Semiconductorlike transport in highly ordered Al-Cu-Ru quasicrystals

2001

Phys. Rev. B

In this work we present a theoretical study on the possible use of quasicrystals as potential thermoelectric materials. By considering a suitable model for the spectral conductivity we show that high values of the thermoelectric figure of merit, beyond the practical upper limit ZTϭ1, may be expected for certain quasicrystalline alloys. We also study their performance at different working temperature ranges, favoring low temperature thermoelectric applications for these materials. By comparing our analytical results with available experimental data on the transport coefficients of different quasicrystalline families, we suggest the icosahedral Cd-Yb and the dodecagonal Ta-Te binary phases as two promising candidates for further research.

Section: Physical Motivationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Theoretical prospective of quasicrystals as thermoelectric materials

2001

Phys. Rev. B

“…2 Quasicrystals ͑QCs͒ are well-ordered metallic alloys exhibiting a broad collection of anomalous transport properties, [3][4][5] resembling more semiconductor-like than metallic character. 6 Thus, a proper classification of these materials, able to account for both their peculiar electronic structure and their related transport properties, remains elusive. 7 In addition, it has been reported that Ohm's law holds in high quality icosahedral QCs, 8 hence, opening the question regarding what other fundamental laws may also be followed by these materials.…”

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confidence: 99%

Do quasicrystals follow Wiedemann–Franz’s law?

Applied Physics Letters

2002

In this work we present a theoretical study on the thermal and electrical conductivities of quasicrystals. By considering a realistic model for the spectral conductivity we derive closed analytical expressions for the transport coefficients which allow us to study the temperature dependence of the Lorenz ratio L(T)ϭ e (T)/T (T) at different temperature regimes. We conclude that quasicrystals closely follow Wiedemann-Franz's law over a wide temperature range. © 2002 American Institute of Physics. ͓DOI: 10.1063/1.1488696͔ According to Wiedemann-Franz's law ͑WFL͒ in most materials thermal and electrical conductivities are mutually related, over certain temperature ranges, through the relationship e (T)/ (T)ϭL 0 T, where e (T) gives the contribution to the thermal conductivity due to the charge carriers, (T) is the electrical conductivity, T is the temperature, and L 0 ϭ(k B /e) 2 0 is the Lorenz number, where k B is the Boltzmann constant, e is the electron charge, and 0 is a constant whose value depends on the nature of the sample. Thus, for metallic systems 0 ϭ 2 /3, and we get the Sommerfeld's value L 0 ϭ2.44ϫ10 Ϫ8 W ⍀K Ϫ2 , while for semiconductors described by Maxwell-Boltzmann statistics we have 0 Ӎ2. 1 The WFL has a broad range of validity, and usually holds for arbitrary band structures provided that the change in energy during an electron collision is small compared with k B T. Then, elastic processes dominate the transport coefficients, and the carriers motion determines both the electrical and thermal currents. 2 Quasicrystals ͑QCs͒ are well-ordered metallic alloys exhibiting a broad collection of anomalous transport properties, 3-5 resembling more semiconductor-like than metallic character. 6 Thus, a proper classification of these materials, able to account for both their peculiar electronic structure and their related transport properties, remains elusive. 7 In addition, it has been reported that Ohm's law holds in high quality icosahedral QCs, 8 hence, opening the question regarding what other fundamental laws may also be followed by these materials. From a fundamental viewpoint it seems then quite pertinent to ascertain whether one may expect the WFL to hold in the case of QCs as well. Furthermore, the study of the WFL validity range is also crucial in order to test the working hypothesis usually made when estimating the phonons contribution to the thermal conductivity, ph (T), by substracting to the experimental data, mes (T), the electronic contribution according to the expression ph ϭ mes ϪL 0 T . In fact, were the WFL not valid for QCs, several conclusions about the phonon dynamics in these materials should be substantially revised, an important question which has been scarcely considered in the literature. 9 Unfortunately, the high electrical resistivity of QCs currently prevents an accurate experimental evaluation of the Lorenz number for these materials. 10,11 The main goal of this work is then to theoretically estimate the validity of WFL for QCs, providing some physical insight aimed to spur...

“…In fact, thermodynamically stable quasicrystals ͑QCs͒ of high structural quality 3 exhibit unusual composition and temperature dependences of their transport coefficients, 4 which resemble more semiconductorlike than metallic character. 5 Theoretical efforts aimed to understand these anomalous transport phenomena have rendered two main results: ͑i͒ the existence of spiky features in the DOS near the Fermi level, 6 and ͑ii͒ the presence of a pronounced pseudogap at the Fermi level. 7 The presence of a pseudogap has received strong experimental support during the last decade.…”

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confidence: 99%

“…Consequently, QCs are marginally metallic and should be properly located at the borderline between metals and semiconductors. 5 In addition, the thermal conductivity of QCs is unusually low for a metallic alloy and it is mainly determined by the lattice phonons ͑rather than the charge carriers͒ over a wide temperature range. 15 The low thermal conductivity of QCs is particularly appealing in the light of Slack's phonon-glass/electron-crystal description, 16 as properly highlighted by some recent studies on thermoelectric properties of QCs.…”

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confidence: 99%

May quasicrystals be good thermoelectric materials?

Applied Physics Letters

2000

We present a theoretical analysis of quasicrystals ͑QCs͒ as potential thermoelectric materials. We consider a self-similar density of states model and extend the framework introduced in ͓G. D. Mahan and J. O. Sofo, Proc. Natl. Acad. Sci. U.S.A. 93, 7436 ͑1996͔͒ to systems exhibiting correlated features in their electronic structure. We show that relatively high values of the thermoelectric figure of merit, ranging from 0.01 up to 1.6 at room temperature, may be expected for these systems. We compare our results with available experimental data on transport properties of QCs and suggest some potential candidates for thermoelectric applications. © 2000 American Institute of Physics. ͓S0003-6951͑00͒03545-2͔During the last few years we have witnessed a growing interest in searching for high performance thermoelectric materials ͑TEMs͒. 1 The efficiency of thermoelectric devices depends on the transport coefficients of the constituent materials and it can be properly expressed in terms of the figure of merit ͑FOM͒ given by the dimensionless expression ϵZTϭ T S 2 /( e ϩ ph ) , where T is the temperature, is the electrical conductivity, S is the Seebeck coefficient and e and ph are the thermal conductivities due to the electrons and lattice phonons, respectively. The appealing question regarding what electronic structure provides the largest possible FOM was recently addressed by Mahan and Sofo 2 concluding that ͑i͒ the best TEM is likely to be found among materials exhibiting a sharp singularity ͑Dirac delta function͒ in the density of states ͑DOS͒ close to the Fermi level, and ͑ii͒, in that case, the effect of the DOS background contribution onto the FOM value may be quite dramatic: The FOM value being inversely proportional ͑in a marked nonlinear way͒ to the DOS value near the singularity.Quite interestingly the electronic structure of quasicrystalline alloys may satisfy these requirements in a natural way. In fact, thermodynamically stable quasicrystals ͑QCs͒ of high structural quality 3 exhibit unusual composition and temperature dependences of their transport coefficients, 4 which resemble more semiconductorlike than metallic character. 5 Theoretical efforts aimed to understand these anomalous transport phenomena have rendered two main results: ͑i͒ the existence of spiky features in the DOS near the Fermi level, 6 and ͑ii͒ the presence of a pronounced pseudogap at the Fermi level. 7