Are Ge-based skutterudites promising thermoelectrica? Ground state - PowerPoint PPT Presentation

ARW Workshop Properties and Applications of Thermoelectric Materials September 20 - 26, 2008 Hvar, Croatia Are Ge-based skutterudites promising thermoelectrica? Ground state properties, electronic and thermal transport E. Bauer Institute of Solid State Physics A - 1040 Wien, Austria 24. September 2008

ARW Workshop Properties and Applications of Thermoelectric Materials September 20 - 26, 2008 Hvar, Croatia Are Ge-based skutterudites promising thermoelectrica? Ground state properties, electronic and thermal transport E. Bauer Institute of Solid State Physics A - 1040 Wien, Austria 24. September 2008

in co-operation with:

in co-operation with: G. Hilscher, H. Kaldarar, H. Michor, E. Royanian; T.U. Vienna, Austria A. Grytsiv, Xing-Qiu Chen, N. Melnychenko-Koblyuk, M. Rotter, R. Podloucky & P. Rogl Uni. Vienna, Austria Work supported by the Austrian FWF, P19165 and by the EU Complex metallic alloys, CMA

Contents • Formation and general properties of skutterudites • Novel skutterudites { Ba , Sr , Eu , Th , U } Pt 4 Ge 12 • Normal state and superconducting properties • Thermoelectric properties of Ge-based skutterudites • Summary and Outlook More details: Phys. Rev. Lett. 99 , 217001, (2007); Adv. Mat. 20 , 1325 (2008) J. Phys. Soc. Jpn., 77 121, (2008); Phys. Rev. B (2008), in press.

Filled skutterudites

Filled skutterudites • structure type: LaFe 4 P 12 c ( CoAs 3 -structure). • lattice parameter: a = 9 . 127 ˚ el.positive A ( PrFe 4 Sb 12 ) element z • a strongly dependent on (e.g. Pr, Nd ) y x pnictogen atom (change as Sb, (P,As) large as 15 % ) • RE ion sixfold co-ordinated d-element (Fe, Co, Rh ...) by X. b • extremely large atomic dis- a placement parameter of fil- ler elements; increases with 2 a -site : Ep increasing cage volume; in- 8 c -site : transition metal creases with decreasing io- 24 g -site : P, As, Sb, Ge nic size.

Formation of skutterudites EpT 4 X 12 4 12 transitional element in the 8c site p-element in the 24g site electopositive element in the 2a site until recently: No skutterudites entirely formed by Pt (Pd) and Ge

Ba-Pt-Ge phase diagram • a = 0 . 87 nm ; lat- tice parameter much smaller than for X = P, As, Sb; • BaPt 4 Ge 12 exhibit the strongest de- viation from Zintl count (6 uncompen- sated electrons per formula) among all known skutterudites! • only example having ~Ba 8 Pt 4 Ge 42 BaPt 4 Ge 12 ~Ba 8 Pt 4 Ge BaPt 4 Ge 42 12 simultaneously cla- thrate and skutteru- dite members.

Structural and electronic properties of EpPt4Ge 12

X-ray diffraction in BaPt4Ge 12 110000 I obs BaPt Ge Im-3; R F = 0.017; a = 0.86889(1) nm 2 4 12 I calc 90000 I I obs calc - Bragg_position Ba Ge 70000 Pt Intensity [counts] 50000 30000 10000 -10000 -30000 8 18 28 38 48 58 68 78 88 98 2 � [ ] • known members: Ep . . . Sr, Ba; La, Ce, Pr, Nd, Eu; Th, U; • a = 0 . 87 nm; much smaller than for X = P, As, Sb;

Is there a rattling mode in EpPt4Ge 12 ? • reduced lattice parameter prohibits “rattling” (at least) in BaPt 4 Sb 12 . • however: atomic displacement parameter of Eu in EuPt 4 Ge 12 twice as large as of Ba in BaPt 4 Ge 12

Oftedal relation in EpPt4Ge 12 • in general for pnictogen: position parameter y + z ≈ 0 . 5 • largest deviation from Oftedal relation in EpPt 4 Ge 12

Stability and Bonding in BaPt 4 Ge 12 Thermodynamical stability of XPt 4 Ge 12 (X=Ba,Sr) by density functional theory (DFT) using the Vienna ab initio simulation package (VASP) • total energy for hypothetical Pt 4 Ge 12 . • bonding energy E X for guest atom X from relation E X = U DF T XPt 4 Ge 12 − U DF T Pt 4 Ge 12 − U DF T X U DF T . . . total energy of compound or elemental solid. • E Ba = -3.24 eV and E Sr = -3.38 eV ⇒ stabilizing effect of the Ba and Sr guest atoms. • binary Pt 4 Ge 12 not stable; different to “ordinary” skutterudites

Electronic density of states of { Sr , Ba } Pt 4 Ge 12 • DOS at E F do- minated by Ge- p states; small Pt- d contributions; vanishing Ba,Sr states • small differences between relativi- stic (s-o coup- ling) and non- relativistic calcu- lations.; • significant el-ph enhancement ⇒ SC!?

