Debye-Callaway Model Research Articles

Electronic and phonon contributions to the Thermoelectric properties of newly discovered half-Heusler alloys XHfPb (X= Ni, Pd, and Pt)

In this work we calculate the thermoelectric figure of merit of XHfPb (X= Ni, Pd, and Pt) by computing the both the power factor and the lattice thermal conductivity by first principles. We make reasonable approximations: we use the Constant Relaxation Time Approximation (CRTA) to compute the electron transport contribution and the modified Debye–Callaway model to calculate the thermal lattice conductivity. We also report the dielectric properties of these semiconductors and the mode Grüneisen parameters. Not surprisingly we find that the average Grüneisen coefficient correlates with the thermal conductivity. Next, we consider a realistic relaxation time τ and carrier concentration n from experimental data on ZrHfPb and obtain the figure of merit ZT as a function of temperature. Our main finding is that despite the Pt is isoelectronic with Ni and Pd, the ZT of PtHfPb is larger and behaves differently from the other two materials, suggesting that PtHfPb is better suited for high temperature thermoelectric generators.

Role of lattice thermal conductivity in thermoelectric properties of chalcopyrite-type antimonides XSiSb2 (X = Mg, Be): A DFT insight

The widely available low-cost materials with high performance acts as a great choice for thermoelectric energy conversion applications. Here, the thermoelectric properties of two environmentally friendly chalcopyrites namely, MgSiSb2 and BeSiSb2 with tetragonal crystal structure, is investigated systematically. With the help of first principles combined with Boltzmann transport equations and modified Debye-Callaway model, electronic and thermal transport properties are studied. From electronic structures, it is inferred that both the chalcopyrites falls under semiconducting region with narrow band gap. The phonon dispersions suggest that these antimonides are thermodynamically stable with strongly coupled acoustic and optical mode of vibrations. Moreover, MgSiSb2 has high figure of merit (zT) of 2.06 (n = 1 × 1020 cm−3) with ultralow lattice thermal conductivity (kL) of 1.01 W m−1 K−1 at 900 K, whereas, BeSiSb2 has low zT of 0.23 due to its larger kL. Besides, these results demonstrate that this prediction can pave the way for experimental explorations.

Thermal conduction in titanium-chromium oxide natural superlattices with an ordered arrangement of nearly pristine interfaces

Thermal conduction was investigated in titanium-chromium oxide natural superlattices with an ordered arrangement of crystallographic shear planes, which were nearly pristine interfaces for thermal phonons. Thermal conductivity exhibited a clear maximum value at around 50 K, which indicates interface roughness as small as 20 pm based on the calculation of thermal conductivity by a modified Debye-Callaway model. With an ordered arrangement of nearly pristine interfaces at nanoscale, the wave contribution to phonon transport was estimated to be predominant at lower temperatures (less than 100 K) and as much as 30 % even at room temperature. We found that the interface roughness greatly influences the thermal conduction in natural superlattice systems, which may lead to variations in the reported value of thermal conductivity. We have demonstrated that the wave contribution of thermal conductivity become apparent in bulk crystal having nano scale periodic structure with pristine interfaces.

Diagonal and off-diagonal thermal conduction with resonant phonon scattering in Ni3TeO6

The coupling between phonon and magnon is ubiquitous in magnetic materials and plays a crucial role in many aspects of magnetic properties, most notably in spintronics. Yet, this academically and technologically interesting problem still poses a severe challenge to a general understanding of the issue in certain materials. We report that Ni3TeO6 exhibits clear evidence of significant magnon-phonon coupling in both longitudinal thermal conductivity ($\kappa_{xx}$) and thermal Hall coefficient ($\kappa_{xy}$). The Debye-Callaway model, a phenomenological description for phonon heat conduction, can explain the measured magnetic field dependence of $\kappa_{xx}(H)$: phonon scattering from spin fluctuation in the paramagnetic phase and additional scattering due to magnon-phonon coupling in the collinear antiferromagnetic phase. We further suggest that a similar approach could be applied to understand the finite $\kappa_{xy}$ values in $Ni_3TeO_6$.

