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Crystal Structure, Stability, and Physical Properties of Metastable Electron-Poor Narrow-Gap AlGe Semiconductor Romain Viennois,*,† Roseline Esmilaire,†,‡ Loïc Perrière,§ Abel Haidoux,† Eric Alleno,§ and Mickael Beaudhuin*,† †

Institut Charles Gerhardt Montpellier, UMR 5253, CNRS-UM-ENSCM, Université de Montpellier, cc 1504, Place Eugéne Bataillon, F-34095 Montpellier Cedex 5, France ‡ Institut Européen des Membranes, UMR5635 Université Montpellier, CNRS, ENSCM, Montpellier, France § Université Paris Est, Institut de Chimie et des Matériaux Paris-Est, UMR 7182 CNRS−UPEC, 2-8 rue H. Dunant, 94320 Thiais, France S Supporting Information *

ABSTRACT: We report for the first time the full crystal structure, the electronic structure, the lattice dynamics, and the elastic constants of metastable monoclinic AlGe. In addition to ultrarapid cooling techniques such as melt spinning, we show the possibility of obtaining monoclinic AlGe by waterquenching in a quartz tube. Monoclinic AlGe and rhombohedral Al6Ge5 are competing phases with similar stability since they both begin to decompose above 230 °C. The crystal structure and electronic bonding of monoclinic AlGe are similar to those of ZnSb and comply with its 3.5 valence electrons per atom: besides classical two electron−two center Al−Ge and Ge−Ge covalent bonds, Al2Ge2 parallelogram rings are formed by uncommon multicenter bonds. Monoclinic AlGe could be used in various applications since it is found theoretically to be an electron-poor semiconductor with a narrow indirect energy bandgap of about 0.5 eV. The lattice dynamics calculations show the presence of low energy optical phonons, which should lead to a low thermal conductivity.

1. INTRODUCTION For a long time, the search for new binary metastable materials with new structure and properties has been an active research field. It strongly grew during the 1960s and the 1970s with the development of new synthesis techniques (i.e., ultrarapid cooling, mechanical-alloying, plasma spray coating, and so on), which have opened the route to new metastable materials with new applications.1−3 Al−Ge is an eutectic metal− semiconductor binary system under thermodynamic equilibrium conditions,4 standing among the most explored systems due to its similarity with the Al−Si system and to the technological interest of aluminum-based alloys. In addition, the existence of several metastable phases in crystalline and amorphous forms is of interest not only from a fundamental point of view4−33 but also for several fields of application. For example, Al−Ge binary system compounds have been considered as low temperature lead free eutectic soldering/ brazing alloys for replacing Au or Au−Si solders in microelectronic devices,22,34 as bonding in electromechanical applications,35,36 as solar absorbers,37 or for their superconducting properties.29 The semiconducting nature of some metastable Al−Ge compounds makes them good candidates for energy applications.23,32 Nowadays, the existence of four © 2017 American Chemical Society

metastable Al−Ge phases is well established following Koester’s and Kaufmann’s pioneer works combining electron diffraction and high resolution X-ray diffraction experiments.6,7,11,12,15 The difficulty to find the detailed crystal structure and the right composition was related to the multiphase nature of the samples. Generally two main phases are obtained by the ultrafast cooling technique: one rhombohedral Al6Ge5 phase (R) (isostructural with the ideal form of β-Zn4Sb3 without defects, i.e., Zn6Sb5), which crystallizes in the R3c̅ space group, and one monoclinic AlGe phase (M) crystallizing in the P21/c space group.6,7,11−13,15,21 However, the crystal structure of these two phases still requires investigation in more detail, and there are still some controversies concerning their exact composition.6,7,11,12,21 In a recent study, we have achieved the structural determination of the R phase confirming its close parentage with Zn6Sb5.23 The M phase crystal structure still needs to be fully solved. Rarely, a third hexagonal phase (H) crystallizing in the P6/mmm space group was found in bulk samples with a poorly established composition, but a Ge concentration smaller than in the R phase.6,11,15 In recrystalReceived: May 23, 2017 Published: September 11, 2017 11591

DOI: 10.1021/acs.inorgchem.7b01318 Inorg. Chem. 2017, 56, 11591−11602

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Inorganic Chemistry lized amorphous films, an additional orthorhombic AlGe phase (O) appears with space group Pbca,7,11,15,17 which is the same as in ZnSb40 and with a relatively broad homogeneity range. In order to obtain the above cited metastable phases, Kaufman and co-workers11,12,15 have suggested that undercooling should be increased in the following sequence: M, R, H, and O. It also seems that the higher the required undercooling, the lower the stability of the phase is.11,12,15 At the highest undercooling and for cooling rates larger than 109 K/s, the least stable amorphous phases are obtained.24,28 There have been other new phases, both with tetragonal symmetry, recently reported in thin films, but still not confirmed by other groups until now: the “τ phase”, very rich in aluminum (Al0.9Ge0.1),18 and another phase with the same structure as β-Sn with a Ge content falling between 40% and 68%.33 When using other outof-equilibrium synthesis methods such as mechanical alloying23−26 or spray techniques,27 the only metastable-formed phase is the R phase. The electronic and vibrational properties of all these metastable Al−Ge binary phases are poorly known, whereas the search for new semiconducting materials based on nontoxic materials is of primary interest for several applications in electronic and energy domains. If we have a look at the crystal structure of Al6Ge5, we can see that it has the same rhombohedral structure as Zn6Sb5, which is the ideal form of the thermoelectric material Zn4Sb3 (best thermoelectric material in the 400−600 K temperature range).21,23,32,38−43 Several works indicated that Al6Ge5 has a semiconducting nature, which makes it of great interest for thermoelectric applications.23,32,41,42 Unexpectedly, Ge-rich metastable phases in the Al−Ge system were reported to be metallic.29,30 As discussed above, although the crystal symmetry of AlGe is known, the exact crystal structure and the properties of monoclinic AlGe are still unknown.6,7,11,12,15,21 Thanks to modern analysis and calculation techniques now available, it is possible to fully investigate the monoclinic AlGe phase. The goals of the present article are therefore to show a simple new synthesis method to obtain the metastable monoclinic AlGe phase, to complete its crystal structure determination, to examine its stability, and to study its electronic, elastic, and lattice dynamics properties in order to estimate its potential for applications.

