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Synthesis and thermal transport of eco-friendly Fe-Si-Ge alloys with eutectic/eutectoid microstructure
Abstract
The beta-FeSi2/Si semiconducting nanocomposite is a promising thermoelectric system with eco-friendly materials. We show that small quantities of Ge can enhance the thermoelectric properties and widen
the design space, if Ge content and spatial disposition can be controlled. We investigated the use of solidification combined with solid-state transformations to reduce the thermal conductivity via hierarchical
modification of microstructure. Solidification of Fe28Si68Ge4 alloys leads to eutectic lamellar microstructure comprised of hyperstoichiometric alpha-FeSi2 and diamond cubic Si1-xGex. The
eutectic lengthscales can be varied over two orders of magnitude depending on solidification rate. Subsequent aging of the eutectic produces eutectoid decomposition, alpha-FeSi2/beta-FeSi2 / Si1-yGey, where the additional diamond cubic product is interleaved with the eutectic lamellae. By controlling both the frequency of beta-FeSi2/diamond cubic heterointerfaces, as well as the degree of Ge segregation into the eutectoid microconstituent, the thermal conductivity of the composite was varied from 22.8 Wm�-1K-�1 down to 8.3 Wm�-1K-�1. We analyze the thermal conductivity in terms of a series thermal resistance model, including thermal boundary conductances at the heterointerfaces, and show that the thermal boundary conductance is reduced by at least an order of magnitude when the diamond cubic microconstituent is enriched from 0 to 30 at% Ge. Avenues for additional microstructural improvements towards thermoelectric applications are discussed.
... Eutectic solidification has been investigated extensively in the context of mechanical properties [2] and is now the subject of investigation in the context of additive manufacturing of metals [3,4]. In addition, eutectic solidification provides a relatively unexplored processing approach for nanocomposite materials and applications including exchange-coupled ferromagnetism, thermoelectrics, [5,6] and photovoltaics. The ability to dictate the lengthscales of the interleaved eutectic microstructure are relevant, for example, in controlling scattering of thermal and electronic carriers, or determining the extent of magnetic exchange interactions [7,8]. ...
Scanning laser melting was employed to investigate directional solidification in Al-Cu thin films, 200 and 500 nm thick. The Al-Cu alloy films, with both eutectic and hypoeutectic compositions, were co-deposited on fused silica substrates by magnetron sputtering. Melting of the films was carried out in air using a CW laser, as a function of the scan velocity, v, up to 5 cm/s. For eutectic films, regular lamellar microstructure was observed over the entire range of velocities studied. Interlamellar spacings, λ, below 50 nm were readily produced. Results were found to be consistent with studies on bulk Al-Cu alloys, obeying the classic steady state lamellar growth relationship, λ²v = K. However, the value of the constant, K is significantly larger in thin films when compared to bulk. This is attributed to constraints on mechanisms for spacing adjustment in two-dimensional eutectic systems. In the hypoeutectic thin films, a complex lamellar structure was observed as the scan velocity was reduced. Regions of straight lamellae, oscillatory lamellae, solitary tilt waves, and recurring extreme lamellar branching events coexisted across the melt track. Fourier analysis was used to quantify the chaotic area fraction of the films. The transition to chaos occurred as the G/v ratio increased, attributed to approaching a re-entrant eutectic-to-dendritic transition from above. Approaches to further refine laser melting in thin eutectic films in order to better control solidification processes are discussed.
A β‐FeSi2–SiGe nanocomposite is synthesized via a react/transform spark plasma sintering technique, in which eutectoid phase transformation, Ge alloying, selective doping, and sintering are completed in a single process, resulting in a greatly reduced process time and thermal budget. Hierarchical structuring of the SiGe secondary phase to achieve coexistence of a percolated network with isolated nanoscale inclusions effectively decouples the thermal and electrical transport. Combined with selective doping that reduces conduction band offsets, the percolation strategy produces overall electron mobilities 30 times higher than those of similar materials produced using typical powder‐processing routes. As a result, a maximum thermoelectric figure of merit ZT of ≈0.7 at 700 °C is achieved in the β‐FeSi2–SiGe nanocomposite.
Synthesis of organophosphorus compounds containing nitrogen as heteroatom and its application as a flame retardant (FR) have attracted much attention in the academic and industrial communities over the past decade. Such compounds are relatively easy to synthesize and offer advantages such as high thermal stability, which is useful for high temperature processing, improved char stability, density, and yield during the thermal decomposition of polymer, and release phosphorus species active in the flame inhibition process. Though a variety of phosphorus–nitrogen (P–N) compounds can be found in the literature, this review mostly summarizes the recent (since 2013) development in phosphorus (O)‐nitrogen containing flame retardants which have been published in peer‐reviewed journals. General strategies of synthesizing P(O)–N compounds as FRs from various phosphorus‐based starting materials are highlighted in this review. Some of the most common classes of researched P(O)–N containing compounds as FRs include the phosphinamides, phosphonamides, phosphoramides, phosphoramidates, phosphorodiamidates, phosphonamidates and their thio counterparts which are usually obtained via a one‐ or two‐step synthetic strategy. Incorporation of these compounds as FRs in various polymer systems such as polyurethane, epoxy resins, polyamides, cellulose, polylactide, poly(butylene terephthalate), polycarbonates, and acrylonitrile–butadiene–styrene are discussed in detail in this review. Special emphasis on the various fire and thermal performances of the new materials are also summarized. The mechanical performance of new materials and the influence of these additives on polymer processing are also briefly discussed. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2020, 137, 47910.
