We have investigated anisotropic electrical resistivity andthermoelectric power of the ypsilon-phase Al-Ni-Co (Y-Al-Ni-Co)decagonal approximant with composition Al(76)Co(22)Ni(2). Thecrystalline-direction-dependent measurements were performed along threeorthogonal directions a*, b and c of the Y-Al-Ni-Co unit cell, where(a, c) monoclinic atomic planes are stacked along the perpendicular bdirection. Anisotropic electrical resistivity is low in all crystallinedirections, appearing in the order rho(a*) &gt; rho(c) &gt; rho(b) andshowing positive temperature coefficient typical of electron-phononscattering mechanism. Thermopower shows electron-phonon enhancementeffect. Anisotropic bare thermopower (in the absence of electron-phononinteractions) was extracted, appearing in the same order as theresistivity, vertical bar S(a*)(bare)/T vertical bar &gt; vertical barS(c)(bare)/T vertical bar &gt; vertical bar S(b)(bare)/T vertical bar

Barišić, Osor S.

Dolinšek, Janez

Gille, Peter

Smontara, Ana

English

Open Access LMU

Phonon-enhanced thermoelectric powerof Y– Al– Ni– Co decagonal approximantJanez Dolinšek*, I, Ana SmontaraII, Osor S. BarišićII and Peter GilleIIII J. Stefan Institute, University of Ljubljana, Jamova 39, 1000 Ljubljana, SloveniaII Institute of Physics, Laboratory for the Study of Transport Problems, Bijenička 46, POB 304, 10001 Zagreb, CroatiaIII Ludwig-Maximilians-Universität München, Department of Earth and Environmental Sciences, Crystallography Section, Theresienstraße 41,80333 München, GermanyReceived May 26, 2008; accepted August 27, 2008Thermoelectric power / Quasicrystals /Decagonal approximants / Y– Al– Ni– Co phaseAbstract. We have investigated anisotropic electrical re-sistivity and thermoelectric power of the ypsilon-phaseAl– Ni– Co (Y– Al– Ni– Co) decagonal approximantwith composition Al76Co22Ni2. The crystalline-direction-dependent measurements were performed along threeorthogonal directions a*, b and c of the Y– Al– Ni– Counit cell, where (a, c) monoclinic atomic planes arestacked along the perpendicular b direction. Anisotropicelectrical resistivity is low in all crystalline directions,appearing in the order qa > qc > qb and showing posi-tive temperature coefficient typical of electron-phononscattering mechanism. Thermopower shows electron-pho-non enhancement effect. Anisotropic bare thermopower(in the absence of electron-phonon interactions) was ex-tracted, appearing in the same order as the resistivity,jSbarea =Tj > jSbarec =Tj > jSbareb =T j.IntroductionDecagonal quasicrystals (d-QCs) can be structurallyviewed as a periodic stack of quasiperiodic atomicplanes, so that d-QCs are two-dimensional quasicrystals,whereas they are periodic crystals in a direction perpen-dicular to the quasiperiodic planes. A consequence of theanisotropic structure are anisotropic magnetic and trans-port properties [1] (electrical resistivity, thermoelectricpower, Hall coefficient, thermal conductivity), when meas-ured along different crystalline directions. Here we re-port an experimental study of the anisotropic electricalresistivity and thermoelectric power of a complex metal-lic alloy Al13x(Co1yNiy)4 [2], known also as the ypsi-lon– Al– Ni– Co phase (Y– Al– Ni– Co), which is amonoclinic approximant to the decagonal phase with twoatomic layers within one periodic unit along the stackingdirection. We show that the thermopower exhibits an elec-tron-phonon enhancement effect, as also observed in therelated d-Al– Ni– Co quasicrystal [3].Structural considerationsand sample preparationThe Al13x(Co1yNiy)4 monoclinic phase belongs to theAl13TM4 (TM ¼ transition metal) class of decagonal ap-proximants. The structure of Al13x(Co1yNiy)4 withx ¼ 0:9 and y ¼ 0:12, corresponding to compositionAl75Co22Ni3, was first described by Zhang et al. [2]. Lat-tice parameters of the monoclinic unit cell (space groupC2/m (No. 12)) are a ¼ 17.071(2) A, b ¼ 4.0993(6) A,c ¼ 7.4910(9) A, b ¼ 116.17 and Pearson symbol mC34–1.8 with 32 atoms in the unit cell (8 Co/Ni and 24 Al),which are placed on 9 crystallographically inequivalentatomic positions (2 Co/Ni and 7 Al). Two of these