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D. Kaczorowski, K. Gofryk Rare-earth-based half-Heusler compounds as prospective materials for thermoelectric applications Institute of Low Temperature.

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Presentation on theme: "D. Kaczorowski, K. Gofryk Rare-earth-based half-Heusler compounds as prospective materials for thermoelectric applications Institute of Low Temperature."— Presentation transcript:

1 D. Kaczorowski, K. Gofryk Rare-earth-based half-Heusler compounds as prospective materials for thermoelectric applications Institute of Low Temperature and Structure Research, Polish Academy of Sciences, Wrocław A. Leithe-Jasper, Y. Grin Max-Planck-Institut für Chemische Physik fester Stoffe, Dresden

2 Outline Motivation: Heusler phases thermoelectricity Bulk properties of REPdSb and REPdBi (RE = Y, Gd, Dy, Ho, Er): Sample characterisation Magnetic behavior Heat capacity Electrical transport Thermoelectric performance Summary

3 Heusler phases Sb Er ErSb ErPdSb ErPd 2 Sb Pd

4 Heusler phases – properties on request metal semiconductor TIP CW paramagnet weak AF strong F simple metal SCES MI transition itinerant magnetism localized magnetism Kondo effect heavy fermions superconductors half metals semimetals magnetic semiconductors giant magnetoresistance shape memory alloys thermoelectrics Pierre, 1997

5 S.Williams, Thermoelectric materials heat electricity Seebeck effect electricity cooling Peltier effect hybrid automobile applications, power generation from waste heat (catalytic converters, motor blocks, heaters, high temperature furnaces, power plants) … reliable (no mechanical parts) environment friendly high cost low efficiency spot cooling of electronic equipment, infrared detectors, car air-conditioners, refrigerators, solar-powered coolers …

6 Thermoelectrical performance coefficient of performance (COP) I p n ThTh T c +- I TcTc ThTh p n coefficient of efficiency (COE) figure of merit spot cooling electric power generation

7 Thermoelectrical performance figure of merit : RECORD VALUES p-type alloy Bi 2 Te 3 /Sb 2 Te 3 /Sb 2 Se 3 : ZT = 1.14 at T = 300 K quantum dots lattice PbTe/PbSe 0.98 Te 0.02 : ZT = 2.0 at T = 550 K thin-film superlattice Bi 2 Te 3 /Sb 2 Te 3 : ZT = 2.4 at T = 300 K state-of-the-art commercial devices e.g. p-type Bi x Sb 2-x Te 3-y Se y ZT ~ 1 for T = 200 - 400 K S = L 1/2 = 157 V/K ZT = 1 S = (2L) 1/2 = 225 V/K ZT = 2 S – Seebeck coefficient – thermal conductivity – electrical resistivity

8 Half-Heusler phases

9 X = Sb YPdSb DyPdSb HoPdSb ErPdSb X = Bi YPdBi GdPdBi DyPdBi HoPdBi ErPdBi REPdX half-Heusler compounds

10 ErPdSb Sample characterization 111 002 022 113 222 004 224 024 133 333 044 ErPdSb single phase samples homogeneous stoichiometry atomic disorder not detectable ErPdSb

11 Magnetic properties CompoundT N (K) p (K) eff ( B ) YPdSbD-- DyPdSb3.3-11.510.5 HoPdSb2.0-9.010.7 ErPdSbP-4.29.4 YPdBiD-- GdPdBi13.5-36.58.0 DyPdBi3.5-11.910.7 HoPdBi2.2-6.110.6 ErPdBiP-4.69.2 weak AF at low temp. Curie-Weiss behavior eff teo for RE 3+ small negative p weak CEF effect

12 Magnetic behavior no magnetic ordering down to 1.72 K Curie-Weiss behaviour: eff teo for Er 3+ (9.58 B ), small negative p weak CEF effect eff ( B ) p (K) ErPdSb9.43-4.2 ErPdBi9.20-4.6

13 Heat capacity no phase transition down to 2 K upturn below 6 K pronounced CEF Schottky effect

14 ErNiSb Karla et al., 1999 220 K 166 K 108 K 92 K Schottky specific heat CEF scheme: doublet-quartet- doublet-quartet-quartet total splitting of 186 K first excited state at 61K Er 3+ : 4 I 15/2 doublet ground state

15 Excess specific heat ? magnetic ordering at T < 2 K ? CEF nuclear contribution ? Schottky ? unlikely

16 Heat capacity in magnetic field B clear Zeeman effect e.g. local distortion, internal-field distribution, … upturn transforms into maximum T max increases for rising B

17 Electrical resistivity semimetallic character - magnitude - temperature dependence anomalies at low temperatures for both AF and P systems !!!

