Recent Trends in Thermoelectric Materials Research: Part Three: 71 (Semiconductors and Semimetals)

Similarly, the Einstein temperature of the rattler is given by Eq. As shown later, Eqs. Ciathratelike Thermoelectric Compounds Room temperature ADP information can be used to estimate the Debye temperature and an average velocity of sound for any compound by Eqs. This result is well known to crystallographers. The only restriction is that the compound should have a small amount of static disorder so that the ADP values correspond to dynamic motion rather than a static displacement of the atoms.

There is a large class of promising thermoelectric compounds that contain open cages or voids in their crystal structures into which guest atoms can be added. If the guest atom is small relative to the size of the cage, the atom will be weakly bonded to the atoms comprising the cage.

These guest atoms are referred to as "rattlers," since at a given temperature these atoms tend to vibrate about their equilibrium positions substantially more than the other atom types in the structure. Filling the open cages with rattlers rapidly reduces the lattice thermal conductivity see Section V , which is desirable for a good thermoelectric material. Slack has proposed that the ideal thermoelectric material with the good electrical properties of a crystal but the poor heat conduction of a glass may be produced in these types of compounds.

A clathrate compound is an inclusion complex in which molecules or atoms of one substance are completely enclosed within another compound. Ice that has trapped an inert gas such as argon can form a new crystalline structure called an ice clathrate, in which the argon resides at the center of a large cage of water molecules. In analogy with these clathrate compounds, thermoelectric compounds with weakly bound atoms rattlers will be referred to as "clathratelike" compounds because as a first approximation, the rattler atoms and the cage framework atoms will be treated as separate phases.

Examples of clathratelike compounds are the filled skutterudites e. Schematic illustration of the dispersion behavior of a Debye solid and a Debye solid with a localized Einstein mode. The qualitative effects on the dispersion curves of the interaction between the Einstein mode and the acoustic phonons of the solid are also sketched. As a first approximation, clathratelike compounds are separated into two phases consisting of framework atoms and rattling atoms. Since the rattling atoms are only weakly coupled to the framework atoms, they are more appropriately treated as individual quantum harmonic oscillators Einstein oscillators.

The remaining framework atoms are treated within the Debye model. In this approximation the entire solid is composed of an Einstein mode in a Debye host solid. In a real solid, the Einstein mode will interact with the acoustic phonons of the Debye host see Fig. The ultimate justification for this approximation, however, is that it results in predictions that are in good agreement with experiment. For a clathratelike solid, an Einstein temperature for the rattler can be determined from the ADP data. If static disorder can be neglected, the Einstein temperature can be estimated from the room temperature ADP value using Eq.

Within this same approximation, the heat capacity of a clathratelike compound will have a Debye contribution from the framework atoms and an Einstein contribution from the rattlers. At high temperatures both the Einstein and Debye models for the heat capacity Cv at constant volume approach the classical Dulong and Petit value of 3R or At low temperatures, however, the Debye heat capacity decreases as T 3, while the Einstein heat capacity has a exponential decrease with temperature. As an example of this analysis, the ADP data from a partially filled skutterudite compound, T l o.

This is the maximum fraction of the voids that can be filled without compensating for the T1 charge by substitution on the Co or Sb sites. Heat capacity measurements o n T l o. The heat capacity difference between these two 0. Isotropic atomic displacement parameters versus temperature for a T The T1 contribution to the heat capacity is accurately described by an Einstein contribution with an Einstein temperature of 55 K. Squares are measured data; circles are calculated. The T1 contribution is accurately described by an Einstein heat capacity with an Einstein temperature of 55 -t- 2 K Fig.

These results are in excellent agreement with Eq. T12SnTe 5 is a tetragonal compound with a thermoelectric figure of merit, ZT, of about 0. The ADPs for this compound from powder neutron diffraction data Fig. The estimated Debye temperatures for the framework atoms all other atom types in the structure are K from single crystal, room temperature X-ray data Agafonov et al. If just the single crystal X-ray ADP data are used, the temperature of the specific heat should be approximately given by Eq.

The calculated heat capacity was determined from the published room temperature X-ray crystallographic data of Agafonov e t al. There were no adjustable parameters. The inset shows the calculated and measured heat capacity. At low temperatures, an Einstein temperature of 30 K provides a better description of the data than does the value of 38 K calculated from the room temperature X-ray data.

There are no adjustable parameters. A comparison between the measured and predicted heat capacity is shown in Fig. The agreement is surprisingly good. At temperatures below 15 K Fig. In a more realistic treatment of lattice thermal conductivity, which is discussed in the next section, the mean free path or relaxation time and heat capacity depend on frequency and temperature, but for the present analysis Cv depends only on temperature, whereas vs and d are treated as scalars. This analysis, which can be applied to all compounds, provides an estimate of the room temperature values of Cv and Vs that appear in Eq.

To estimate the lattice thermal conductivity using Eq. There have been several phenomenological expressions derived in the literature that relate the lattice thermal conductivity to the Debye temperature and the Grfineisen parameter 7 or to the melting temperature and the Griineisen parameter. Many of these are discussed by Goldsmid , pp. Most of the formulas are related to one another through various thermodynamic relations. Since all of the quantities in 16 can be obtained from the crystallography data, equations such as Eq. The estimates may be off, however, by as much a factor of For example, if the thermal conductivity of the filled and unfilled skutterudites are analyzed using Eq.

