Intermetallic Clathrates A Challenge for Thermoelectrics Structure - - PowerPoint PPT Presentation

Intermetallic Clathrates

A Challenge for Thermoelectrics

Structure - Property Relations

Peter Rogl1

• N. Melnychenko-Koblyuk1, A. Grytsiv1, E. Bauer2, H. Kaldarar2, H. Michor2
• F. Röhrbacher2, Royanian1,2, H. Schmidt1, G. Giester3

1 Institute of Physical Chemistry, University of Vienna, Austria 2Institute of Solid State Physics, Vienna University Technology, Austria 3Institute Mineralogy, Crystallography, University of Vienna, Austria

Research sponsored by Austrian FWF-projects: 16370 & 16778

Contents

Crystal Chemistry of Clathrates Formation and Crystal Structure Phase Equilibria Ba,Sr-M-Ge,Si Properties - Clathrates Type I

Definitions

Clathrate: An inclusion complex in which particles of one

substance are completely enclosed in cavities formed by the crystal lattice or are present in large molecules of another substance, i.e. the crystal takes in foreign molecules during growth, which cannot escape until the crystal is decomposed [1962Wel, 2001Lew].

Zeolite: Consists of (Si,Al)nO2n framework with a negative

charge which is balanced by positive ions in the cavities. A characteristic property of zeolites is the ease with which they take up and lose water, which is loosely held in the structure, and other

• substances. These foreign molecules can enter or leave the crystal

without disturbing the structure [1962Wel].

Clathrasil: Silicate material with clathrate type structure

(usually listed in “Zeolite Atlas”).

[1962Wel] A.F. Wells, Structural Inorganic Chemistry, 3rd Ed., Oxford. [2001Lew] R.J. Lewis, Sr., Hawley’s Condensed Chemical Dictionary, Wiley.

Clathrate Research - History

First intermetallic type IV clathrate

• Q. Lin

2008 INSPEC <2007: 2420 hits for „Clathrate(s)“ Term „Clathrate“ for ß-Quinol Complexes

• H. Powell

1948 Ice-gas clathrates of Type I and II Stackelberg 1950 Chiral clathrate Ba6In4Ge21 (type IX)

• R. Kroener

1988 Thermoelectric Properties Sr8Ga16Ge30

• G. Nolas

1998 First binary type IX clathrates

• H. Fukuoka

2000 First type VIII clathrate Ba8Ga16Sn30

• B. Eisenmann

1986 First ternary X8A8Ge38 (X=Cl,Br,I; A=P,As,Sb)

• H. Menke

1973 First intermetallic clathrate: Na8Si46, NaxSi136

• J. Kaspar

1965 Crystal structure of 6Cl2*46H2O Solved

• L. Pauling

1952 First ice-chlorine clathrate “Cl2*10H2O”

• H. Davy

1811

Clathrate Hydrate (Cl2)8-x[H2O]46 Intermetallic Clathrate Eu2Ba6[Cu4Si42]

Filler atoms form dual structure: Cr3Si-type Framework atoms: Si + Cu Guest atoms : Larger cage Ba Smaller cage Eu

Melanophlogite M8-x[SiO2]46

Framework-Cage Assembly in Type I Clathrates

Space group : Pm-3n; Clathrate type I; a ≈ 1.1 nm Framework []: 46 atoms: 40 Ge in 24k, 16i and 6 Cu in 6d Filleratoms (): Smaller cage: Ba in 2a; Larger cage: Ba in 6c

(Ba2Ba6)[Cu6Ge40]

Isolated Pentagondodecahedra Channel-like connected Tetrakaidekahedra Small cages Larger cages

Structural Units of Intermetallic Clathrates

Pentagondodekahedron

512

Clathrate VIII Polyhedron with 3 additional atoms

334359

Tetrakaidekahedron

51262

Pentakaidekahedron

51263

Hexakaidekahedron

51264

Clathrate Types (based on [1984Jef, 1992Mak])

a X – big cage, Y – small cage, T – four-coordinated framework atom d cage not exactly defined e structure consists of both clathrate and typical intermetallic units

[1984Jef] G.A. Jeffrey „Inclusion Compounds”, Academic Press [1992Mak] T.C.W. Mak, G.-D. Zhou, “Crystallography in Modern Chemistry”, J. Wiley & Sons

Type Ideal unit cell formula Polyhedra Space group Intermetallic Clathrate I 6X*2Y*46T

a

[51262]6[512]2 Pm-3n K

8Ge46-x, Ba8Al16Ge30,

Eu2Ba6Cu4Si42 II 8X*16Y*136T [51264]8[512]16 Fd-3m NaxSi136, Cs8Na16Ge136 III 20X*10Y*172T [51262]16[51263]4[512]10 P42/mnm Cs30Na(1.33x-10)Sn(172-x), x = 9.6 IV 8X*6Y*80T [51262]4[51263]4[512]6 P6/mmm Li14.7Mg36.8Cu21.5Ga 66 P-6m2 V 4X*8Y*68T [51264]4[512]8 P63/mmc

• VI

16X*156T [43596273]16[4454]12 I-43d

• VII

2X*12T [4668]2 Im-3m

• VIII

8Y*46T [334359]8

d

Im-3m Ba8Ga16Sn30, Eu8Ga16Ge30 IX 16Y*8X*100T [512]8 + [410]4+...e P4132 Ba6Ge21In4, Ba6Ge25

