation is fitted to a DL model and the dc conductivity is estimated by extrapolation to zero frequency. A typical result shows in Figure 8, illustrating the quality of the fitting procedure. In the Figure, the original and the fitted infrared reflectivity spectra at 10.5 GPa are compared. The dc conductivities are obtained with this procedure (Figure 9), where an almost linear dependence with pressure. The dc conductivity is 80 S cm⁻¹ at ambient pressure and reaches 300 S cm⁻¹ at 14.1 GPa, a fourfold increase. It is apparent that there are two “plateau” regions in the dc conductivity at ca. 6 and 10 GPa. However, due to the simplicity of the Drude-Lorentz model and the limited low frequency range accessible by IR radiation, there is not enough firm data to make a definitive statement. Nevertheless, the results indicate that the dc conductivity of Al-doped Mg₂Si can be improved significantly by increasing pressure.

In the free electron model, the electron scattering relaxation time (τ) is related to be the electrical conductivity. This parameter can be extracted from the fitting the reflectivity data to the Drude-Lorentz model.³³ The relaxation times obtained at different pressures are summarized in Table I. The derived relaxation times of ca. 10⁻¹⁴s is consistent with other doped semiconductors.

To understand the mechanism for the pressure enhancement of the thermoelectric power factor, theoretical density functional calculations were performed at several pressures using a Mg₆₃Si₃₂Al₁ supercell model (vide supra). No GW corrections were needed since the model system is already metallic-like. The aim of the calculations was to investigate the total and projected DOS and how they affect the thermopower with pressure. The results of the calculations are shown in Figure 10.

At zero pressure, Al-doped Mg₂Si already has a metallic-like behaviour. The Al impurity produced a distinct narrow band with very high DOS located between the valence and conduction band of the Mg₂Si host. The sharp feature is due to localized interactions between the Al dopant with Mg and Si electronic states of the host.

From 0.1 to 3.3 GPa, a localized energy band was predicted to situate between the original gap of pristine Mg₂Si. As the pressure was increased, this electronic band broadened and became more “free-electron” like. This trend explains the observed increase in metal-like behaviour, as well as the higher electrical conductivity and infrared reflectivities. It is known that the thermoelectric power factor is dependent on both the density of states and the derivative at the Fermi energy.^33,34 A significant increase in the thermoelectric power factor is usually caused by the existence of a sharp localized DOS at the Fermi level.^35,36 The calculate DOS at the Fermi level N(E_f) was found to decrease from 19 electronic states/eV/spin at 0.1 GPa to 9 electronic states/eV/spin at 10.3 GPa. In comparison, the slope of the density of states (dN(E)/dE)|E_f increased from 561 states/eV² at zero pressure to a maximum value of 604 states/eV² at 1.9 GPa and then decreased rapidly to 104 states/eV² at 10.3 GPa (Figure 11 and Table II). On theoretical ground, it is expected the effect of N(E_f) and (dN(E)/dE)|E_f will result in an initial increase in the thermopower to 1.9 GPa then followed by a rapid drop. The predicted trend is in qualitative agreement with the measured thermopower, which has a maximum at 2.3 GPa.¹⁰ 

Although the trend of increasing electrical conductivity with pressure is the same as obtained from IR reflectivities and four-probe conductivity measurements,¹⁰ the comparison of the absolute magnitude is less satisfactory. One contributing factor may be the infrared beam that only surveyed a very small region (20 × 20 μm²) and penetrated only a few microns into the sample surface. This process is different from the quasi-four-probe conductivity method, which is a bulk sensitive technique. At the sample surface, the atom density is less than the bulk, and the chemical bonding in the surface is also stronger.^37,38 Therefore, there are fewer free electrons near the sample surface, thus reducing the electrical conductivity. Although plausible, this effect cannot satisfactory explain the discrepancy observed here. Since the dc conductivity was obtained from the extrapolation of the frequency dependent conductivity to zero frequency, it is not certain if the omission of reflectivity at very low energy (i.e., <200 cm⁻¹) may have an effect. From past experience, we expect the dc conductivity derived from an IR measurement should agree within an order of the magnitude of the value obtained from the bulk technique.^39,40 We found no systematic error in the experiment, nor in the treatment of the data. In a previous study, we have compared the dc conductivity derived from IR reflectivities to bulk measurements on doped Mg₂Si and the agreements were favorable.³⁹ We suspect the most likely source of the disagreement may be related to the differences in the concentration of the dopant on the surface. The Al-doped Mg₂Si used in this study was synthesized by plasma spark sintering method. With this technique, this is difficult to control the precise stoichiometry and the homogeneity of the doped samples. As mentioned above, compared to the pure crystal, the cubic lattice constant of doped Mg₂Si is expanded by the inclusion of the Al dopants. The unit cell parameter for the sample used in this study is 6.2878(9) Å, which is noticeably shorter than the reported lattice constant of 6.396(1) Å on a previous sample. A larger unit cell suggests the concentration of Al in the sample used in the earlier investigate is probably higher.