The room temperature lattice thermal conductivity of LaFe4Sbx2, however, is 5 to 6 times lower than that of Co48b In general there is no easy way to estimate the value of d at room temperature using just crystallographic data. Hence, for most compounds there is no obvious way to estimate the lattice thermal conductivity to better than about a factor of 5.

For clathratelike compounds, it has been experimentally observed by several groups Nolas et al. Variation of the room temperature lattice thermal resistivity vs the fraction of the voids filled with the rattler T1. The square circles refer to charge compensation with Sn Fe. This mechanism is believed to be similar to the resonant scattering described by Pohl for insulating crystals Pohl, and by Zakrzewski and White in insulating organic clathrates. It has been demonstrated that mass fluctuation scattering is much too weak to explain the rapid decrease in thermal conductivity Nolas et al.

Thermal resistivity is shown rather than thermal conductivity because as a first approximation, the scattering rates for different scattering processes should add Mathiesson's rule. There is a rapid initial increase in the thermal resistance, followed by a gradual saturation of the thermal resistance as higher concentrations of T1 are added to the voids. Within experimental error, there is no clear maximum in the thermal resistance data as a function of T1 concentration, and the maximum thermal resistance occurs near complete filling for both the Fe and Sn compensated compounds.

The maximum attributed to mass fluctuation scattering by Meisner et al. The simplest estimate of the phonon mean free path is therefore the average distance between the T1 atoms. This implies that the phonon scattering from the T1 is so strong that d attains a minimum distance given by the average T1-T1 separation. The scattering of acoustic phonons by the T1 atoms should be a maximum when the acoustic phonon and rattling frequency are equal Pohl, ; however, even at resonance it seems physically unlikely that d could be less than the T1-T1 separation distance.

A plausible approximation for d in clathratelike compounds is therefore the average separation distance between the rattlers, which is known from the crystallography data. At room temperature, this argument works well for the Tl-filled skutterudites Fig. The real test of this hypothesis is whether this analysis gives good estimates of the room temperature lattice thermal conductivity for a variety of clathratelike compounds.

As shown in Section VI, for many clathratelike systems replacing d in Eq. This means that for clathratelike compounds room temperature crystallography data can be used to provide a reasonable estimate of the lattice thermal conductivity. This is significant since a low lattice thermal conductivity is a requirement for a good thermoelectric material. Within the Debye model, the specific heat per angular frequency is obtained from Eq. For the present purposes we will follow the approach described by Pohl and Walker and Pohl and consider the minimum number of scattering mechanisms that can account for the experimental data.

These various scattering terms are given by. Equation 23 is a phenomenological expression that accounts for both umklapp and normal phonon-phonon scattering Walker and Pohl, These three scattering processes Eqs. With regard to the clathratelike compounds, simple calculations using only Eqs. The calculated thermal resistance increases linearly with the rattler concentration A o and does not saturate as is indicated in Fig. One of the key ideas to understanding the data displayed in Fig. This hypothesis, which is born out by experiment Cahill et al. For materials with thermal conductivities that approach within an order of magnitude or so of the minimum value, Eq.

To see if this approach produces reasonable results, the temperature dependence of thermal conductivity of the unfilled skutterudite C o 4 S b 12 n o rattlers was fit using Eqs. The measured Debye temperature K , velocity of sound 2. The three constants C, B, and b in Eqs. These values are in the same range as found by Walker and Pohl, The resonant phonon scattering due to the addition of T1 rattlers was then modeled using the same parameters used to fit the Co4Sbx2 data plus a resonant term Eq.

An Einstein frequency was taken from the experimental data Fig. Fit to the lattice thermal conductivity of a polycrystalline CoSb 3 sample with an average grain size of 0. Log of lattice thermal conductivity vs log T calculated using Eqs. The strength of the resonant scattering and the concentration of rattlers is proportional to the parameter A Eq. The other parameters are the same as used to fit the Co4Sb12 data. In this simple model there is expected to be a dip in the thermal conductivity at a temperature between 10 and 20 K for an Einstein temperature of 55 K.

Careful thermal conductivity measurements in this temperature range have not been made for the T1 filled skutterudites. A dip has been seen, however, in a related compound, SrsGa 16Ge3o Cohn et al. The motivation, however, for calculating the lattice thermal conductivity as a function of T1 concentration was to see if the behavior in Fig.

The room temperature thermal resistance from the calculated data shown in Fig. A least squares fit of a power law to the data yield an exponent of 0. This exponent is relatively constant for large variations in A and is surprisingly close to the value of 89obtained by simply using the average distance between rattlers for d Subsection 1 of this section.

The calculated and measured thermal resistivity data can be compared directly if the proportionality constant between A and the T1 concentration x is determined. The room temperature thermal resistance of the Tlo. A comparison between the calculated and measured thermal resistance is shown in Fig. The agreement is good.