A critical issue, central to microstructural selection in highly driven systems, is the role of nonequilibrium solute partitioning and the formation of metastable phases. When local chemical equilibrium breaks down at very high undercoolings, solidification dynamics are influenced by limitations to atomic attachment kinetics, decreasing solute diffusivities, changing thermodynamic driving forces, and the energetics of ordering or clustering in the liquid phase. The scope of the current study is to employ free-jet melt spinning along with advanced e-beam, x-ray diffraction techniques to investigate the degree of solute partitioning and metastable phase formation during rapid solidification of Al-Sm alloys with compositions at or near the Al-rich eutectic (15wt.% or 3 at.%). At all melt spinning rates employed (10-40m/s), solidification morphologies consist of the Al (fcc) and Al11Sm3 (tetragonal) phases. Certain morphological transitions occur through the thickness of the ribbon, indicating a change in the prevailing cooling conditions as solidification proceeds. In addition, x-ray diffraction analysis indicates that the Sm content in the fee Al phase is well above that given by local two-phase (fcc+liquid) equilibrium.
Thermoelectric properties of semiconducting b-FeSi 2 containing a homogeneous distribution of Si secondary phase have been studied. The synthesis was carried out using arc melting followed by the densification by uniaxial hot pressing. Endogenous b-FeSi 2 /Si composites were produced by the eutectoid decomposition of high-temperature a-Fe 2 Si 5 phase. The aging heat treatments have been carried out at various temperatures below the equilibrium eutectoid temperature for various durations in order to tune the size of the eutectoid product. Thermal properties of the samples were studied in the temperature range of 100–350 °C. The microstructural investigations support the fact that the finest microstructure generated through the eutectoid decomposition of the a-Fe 2 Si 5 metastable phase is responsible of the phonon scattering. The results suggest an opportunity to produce bulk iron silicide alloys with reduced thermal conductivity in order to enhance its thermoelectric performance.
The applicability of Fourier's law to heat transfer problems relies on the assumption that heat carriers have mean free paths smaller than important length scales of the temperature profile. This assumption is not generally valid in nanoscale thermal transport problems where spacing between boundaries is small (<1 μm), and temperature gradients vary rapidly in space. Here we study the limits to Fourier theory for analysing three-dimensional heat transfer problems in systems with an interface. We characterize the relationship between the failure of Fourier theory, phonon mean free paths, important length scales of the temperature profile and interfacial-phonon scattering by time-domain thermoreflectance experiments on Si, Si0.99Ge0.01, boron-doped Si and MgO crystals. The failure of Fourier theory causes anisotropic thermal transport. In situations where Fourier theory fails, a simple radiative boundary condition on the heat diffusion equation cannot adequately describe interfacial thermal transport.
Silicon-on-insulator (SOI) technology has sparked advances in semiconductor and MEMs manufacturing and revolutionized our ability to study phonon transport phenomena by providing single-crystal silicon layers with thickness down to a few tens of nanometers. These nearly perfect crystalline silicon layers are an ideal platform for studying ballistic phonon transport and the coupling of boundary scattering with other mechanisms, including impurities and periodic pores. Early studies showed clear evidence of the size effect on thermal conduction due to phonon boundary scattering in films down to 20 nm thick and provided the first compelling room temperature evidence for the Casimir limit at room temperature. More recent studies on ultrathin films and periodically porous thin films are exploring the possibility of phonon dispersion modifications in confined geometries and porous films.
The thermal conductivities of micron-thick epitaxial layers of dilute
Si1-xGex alloys,
2×10-4<x<0.01 , are measured in the temperature
range 297<T<550K using time-domain thermoreflectance. These new
data are used to test competing models for the strength of phonon
scattering by heavy impurity atoms. Even though the mass difference
between Ge and Si is much larger than the Si atomic mass, we find that
the thermal conductivity of dilute SiGe alloys is adequately described
by the scattering strength for point defects derived by perturbation
theory by Klemens in 1955.
We present an analytic solution for heat flow in a multilayer
two-channel system for the interpretation of time-domain
thermoreflectance (TDTR) experiments where nonequilibrium effects are
important. The two-channel solution is used to analyze new room
temperature TDTR measurements of Al/Cu and
Al/Si0.99Ge0.01 systems. Cu and
Si0.99Ge0.01 are examples of materials well suited
for analysis with a two-channel model because thermal excitations
responsible for the vast majority of the heat capacity in these solids
contribute little to their thermal conductivity. Nonequilibrium effects
are found to be unimportant for the interpretation of the Al/Cu TDTR
data but dramatic for the Al/Si0.99Ge0.01 TDTR
data. The two-channel model predicts a significant reduction in the
effective thermal conductivity of Si0.99Ge0.01 in
a region within 150 nm of the Al/Si0.99Ge0.01
interface. The extra thermal resistance in this region is a result of
the disparate heat flux boundary conditions for low- and high-frequency
phonons in combination with weak coupling between low- and
high-frequency phonons. When the experimental data are analyzed with a
single-channel model, both the conductance and thermal conductivity
appear to depend on pump-modulation frequency, consistent with the
two-channel model's predictions. Finally, we compare the results of our
diffusive two-channel model to a nonlocal description for steady-state
heat flow near a boundary and show they yield nearly identical results.