H He Li Be B C N O F Ne Na’ Mg Al Si P S Cl Ar K Ca Sc Ti V Cr Mn Fe Co Ni Cu Z n Ga° Ge° As Se Br Kr Rb’ Sr Y Zr Nb Mo Tc Ru Rh Pd Ag C d In Sn°’ Sb Te I Xe Cs’ Ba° La Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn Fr Ra Ac Ku Ns La Ce* Pr Nd Pm Sm Eu° Gd Tb Dy Ho Er Tm Yb Lu Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr

Elements Forming Intermetallic Clathrates I

“Guest atoms” – occupy large cages. M Elements forming clathrate II compounds Most important framework elements Elements forming clathrate IX compounds Elements randomly substitute Si,Ge,Sn

‘ Elements forming clathrate III compounds

Elements form clathrates with halogens only. Sb can also partially substitute Ge.

° Elements forming clathrate VIII compounds

Elements forming “Cordier” phases only

*

Ce-compound not confirmed

Clathrate-like Structures

• S. Bobev, S. Sevov, JACS 124 (2002) 3359 S. Bobev, S. Sevov, InorgChem 39 (2000)

5930

Na204Ba16Sn310 a=2.52 F-43m Na10Cs3Sn23 a=1.24 c=5.15 R-3m

Dual Structures

s

Definition: A dual structure is a packing of polyhedra (with three faces meeting at each vertex), whose vertices are at the tetrahedral holes of the parent structure. Examples: The regular pentagonal dodecahedron (with 12 pentagon faces [512]) is dual to the icosahedron. [51262], [51263], [51264] are dual to the Frank-Kasper polyhedra of 14,15,16 vertices

• Type I hydrate dual to Cr3Si type
• Type II hydrate dual to MgCu2 type
• Type IV clathrate dual to Zr4Al3 type

The water molecules are centered in each of the tetrahedra of the triangulated metal coordination polyhedra. ⇒ Intergrowth structures combining types I, II, IV

Dual Structure, NaxSi136, Fd-3m

Definition: A dual structure is a packing of polyhedra (with three faces meeting at each vertex), whose vertices are at the tetrahedral holes of the parent structure.

Intergrowth structures among clathrate I, II, IV

based on [1998OKe]

Type Ideal unit cell formula Polyhedra Space group Lattice param. Intermetallic Clathrate I + II 98X*18Y*46P* 920T [512]98[51262]18[51264]46 dual type: deriv.- Mg32(Al,Zn)49 Pm-3n a ~ 2.74 nm ? II + IV 98X*12Y*12Z* 40P*920T [512]98[51262]12[51263]12 [51264]40 dual type Mg32(Al,Zn)49 Im-3 a ~ 2.78 nm ? II + IV 21X*6Y*6Z*6P* 222T [512]21[51262]6[51263]6 [51264]6 dual type μ-phase W6Fe7 R-3m a ~ 1.0 c ~ 5.6 nm ? III=I+IV 10X*16Y*4Z* 172T [512]10[51262]16[51263]4 dual type σ phase Cr6Fe7 P42/mnm a ~ 2.3 c ~ 1.2 nm Cs30Na(1.33x-10)Sn(172-x) x = 9.6

• M. O’Keeffe, G.B. Adams, O.F. Sankey, Phil. Mag. 78 (1998) 21

Clathrasils-Topologically distinct frameworks

• H. Gies, in Inclusion Compounds, Vol. 5, Oxford Univ. Press, NY, 1991

Clathrasil Family Cell Formula# Space Group Unit Cell

in nm

Cage Types

cages/unit cell Melanophlogites (Mel) 46Si02* 2M12* 6M14 Pm-3n a =1.344 2[512]*6[51262] clathrate I Dodecasils 3C (D3C) 136SiO2*16M12* 8M’16 Fd-3m a =1.940 16[512]*8[51264] clathrate II Dodecasils 1H (D1H) 34SiO2*3M12*2M’12*M20 P6/mmm a =1.378 c =1.119 3[512]*[435663]* [51268] Deca-dodecasils 3R(DD3R) 120SiO2*6M10* 9M12*6M’19 R-3m a =1.386 c =4.089 6[435661] 9[512] 6[435126183] Nonasils (Non) 88SiO2*8M8*8M’9*4M’’20 Fmmm a =2.223 b =1.506 c =1.363 8[5464]*8[4158]* 4[58612] Deca-dodecasils 3H (DD3H) 120SiO2*6M10*9M12 M15*4M19*1M23 R3 to R-3m a =1.389 c= 4.099 6[435661]*9[512]* [465683]*4[4351261 83]* [5186283] Silica-sodalites (Sod) 12SiO2*2M14 Im-3m a =0.884 2[4668] clathrate VII

# Mf guest molecule located in a cage with f faces.

Clathrasils – Cages and Cage Volumes

Cage Number

• f

Faces Free Volume 1000nm3 [5464] 8 25 [4158] 9 30 [435661] 10 35 [512] 12 80 [435663] 12 100 [4668] 14 130 [51262] 14 160 [465683] 15 200 [51264] 16 250 [435126183] 19 350 [58612] 20 290 [51268] 20 430 [5186283] 23 540 [1992Mak] T.C.W. Mak, G.-D. Zhou, “Crystallography in Modern Chemistry”, Wiley&Sons

Are Clathrates „Zintl Compounds“ ?

