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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.


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The temperature dependence of F333 on an absolute scale for samples A and B from single-crystal diffraction data.
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fig9: The temperature dependence of F333 on an absolute scale for samples A and B from single-crystal diffraction data.

Mentions: The diffraction studies supporting the phase transition are from the 1970s. In 1975, a neutron study (Iizumi et al., 1975 ▸) measured the (333) reflection on a sample with p77K = 0.88 × 1020 cm−3. The (333) reflection appeared to fall in intensity when increasing the temperature above 98 K. Since in a rock salt structure, all the structure factors with hkl all odd are proportional to the difference in the scattering lengths or form factors of the cation and the anion, it was speculated that the decreasing intensity of the (333) reflection results from centring of the Sn and Te atoms from a rhombohedral to a cubic lattice. Given that (i) the intensity was not reported on an absolute scale, (ii) the effect of the thermal motion was deliberately neglected and (iii) the setting of the diffractometer was not changed to follow the peak position between 20 and 100 K as mentioned by the authors, we feel that their evidence is not entirely persuasive. As a counterproof, we plot the (333) reflection as a function of temperature from the present data in Fig. 9 ▸. The (333) reflection does not approach zero above 100 K but depends on the different increment of Uiso(Sn) and Uiso(Te) with temperature and on the occupancy of Sn. The increase of the hkl all odd X-ray structure factors with temperature is confirmed if the values of Uiso(Sn) and Uiso(Te) obtained from neutron measurements at HB-3A and TOPAZ reported by Li, Ma et al. (2014 ▸) on a sample with Tc = 42 K are used to calculate the (333) structure factor (Fig. 10 ▸).


Carrier concentration dependence of structural disorder in thermoelectric Sn 1 − x Te
The temperature dependence of F333 on an absolute scale for samples A and B from single-crystal diffraction data.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig9: The temperature dependence of F333 on an absolute scale for samples A and B from single-crystal diffraction data.
Mentions: The diffraction studies supporting the phase transition are from the 1970s. In 1975, a neutron study (Iizumi et al., 1975 ▸) measured the (333) reflection on a sample with p77K = 0.88 × 1020 cm−3. The (333) reflection appeared to fall in intensity when increasing the temperature above 98 K. Since in a rock salt structure, all the structure factors with hkl all odd are proportional to the difference in the scattering lengths or form factors of the cation and the anion, it was speculated that the decreasing intensity of the (333) reflection results from centring of the Sn and Te atoms from a rhombohedral to a cubic lattice. Given that (i) the intensity was not reported on an absolute scale, (ii) the effect of the thermal motion was deliberately neglected and (iii) the setting of the diffractometer was not changed to follow the peak position between 20 and 100 K as mentioned by the authors, we feel that their evidence is not entirely persuasive. As a counterproof, we plot the (333) reflection as a function of temperature from the present data in Fig. 9 ▸. The (333) reflection does not approach zero above 100 K but depends on the different increment of Uiso(Sn) and Uiso(Te) with temperature and on the occupancy of Sn. The increase of the hkl all odd X-ray structure factors with temperature is confirmed if the values of Uiso(Sn) and Uiso(Te) obtained from neutron measurements at HB-3A and TOPAZ reported by Li, Ma et al. (2014 ▸) on a sample with Tc = 42 K are used to calculate the (333) structure factor (Fig. 10 ▸).

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.


Related in: MedlinePlus