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Carrier concentration dependence of structural disorder in thermoelectric Sn 1 − x Te

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ABSTRACT

SnTe is a promising thermoelectric and topological insulator material. Here, the presumably simple rock salt crystal structure of SnTe is studied comprehensively by means of high-resolution synchrotron single-crystal and powder X-ray diffraction from 20 to 800 K. Two samples with different carrier concentrations (sample A = high, sample B = low) have remarkably different atomic displacement parameters, especially at low temperatures. Both samples contain significant numbers of cation vacancies (1–2%) and ordering of Sn vacancies possibly occurs on warming, as corroborated by the appearance of multiple phases and strain above 400 K. The possible presence of disorder and anharmonicity is investigated in view of the low thermal conductivity of SnTe. Refinement of anharmonic Gram–Charlier parameters reveals marginal anharmonicity for sample A, whereas sample B exhibits anharmonic effects even at low temperature. For both samples, no indications are found of a low-temperature rhombohedral phase. Maximum entropy method (MEM) calculations are carried out, including nuclear-weighted X-ray MEM calculations (NXMEM). The atomic electron densities are spherical for sample A, whereas for sample B the Te electron density is elongated along the ⟨100⟩ direction, with the maximum being displaced from the lattice position at higher temperatures. Overall, the crystal structure of SnTe is found to be defective and sample-dependent, and therefore theoretical calculations of perfect rock salt structures are not expected to predict the properties of real materials.

No MeSH data available.


(a) The cell parameters of samples A and B from synchrotron single-crystal X-ray diffraction (SXRD) and conventional powder X-ray diffraction (PXRD). (b) The (204) reflection plotted as a function of temperature collected with a conventional X-ray source (sample B). (c) A high-resolution synchrotron PXRD pattern showing asymmetries at 550 K (sample B).
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fig3: (a) The cell parameters of samples A and B from synchrotron single-crystal X-ray diffraction (SXRD) and conventional powder X-ray diffraction (PXRD). (b) The (204) reflection plotted as a function of temperature collected with a conventional X-ray source (sample B). (c) A high-resolution synchrotron PXRD pattern showing asymmetries at 550 K (sample B).

Mentions: Tin telluride is non-stoichiometric, and the ratio of Sn:Te is always less than one. The effect of each Sn vacancy is the creation of two electron holes, rendering tin telluride a p-type semi-metal (Salje et al., 2010 ▸), i.e. a zero-gap semiconductor, due to the small overlap between the bottom of the conduction band and the top of the valence band. The carrier concentration ranges from 1019 to 1021 cm−3. Crystals with a low carrier concentration (fewer Sn vacancies) have relatively larger cell parameters (Bis & Dixon, 1969 ▸). The cell parameters determined for the two different samples reflect the preparation method employed. The vapour transport synthesis is more prone to giving samples with a low tin content, due to the higher vapour pressure of tellurium. The opposite happens when the sample is synthesized by directly melting Sn in excess and Te. As shown in Fig. 3 ▸, the cell expansion is linear in the range 20–400 K for both samples, the slope being slightly different in the two cases. For sample B, the cell volume does not vary appreciably in the range 450–550 K. The clear broadening of the Bragg peaks at 500 K indicates a conspicuous increase in microstrain. The appearance of shoulders and asymmetries for T ≥ 500 K can be ascribed to the formation of multiple phases with different contents of tin and hence with different carrier concentrations. Above 700 K a further broadening is detected and the scattering power decreases due to the formation of SnO2. The cell expansion curve is not reversible in the sense that, upon cooling, the cell parameters are systematically lower than on warming. The broadness of the peaks and the presence of multiple phases with slightly different unit-cell volumes persist even at room temperature. However, the trend shown in Fig. 3 ▸ is not entirely general since, on increasing the temperature ramping rate or the time of acquisition at each temperature, the formation temperature of multiple phases increases and the cell thermal expansion changes accordingly.