Rule of thumb for quick selection of TE compositions

In a Zintl compound, each constituent attains a closed valence shell via a formal charge transfer for the formation of covalent bonds. The electropositive ‚guest‘ atoms donate electrons to the more electronegative host atoms (cage). The host atoms complete their valence requirement (octet rule) and establish a covalently bonded cage structure. Engaging all valence electrons in covalent bonds would render clathrates to be semiconductors.

Ba8Ge43฀3 ≡ [Ba2+]8[Ge0]43[฀-4]3 ≡ 4 electrons Sr8Ga16Ge30฀0 ≡ [Sr2+]8[Ga1-]16[Ge0]30 ≡ semicond Ba8(Zn,Cd)8Ge38฀0 ≡ [Ba2+]8[Zn2-]8[Ge0]38 ≡ semic.

• E. Zintl, Angewandte Chemie, 52 (1939) 1

Halogen-Based Inverse Clathrates (Type I)

X-

8A+ 8Ge38

(X=Cl,Br,I; A=P,As,Sb)

H.Menke, Z.An.Allg. Chem. 395 (1973) 223

I(-)

8[Ge46-xI(3+) x]

x = 8/3

• R. Nesper, Ang. Chem. 98(4) (1986) 369

I8[Si46-xIx] x = 1.8 HP- phase

• E. Reny, Chem. Commun. 24 (2000) 2505

Tin-based Iodine Clathrates

• M. Shatruk, Inorg. Chem. 38 (1999) 3455

I-

8Sn24A+ 22 (A = P, As)

Ideal : I2aI6cSn24kA6dA16i

22 – 8 = 14 additional electrons from pnictides are compensated by 14/5 = 2.8 phosphorous or arsenic defects.

⇒ defect Zintl phase I8Sn24A19.2

Substitution Compounds with Phosphorus

I8Sn19.3Cu4.7P22 Substitution of Sn by Cu: 14/(4 – 1) = 4.7 Cu atoms I8Sn10In14P22 Substitution of Sn by In: 14/(4 – 3) = 14 In atoms I8Sn14In10P21.2฀0.8 Defects + Substitution of Sn by In: 14 - 10*(4–3)=4; 4/5 = 0.8 defects. Superstructure to clathrate I compound (5 times enlarged unit cell).

• M. Shatruk, Inorg. Chem. 38 (1999) 3455, Zhur. Neorg. Khimii 45(2) (2000) 203;
• J. Solid State Chem. 161 (2001) 233.

Bonding in Clathrates

Atoms in larger cages off centre ⇒tetrag. distortion (M8Ga16Ge30: Ge in 16i site, tetrahedral arrangement) Ga-Ga less favourable contacts, Ga in 6c, 24k-sites Low vibrational guest atom frequencies Lack of directional bonds Low-guest host interaction DFT-calculation1 shows strong bonding Ba-framework: valence orbital of Ba overlap with all orbitals of FW

1 N.P. Blake, J. Chem Phys. 114 (2001) 10063

Phase Stability - Melting Point Data

Ba8Ga16Si30 Tm = 1197°C (1111) Ba8Ga16Ge30 Tm = 974°C (963) Sr8Ga16Ge30 Tm = 774°C (770) Ba8Ga16Sn30 Tm = 467°C (450) βEu8Ga16Ge30 Tm = 699°C (688)

V.L. Kuznetzov et al., J.Appl.Phys. 87 (2000) 7871

• S. Paschen et al. Phys. Rev. B 64 (2001) 214404.

αEu8Ga16Ge30 to βEu8Ga16Ge30 transformation Ttr = 696°C Stability range of βEu8Ga16Ge30 696<T<699 Ba6Cu15.5P30.5 (Pbcn) decomposes >360°C [1995Due] Binding Energies from DFT: SiClath-Sidiam ≈ 0.8 eV/atom at RT, >11 GPa Si136 ⇒ SiβSn

Structural Relations - Intermetallic Clathrates

TE Figure of Merit Bulk Materials

Bi Te3

2

La Te

2 3

CoSb3 Ba Co Ni Sb

0.3 3.95 0.05 12

Ba Ga Ge

8 16 30

PbTe SiGe

n - type, ZT

0.0 0.4 0.8 1.2 1.6 200 400 600 800 T, °C

(Bi,Sb) Te

2 3

Zn Sb

4 3

TAGS CeFe Sb

4 12

PbTe SnTe

SiGe p - type, ZT 0.0 200 0.4 0.8 1.2 400 600 800 T, °C 1.6

Yb MnSb

14 11

S2σ Power factor: consists of electronic contributions only Total thermal conductivity: κ = κe + κL > κe Wiedemann Franz Law: κe = L σ T

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TE - Properties

Clathrate Type Phase Seebeck coefficient S300, μV/K Electrical resistivity ρ300, mΩcm Thermal conductivity κ300,, W/mK I Na8Si46

• 7

9.6 9 I K8Ge46

• 160

I Cs8Sn44

• 304 (-291)

(-353 at 1.2GPa) 59.4 (100) 1 I Ba8Ga16Si30

• 47

0.85 1.1 I Ba8Ga16Ge30

• 66 (-50)

0.66 I Ba8In16Ge30

• 75

2.2 I Ba8Ga17.31Sb2.15Ge25.90 100 I I8P8Ge38 1000 I Sr8Ga16Ge30

• 313

12.8 1.16 I Sr8Ga16Ge30

• 71 to -100
• 185 at 7GPa

0.77 (0.6) 0.9 I βEu8Ga16Ge30

• 152 (-50)

