High pressure structural and transport measurements of InTe, GaTe, and InGaTe2

Journal of Physics and Chemistry of Solids 74 (2013) 723–728

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High pressure structural and transport measurements of InTe, GaTe, and InGaTe2 M.K. Jacobsen a,n, Y. Meng b, R.S. Kumar a, A.L. Cornelius a a b

High Pressure Science and Engineering Center and Department of Physics and Astronomy, University of Nevada, Las Vegas, Las Vegas, NV 89154, United States HPCAT, Geophysical Laboratory, Carnegie Insitute of Washington, Argonne, IL 60439, United States

a r t i c l e i n f o

abstract

Article history: Received 20 December 2011 Received in revised form 25 November 2012 Accepted 12 January 2013 Available online 21 January 2013

In this paper, the effect of pressure on the transport and structural properties of GaTe, InTe, and InGaTe2 is reported. All materials were found to exhibit pressure-induced structural transitions. For GaTe, the ambient structure transforms to a mixed state at 8 GPa, which transforms at 15 GPa to an ordered state. InTe, which crystallizes in a tetragonal structure, shows transformations at 6 and 14 GPa. InGaTe2, also initially tetragonal, undergoes two transitions at 9.25 GPa and 13 GPa. These transitions have shown noticeable effects on the transport properties. In particular, the Seebeck coefficient for the solid solution changes sign at the first phase transition. From these results, the thermoelectric figure of merit has been evaluated for each material. For some of these materials (InTe and InGaTe2) this yields a lower efficiency than ambient conditions. However, for GaTe, this has been shown to increase the figure of merit by 14 times to 8 GPa. & 2013 Elsevier Ltd. All rights reserved.

Keywords: A. Semiconductors A. Chalcogenides C. High pressure D. Transport properties

1. Introduction Recently, interest in renewable energy materials has dramatically increased, due to the need for alternate sources of energy. One potential candidate in this area is thermoelectric materials, for which the governing relation [1–3] at temperature T is ZT ¼

a2 sT l

ð1Þ

with s (r) and l (R) being the electrical and thermal conductivity (resistivity), respectively, a being the Seebeck coefficient, and Z being the thermoelectric figure of merit. One issue with improving thermoelectric materials lies in the interconnectedness of these parameters. As an example, all the important properties are influenced by electron behavior. As such, investigations into materials that limit the lattice thermal conductivity have become more frequent. Some materials thought to achieve this include layered and lower-dimensional compounds. For this work, (Ga,In)2Te2 compounds have been investigated, which exhibit such layered structures. These materials crystallize under ambient conditions in either the monoclinic B2/m or the tetragonal I4/mcm structures and form with band gaps between 0.03 eV (InTe [4]) and n Corresponding author. Present address: Mineral Physics Institute, Department of Geosciences, Stony Brook University, Stony Brook, NY 11794, United States. E-mail addresses: [email protected], [email protected] (M.K. Jacobsen).

0022-3697/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jpcs.2013.01.011

1.5 eV (GaTe [5]). As these materials may prove to be interesting potential thermoelectric materials, this work probes the effect of pressure to determine the thermoelectric effectiveness. This is particularly important as previous investigations involving pressure have only explored the resistivity and structure for some of the materials, leaving a large amount of information unaccounted for. Further, through simultaneous measurement of the relevant properties, which removes sample to sample doping level variations from the problem, a complete thermoelectric characterization of these materials can be achieved.