Carrier concentration dependence of structural disorder in thermoelectric Sn 1 − x Te
(a) The cell parameters of samples A and B from synchrotron single-crystal X-ray diffraction (SXRD) and conventional powder X-ray diffraction (PXRD). (b) The (204) reflection plotted as a function of temperature collected with a conventional X-ray source (sample B). (c) A high-resolution synchrotron PXRD pattern showing asymmetries at 550 K (sample B).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5391859&req=5

fig3: (a) The cell parameters of samples A and B from synchrotron single-crystal X-ray diffraction (SXRD) and conventional powder X-ray diffraction (PXRD). (b) The (204) reflection plotted as a function of temperature collected with a conventional X-ray source (sample B). (c) A high-resolution synchrotron PXRD pattern showing asymmetries at 550 K (sample B).
Mentions: Tin telluride is non-stoichiometric, and the ratio of Sn:Te is always less than one. The effect of each Sn vacancy is the creation of two electron holes, rendering tin telluride a p-type semi-metal (Salje et al., 2010 ▸), i.e. a zero-gap semiconductor, due to the small overlap between the bottom of the conduction band and the top of the valence band. The carrier concentration ranges from 1019 to 1021 cm−3. Crystals with a low carrier concentration (fewer Sn vacancies) have relatively larger cell parameters (Bis & Dixon, 1969 ▸). The cell parameters determined for the two different samples reflect the preparation method employed. The vapour transport synthesis is more prone to giving samples with a low tin content, due to the higher vapour pressure of tellurium. The opposite happens when the sample is synthesized by directly melting Sn in excess and Te. As shown in Fig. 3 ▸, the cell expansion is linear in the range 20–400 K for both samples, the slope being slightly different in the two cases. For sample B, the cell volume does not vary appreciably in the range 450–550 K. The clear broadening of the Bragg peaks at 500 K indicates a conspicuous increase in microstrain. The appearance of shoulders and asymmetries for T ≥ 500 K can be ascribed to the formation of multiple phases with different contents of tin and hence with different carrier concentrations. Above 700 K a further broadening is detected and the scattering power decreases due to the formation of SnO2. The cell expansion curve is not reversible in the sense that, upon cooling, the cell parameters are systematically lower than on warming. The broadness of the peaks and the presence of multiple phases with slightly different unit-cell volumes persist even at room temperature. However, the trend shown in Fig. 3 ▸ is not entirely general since, on increasing the temperature ramping rate or the time of acquisition at each temperature, the formation temperature of multiple phases increases and the cell thermal expansion changes accordingly.

View Article: PubMed Central - HTML - PubMed

ABSTRACT

SnTe is a promising thermoelectric and topological insulator material. Here, the presumably simple rock salt crystal structure of SnTe is studied comprehensively by means of high-resolution synchrotron single-crystal and powder X-ray diffraction from 20 to 800 K. Two samples with different carrier concentrations (sample A = high, sample B = low) have remarkably different atomic displacement parameters, especially at low temperatures. Both samples contain significant numbers of cation vacancies (1–2%) and ordering of Sn vacancies possibly occurs on warming, as corroborated by the appearance of multiple phases and strain above 400 K. The possible presence of disorder and anharmonicity is investigated in view of the low thermal conductivity of SnTe. Refinement of anharmonic Gram–Charlier parameters reveals marginal anharmonicity for sample A, whereas sample B exhibits anharmonic effects even at low temperature. For both samples, no indications are found of a low-temperature rhombohedral phase. Maximum entropy method (MEM) calculations are carried out, including nuclear-weighted X-ray MEM calculations (NXMEM). The atomic electron densities are spherical for sample A, whereas for sample B the Te electron density is elongated along the ⟨100⟩ direction, with the maximum being displaced from the lattice position at higher temperatures. Overall, the crystal structure of SnTe is found to be defective and sample-dependent, and therefore theoretical calculations of perfect rock salt structures are not expected to predict the properties of real materials.

No MeSH data available.