68 5.20 (a) Dependence of the lattice constant on the actual Yb content, x, in YbxCo4+ySb12+z; (b) Dependence of the lattice constant on the nominal content of Yb, x, in. The temperature dependence of: (a) electrical resistivity, (b) Seebeck coefficient, (c) thermal conductivity, (e) thermoelectric figure of merit (zT ) are shown in.
LIST OF SYMBOLS AND NOTATIONS
Ξ: scattering parameter for point defect scattering πππππ·π·: point defect scattering relaxation time ππππππ: electron-phonon scattering relaxation time. DOS: density of states JDOS: joint density of states CB2: secondary conduction band ADP: atomic displacement parameter PDOS: partial density of phonon states NIS: nuclear inelastic spectroscopy.
Introduction
- Thermoelectric (TE) materials
- Skutterudites
- Summary of research
- Summary
- Synthesis procedures
- Characterization
- Phase and chemical composition identification
- Transport property characterization
- Optical property characterization
- Ab initio DFT Calculation
The synthesis of single-phase homogeneous skutterudites is a non-trivial task due to the complexity of the equilibrium phase diagram of the Co-Sb binary system. Microstructures of the annealed samples were checked with a ZEISS 1550VP Field Emission Scanning Electron Microscope (SEM).
Electronic origin of high zT in n-CoSb 3 skutterudites
- Summary
- Background introduction
- Results and discussion
- Multiple conduction band behavior in n-CoSb 3
- Linear or kane bands do not increase Seebeck mass
- Band convergence at high temperatures
- Conclusion and future work
A clear demonstration of complex band behavior is seen in the doping-dependent Seebeck coefficient (Pisarenko plot at 300K) shown in Figure 3.1a. In other words, although ππππβ(πΈπΈ) increases with energy in a Kane band, the Seebeck coefficient and ππππβ(πΈπΈ) should actually decrease relative to that of a parabolic figure as shown in Figure 3.2. tape.
Role of filler in thermal transport
Summary
In Section 4.4 some attempts are presented to reveal the underlying mechanisms of the reduction of lattice thermal conductivity in RxCo4Sb12, with the possibility of electron-phonon scattering (Section 4.4.1) and lattice softening (Section 4.4.2).
Complex phonon modes
- Rattling β resonant scattering or avoided crossing
- Point defect scattering
- Electron-phonon scattering
From Figure 4.1 we can see that both the resonance scattering effect (reduction of scattering time ππ(π€π€)) and the effect of avoided crossing on the phonon spectra (reduction of group velocity ππππ2(π€π€) will result in the corresponding reduction of lattice thermal conductivity. In that region, where the electron-phonon scattering dominates, the thermal conductivity of the lattice increases proportionally to the temperature π π πΏπΏβ ππ.
Thermal transport calculation .1 Minimum thermal conductivity .1 Minimum thermal conductivity
- Electronic contribution to thermal conductivity
- Callaway model
According to Slack, the minimum thermal conductivity at high temperatures can also be estimated using the Debye approximation as:. These values ββ(Eq. 4.34 and Eq. 4.35) should serve as a guide in finding a lower lattice thermal conductivity. This is very useful in accessing the role of fillers in reducing lattice thermal conductivity.
The Callaway model is based on a Debye approximation, which allows the lattice thermal conductivity to be calculated as follows: is the boundary scattering relaxation time, which is determined by the speed of sound in the material π£π£π π and the average grain size πΏπΏ. Cf. 4.43) is the Umklapp scattering relaxation time.
Results and discussion
- Possible electron-phonon scattering in R x Co 4 Sb 12
- Lattice softening due to fillers
Thermal conductivity of the lattice versus doping level x with both experimental and calculated results from the Klemens model. The green line shows the modeling results where a) only mass effect is considered and b) both mass and strain effects are considered (Ξππ calculated from Yang's formula, Ξπ π with = 5E5). By subtracting the thermal resistance due to point defect scattering from the mass effect (ignoring the voltage effect due to its small magnitude), we obtain the good linear dependence of the residual thermal resistance on the carrier concentration, shown in Figure 4.5. Cf. 4.46). Thermal resistance due to electron-phonon scattering versus measured Hall carrier concentration in YbxCo4Sb12.
The measured sound velocities as well as the calculated elastic moduli (Eq. 4.47 and Eq. 4.48) and theoretical densities (Eq. 4.50) for this group of ball-milled samples are listed in Table 4.4.
Conclusion and future work
A decreasing linear trend in elastic moduli (both K and G) with doping content xEPMA can be observed in Figure 4.6. The decrease in speed sound velocities with doping is another piece of evidence supporting the avoided crossover mechanism to reduce thermal conductivity through fillers.