Examples In this section, ADP data are used to extract as much information as possible about the properties of several different families of clathratelike compounds. Because the vast majority of crystallographic data reported in the literature are taken with X-rays, where possible X-ray ADP data are used in the analysis. The predicted results from the analysis of the ADP data are compared to the results from a variety of different measurements. The room temperature X-ray data from each compound were analyzed using Eqs.

Room temperature velocity of sound data Sales et al. Calculated thermal resistance at room temperature vs the resonant scattering amplitude, A. The room temperature thermal resistance is from the calculated data shown in Fig. A is proportional to the concentration of rattlers, x. Thermal resistivity vs T1 concentration, a comparison between the model calculation and the experimental data.

The thermal resistance of the Tlo. The incident neutron energy was 30 meV and the energy resolution was 2 meV. CeFe4Sb12 was used as a reference because the neutron scattering cross section of Ce is much smaller than that of La. The difference spectra therefore reflects the vibrational density of states DOS associated with the La atoms. The peaks at 7 and 15 meV correspond to temperatures of 80 and K Keppens et al.

The estimated room temperature lattice thermal conductivity from the room temperature X-ray ADP data using Eq. These values can be compared to the measured values of 0. The La phonon density of states has been measured using inelastic neutron scattering Keppens et al. A clear peak in the La phonon density of states was observed at 80 K along with a weaker and broader peak near K Fig. Both peaks can be understood within the framework of a detailed investigation of the lattice dynamics of LaFe4Sb12 Feldman et al. Qualitatively the two peaks result from a hybridization process similar to that sketched in Fig.

A summary of ADP information from a variety of filled skutterudite phases has been reported by Kaiser and Jeitschko and Chakoumakos et al. The Wiedemann-Franz law has been used to estimate and subtract the electronic portion of the thermal conductivity. The lines through the data are guides to the eye. This compound has a room temperature value for Z T of 0. The compound is tetragonal with columns of T1 ions along the crystallographic c axis.

There are two distinct T1 sites in the structure, and at one of the sites the T1 atoms sit near the center of a large, oversized distorted cube. The T1 ADP parameter at this site is considerably larger than for the other atoms in the structure and the T1 at this site will be treated as a rattler. As was shown in Section IV, these values can be used to estimate the temperature dependence of the heat capacity, and the calculated heat capacity is in good agreement with the measured values Fig. The estimate of the room temperature lattice thermal condutivity from the ADP data is 0.

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The measured lattice thermal conductivity for TlzSnTe 5 is shown in Fig. LaB 6 LaB 6 is not a good thermoelectric material, but it is a clathratelike compound. Model of LaB 6 crystal structure. La atoms large ball sit at the center of a cube with B 6 "molecules" at each cube corner. As a first approximation, the La atoms can be treated as Einstein oscillators in a Debye solid composed of B atoms. La at the cube center and B 6 octahedral clusters at each cube corner Fig. Because of its technological importance, much is known about the properties of LaB 6.

When normalized by mass, the lanthanum ions "rattle" significantly more about their equilibrium positions than do the boron atoms. Using published ADP data Korsukova et al. The extrapolation graph shown in Fig. The Debye temperature was adjusted to K rather than K to provide a better fit to the data. The agreement between the calculated heat capacity and the measured values is shown in Fig. An unusually energy-independent phonon mode was found over most of the Brillioun zone at energies corresponding to an Einstein temperature of K; a value close to the K value estimated from the ADP data.

This mode was attributed by Smith et al. Calculated and measured heat capacity of LaB 6. The thermoelectric properties of SrsGa16Ge3o and similar compounds were first reported by Nolas et al. The structure can be thought of as a tetrahedral framework of Ga and Ge atoms. The framework atoms form large cages of 20 or 24 atoms that surround the Sr or Ba atoms in the structure. The alkaline earth atoms in the larger cage have unusually large ADP values. This results in a Debye sound velocity of 2.

The measured lattice thermal conductivity Fig. Although the measured lattice thermal conductivity is about twice the predicted value, this is still better agreement than most other simple methods of estimating lattice thermal conductivity. In general it should be expected that the estimate will be lower than the measured value, since it is assumed in this simple analysis that the rattlers scatter phonons at the maximum possible rate corresponding to d given by the rattler separation distance.

The thermal conductivity of the Ba clathrate, although small, has a crystalline temperature dependence, whereas the temperature dependence of the Sr clathrate is glasslike. There are no published single crystal X-ray ADP data for the Sr clathrate, so the neutron data reported by Chakoumakos et al. ADP data for this compound are available from room temperature down to 11 K Fig. The ADP values of Sr atoms in the large cage Sr2 in the figure are huge relative to the other atoms in the structure. The temperature dependence of the Sr2 ADP data is unusually weak, however, suggesting a large amount of static disorder.

Such a large amount of static disorder in a nominally stochiometric compound is unusual, as can be seen from comparing the ADP data in Figs. If just the room temperature ADP data are used, the Sr rattlers appear to have at, Einstein temperature of 44 K and a Debye temperature for all the atoms oi K without the rattler, this value would be K.

For this compound, however, static disorder cannot be i g n o r e d - - a t least for the Sr2 site. The estimated room temperature lattice thermal conductivity is 0. If only the room temperature ADP data were used, the estimated lattice thermal conductivity would be lowered to about 0. The measured value of the room temperature lattice thermal conductivity of Sr8Ga16Ge30 is about 0. The large amount of static disorder at the Sr2 site is due to the tendency of the Sr atoms at this site to move or tunnel off center to one of four nearby sites located about 0.