thermal treatment to minimize the heat losses while the tube falls during the water-quenching step. We have used quartz tubes of about 1 mm thickness and 3 mm inner diameter in order to optimize the cooling rate during the water-quenching step. The following thermal treatment was used: the mixture of aluminum and germanium was heated at 950 °C for 4 h; the melt was naturally cooled in the furnace down to a temperature 100 °C above the temperature of the liquidus for a given Al:Ge ratio4 (which means 520 °C for 70:30 Al:Ge ratio); the melt is maintained at this temperature during 10 min before quenching. We have found that this last step was crucial for obtaining the metastable monoclinic AlGe phase. 2.2. Sample Characterization. The sample phase fractions and crystal structures were characterized by classical powder X-ray diffraction (XRD) with an Xpert X-ray Diffractometer and using Cu Kα1 (1.54060 Å) and Cu Kα2 (1.54443 Å) radiation. Full structure determination was performed by Rietveld refinement using the Fullprof software.44 The microstructure, chemical homogeneity, and composition of the samples were checked using an energy dispersive X-ray (EDX) analysis system (Hitachi S4800) mounted on a Hitachi S2600N scanning electron microscope (SEM). Stability of the samples was determined by the differential thermal analysis (DTA) technique with a SETARAM LABSYS apparatus under a flowing argon (5.2N) atmosphere (about 1 L/h) in an open alumina crucible with a heating rate of 10 K/min. The resulting powder was subsequently analyzed by XRD. Micro-Raman spectroscopy experiments were performed by using two different spectrometers: for determining the full Raman spectra including low wavenumber Raman modes, we used a Horiba/ Jobin-Yvon T64000 spectrometer in triple-monochromator configuration and 514.5 nm wavelength laser with a power of about 1 mW on the sample; for the high resolution mapping of the eutectic zone in the water-quenched sample, we used a Horiba/Jobin-Yvon LabRam Aramis spectrometer equipped with 633 nm wavelength He−Ne laser with a power of about 0.7 mW on the sample. With such power levels, the samples were not heated. 2.3. Computation Details. First-principles calculations were carried out in the frame of the density functional theory (DFT), principally with the ABINIT package,45 by means of norm-conserving Troullier−Martins pseudopotentials46 within the local density approximation (LDA) of the exchange-correlation functional parametrized by Perdew and Wang.47 In the case of the structure and atomic relaxations of the monoclinic AlGe compound, we used an energy cutoff of 69 hartree and a 12 × 12 × 12 k-point mesh grid within a Monkhorst−Pack scheme.48 The structure relaxation and atomic relaxation were performed until the maximum residual forces on each atom were less than 5 × 10−6 Ha/bohr. Relaxation calculations of the AlGe compound with the parent Pbca orthorhombic structure of ZnSb were also performed under the same conditions for comparison. The vibrational and dielectric properties were calculated in the case of a fully relaxed cell for monoclinic AlGe. Density functional perturbation theory (DFPT) was used in its variational approach in order to calculate the dynamical matrix, elastic constants, the dielectric constant and Born charges.49 The phonon dispersion curves were calculated using a 2 × 2 × 2 qpoint mesh grid. For the electronic structure calculations of both AlGe structures, we have used the tetrahedron method and a finer 20 × 20 × 20 k-point mesh grid. Note that, in all the calculations, the monoclinic axis was taken as the y-axis. In order to better estimate the energy bandgap of monoclinic AlGe, calculations with the modified Becke− Johnson (mBJ) meta-GGA exchange-correlation functional as implemented by Tran and Blaha were also carried out. The mBJ functional was shown to satisfactorily determine the energy bandgap of semiconductors at a computational cost lower than the hybrid functionals or the GW method.50 This calculation was performed using the all-electron code Elk implemented with a full linear augmented plane wave (FLAPW) basis,51 using a small Fermi−Dirac smearing of 1 mRy and a fine 20 × 20 × 20 k-point mesh grid. We used the structure previously relaxed by the LDA calculations. Prior to the meta-GGA calculation, the electronic structure was calculated with LDA using the Elk code and found in excellent agreement with the LDA calculations using the ABINIT code.

2. EXPERIMENTAL DETAILS 2.1. Sample Preparations. Two synthesis methods have been explored. In both cases, high purity Al pieces (99.9%) from Alfa Aesar and very high purity Ge pieces (99.999%, 3−9 mm) from SigmaAldrich were used. In the first case, we have followed the classical method for producing metastable phases in the Al−Ge binary system, i.e., ultrarapid cooling synthesis. For this purpose, we have used the chill block melt-spinning technique developed “in house” at the ICMPE in Thiais. The wheel, made of Co−Cu−Be alloys, has a diameter of 20 cm, and its velocity was fixed to 30 m/s. The ejection pressure of the Ar gas was 150 mbar, and the diameter of the nozzle was 1 mm. We have used a variation of this technique known as drop melting. In a first step, a mixture with the composition of 55% of aluminum and 45% of germanium was homogeneously prealloyed in an induction furnace. Then, this prealloy was melted and quenched within the meltspinning system. The second synthesis path derives from our previous work23 where mechanical alloying was shown to be inefficient for producing the monoclinic AlGe phase. In the present paper, we thus describe a new way to produce this phase by water-quenching in a quartz tube. The crucial point is to optimize both the geometry of the tube and the 11592


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Figure 1. XRD patterns for the samples A and B obtained by melt-spinning (a) and water-quenching from the melt (b).