Since Al-doped Mg₂Si is n-doped with the Al atoms providing electrons into the conduction band, a higher Al content will increase the carrier concentration and enhance the electrical conductivity. It is noteworthy that from the diffraction patterns, unlike in the previous study, the Al-doped Mg₂Si sample used in this study is free of MgO and other impurities. Another possible source of the discrepancy may be due to non-uniform distribution of Al in the sample.

In a study of Sb and Bi doped-Mg₂Si, it was found by high resolution transmission microscopy (TEM) that due to the limited solubility excess Sb and Bi atoms are present in the grain boundaries that may enhance the conductivity of the bulk sample.³⁹ In comparison, IR measurements only examine a very small spot of the sample so this may produce different results. A careful characterization of both samples is critical to resolve the discrepancy. For this purpose, we examined the chemical compositions of the Al-doped Mg₂Si sample using scanning electron microscopy (SEM). The chemical compositions of several randomly chosen spots on the surface of a compressed sample were analyzed (Figure 12). The results of the analysis are summarized in Table III, showing that the doping is highly non-uniform. The concentrations of the doped Al can vary between a minimum of 0.27% at site #4 to a maximum of 1.42% at site #6. The large inhomogeneity in the dopant concentrations will certainly affect the local electronic. Since infrared reflectivity only probes a small spot, we believe that this is the main reason for the discrepancy between the electrical conductivity determined from infrared reflectivities and the bulk measurements.

The structural transformation and electrical conductivity of a nominally 1 at. % Al-doped Mg₂Si sample synthesized from spark plasma sintering have been investigated by angle dispersive synchrotron radiation X-ray diffraction and infrared reflectivity up to 16.6 GPa at room temperature. Contrary to two earlier reports, no structural transformation was observed in pure Mg₂Si up to 15 GPa when helium was used as the quasi-hydrostatic pressure transmission medium. The electronic band structures of pure Mg₂Si were calculated at selected pressures with density functional theory including the correction for electron correlation effect with the GW approximation. It is found that the band gap of Mg₂Si does not close at 11 GPa. The theoretical result is consistent with electrical resistivity measurements, which show that Mg₂Si remains an insulator at least up to 22 GPa. Both studies contradict the reported structural phase transition to metallic anti-cotunnite and Ni₂In phases 7 and 11 GPa, respectively. However, in Al-doped Mg₂Si, a structural phase transition from the cubic anti-fluorite to the anti-cotunnite structure was found to occur around 11.9 GPa. Infrared reflectivity show the Al-doped Mg₂Si already has a metallic-like behaviour under ambient conditions.

The dc conductivities at high pressure were calculated from the analysis of the infrared reflectivity spectra employing the Drude-Lorentz model. In agreement with bulk four-probe measurements, the electrical conductivity was found to increase with pressure as the sample became more metallic-like. However, the values of the dc conductivity derived from IR reflectivities are consistently lower. We attribute this difference to the difference in the stoichiometry of the sample used in the experiment and non-uniform doping. Theoretical density functional calculations reveal the presence of a mid-gap localized electronic band below 3.3 GPa. The sharp mid-gap DOS is the result of hybridization between the electron orbitals of the host elements with the dopant. As the pressure is increased further, the localized band broadened and the profile became more free-electron like. The derivative of the electron density of states N(E) at the Fermi energy (E_f) is found to maximize at 1.9 GPa. Thus, the theory predicted a maximum thermoelectric power factor, which is in agreement with the experimental observation at 2–3 GPa.

The present study provides new results and insight on the high pressure structures and transport properties of pure and Al-doped Mg₂Si. The diffraction experiments found no phase transition at 6–7 GPa, suggested by the Raman study.¹⁰ However, transformation to an orthorhombic anti-cotunnite (Pnma) structure is confirmed at 11 GPa. The information obtained here may help to further enhance the performance of Mg₂Si-based thermoelectric materials.

Ambient pressure synchrotron X-ray diffraction experiments were performed at the CMCF beamline, Canadian Light Source, which was made possible by support from NSERC, NRC, CIHR, and the University of Saskatchewan. High pressure synchrotron X-ray diffraction experiments were performed at sector 20 at the Advanced Photon Source, supported by the U.S. Department of Energy—Basic Energy Sciences, the Canadian Light Source and its funding partners, the University of Washington, and the Advanced Photon Source. Use of the Advanced Photon Source, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science by Argonne National Laboratory, was supported by the U.S. DOE under Contract No. DE-AC02-06CH11357. The use of U2A beamline was supported by COMPRES under NSF Cooperative Agreement EAR 11-57758 and CDAC (DE-FC03 03N00144). The National Synchrotron Light Source, Brookhaven National Laboratory, was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC02-98CH10886. The electron microprobe analysis was supported by the Microscopy Lab, Department of Geological Sciences, University of Saskatchewan. J.Z. and J.S.T. thank AUTO21 for a Research Grant and to T. Bonli for the SEM measurements and J. Smith of HPCAT, Advanced Photon Source, for assistance with the high pressure diffraction experiments. We thank S. Tkachev for the help in using the gas-loading system, which is supported by GSECARS and COMPRES. APS is a user facility operated for the DOE Office of Science by ANL under Contract No. DE-AC02-06CH11357.