Low lattice thermal conductivity suppressed by Sr-deficiency in Sr0.9Ca0.1Si2

Low lattice thermal conductivity suppressed by Sr-deficiency in Sr0.9Ca0.1Si2 C. S. Lue,1 Y. S. Tseng,1 J. Y. Huang,2 H. L. Hsieh,2 H. Y. Liao,3 and Y. K. Kuo3,a 1Department of Physics, National Cheng Kung University, Tainan 70101, Taiwan 2New Material Research & Development Department, China Steel Corporation, Kaohsiung, 81233, Taiwan 3Department of Physics, National Dong Hwa University, Hualien 97401, Taiwan

FIG. 1. Powder x-ray diffraction patterns for the Sr 0.9-δ Ca 0.1 Si 2 alloys.The major diffraction peaks can be indexed according to the space group P4 3 32.A minor impurity peak arising from the P-3m1 phase is indicated by the asterisk.and naturally abundant elements in the earth's crust.Recently, we found that the room-temperature Seebeck coefficient of 10% Ca substituted SrSi 2 (Sr 0.9 Ca 0.1 Si 2 ) is about 225 μV/K, nearly a factor of two larger than that of the parent compound SrSi 2 . 14Such an enhancement in the Seebeck coefficient leads to a considerably high thermoelectric power factor, S 2 /ρ ∼ 2.7 × 10 −3 W/m-K 2 for Sr 0.9 Ca 0.1 Si 2 .However, one of the challenges which still remain is to reduce the lattice thermal conductivity for further improvement on their thermoelectric performance.In this work, we report on a substantial decrease of the thermal conductivity (κ) in the Sr-deficient Sr 0.9-δ Ca 0.1 Si 2 alloys with the deficient level δ ≤ 0.2.Remarkably, a considerably low thermal conductivity of 1.67 W/m-K at room temperature is achieved for sample with Sr deficient level of δ = 0.13.As a result, a relatively high ZT value up to 0.27 is obtained for Sr 0.77 Ca 0.1 Si 2 .
3][14][15] Mixture of high-purity elemental metals of the corresponding samples were placed in a water-cooled copper crucible and then melted several times in an argon arc-melting furnace.The weight loss during melting is less than 1% for each compound.To promote homogeneity, the ingots of the samples were annealed in a vacuum-sealed quartz tube at 800 • C for three days, and followed by furnace cooling.Room-temperature x-ray analysis taken on powder specimens of Sr 0.9-δ Ca 0.1 Si 2 with Cu Kα radiation is consistent with the cubic crystal structure with space group P4 3 32, [17][18][19] as shown in Fig. 1.A tiny peak marked by the asterisk arises from the diffraction plane of (011) of the impurity phase of P-3m1 space group and the intensity of the peak becomes stronger with increasing the Sr deficient level.However, such a minor impurity phase is not likely to affect the thermoelectric properties of the Sr 0.9-δ Ca 0.1 Si 2 system.
The temperature dependence of the electrical resistivity, ρ(T), for the Sr 0.9-δ Ca 0.1 Si 2 alloys is illustrated in Fig. 2. The magnitude of the electrical resistivity of Sr 0.9-δ Ca 0.1 Si 2 does not show a systematic trend with increasing the Sr deficient level.In general, the increase in Sr deficiency has an effect to lower the magnitude of ρ.The room-temperature ρ varying from 0.8 to 2 m -cm have been observed for these alloys.At lower temperatures, the temperature coefficient of resistivity (TCR) is found to be negative, indicative of a strong disordered nature for the electrical transport in these alloys.It is worthwhile mentioning that the exception of Sr 0.77 Ca 0.1 Si 2 (δ = 0.13) specimen exhibits a semiconducting-like behavior with a negative TCR above 220 K.As a consequence, ρ < 1 m -cm can be reasonably estimated for T > 600 K, advantageous for obtaining high ZT at elevated temperatures.
Figure 3 shows the Seebeck coefficient as a function of temperature for the Sr 0.9-δ Ca 0.1 Si 2 alloys.For each individual composition, the Seebeck coefficient develops a broad maximum below  120 K.This feature has been attributed to the contribution of the thermally excited electrons across the gap or pseudogap. 20The positive sign of S of these materials suggests that the hole-type carriers dominate the thermoelectric transport, consistent with a hole pocket in the vicinity of the Fermi level between G and R points of the electronic structure. 20As mentioned, the room-temperature S of 225 μV/K for Sr 0.9 Ca 0.1 Si 2 has been observed, 14 the highest one among those of the SrSi 2 -based alloys investigated so far.Upon increasing the Sr deficient level in Sr 0.9 Ca 0.1 Si 2 , S gradually reduces to the values between 120 and 145 μV/K.From the stoichiometry point of view, the Sr deficiency is equivalent to the decrease in the number of the hole carriers.This would modify the electronic band structure of Sr 0.9 Ca 0.1 Si 2 and consequently lead to the reduction of both electrical resistivity and Seebeck coefficient.While the decrease in the magnitude of S is unfavorable for achieving high thermoelectric performance, the moderate drop in S with temperature could still yield an increasing trend for the ZT value at high temperatures.For instance, the magnitude of S of Sr 0.77 Ca 0.1 Si 2 is expected to be larger than that of Sr 0.9 Ca 0.1 Si 2 as T > 600 K, since the latter shows a rapid decrease in S with raising temperature.