Temperature dependence of the isotropic atomic displacement parameters for SrsGa16Ge3o. Note the large and weak temperature dependence of the ADP values for Sr at site 2 in the structure. See text for details Chakoumakos et al. The rattling of the Ba results in a low thermal conductivity, but the temperature dependence is crystal-like, whereas the rattling and tunneling of the Sr results in a true glasslike thermal conductivity Fig.

CeRuGe 3 To further test some of the simple ideas discussed in this chapter, room temperature A D P information was used to identify a compound that should have a very low lattice thermal conductivity. Thermal conductivity vs temperature for CeRuGe3. The electronic thermal conductivity was subtracted from the total using the Wiedemann-Franz law.

The distance between the Ce rattlers is 7. CeRuGe 3 has a low lattice thermal conductivity, but also has a low Seebeck coefficient and hence is not a promising thermoelectric material. Summary A new structure-property relationship is discussed that links atomic displacement parameters and the lattice thermal conductivity of clathratelike compounds. For many clathratelike compounds in which one of the atom types is weakly bound and "rattles" within its atomic cage, it is demonstrated that room temperature ADP information can be used to estimate the room temperature lattice thermal conductivity, the vibration frequency of the "rattler," and the temperature dependence of the heat capacity.

X-ray and neutron diffraction crystallographic data, reported in the literature, are used to apply this analysis to several promising classes of thermoelectric materials. Less Common Metals 72, Alloys and Compounds , Less-Common Metals , Semiconductor Thermoelements and Thermoelectric Cooling. Alloys Compounds , Introduction to Solid State Physics, 3rd ed. John Wiley and Sons, New York, pp. Academic Press, New York. Promising Candidates for Thermoelectric Applications," Appl. Electron Crystals and Phonon Glasses," Phys. Mahan, and Hylon B. A Chemical Bond Approach," Phys. Thermal Vibrations in Crystallography.

Cambridge University Press, London. Bandgap Features Inferred f r o m Doping Studies. Impurity B a n d Transport Properties. For a majority of the Heusler phases, M' is either a transition metal or noble metal, and M is a transition metal, a noble metal, or a 37 Copyright 9 by Academic Press All fights of reproduction in any form reserved. Crystalstructure of the half-Heusler MgAgAs type phase. In the case of ZrNiSn, Zr and Sn in the rock-salt substructure are denoted by large filled and unfilled circles. Half of the cubic interstices of the ZrSn substructure are occupied by Ni small filled circles.

The crystal structure of the Heusler phase is of the Bi3F type space group Fm3m and its unit cell consists of four interpenetrating face-centered cubic fcc sublattices. Each of the four fcc sublattices has the same unit cell size as that of the Heusler phase. There are a total of 16 atoms per unit cell. Two of the fcc sublattices, denoted by MX, form a rock-salt substructure. With each of the cubic interstices of MX being filled by an M' atom, the Heusler phase can be described as a "stuffed rock salt.

The latter phase, which is now a "half-stuffed rock salt," has 12 atoms per unit cell see Fig. Typical X-ray diffraction powder patterns of half-Heusler phases and their multinary solid solutions have been published e. Both Heusler and half-Heusler phases are chemically diverse and are known to exist in more than and alloy systems, respectively Villars and Calvert, The presence of tetrahedral coordinated bonding sites reduces the overlap between d wave functions as well as that between d and sp wave functions, which gives rise to narrower bands in the energy spectra.

These bonding configurations have implications for the phase stability as well as the occurrence of bandgaps and unusual magnetic states. The penchant for covalency is evident from the fact that most of the half-Heusler phases are found within a restricted range of valence electron count VEC , which is centered at 8 or 18 electrons per formula unit. In the early s, a group of half-Heusler compounds, notably NiMnSb and PtMnSb, first attracted attention for the peculiar electronic structure properties they exhibit de Groot et al.

These compounds, now widely known as half-metallic ferromagnets, are characterized by the appearance of a metallic spin-up band and a gapped spin-down band inside which the Fermi level lies de Groot et al. The half-metallic behavior is due to the strong magnetic splitting of the energy bands. A decade ago, a group of half-Heusler compounds of formula MNiSn M - - T i , Zr, Hf was found to exhibit semiconducting behavior in electrical and optical measurements Aliev et al. A bandgap on the order of 0.

In fact, a semiconducting gap is obtained in the density of states DOS of all the systems investigated, and whether the compound is semiconducting or metallic is determined by the position of the Fermi level E v with respect to the gap Tobola et al. For alloys with VEC of 18, E v is found to lie at the top of the highest occupied valence band. As the VEC decreases or increases, E v is seen to fall below the top of the highest occupied valence band or rise above the bottom of the lowest conduction band, which results in a p-type or n-type metallic state, respectively.

