Rare Rare Rare-earth Rare-earth earth-based half earth-based - PowerPoint PPT Presentation

Rare Rare Rare-earth Rare-earth earth-based half earth-based half based half-Heusler based half-Heusler Heusler Heusler compounds as prospective materials compounds as prospective materials p p p p p p for thermoelectric applications for thermoelectric applications Dariusz Kaczorowski Dariusz Kaczorowski Institute of Low Temperature and Structure Research, Polish Academy of Sciences, Wroc ł aw, Poland

Co-workers Co workers K. Gofryk , T. Plackowski Institute of Low Temperature and Structure Research, Polish Academy of Sciences, Wroc ł aw A. Leithe-Jasper, Yu. Grin Max Planck Institut Max-Planck-Institut für Chemische Physik fester Stoffe, Dresden

Outline Outline � Motivation: � Motivation: Heusler phases Heusler phases thermoelectricity � Bulk properties of RE PdSb and RE PdBi � B lk ti f RE PdSb d RE PdBi ( RE = Y, Gd, Dy, Ho, Er): Sample characterisation Magnetic behavior g Heat capacity Electrical transport p � Thermoelectric performance � Summary

Heusler phases Heusler phases Pd Pd Er Er Er Er Sb Sb ErSb ErPdSb ErPd 2 Sb Compound Co pou d St uctu e Structure Space g oup Space group Atomic positions to c pos t o s type Er Sb Pd ErSb NaCl 4b, (½ ½ ½) 4a, (0 0 0) - Fm 3 m ErPdSb MgAgAs 4b, (½ ½ ½) 4a, (0 0 0) 4c, (¼ ¼ ¼) F 3 4 m ErPd 2 Sb E Pd Sb M C MnCu 2 Al Al 4b (½ ½ ½) 4b, (½ ½ ½) 4a, (0 0 0) 8c, (¼ ¼ ¼) 4 (0 0 0) 8 (¼ ¼ ¼) Fm 3 m

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

Thermoelectric materials e oe ec c e s heat → electricity Seebeck effect hybrid automobile applications, power generation from waste heat (catalytic converters, motor blocks, heaters, high bl k h hi h temperature furnaces, power plants) … electricity → l t i it cooling P lti Peltier effect ff t spot cooling of electronic equipment, infrared detectors, car air-conditioners, refrigerators solar powered coolers refrigerators, solar-powered coolers … S.Williams, www.thermoelectrics.com ☺ reliable ( ☺ reliable (no mechanical parts) ☹ high cost ☹ high cost h i l t ) ☺ environment friendly ☹ low efficiency

Thermoelectrical performance Thermoelectrical performance spot cooling electric power generation T c T h p p n n p n T h T c I I I - + + coefficient of efficiency (COE) coefficient of performance (COP) ( )( ) 1 γ T − T T − T γ − c h h c φ = η = 1 ( ( )( )( ) ) 1 T − T + γ γ T + γ γ T ( ( ) 2 ) 2 γ γ = 1 1 + + ZT ZT h h c c c c h h figure of merit

Thermoelectrical performance Thermoelectrical performance figure of merit : figure of merit : 2 2 2 2 σ S S T T S S ZT = = κ L 2 TS ZT ZT = S = L 1/2 = 157 µ V/K ⇒ ZT = 1 κρ S = (2L) 1/2 = 225 µ V/K ⇒ ZT = 2 S – Seebeck coefficient κ – thermal conductivity state-of-the-art commercial devices ρ – electrical resistivity e.g. p-type Bi x Sb 2-x Te 3-y Se y ZT ~ 1 for T = 200 - 400 K RECORD VALUES p-type alloy Bi 2 Te 3 /Sb 2 Te 3 /Sb 2 Se 3 : ZT = 1.14 at T = 300 K 2 3 2 3 2 3 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