Vacancy-induced heterogeneity for regulating thermoelectrics in n-type PbTe

The fact that the thermoelectric performance is far inferior to that of p-type PbTe has inspired many strategies to develop n-type PbTe thermoelectrics. Alloying PbS in n-type PbTe effectively changes the shape of a valley to trigger a heavier conduction band for improving the Seebeck coefficient, while the resulting small orbital overlap inevitably leads to phase separation hindering electron transport. The effect of vacancies on the solubility of sulfur in n-type PbTe is ambiguous; especially, the heterostructure due to phase separation in high-content PbS-alloyed PbTe also requires sufficient modification to optimize the electroacoustic transport. This motivates the current work on the introduction of vacancies by charge-balancing doping via Sb2Te3 and discovers striking new insight that the introduced vacancies can induce a new heterostructure of Pb2Sb2S5 and suppress the aggregation of Sb and PbS in high-solubility n-type PbTe–PbS. The modification of the band structure and optimization of the electron transport give rise to a prominent enhancement in electronic performance. Furthermore, the Debye–Callaway model validates the dramatic contribution of vacancy aggregation and heterostructures to lattice thermal conductivity. As a result, the synergistic modulation of electroacoustic characteristics achieves a significant improvement in both the maximum zT and the near-room-temperature zT. Understanding such unique findings is critical for applicability to other thermoelectric materials.

Thermal decay in the one-dimensional transient thermal grating experiment using modified Debye-Callaway model

We calculate the thermal decay in the one-dimensional transient thermal grating (TTG) experiment by solving the transient Boltzmann-Peierls transport equation (BPTE) within the framework of the single-mode relaxation time approximation and using modified Debye-Callaway model in which both longitudinal and transverse phonon modes are included explicitly. We consider surface heating of an opaque thick semiconductor (SC) crystal film that we assume to have a cubic symmetry and is treated as a continuum, elastic, isotropic, and dispersionless medium. We obtain a nonuniversal spectral suppression function (SSF) in the integrand of the effective apparent thermal conductivity that is similar to the one obtained by Chiloyan et al. [Phys. Rev. B 93, 155201 (2016)] using the standard single-mode relaxation time approximation (RTA) model. Therefore, the nonuniversal character of the SSF in the TTG experiment does not depend on the form of the collision operator approximation in the BPTE: Callaway's or standard. Moreover, the analysis of the behavior of the thermal decay rate shows how the peculiar crystal momentum shuffling effect of phonon-phonon scattering Normal processes (N processes) that is captured by Callaway's model influences the onset of the nondiffusive (quasiballistic) regime in the phonon transport process in SC crystals. This effect tends independently from the other phonon scattering processes to favor the maintenance of the phonon diffusive regime over a large length-scale range, a remarkable feature that cannot be put into light with the standard RTA model used in previous works. Hence, the implicit effect of N processes has certainly an important impact on the extraction of the phonon mean-free path spectrum distribution, especially in the high-temperature regime.

Thermoelectric properties of a series of polycrystalline Mo(Se1−xTex)2

AbstractTransition metal dichalcogenides have being actively studied on the account of their large density‐of‐state effective mass and low lattice thermal conductivity. Herein, thermoelectric and electrical transport properties of MoSe2–MoTe2 system are investigated. A series of Mo(Se1−xTex)2 (x = 0, .25, .5, .75, and 1) polycrystalline samples was synthesized by conventional solid‐state reaction. Single hexagonal phase was identified for each sample without secondary phase, confirming the formation of complete solid solutions between MoSe2 and MoTe2. The electrical conductivity and magnitude of the Seebeck coefficient increased simultaneously with increasing Te content x at high temperatures, with the power factor following the same trend. As results, the MoTe2 sample exhibited the maximum power factor of .014 mW/(m K2) at 823 K. The lattice thermal conductivities of the alloyed samples (x = .25, .5, and .75) significantly decreased compared to MoSe2 and MoTe2 owing to point defect phonon scattering via anion substitution, which is verified by the Debye–Callaway model. A maximum zT of .0044 was obtained for MoTe2 sample at 773 K; however, the calculated quality factor B values of the samples with x = .75 and 1 at 773 K were almost identical, suggesting that a further enhancement of zT can be achieved by optimizing an nH of the Mo(Se0.25Te0.75)2 sample.

