Cours École TE juin 2014 Lattice dynamics of nanocages

Localized modes and rattling

Uncorrelated and independent vibrations

K(x) = 2 K2 + 12 K4 Dx2(T) + ….

Weak bondings

Large Debye-Waller factors

a) Unusual anharmonic behaviour

c) vg2 (Q) = 0

b) Absence of phase coherence: S(Q, w) Q2

Case of skutterudites andclathrates

Harmonicity of low energy mode

Dispersion of low-energy modes

Coherence of R low-energy modes

Skutterudites ≠ phonon glass

Cours École TE juin 2014

Lattice dynamics of nanocages compounds

Anti-crossing btw acoustical and

optical branches ?

Transfer of optical character to acoustical

branches at large Q ?

Christensen DT 2009


Lattice dynamics of type 1 clathrate

Euchner PRB 2012

Due to umklapp scattering of acoustical

phonons by low-energy optical modes ?

Lee JPSJ 2007

Koza NM 2008

Kleinke, CM 2010


Antimonides zintl phases

Zn4Sb3 : crystal structure

Ideal b-Zn4Sb3 a-Zn4Sb3

Kim, PRB 2007

Nylen, JACS 2004

Ideal rhombohedral structure Zn6Sb5 :

SG R-3c, n°167

Real phase b:

36 Zn on substitutional sites

3 Zn on distinct interstitial sites

Real phases a, a’ :

Ordering of the interstitial Zn at low T


Nylen, JSSC 2007

a-Zn4Sb3 a’-Zn4Sb3

Nylen, Chem Mat. 2007


Ideal b-Zn4Sb3

Zn4Sb3 : crystal structure

Mikhaylishkin Chem Eur J 2005

Ideal structure Zn6Sb5: too high number of charge carriers

Nakamoto JAC 2004

Metallic type conduction: degenerated semiconductors

Indirect bandgap semiconductors of about 1.2 eV

Moechel PRB 2011

Cours École TE juillet 2012 Cours École TE juin 2014

Zn4Sb3 : electronic structure

Caillat JPCS 1997

Snyder Nat. Mat.2004


Zn4Sb3 : thermoelectric properties

No doping has improved the ZT Only p-type doping

Zn4Sb3 is metastable => problems of thermal stability

Liu, JCT, Calphad 2010



Zn4Sb3 : Stability

Pomrehn PRB 2011

Yin CC 2013

Stabilization of Zn4Sb3 by addition of oxide nps

350°C heating


Zn4Sb3 : recent improvements of ZT and stability

Superionic diffusion of Zn above 425 K

SP : stoichiometric ZR : zinc rich Li JACS 2014

Mozharivskyl, Chem Mat. 2004


Zn Sb

ZnSb : crystal structure

Orthorhombic structure

SG Pbca, n° 61

Similarities with Zn4Sb3 :

presence of the same motifs Zn2Sb2 et dimers Sb2


-2

-1

0

1

2

En

erg

y E

-Efe

rmi (

eV

)

Z T Y S X U R-12 -10 -8 -6 -4 -2 0 2 4 6

0

1

2

Energy E-Efermi

(eV)

Sb-5s

Sb-5p

Sb-4d

0.5

1.0

To

tal a

nd

Pa

rtia

l D

OS

(sta

tes/e

V/a

tom

)

Zn-4s

Zn-3p

Zn-3d

1

2

total

Indirect bandgap of 0.5 eV (experiment)

More stable defect (experimentally confirmed) : VZn

=> Explains intrinsic p-type doping

Jund, PRB 2012

Bjerg CM 2012


ZnSb : electronic structure

0

2

4

6

8

10

12

14

16

18

20

22

24

0

2

4

6

8

10

12

14

16

18

20

22

24

SX Z

E (

meV

)

Y 0.00 0.05 0.10 0.15 0.20 0.25

PDOS (states/meV)

Présence of low energy peak in both materials Jund, PRB 2012

Weaker thermal conductivity in Zn4Sb3 not only due to defects and disorder ?

