Supplementary Information
Thermoelectric performance enhancement in n-type Bi2(TeSe)3 alloys by nanoscale inhomogeneity combined with spark plasma textured microstructure
Yu Pan, Jing-Feng Li*
State Key Laboratory of New Ceramics and Fine Processing,
School of Materials Science and Engineering, Tsinghua University,
Beijing 100084, China.
E-mail: ;
Fax: +86-62771160;
Tel: +86-10-62784845.
Table S1 Calculated Lorenz number.
Temperature / no TP / TP 400 / TP 460 / TP 480 / TP 500323 K / 1.728 / 1.698 / 1.701 / 1.729 / 1.736
348 K / 1.716 / 1.687 / 1.685 / 1.718 / 1.725
373 K / 1.701 / 1.675 / 1.674 / 1.704 / 1.709
398 K / 1.689 / 1.666 / 1.663 / 1.692 / 1.693
423 K / 1.679 / 1.656 / 1.655 / 1.683 / 1.685
448 K / 1.671 / 1.650 / 1.649 / 1.673 / 1.674
473 K / 1.666 / 1.646 / 1.645 / 1.666 / 1.669
498 K / 1.663 / 1.646 / 1.643 / 1.662 / 1.662
523 K / 1.662 / 1.646 / 1.645 / 1.661 / 1.662
548 K / 1.664 / 1.651 / 1.650 / 1.662 / 1.665
573 K / 1.672 / 1.662 / 1.661 / 1.669 / 1.667
The Lorenz numberL is calculated according to equation (1), in whichscattering parameter is selected as -0.5 for dominant acoustic phonon scattering mechanism,1
(1)
where Fj donates the Fermi integration
(2)
The reduced Fermi energy can be derived from the Seebeck coefficient on the basis of single band approximation,
(3)
Figure S1Specific heat of the samples, with referencevalues 2, 3 for comparison.
Note that although the measured Cp values is slightly lower than the values of Dulong-Petit law, the conclusion that texture treatment at 733 K could improve ZTis still safe, which benefits from texture-enhanced electrical properties and nanoscopic defects suppressed thermal conductivity.As all the samples share the same Cp values with unchangedchemical composition.
Figure S2(a) Thermal conductivity of TP 460 at low temperatures (4-323 K), thesolid red lineis are calculated fromDebye approximation. (b) Frequency dependence of thermal conductivity considering Umklapp-process scattering (U), grain boundary scattering (GB), electron-phonon scattering (E)and point defect scattering (PD).
The magnitudes of A, B and C were determinedby fitting the data of low temperature (4-323 K) dependence thermal conductivityvia Debye approximation:4
(4)
FigureS2(a) shows that the low temperature thermal conductivities arewell fitted and parameters A, B, C are hence determined. With all the parameters confirmed, FigureS2 (b) illustrates the frequency dependence of the lattice thermal conductivity using Callawaymodel:5
(5)
The contribution of Umklapp-process, boundary scattering, point defect scattering andelectron-phonon scattering is taken into account, as visualized by the lines with different colors (grey, green, blue and red). Consequently, the thermal conductivity can be judged from the area beneath the red curve. Extra phonons scattering mechanism thateffectively reduces the thermal conductivity would further shrink this area.
As measuring principle of PPMS and diffusivity is different, it is difficult to avoid the inconsistency of the data between the two methods. Although the measuring data of the PPMS may be somewhat inaccurate, but we only used it for modeling. The calculation of the thermal conductivity and ZT values at higher temperatures adopts the diffusivity results and the analysis in the manuscript is reliable.
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