The efficiency in modern technologies and green energy solutions has boiled down to a thermal engineering problem on the nanoscale. Due to the magnitudes of the thermal mean free paths approaching or overpassing typical length scales in nanomaterials (i.e., materials with length scales less than one micrometer), the thermal transport across interfaces can dictate the overall thermal resistance in nanosystems. However, the fundamental mechanisms driving these electron and phonon interactions at nanoscale interfaces are difficult to predict and control since the thermal boundary conductance across interfaces is intimately related to the characteristics of the interface (structure, bonding, geometry, etc.) in addition to the fundamental atomistic properties of the materials comprising the interface itself. In this paper, I review the recent experimental progress in understanding the interplay between interfacial properties on the atomic scale and thermal transport across solid interfaces. I focus this discussion specifically on the role of interfacial nanoscale “imperfections,” such as surface roughness, compositional disorder, atomic dislocations, or interfacial bonding. Each type of interfacial imperfection leads to different scattering mechanisms that can be used to control the thermal boundary conductance. This offers a unique avenue for controlling scattering and thermal transport in nanotechnology.
We measure the thermal conductivities of nano-grained strontium titanate (ng-SrTiO3) films deposited on sapphire substrates via time-domain thermoreflectance. The 170 nm thick oxide films of varying grain-size were prepared from a chemical solution deposition process. We find that the thermal conductivity of ng-SrTiO3 decreases with decreasing average grain size and attribute this to increased phonon scattering at grain boundaries. Our data are well described by a model that accounts for the spectral nature of anharmonic Umklapp scattering along with grain boundary scattering and scattering due to the film thickness.
We investigate thermal transport in Si/Ge and Si 1−x Ge x /Si 1−y Ge y alloy superlattices based on solving the single-mode phonon Boltzmann transport equation in the relaxation-time approximation and with full phonon dispersions. We derive an effective interface scattering rate that depends both on the interface roughness (captured by a wave-vector-dependent specularity parameter) and on the efficiency of internal scattering mechanisms (mass-difference and phonon-phonon scattering). We provide compact expressions for the calculations of in-plane and cross-plane thermal conductivities in superlattices. Our numerical results accurately capture both the observed increase in thermal conductivity as the superlattice period increases and the in-plane vs cross-plane anisotropy of thermal conductivity. Owing to the combined effect of interface and internal scattering, an alloy/alloy superlattice has a lower thermal conductivity than bulk SiGe with the same alloy composition. Thermal conductivity can be minimized by growing short-period alloy/alloy superlattices or Si/Si 1−x Ge x superlattices with the SiGe layer thicker than the Si one.
We report here in situ measurements of the evolution of the Ag(110) surface during Si growth, using scanning tunneling microscopy and grazing incidence x-ray diffraction. We provide compelling evidence of an Ag(110) surface reconstruction associated with the release of Ag atoms induced by the growth of Si nanoribbons. Our results are in agreement with a missing row reconstruction of the Ag layer underneath the nanoribbons. This challenges the current understanding of the Si growth on nonreconstructed Ag(110), interpreted within the framework of silicene models.
The thermal conductivity of epitaxial layers of Si is measured in the temperature range 300<T<550 K using time-domain thermoreflectance. The analysis of the thermoreflectance data uses the ratio of the in-phase and out-of-phase signals of the lock-in amplifier to achieve a precision of ±5%. Comparisons are made between epitaxial layers of isotopically pure 28Si, Si with a natural isotope abundance, and Ge-doped Si. At 297 K, the thermal conductivity of 28Si epitaxial films is 16±5 % larger than the thermal conductivity of natural Si. The thermal resistance created by mass-disorder scattering of phonons is in good agreement with theory for natural Si and for Ge-doped Si with a Ge concentration of 1.4×1019 cm−3.
We experimentally investigate the role of size effects and boundary scattering on the thermal conductivity of silicon-germanium alloys. The thermal conductivities of a series of epitaxially grown Si_{1-x}Ge_{x} thin films with varying thicknesses and compositions were measured with time-domain thermoreflectance. The resulting conductivities are found to be 3 to 5 times less than bulk values and vary strongly with film thickness. By examining these measured thermal conductivities in the context of a previously established model, it is shown that long wavelength phonons, known to be the dominant heat carriers in alloy films, are strongly scattered by the film boundaries, thereby inducing the observed reductions in heat transport. These results are then generalized to silicon-germanium systems of various thicknesses and compositions; we find that the thermal conductivities of Si_{1-x}Ge_{x} superlattices are ultimately limited by finite size effects and sample size rather than periodicity or alloying. This demonstrates the strong influence of sample size in alloyed nanosystems. Therefore, if a comparison is to be made between the thermal conductivities of superlattices and alloys, the total sample thicknesses of each must be considered.
We have used an atomistic ab initio approach with no adjustable parameters to compute the lattice thermal conductivity of Si0.5Ge0.5 with a low concentration of embedded Si or Ge nanoparticles of diameters up to 4.4 nm. Through exact Green’s function calculation of the nanoparticle scattering rates, we find that embedding Ge nanoparticles in Si0.5Ge0.5 provides 20% lower thermal conductivities than embedding Si nanoparticles. This contrasts with the Born approximation, which predicts an equal amount of reduction for the two cases, irrespective of the sign of the mass difference. Despite these differences, we find that the Born approximation still performs remarkably well, and it permits investigation of larger nanoparticle sizes, up to 60 nm in diameter, not feasible with the exact approach.
The iterative algorithm of Feldman for heat flow in layered structures is solved in cylindrical coordinates for surface heating and temperature measurement by Gaussian-shaped laser beams. This solution for the frequency-domain temperature response is then used to model the lock-in amplifier signals acquired in time-domain thermoreflectance measurements of thermal properties.