The most remarkable aspect of these Sr 0.9-δ Ca 0.1 Si 2 samples is the result of the thermal conductivity, as shown in Fig. 4(a).For each individual composition, the κ value exhibits a maximum in the temperature range between 30 and 80 K.This is a typical feature for the reduction in thermal scattering in solids at low temperatures.It is promising that the room-temperature κ drops substantially with increasing the Sr deficient level in Sr 0.9 Ca 0.1 Si 2 .It should be noted that our previous attempts on the suppression of κ by alloying other elements in SrSi 2 has only a marginal effect on the reduction of κ to a value of about 5 W/m-K. 12,14 n this study, however, a significantly low κ of 1.67 W/m-K at room temperature is obtained for Sr 0.77 Ca 0.1 Si 2 .Such an observation clearly demonstrates that the thermal conductivity can be effectively suppressed by introducing lattice imperfections in the Sr 0.9 Ca 0.1 Si 2 system.
In principle, the total thermal conductivity for ordinary metals or semimetals is a sum of electronic and lattice thermal conductivities.The electronic thermal conductivity (κ e ) can be evaluated using the Wiedemann-Franz law κ eρ /T = L o , where ρ is the measured dc electrical resistivity and L o = 2.45 × 10 −8 W /K 2 is the Lorentz number.The lattice thermal conductivity κ l can be thus obtained by subtracting κ e from the observed κ.We thus decomposed the contributions from κ e and κ l for Sr 0.77 Ca 0.1 Si 2 , and the result is displayed in Fig. 4(b).It is clear that the slight upturn of κ above 230 K is mainly due to the increase of κ e upon heating.This estimation also reveals a low κ l of about 1.1 W/m-K at room temperature.Hence, it is instructive that the phonon scattering can be effectively enhanced by lattice imperfections in this material.
According to the Debye model, the lattice thermal conductivity of crystalline solids depends mainly on the combination of three scattering mechanisms, i.e., the scattering between phonons and grain-boundary, phonons and point defect, and phonon-phonon Umklapp scattering.Generally, the grain boundary scattering is a dominant mechanism for the low-temperature lattice thermal conductivity and phonon-phonon Umklapp scattering is usually activated at high temperatures; however, the point-defect scattering on the other hand has a strong influence on the appearance of the shape and position of the low-temperature phonon peak.It is clearly seen that the shape and position of the phonon peak vary drastically in these alloys; we hence conclude that the point defect scattering is likely to be the predominant mechanism for the strong phonon scattering that leads to the observed reduction in κ l .The fact that the Sr 0.77 Ca 0.1 Si 2 alloy has the lowest κ l together with a relative weak phonon peak feature in compared to other Sr-deficient samples is in support of this scenario.The obtained small κ l of Sr 0.77 Ca 0.1 Si 2 is comparable to those of other high-ZT materials.2][23] Furthermore, with extrapolating data to high temperatures, the value of κ l less than 1 W/m-K can be realistically expected for Sr 0.77 Ca 0.1 Si 2 as T > 500 K.
Figure 5 shows the evaluated ZT value as a function of temperature for these Sr 0.9-δ Ca 0.1 Si 2 alloys.A highest room-temperature ZT of about 0.27 is achieved for the Sr 0.77 Ca 0.1 Si 2 specimen, about five times larger than that of stoichiometric SrSi 2 .Moreover, it is clearly seen that ZT tends to increase rapidly with raising temperature for Sr 0.77 Ca 0.1 Si 2 .A realistic extrapolation of the ρ, S, and κ data to high temperatures yields a possible maximum ZT ∼ 0.52 at 850 K for this material.Such a promising result is mainly associated with the significant suppression in κ through introducing  Sr-deficiency in Sr 0.9 Ca 0.1 Si 2 , demonstrating that the thermoelectric performance can be effectively improved with a suitable Sr deficient level in the Sr 0.9-δ Ca 0.1 Si 2 system.Such a simple scenario may also be applicable to other thermoelectric systems for enhancing their ZT value by introducing lattice imperfection.
In conclusion, efforts to employ Sr deficiency for the enhancement of phonon scattering have been found to be quite effective to reduce the lattice thermal conductivity of Sr 0.9 Ca 0.1 Si 2 .In particular, a low lattice thermal conductivity of 1.1 W/m-K and a relatively high ZT of 0.27 at room temperature are accordingly achieved for Sr 0.77 Ca 0.1 Si 2 with such a viable strategy.It thus indicates that the Sr 0.9-δ Ca 0.1 Si 2 system represents a good opportunity for improving its ZT, making this system attractive for possible candidates for developing highly efficient thermoelectrics.

FIG. 4 .
FIG. 4. (a)Temperature variation of the total thermal conductivity for the Sr 0.9-δ Ca 0.1 Si 2 alloys.The room-temperature κ value shows a substantial reduction as compared to that of Sr 0.9 Ca 0.1 Si 2 .A lowest room-temperature κ of about 1.67 W/m-K is achieved for δ = 0.13.(b) Total, lattice, and electronic thermal conductivity of Sr 0.77 Ca 0.1 Si 2 between 10 and 300 K.A low κ l value of approximately 1.1 W/m-K at 300 K for δ = 0.13 is estimated.