3. RESULTS AND DISCUSSION 3.1. Synthesis and Microstructure. 3.1.1. Melt-Spun Samples. Two kinds of samples were obtained by melt spinning: • A: thin ribbons, about 40−60 μm thick with few of them being up to 120 μm thick, were obtained by quenching in the stationary regime of the wheel. • B: thick ribbons, about 200−300 μm thick, were obtained by slow quenching in transient regimes of the wheel (beginning or end of the quenching). The powder diffraction patterns of both samples are shown in Figure 1a. Both rhombohedral Al6Ge5 (R phase) and monoclinic AlGe (M phase) are present in the sample A, with additional residual elementary Ge alloyed α-Al and Al alloyed β-Ge phases. Our results are in line with previous results obtained with a similar technique.10−12,22,32 One should note that the Bragg peaks of the phase denoted Al3Ge2 in the powder patterns by Kumagai et al.32 correspond to those of the M phase. In sample B, the M phase and α- and β-phases are the majority phases accompanied by small amounts of the R phase. These results are consistent with the literature, which indicates that lower cooling rate and lower undercooling favors the M phase.12,32 From Rietveld refinement (see Figure 2), we were able to determine for the first time the atomic positions in the M phase (see Tables 1 and 2). The lattice parameters and monoclinic angle are found in good agreement with the prior experimental results reported in the literature6,11 (for more details about the structure, see the Supporting Information). We also report the microstructures of the various samples obtained by melt-spinning in Figure 3 (see the Supporting Information for more details). In Figure 3a, one can observe three different types of morphologies corresponding to different phases: • The dendritic-like structure is Ge-rich and corresponds to the β-phase growing on the primarily crystallized αphase, as already described in the literature.6,7,12 • The well-crystallized faceted crystals correspond to the M phase as shown by the Al:Ge ratio of 50.55:49.45 found by EDX spectroscopy. The difference with respect to a 50:50 ratio is within the experimental uncertainty, and our results agree well with the most recent works of Laoui and Kaufmann, who also found that the M phase is growing as faceted crystals with similar composition.12 • The mushy structure corresponds to the R phase with an Al:Ge ratio of 54.7:45.3, very close to 6:5.

Figure 2. Rietveld refinement of the XRD pattern of the sample B obtained by melt-spinning. Red hollow circles are the observed pattern, the solid black line is the calculated pattern, small bars correspond to the Bragg peak positions of the various phases, and blue solid lines correspond to the difference between the calculated and observed patterns.

In Figure 3b, we report our results for sample B where one can see similar faceted crystals corresponding to the M phase, with an average Al:Ge ratio of about 51:49. The white zone still contains faceted crystals of the β-phase as in the sample A, whereas the intermediate darker zone has eutectic-like appearance. This is confirmed by chemical analysis as we found an Al:Ge ratio of about 69.5:30.5, which is very close to the ratio expected for the metastable eutectic between the α phase and the metastable M phase. A similar microstructure was found by Laoui and Kaufmann for this metastable eutectic mixture.12 In the past, there were many disagreements concerning the exact compositions of the various phases, especially in the case of the R phase. In the present work, our results confirm the AlGe and Al6Ge5 stoichiometries for respectively the M and R phases as found by Laoui and Kaufman in 199112 and by Koester in 1972.6,7 Their results were obtained by accurate chemical analysis using wavelength dispersive spectroscopy (WDS) microprobe and disagree with other works using EDXS.11,15,21 To summarize, we were able to completely determine the crystal structure of the M phase and to confirm the stoichiometry of both the M and the R phases, closing the controversies about their stoichiometry and crystal structure. 11593


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Table 1. Lattice Parameters of the Monoclinic AlGe Phase Obtained from Rietveld Refinement of the XRD Pattern of the MeltSpinning Sample with a Lower Cooling Rate (Sample B) and Compared to Our DFT Results and Prior Experimental Data in the Literature sample B expt6,11 DFT

a (Å)

b (Å)

c (Å)

β (deg)

V (Å3)

density (g/cm3)

6.7305(3) 6.734 6.63228

5.8173(2) 5.818 5.67213

8.0427(4) 8.045 7.93178

147.853(2) 147.85 147.831

167.559 167.798 158.87

3.947 3.941 4.163

Table 2. Atomic Positions of the Monoclinic AlGe Phase Obtained from Rietveld Refinement of the XRD Pattern of the MeltSpinning Sample with a Lower Cooling Rate (Sample B) and Compared to Our DFT Resultsa sample B DFT a

xAl

yAl

zAl

xGe

yGe

zGe

0.1166(17) 0.10883

0.5962(20) 0.59825

0.9358(12) 0.92759

0.2005(7) 0.20176

0.1448(7) 0.14698

0.0640(6) 0.06856

Both the Al and Ge atoms occupy a 4e general position in P21/c.

of the metastable eutectic between α-phase and M phase as observed previously in the melt-spun sample B and by Laoui and Kaufmann.12 This is confirmed by the chemical analysis indicating that the Al:Ge ratio is about 0.7:0.3, in agreement with the starting composition. To our knowledge, this is the first time that the quenching of Al−Ge alloys in a quartz tube is reported to successfully work for producing a significant amount of the M phase. Previous water-quenching synthesis of the M phase was carried out either in Pyrex tubes with small yield9,10 or by direct quenching of melted alloys dropped in water.6 3.2. Stability from DTA Experiments. We have studied the stability of the melt-spun samples A and B with DTA experiments in order to investigate the origin of the thermal signals. There are many contradictions in the literature,5,8,22,24−27,34,52 mainly between early works where knowledge of these metastable phases was poor5,8 and more recent works.22,34 Note that the different results found in the literature can be related to the different heating rates used, which range from 5 K/min34 to 20 K/min,5,8,22,26 and/or the different types of sample holders used (in the older works, Al sample holders were used) and/or the different synthesis techniques used. In Figure 5, we report temperature scans for the range room temperature to 350 °C in samples A and B with 10 K/min as a heating rate. For both samples, two irreversible features can be seen: a small bump at low T (150−200 °C) and a peak at about

Figure 3. SEM images obtained with backscattered electrons of one region of sample A obtained by melt-spinning (left) and one region of sample B obtained by melt-spinning (right).

3.1.2. Fast Water-Quenching Samples. In the case of the fast water-quenching synthesis technique, we could not observe the metastable phases for the compositions ranging between Al0.6Ge0.4 and Al0.5Ge0.5. Only a mixture of Al and Ge as well as Si1−xGex and Al2O3 arising from a partial reaction of respectively Ge and Al with the quartz tubes was obtained. Monoclinic AlGe could only be synthesized for the starting composition Al0.7Ge0.3, as shown by the XRD pattern (Figure 1b). Similarly to the other starting compositions, it was accompanied by Si1−xGex and Al2O3 phases despite the carbon coating of the quartz tube. The attempts to shorten the duration of the high temperature dwell did not lead to smaller secondary phase fractions. There were also additional lines arising from an unknown phase, preventing an accurate determination of the amount of the M phase in this sample. The SEM images displayed in Figure 4 confirm the XRD phase identification. The microstructure entirely corresponds to that

Figure 4. SEM images of the water quenched sample. Image obtained with backscattered electrons of the whole sample (left); high resolution image obtained with backscattered electrons (right).