Phase diagram studies in n-CoSb 3 skutterudites
Summary
Methodology
The red line shows the temperature dependence of the actual Yb content in the stable composition of skutterudite shown as a red dot (maximum solubility) in Figure 5.4. The blue line shows the temperature dependence of the actual Yb content in the stable skutterudite composition shown as a blue dot in Figure 5.4. For example, if the annealing temperature in the Yb-Co-Sb system is chosen to be 873K, then the nominal composition (red triangles and diamond samples in Figure 5.6) should lie in the three-phase Co-rich region (YbSb2, CoSb2 and YbxCo4Sb12 ).
If the annealing temperature is chosen to be 1023 K, the nominal composition (blue circle pattern in Figure 5.7) should remain in the Sb-rich three-phase region (YbSb2, liquid Sb and YbxCo4Sb12).
Soluble site other than the void .1 Solubility debate of In and Ga .1 Solubility debate of In and Ga
- DFT calculations of In-doped CoSb 3 systems
- Phase diagram study of In-Co-Sb system
- Thermoelectric Properties of In-CoSb 3
- Discussion about In-CoSb 3
Indium content in bold corresponds to the same skutterudite phase composition In0.27Β±0.01Co4Sb11.9 represented by a magenta circular symbol in Figure 5.14b. The proposed phase diagram of the In-containing skutterudites at 873K is shown in Figure 5.14a and is based on general knowledge of the binary phase diagrams. The mixed defect types (complex compound defects) can also lead to a slight change in the direction of the single-phase region (red line) in Figure 5.14b.
This is fully consistent with our band structure calculations shown in Fig. 5.9 and the discussions in Section 5.3.2.
Stable compositions and Vegardβs law
- Solubility debate of Yb
- Skutterudite lattice expansion due to Yb filling
- Stable compositions in ternary phase diagram system
- Vegardβs law in ternary phase diagram system
- Discussion about Yb-CoSb 3
Lattice constants were also plotted against the nominal Yb content to compare with Dilley's data139 in Figure 5.20(b). Here, the Yb content in the schucker terudite phase reaches the maximum filling fraction limit at 873K (red point in Figure 5.4a). The blue dashed line shows another plateau of lattice constant when the nominal composition is in a Sb-rich three-phase region where the schutzterudite phase has a stable composition with a lower Yb content (Yb0.13Co4Sb12, blue point in Figure 5.4a) .
As a result, the Yb content of the skutterudite phase decreases as the nominal composition becomes richer in Sb, which is confirmed by the decrease in the lattice constant in Figure 5.21(b).
Solubility design strategies
- Solubility barrier of Ce in Ce-CoSb 3
- Optimum doping of Ce-CoSb 3 skutterudites
- Ultra-high FFL of Ce in Ce-CoSb 3 skutterudites
- Thermoelectric properties of optimized Ce-CoSb 3 skutterudite
- Discussion about Ce-CoSb 3
This is most likely due to the reported small filling fraction limit x = 0.09 in CexCo4Sb12. Thus, the filling fraction limit of Ce is worth re-examining through solubility design using an equilibrium phase diagram approach. To optimize the thermoelectric properties of Ce singly filled CoSb3 skutterudites, a higher filling fraction of Ce is required.
This solubility design strategy is also applied in the study here for improving the filling fraction limit of Ce in CoSb3: increase the annealing temperature.
Stability of optimized compositions
Ce singly filled schutterudites in previous literature studies have been underdoped and fall out of the high power factor region due to the assumed low filling fraction limit for Ce (x=0.09). In heavily doped SiGe, the precipitation and re-dissolution of dopants during high-temperature transport measurements was also reported165. The speed and size of the precipitates will depend on temperature and time. Reducing the Yb content will also reduce the carrier concentration, which will increase the electrical resistivity of the material.
Despite the formation of impurity phases, the maximum performance of the material may not be dramatically reduced because a lower carrier concentration at low temperature may actually increase the zT at that temperature4.
Conclusion
The temperature-dependent solubility limit predicts the precipitation of impurity phases at intermediate temperatures, as shown schematically in Figure 5.30. Since the optimal carrier concentration corresponds to approximately x = 0.3, Yb0.3Co4Sb12 material above 873K will be stable indefinitely. The Yb0.3Co4Sb12 material will be thermodynamically unstable but kinetically stable at low temperatures because precipitation requires Yb diffusion, which will be low at low temperatures.
In the intermediate temperature range, some precipitation of impurity phases is expected (see more discussion in Chapter 8).