Electron delocalization enhances the thermoelectric performance of misfit layer compound (Sn1−x Bi x S)1.2(TiS2)2

The misfit layer compound (SnS)1.2(TiS2)2 is a promising low-cost thermoelectric material because of its low thermal conductivity derived from the superlattice-like structure. However, the strong covalent bonds within each constituent layer highly localize the electrons thereby it is highly challenging to optimize the power factor by doping or alloying. Here, we show that Bi doping at the Sn site markedly breaks the covalent bonds networks and highly delocalizes the electrons. This results in a high charge carrier concentration and enhanced power factor throughout the whole temperature range. It is highly remarkable that Bi doping also significantly reduces the thermal conductivity by suppressing the heat conduction carried by phonons, indicating that it independently modulates phonon and charge transport properties. These effects collectively give rise to a maximum ZT of 0.3 at 720 K. In addition, we apply the single Kane band model and the Debye–Callaway model to clarify the electron and phonon transport mechanisms in the misfit layer compound (SnS)1.2(TiS2)2.

Enhanced Thermoelectric Performance in Oxide Composites of La and Nb Codoped SrTiO3 by Using Graphite as the Electron Mobility Booster.

Inherent insulating nature of oxides makes it challenging for use in thermoelectric applications that warrant reasonable electrical conductivity. In the present work, we have used graphite (G) to improve the electron transport in La0.07Sr0.93Ti0.93Nb0.07O3 (LSTN) by making composites. Graphite acts as the electron momentum booster in the LSTN matrix, which otherwise suffers from Anderson localization of electrons, causing an order of magnitude increase in weighted mobility and electrical conductivity. As a result, the thermoelectric power factor increases more than 6 times due to graphite incorporation in LSTN. Furthermore, the lattice thermal conductivity is suppressed due to enhanced Umklapp scattering, as derived from the Debye-Callaway model. Hence, we have recorded ∼423% increment in the figure of merit (ZT) in LSTN + G composites. The maximum ZT obtained is 0.68 at 980 K for the LSTN with 1 wt % graphite composite. Furthermore, we have fabricated a four-legged n-type thermoelectric power generator demonstrating a milliwatt level power output, which hitherto remained unattainable for oxide thermoelectrics.

Enhanced thermoelectric performance of Hafnium free n-type ZrNiSn half-Heusler alloys by isoelectronic Si substitution

In this work, cheap element Si is added into Hafnium-free ZrNiSn half-Heusler (HH) compound to reduce its lattice thermal conductivity. We report a comprehensive analysis of the isoelectronic Si substitution on the electrical and thermal conductivity for ZrNiSn half-Heusler alloys. The first-principles calculations show that Si doping has a negligible effect on the electronic structure of ZrNiSn1-xSix HH materials. The band gap of 0.48 eV for ZrNiSn sample is compared to that of 0.49 eV for Zr27Ni27Sn26Si. The transmission electron microscopy (TEM) images display the nano structure in the ZrNiSn0.98Si0.02 sample, which strongly affects the lattice thermal conductivity. The contribution of point defect scattering by Si substitution on the lattice thermal conductivity is quantitatively analyzed by using Debye-Callaway model, suggesting that the strain fluctuation is the main factor to reduce lattice thermal conductivity. Finally, the maximum zT value reaches 0.78 at 873 K for the ZrNiSn0.98Si0.02 sample.

Pressure-driven thermoelectric properties of defect chalcopyrite structured ZnGa2Te4: ab initio study.

The pressure induced structural, electronic, transport, and lattice dynamical properties of ZnGa2Te4 were investigated with the combination of density functional theory, Boltzmann transport theory and a modified Debye–Callaway model. The structural transition from I4̄ to I4̄2m occurs at 12.09 GPa. From the basic observations, ZnGa2Te4 is found to be mechanically as well as thermodynamically stable and ductile up to 12 GPa. The direct band gap of 1.01 eV is inferred from the electronic band structure. The quantitative analysis of electron transport properties shows that ZnGa2Te4 has moderate Seebeck coefficient and electrical conductivity under high pressure, which resulted in a large power factor of 0.63 mW m−1 K−2 (750 K). The ultralow lattice thermal conductivity (∼1 W m−1 K−1 at 12 GPa) is attributed to the overlapping of acoustic and optical phonon branches. As a result, the optimal figure of merit of 0.77 (750 K) is achieved by applying a pressure of 12 GPa. These findings support that ZnGa2Te4 can be a potential p-type thermoelectric material under high pressure and thus open the door for its experimental exploration.