Figure 5. DTA signal vs temperature for the two samples A and B obtained by melt-spinning. 11594


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maximum at about 260−270 °C. Additional work will be required to understand the high temperature part of the Al−Ge metastable phase diagrams. 3.3. Stability from DFT Calculations. DFT calculations on monoclinic and orthorhombic AlGe have been performed at 0 K. The energies of the reference elements Al and Ge have been calculated as in our previous paper.23 This allows us to find that the formation energy of the monoclinic AlGe phase (0.0409 eV/atom) is comparable to that of rhombohedral Al6Ge5 phase (0.0391 eV/atom)23 (When calculating the formation energy of the metastable phases, we found that there was a mistake for the calculated formation energy of rhombohedral Al6Ge5 reported in ref 23. Instead of 0.051 eV/at., the correct value is 0.0391 eV/at. This does not change the conclusion drawn in ref 23.) and slightly lower than that of the orthorhombic AlGe (0.047 eV/atom). In all three cases, the formation energy is positive compared to that of parent elements Al and Ge, in agreement with the metastable character of the three M, R, and O phases. Our observation of similar decomposition temperatures for both M and R phases is also an indication of similar stability for both metastable phases. Our calculations show that the O phase is significantly less stable than the M and R phases, which is in agreement with the conclusion drawn from experimental observations by Laoui and Kaufmann.12 However, they slightly differ from the observations of these last authors, who found that the M phase is more stable than the R phase.12 In our calculations, the difference of stability between the M and R phases is less than 2 meV, i.e., close to the calculation uncertainty. Moreover, our calculations were performed at 0 K and do not take into account either the vibrational contribution at zero point or the temperature effect. In addition, we must note that our experimental observation of larger amounts of the M phase compared to the R phase when the cooling rate is smaller agrees with Laoui’s results.12 Interestingly, very recently Amsler et al. have predicted that a fictitious ZnSb phase with a monoclinic P21/c crystal structure (but with a much smaller monoclinic angle β) would have a similar stability as the experimental orthorhombic structure observed experimentally and another compound with orthorhombic structure that they were predicting.53 3.4. Crystal Structure. The results of the structure relaxation calculations are reported in Tables 1 and 2 for comparison with the experimental results. The lattice parameters found by DFT calculations are smaller than the experimental ones as usual with the LDA exchange-correlation functional, but the monoclinic angle value agrees quite well with the experiments. The agreement between the atom coordinates found in the calculations with those found in the experiments is quite satisfactory, although not perfect. Indeed, the agreement for the coordinates of Ge is fine, but for the Al positions, the difference is rather large for the x and z coordinates. We have found rather large isotropic atomic displacement parameters (ADP) Biso for Al (1.24 ± 0.25 Å2) and Ge (0.98 ± 0.14 Å2), which could arise from rather significant static disorder. In order to get more accurate values of ADPs and distinguish both static and dynamic contributions, powder neutron diffraction experiments at low temperatures could be useful. Monoclinic AlGe can be described as composed of planar parallelogram Al2Ge2 rings bonded to each other as in the case of orthorhombic ZnSb and CdSb,40−42,54 but with a different arrangement.

230−300 °C. Both samples were analyzed by XRD after the DTA experiments, and only Bragg peaks of the two stable phases at thermodynamic equilibrium (α- and β-phases) were observed. Additional XRD experiments on sample A heated up to 200 °C showed that the two metastable R and M phases are stable at least up to this temperature. This means that the features observed in the DTA experiments above 200 °C correspond to the decomposition of the metastable phases. From a comparison with prior results on the R phase obtained by mechanical alloying,24−27,52 the signal corresponding to its decomposition has a maximum at about 250−270 °C. In sample B, we have observed an unexpected two-step signal with maxima at about 256 and 270 °C. Other DTA experiments (not shown) on the water-quenched samples containing the M phase exhibit a small, broad signal with maximum at 266 °C,52 confirming that the M phase is decomposing in the same temperature range as the R phase. To determine the onset of the decomposition process, we followed the work of Kato et al.27 and found in reasonable agreement Tonset = 230−240 °C for both samples. The small differences between our measurement and the work of Kato, who found Tonset = 226 °C for the R phase, can arise from the lower heating rate (5 K/min) and/ or the difference in the samples due to the different synthesis technique used. Our results are further confirmed by the in situ high temperature XRD study of Schubert et al., who found that both metastable phases begin to decompose at the same temperature of about 225−250 °C and are fully decomposed at about 275 °C.22 From their in situ XRD experiments, one can also understand the origin of the broad bump at about 150− 200 °C in our DTA experiments. Indeed, they found an anomalous temperature dependence of the lattice parameter of the α-phase, which corresponds to the Al phase oversaturated with Ge. They explain the plateau at about 150−200 °C as due to Ge precipitation from the metastable α-phase. This is expected to give a signal in the DTA experiments. In our samples A and B, one finds an unexpected larger lattice parameter for the α-phase compared to pure Al and for the βphase compared to pure Ge (see the Supporting Information for details). Therefore, the α-phase is aluminum oversaturated with Ge and the β-phase is germanium oversaturated with Al. After the thermal treatment of the DTA experiment up to 350 °C, we observed a significant variation of the lattice parameters for both the α- and β-phases (see the Supporting Information for details). In an additional XRD experiment on sample A heated up to 200 °C, one finds similar significant change of the lattice parameters for both phases (see the Supporting Information for details). Thus, we interpret the bump in our DTA signal below 200 °C as due to the rejection of Ge from the α-phase and of Al from the β-phase. Interestingly, a thermal signal was already observed at about 180 °C in the first thermal experiments made on these metastable alloys,5,8 and we assume that it can be interpreted in a similar way. In agreement with previous other works,24−27,34,52 we did not observe a thermal signal at about 300 °C in any of our experiments. This is in contradiction with the work of Schubert et al. and previously cited works5,8,22 in which a larger heating rate (20 K/min) was used. We nonetheless note that Illgen et al. (with 5 K heating rate) found that the thermal signal of decomposition shifts from 255 °C for 30% Ge to 340 °C for hypoeutectic compositions (down to 21% Ge).34 This could explain some of the prior inconsistencies in the literature. To summarize this part, we have clearly established that the two metastable phases begin to decompose at about 230 °C and that this thermal signal has a 11595


