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

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

1 Rare-earth-based half-Heusler compounds as prospective materials for thermoelectric applications
D. Kaczorowski, K. Gofryk 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 ErPd2Sb Pd

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

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

6 Thermoelectrical performance electric power generation
spot cooling electric power generation + - I Tc Th p n I p n Th Tc coefficient of performance (COP) coefficient of efficiency (COE) figure of merit

7 Thermoelectrical performance state-of-the-art commercial devices
figure of merit : S = L1/2 = 157 mV/K  ZT = 1 S = (2L)1/2 = 225 mV/K  ZT = 2 S – Seebeck coefficient k – thermal conductivity r – electrical resistivity state-of-the-art commercial devices e.g. p-type BixSb2-xTe3-ySey ZT ~ 1 for T = K RECORD VALUES p-type alloy Bi2Te3/Sb2Te3/Sb2Se3 : ZT = 1.14 at T = 300 K quantum dots lattice PbTe/PbSe0.98Te0.02 : ZT = 2.0 at T = 550 K thin-film superlattice Bi2Te3/Sb2Te3 : ZT = 2.4 at T = 300 K

8 Half-Heusler phases

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

10 Sample characterization
ErPdSb 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 weak AF at low temp. Curie-Weiss behavior
Magnetic properties Compound TN (K) qp (K) meff (mB) YPdSb D - DyPdSb 3.3 -11.5 10.5 HoPdSb 2.0 -9.0 10.7 ErPdSb P -4.2 9.4 YPdBi GdPdBi 13.5 -36.5 8.0 DyPdBi 3.5 -11.9 HoPdBi 2.2 -6.1 10.6 ErPdBi -4.6 9.2 weak AF at low temp. Curie-Weiss behavior meff  mteo for RE3+ small negative qp weak CEF effect

12 Magnetic behavior no magnetic ordering down to 1.72 K
meff (mB) qp (K) ErPdSb 9.43 -4.2 ErPdBi 9.20 -4.6 no magnetic ordering down to 1.72 K Curie-Weiss behaviour: meff  mteo for Er3+ (9.58 mB) , small negative qp weak CEF effect

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

14 Er3+: 4I15/2 Schottky specific heat doublet ground state CEF scheme:
ErNiSb Karla et al., 1999 220 K 166 K 108 K 92 K doublet ground state CEF scheme: doublet-quartet- doublet-quartet-quartet total splitting of 186 K first excited state at 61K

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

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

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

18 Electrical resistivity
Eg = meV

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

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

21 Model calculations Eg  10 – 100 meV R = 0.73 cm/K Eg = 26 meV
N = 8.04 eV-1 for QD = 270 K 0 = 1.86 mcm

22 Thermoelectric power positive large: 150-200 mV/K positive 40-90 mV/K
REPdSb: EF = meV n  1019 cm-3 REPdBi: EF = meV n  1020 cm-3

23 Thermopower: two-band model
positive holes large magnitude n ~ 1019 cm-3 phonon drag? crystal field? two-band model: - 4f band - conduction band Gottwick et al., 1985

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

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

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

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

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

29 Thermal conductivity Wiedemann-Franz law D=208 K

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

31 Thermoelectric performance
ZT  0.15 ZT  0.32 figure of merit : state-of-the-art commercial devices e.g. p-type BixSb2-xTe3-ySey ZT ~ 1 for T = K

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

33 Summary novel compounds : REPdSb and REPdBi RE = Y, Gd, Dy, Ho, Er
structural, magnetic, electrical and thermal properties : cubic (MgAgAs-type) paramagnetic (Er), antiferromagnetic (Gd,Dy,Ho); RE3+ ions semimetallic (narrow band semiconductors) electron and 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) electronic band structure (role of disorder) Open problems high-temperature behaviour (LT for ErPdX) optimization of figure of merit

34 YPdSb: Heat capacity D=290 K =15 mJ/mol K2 p =0.19 E=126 K
Rocha, 1999 D=290 K =15 mJ/mol K2 p =0.19 E=126 K

35 Własności elektryczne
ErPdSb ?

36 Low-temperature magnetism
5.6 mB ErPdBi T B ErPdBi c(T) featureless down to 1.72 K Brillouin-like behaviour of s(B) m(1.72 K, 5 T) « gJ for Er3+ (9.0 mB) no anomaly in c’(T) ; upturn below 10 K in c”(T) ac susceptibility:

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

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

39 Zjawiska termoelektryczne
Poznań 2–12–2005 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 T1 T2

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

41 Zjawiska termoelektryczne
Poznań 2–12–2005 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.


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