Half Heusler phases Half-Heusler phases

RE Pd X half-Heusler compounds RE Pd X half Heusler compounds X = Bi X = Sb YPdBi YPdSb GdPdBi DyPdSb DyPdBi HoPdSb H PdBi HoPdBi ErPdSb dSb E PdBi ErPdBi

Sample characterization S p e c c e o 022 ErPdSb ErPdSb ErPdSb dSb 224 111 002 004 113 222 222 024 024 044 044 133 133 333 ErPdSb � single phase samples � homogeneous stoichiometry � homogeneous stoichiometry � atomic disorder not detectable

Magnetic properties g p p Compound T N (K) θ p (K) µ eff ( µ B ) weak AF at low temp. Curie-Weiss behavior YPdSb D - - ≈ µ teo for RE 3+ µ eff ≈ µ DyPdSb DyPdSb 3.3 3.3 -11.5 11.5 10.5 10.5 small negative θ p small negative θ weak CEF effect HoPdSb 2.0 -9.0 10.7 ErPdSb P -4.2 9.4 1.3 HoPdSb 20 u/mol) 1.2 YPdBi D - - u) mol/emu χ (emu 15 1.1 T N = 2 K GdPdBi 13.5 -36.5 8.0 100 1.0 1.5 2.0 2.5 3.0 3.5 4.0 80 10 -1 (m T (K) g) σ (emu/g 60 60 DyPdBi 3.5 -11.9 10.7 40 χ 5 20 T = 1.7 K HoPdBi 2.2 -6.1 10.6 0 B 0.1 T B = 0.1 T 0 1 2 3 4 5 B (T) B (T) 0 0 50 100 150 200 250 300 ErPdBi P -4.6 9.2 T (K)

Magnetic behavior g e c be v o 30 1.8 B = 0.1 T 1.5 ol) 25 25 χ (emu/mo l/emu) 1.2 µ eff ( µ B ) θ p (K) 0.9 20 0.6 0.3 ErPdSb E PdSb 9 43 9.43 -4.2 4 2 -1 (mol 15 0 5 10 15 20 25 30 T (K) 10 ErPdBi 9.20 -4.6 ErPdBi χ χ 5 B = 0.1 T 0 0 50 100 150 200 250 300 T (K) � no magnetic ordering down to 1 72 K � no magnetic ordering down to 1.72 K � Curie-Weiss behaviour: µ eff ≈ µ teo for Er 3 (9.58 µ B ) , small negative θ p for Er 3+ (9 58 µ ) small negative θ µ ≈ µ � weak CEF effect

Heat capacity e c p c y 80 ErPdSb ( ( ) ) C C T T = C C + + C C + + C C 10 p el ph CEF 60 8 mol K) l K) 6 ( ( ) ) C C el T T = = γ γ T T (J/mol C p (J/ 4 40 2 3 Θ T ⎛ ⎞ D 4 YPdSb x ∫ ∫ T e x dx 0 ⎜ 0 4 8 12 16 20 ( ( ) ) 9 C T = Nk ⎜ ⎜ T (K) T (K) 2 2 ph ph B B 20 20 ( ( 1 1 ) ) C p x x ⎝ ⎝ Θ ⎠ ⎠ Θ e − Fit : Θ D = 264 K D 0 2 γ = 0.22 mJ/molK ⎛ ⎞ ∑ ∑ n 1 R ⎜ ⎜ 0 2 / ( ( ) ) − E k T C C T T = = E E e e i i B 0 0 50 50 100 100 150 150 200 200 250 250 300 300 ⎜ ⎜ 2 2 CEF i k T Z ⎝ ⎠ T (K) B 1 i = 2 ⎛ ⎞ n ∑ ∑ 1 R ⎜ ⎜ / − E k T − E E e � no phase transition down to 2 K i i B B ⎜ 2 2 i k T Z ⎝ ⎠ B 1 i = � upturn below 6 K ∑ ∑ n � pronounced CEF Schottky effect − E E k k T T Z = e i B 0 i =