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Figure 6. Crystal structure of monoclinic AlGe (a) and orthorhombic AlGe (b) obtained from relaxation calculations with DFT. Local coordination around the Al atoms in monoclinic AlGe (c) and orthorhombic AlGe (e). Local coordination around the Al atoms in monoclinic AlGe (d) and orthorhombic AlGe (f).

In order to understand the similarities and differences between the monoclinic AlGe and these two compounds, we have also performed relaxation calculations on the orthorhombic AlGe structure with the same structure as ZnSb and CdSb. As for the monoclinic AlGe phase, the lattice parameters of the orthorhombic AlGe phase calculated with LDA (a = 5.59254 Å, b = 7.21733 Å, and c = 7.56573 Å) are slightly smaller than the experimental lattice parameters11 (see the Supporting Information for details). For a better comparison of the two AlGe polymorphs, we discuss the crystal structures of both phases (Figure 6) as obtained by the DFT calculations. In both AlGe structures, the interatomic distances are very similar and each Al2Ge2 motif is surrounded by 10 other similar motifs but organized in a different way. There are several significant differences between the monoclinic and orthorhombic phases, which will be discussed in detail below (see also Figure 6). Although the Al and Ge atoms have the same coordination in both phases, there are significant differences for the positions of their first neighbors. Indeed, for the case of monoclinic AlGe, the intermotif Ge−Ge bonds are almost parallel to the Al2Ge2 motifs, whereas they are almost perpendicular in the case of the orthorhombic structure. Another important difference with respect to the orthorhombic structure is that, in monoclinic AlGe, the intermotif Al−Ge−Al and Ge−Al−Ge bond angles are the same (about 119° in the experimental structure and about 118.3° in the relaxed structure, see the angles labeled in bold in Figure 6c−f) whereas they are quite different in orthorhombic AlGe and antimonides. The reason why these angles have the same value is probably related to the layer

stacking in the monoclinic structure. In monoclinic AlGe, the Al2Ge2 motifs are parallelograms as in the case of the M2Sb2 motifs in the orthorhombic antimonides,40−42,54,55 in contrast with orthorhombic AlGe, where surprisingly they form almost regular lozenges. Note that the Al−Al distances within the motifs are the same in both the monoclinic and orthorhombic AlGe phases. In both AlGe phases, as in ZnSb40,55 and CdSb,54 the intermotif bonds are shorter than the intramotif bonds. In monoclinic AlGe, the intermotif Ge−Ge bonds are only slightly longer than the intermotif Al−Ge bonds and are shorter than all the bonds in the Al2Ge2 motifs (see Table 3 and Figure 6). Table 3. Interatomic Distances (in Å) in the Monoclinic AlGe Phase Obtained from Rietveld Refinement of the XRD Pattern of the Melt-Spinning Sample with Lower Cooling Rate (Sample B) and Compared to Our DFT Resultsa sample B DFT a

dG1−A1

dG1−‑A3

dG1−G2

dG1−A2

dG1−A4

dA2−A4

2.465 2.453

2.503 2.466

2.545 2.49

2.614 2.538

2.7 2.649

2.744 2.73

The labeling of the atoms follows the nomenclature of Figure 6.

In orthorhombic AlGe, the intermotif Ge−Ge bonds are slightly shorter than the intermotif Al−Ge bonds and are therefore the shortest bonds for this phase, similar to the case of CdSb.54 This contrasts to the case of ZnSb, where the intermotif Sb−Sb bonds are significantly longer than the other intermotif Zn−Sb bonds.40,41,55 This is because Al and Ge have similar covalent radii (1.21 Å for Al and 1.2 Å for Ge).56 If for 11596


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Inorganic Chemistry ZnSb and CdSb40,41,54 the lengths of the Sb−Sb bonds are slightly larger by about 0.025 Å than the sum of the covalent radii, the length of the Ge−Ge bonds is also slightly larger by about 0.04 than the sum of the covalent radii, whereas they are significantly larger (∼0.09 and 0.14 Å for the experimental and calculated structures respectively) in the case of monoclinic AlGe. For the intermotif Al−Ge bonds, their lengths are slightly larger by about 0.05−0.1 Å than the sum of covalent radii for both AlGe structures. In both AlGe structures, the intramotif Al−Ge bonds are much larger than the intermotif Al−Ge bonds and hence than the sum of covalent radii, and they are closer to the order of magnitude of the sum of the metallic radii, which is 2.8 Å (with 1.43 Å for Al and 1.37 Å for Ge).57 In the case of CdSb, Wang et al. has noted that the Cd−Cd bond length in the Cd2Sb2 motif is close to the sum of the metallic radii.54 From experimental data on ZnSb,40,55 the same observation can be drawn concerning the Zn−Zn bond length (2.76−2.8 Å) as the metallic radius of Zn is 1.39 Å.57 In both monoclinic and orthorhombic AlGe, the Al−Al bond length in the Al2Ge2 motif is smaller by about 0.12−0.13 Å than the sum of the metallic radii. This could mean a larger covalent participation of Al atoms to the bonds in both AlGe phases than in the case of the metallic atoms in the antimonides. This could be related to the larger number of valence electrons carried by the aluminum atoms compared to the zinc and cadmium atoms. Despite these small differences between the structures of the AlGe compounds and of the orthorhombic antimonides, they are very similar, and it is clear that the intermotif bonds are much stronger than the intramotif bonds in AlGe. The difference of electronegativity is rather small in Al−Ge compounds (Δχ = 0.458). It displays the same value in Zn−Sb, and it is slightly smaller in Cd−Sb (Δχ = 0.3658). As in the case of orthorhombic antimonides, one can understand the crystal bonding scheme in both AlGe compounds using a generalized octet rule. As there is one Ge−Ge two-electron bond, only three electrons of the Ge atom can participate in the other types of bonds. One can use the general octet rule as defined by Pearson:59 (ne + ba − bc)/na = 8, where ne is the total number of valence electrons, na is the number of anions, ba is the number of electrons involved in forming anion−anion bonds, and ba is the number of electrons involved in forming cation−cation bonds. For one AlGe formula unit, one finds ne = 7, ba = 1, bc = 0, and na = 1, which fulfill the above general octet rule. However, if the valence electron counting rules indicate that the valence charge is balanced and that both AlGe phases should be semiconducting, it does not tell us what the nature of the bonds is. Because there is a strong structural similarity and similar electronegativity in the AlGe phases and in both CdSb and ZnSb, we will discuss in the following the electronic properties of the AlGe phases by analogy with these antimonides. This analogy suggests to classify both AlGe phases as electron-poor semiconductors because their average valence is 3.5 and therefore lower than 4 as in the case of CdSb and ZnSb.54,60 Indeed, only the materials with an average valence of 4 and such as GaAs or ZnTe are normal valence semiconductors,54,59 and electron-rich semiconductors should have an average valence larger than 4. However, as will be seen later, whereas monoclinic AlGe can be well described by this picture, this is not the case for orthorhombic AlGe. We will not try to explore the reason because this is beyond the scope of the present study, which focuses on monoclinic AlGe.