2. Experimental details 2.1. Sample preparation and ambient pressure measurements The materials used in this study have been prepared from raw materials obtained from Sigma Aldrich (Ga, 99.999%, lump; In, 99.99% bar) and Spectrum Chemicals (Te, 99.5%, powder). In each case, the tellurium was prepared separately as pellets, due to the gallium and indium both having low melting temperatures. The Ga and In portions were cut into the appropriate stoichiometric ratios and refrigerated until sealed in evacuated (10  3 Torr internal pressure) quartz ampoules. The materials were reacted at 800 1C for 3 days in a tube furnace, with occasional shaking to homogenize the mixture, and then quenched to room temperature. The resulting material was ground into a fine powder, with the material used for transport measurements being pelletized in a 3.4 mm die. The structure of the materials was checked using

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facilities available through the geoscience department at UNLV (PANalytical X’pert Pro X-ray diffractometer, Cu Ka radiation), with reference patterns were used to confirm the desired compounds.

2.2. High pressure structure measurements The high pressure structure of these compounds was studied using the ID-B beamline at HPCAT (Sector 16) of the Advanced Photon Source at Argonne National Laboratory. For each, some powder was loaded into a Merrill-Bassett diamond anvil cell with a stainless steel retaining gasket and diamonds of 400 mm culet diameter. Silicone fluid was used as a pressuring medium to preclude reaction of the sample. A ruby marker was used to determine the internal pressure of the cell and a MAR CCD ˚ collected the diffraction patterns at a wavelength of 0.41198 A. The resulting ring patterns were converted to intensity vs. 2y plots using Fit2D [6] and then exported. MDI’s Jade [7] was then used to determine the cell parameters and volumes from these plots. Using EOSFit [8], these volume–pressure points were fit to a third-order Birch–Murnaghan equation of state [9,10], which is represented as "  # "    5=3 # 3B0 V 0 7=3 V0 3 V 0 2=3 ðB00 4Þ PðVÞ ¼  1 ð2Þ 1þ 4 2 V V V where V, B0, and B00 are the volume, bulk modulus, and pressure derivative of the bulk modulus, respectively. The subscript 0 refers to the ambient pressure value and denotes fit parameters, where the non-subscripted parameters are the determined cell volumes/ pressures.

Heating Element

Thermocouple 1

Thermocouple 2

AC Resistance Bridge

Sample Chamber Thermocouple Amplifier/Switch

Multimeter

Cell

Hydraulic Press

Transducer

Heater Controller

PC Stepper Motor

2.3. High pressure transport properties The setup used to determine the transport properties is a modified opposed anvil Bridgman cell, similar to that presented by Jaccard and Sengupta [11] and Lortz et al. [12]. The cell has tungsten carbide anvils with a 6 mm working face and a 101 taper angle. Pressure is applied to the setup through a 25-ton hydraulic press, modified to allow for semi-automated operation using a computer interface. A schematic diagram of the setup is presented in Fig. 1. The sample chamber is prepared from pyrophyllite annuli and steatite filler, with the wire placement shown in the inset of Fig. 1. The electrical leads used are type K thermocouples, with a chromel filament heater placed a slight distance off one end of the sample to prevent electrical ground loops. This heater is powered by a 150 W power supply controlled through the computer. More details on the measurement setup and theory are presented in the dissertation by Jacobsen [13].

3. Results and discussion 3.1. Structure InGaTe2. The ambient pressure structure of this compound is I4/mcm, with the unit cell parameters and equation of state results in Table 1. Under compression, this material was determined to undergo two phase transitions, one between 9 and 9.5 GPa and one between 13 and 14 GPa. The first transition had a best fit structure of I4 cm, with the second being P21/c (b ¼ 137:541 70:231). As the first transition was rather subtle, some selected X-ray patterns are presented in Fig. 2, illustrating the transition. A graphical representation of the equation of state for each phase is shown in Fig. 3(a). GaTe. The ambient pressure structure for GaTe is B2/m ðg ¼ 104:631 70:041Þ structure, with unit cell parameters as tabulated in Table 1. The effect of pressure on this material showed a loss of discernible structure occurring at 8 GPa. This mixed phase remained until 15 GPa, where the structure transformed to a new cubic Fm3m structure. This structure remained until the limit of the experiment. Upon decompression, the cubic high pressure phase remained until 6 GPa, when the structure peaks Table 1 Unit cell parameters and equation of state data: this table reports the unit cell parameters (a, b, and c) and equation of state fit parameters (V0, B0, and B00 ) for all three materials. The V0, B0, and B00 parameters are the ambient pressure volume, bulk modulus, and pressure derivative of the bulk modulus, respectively. The numbers in parenthesis in this table represent the determined uncertainties on the last digit(s) of the reported values. Sample