18 Electrical resistivity E g = 30-100 meV

19 Mastronardi et al., 1999 indirect gap – X : 0.1 eV direct gap – : ca. 0.4 eV valence bands at : parabolic with different curvature conduction band at X : nonparabolic Lu 4f EFEF heavy and light holes in p-type material different effective masses of doped electrons and doped holes LuPdSb bands near E F : strongly hybridized Pd-d and Lu-d states Electronic structure

20 Conductivity model DOS narrow gap E g slightly above E F metallic conductivity at LT activation behaviour at HT total resistivity occupation of states Fermi-Dirac distribution carrier concentration Bloch-Grüneisen law Berger, 2003

21 Model calculations R = 0.73 cm/K E g = 26 meV n 0 = 0.25 N = 8.04 eV -1 for D = 270 K 0 = 1.86 m cm E g 10 – 100 meV

22 Thermoelectric power positive large: 150-200 V/K positive 40-90 V/K REPdSb: E F = 30-60 meV n 10 19 cm -3 REPdBi: E F = 50-140 meV n 10 20 cm -3

23 Thermopower: two-band model positive holes large magnitude n ~ 10 19 cm -3 two-band model: - 4f band - conduction band phonon drag? crystal field? Gottwick et al., 1985

24 Thermopower: three-band model three-band model: - narrow (4f) band - broad (4f) band - conduction band Bando et al., 2000

25 positive large dominant holes low carrier concentration Hall effect strongly dependent on temperature and field multiple electrons and holes bands

26 Hall effect small mean carrier concentration relatively large mobility at 300 K scatt. on ionized impurities scatt. on acoustic phonons semimetal

27 Thermal conductivity electronic : Wiedemann-Franz law lattice : Callaway model input : D = 270 K ( = 2400 m/s)

28 discrepancies for T > 170 K radiation losses T-dependent Lorenz number ? error in D input value ? bipolaron contribution ? Przewodnictwo cieplne OPTIMIZATION by rising disorder level controlled doping controlled doping amorphization amorphization Thermal conductivity Cahill, 1989

29 D =208 K Wiedemann-Franz law Thermal conductivity

30 Very large power factor !!! esp. for ErPdSb and DyPdBi Thermoelectric performance

31 figure of merit : state-of-the-art commercial devices e.g. p-type Bi x Sb 2-x Te 3-y Se y ZT ~ 1 for T = 200 - 400 K ZT 0.32 ZT 0.15

32 DyPdBi ErPdSb comp.: 3d-metal half-Heusler phases, skutterudites, clathrates, … Thermoelectrical performance

33 Summary novel compounds : REPdSb and REPdBi RE = Y, Gd, Dy, Ho, Er optimization of figure of merit electronic band structure (role of disorder) high-temperature behaviour (LT for ErPdX) Open problems structural, magnetic, electrical and thermal properties : cubic (MgAgAs-type) paramagnetic (Er), antiferromagnetic (Gd,Dy,Ho) ; RE 3+ ions semimetallic (narrow band semiconductors) electronand hole bands low concentrations of carriers (REPdSb) strongly T-dependent concentrations and mobilities electronic structure very sensitive to magnetic field (LT) promising thermoelectric characteristics (ErPdSb, DyPdBi)

34 YPdSb: Heat capacity Rocha, 1999 D =290 K =15 mJ/mol K 2 E =126 K p =0.19

35 Własności elektryczne ErPdSb ?

36 Low-temperature magnetism (T) featureless down to 1.72 K Brillouin-like behaviour of (B) 1.72 K, 5 T) « gJ for Er 3+ (9.0 B ) B T 5.6 B no anomaly in (T) ; upturn below 10 K in (T) ac susceptibility: ErPdBi

37 Electrical Resistivity electr. contacts: ultrasonic welding / silver paste !!! 37% 16% 42% 19%

38 missing entropy !!! LT Puzzle phase transition ??? featureless (T) and C(T) superconductivity ? but not detected by SEM fully reproducible restricted to Er-phases ? high T c and B cr magnetism ? featureless (T) & C(T) amplitude-modulated structure? multiaxial multi-Q structure ??? thin films of Sb/Bi on grain boundaries ??? intrinsic? extrinsic? ? nearly same T C

39 Zjawiska termoelektryczne Efekt Seebecka Kreowanie napięcia elektrycznego pod wpływem różnicy temperatur (gradientu pola elektrycznego pod wpływem gradientu temperatury), gdy nie ma przepływu pola elektrycznego. V Materiał A Materiał B T1T1 T2T2 Poznań 2–12–2005

40 Zjawiska termoelektryczne Efekt Peltiera Przepływ ciepła, którego strumień jest proporcjonalny do strumienia prądu elektrycznego U = J przy T = 0 J J Materiał A Materiał B Poznań 2–12–2005

41 Zjawiska termoelektryczne Efekt Thomsona Wydzielanie lub pochłanianie ciepła w czasie przepływu prądu przez przewodnik, gdy ma on niezerowy gradient temperatury. Ilość ciepła wydzielanego lub pochłanianego w jednostce czasu w trakcie zachodzenia zjawiska Thomsona zależy od natężenia prądu, rodzaju przewodnika i gradientu temperatury. Ustalenie związku między współczynnikami Peltiera i Seebecka - wykrycie symetrii współczynników kinetycznych. Poznań 2–12–2005

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