2.52 (0.5) 0.5 I Sr4Eu4Ga16Ge30

• 88

1.00 II Na3Si136

• 300

ED = 0.04 eV II Na11Si136 MIT x>11

• 60

ED = 0.013eV II Cs8Na16Si136

• 29

48 II ฀8Ba16Ga32Sn104 VIII Ba8Ga16Sn30

• 185

11.0 IX Ba6Ge23.32Sn1.68

• 14

IX Ba6Ge21.93In3.07

• 32

IX Ba6Ge25-x

• 18

0.2 1.9

Compounds Superconducting transition, K Ba8AuxSi46-x (x = 0 – 3) (type I) 5.3 – 5.8 Ba8AgxSi46-x (x = 0 – 4) (type I) 5.0 – 6.1 Ba8Cu4xSi46-x (x = 0 – 4) (type I) 5.5 – 6.3 K2.9Ba4.9Si46 (type I) 2.5-3.5 Ba8Ga16Ge30 (type I) 7.5 type II Ba8Si46 (HP phase) (type I) 8 Na2.9Ba4.5Si46 (type I) 4 type II Ba8AuxSi46-x (x = 0 – 3) (type I) 5.3 – 5.8 Ba6Ge25 (type IX) 0.24 Na2Ba4Ge25 (type IX) 0.84 3.8 K at 2.7 GPa

Superconducting Clathrates

Ba-states are hybridized with those of Si46-fw forming the conduction band ⇒ high DOS at EF

Magnetic Clathrates

Compound Ferromagnetic ordering temperature Tc Ba8Mn2Ge44 (clathrate I) 10 K; μs=0.8 μB/Mn Eu2Ba6Al8Si36 (clathrate I) 32 K β-Eu8Ga16Ge30 (clathrate I) HT 35 K α-Eu8Ga16Ge30 (clathrate VIII) LT 10 K

Structure - Properties

How to understand Thermoelectric Properties of Clathrates I in Systems Ba(Sr)-{Pd,Pt,Cu,Zn,Cd}-Ge(Si) Phase Relations Ba(Sr)-M-Ge(Si) (> 60 at.% Ge) M = Pd, Pt, Cu, Zn, Cd (Synthesis, X-ray, EPMA) Crystal Chemistry of Type I Clathrates Ba8MxGe46-x-y฀y; Ba8MxSi46-x-y฀y Physical Properties of Type I Clathrates

(Electrical Resistivity, Hall-effect, Specific Heat, Inelastic ND, Thermal Conductivity, Thermopower)

H He Li Be B C N O F Ne Na’ Mg Al Si P S Cl Ar K Ca Sc Ti V Cr Mn Fe Co Ni Cu Z n Ga° Ge° As Se Br Kr Rb’ Sr Y Zr Nb Mo Tc Ru Rh Pd Ag C d In Sn°’ Sb Te I Xe Cs’ Ba° La Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn Fr Ra Ac Ku Ns La Ce* Pr Nd Pm Sm Eu° Gd Tb Dy Ho Er Tm Yb Lu Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr

Elements Forming Intermetallic Clathrates I

“Guest atoms” – occupy large cages. M Elements forming clathrate II compounds Most important framework elements Elements forming clathrate IX compounds Elements randomly substitute Si,Ge,Sn

‘ Elements forming clathrate III compounds

Elements form clathrates with halogens only. Sb can also partially substitute Ge.

° Elements forming clathrate VIII compounds

Elements forming “Cordier” phases only

*

Ce-compound not confirmed

Ba8MxGe46-x-y฀y

Binary Ba8Ge43 ฀3

Phase Diagram Ba-Ge; Ba8Ge46-x฀x, x=3

• W. Carrillo-Cabrera, S. Budnyk, Y. Prots, Y. Grin, Z. Anorg. Allg. Chemie, 630 (2004) 2267

*first discovered by F.Herrmann,K.Tanigaki,T.Kawaguchi etal. Phys. Rev. B60 (1999) 13245

2a0 = 2.1312 nm

defect- ordering*

chiral helix around 41 along [001]

The case of „Ba8Mn2Ge44“

TC=10 K μs=0.8μB/Mn

• C. Yang, J. Zhao, J.P. Lu, Phys. Rev. B70, 073201 (2004)

Calculation of the electronic structure of Ba8Mn2Ga44 μs=0.77μB/Mn for Mn2, μs=2.56μB/Mn for Ba8Mn4Ga42

The case of „Ba8Mn2Ge44“

Solidus 800°C

Ba8Mn0.1Ge46

200μm 10μm

The case of „Ba6Fe3Ge22“

• Y. Li, J. H. Ross, Jr. Appl. Phys. Lett. 83, 2868 (2003)

New Transition Metal Doped Germanium Clathrates Ba6Fe3Ge22 TC=175 K, μs= 0.7μB/Fe with transition to spin glass

800°C

Ba6Fe0.2Ge25 Ba8Fe0Ge43

• N. Koblyuk, A. Grytsiv, P. Rogl, 2006

The case of „Ba8CoxGe46-x“

• Y. Li, J. H. Ross, Jr., J.A. Jarra et al. Physica C 408 (2004)

Study of Superconducting Ba-Ge-Co Compounds Ba8CoxGe46-x: 100 Oe; TSC= 10K (x=0), TSC= 4K (x=4), TSC= 4K (x=6)

• N. Koblyuk, A. Grytsiv, P. Rogl, 2006

Ba8Co1Ge45 Ba6Co0Ge25

No bulk superconduct., multiphase samples – no clathrates !