The thermal conductivity of Si–Ge superlattices with superlattice periods 30≪L≪300 Å, and a Si 0.85 Ge 0.15 thin film alloy is measured using the 3 ω method. The alloy film shows a conductivity comparable to bulk SiGe alloys while the superlattice samples have a thermal conductivity that is smaller than the alloy. For 30≪L≪70 Å, the thermal conductivity decreases with decreasing L ; these data provide a lower limit to the interface thermal conductance G of epitaxial Si–Ge interfaces: G ≫ 2 × 10 9 W m -2 K -1 at 200 K. Superlattices with relatively longer periods, L≫130 Å, have smaller thermal conductivities than the short-period samples. This unexpected result is attributed to a strong disruption of the lattice vibrations by extended defects produced during lattice-mismatched growth. © 1997 American Institute of Physics.
The thermal conductivities of individual single crystalline intrinsic Si nanowires with diameters of 22, 37, 56, and 115 nm were measured using a microfabricated suspended device over a temperature range of 20-320 K. Although the nanowires had well-defined crystalline order, the thermal conductivity observed was more than two orders of magnitude lower than the bulk value. The strong diameter dependence of thermal conductivity in nanowires was ascribed to the increased phonon-boundary scattering and possible phonon spectrum modification. (C) 2003 American Institute of Physics.
This is a graduate level textbook in nanoscale heat transfer and energy conversion that can also be used as a reference for researchers in the developing field of nanoengineering. It provides a comprehensive overview of microscale heat transfer, focusing on thermal energy storage and transport. Chen broadens the readership by incorporating results from related disciplines, from the point of view of thermal energy storage and transport, and presents related topics on the transport of electrons, phonons, photons, and molecules. This book is part of the MIT-Pappalardo Series in Mechanical Engineering.
Semiconducting β-FeSi2 is a candidate thermoelectric material whose constituents are abundant and eco-friendly, but significant improvements in the relevant properties are needed. This work investigates eutectoid decomposition, α-FeSi2 → β-FeSi2 + Si, as a means to modify microstructure and control thermal transport. Process conditions are adjusted to strongly affect both the microstructural lengthscales and morphology, and hence the thermal conductivity. Low temperature annealing of a hypoeutectic sample produces cooperatively-grown Si lamellae, which then decompose into Si nanowires by Rayleigh instability upon further aging. We show that nucleation of eutectoid colonies occurs preferentially on cracks, while at smaller undercooling, nucleation also occurs on eutectic Si particles. The growth velocity, v, and interlamellar spacing, λ, of the pearlitic colonies obey a relation of the type vλⁿ = f(T). This sets the bounds of the activation energy for the diffusion mechanism, although the exact mechanism cannot be specified. Nanostructuring of eutectoid Si increases heterointerface density by 40x, with a concomitant reduction in thermal conductivity of 2x. The thermal boundary conductance is determined for the β-FeSi2/Si heterointerface, which shows that this interface only weakly scatters phonons.
The thermal boundary conductance (TBC) of materials pairs in atomically intimate contact is reviewed as a practical guide for materials scientists. First, analytical and computational models of TBC are reviewed. Five measurement methods are then compared in terms of their sensitivity to TBC: the 3ω method, frequency- and time-domain thermoreflectance, the cut-bar method, and a composite effective thermal conductivity method. The heart of the review surveys 30 years of TBC measurements around room temperature, highlighting the materials science factors experimentally proven to influence TBC. These factors include the bulk dispersion relations, acoustic contrast, and interfacial chemistry and bonding. The measured TBCs are compared across a wide range of materials systems by using the maximum transmission limit, which with an attenuated transmission coefficient proves to be a good guideline for most clean, strongly bonded interfaces. Finally, opportunities for future research are discussed.
We present measurements of thermal interface conductance as a function of metal alloy composition. Composition spread alloy films of AuxCu1−x and AuxPd1−x solid solutions were deposited on single crystal sapphire substrates via dual electron-beam evaporation. High throughput measurements of thermal interface conductance across the (metal alloy)-sapphire interfaces were made by positional scanning of frequency domain thermoreflectance measurements to sample a continuum of Au atomic fractions (x∼0→1). At a temperature of 300 K, the thermal interface conductance at the AuxCu1−x-sapphire interfaces monotonically decreased from 197±39MWm−2K−1 to 74±11MWm−2K−1 for x=0→0.95±0.02 and at the AuxPd1−x-sapphire interfaces from 167±35MWm−2K−1 to 60±10MWm−2K−1 for x=0.03→0.97±0.02. To shed light on the phonon physics at the interface, a Diffuse Mismatch Model for thermal interface conductance with alloys is presented and agrees reasonably with the thermal interface conductance data.
This chapter deals with diffusional phase transformations. We first define a phase and move on to discuss various ways of classifying phase transformations. We then discuss in detail the energetics (thermodynamics) and kinetics of diffusional phase transformations. Transformations discussed include: precipitation, atomic ordering, spinodal decomposition, massive and cellular transformations in the light of the sections on energetics and kinetics. A final section of the role of symmetry in developing microstructure concludes the chapter.