˚ a (A)

˚ b (A)

˚ c (A)

GaTe I GaTe II InTe I InTe II InGaTe2 I InGaTe2 II InGaTe2 III

17.229 (8) 5.503 (7) 8.437 (2) 5.969 (3) 8.391 (2) 7.618 (3) 6.733 (37)

10.391 (4) – – – – – 3.575 (5)

4.036 – 7.127 – 6.854 6.566 5.361

V0 (A˚ 3)

B0 (GPa)

B00

698.9 204.4 507.3 229.7 483.0 457.3 111.3

36.1 (4) 43.0 (23) 28.7 (5) 66.7 (5) 23.97 (56) 35.7 (12) 46.3 (5)

4.45 (12) 5.4 (6) 4.2 (3) 4.1 (1) 4.28 (22) 4.03 (29) 2.01 (5)

(2) (3) (2) (4) (19)

Motor Controller

Fig. 1. Semi-automated press setup: this figure shows the main components of the setup. This consists of the pressurization system (press, stepper motor, motor controller, and transducer), the measurement system (AC resistance bridge, multimeter, and thermocouple amplifier/switch), and the heater controller. All of these parts are interfaced with the PC. The inset shows a schematic of the sample chamber, presenting the sample with thermocouple junctions placed at both ends and an offset heater, to prevent electrical shorts.

GaTe I GaTe II InTe I InTe II InGaTe2 I InGaTe2 II InGaTe2 III

(4) (14) (3) (1) (6) (13) (2)

M.K. Jacobsen et al. / Journal of Physics and Chemistry of Solids 74 (2013) 723–728

are lost. These results agree with previous experiments of Schwarz et al. [14]. The equations of state fits, along with the measured volumes, are shown in Fig. 3(b).

725

InTe. The ambient structure of InTe is the tetragonal I4/mcm, with unit cell parameters as shown in Table 1. This structure remained until 6.1 GPa, where a transformation to the cubic Fm3m occurred. This structure was found to transform to the primitive cubic structure Pm3m structure at nearly 14 GPa, which remained until the limit of the experiment. Decompression showed a return to the original tetragonal structure. This data is in agreement with the reports of Chattopadhyay et al. [15]. Data on the third form of InTe is not reported in the table, as only two recorded diffraction patterns for this structure were present. The measured equations of state are shown in Fig. 3(c).

3.2. Transport properties InGaTe2. The transport properties of InGaTe2 at ambient temperature and pressure are shown in Table 2. The results have been found to be in agreement with reports by Gojaev et al. [20] and Guseinov et al. [19]. Under pressure, the thermal conductivity is seen to increase slowly, with a discontinuity occurring near 4 GPa and 9 GPa, as shown in Fig. 4(a). In contrast, the resistivity and Seebeck coefficient are both suppressed, with the resistivity exhibiting a small shoulder between 3 and 4 GPa as shown in Fig. 5(a). Thus, the second discontinuity from the thermal conductivity is likely caused by the structural transition. However, the shoulder in the resistivity and first discontinuity of the thermal conductivity are unexplained by structural means.

Fig. 2. Selected diffraction patterns for InGaTe2: this figure shows diffraction patters for the InGaTe2 sample at four pressures, crossing the phase boundary mentioned in the text. It is seen clearly that there are several new peak appearing, with the most prominent being near 121. The pressure was determined from the first appearance of the new peaks.