High-performance in n-type PbTe-based thermoelectric materials achieved by synergistically dynamic doping and energy filtering

The development of n-type high-performance PbTe thermoelectric materials for matching its p-type counterparts is an urgent matter to expand its practical applications. Here, we introduce Ag2Te into n-type Pb0.975Cr0.025Te for achieving a high peak figure of merit of 1.5 at 773 K. Such a high value is attributed to the synergistic optimization of carrier and phonon transports by Ag2Te introducing and the dynamic doping of Ag. From the detailed structure and property analysis, we found that Ag2Te nanoprecipitates establish coherent interfaces and hence potential barriers with the matrix to induce energy-dependent carrier scattering and maintain relatively high carrier mobility, leading to an optimal electrical-transport properties over a wide temperature range. Moreover, we employ comprehensive electron microscopy investigations and approximate Debye-Callaway model to reveal the origin of the significantly reduced lattice thermal conductivity in Ag2Te-alloyed Pb0.975Cr0.025Te. The strategies used here provide an effective method for designing high-performance thermoelectric material systems.

Enhancing Thermoelectrics for Small-Bandwidth n-Type PbTe-MnTe Alloys via Balancing Compromise.

Small-bandwidth n-type PbTe-MnTe alloys effectively modify the valley shape, while it also inevitably aggravates the deterioration of carrier mobility as nonpolar phonons dominate the scattering. It is found that a trace amount of Cu doping can alleviate the compromises among thermoelectric parameters, thereby significantly optimizing the electrical-transport performance near room temperature of n-type PbTe-MnTe alloys. The single-Kane model reveals that the physical origin of performance improvement lies in the carrier mobility enhancement and self-optimization of carrier concentration. The Debye-Callaway model further quantifies the contribution of copper defect scattering to the lattice thermal conductivity. Notably, the high thermoelectric quality factor obtained in this work rationalizes their superior properties and reveals immense potential for achieving higher zT. Herein, an extremely high zT of ∼0.52 at room temperature and a maximum zTmax of ∼1.2 at 823 K are achieved in 0.3% Cu-intercalated n-type PbTe-MnTe. The mechanism in balancing compromise elaborated in principle contributes to an improvement of thermoelectric properties of the n-type PbTe alloys in a broad temperature range.

Advancing thermoelectrics by vacancy engineering and band manipulation in Sb-doped SnTe–CdTe alloys

A decrease in valence band energy offset can considerably improve the thermoelectric performance of SnTe, and alloying CdTe in SnTe has been confirmed to be efficient for inducing band convergence. However, the low solubility of CdTe in SnTe severely limits the further decrease in the energy offset and the reduction of lattice thermal conductivity. Inspired by the high solubility of Sb in SnTe-based thermoelectric materials, the trivalent Sb is introduced into SnTe–CdTe alloys, aiming at manipulating the thermoelectric transport properties. Combined with the valence band model, it is demonstrated that high concentration of Sb in SnTe–CdTe enables a further optimization in valence band structures, resulting in an improvement in density-of-state effective mass, thus significantly reinforces the power factor in the whole temperature range. Meanwhile, we propose the solid solution mode of Sb in SnTe, which always generates vacancies to balance the valence state, and the introduction of vacancies explains the reduced lattice parameters and almost constant carrier concentration. Particularly, the Debye–Callaway model quantitatively compares the contribution of Sb substitutional defects and vacancy defects. As a result, an enhanced zT of ∼1.1 has been achieved for Sn0.83Cd0.05Sb0.12Te at 823 K. This work clearly shows the critical role of Sb for enhancing the thermoelectric performance of SnTe–CdTe materials.