Phase Relations

Systems Ba-M-{Ge,Si} M = Pd, Pt, Cu, Zn, Cd for > 60 at.% Ge Isotherms T=800°C, Liquidus Projections

M (at.%) Ge (at.%) Ba (at.%) Phase/Composition 11.11 74.07 14.81 Ba8Ge40M6 5.88 78.43 15.69 Ba8Ge40M3 ฀ 3 5.55 79.63 14.81 Ba8Ge43M3

• 84.31

15.69 Ba8Ge43 ฀ 3 M, ฀ to be defined by combined EPMA + X-ray SC analyses !

20 60 80 100

a t . % G e PdGe BaGe2 Ba Ge

8 43

Ba Ge

6 25

L

BaPdGe

3

Ba8PdxGe46-x-y฀y

Solubility limit of Pd in κI at 800°C: Ba8Pd3.8Ge42.2฀0 Isotherm 800°C τ1 τ1 κI κIX

Liquidus Projection DTA

U2 764°C L + κI ⇔ τ1 + (Ge) E 719°C LE⇔ τ1+PdGe +(Ge)

τ1 BaPdGe3

70 50 90 10 30

PtGe Pt Ge

2 3

PtGe2 L BaGe2 Ba Ge

8 43

Ba Ge

6 25

a t . % G e

• at. % Ba

Ba-Pt-Ge a double thermo-electric system?

Clathrate Ba8Pt3.6Ge41.4฀1.0 and Skutterudite BaPt4Ge12 800°C τ1 τ1 τ2 τ2

τ2-BaPt4Ge12 is a novel superconducting Skutterudite,TC=5 K Solubility limit at 800°C

Ba8Pt3.6Ge41.4฀1.0

E.Bauer,N.Melnychenko,A.Grytsiv,P.Rogl et al., Phys.Rev.Lett.,Nov. 2007

20 40 60 80 100

• at. % Ge
• at. % Ba

Cu Ge

3

BaGe2 Ba Ge

6 25

Ba Ge

8 43

L

20

Ba8CuxGe46-x-y฀y

Clathrate solubility limit Ba8Cu6Ge40

800°C

τ1 Ba(Cu,Ge)2 τ2 BaCu9Ge4 τ1 τ2

Cu content, x Lattice parameter, nm

single crystal data powder data

This work:

Ba Ge

8 46-x-y y

Cux

1 2 3 4 5 6 1.062 1.064 1.066 1.068 1.070 1.072 1.074 1.076

1991Cor, 2005Hok

Literature data:

2005Joh 2004Car 2003Yan 2005Yan 2006Joh 2006Oka

Maximum at xCu=5.3 for V vs Cu due to two competing influences: 1) increase of V when Cu fills ฀ 2) decrease of V when Cu for Ge

20 40 60 80 100

• at. % Ge
• at. % Ba

BaGe2 Ba Ge

8 43

Ba Ge

6 25

L

Ba8ZnxGe46-x-y฀y

800°C

solubility limit (800°C) Ba8Zn8Ge38 liquid in large parts of diagram, equilibrium liqu. + clathrate enables easy crystal growth

τ1 BaZn2Ge2

BaAl4-type

τ1

N.Melnychenko,A.Grytsiv,E.Bauer,P.Rogl et al., JPhysCondMat. May 2007

Ba8ZnxGe46-x Single Crystals-Bridgman

Ba8Zn4Ge42 Ba8Zn6Ge40 Ba8Zn2Ge44 Ba8Zn8Ge38

3 mm 50 μm

Ba8CdxGe46-x Ba8Cd7.6Ge36.4

800°C Solidus

Ba8CdxGe46-x Single Crystals-Bridgman

Ba8Cd4Ge42 Ba8Cd6Ge40 Ba8Cd2Ge44 Ba8Cd8Ge38

50 μm 5 mm

Summary on Phase Relations

Clathrates Type I Ba-{Pd,Pt,Cu,Zn}-Ge

All solid solutions derive from binary Ba8Ge43฀3. Continuous solid solutions at 800°C, as Ba8Ge43฀3 stable

• nly for 770°C < T < 810°C .

Large ternary stability regions at T=900°C and T=700°C. Large single crystals due to tie-lines: type I + liquid. Type I for all samples investigated Ba8MxGe46-x-y฀ y (x ≥ 2). Second order transition: Ia-3d Pm-3n at x < 2 ?

Crystal Chemistry Ba8MxGe46-x-y฀y

Mode of incorporation of M-atoms Atom site occupancy Cage filling atoms ADP‘s - Atom displacement parameters

Incorporation of M-atoms in Type I Framework

Three Limiting Cases

Ba

2a 6c

Ge

6d 16i 24k

฀

6d 16i Ba8Ge43฀3

2nd order transition?