58

120

56 54

Volume/Z(Å3)

Volume/Z(Å3)

110

100

52 50 48 *

46

90

44

*

42 80 0

2

4

6

8

10

12

14

16

40

18

0

2

4

6

P(GPa)

8

10

12

14

16

18

P(GPa)

65

Volume/Z(Å3)

60

55

50

45 0

2

4

6

8

10

12

14

16

P(GPa) Fig. 3. Pressure vs. volume and equation of state for materials under study: in all graphs, the spheres are the measured volumes, with the lines representing the equation of state fits, as described in the text, for each phase. In (b), the starred points are values measured on decompression and were used in the fitting process. (a) InGaTe2. (b) GaTe. (c) InTe.

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The slope of the lattice thermal conductivity has been theorized [21] to be proportional to n=B0 , with n being a numerical constant. It is suggested in the reference that this value would take on a value of either 4 or 6, depending on the model used. By taking the electronic thermal conductivity, using the Wiedemann–Franz law, and subtracting it from the total thermal conductivity, as measured, the lattice component can be obtained. This, however, is only true if one assumes that electrons and phonons are the only conductors of heat, as has been proposed elsewhere [22]. By taking this result and applying a linear fit, the slope is found to be 0.15970.007 W/m K GPa, which is remarkably close to that predicted using an n of 4. From the transport data presented here, the figure of merit ZT has been calculated, as shown in Fig. 6(a). A slight initial improvement is found, but the trend reverses and decreases by a factor of 2 by 4 GPa. This suggests, as would be concluded from the resistivity results, that the application of pressure drives this material towards a metallic state and, thus, not a more effective thermoelectric.

Table 2 Average ambient pressure transport properties: the center column presents results from this work for the ambient pressure and temperature transport properties, with errors (numbers in parenthesis) in the least significant digit(s) shown. For comparison, reference data is shown in the third column, with Seebeck coefficient ranges where available (N.A. is not available). Results

Reference Data

GaTe r ðmO cmÞ l (W/m K) a ðmV=KÞ

1695 (10) 1.18 (8) 179 (30)

100–1600 [16] 8.7 (? c), 1.4 (Jc) [17] 175 [18]

InTe r ðmO cmÞ l (W/m K) a ðmV=KÞ

135 (1) 1.32 (9) 98 (6)

11 (Jc), 223 (? c) [4] 1.8 [19], 1.7/0.6 [17] N.A.

InGaTe2 r ðmO cmÞ l (W/m K) a ðmV=KÞ

547 (110) 1.31 (9) 150 (21)

450 [20] 1.59 [19] N.A.

4.5

3.2

4.0

4.0

2.8

3.5

3.5 2.4

3.0

1.6 1.2

2.5 2.0 1.5

0.8

1.0

0.4

0.5

0.0

λ(W/m-K)

λ(W/m-K)

λ(W/m-K)

3.0 2.0

2

4

6

8

10

2.0 1.5 1.0 0.5 0.0

0.0 0

2.5

0

2

6

4

P(GPa)

8

10

0

2

4

6

8

10

P(GPa)

P(GPa)

Fig. 4. Thermal conductivity vs. pressure for materials under study: in all graphs, the total thermal conductivity is represented by the solid spheres, with the open stars representing the electronic component. The electronic component is determined from the Wiedemann–Franz law, assuming no doping. In each graph, a representative error bar is shown for the measured total thermal conductivity. The error for the electronic component is represented by the size of the symbol. (a) InGaTe2. (b) GaTe. (c) InTe.

150

5

100

0

100

200

50

78

9

10

α (μV/K)

α (μV/K)

α (μV/K)

150

100

50

11 50

0

0

0

1.2

0.25

ρ (mΩ-m)

1.5

ρ (Ω-m)

ρ (Ω-m)

0.50

1.0

0.9

0.6

0.5 0.3

0.