Optimization of the Intrinsic Electrical and Thermal Transport Properties of Sb2Si2Te6 via Tensile Strain: A First-Principles Study

A promising thermoelectric material, Sb2Si2Te6, which has an intrinsically low thermal conductivity and a considerable figure of merit (ZT) of 1.08 at 823 K, was recently reported. In this work, we study the effect of strain on the electronic structure and electrical transport performance of Sb2Si2Te6 via density-functional calculations. When the out-of-plane tensile strain is applied, the Seebeck coefficient of p-type Sb2Si2Te6 increases due to the flattened electronic dispersion near the valence band edge and the larger DOS effective mass. An enhancement of the power factor along the out-of-plane direction of strained p-type Sb2Si2Te6 is observed in a wide range of carrier concentrations. Meanwhile, the change of lattice thermal conductivity of strained Sb2Si2Te6 is estimated by the modified Debye–Callaway model. The lattice thermal conductivity of Sb2Si2Te6 decreases under out-of-plane tensile strain due to the smaller phonon group velocities and larger Grüneisen parameters.

Thermal Conductivity of β-Phase Ga2O3 and (AlxGa1-x)2O3 Heteroepitaxial Thin Films.

Heteroepitaxy of β-phase gallium oxide (β-Ga2O3) thin films on foreign substrates shows promise for the development of next-generation deep ultraviolet solar blind photodetectors and power electronic devices. In this work, the influences of the film thickness and crystallinity on the thermal conductivity of (2̅01)-oriented β-Ga2O3 heteroepitaxial thin films were investigated. Unintentionally doped β-Ga2O3 thin films were grown on c-plane sapphire substrates with off-axis angles of 0° and 6° toward ⟨112̅0⟩ via metal-organic vapor phase epitaxy (MOVPE) and low-pressure chemical vapor deposition. The surface morphology and crystal quality of the β-Ga2O3 thin films were characterized using scanning electron microscopy, X-ray diffraction, and Raman spectroscopy. The thermal conductivities of the β-Ga2O3 films were measured via time-domain thermoreflectance. The interface quality was studied using scanning transmission electron microscopy. The measured thermal conductivities of the submicron-thick β-Ga2O3 thin films were relatively low as compared to the intrinsic bulk value. The measured thin film thermal conductivities were compared with the Debye-Callaway model incorporating phononic parameters derived from first-principles calculations. The comparison suggests that the reduction in the thin film thermal conductivity can be partially attributed to the enhanced phonon-boundary scattering when the film thickness decreases. They were found to be a strong function of not only the layer thickness but also the film quality, resulting from growth on substrates with different offcut angles. Growth of β-Ga2O3 films on 6° offcut sapphire substrates was found to result in higher crystallinity and thermal conductivity than films grown on on-axis c-plane sapphire. However, the β-Ga2O3 films grown on 6° offcut sapphire exhibit a lower thermal boundary conductance at the β-Ga2O3/sapphire heterointerface. In addition, the thermal conductivity of MOVPE-grown (2̅01)-oriented β-(AlxGa1-x)2O3 thin films with Al compositions ranging from 2% to 43% was characterized. Because of phonon-alloy disorder scattering, the β-(AlxGa1-x)2O3 films exhibit lower thermal conductivities (2.8-4.7 W/m·K) than the β-Ga2O3 thin films. The dominance of the alloy disorder scattering in β-(AlxGa1-x)2O3 is further evidenced by the weak temperature dependence of the thermal conductivity. This work provides fundamental insight into the physical interactions that govern phonon transport within heteroepitaxially grown β-phase Ga2O3 and (AlxGa1-x)2O3 thin films and lays the groundwork for the thermal modeling and design of β-Ga2O3 electronic and optoelectronic devices.

Phonon heat conduction in Al1-xScxN thin films

Aluminum scandium nitride (Al1-xScxN) is regarded as a promising material for high-performance acoustic devices used in wireless communication systems. Phonon scattering and heat conduction processes govern the energy dissipation in acoustic resonators, ultimately determining their performance quality. This work reports on phonon scattering processes and thermal conductivity in Al1-xScxN alloys grown by molecular beam epitaxy with the Sc content (x) up to 0.26. The thermal conductivity shows a descending trend with increasing Sc content. Temperature-dependent measurements show an increase in thermal conductivity as the temperature increases at temperatures below 200 K, followed by a plateau at higher temperatures (T > 200 K). Application of an analytical Debye-Callaway model allows us to estimate the effects of boundary and alloy scattering on the observed thermal conductivity behavior. This work provides insight for phonon scattering mechanisms and the resultant thermal conductivity in Al1-xScxN, paving the way for future investigation of materials and design of acoustic devices.