are par-tially occupied (Al(6) by 90% and Al(60) by 10%). Thestructure of Al13x(Co1yNiy)4 is built up of one type offlat atomic layers, which are related to each other by a 21axis, giving 0.4 nm period along the [010] direction(corresponding to the periodic direction in the relatedd-Al– Ni– Co quasicrystal) and two atomic layers withinone periodicity unit. Locally, the structure shows close re-semblance to the d-Al70Co15Ni5 quasicrystal [4], which alsoconsists of only one type of a quasiperiodic layer, repeatedby a 105-axis and giving the same 0.4 nm period.The single crystal used in our study was grown froman incongruent Al-rich melt of initial compositionAl81.9Co14.5Ni3.6 by the Czochralski method using a nativeseed. The composition of the crystal (rounded to the clo-sest integers) was Al76Co22Ni2 and its structure matchedwell to the monoclinic unit cell of the Zhang et al. [2]model (who studied the composition Al75Co22Ni3). In or-der to perform crystalline-direction-dependent studies, wehave cut from the ingot three bar-shaped samples of di-mensions 2 2 6 mm3, with their long axes along threeorthogonal directions. The long axis of the first samplewas along [0 1 0] direction (designated in the following asb), which corresponds to the periodic direction in the re-lated d-Al– Ni– Co quasicrystal. The (a, c) monoclinicplane corresponds to the quasiperiodic plane in d-QCs andthe second sample was cut with its long axis along [001](c) direction, whereas the third one was cut along the di-rection perpendicular to the (b, c) plane. This direction is64 Z. Kristallogr. 224 (2009) 64–66 / DOI 10.1524/zkri.2009.1033# by Oldenbourg Wissenschaftsverlag, München* Correspondence author (e-mail: jani.dolinsek@ijs.si)Properties/ApplicationsUnangemeldetHeruntergeladen am | 28.08.17 16:58designated as a* (it lies in the monoclinic plane at anangle 26 with respect to a and perpendicular to c). Theso-prepared samples enabled us to determine the anisotro-pic electrical resistivity and thermopower of the investi-gated monoclinic Al76Co22Ni2 (abbreviated asY– Al– Ni– Co in the following) along the three orthogo-nal crystalline directions.Electrical resistivityElectrical resistivity was measured between 300 and 2 Kusing the standard four-terminal technique and the qðTÞdata are displayed in Fig. 1. The resistivity is the lowestalong the b direction perpendicular to the atomic planes,where its room-temperature (RT) value amountsq300 Kb ¼ 25 mW cm and the residual resistivity isq2Kb ¼ 10 mW cm. The two in-plane resistivities are higher,amounting q300 Kc ¼ 60 mW cm and q2 Kc ¼ 29 mW cm for thec direction and q300 Ka ¼ 81 mW cm and q2 Ka ¼ 34 mW cmfor the a* direction. While qb is considerably smaller thanqa and qc by a factor of about 3, the two in-plane resistiv-ities are much closer, qa=qc  1:3. The above resistivityvalues, appearing in the order qa > qc > qb, reveal thatY– Al– Ni– Co is good electrical conductor along all threecrystalline directions. The strong positive temperature coef-ficient (PTC) of the resistivity along all three crystalline di-rections demonstrates predominant role of the electron-pho-non scattering mechanism.Thermoelectric powerThe thermoelectric power (the Seebeck coefficient S) wasmeasured between 300 and 2 K by applying a differentialmethod with two identical thermocouples (chromel-goldwith 0.07% iron), attached to the sample with silver paint,and the data are displayed in Fig. 2. Thermopower is ne-gative for all three directions, suggesting that electron-typecarriers dominate the thermoelectric transport. The RT val-ues are in the range between –2 and 20 mV=K in theorder jSaj > jScj > jSbj. The SðTÞ characteristics for alldirections are qualitatively similar, except for the variationin magnitude. In all cases, a change of slope is observedat about 70 K, where the low-temperature slope is higherthan the high-temperature one. Nonlinearities in the ther-mopower in this temperature range are often associatedwith electron-phonon effects, which typically reach theirmaximum value at a temperature that is some fraction ofthe Debye temperature qD. The thermopower in all threedirections extrapolates approximately linearly to zero uponT ! 