0.0 0

2

4

6

P (GPa)

8

10

0.0 0

2

4

6

P (GPa)

8

10

0

2

4

6

8

10

P (GPa)

Fig. 5. Resistivity and Seebeck coefficient vs. pressure for materials under study: in all graphs, the Seebeck coefficient is in the top panel, with the resistivity in the bottom. In (a), the inset in the top panel shows the Seebeck coefficient changing sign, suggesting that the Fermi surface of the material intersects the Brillouin zone boundary at this pressure. In each graph, representative error bars are shown for the Seebeck coefficient. The Seebeck coefficient error shown in (a) is the value representative below 3 GPa. Above this pressure, the error is represented by the size of the symbol. For the resistivity, the error is represented by the size of the symbol in all cases. (a) InGaTe2. (b) GaTe. (c) InTe.

M.K. Jacobsen et al. / Journal of Physics and Chemistry of Solids 74 (2013) 723–728

15.0

75

12.5

60

727

10.0

μZT

45

μZT

7.5

30

5.0 2.5

15

0.0 0 0

2

4

6

8

10

0

2

4

P (GPa)

6

8

10

P (GPa)

0.0030 0.0025

ZT

0.0020 0.0015 0.0010 0.0005 0.0000 0

2

4

6

8

10

P (GPa)

Fig. 6. ZT vs. pressure for the materials under study: in each graph, representative error bars are presented. In (b), the second error bar is to denote the error representative of the three values surrounding the peak. It should be noted that the magnitude of ZT in (a) and (b) is extremely small (10  6), as is indicated by the axis label. All three curves are determined with T¼ 305 K, as that was the average temperature of the sample in all experiments. (a) InGaTe2. (b) GaTe. (c) InTe.

GaTe. The ambient pressure properties for GaTe are shown in Table 2. These values have been found to be in agreement with previously reported ambient values from Manfredotti et al. [16], Al-Ghamdi [18], and Spitzer [17]. It is further presented in the work of Manfredotti, that the sample resistivity is strongly dependent on the method of preparation. It is also likely that the other properties are subject to this effect, but that remains unclear at this point. The measured resistivity was also compared with the values of Milne and Anderson [23]. However, Milne’s value is single crystalline and on the lower end of the spectrum reported by Manfredotti. Due to this extreme variability in this materials resistivity, it is highly likely that the grain boundaries and polycrystalline nature of the sample used in this work contribute a significant amount to the overall resistance. For the thermal conductivity, it is found that the heat conduction increases linearly with pressure until 8–9 GPa. At this point, the slope of the thermal conductivity increases, as shown in Fig. 4(b). The resistivity was found to drop rapidly up to 5 GPa, with a shoulder at 2.5 GPa, as shown in Fig. 5(b). Further measurements will be needed to determine the nature of this shoulder. In the Seebeck coefficient, the results show a linearly decreasing trend up to 8 GPa, where a slower rate is found, suggesting the mixed phase is trending towards metallicity at higher pressures. As with InGaTe2, the lattice thermal conductivity was calculated and used to compute the slope. In this case, the structure transition at 8 GPa has affected the thermal conductivity of this material and pressures above this were excluded. A slope of 0.201 70.011 W/m K GPa was found, which unlike the previous sample, is larger than either suggested value from Hofmeister’s