As seen previously and in the case of CdSb and ZnSb, the two short Al−Ge intermotif bonds and the Ge−Ge intermotif bond can be seen as classical two electron−two center (2e−2c) bonds. For the case of ZnSb and CdSb, it was shown that the M 2 Sb 2 rings form multicenter (4e−4c) bonds.54,60 In monoclinic and orthorhombic AlGe, since similar Al2Ge2 rings exist, similar multicenter bonds are expected. Thus, the electrons of germanium atoms are shared as follows: three electrons in three 2e−2c (one Ge−Ge and two Ge−Al) bonds and one electron in the multicenter bonds. Similarly, the electrons of aluminum atoms are shared as follows: two electrons in two 2e−2c Ge−Al bonds and one electron in the multicenter bonding. 3.5. Electronic Structure from DFT Calculations. As can be seen in Figures 7 and 8, where the electronic density of

Figure 7. Total electronic density of states of monoclinic and orthorhombic AlGe. Inset: zoom of the total electronic density of states in the region around the Fermi level for both compounds.

states and the band structure of monoclinic AlGe calculated within LDA using the ABINIT code are reported, our DFT calculations confirm the above picture drawn from the above discussion of the crystal structure and valence electron counting. One finds that monoclinic AlGe is a narrow-gap semiconductor with a LDA energy bandgap equal to 0.17 eV.

Figure 8. Electronic band structure of monoclinic AlGe. We have used the following notation for the different special points in the Brillouin zone: Γ (0, 0, 0), Y (1/2, 0, 0), Z (0, 1/2, 0), B (0, 0, 1/2), C (1/2,1/ 2, 0), D (0, 1/2, 1/2), A (−1/2, 0, 1/2), and E (−1/2,1/2, 1/2). 11597


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Table 4. Raman Active (Ag and Bg) Vibrational Modes and Infrared Active (Au and Bu) Vibrational Modes Calculated by DFPT at the Γ Point with Their Frequencies in cm−1a mode symmetry Ag (DFT) Bg (DFT) Au (DFT) Bu (DFT)

TO mode freq 68.8, 122.8, 378 66.2, 142.1, 362 80.2, 121.3, 87.4, 202.4,

LO mode freq

mode chargesb

80.5b, 134.5b, 240.2b, 279.5b, 345.5b 87.5a (87.5c), 204.9a (202.4c), 307.8a (297.2c), 357.5a (364c)

0.775b, 5.67b, 6.78b, −3.66b, −0.43b 0.29a (−0.2c), 1.675a (−0.06c), 4.24a (−1.21c), −0.86a (3.43c)

157.5, 226.2, 348.4, 171.2, 254.3, 333, 225.4, 270.5, 345.4 296.3, 357

a

The LO infrared active vibrational modes are calculated with polarization along the a or c directions for the Bu modes and with polarization along the b direction for the Au modes. All the other modes are TO vibrational modes. bMode effective charges of the infrared active (Au and Bu) vibrational modes calculated by DFPT at the Γ point.

Figure 9. (a) Raman spectrum of the monoclinic AlGe phase obtained in the sample B. (b) Raman spectra obtained for the AlGe−α-Al eutectic region in the water-quenched sample. The spectra between 3 and 8 μm correspond mainly to the contribution from the monoclinic AlGe phase.

bandgap in fictitious orthorhombic AlSi, which was found to be less stable than the semiconducting R phase Al6Si5.41 In order to gain more information about the electronic and optical properties of monoclinic AlGe, we calculated the optical dielectric tensor corresponding to the purely electronic response to a static electric field within LDA. We have found that the off-diagonal elements ε∞xz are small compared to the diagonal elements (see the Supporting Information for details). The diagonal elements ε∞xx and ε∞zz have almost the same values (24.21 and 22.31 respectively) and are much smaller than the diagonal elements ε∞yy (46.39) in the monoclinic direction. These values correspond to the following refraction indexes: nx = 4.92, ny = 6.805, and nz = 4.72. Note that the values in a and c directions are of the same order as those found in ZnSb,40 whereas the value in the y direction is much larger. 3.6. Lattice Dynamics and Raman Spectroscopy. In the monoclinic AlGe phase, there are 8 atoms per unit cell and therefore 24 distinct vibrational modes. Their decomposition in irreducible representations is the following:

The band structure plot in Figure 8 shows that energy bandgap is indirect with the minimum of the conduction band located at Y (1/2, 0, 0) and the maximum of the valence band located at (−0.1, 0.4, 0.3). As usual with DFT calculations, this value of the energy bandgap is underestimated. Indeed, by performing modified Becke−Johnson meta-GGA calculations using the LDA relaxed structure with the Elk code, one gets a larger indirect energy bandgap of 0.46 eV. Moreover, the minimum direct energy bandgap increases from 0.72 eV with LDA to 1.125 eV with meta-GGA. As can be seen in Figure 8, the lowest conduction band is quite dispersive mainly in the Γ−Y direction for low charge carrier concentration as shown by the low density of states up to 0.3 eV above the conduction band minimum. Our calculations of partial electronic density of states also indicate a large hybridization between Al and Ge based states in the valence band and hence strong and covalent bondings between both types of atoms. This is consistent with the bonding picture discussed earlier and favors the covalent bonding picture for describing the electronic structure of monoclinic AlGe. This permits us to classify monoclinic AlGe as a weakly polar framework as in the case of ZnSb.42 The calculated LDA energy bandgap for AlGe is significantly smaller than the LDA energy bandgap of 0.45 eV that we have previously found in the case of Al6Ge5.23 We have also calculated the electronic structure of orthorhombic AlGe and did not find any energy bandgap. This is in contrast with the bonding picture that was discussed previously and that is expected to apply as well for the orthorhombic structure. We note that the two M and R phases, which are semiconducting, are also more stable than the O phase, which has no energy bandgap. Similarly, Mikhaylushkin et al. did not find any energy

Γ = 6A g ⊕ 6Bg ⊕ 6A u ⊕ 6Bu

(1)

Among these modes, three are acoustic (Au ⊕ 2 Bu), nine are infrared-active (5 Au ⊕ 4 Bu), and 12 are Raman-active (6 Ag ⊕ 6 Bg). We have calculated the energies of these modes from our DFPT calculations at the Γ point (see Table 4). In the case of the Raman-active modes, their positions in wave numbers are reported in Figure 9a as tick bars together with our experimental Raman spectra for two different crystallites in sample B, which are certainly oriented differently. A rather good overall agreement between our calculations and experimental results is obtained. The peak observed experimentally at about 66 cm−1 is due to the two lowest energy 11598


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Inorganic Chemistry modes with symmetries Bg (66 cm−1) and Ag (69 cm−1). Due to their close proximity, it is not possible to resolve them. These two modes involve motions of both kinds of atoms mainly along the c direction. The lowest infrared modes are located at higher energies around 80 cm−1 (Au) and 87.5 cm−1 (Bu) and involve motions of both atoms mainly along the c and b directions, respectively. As in Zn−Sb compounds,40 the lowest energy vibrational modes involve both Al and Ge,40 and we do not expect any kind of “rattling” modes due to the Ge− Ge dumbbells in monoclinic AlGe. In Figure 10, the phonon

Ge atoms predominantly move in the b and a directions respectively for the first two modes and in the a and b directions respectively for the last mode in opposite directions in all three cases. These vibrations strongly deform the Al2Ge2 ring. The diagonal elements of the Born charges of Al and Ge are ±1.69, ±3.32, and ±1.39 for the a, b, and c directions, respectively. The larger Born charges ZB* for the b direction agree with the previous observations. Note that the LO splitting of the two lowest polar modes is larger than for any polar infrared-active modes in ZnSb (see ref 40). In Figure 9b, we report a Raman spectrum map from the water-quenched sample. This Raman spectrum was obtained in a zone where the metastable eutectic between α-phase and M phase occurs. One can see two main types of Raman spectra: one containing mainly a contribution due to the M phase and one containing some broad peaks at about 270 and 340 cm−1. These last features most likely arise from some residual small crystals of the β-phase, i.e., of oversaturated Al-alloyed Ge. Indeed, similar Raman spectra were found for some small crystallites of the β-phase in the sample B. The Raman mode of the β-phase is strongly downshifted to lower energy compared to pure Ge where it is at ∼300 cm−1. A recent work shows the presence of a Raman mode at about 270 cm−1 in ultrathin amorphous Ge layer and at about 280 cm−1 after recrystallization at 900 °C of a 1.9 nm Ge film grown on a 0.5 nm Al layer deposited on Al2O3 substrate.61 More investigation is needed to understand the origin of the Raman modes at 270 and 340 cm−1, but this is beyond the scope of the present work. 3.7. Elastic Constants. In order to evaluate both the elastic properties and the Debye temperature of the monoclinic AlGe, we have calculated its elastic constants using the DFPT. The 13 different elastic constants Cij in a monoclinic structure are reported in Table 5. The elastic constants fulfill the criterion of mechanical stability for the monoclinic structure as defined, e.g., by Wu et al.62 From these elastic constants, we have calculated the different polycrystalline averages of the bulk modulus BH, the shear modulus GH, the Young modulus EH, and the Poisson coefficient νH in the Hill formalism, following the work of Wu et al. for the monoclinic structure62 (see Table 6). The ratio BH/GH is equal to 1.294, which indicates that monoclinic AlGe is quite brittle as this is much lower than 1.75, the limit between brittleness and ductility proposed by Pugh.63 This is expected as AlGe is a semiconductor and has a rather small Poisson coefficient νH. 3.8. Thermal Conductivity. In the present section, we discuss the lattice thermal conductivity κl of monoclinic AlGe that will be evaluated using the Slack equation:64

Figure 10. Phonon dispersion curves of monoclinic AlGe. We have used the following notation for the different special points in the Brillouin zone: Γ (0, 0, 0), Y (1/2, 0, 0), Z (0, 1/2, 0), B (0, 0, 1/2), C (1/2,1/2, 0), D (0, 1/2, 1/2), A (−1/2, 0, 1/2), and E (−1/2,1/2, 1/ 2). The red and green colors highlight motions dominated by Al and Ge atoms, respectively. The discontinuities near the Γ point are due to the splitting between TO and LO modes. These discontinuities have not been corrected in the figure to better estimate the strength of this splitting.