Electron density in BaPt 4 Ge 12 Isosurfaces of the electron density (0.14 electrons per ˚ A 3 ) for the states of the DOS peak at Fermi energy; view along [1,1,1] • spherical shapes around Pt atoms representing metal-like • tubes connecting Ge atoms states formed by the Pt 5d-like visualizing strongly directed states. bonds;

Superconductivity in EpPt4Ge 12

Electrical resistivity of { Sr , Ba } Pt 4 Ge 12 100 0 T 0 T 100 0.5 T 0.1 T (a) 1 T 0.5 T 80 1.5 T 1 T BaPt 4 Ge 12 SrPt 4 Ge 12 80 2 T 1.25 T 1.5 T 50 60 ρ [ μΩ cm] 30 2 T ρ [ μΩ cm] 60 40 ρ [ μΩ cm] ρ [ μΩ cm] 30 20 40 40 20 2.25 T 2.5 T 10 10 20 2.75 T 20 0 T [K] 3 T T [K] 0 3.25 T (b) 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0 0 0 50 100 150 200 250 300 50 100 150 200 250 300 T [K] T [K] • Woodward & Cody: ρ = ρ 0 + ρ 1 T + ρ 2 exp( − T 0 /T ) ; T 0 ≈ 130 K • T c = 5 . 1 and 5.35 K for Sr and Ba-based compounds

Specific heat of BaPt 4 Ge 12 • γ ≈ 42 mJ/molK 2 θ D ≈ 245 K • ∆ C p /T ( T = T c ) ≈ 58 mJ/molK 2 ⇒ ∆ C p / ( γ n T c ) ≈ 1 . 35 , BCS theory: ∆ C p / ( γT c ) ≈ 1 . 43 .

Specific heat of { Sr , Ba , Ca } Pt 4 Ge 12 Δ (0) = 9.7(1) K Ba 0.8 Ca 0.2 Pt 4 Ge 12 0.20 Δ (0) = 9.4(1) K 0 T Δ (0) = 8.8(1) K 1 3 T Ba 0.8 Ca 0.2 Pt 4 Ge 12 Cp/T [J/(mol K 2 )] 0.15 BaPt 4 Ge 12 Ces/ γ Tc SrPt 4 Ge 12 SrPt 4 Ge 12 0 T 0.10 3 T BaPt 4 Ge 12 0.1 0.05 0 T 3 T (b) (a) 0.00 1.5 2.0 2.5 3.0 3.5 4.0 4.5 0 1 2 3 4 5 6 7 T [K] Tc/T • T c = 5 . 1 and 5.35 K for Sr and Ba-based compounds • γ (Ba) ≈ 42 mJ/molK 2 γ (Sr) ≈ 41 mJ/molK 2 • θ D (BaPt 4 Ge 12 ) ≈ 245 K; θ D (SrPt 4 Ge 12 ) ≈ 220 K!!!

SC features of { Ba , Sr } Pt 4 Ge 12 • Electron - phonon enhancement factor λ ≈ 0 . 7 ⇒ SC beyond weak coupling limit • smaller mass of Sr-compound does not produce larger Debye temperature; smaller atomic volume of Sr responsible for weaker bonding in cage; less oscillator strength; larger thermal displacement, smaller T c • mostly Ge- p states at the Fermi energy! SC due to Ge-electrons • comparable cage-forming compounds like { Ba , Sr } 8 Si 46 : states at E F predominantly formed from Ba- 5 d and Sr-4d states T c (Ba 8 Si 46 ) ≈ 8 K.