We develop a solution to the two-temperature diffusion equation in axisymmetric cylindrical coordinates to model heat transport in thermoreflectance experiments. Our solution builds upon prior solutions that account for two-channel diffusion in each layer of an N-layered geometry, but adds the ability to deposit heat at any location within each layer. We use this solution to account for non-surface heating in the transducer layer of thermoreflectance experiments that challenge the timescales of electron-phonon coupling. A sensitivity analysis is performed to identify important parameters in the solution and to establish a guideline for when to use the two-temperature model to interpret thermoreflectance data. We then fit broadband frequency domain thermoreflectance (BB-FDTR) measurements of SiO2 and platinum at a temperature of 300 K with our two-temperature solution to parameterize the gold/chromium transducer layer. We then refit BB-FDTR measurements of silicon and find that accounting for non-equilibrium between electrons and phonons in the gold layer does lessen the previously observed heating frequency dependence reported in Regner et al. [Nat. Commun. 4, 1640 (2013)] but does not completely eliminate it. We perform BB-FDTR experiments on silicon with an aluminum transducer and find limited heating frequency dependence, in agreement with time domain thermoreflectance results. We hypothesize that the discrepancy between thermoreflectance measurements with different transducers results in part from spectrally dependent phonon transmission at the transducer/silicon interface.
Pump-probe transient thermoreflectance (TTR) techniques are powerful tools for measuring the thermophysical properties of thin films, such as thermal conductivity, Lambda, or thermal boundary conductance, G. This paper examines the assumption of one-dimensional heating on, Lambda and G, determination in nanostructures using a pump-probe transient thermoreflectance technique. The traditionally used one-dimensional and axially symmetric cylindrical conduction models for thermal transport are reviewed. To test the assumptions of the thermal models, experimental data from Al films on bulk substrates (Si and glass) are taken with the TTR technique. This analysis is extended to thin film multilayer structures. The results show that at 11 MHz modulation frequency, thermal transport is indeed one dimensional. Error among the various models arises due to pulse accumulation and not accounting for residual heating. [DOI: 10.1115/1.4000993]
Among various thermoelectric (TE) materials, iron disilicide (FeSi2) has relatively low cost and non-toxic characteristics which make it appropriate for large scale applications. To enhance the dimensionless figure of merit (ZT) of this material, a composite of FeSi2–Si0.8Ge0.2 with high fraction of α-FeSi2 was prepared by mechanical alloying and sintering. The process was followed by thermal annealing to transform α to β phase FeSi2 through a slow peritectoid reaction (several hours). The thermoelectric properties were significantly improved upon the completion of the phase transformation. At temperatures above 900 °C, FeSi2 component rapidly changed from β to α phase (several minutes) leading to sudden increase of the thermal conductivity. For comparison, the thermoelectric alloy of β-FeSi2 was prepared through a similar process. The effect of sintering conditions and annealing time were studied and a comparison was drawn between the thermoelectric properties of β-FeSi2 and FeSi2–Si0.8Ge0.2 nanocomposite. Overall, (FeSi2)0.75(Si0.8Ge0.2)0.25 showed 170% enhancement in ZT compared with β-FeSi2 making it suitable for medium to high temperature applications (500 °C −850 °C).
We study the effect of grain size on thermal conductivity of thin film barium titanate over temperatures ranging from 200 to 500 K. We show that the thermal conductivity of Barium Titanate (BaTiO3) decreases with decreasing grain size as a result of increased phonon scattering from grain boundaries. We analyze our results with a model for thermal conductivity that incorporates a spectrum of mean free paths in BaTiO3. In contrast to the common gray mean free path assumption, our findings suggest that the thermal conductivity of complex oxide perovskites is driven by a spectrum of phonons with varying mean free paths.
The thermal boundary resistance present at interfaces between helium and solids (Kapitza resistance) and the thermal boundary resistance at interfaces between two solids are discussed for temperatures above 0.1 K. The apparent qualitative differences in the behavior of the boundary resistance at these two types of interfaces can be understood within the context of two limiting models of the boundary resistance, the acoustic mismatch model, which assumes no scattering, and the diffuse mismatch model, which assumes that all phonons incident on the interface will scatter. If the acoustic impedances of the two media in contact are very different, as is the case for helium (liquid or solid) in contact with a solid, then phonon scattering at the interface will reduce the boundary resistance. In the limiting case of diffuse mismatch, this reduction is typically over 2 orders of magnitude. Phonons are very sensitive to surface defects, and therefore the Kapitza resistance is very sensitive to the condition of the interface. For typical solid-solid interfaces, at which the acoustic impedances are less different, the influence of diffuse scattering is relatively small; even for the two limiting cases of acoustic mismatch and diffuse mismatch the predicted boundary resistances differ by very little (≲ 30%). Consequently, the experimentally determined values are expected to be rather insensitive to the condition of the interface, in agreement with recent observations. Subsurface (bulk) disorder and imperfect physical contact between the solids play far more important roles and led to the irreproducibilities observed in the early measurements of the solid-solid thermal boundary resistance.
We present an analytical model for the size-dependence of thin film and nanowire thermal conductivity and compare the predictions to experimental measurements on silicon nanostructures. The model contains no fitting parameters and only requires the bulk lattice constant, bulk thermal conductivity, and an acoustic phonon speed as inputs. By including the mode-dependence of the phonon lifetimes resulting from phonon-phonon and phonon-boundary scattering, the model captures the approach to the bulk thermal conductivity of the experimental data better than gray models based on a single lifetime.
The microstructures of Fe2Si5 based alloys fabricated by spark plasma sintering and the subsequent heat treatment were investigated by X-ray diffraction (XRD) analysis and scanning electron microscope (SEM). The results showed that a two-phase structure consisting of β-FeSi2 and Si dispersoids was obtained by the eutectoid decomposition of α-Fe2Si5 phase during annealing. The thermoelectric properties of Fe2Si5 based alloys were also investigated as compared with the stoichiometric FeSi2 based alloys. It was found that Fe2Si5 based alloys have the same conduction mechanism with stoichiometric FeSi2 alloys doped with Mn and Co, respectively. An increase in carrier scattering caused by Si particles was observed in both Mn- and Co-doped alloys. The effect of Si dispersoids on Seebeck coefficient and electrical resistivity was discussed. Results show that the excessive Si dispersoids in Fe2Si5 based alloys could improve the transport properties of the material, especially for the Co-doped alloys.