In addition, spin-polarized states in several metallic phases are also observed in the calculations Tobola et al. The parameters S and o, which tend to manifest an inverse relationship, are strong functions of the doping level and chemical composition, which must therefore be optimized for good thermoelectric performance. It has been noted that the product factor SzG, known as the power factor, can be maximized via doping to attain the semiconductor-to-semimetal SCSM transition Mahan et al. Understanding these various effects and selecting optimization strategies can be an exceedingly difficult problem, because in complex materials there are often many possible degrees of freedom.

In , Slack suggested that the best thermoelectric material would behave as a "phonon-glass, electron-crystal" material Slack, That is, the materials would have the thermal properties of a glass and the electronic properties of a crystal. There are ongoing efforts to improve the performance of the well-known TE alloys.

Meanwhile, researchers have also been investigating other lesserknown compounds and exploring new alloy systems as potential TE materials. For commercialization purposes, it is desirable that the TE materials be relatively simple to synthesize and process, and that their electronic and lattice properties can be conveniently tuned and also reproduced. In addition, when used in a high-temperature environment, the materials are required to be chemically and thermally stable.

Metal-rich intermetallic compounds tend to possess many of these desirable properties and may therefore serve as better alternatives to some of the traditional TE alloys. Many research groups are now actively investigating new intermetallic compounds based on rare-earth lanthanide metals and transition metals as prospective TE materials. In view of their large thermopower and only moderately high resistivity, their potential as TE materials was readily pointed out Cook et al. Thus, the SCSM transition can be monitored easily by doping the host alloy.

Also, the high lattice thermal conductivity, which is the least desirable property of these alloys, may be reduced via elemental substitution at the sublattice sites or addition into the unfilled sites to enhance phonon scattering Hohl et al. There are other attributes that also make the half-Heusler alloys potentially attractive for thermoelectric applications above room temperature. The materials are relatively easy to synthesize, and multinary alloys with designed stoichiometry can be produced using a conventional arc furnace. Since the ingots can be cut using a diamond saw, their mechanical sturdiness suggests that they should be easy to process.

Furthermore, their isotropic structure suggests that neither single crystals nor oriented films are required for maximizing the performance. Many of these intermetallic compounds, including those half-Heusler phases based on rare-earth metals Mastronardi et al. In particular, extensive electrical and thermal transport characterization of alloys that span a wide range of compositions 42 S. Fundamental issues that involve bandgap structure, magnetic state, charge transport, and localization properties are addressed.

Thermal conduction by charge and phonon in these nontraditional semiconducting phases is also discussed. These basic issues can be further studied by examining the effects due to doping and substitution on properties. Experimental results are discussed in light of band-structure calculations and transport models. Based on the discussion of electronic and lattice effects on power factor and ZT, the feasibility of using half-Heusler alloys as thermoelectric materials is evaluated.

Thus, the investigative approach is designed to supplement the commonly used "synthesis and measure" approach with a fundamental basis in optimizing TE properties. This chapter is organized as following: Experimental methods are described in Section II. In Section III, electronic and thermal transport properties as well as magnetic properties of undoped compounds are discussed. Section IV reports on the properties of doped alloys.

In Sections III and IV, comparison with band structure and transport models is made, and thermoelectric properties of both doped and undoped alloys are discussed. Section V is the conclusion. Experimental Procedures The experimental methods described herein are those used by the author's group.

Ingots of the alloys studied were prepared by arc melting appropriate quantities of the constituent elements together under an argon atmosphere. The overall purity of the starting materials was The ingots' compositions were also checked by chemical analysis. Further improvement of the samples' chemical homogeneity was also attempted by melting pressed pellets of thoroughly mixed elemental powders. Both types of samples were found to exhibit almost identical properties. Two-step annealing was carried out in an evacuated and sealed quartz tube with the sample wrapped in a tantalum foil.

The phase MgAgAs purity of our alloys was assessed via X-ray diffraction.

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DC resistivity was measured from 4. Thermopower was measured by the standard differential technique. Copper-constantan thermocouples were used to measure the hot and cold end temperatures. The copper leads of the thermocouples were used to measure the thermo-emf. Specific heat and Hall coefficient were measured from 2 to K by using a commercial Physical Property Measurement System.

Hall effect was measured up to 5 T. Thermal conductivity and high-temperature resistivity and thermopower measurements were performed as described elsewhere see Chapter 2. In substituted alloys, one can examine the changes in electronic properties by varying the level and type of chemical disorder. After all, thermoelectric materials are substituted alloys that exhibit both doping and disorder effects. Discussion of electronic structure properties as a function of VEC is featured in Subsection 4 of this section. Room-temperature p values are given in the figure caption.

It is seen that the order of magnitude of the resistivity ratio R normalized resistivity at 4. Bottom plot Same for Zro. Inset p K from top to bottom plot ZrNiSn: Resistivity versus temperature, plotted from top to bottom, for Tio. Hall coetficient versus temperature for ZrNiSn and Zro. Data for ZrNiSn above K are additionally shown on a magnified scale. Thermopower versus temperature for Zr, Hf NiSn alloys. The uppermost plot is for ZrNiSn taken from Uher et al.

For this alloy and ZrNiSn, the saturation of resistivity and the opposite signs exhibited by R n positive and S negative at low T indicate band overlapping at the Fermi level. These experimental results, coupled with S being negative from 4. Electron mass in the range of 2 - 5 times the free electron value is obtained from transport experiments, which is in good agreement with band-structure results.