Pm-3n Ia-3d

Atom Site Distribution in Ba8CdxGe46-x-y฀y

Ba-sites 2a,6c complete SC data Split site Ge in 24k

Ba8Ge43฀3 ฀ Ba8Cd8Ge38

56Ba 32Ge 30Zn 48Cd

Cages in Ba8CdxGe46-x-y฀y

normal ADP for Ba1 Einstein Oscillator Ba2 vacancies in 6d-site with Cd large ADP for Ge3-atoms directed to Cd and Ba1 ADP (Ge3) vanishes with decreasing defect = increasing Cd content some Cd in 16i sites (M2)

Assuming a simple Debye solid; rattling Ba as a single harmonic Einstein oscillator; we extract ΔUij/ΔT ⇒ force constant KF, vibration frequency νBa, Einstein temperature θE. θE(6Ba,U22) = 64 K; θE(6Ba,U11) = 85 K; θ (Ge,Uequiv) = 112 K Examples: θE (EuRu4Sb12) = 78 K and θE (EuOs4Sb12) = 74 K. ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = 2T θ coth θ mk 8π h U

E E B 2 2 iso

Uequiv(6Ba): KF=kBΔT/ΔUequiv KF = 4π2mνBa

2 = 15339 gs-2

νBa(Uequiv) = 1.31 • 1012 s-1 θE(6Ba,Uequiv)=hνBa/kB=68 K for T>>0 (hν << 2kBT) ⇒ Uiso = kBT/KF

Thermal Displacement Parameters f(T)

U22=U33 (6Ba) Uequiv(6Ba) U11(6Ba) U11(2Ba) Uequiv(6Cd) Uequiv(16Ge, 24Ge)

Ba8Cd8Ge38

Biso= 8π2Uiso

Physical Properties of Ba8MxGe46-x-y฀y Specific Heat Electrical Resistivity, Hall Data Thermal Conductivity Thermopower

Realistic PDOS [1983Jun] represented by spectral function F(ω) [1961Cha] ω = phonon frequency Standard evaluation: γ=2 mJ/molK2; β=0.00844 J/molK4 ⇒ θD=235K Difficulties already > 4K: ⇒ θE1 = 48±5.6K, θE2 = 85±4K, θD=225K

Specific Heat (Cp–γT)/T3 vs lnT of Ba8Zn7.7Ge38.3

• A. Junod, T. Jarlborg, J. Muller, Phys. Rev. B27 (1983) 1568

R.G. Chambers, Proc. Phys. Soc. London 78 (1961) 941

F(ω) = δ(ω) and F(ω) ~ ω2 cut-off at ωD F(ω) normalized to the number of branches θD=225K

Realistic PDOS [1983Jun] represented by spectral function F(ω) [1961Cha] ω = phonon frequency Standard evaluation: γ=0.05 mJ/molK2; ⇒ θD=268K Difficulties already > 4K: ⇒ θE1 = 54±3.8K θE2 = 87±3.5K, θD=226K

Specific Heat (Cp–γT)/T3 vs lnT of Ba8Pd3.8Ge42.2

• A. Junod, T. Jarlborg, J. Muller, Phys. Rev. B27 (1983) 1568

R.G. Chambers, Proc. Phys. Soc. London 78 (1961) 941

F(ω) = δ(ω) and F(ω) ~ ω2 cut-off at ωD F(ω) normalized to the number of branches

Inelastic TOF neutron diffraction for Ba8Zn7.7Ge38.8

Two low-energy Einstein modes in a wide Q-range. At any Q line shape is more structured than for a single excitation. Nonmonotonic intensity change of the two Einstein modes suggests coupling between Ba-modes and Zn-Ge dynamics.

125K 250K 325K G(ω) general. dens. states

Inelastic TOF cold neutron diffraction for Ba8Pd3.8Ge42.2

Two low-energy Einstein modes in a wide Q-range. At any Q line shape is more structured than for a single excitation. Nonmonotonic intensity change of the two Einstein modes suggests coupling between Ba-modes and Pd,Zn-Ge dynamics.

125K 250K 325K

Lowest frequencies due to Ba. Pd: Peak-shift to higher energies (~0.5 meV); Pd with higher mass couples better with Ba than Zn.

Resistivity for Ba8ZnxGe46-x-y฀y

Bloch-Grüneisen + T dependent charge carrier density: (1) assuming a DOS of rectangular bands N(E) and (2) a gap in the DOS slightly above EF with width Eg (3) Calculation of density of electrons nn and holes nP involving Fermi-Dirac distribution f(E,T); N=band hight

E

N(E ) E

F

E

g

n0 residual DOS

N.Melnychenko, A.Grytsiv, E.Bauer, P.Rogl et al.,

• J. Phys. Cond. Matter, May 2007

Eg=1650K

Metal to Insulator Transition

Resistivity for Ba8PdxGe46-x (1)

Bloch-Grüneisen + T dependent charge carrier density: (1) assuming a DOS of rectangular bands N(E) and (2) a gap in the DOS slightly above EF with width Eg (3) Calculation of density of electrons nn and holes nP involving Fermi-Dirac distribution f(E,T); N=band hight

E

N(E ) E

F

E

g

n0 residual DOS

N.Melnychenko,A.Grytsiv,E.Bauer, P.Rogl, M.Koza et al., Phys.Rev.B, December 2007

Eg=1000K Eg=2200K

Metal to Insulator Transition

Hall Data for Ba8PdxGe46-x

N.Melnychenko,A.Grytsiv,E.Bauer, P.Rogl, M.Koza et al., Phys.Rev.B, Dec 2007

Metal to Insulator Transition

At 10 K, 3 Tesla: mobilities μ = 0.64 (x = 2), 1.6, 0.9 and -0.07 cm2/Vs

ne R R

H H

1 − = = μ ρ

n=-3.5*1021cm-3 n=-3.2*1021cm-3 n=-0.83*1021cm-3 n=-0.56*1021cm-3

Thermal conductivity for Ba8ZnxGe46-x-y฀y

Suppression of lowT maxima in λ(Τ) by resonance scattering of phonons based on static and dynamic disorder. λmin(300 K) = 4.3 mW/cmK. τE

• 1 :

x=4.6 has lowest ρ highest n highest τE lowest λlatttice!