The addition of a small amount of Cu is effective in accelerating the a ? ß + Si eutectoid decomposition. Some elements (Pd, Pt, Ag and Au) that are expected to have similar chemical properties were added to an Fe2Si5 based alloys up to 1.0 at.% to examine whether a similar effect could be revealed. The microstructures, X-ray diffraction and differential thermal analysis (DTA) of slowly solidified or heat treated specimens were investigated in detail. The solubility of all containing elements into the a phase was less than 0.2 at.% for the slowly solidified specimen. The excess of the additive solidified as a phase of a eutectic with the Si phase. On the other hand, the solubility of these additives in the ß phase was classified into two groups. The first group had higher solubility in the ß phase than that in the a phase. The solubility of the other group was as low as that in the a phase. Pd and Au belonged to the former and Pt and Ag belonged to the later. The acceleration of the eutectoid decomposition was only observed in the former group but it was negligible in the later group. The existence of the eutectic melt at the annealing temperature was effective on the coarsening of the eutectoid structure but not essential for the acceleration. The eutectoid decomposition strongly depended on the solubility of these elements into the ß phase.
The resistivity and thermoelectric power of β-FeSi2 single crystals and polycrystalline β-FeSi2+x thin films doped with 3d transition metals, have been investigated for dependence on the deviation from strict stoichiometry and on the purity of the source material. It has been found that in single crystals, the thermoelectric power is characterized by a large phonon drag effect which is more pronounced in samples grown with the source material of higher purity, and by large absolute values of >500 μV/K in a broad temperature range. The values of the resistivity prepared at the Si-rich and Fe-rich phase boundaries do not show any correlation with the deviation from strict stoichiometry, but its temperature dependence ρ(T) is controlled by native defects. Polycrystalline β-FeSi2+x thin films doped with Co and Cr, and prepared by electron beam evaporation and magnetron sputtering, were found to have maximum power factors outside the homogeneity region at approximately x=0.15±0.05. Their thermoelectric power remains below that of single crystals.
The intrinsic optical absorption spectrum for the germanium-silicon alloy system has been measured as a function of temperature and composition. Over the entire composition range the absorption near the threshold ( {\mathrm{cm}}^{-{}1}) exhibits a temperature dependence which is characteristic of phonon-assisted indirect electronic transitions. There appears to be no temperature-independent component of the absorption attributable to disorder-assisted transitions. When the phonon contribution to the absorption is explicitly taken into account, as in a Macfarlane-Roberts type analysis, the experimental data yield an equivalent phonon temperature which varies from 270\ifmmode\pm\else\textpm\fi{}20\ifmmode^\circ\else\textdegree\fi{}K for pure Ge to 550\ifmmode\pm\else\textpm\fi{}50\ifmmode^\circ\else\textdegree\fi{}K for pure Si, with most of the variation occurring in the middle of the composition range. The composition dependence of the derived energy gap shows an abrupt change in slope at about 15 atomic percent Si. This is due to a switch from a Ge-like ([111]) to a Si-like ([100]) conduction band structure. The onset of direct electronic transitions ({10}^{2} {\mathrm{cm}}^{-{}1}-{}1}) was observed as a function of composition in the Ge-rich alloys. The data show that the [000] conduction band minimum moves more rapidly than the [111] minima as Si is added to Ge. In an attempt to account for the observed variation of the phonon equivalent temperature with composition, certain lattice vibrational modes were computed on the basis of a number of simplified models. The one which gives the most realistic results emphasizes the presence of atoms of different masses and some short-range order in the alloy lattice.
The Hall effect and thermoelectric properties of sintered iron disilicide FeSix (1.9 less than or equal to x less than or equal to 2.4) have been investigated. The Hall coefficient of FeSix at 300 K is positive at 1.9 less than or equal to x less than or equal to 2.05 and x = 2.40 but negative at 2.10 less than or equal to x less than or equal to 2.30. The carrier concentration at 300 K has a large composition dependence. The Seebeck coefficient below 750 K has a strong composition dependence, but above 750 K it has almost no composition dependence. The mobility shows the highest value of 3.6 cm(2)/Vs at x = 2.05 which has the lowest carrier concentration of 3.1 x 10(17) cm(-3) in the composition range of 2.00 less than or equal to x less than or equal to 2.30. It is suggested that the amount of Si or Fe point defects in beta-FeSi2 is closely related to the transport properties of carriers.
The high-temperature thermal conductivity of a disordered semiconductor alloy is derived using the Klemens-Callaway theory. It is assumed that the reciprocal relaxation times depend on frequency omega as omega4 for strain and mass point defects and as omega2 for normal and umklapp three-phonon anharmonic processes. The thermal conductivity is expressed in terms of the lattice parameters and mean atomic weights of the alloy and its constituents. Agreement is obtained between theory and published experimental data on Ge-Si alloys at temperatures 300-1200°K, and on (Ga,In)As alloys at 300°K, using the value 2.5 for the ratio of umklapp to normal relaxation times. It is found that the large thermal resistivity of Ge-Si alloys is predominantly due to mass defect scattering, whereas that of (Ga,In)As alloys is mainly due to strain scattering.