Phonons in ZnSb


Zinc antimonides : lattice dynamics and thermal properties

Phonons in ideal Zn6Sb5

Bjerg, PRB 2014

Also due to large anaharmonicity of Sb1 bonding ?

Sb1 Sb2

Yb14MnSb11 : crystal structure

Yb has mixte valence

Brown, CM 2008

Kastbjerg, CM 2011

Body centered tetragonal symmetry: SG I 41/acd, n° 142



Yb14MnSb11 : thermal properties and lattice dynamics

Phonons in Yb14MnSb11

Low sound velocity and thermal conductivity

due to complex structure

Toberer, AFM 2008


Yb14MnSb11 : electronic and thermoelectric properties

Yb14AlSb11 is a ferromagnetic metal Eg = 1 eV (optics) for Yb14AlSb11


Other antimonides

Toberer, CM 2010

Cao, JAP 2010

RM2Sb2

Body centered tetragonal, SG P 4/nmm


Cao, JAP 2010

Yb1-xCaxCd2Sb2

Zintl phase that can be seen as A2+(Zn2Sb2) 2-

Toxicity problem with Cd

Band structure

Pomrehn, ACIE 2013

Kleinke, CM 2010 Body centered cubic, SG I m-3m

Shi, EES 2011

NiyMo2Sb7


Vining, CRC Handb. TE 1995

Since1995, progress only for the Mg2Si alloys


TE silicides


Krishnamurty, PRB 1986

Si-Ge alloys

Band structure of diamond Si-Ge

Ge Si Eg : -X Eg : L

Eg : -X Eg : L


Bux AFM 2009

Si-Ge alloys

Nanostructuration of Si

Very large decrease of the thermal conductivity => increase of ZT, but still insufficient


Lan AFM 2009

Si-Ge alloys

Nanostructuration of Si-Ge alloys

Large decrease of the thermal conductivity => increase of ZT


Si-Ge alloys

Nanocomposites based on Si-Ge alloys

Even larger ZT than with nano-Si-Ge Lan AFM 2009

Mg2Si based compounds

Possibility of interacalation

on 4b site

Si

Mg

Body centered anti-fluoride structure SG Fm-3m (225)


Several doping of Mg2Si0.6Sn0.4

Zaitsev, PRB 2006

Mg2X with X = Si, Ge, Sn

Indirect bandgap semiconductors with Eg = 0.3-0.4 eV (X = Sn) to 0.7-0.8 eV (X = Si)

Mg2Si : electronic structure and thermal properties


Pullikotil, PRB 2012

Mg2Si

High sound velocity => relatively large kL

Linl, PRB 2012

Tin alloying decreases the thermal conductivity

Liu PRL 2012


Mg2Si1-xSnx : best improvements in n doping during the 2 last years

Sb doped Mg2Si1-xSnx Bi doped Mg2Si0.4Sn0.6

See also Zhang APL 2013

Khan SM 2014

Presence of nano-inclusions

Liu JSSC 2013

Doping of Mg2Si with Bi, slightly better than with Sb

Bux, JMC 2011


Mg2Si : other n doping

Mg2Si : crucial importance of the defects for the doping

p and n doping due to defects :

See also Kato, JPCM 2009


Jund, JPCM 2013 ; Viennois, JSSC 2012

VMg2Ge

n p p p

p

n

Doping

n doping due to notably IMg, which is much more stable in Mg2Si

p doping due to notably rich-Mg vacancies. VMg is much more stable in Mg2Ge and in Mg2Ge

This explains why it is necessary to alloy Mg2Si with Ge or Sn to get more easily p doping.


Mg2X : p-doping

Jiang Int. 2013

p-type Mg2(Ge0.4Sn0.6)1-xAgx

Ihou-Mouko JAC 2011

p-type Mg2(X)1-xGax

Best p-type compounds has ZT of about 0.4

This is only slightly smaller than usual values (about 0.4-0.6) found in HMS

=> Maybe TE generator based only on Mg2Si ?