Callaway + T3

λlattice λe λtotal Vacancies are more efficient in reducing λlattice than rattling modes !

Thermal conductivity for Ba8PdxGe46-x

Vanishing of vacancies in 6d sites with x, although Ge/Pd disorder rises: Intense scattering of phonons on vacancies. λ(T)= function of growing masses Zn, Cd, Pd. Suppression of lowT maxima in λ(T) by resonance scattering of phonons based on static and dynamic disorder. Cahill & Pohl: n = 4.3 1022 cm-3, θD=268 K λmin(300 K) = 5.1 mW/cmK.

Callaway + T3

λtotal

Linearity in Sd(T) from free electron model: For m = me, (at T>>RT for weak el. correl.) n ≈ 6.1020 cm-3. ZTcorr(300K) = S2/(ρλ) ≈ 0.087; ZTcorr(700K) = 0.42

Seebeck Coefficient for Ba8ZnxGe46-x-y฀y

Seebeck Coefficient for Ba8PdxGe46-x

Linearity in Sd(T) from free electron model: For m = me, 2<x<3.6; T<400 K n ≈ 2.9 1021 cm-3 for x=2; n ≈ 3.4 1020 cm-3 for x=3.6 agrees with Hall-data Minimum in SV likely due to concentration dependent gap Eg in ΝΕ above EF !

Systems Ba-{Pd,Pt,Cu,Zn}-Si

System Ba-Si

No binary Ba8Si46 at normal P

hP-Ba8-xSi46 stable > 3 GPa, > 800 K superconducting TC = 9.0 K for Ba7.76Si46

• H. Fukuoka et al., J. Phys. & Chem. Solids 65 (2004) 333

hP-Ba8-xSi46

Ba8PdxSi46-x

Type I Limited field of existence at 900 °C 2.5 < x < 4.1 At x = 4.1 0.5 Pd + 0.5 Si in 6d no vacancies in 6d !

[1991Cor] G.Cordier, P.Woll, J. Less Common Metals 169 (1991)

Ba8PtxSi46-x

Type I Limited field of existence at 900 °C 2.8 < x < 4.9 At x = 4.9 0.5 Pd + 0.5 Si in 6d no vacancies in 6d !

[1991Cor] G.Cordier, P.Woll, J. Less Common Metals 169 (1991)

Ba8PtxSi46-x

ADP’s of Ba2 >> Ba1 atoms temperature dependencies of ADP’s practically constant for all atoms of the lattice Thus no special rattling effect for Ba-atoms

• N. Melnychenko-Koblyuk, A. Grytsiv, P. Rogl
• E. Bauer, R. Lackner, E. Royanian, M.Rotter
• G. Giester, Phys.Rev.B. (2008)

Ba8{Pd,Pt}xSi46-x

Resistivity changes from metallic (Pd-poor) to semiconducting behaviour (Pd-rich)

Thermal Conductivity

Point defect scattering, increases upon increasing Pd content. Scattering on point defects = Pd/Ge substitution is an extremely efficient scattering process.

Ba8{Pd,Pt}xSi46-x

Thermal Conductivity Seebeck Coefficient

germanides have significantly smaller λ

T>50K x=3.8 n=3.2×1021cm−3

System Ba-Zn-Si

800°C τ1 Ba8Zn7Ge39 τ2 BaZn2Ge2

Electrical Conductivity – Fermi Dirac Function

Thermal Conductivity – Callaway Formula

Additional T3 term to compensate radiation losses Cahill & Pohl: theoretical lower limit of λph

scattering processes

τB boundaries τD dislocations τU Umklapp τE electrons

Seebeck Coefficient SV

T

Multicomponent Clathrates Ba8MxM‘yGe46-x-y-z฀z Can we reach p-type clathrates ?

by extending the type I solubility limit and by simultaneously tuning the electron/hole carrier balance? M, M‘ = Pd, Cu, Zn

Lattice Parameters and Solubility Limits for Ba8CuxZn6-xGe40 and Ba8PdxZnyGe40-x-y฀y

Phase relations around type I clathrate Ba-Pd-Zn-Ge

metallic Ba8Ge43 metal to insulator transition

System

Ba8Pd3.8Ge42.2

Ba8Pd3.8Zn3.6Ge42.2

No vacancies at PdZn-rich boundary

800°C

Resistivity for Ba8MxZnyGe46-x-y, M=Cu, Pd

Seebeck Coefficient

Ba8Cu5.2Zn0.8Ge40.0 Ba8Pd2.4Zn3.3Ge40.3 No positive Seebeck coefficient yet Cu+1.23Zn2+ Pd+0.0 Zn2+

Off-Center Rattling in Ba8MxM‘46-x-y฀y

Nuclear density at cage centres X8Ga16{Si,Ge}30

B.C. Sales et al., Phys. Rev.B. 63 (2001) 245113

• S. Paschen et al., Phys. Rev.B. 64 (2001) 214404
• A. Bentien et al., J. Appl. Phys. 91 (2002) 5694