The structure, lattice dynamics, and some thermodynamic properties of β-FeSi2 were investigated using first-principles calculations that are based on density functional theory. The fully relaxed structure parameters of β-FeSi2 are in good agreement with previous experimental data. The linear response method is applied in order to determine the phonon dispersion relations, phonon density of states, and the Born effective charge. The computed thermodynamic quantities such as vibrational entropy, specific heat, and Debye temperature are in agreement with previous experimental data.
Heat capacity of needle-like (length=5 mm, diameter=1 mm) β-FeS2 single crystal grown by chemical vapor transport has been measured. Two anomalies are found; a broad deviation centered around 160 K and a clear deviation at a temperature of (approximately) 255 K. We have attempted to relate these to the anomalies previously reported in the case of the resistivity data. The transient thermoelectric effect (TTE) results lead us to the inference that the system under-goes a transition from a single carrier system to at least a two carrier system at 220 K. Our heat capacity results seem to provide further independent evidence for this transition in this system.
Direct preparation of non-doped, and Ru- or Ge-doped β-FeSi2 films from the gaseous phase have been studied using a ternary simultaneous electron beam deposition apparatus so as to clarify the effect of these doping elements on the thermoelectric properties and electric conductivity of β-FeSi2. Substitution of Ru for Fe in β-FeSi2 up to approximately 7 at.% of Ru seemed to be possible from the X-ray diffraction pattern. On the other hand, substitution of Ge for Si as small as 1.4 at.% Ge brought about the segregation. This feature was also clearly observed in scanning electron micrographs. Therefore, Ru could be successfully doped in β-FeSi2, however, Ge could not. Though the Seebeck coefficient of β-FeSi2 has been slightly decreased by doping of Ru, its electric conductivity has been increased by one order of magnitude.
Previous efforts to enhance thermoelectric performance have primarily focused on reduction in lattice thermal conductivity caused by broad-based phonon scattering across multiple length scales. Herein, we demonstrate a design strategy which provides for simultaneous improvement of electrical and thermal properties of p-type PbSe and leads to ZT ∼ 1.6 at 923 K, the highest ever reported for a tellurium-free chalcogenide. Our strategy goes beyond the recent ideas of reducing thermal conductivity by adding two key new theory-guided concepts in engineering, both electronic structure and band alignment across nanostructure-matrix interface. Utilizing density functional theory for calculations of valence band energy levels of nanoscale precipitates of CdS, CdSe, ZnS, and ZnSe, we infer favorable valence band alignments between PbSe and compositionally alloyed nanostructures of CdS1-xSex/ZnS1-xSex. Then by alloying Cd on the cation sublattice of PbSe, we tailor the electronic structure of its two valence bands (light hole L and heavy hole Σ) to move closer in energy, thereby enabling the enhancement of the Seebeck coefficients and the power factor.
The time–temperature–transformation diagrams for the eutectoid decomposition (α→β+Si) in slowly solidified Fe2Si5 alloys with small amounts of Mn and Cu were obtained in the temperature range 873 and 1173 K. The shape of the diagrams can typically be described by the character C. The nose temperature in a binary Fe2Si5 alloy was about 1023 K and increased by about 50 K in the Cu added alloy. The addition of small amounts of Cu drastically shifted the diagram to shorter times. The start of the eutectoid decomposition in the Cu added alloy was more than 240 times faster than that in the Cu free alloy at the nose temperature. The shape of the Si dispersoids formed by the eutectoid decomposition changed from lamella in the Cu free alloy to granular in the Cu added alloy. In the FeSi2 alloy, the peritectoid reaction (α+ε→β) was also enhanced by the addition of Cu. These results suggest that the existence of Si is not significant for the acceleration of the β formation. The kinetic analysis of the β-phase transformation based on the Johnson–Mehl–Avrami equation suggests that the addition of Cu does not change the transformation mechanism but changes the growth kinetics. The size of the Si dispersoids was quite fine when heating below 1023 K.
The β phase transformation from the rapidly solidified Fe2Si5 based alloys was examined by SEM and TEM observation, cyclic differential thermal analysis (DTA) and X-ray diffraction. The rapid solidification enhanced the transformation rate to a value about 3 times higher than that in conventionally solidified alloys. A sharp endothermic peak at the equilibrium eutectoid temperature was observed only once during the first heating cycle and no peaks were observed in further heating or cooling cycles. The most important reaction for the accelerated transformation was the rapid decomposition of the supersaturated α phase with Si, formed by rapid solidification, into the β-Si eutectoid. A few part of the metastable ε phase contributed to the β phase formation by the peritectic reaction with the α phase. TEM observation showed that most of the ε phase was dissolved into the α phase before the α phase was decomposed into the β phase and Si. The result of a Johnson–Mehl–Avrami analysis for the β phase formation by isothermal annealing showed that there was no significant difference in the transformation mechanism between the rapidly solidified specimen and the slowly solidified specimen. This suggests that nucleation became saturated in the first stage of the annealing and subsequently growth controlled the transformation.
The zinc-rich solid phase in zinc-cadmium alloys has been studied after splat quenching to −196°C. Alloys containing from zero to 5 wt.% were examined by X-ray lattice parameter measurements. The compositions of the resulting solid were found to be larger than the stable or metastable solidus composition at any temperature and therefore a departure from local equilibrium at the liquid-solid interface occurred in the solid. The sign of the departure is opposite to that predicted by theories of Jackson and Borisov for non-equilibrium alloy solidification, which therefore are invalid. Key aspects of a correct theory are discussed.