0, a feature that is usually associated with metallicdiffusion thermopower. These features allow comparingthe SðTÞ data from Fig. 2 to the behavior expected for theelectron-phonon enhancement of diffusion thermopower,as observed in several metallic glasses [5] and also in therelated d-Al73Co10Ni17 quasicrystal [3]. The importance ofphonons in the temperature-dependence of the thermo-power of Y– Al– Ni– Co is analogous to the temperature-dependent electrical resistivity of this compound, whereelectron-phonon interaction represents the main scatteringmechanism, leading to the PTC of the resistivity.The electron-phonon enhancement of the diffusion ther-mopower can be written as [3, 5]ST¼ SbareT½1þ lðTÞ ; ð1Þwhere Sbare is the bare thermopower in the absence of theelectron-phonon interaction and lðTÞ is the electron-pho-non mass enhancement parameter given by [5]lðTÞ ¼ð10dwa2FðwÞwGhwkBT : ð2ÞHere a2FðwÞ is the Eliashberg function and Gðhw=kBTÞis a universal function, introduced by Kaiser [5]. Full treat-ment of the anisotropic thermopower should take into ac-count the anisotropy of a2FðwÞ, which is beyond our pos-sibilities. To simplify the problem, we adopt the sameapproximation as applied before to the d-Al– Ni– Co qua-Thermopower of Y– Al– Ni– Co decagonal approximant 65Fig. 1. (Color online) Temperature-dependent electrical resistivity ofY– Al– Ni– Co along three orthogonal crystalline directions a*, b andc (note that the vertical scale is logarithmic).Fig. 2. (Color online) Temperature-dependent thermoelectric power(the Seebeck coefficient S) of Y– Al– Ni– Co along three orthogonalcrystalline directions a*, b and c. Solid curves are fits with Eqs. (1)and (3) and the fit parameters are given in Table 1. Bare thermo-powers (in the absence of electron-phonon interactions) are shown bydashed lines.Properties/ApplicationsUnangemeldetHeruntergeladen am | 28.08.17 16:58sicrystal [3] using the Debye model, a2FðwÞ ¼ CDwn,with a cutoff frequency wD ¼ kBqD=h, where the anisotro-py is introduced phenomenologically through the orienta-tion-dependent parameters CDand n. Eq. (2) then becomeslðTÞ ¼ CDðwD0dw wn1GhwkBT : ð3ÞOur fits of the anisotropic thermopower (solid curves inFig. 2) could be made satisfactorily with n ¼ 2, so thatonly CD was varied for different crystalline directions. Weobserve that Eqs. (1) and (3) reproduce well the change ofslope in the thermopowers at about 70 K. While the fitsfor the b and c directions are satisfactory up to the RT, thefit for the a* direction is good up to 150 K, whereas itstarts to deviate from the measured data at higher tempera-tures. At present we do not have an explanation for thisdeviation. The fit parameters are given in Table 1, wherethe value lð0Þ ¼ CDw2D2 is given instead of CD (takinginto account that limT!0Gðhw=kBTÞ ¼ 1 in Eq. (3)). TheDebye temperature was taken as qD ¼ 320 K. The barethermopowers Sbare for all three crystalline directions areshown as dashed lines in Fig. 2.The anisotropy of the so-extracted bare thermopowerscan now be analyzed using the well-known expression de-rived from the linearized Boltzmann transport equationSbare ¼ p23ðeÞ k2BT@ ln sðEÞ@E E¼z: ð4Þwhere z is the chemical potential and sðEÞ is the spectralconductivity in the vicinity of the Fermi level. Since sðEÞis not known, we made the following qualitative analysis.The geometry of our samples requested that we have ex-perimentally measured the diagonal elements of the ther-mopower tensor in the Cartesian coordinate systemi ¼ x; y; zSbareii ¼p23ðeÞ k2BTqii@siiðEÞ@E E¼z: ð5ÞWe assume that sðEÞ exhibits no sharp features in the vici-nity of the Fermi level EF, so that no singularities in its deri-vative are expected. Within the approximation that the deri-vative ð@siiðEÞ=@EÞE¼z does not depend significantly onthe crystalline direction, the magnitude of the thermopowerin the direction i is predominantly determined by the magni-tude of the resistivity qiiin that direction. The geometry ofour samples (their long axes were along three orthogonaldirections a*, b and c) and