Cumulative defect structures for experimentally attainable low thermal conductivity in thermoelectric (Bi,Sb)2Te3 alloys

Manipulation of thermal transport properties by defect engineering is an important but yet unresolved issue in thermoelectrics, since rational design strategies of multiple defect structures for minimizing lattice thermal conductivity are lacking. The key is to comprehend complex interaction between different frequency-dependent phonon scattering processes by multiple defect structures. Herein, individual contributions in lattice thermal conductivity reduction from each defect structure—point defects (0-dimensional, 0D), dislocations (1D), grain boundaries (2D), and nanoparticles (3D)—are characterized based on experimental results of commercial (Bi,Sb)2Te3-based alloys fitted to Debye-Callaway model. Then, the cumulative contributions by multiple defect structures are investigated interactively by estimating total phonon relaxation time. Therefore, the interactive role of multiple defect structures in reducing lattice thermal conductivity is elucidated. To extend the approach to other thermoelectric materials, PbTe-based alloys with multiple defect structures of point defects and grain boundaries were modeled as well. This approach enables to provide a thorough design of defect structures for realizing the experimentally attainable low lattice thermal conductivity in thermoelectric materials.

Structural Evolution of High-Performance Mn-Alloyed Thermoelectric Materials: A Case Study of SnTe.

Mn alloying in thermoelectrics is a long-standing strategy for enhancing their figure-of-merit through optimizing electronic transport properties by band convergence, valley perturbation, or spin-orbital coupling. By contrast, mechanisms by which Mn contributes to suppressing thermal transports, namely thermal conductivity, is still ambiguous. A few precedent studies indicate that Mn introduces a series of hierarchical defects from the nano- to meso-scale, leading to effective phonon scattering scoping a wide frequency spectrum. Due to insufficient insights at the atomic level, the theory remains as phenomenological and cannot be used to quantitatively predict the thermal conductivity of Mn-alloyed thermoelectrics. Herein, by choosing the SnTe as a case study, aberration-corrected transmission electron microscopy (TEM)/scanning transmission electron microscopy (STEM) to characterize the lattice complexity of Sn1.02- x Mnx Te is employed. Mn as a "dynamic" dopant that plays an important role in SnTe with respect to different alloying levels or post treatments is revealed. The results indicate that Mn precipitates at x= 0.08 prior to reaching solubility (≈10mol%), and then splits into MnSn substitution and γ-MnTe hetero-phases via mechanical alloying. Understanding such unique crystallography evolution, combined with a modified Debye-Callaway model, is critical in explaining the decreased thermal conductivity of Sn1.02- x Mnx Te with rational phonon scattering pathways, which should be applicable for other thermoelectric systems.

Ultralow Lattice Thermal Conductivity of A0.5RhO2 (A = K, Rb, Cs) Induced by Interfacial Scattering and Resonant Scattering

Recently, superionic conductors featured with melted ionic sublattices have been proved to possess ultralow thermal conductivity, but the underlying physical mechanism is under hot debate. In this article, we report ultralow out-of-plane thermal conductivity (0.4 ∼ 0.6 W m–1 K–1 at 300 K) in A0.5RhO2 (ARO, A = K, Rb, Cs) crystals with a layered structure. Analyzed by the empirical Debye–Callaway model, it reveals that both interfacial scattering and resonant scattering play dominant roles in ultralow thermal conductivity observed in RRO and CRO crystals, while in KRO crystals, resonant scattering is nearly negligible, and both interfacial scattering and three-phonon Umklapp scattering are contributed to the low thermal conductivity. Moreover, the frequency of resonant modes in ARO is dependent on ionic species, which makes it possible to modulate thermal conductivity by intercalation of different ions in the matrix. This work provides crucial information to the physical origin of ultralow thermal conductivity in superionic conductors.