Neutron SC data on 153Eu, Ba

αBa8Ga16Sn30 type: space group I-43m βBa8Ga16Ge30 type: space group Pm-3n Eu-atoms move from 24-cage centre 4 separate peaks at dEu-Eu=0.04 nm replacing Eu in 6c by Eu in 24k (24j) Eu-ADP data are independent of T large ADP: static&dynamic component

Neutron Diffraction of SC-Ba8Zn8Ge38

M Christensen et al. J. Phys.: Cond. Matter 20 (2008) 104244

Difference Fourier: Density for Ba2 in Ba8Zn7.7Ge38.3

Difference Fourier: Density for Ba2 in Ba8MxM‘46-x-y฀y

100 K

Electron Density Ba8Zn7Si39 at 100 K

Conclusions

Ba8MxGe46-x-yy clathrates type I for M=Pd,Pt,Cu,Zn,Cd

• Ternary solid solutions starting from binary Ba8Ge433
• Precise mode of filling the voids and Ge/M substitution
• Large ADP‘s only for Ba2 in 6c and Ge3 in 24k (split p.)
• M-incorporation drives metal to insulator transitions
• Cp, INS indicate coupling between Ba modes and host
• Vacancy level effient in reducing thermal conductivity
• Potential for nanostructuring the bulk clathrates.

Acknowledgements

Research sponsored by

FWF-Austrian National Science Foundation P-16370 & P-16778 NEDO-research grant from Japan Ministry of Energy Bridge project FFG – AVL List

• Univ. Wien
• N. Koblyuk, Y. Mudryk, A. Grytsiv, M. Rotter,
• N. Nasir

TU-Wien

• C. Röhrbacher, C. Paul, S. Berger, H. Kalderer
• H. Michor, G. Hilscher, E. Bauer

Resistivity for Ba8CdxGe46-x

Bloch-Grüneisen + Temperature dependent charge carrier density: (1) assuming a DOS represented by rectangular bands N(E) and (2) a gap in the density of states slightly above EF with width Eg. (3) Calculation of density of electrons nn and holes nP involving Fermi-Dirac distribution f(E,T)

Eg=2570K Eg=2570K

Seebeck Coefficient for Ba8CdxGe46-x

Thermoconductivity for Ba8CdxGe46-x

τc overall relaxation time for scatt. proc.

Conclusion

De hoc, multi nosciunt multa, omnes aliquid, nemo satis

(Concerning this, many know much, each a little, none enough)

• Anonymous Latin epigram

Ba8CuxGe46-x

• S. Johnsen, A. Bentien, G. K. H. Madsen, B. B. Iversen, Chem. Materials 18, 4633 (2006)

Ba8NixGe46-x

S.Johnsen, A.Bentien, G.K.H.Madsen, M.Nygren, B.B.Iversen, Phys.Rev.B 76, 245126 (2007)

Clathrate Types III and VI

Clathrate III structure {(Br2)20฀10}[H2O]172 Clathrate VI structure {(CH3)3CNH2}[H2O]156 ? Cs30Na(1.33x-10)Sn172-x

• S. Bobev, JACS 123 (2001) 3389

Tectosilicates

Tectosilicates = Framework Silicates Aa[Si1-xTxO2]XyMz

(*)

A cations not replacing Si, X anions, M neutral molecules in the voids of the tetrahedral framework, T usually Al3+; Be2+, Mg2+, B3+, Fe3+, Ti4+, Ga3+, Ge4+. Examples: Nephelin (Na,K)[SiAlO4]; feldspars Na1-xCax[Si2+xAl2-xO8] Classification of Tectosilicates: shape and size of framework voids chemical character of fw-cations

(*) Excluding few cases of octahedral [(Si,T]O6] units; Excluding few cases of interrupted frameworks

Voids in tetrahedreal Tectosilicates

• H. Gies, in Inclusion Compounds, Vol. 5, Oxford Univ. Press, NY, 1991

Short Reminder in Thermoelectricity

Thermodynamic circuit for the Seebeck effect A B T T + T Δ Thermodynamic circuit for the Peltier effect

A B T - T

1 Δ

T + T

2

Δ

Schematic dependencies of SV,λ,σ

• n the carrier concentration

Thermoelectricity – General Considerations (1)

Dimensionless Figure of Merit S...Thermopower σ...electrical conductivity κ... thermal conductivity T... Temperature S2σ Power factor: consists of electronic contributions only Total thermal conductivity: κ = κe + κL > κe Wiedemann Franz Law: κe = L σ T Maximal temperature difference with thermoelectric cooling: To obtain ZT=1 :

Typical Values for ZT=1, S=200μV/K, 1/σ=1200μΩcm, κ=1 W/mK, T=300K

Thermoelectricity – General Considerations (2)

At a first approximation: g... Electronic density of states ε... electron energy εF....Fermi Level

Peak structure Peak structure of g(ε) around the Fermi level is important for enhanced S Peltier Device

Intermetallic Clathrate Types

Clathrate I Eu2Ba6Cu4Si42

Pentagondodecahedra Tetrakaidecahedra

Clathrate II NaxSi136

Pentagondodecahedra Hexakaidecahedra

Clathrate VIII Ba8Ga16Sn30

Deformed Pentagondodecahedra

Clathrate IX Ba6Ge25

Pentagondodecahedra

• Intermet. framework