Schottky specific heat Sc o y spec c e Er Er 3+ Er Er 3+ 3+ : 4 I 3+ : : 4 I 15/2 15/2 ErNiSb doublet ground state 220 K 166 K 108 K 92 K � CEF scheme: doublet-quartet- doublet-quartet-quartet � t t l � total splitting of 186 K litti f 186 K � first excited state at 61K Karla et al., 1999

Excess specific heat cess spec c e 10 ErPdSb CEF CEF mol K) 8 5 6 6 C (J/m 4 /mol K) 3 4 ? ? Schottky ? ∆ C ∆ C (J 2 2 1 0 0 0.0 0.1 0.2 0.3 10 100 -2 (K -2 ) T (K) T magnetic ordering at T < 2 K ? ? ? nuclear contribution l ib i unlikely

Heat capacity in magnetic field e c p c y g e c e d 2.1 E PdSb ErPdSb 1.8 2 ) B = 0 T ol K B = 1 T � upturn transforms 1.5 B = 2 T B = 4 T T (J/m into maximum 1.2 B = 6 T B = 9 T B 0.9 � T max increases max C p /T 0.6 for rising B 0.3 0.0 0 5 10 15 20 25 30 T (K) � clear Zeeman effect e.g. local distortion, internal-field distribution, …

Electrical resistivity ec c es s v y � semimetallic character - magnitude - temperature dependence � � anomalies at low temperatures li t l t t for both AF and P systems !!!

Electrical resistivity ec c es s v y ⎛ ⎛ − E g ⎞ ⎞ 1 1 ⎜ ⎜ exp g = σ + B ⎜ ⎟ E g = 30-100 meV a 2 ⎝ ⎠ ρ ( Τ ) k T B

Electronic structure LuPdSb indirect gap Γ – X : ∆ ≈ 0 1 eV ∆ ≈ 0.1 eV direct gap Γ – Γ : ca. 0.4 eV valence bands at Γ : parabolic with different curvature conduction band at X : E F nonparabolic → heavy and light holes in p-type material → different effective masses different effective masses of doped electrons and doped holes Lu 4f bands near E : bands near E F : strongly hybridized Pd-d and Lu-d states Mastronardi et al., 1999

Co duc v y Conductivity model ode Berger, 2003 DOS total resistivity narrow gap E slightly above E narrow gap E g slightly above E F ( ) ρ + ρ T � metallic conductivity at LT 0 ( ) ph ρ T = � activation behaviour at HT ( T ( ) ) n n T occupation of states ( ( ) ) ( ( ) ) ( ( ) ) Fermi-Dirac distribution Fermi Dirac distribution n n T T = = n n T T n n T T + + n n 0 n p 1 − ⎡ ⎤ ⎛ ⎞ E − E ⎡ ⎤ ⎛ ⎞ ⎜ ⎟ ( ) exp 1 E ⎢ ⎥ F f E = + ⎜ ⎜ ( ( ) ) ln 1 exp p g ⎢ ⎢ ⎥ ⎥ n T = − NE + Nk T + ⎜ ⎜ ⎝ ⎝ ⎠ ⎠ k B k T T ⎣ ⎣ ⎦ ⎦ n n g g B B ⎝ ⎠ ⎣ k T ⎦ B ( ) ln 2 n T = − Nk T carrier concentration p B ∫ ∞ Bloch-Grüneisen law ( ) ( ) ( , ) n T = N E f E T dE n E Θ T F 5 D ⎛ ⎛ ⎞ ⎞ ∫ ∫ 5 ∫ ∫ ∞ E E T T z z dz dz F F ⎜ ( ) 4 [ ] ( ) ( ) 1 ( , ) ρ T = R ⎜ ⎟ n T = N E − f E T dE ph ( 1 )( 1 ) z − z p ⎝ ⎠ Θ e − − e D − 0