However, the shape of S T differs quite significantly among the reported results, as illustrated in Fig. A plausible origin of the enhanced S T observed is given in the following subsection. The effective carrier density neff and mobility are estimated from Hall effect and resistivity measurements using a o n e - b a n d model. The precision of the parameters is according to that given in the references.

The coefficient 7 of the electronic term in the specific heat and the Debye temperature 0D of several alloys are tabulated in Table II. The small upturn may be due to the presence of magnetic impurities or structural defects or other unknown effects. For comparison, our measurements of high-purity The specific-heat plot for ZrNiSn exhibits an anomalous trend at low T. Significantly smaller 0o values are seen in the Zr alloys in comparison with those based on Ti. Whether these results can be accounted for by band-structure effect alone awaits further investigation.

Other four plots from top: Our multinary alloys are not restricted to those with VEC -- Quite surprisingly, drastic modifications of the electronic structure properties of the base compounds are observed. SC behavior is seen in some of the high p alloys. Clearly, these compounds deserve our further attention. Other Phases Since the early s, new half-Heusler compounds that are not listed in Pearson's Handbook Villars and Calvert, have continued to be found.

There are also new compounds based on the rare-earth metals. The transport properties reported on the nonlanthanide alloys can be compared with those observed in YNiSb as well as the lanthanide series LnNiSb Sportouch et al. The transport parameters of several of these alloy systems are listed in Table I. The high S K values observed are comparable to those seen in the former group of alloys.

Apparently, the relative contributions of electron band mass and hole band mass are different in the two groups. Furthermore, the Ln alloys exhibit resistivities that are only weakly dependent on temperature i. Thus, taking the structural order of the samples into account, even smaller experimental gaps are to be expected. To facilitate the discussion, key features of the measured transport properties are summarized: In many compounds, SM behavior is noted below the temperature region K.

Meanwhile, RH T can be positive or negative at low T. Features a and b give direct evidence to the proposal of band overlapping. In particular, feature b further underscores the important role of electron band mass at the Fermi level pointed out earlier Uher et al. For the latter system, measurements have revealed a small neff 4. Clearly, the observed properties of the half-Heusler phases, which are based on metals, are not those expected of an intrinsic semiconductor. In other words, a semiconducting gap in the absolute sense is not attained.

The results are most likely due to the fact that it is difficult, if not impossible, to achieve perfect crystallographic order in the half-Heusler alloys. Early on, site exchange between the atoms in different sublattices was pointed out Aliev et al. As a matter of fact, the transport properties of the samples are reported to be strongly dependent on annealing conditions Aliev et al. One of the band-structure studies also indicates that the width of the gap depends strongly on the degree of disorder of M and Sn atoms Ogut and Rabe, A gap as large as 0. Not surprisingly, structural disorder has also been found to affect the magnetic properties of ferromagnetic half-Heusler phases Subsection 4.

In order to account for feature c noted in Zr, Hf NiSn, the formation of intragap states or bands in the band-overlapping region must be invoked. The Fermi level lies in the region where the intragap band and conduction band overlap. At low T, carrier transport takes place in the band-overlapping region where the conduction band mass is moderately heavy.

As T increases, more carriers are excited to the conduction band. In lieu of a two-band analysis of the Hall coefficient, the values listed should be treated as order-of-magnitude estimates only. Comparable low values of p for the Ln-based half-Heusler alloys can be inferred from transport measurements Sportouch et al. Conventional thermoelectric alloys possess values that are at least one order of magnitude higher than those shown in Table I. Despite the high p and low g obtained, the carrier mobilities in halfHeusler alloys are at least one order of magnitude higher than those estimated for metallic glasses and quasicrystals Poon et al.

The latter classes of alloys are known to possess a very high degree of structural complexity. Even for the highly substituted Zro. Extending the comparison further, it is noted that decreases with T in the half-Heusler alloys, but increases with T in the QCs. In fact, carrier localization has been seen in the QCs Poon et al. However, it should be pointed out that the effects of structural quality on carrier conduction in the latter alloys have yet to be investigated. Present investigation of substituted half-Heusler alloys, which possess much simpler structure than QC alloys, has shown that substitution disorder alone is not sufficient for carrier localization.

These findings have helped to clarify the role of structural complexity in carrier localization. The VEC of these phases ranges from 17 to The largest gap, which is about 0. The readers can refer to the many DOS spectra illustrated in the papers by Tobola et al. As VEC increases from 17 to 19, the position of the Fermi level is seen to shift from being inside the valence band to inside the conduction band. Consequently, a metallic-semiconducting-to-metallic sequence of conducting states is obtained.

Earlier, a moderately high specific heat 7 was measured in TiCoSn Kuentzler et al. Thus, the occurrence of ferromagnetic state can be understood in light of the itinerant-electron hole magnetism picture. The magnetization in these alloys is found to follow an "M 2 linear in T 2'' law, which is characteristic of an itinerant ferromagnet. The SC-SM crossover and onset of magnetic moment observed in the pseudoternaries are found to be in good agreement with band-structure results.