theory. It is possible that this is due to an anisotropy of the properties of the sample, as has been seen in other references [17]. However, the more likely cause is grain boundary effects, as mentioned with the resistance results. From the information presented here, the figure of merit has been calculated and shown in Fig. 6(b). This shows the applied pressure increases the thermoelectric efficiency by nearly a factor of 14 from ambient to 6 GPa. This is particularly interesting as it suggests that the degradation of the structure as the phase transition is approached results in an increase in thermoelectric ability. InTe. The ambient pressure values for InTe are shown in Table 2. These values have been found to be in good agreement with Parlak et al. [4] and Spitzer [17]. For the thermal conductivity, as with GaTe, this material shows a strong degree of anisotropy in reference data, with the reported values between 1.7 [24] and 0.6 W/m K. The reason for the discrepancy was not addressed in Spitzer’s paper and, due to a lack of information on the measurement process, remains an unclear disagreement. Regardless, the value from this work is within the range reported from these works. With applied load, a trend similar to the other materials is observed. The thermal conductivity shows a marked increase up to 6 GPa, where a slight drop in the value corresponds with the structural phase transition already mentioned. This is followed by an increase in the thermal conductivity with further increasing load, as shown in Fig. 4(c). The resistivity decreases up to 4 GPa, with a sudden drop occurring, and shows a similar trend to that reported by Pal et al. [25] (Figs. 4 and 5). This effect might be a precursor to the structural phase transition at 6 GPa, but this is

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M.K. Jacobsen et al. / Journal of Physics and Chemistry of Solids 74 (2013) 723–728

unclear at this point. The Seebeck coefficient shows a similar trend, without the sharp discontinuity seen in the resistivity. These suggest metallization, in agreement with Chattopadhyay et al. [15]. These results are shown graphically in Fig. 5(c). In the same manner as the other samples, the lattice thermal conductivity has been used to determine a slope, for pressures less than 4 GPa, of 0.16270.016 W/m K GPa. This value is between the theoretical values reported previously, but closer to n being 4. In addition, the figure of merit ZT for this material is shown in Fig. 6(c), where the thermoelectric effectiveness shows a slight increase upon initial loading, but rapidly decreases until the phase transition. After the structure changes, the material’s effectiveness recovers slightly and plateaus at 8 GPa, showing no significant change for the remainder of the pressure range.

Acknowledgments Work at UNLV is supported by DOE cooperative agreement DEFC52-06NA27684. Portions of this work were performed at HPCAT (Sector 16), Advanced Photon Source (APS), Argonne National Laboratory. HPCAT is supported by CIW, CDAC, UNLV and LLNL through funding from DOE-NNSA, DOE-BES and NSF. Use of the Advanced Photon Source was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under contract number DE-AC02-06CH11357. The authors would like to thank Amadeo Sanchez, James Norton, and William O’Donnell of UNLV for their ongoing assistance with the development of the high pressure transport system. In addition, the authors would like to thank the anonymous reviewers for their helpful comments. References

4. Conclusions In conclusion, the transport properties and structure with pressure have been determined for GaTe, InTe, and InGaTe2. From this, there are several pieces of new information gained. First, no previous studies of the high pressure structure or properties of InGaTe2 have been undertaken. With specific regard to this material, some of the most interesting results have been found. The change of sign of the Seebeck coefficient measured suggests that, from the theory in Ziman [22], the Fermi surface is crossing the Brillouin zone. In turn, this means the dominant carrier of the system has changed through the transition at 9 GPa. In addition, the electrical behavior of the parent compounds would be consistent with that expected of materials undergoing an electronic topological transition (electronic structure change not associated with a crystal structure change). This is suggested by the decreases present in the resistivity not correlated with structural changes, and is more interesting due to the lack of such an occurrence in the solid solution. While the parent compounds have both been previously studied using resistivity and structure as probes, there is a distinct lack of information regarding the thermoelectric and thermal behaviors of these materials with applied pressure. To address this, this work has demonstrated the application of pressure to all materials results in an increase in thermal conductivity, consistent with theoretical expectations. In contrast, the solid solution shows no such effect with the application of pressure. Further, all three materials appear to trend towards metallic behavior, as evidenced both in the resistivity and the Seebeck coefficient trends present. From these results, it was found that the effect of pressure decreased the thermoelectric efficiency of both InTe and InGaTe2. In GaTe, the efficiency was found to increase with pressure to 6 GPa, near the onset of the mixed phase. Despite this, all three are found to be ineffective as thermoelectric materials. This particular result demonstrates clearly the view that unusual structural effects can improve the thermoelectric response [26–30].

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