Lattice contribution to { Ba , Sr } Pt 4 Ge 12 � ∞ ( ω 2 T ) 2 C ph ( T ) = R F ( ω ) sinh 2 ( ω 2 T ) 0 0.25 BaCa 0.2 Pt 4 Ge 12 (4/5)R π 4 ω −2 F( ω ) [mJ/(g-atomK 4 )] SrPt 4 Ge 12 6 0.20 least squares (C p - γ T )/ T 3 [mJ/g-atomK 4 ] fit • low lying pho- BaPt 4 Ge 12 non mode 0.15 4 responsible for superconducti- 0.10 Sr vity? Ba 2 Ca 0.05 ( Junod et al., 83) 0.00 0 2 5 10 20 50 100 200 T [K] ( ω /4.93) [K]

Upper critical field of { Sr , Ba } Pt 4 Ge 12 2.0 BaPt 4 Ge 12 magnetisation resistivity specific heat 1.5 • Hake et al: μ 0 H c2 [T] H ′ c2 ∝ 1 / v F 1.0 • free electrons -0.53 T/K v F = ( N / V ) ( 1 / 3 ) -0.46 T/K SrPt 4 Ge 12 0.5 magnetisation resistivity • volume -0.31 T/K specific heat -0.275 T/K increases 0.0 0 1 2 3 4 5 6 from Sr to Tc [K] Ba ⇒ v F • BaPt 4 Ge 12 : decreases ! µ 0 H c 2 ≈ 1 . 8 T; µ 0 H ′ c 2 = − 0 . 46 T/K • SrPt 4 Ge 12 : µ 0 H c 2 ≈ 1 . 0 T; µ 0 H ′ c 2 = − 0 . 27 T/K

Upper critical field of { Sr , Ba } Pt 4 Ge 12 2.0 BaPt 4 Ge 12 magnetisation resistivity specific heat 1.5 Maki parame- μ 0 H c2 [T] ter: 1.0 • BaPt 4 Ge 12 : -0.53 T/K α ≈ 0 . 18 -0.46 T/K SrPt 4 Ge 12 • SrPt 4 Ge 12 : 0.5 magnetisation α ≈ 0 . 14 resistivity -0.31 T/K specific heat -0.275 T/K 0.0 0 1 2 3 4 5 6 Tc [K] • WHH model applicable; • Contribution of α compensated by λ so !

Pressure response of T c of SrPt 4 Ge 12 1.0 bar SrPt 4 Ge 12 100 3.5 kbar 8.6 kbar 13.5 kbar 14 DOS(E=E F ) [states/(ev . f.u.)] 17.5 kbar 80 19.2 kbar 12 20.5 kbar ρ [ μΩ cm] 10 60 5.4 SrPt 4 Ge 12 8 Tc [K] 40 6 5.2 4 20 SrPt 4 Ge 12 2 5.0 0 5 10 15 20 0 Pressure [kbar] 0 0 5 10 15 20 0 50 100 150 200 250 300 p [kbar] T [K] • Bogolyobov et al.: • θ D = 220 K; pressure inde- pendent; normal state region: � 1 � T c = 1 . 14¯ hω D exp − , model of Woodward & Cody λ − µ ∗ T 0 = 123 K • non-monotonous variation of λ = N ( E F ) V T c ( p )

Ground state of { Th , U } Pt 4 Ge 12 200 5 UPt 4 Ge 12 ThPt 4 Ge 12 0.25 H c2 ' = -0.064 T/K 4 0.30 ThPt 4 Ge 12 150 H c2 (0, theor.) = 0.21 T γ = 35 mJ/mol K 2 α = 0.017 0.20 0.25 λ so = 15 3 ρ [ μΩ cm] ρ [ μΩ cm] Cp/ T [J/(mol K 2 )] 0 T 0.20 100 0.15 0.05 T μ 0 H [T] 0.1 T 2 0.2 T ThPt 4 Ge 12 0.15 μ 0 H c2 0.10 WHH 50 model 0.10 1 μ 0 H c 0.05 0.05 (a) (b) 0 (b) (a) 0 0.00 0.00 0 50 100 150 200 250 0 2 4 6 8 10 12 14 0 1 2 3 4 5 6 7 0 1 2 3 4 5 T [K] T [K] T [K] T [K] • γ = 35 mJ/molK 2 ; θ D = • ThPt 4 Ge 12 ; T > T c : model of Woodard & Cody T 0 = 12 1 K; 260 K T c = 4 . 8 K • λ e − ph = 0 . 66 • UPt 4 Ge 12 ; spin fluctuations; • µ 0 H ′ c 2 = − 0 . 064 T/K ρ ( T ) = ρ 0 + AT n T ≪ : with ρ 0 = 14 . 5 µ Ω cm, A = 0 . 42 µ Ω cm/K 1 . 5 ; n = 1 . 5 .