Mg2X : quasi-binary phase diagrams

Viennois, Int 2012

See also Zhang, Int 2008

See also Kozlov,JAC 2011

There are still uncertainties about range of the miscibility gap in Mg2X-Mg2Sn phase diagrams

Uncertainties related to possible evaporation of Mg and formation of MgO

There is a full solid solution for Mg2Si-Mg2Ge

Chen, JMR 2011


Mg2Si : stability issue

Bourgeois, FML 2013 Use only below 600-650 K ?

Weak stability (especially of powder) under air

Sondergaard, JMS 2013

Chimney lattice

Higgins, 2008

Ladder lattice

Miyazaki, 2008


Few studies of the stability of the different phases Combination of two different sub-lattices

HMS : crystal structure of MnSi2-x

Higgins, 2008

Miyazaki, PRB 2008

VEN < 14 => Nowotny chimney-ladder metallic phases

Here: 13.9 < CEV < 14 Periodicity depending on Mn/Si ratio

Proposition:

2 sub-lattice superposed in an

icommensurate order

Valence electron number

Mn11Si19 Mn15Si26

Mn27Si47

Mn4Si7


Main crystal structures of the HMS

Electronic structure of HMS

Mn4Si7 Mn11Si19

Mn15Si26 Mn27Si47

Mn4Si7

Calculations : Eg = 0.7-0.8 eV (indirect)

Exper. : Eg = 0.4 eV (indirect)

Eg = 0.96 eV (direct)


HMS : electronic structure of MnSi2-x

Zaitsev, CRC Handb. TE 1995


HMS : thermoelectric properties of MnSi2-x

No successes in doping attempts for improving the ZT

Maximum ZT = 0.7 at 1000 K

Other studies found ZT not larger than 0.6

Goncalves, JMC 2010

Amorphous compounds


Limits of the amorphous compounds

Bad stability at HT

Weak abundance and high cost of the elements :

Ge, Ga, Te, …

Difficulties to reduce the resistivity

Segregation of the atoms for T < Tc

Goncalves, JMC 2010 Goncalves, JSSC 2012



=> Doped conjugated polymers

Why ? => Class of semiconducting or even metallic

TE Polymers => must be sufficiently conducting

Insulating polymers=> C sp3 Conjugated polymers => C sp2

3 electrons in s bondings

=> Stabilization of the chain structure

One electron 2p/C => liaisons p

délocalized in the plan => 1D chains

First and best known case of conducting

polymer : polyacétylène

Peierls distortion of 1D chains

=> Opening of 1-4 eV bandgap

Trans-polyacétylène

Polymers Bubnova, EES 2012

Zhang, AM 2014


Differents types of conjugated polymers

PEDOT


Formation of polymer films and polarons

Formation of chains by solubilization of the chains

Rigidity of chaines and their weak inter-chain p-p interactions

=> agregats and crystalline domains formation in the films

Conjugated polymer films are not 1D semiconductors but 2D ou 3D disordered semiconductors

Band of width of W due to inter-chain p-p interactions

When t = ħ/W < characteristic time of vibration mode

=> Strong charge carrier cupling with vibrations : polaron

This is the case when W > 0,2 eV

In this case => polaron hopping transport

Importance of good crystallinity of the films


Doping ways

2 main ways:

- Electrochemical. Additional charge carriers are given by the metal electrode

- Redox reactions. Oxidizing agents coming from gaz or oxidizing solution (ex. iodine)

3 distinct doping types:

- Charged solitons

- Polarons

- Bipolarons

Oxidization of conjugated polymers => « conductor polymers » (p type)

Reduction of conjugated polymers => n type but unstable polymers


Doped PEDOT

Doping with Tosylate (Tos) Bubnova, EES 2012

Bubnova, NM 2011


Zhang, AM 2014 Doping with PSS


Lee, JMCA 2014

Doping with Hydrazine

Documents

Cours École TE juin 2014 Lattice dynamics of nanocages