In this study, the new technique of transmission Kikuchi diffraction (TKD) in the scanning electron microscope (SEM) has been applied for the first time to enable orientation mapping of bulk, nanostructured metals. The results show how the improved spatial resolution of SEM-TKD, compared to conventional EBSD, enables reliable mapping of truly nanostructured metals and alloys, with mean grain sizes in the 40-200 nm range. The spatial resolution of the technique is significantly below 10nm, and contrasting examples are shown from both dense (Ni) and lighter (Al-alloy) materials. Despite the burden of preparing thin, electron-transparent samples, orientation mapping using SEM-TKD is likely to become invaluable for routine characterisation of nanocrystalline and, potentially, highly deformed microstructures.
The transformation kinetics of the β-phase from an as-solidified structure composed of α and ε in the Fe–Si system was investigated
by using rapidly, unidirectionally or conventionally solidified FeSi2 alloys containing a small amount of Cu (0.1–1 at%). The addition of Cu decreased the size of primary ε and slightly changed
the solidified eutectic morphology. The solubility of Cu in the α-Fe2Si5 phase was estimated to be less than 0.2 at%. A needle-like Cu enriched phase was newly formed in the conventionally solidified
alloys containing more than 0.2 at % Cu. Microdifferential thermal analysis (DTA) clearly showed that the addition of Cu drastically
accelerated β-phase formation. X-ray diffraction analysis and microstructural observation of the isothermally heat-treated
specimens showed that Cu addition was effective in increasing the rate of eutectoid decomposition (α → β + Si) and the initial
stage of the peritectoid reaction (α + ε → β). For complete β formation, heat treatment for a long time was still required
because it took a long time for the coarse ε-phase in the slowly solidified alloy to be eliminated by peritectoid reaction.
The effect of Cu depended on the annealing temperature. The decomposition rate of α in the Cu-added cast specimen was about
15 times higher at 1073 K than that of the binary cast specimen and exceeded more than 30 times at 873 K.
We proposed Fe2Si5 based alloys with a small amount of Cu as new Fe–Si thermoelectric materials. A few acicular structures enriched in Cu were newly formed in slowly solidified alloys containing Cu above 0.2 at%. single phase structure was formed by a conventional solidification process in alloys below 0.2 at% Cu. phase was only formed by the eutectoid reaction (+Si). Differential thermal analysis, X-ray diffraction and structure observation clearly confirmed that the eutectoid reaction rate was drastically enhanced by the addition of a small amount of Cu and its rate decreased with decrease of Cu content. Its rate also depended on the annealing temperature and it was maximum at about 1073 K for most alloys. The addition of only 0.1 at% Cu was still very effective in Mn or Co doped alloys. The final structure after the eutectoid reaction in these alloys was duplex composed of and Si. The size of Si decreased with decrease of Cu content and the annealing temperature. Transmission electron microscope observation showed that was transformed from with many planar faults (stacking fault) that will act as a drag resistance for the transformation. We speculated that the addition of Cu probably decreased the stacking fault energy so as to decrease the drag force and to enhance the formation rate.
Iron disilicide based thermoelectric materials Fe0.92Mn0.08Six (1.9⩽x⩽2.5) were prepared by rapid solidification (melt spinning) and hot uniaxial pressing at 1248 K with 50 MPa for 30 min, followed by annealing at 1073 K for 20 h. X-ray diffraction and scanning electron microscopy showed excess silicon phase for samples with x⩾2.1, and both the configurations and the amounts of secondary silicon particles varied with an increase in x. Hall measurements carried out at room temperature showed that the carrier concentrations for Fe0.92Mn0.08Six (1.9⩽x⩽2.5) were between 2.6×1018 and 5.6×1018 cm−3. The Seebeck coefficient, electrical conductivity and thermal conductivity were measured from room temperature to 973 K. It was found that a little excess silicon in the sample, x=2.1, enhanced the Seebeck coefficient weakly, but was effective for decreasing the thermal conductivity. A maximum figure of merit, ZT=0.17, was obtained for Fe0.92Mn0.08Si2.0 at 973 K.
The relationship between pulse accumulation and radial heat conduction in pump-probe transient thermoreflectance (TTR) is explored. The results illustrate how pulse accumulation allows TTR to probe two thermal length scales simultaneously. In addition, the conditions under which radial transport effects are important are described. An analytical solution for anisotropic heat flow in layered structures is given, and a method for measuring both cross-plane and in-plane thermal conductivities of thermally anisotropic thin films is described. As verification, the technique is used to extract the cross-plane and in-plane thermal conductivities of highly ordered pyrolytic graphite. Results are found to be in good agreement with literature values.
We theoretically show that the thermal conductance associated with electron–phonon coupling in a metal near a metal–nonmetal interface can be estimated as h ep = Gkp , where G is the volumetric electron–phonon coupling constant and kp is the phonon or lattice thermal conductivity of the metal. The expression suggests h ep ≈1/ T at temperatures comparable to the Debye temperature of the metal. The predicted values of h ep fall within the range of conductance values experimentally observed (0.3–1 GW/m 2 K ), suggesting that it cannot be ignored, and could even play a dominant role at high temperatures. Predictions of the total thermal conductance, that include both electron–phonon and phonon–phonon interfacial conductances, show reasonable agreement in its temperature dependence with experimental data for TiN/MgO interfaces. © 2004 American Institute of Physics.
We theoretically compute the thermal conductivity of SiGe alloy nanowires as
a function of nanowire diameter, alloy concentration, and temperature,
obtaining a satisfactory quantitative agreement with experimental results. Our
results account for the weaker diameter dependence of the thermal conductivity
recently observed in SiGe nanowires (), as compared to pure
Si nanowires. We also present calculations in the full range of alloy
concentrations, , which may serve as a basis for comparison
with future experiments on high alloy concentration nanowires.