Despite the success of the latter model in explaining the various properties, however, some discrepancies remain. For example, the calculations predict a ferromagnetic state for TiFeSb and a fully polarized state for VCoSb, which are not observed. The authors contend that crystallographic disorder in the real systems could lead to the discrepancies, similar to those reported on observed transport properties see Subsection 2. In fact, depending on sample preparation, VCoSb is found to exhibit a range of magnetic properties: Top to bottom plot: Summing up the various transport and magnetic studies reported, it can be seen that the interplay of orbital hybridization, Coulomb direct and exchange interaction, atomic disorder, and localization effects is responsible for the interesting properties observed in half-Heusler alloys.

Similar effects are also known to be responsible for many of the novel properties found in the manganites and heavy-fermion compounds. The magnetic properties of many lanthanide phases have been reviewed Karla et al. In addition to the investigation of electronic structure properties of intermetallic phases, the band-structure approach has also been taken to study thermoelectric properties see, for example, Chapter 5, by D. The power factor sZtr of these alloys was seen to increase from about 7. The TE parameters obtained thus indicated Z T to be 0.

Meanwhile, extensive studies of halfHeusler phases Uher et al. A similar range of power factor values is also found in alloys with the heavy lanthanides replacing the M elements Cook et al. Despite the low room-temperature Z T of less than 0. Indeed, in view of the promising Seebeck coefficients, a considerable amount of effort has been devoted to reducing the high lattice thermal conductivity, which is the least desirable property of the halfHeusler alloys. Utilizing the high substitutability of half-Heusler alloys, one may employ elemental substitution at the sublattice sites or addition into the unfilled sites to increase phonon scattering.

An initial effort was made to reduce x by introducing mass fluctuation via substitution in the M sites of MNiSn phases Hohl et al. A significant decrease of x in the pseudoquaternary solutions by as much as a factor of 2 was found Table I. More recent studies of the pseudoternaries Uher et al. It is also found that K increases with the improved structural order in well-annealed samples Uher et al. It seems that K in many of the samples studied tends to increase, and in some cases quite noticeably, in the high T region e.

Whether such a trend is due to intrinsic or radiation effects will need to be clarified. Also, quantitative analysis of K T in light of various phonon scattering models is just beginning. Recent substitution studies have also involved the Sn sublattice. Thermal conductivity versus temperature for alloys based on ZrNiSn.

Top to bottom plot refer to values at K: ZrNiSn Uher et al. The mechanisms for achieving low K values in the M- and R-based alloys certainly deserve further investigation. Similar low tr values have been reported for the cubic LnaAu3Sb4-type phases with a more complex crystal structure Young et al. Apart from structural complexity, the preceding studies suggest that low thermal conductivity can be realized in solid solutions that contain heavy elements, particularly in the readily realized lanthanide compounds. Doped Alloys Further studies of bandgap characteristics and carrier conduction have been carried out in doped alloys.

The variation of electronic structure properties as a function of the type and level of doping have been studied. Evolution of bandgap properties, particularly with regard to the SC-SM crossover, has been of fundamental interest in the study of semiconductors Mott and Davis, Since it is known that the power factor of a thermoelectric material is optimized in the vicinity of the SC-SM crossover Mahan et al.

Considering the crystallography of halfHeusler phases, the variation of properties will need to be examined for each of the three different sites in the MgAgAs structure. Isoelectronic substitutions of the Ti site with Hf, and the Ni site with Pd and Pt, are also performed. For some dopants, it may be necessary to extend the study to higher concentrations, and thus the issue of substitutability must be considered. Temperaturedependent resistivity plots for the Sb-doped alloys are shown in Fig.

The SM behavior of the Sb-doped alloys can be seen from the plots. Semimetallic p T behavior is also seen in the V-doped alloys. To minimize effects due to thermal scattering at high T, the alloys' conductivities measured at 4. The plots reveal different dependences on dopants. Although the dependence of p 4. Previous study had shown a similar slow decrease for Xco 60 S. From top to bottom: The latter alloys indicate SM behavior at low T Fig. Previous studies have also found efficient doping in the Sn site of Zro.

In the efficiently doped alloys, both p and S decrease quite rapidly. Some representative results are illustrated in Table III. In addition to electron doping, the latter groups of authors have demonstrated the effects on S T due to hole doping by using Y and In as dopants. Doping transition metals into the three sublattices of TiCoSb produces results that are drastically different from those seen in TiNiSn.

However, upon doping V and Mn in 0. The latter group of dopants exhibits doping trends similar to those seen in TiNiSn. Figure 13 summarizes p 4. To further study the anomalous behavior observed in the V-doped TiCoSb alloys, we turn now to the p T plots shown in Fig. Plotted on the log lo scale, p T for the V-doped samples displays shoulderlike features between 50 K and K.

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The trend suggests two activation processes, with one occurring at T K. Future study will also include investigation of magnetic properties in the crossover region. Unlike M-based phases, the observed properties of the Ln phases do not indicate a clear trend as a function of VEC. Apparently, because of the mixed valence nature of the rare earth elements, the alloys' VEC values are not easily defined. However, significant changes in transport properties upon alloying are observed, which seem to indicate some kind of doping effects. In view of the strong dependence of doping effects on host alloys, it is pertinent to review the role of the sublattice in gap formation.