Defect study in intrinsic CoSb 3
- Summary
- Literature study
- Bonding chemistry of CoSb 3
- Results and discussion
- Phase width of CoSb 3
- Defect type in intrinsic CoSb 3
- Conclusion and future work
Liu et al31 then studied the effect of Sb compensation on the point defects of CoSb3. The secondary Sb phase for the nominal composition Co4Sb12 (as seen in Fig. 6.4b) disappears after hot pressing in Fig. 6.3 (there is no Sb peak in the green curve), which is consistent with previous findings34. Combining all the information collected at each temperature, a rough estimate of the temperature-dependent phase width of CoSb3 can be shown in Figure 6.9.
The excess Ni impurity doping as well as the possible influence of hot pressing can change the intrinsic defect type of CoSb3.
Phase diagram study of Ce-Fe-Co-Sb quaternary system
- Summary
- Charge-compensating defects
- Phase space of Ce y Co x Fe 4-x Sb 12 skutterudites at 700 β
- n-p change in Ce y Co 3.25 Fe 0.75 Sb 12 materials
- Conclusion and future work
As can be seen from the phase diagram in Figure 7.8 below, the phase region changes as the amount of substitutional Fe increases. However, for sample no. 7 observed a small amount of skutterudite phase Co4-xFexSb12 (see Fig. 7.10f), while we expect a single-phase region (Co, Fe)Sb2. This must be the result of a shift in composition during synthesis, as can be seen from the resulting phase diagram in Figure 7.11.
Based on the results of phase identification and composition analysis, the experimental isothermal section of the ternary Co-Fe-Sb system is determined, as shown in Figure 7.11.
Nano-structuring in bulk skutterudites
Summary
Experimental results
For each composition, samples held for different precipitation times at 600 β were different pieces cut from the same homogenized (at 750 β) bar, so the only variable is the precipitation time. According to the lever rule, when the precipitation temperature decreases, for the same initial composition, the amount of secondary phases will increase, which will also facilitate our experimental observation. However, the homogenization temperature should not exceed the peritectic temperature of CoSb3 (874β), nor should the precipitation temperature be too low so that kinetics prevent the precipitation from actually happening.
Although the effective distribution length for precipitates in skutterudite is not entirely clear167, the observed precipitate size is much larger if we aim for nanoscale precipitates in general, and thus a smaller increase in precipitation time and or a lower precipitation temperature. .
Conclusion and future work
Furthermore, the size of the precipitate after 3 days of precipitation is on the order of 2β10 micrometers. Most of the precipitates observed are the YbSb2 phase, while the CoSb2 phase is rare. No grain precipitation is observed, which is reasonable due to the high degree of defects along the grain boundaries and the lower energy barrier.
Future work
The study of the phase diagram of the quaternary system Ce-Co-Fe-Sb is mostly done, with the phase space of skutterudites at the stoichiometric section (Co+Fe):Sb = 1:3 determined at 700 β. In order to enable the discovery of optimal compositions for p-type thermoelectric skutterudites, carrier concentration mapping of samples synthesized in the skutterudite phase space is required. Nanostructuring by secondary phase precipitation in skutterudites shows some promise, but more effort is needed to engineer the amount and size of these precipitates so that they are effective in lowering the lattice thermal conductivity.
It can not only serve as a reference to elucidate the advantages of nano-precipitates on thermal transport, but is also enlightening in the defect study of intrinsic CoSb3.
From Boltzmann Transport Equation to Thermoelectric Properties 182-184
Normally it is assumed that the distribution function is not too far from equilibrium, so for simplicity we can replace and with and. As shown in Table A.1, the external force is the electric field E and the temperature gradient is βT 0 (no electric current at equilibrium). So we have the expression for electrical conductivity with the assumption that there is only one predominant scattering mechanism.
The derivation of the Hall coefficient RH is similar to that of electrical conductivity except with a different force F= -eE-evΓH.
TE properties from SPB model with acoustic phonon scattering
TE properties from SPB model in non-degenerate and degenerate limit
TE properties from a multi-band model
Mott relation for SPB and SKB with acoustic phonon scattering
Thermoelectric properties of Ni-doped n-type Ba[sub 0.3]Co[sub 4]Sb[sub 12] filled skutterudite. High-temperature thermoelectric properties of Co4Sb12-based Skutterudites with multiple filler atoms: Ce0.1InxYbyCo4Sb12. Synthesis and high-temperature transport properties of barium- and indium-doped double skutterudites BaxInyCo4Sb12βz.
Synthesis and thermoelectric properties of p- and n-type filled skutterudite R[sub y]M[sub x]Co[sub 4βx]Sb[sub 12](R:Ce,Ba,Y;M:Fe ,Ni) .
