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, Wrocaw A. Leithe-Jasper, Y. Grin Max-Planck-Institut
fr Chemische Physik fester Stoffe, Dresden Slide 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 Slide 3 Heusler phases Sb Er ErSb ErPdSb ErPd 2
Sb Pd Slide 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 Slide 5 S.Williams,
www.thermoelectrics.com 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 Slide 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 Slide 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 Slide 8 Half-Heusler
phases Slide 9 X = Sb YPdSb DyPdSb HoPdSb ErPdSb X = Bi YPdBi
GdPdBi DyPdBi HoPdBi ErPdBi REPdX half-Heusler compounds Slide 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 Slide 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 Slide 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 Slide 13 Heat capacity no phase transition down to 2
K upturn below 6 K pronounced CEF Schottky effect Slide 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 Slide 15 Excess specific heat ? magnetic
ordering at T < 2 K ? CEF nuclear contribution ? Schottky ?
unlikely Slide 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 Slide 17
Electrical resistivity semimetallic character - magnitude -
temperature dependence anomalies at low temperatures for both AF
and P systems !!! Slide 18 Electrical resistivity E g = 30-100 meV
Slide 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 Slide 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-Grneisen law Berger, 2003 Slide 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 Slide 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 Slide 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 Slide 24 Thermopower:
three-band model three-band model: - narrow (4f) band - broad (4f)
band - conduction band Bando et al., 2000 Slide 25 positive large
dominant holes low carrier concentration Hall effect strongly
dependent on temperature and field multiple electrons and holes
bands Slide 26 Hall effect small mean carrier concentration
relatively large mobility at 300 K scatt. on ionized impurities
scatt. on acoustic phonons semimetal Slide 27 Thermal conductivity
electronic : Wiedemann-Franz law lattice : Callaway model input : D
= 270 K ( = 2400 m/s) Slide 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 Slide
29 D =208 K Wiedemann-Franz law Thermal conductivity Slide 30 Very
large power factor !!! esp. for ErPdSb and DyPdBi Thermoelectric
performance Slide 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 Slide 32 DyPdBi ErPdSb comp.: 3d-metal
half-Heusler phases, skutterudites, clathrates, Thermoelectrical
performance Slide 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)
Slide 34 YPdSb: Heat capacity Rocha, 1999 D =290 K =15 mJ/mol K 2 E
=126 K p =0.19 Slide 35 Wasnoci elektryczne ErPdSb ? Slide 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 Slide 37 Electrical Resistivity electr.
contacts: ultrasonic welding / silver paste !!! 37% 16% 42% 19%
Slide 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 Slide
39 Zjawiska termoelektryczne Efekt Seebecka Kreowanie napicia
elektrycznego pod wpywem rnicy temperatur (gradientu pola
elektrycznego pod wpywem gradientu temperatury), gdy nie ma
przepywu pola elektrycznego. V Materia A Materia B T1T1 T2T2 Pozna
2122005 Slide 40 Zjawiska termoelektryczne Efekt Peltiera Przepyw
ciepa, ktrego strumie jest proporcjonalny do strumienia prdu
elektrycznego U = J przy T = 0 J J Materia A Materia B Pozna
2122005 Slide 41 Zjawiska termoelektryczne Efekt Thomsona
Wydzielanie lub pochanianie ciepa w czasie przepywu prdu przez
przewodnik, gdy ma on niezerowy gradient temperatury. Ilo ciepa
wydzielanego lub pochanianego w jednostce czasu w trakcie
zachodzenia zjawiska Thomsona zaley od natenia prdu, rodzaju
przewodnika i gradientu temperatury. Ustalenie zwizku midzy
wspczynnikami Peltiera i Seebecka - wykrycie symetrii wspczynnikw
kinetycznych. Pozna 2122005