dispersion curves of monoclinic AlGe are reported. The high energy vibrational modes mainly involving Al are separated from the other modes involving motions of both Al and Ge by a gap. One can see that the dispersion of the two lowest energy modes is rather anisotropic with quite flat dispersion along the (0 1/2 0) direction in contrast to their dispersion along the two other directions. From our DFPT calculations, one can determine the fixed-strain relaxed ion dielectric tensor (εη) knowing the electronic contribution ε∞ and the phonon contribution εph. The off-diagonal elements are rather small (see the Supporting Information for details). One finds that the εηxx and εηzz diagonal elements are very close to each other (26.92 and 23.38 respectively) and are only slightly larger than the electronic diagonal elements, meaning that the phonon contributions are quite small for these directions perpendicular to the monoclinic axis. The diagonal element ε∞yy (69.71) for the monoclinic direction is much larger not only because of its larger electronic contribution but also because of its much larger phonon contribution. This is related to the rather large mode effective charge and hence the rather large LO−TO splitting for polarization along the b direction of some of the polar infrared-active modes of Au symmetry at rather small frequencies (at 121.3, 225.4, and 270.5 cm−1) as can be seen in Table 4 and also in Figure 10. In these three modes, the Al and

κl =

AMat (Vat)1/3 θD3 T (n1/3γ )2

(2)

where Mat is the average atomic mass, Vat is the volume per atom, θD is the Debye temperature, A is a constant equal to 3.04 × 10−8 s−3 K−3, n is the number of atoms in the primitive cell, and γ is the Grüneisen parameter. In order to determine the thermal conductivity from our calculations, one needs to determine the Grüneisen parameter, γ. One can evaluate γ from

Table 5. Elastic Constants Cij of Monoclinic AlGe Calculated by DFPT (in GPa) C11

C22

C33

C12

C13

C23

C44

C55

C66

C15

C25

C35

C46

131.5

123.2

145.6

25.1

52.6

3.6

29

51.1

65

−5

2.6

−6.3

6.6

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Table 6. Polycrystalline Average of the Bulk Modulus BH, the Shear Modulus GH, the Young Modulus EH (in GPa), Longitudinal Velocity vl, Transverse Velocity vt, Sound Velocity v (in m/s), and Debye Temperature θD (in K) for Monoclinic AlGe Calculated by DFPTa

a

BH

GH

EH

νH

BH/GH

vl

vt

v

θD

61.5

47.6

113.5

0.193

1.294

5579.2

3475.7

3830.2

421.1

The polycrystalline average of the Poisson coefficient νH and the ratio BH/GH are also shown.

decompose from 230 to 270 °C. DFT calculations confirm the similar stability of both phases, explaining why they are competing with each other and the lower stability of orthorhombic AlGe. We show the close proximity of the crystal structure of the monoclinic AlGe to that of orthorhombic ZnSb and AlGe, in both cases the crystal structures being described by arrays of isolated X2Y2 parallelogram rings which are 10-fold coordinated between them. As in the case of ZnSb, AlGe contains three types of two center−two electron bonds, including one Ge−Ge bonding, and one multicenter bond within the Al2Ge2 ring. As its electronic properties and bonding are rather covalent and its average valence is 3.5, monoclinic AlGe can be seen as a poor electron framework semiconductor. Monoclinic AlGe is a narrow-gap semiconductor with an indirect energy bandgap of about 0.5 eV, which could be used in several applications if it could be obtained as a pure phase. In contrast, our DFT calculations show that the orthorhombic form is not semiconducting although its electronic density of states at the Fermi level is very low. We also found several rather low energy modes which involve motion of both types of atoms. However, a rough estimation of the thermal conductivity indicates that the thermal conductivity could be lower than 10 W·m−1·K−.

the knowledge of the Poisson coefficient ν using the following equation:65 γ=

(3/2)(1 + v) (2 − 3v)

(3)

With ν = 0.193, one finds γ = 1.26, which is rather low. Using this value of γ and the Debye temperature θD found from the elastic constants (see Table 6), one obtains a rough estimation of κ around 15 W/m·K at room temperature using the Slack relation. This rather large value of the thermal conductivity of pure monoclinic AlGe is mainly due to the rather large Debye temperature of AlGe, which is comparable to that found in Mg2Si or CrSi2.64,66 However, it is well-known that Slack’s equation overestimates the value of the thermal conductivity,64,67 because it does not take into account the increased umklapp interactions between low energy optical phonons with acoustic phonons, which occurs in compounds such as filled skutterudites68 or ZnSb,40,55,67 for instance. As noted previously, in monoclinic AlGe there are some rather low energy optical modes able to interact with acoustical phonons. In contrast, there are not such low energy optical modes in Mg2Si nor in CrSi2 with a lattice thermal conductivity of about 10−15 W·m−1·K−164,66,69 and we therefore expect a lower thermal conductivity for monoclinic AlGe. These low energy optical modes have similar energies (about 8 meV) to filled skutterudites such as LaFe4Sb12 (7 meV)68 or in ZnSb (5 meV).40,55,67 However, contrary to the case of skutterudites, but similarly to the case of ZnSb, the symmetry of these low energy optical modes is different from those of the acoustic modes. Thus, the interaction between these low energy optical modes and acoustic modes is forbidden by symmetry,40,55 but this could be relaxed due to anharmonic coupling.55 As umklapp phonon−phonon scattering becomes significantly large above the Debye temperature,55 the rather high Debye temperature of monoclinic AlGe makes it improbable to have a very low thermal conductivity. In addition, except along the (0 1/2 0) direction, the low energy optical modes are more dispersive and less localized in monoclinic AlGe than in orthorhombic ZnSb. Taken all together, one expects a larger thermal conductivity for monoclinic AlGe than for ZnSb. Additional studies of the anharmonicity and of the thermal properties of monoclinic AlGe, if single-phase sample can be obtained, are required to conclude on the potential of monoclinic AlGe for thermoelectric applications.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b01318. Rietveld refinement, SEM, EDX, interatomic angles, dielectric tensors, and Born charges (PDF)

■

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Romain Viennois: 0000-0003-4542-2699 Mickael Beaudhuin: 0000-0002-2568-546X Notes

The authors declare no competing financial interest.

■

4. CONCLUSION We report for the first time the full crystal structure, the electronic structure, the lattice dynamics, and the elastic constants of metastable monoclinic AlGe. We show that monoclinic AlGe can be obtained by fast water-quenching, but not the rhombohedral phase Al6Ge5. As in the case of the meltspinning process, there are still secondary phases. We also confirm the chemical composition of both monoclinic AlGe and rhombohedral Al6Ge5 phases and that both phases

REFERENCES

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