the direction of the electric fieldapplied along their long axes imply that diagonal elementsof the resistivity tensor qxx ¼ qa, qyy ¼ qb and qzz ¼ qcwere measured in our experiments. Since qa > qc > qb(Fig. 1), this requires bare thermopowers in the orderjSbarea =Tj > jSbarec =Tj > jSbareb =T j. Figure 2 and Table 1show that this was indeed observed experimentally. Here itshould be emphasized that the above relation of the aniso-tropic thermopower to the anisotropic electrical resistivityis qualitative only. The microscopic origin of the anisotro-py of any electron transport coefficient is the anisotropy ofthe Fermi surface, arising from the anisotropy of the elec-tronic structure due to the specific atomic structural andchemical details of the crystalline lattice.ConclusionsWe have investigated anisotropic electrical resistivity andthermoelectric power of the Y– Al– Ni– Co decagonal ap-proximant. Electrical resistivity is low in all three crystallinedirections, with the RT values in the range 25–81 mW cm.There exists significant anisotropy between the in-plane re-sistivity and the resistivity along the perpendicular b direc-tion by a factor about 3, whereas the anisotropy between thetwo in-plane directions a* and c is much smaller. The aniso-tropic resistivity appears in the order qa > qc > qb, so thatb direction is the most electrically conducting one. Thermo-power of Y– Al– Ni– Co is negative, suggesting dominantelectron-type carriers, and shows electron-phonon enhance-ment effect that results in a change of slope in the Seebeckcoefficient SðTÞ at about 70 K for all three investigated crys-talline directions. Bare thermopower (in the absence of elec-tron-phonon interactions) was extracted and its anisotropywas analyzed within the frame of the linearized Boltzmanntransport equation. Assuming that the spectral conductivitydoes not exhibit sharp features in the vicinity of the Fermilevel and the derivative of the spectral conductivity does notdepend significantly on the crystalline direction, the magni-tude of the thermopower in a given direction is then predo-minantly determined by the magnitude of the resistivity inthat direction. This suggests anisotropic bare thermopowersin the same order as the anisotropic electrical resistivity,jSbarea =T j > jSbarec =T j > jSbareb =T j, which was also observedexperimentally.Acknowledgments. This work was done within the activities of the 6thFramework EU Network of Excellence “Complex Metallic Alloys”(Contract No. NMP3-CT-2005–500140).References[1] Dolinšek, J.; Jeglič, P.; Komelj, M.; Vrtnik, S.; Smontara, A.;Smiljanić, I.; Bilušić, A.; Ivkov, J.; Stanić, D.; Zijlstra, E. S.;Bauer, B.; Gille, P.: Origin of anisotropic nonmetallic transport inthe Al80Cr15Fe5 decagonal approximant. Phys. Rev. B 76 (2007)174207, and references therein.[2] Zhang, B.; Gramlich, V.; Steurer, W.: Al13x(Co1yNiy)4, a newapproximant of the decagonal quasicrystal in the Al–Co–Ni sys-tem. Z. Kristallogr. 210 (1995) 498.[3] Shuyuan, Lin; Guohong, Li; Dianlin, Zhang: Thermopower ofdecagonal Al73Ni17Co10 single quasicrystals: Evidence for astrongly enhanced electron-phonon coupling in the quasicrystal-line plane. Phys. Rev. Lett. 77 (1996) 1998.[4] Steurer, W.; Haibach, T.; Zhang, B.; Kek, S.; Lück, R.: The struc-ture of decagonal Al70Co15Ni15. Acta Crystallogr. B 49 (1993) 661.[5] Kaiser, A. B.: Electron-phonon enhancement of thermopower:Application to metallic glasses. Phys. Rev. B 29 (1984) 7088.66 J. Dolinšek, A. Smontara, O. S. Barišić et al.Table 1. Fit parameters of the anisotropic thermopower using Eqs.(1) and (3).crystallinedirectionSbare=T (mV=K2) lð0Þa* 5.8 102 1.0b 5.5 103 5.0c 1.9 102 1.6Properties/ApplicationsUnangemeldetHeruntergeladen am | 28.08.17 16:58

Phonon-enhanced thermoelectric power of Y-Al-Ni-Co decagonal approximant

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Phonon-enhanced thermoelectric power of Y–Al–Ni–Co decagonal approximant

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Phonon-enhanced thermoelectric power of Y-Al-Ni-Co decagonal approximant

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