For ZrNiSn and TiNiSn, the strong pd hybridization in the ZrSn and TiSn substructures is found to play an important role in the gap formation by significantly reducing band crossing near the Fermi level. However, the actual opening of the gap is due to the coupling between the Ni sublattice and ZrSn or TiSn substructure via the d 64 S.

A much more sensitive doping response in the TiSn and ZrNi rock-salt substructure compared to that in the Ni site would suggest that the rock-salt substructure must play a more prominent role in bandgap formation than indicated by the calculations. On the other hand, the results in TiCoSb cannot be readily related to band-structure calculations.

In Subsection 2 of Section III, the SM trend observed at low T in the pure alloys is attributed to a bandgap structure with the Fermi level located in the region where the electron and hole bands overlap. However, different from undoped ZrNiSn and HfNiSn, which exhibit near-zero and almost temperature-independent negative thermopower at low T Uher et al.

Meanwhile, R n is found to remain negative up to ambient temperature in both pure and doped TiNiSn alloys. Meanwhile, quite large room-temperature S values are retained at low doping level. As can be seen in Fig. The near-linear S T dependence and the quite high room-temperature values retained in the semimetallic phases have implications on high-temperature TE properties, to be discussed in Subsection 4 of this section. It is found that Co and Mn, with their larger ionic charges, tend to retain their valence electrons upon dissolution in the host alloys Tobola et al.

Thus, it is plausible that doping Mn and V has led to the formation of an impurity band below the conduction band and a reduction in the effective carrier density. The electronic states in the region where the conduction band overlaps with the impurity-band tail, and where the Fermi level lies, can either be localized or extended, depending on whether the Anderson condition is fulfilled or not Subsection 3 of Section III.

At low T, conduction is via activation near the mobility edge. Based on the upturn exhibited in p at low T, the hopping energy is estimated to be of the order of 0. At high T, more carriers are excited from the main part of the impurity band to the conduction band. The observation of more distinctive semiconducting features in TiCoSb is consistent with the presence of a gap that is wider, and presumably better defined, than those in other half-Heusler alloys Pierre et al.

These results again indicate band overlapping and heavy electron band mass at the Fermi level. It is noted that S T is enhanced significantly in the V-doped alloys. The enhancement can be ascribed to the reduction in carrier density near the Fermi level due to the formation of an impurity band in the V-doped alloys mentioned above see discussion on S T enhancement due to the formation of an intragap band 66 S. In view of the proximity of magnetic V d-states at the Fermi level in VCoSb, the evolution of bandgap structure and the nature of semiconductor-metal crossover in V-doped TiCoSb are naturally of fundamental interest see also Subsection 1 of this section.

Based on several studies, the most efficient dopants for these phases appear to belong to the group Va elements V, Nb, and Ta Hohl et al. These values are three to five times larger than those found in the undoped phases Subsection 5 of Section III. Furthermore, the promising results on TE properties at high T Subsection 5 of Section III and the following coupled with high thermal stability indicate that these alloys are likely to be used above ambient temperature.

These power factor values, which are high, are comparable to those measured on practical TE materials Goldsmid, ; also articles in C R C Handbook of Thermoelectrics, edited by D. Rowe, ; Tritt, In view of these results, measurements on Sb-doped Tio. The latter is selected for its lower thermal conductivity.

Upper plot is for alloys based on TiNiSn Bhattacharya et al. Lower two plots are for alloys based on Tio. Long-term annealing is performed to promote structural order. In doped alloys, long-term annealing can in addition promote E 0 d Enhancing the uniform dissolution of dopants has the effect of decreasing p and S. Clearly, long-range atomic diffusion must be involved in achieving the desired structural state. Apparently, the combined annealing effects on the structural order and the dissolution of dopant atoms have led to the observed trends in p and S. Figure 15 illustrates annealing results for Sb-doped Tio.

The power factor obtained in the solid solution system is comparable to that reported for Sb-doped Zro. In doped Zr, Hf NiSn alloys, these values are found to reach , The results are shown in Fig. It is seen that S is doubled while p increases 0 0. S and p of Tio. Measured power factor versus temperature. From top to bottom plot: Especially for the Ti alloys, the power factors of half-Heusler phases obtained at high T are comparable to those found in state-of-the-art TE alloys Tritt, ; also papers in M R S Symp.

I C T '99 Compared with the Zr alloys Fig. The x of Tio. Thus, Xe is assumed to be constant above K. Estimated dimensionless figure of merit Z T versus temperature for the alloy shown in Fig. Similar low carrier mobility and large electron band mass have also been noted in Sb-doped Zr, Hf NiSn alloys Uher et al. Thus, for the half-Heusler alloys, it is the moderately large effective mass that leads to the quite high SZa values. Despite the low , large Seebeck coefficients are obtained in many of these alloys.

These findings have revealed some unique relationships between the various thermoelectric properties. You can get the remaining amount to reach the Free shipping threshold by adding any eligible item to your cart. We will send you an SMS containing a verification code.

Recent Trends in Thermoelectric Materials Research: Part Three -- Tritt, Terry -ѕ©¶«ФД¶Б-ФЪПЯФД¶Б

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