« thermoelectricity » summer school...

Thermoelectric materials synthesis: from the phase diagram to the materials

« Thermoelectricity » Summer School 2014

David Bérardan Institut de Chimie Moléculaire et des Matériaux d’Orsay Université Paris-Sud

« thermoelectricity » - summer school 2014 « from the phase diagram to the materials »

outline

Prologue : binary phase diagrams

I. single-crystalline and polycrystalline materials

II. nanocrystalline materials : top-down approaches

Epilogue : and… after the synthesis?

Binary phase diagrams

Assuming a complete solubility between A and B

Stable liquid phase

Stable solid phase

The liquid and solid compositions can be read on the liquidus and solidus curve

Their respective moral ratio are given by the lever rule


Mixture of two components A and B → Gibbs free energy of mixing DGm

DGm = DHm - TDSm

enthalpy of mixing entropy of mixing

Linked to the difference between EAB

and the average between EAA and EBB

(bonding energies)

DHm = u XA.XB

u : positive or négative

→ DHm positive or négative

always positive

DSm = -R[XA ln(XA) + XB ln(XB)]

AB bonds favored, miscibility AA and BB bonds favored,

Partial or total immiscibility



what happens when Hm is positive…

at T ↑ DSm is predominant

at T ↓ DHm is predominant

immiscibility dome at « low » temperature



example of binary phase diagram

eutectic

congruent melting incongruent melting

(peritectic)

phase rule:

F = C – P + 2

F = degrees of freedom

C = nb of components

P = nb of phases

(for fixed pressure: C – P +1)

ex : eutectic → F = 0

L → F = 2



Congruent melting compound

Example : synthesis of single-crystalline Bi2Te3

possible direct synthesis from a melted bath → several possible methods

difficulty: fine control of the carriers’ concentration


Liquidus maximum around Te 60%

Slight difference in the initial stoichiometry → strong influence on the carriers concentration

Strong influence of the sintering temperature on the concentration+ p/n switching ~ 583.5 °C

Satterthwaite et al., Phys Rev 108, 1164 (1957)



• growth from a seed

czochralski

• slow epitaxial solidification



Zone melting

• start from a polycrystalline ingot

• slow move of the melted zone

image furnace



Using both methods, impurities (dopants) segregation during the synthesis

[dopant] ↑ in the liquid phase

[dopant] ↓ in the solid phase

in both methods, the dopant concentration depends on the position in the ingot

1

0 1

effk

effs gCkC

[C0] : starting concentration

g : fraction of liquid



Peritectic compound

Example : synthesis of single crystalline CoSb3

Peritectic decomposition temperature at 873°C

Direct growth from a stoichiometric

« CoSb3 » liquid not possible

L CoSb3 reaction: possible between

91% < xSb < 97%

Possible growth usingBridgman method


• melting of the precursors in sealed silica tubes

• slow moving of the tube in a thermal gradient

• CoSb3 solidification as mm cristals,

[Sb] ↑ in the liquid phase

• at (T=621°C, xSb=97%), eutectic temperature

Simultaneous solidification of Sb major phase and

CoSb3 minor phase

part of the ingot: CoSb3 crystals

part of the ingot: Sb rich and CoSb3 poor mixture

Peritectic compound


Example : synthesis of polycrystalline CoSb3

Possible synthesis from a stoichiometric

« CoSb3 » mixture

• melting of the precursors in sealed silica tube

• quenching

• long sintering at T < Tpéritectique

Polycrystalline CoSb3, grains > 10 µm

Peritectic compound


Materials homogenization

Solid phase diffusion << liquid

Grains heart Average

composition grains surface

Composition

gradient

depends on • speed of cooling (time required to reach the equilibrium)

• diffusion coefficient, and temperature → post-annealing

In real life, possibly out-of-equilibrium


Refractory compounds

Example: Yb11MnSb14

• ternary phase diagram

Yb-Mn-Sb not well established

but

• in the Yb-Sb binary, high Tm

compounds

ex: Yb4Sb3, Tm > 1850 °C

>> Teb (Sb)

not really possible to synthesize

from a melt


Solution: use of a flux

Synthesis using Sn flux

• Sn-Yb binary:

Tm at xSn

Possible synthesis from a Yb-

Mn-Sb melt


Example: Yb11MnSb14


Initial composition : Yb14Mn6Sb11Sn86

• keep at 500°C → Sn melting

• total melting of the precursors

during the heating up to 1100°C

• precursors mixed in an alumina crucible

sealed in a silica tube under Ar

• mm-size cristals during slow cooling

• flux removed by decantation or

centrifugation (hot temperature)



Choice of the best flux depends on the targeted material:

• must enable a total melting of the precursors at a « reasonnable » temperature

• should not react with the precursors in the synthesis conditions

• solubility of the flux in the targeted material as small as possible (or

if slighlty soluble, not electrically active)

no un-intentional doping !

• should be removed without major difficulty (decantation, dissolved)

generally not one single possible choice

• common flux: self-flux (an element of the targeted material),

low Tm metals (Sn, Sb, Pb),

salts (NaOH, NaCl/KCl)



Example of a possible synthesis method:

Also possible using of hot centrifucation

NaCl/KCl, NaOH: dissolved in water



the particular case of oxides

Similar synthesis process, but possible air synthesis

Most often, grinding/mixing + sintering

decarbonation, ex: CaCO3 → CaO + CO2 (>900°C)

deshydration, ex: 2 La(OH)3 → La2O3 + 3 H2O (>900°C)

Calcination steps often required:

strong influence of the synthesis atmosphere on the properties


oxides, influence of PO2

oxides → [n] strongly influenced by the oxygen stoichiometry

OeVO O

X

O 22

1'2

Equilibrium reaction fonction of PO2

22/1]].[.[

2nVPK OO

with K that depends on the formation energy of oxygen vacancies

leads to 6/1

2][

OPn (assuming a single mechanism and K = constant)

and ].[2][

OVn


PO2 influence decreases if the formation energy is large or if the material is doped

example:

In2-xSnxO3

Ohya, J. am. ceram. soc. 91, 240 (2008)

faint influence when [Sn] > 0.1%



But cannot be neglected in all materials

0.000 0.005 0.010 0.015 0.02010

19

1020

1021

1400°C 5h, air

1400°C 5h, N2

[n]

(cm

-3)

Al fraction (x)

example:

Zn1-xAlxO

[n] 3 times larger for PO2 = 10-5 than for PO2 ~ 1

(formation of neutral clusters at large PO2)

PO2 influence decreases if the formation energy is large or if the material is doped



2

3

4

5

6

7

89

0.1

2

3

4

5

6

7

89

1

O2 P

ressu

re (

ba

r)

0.0016 0.0015 0.0014 0.0013 0.0012 0.0011

1/T (K-1

)

900800700650Temperature (K)

YBa2Cu3O7-x

130 110

10

0

90

90

80

70

60

60 50

40

30

30

30

20

Low formation energy → very strong influence « isovalue » lines of S

(µV

/K

)

example:

YBa2Cu3Ox



→ PO2 = one supplementary degree of freedom for the materials optimization

example:

SrxBa1-xNb2O6-d PO2 : A = 10-16

B = 10-14

C = 10-12

D = 10-10

For a single cationic composition, transport properties can be optimized in a wide range

If PO2 during synthesis ≠ 0.2 atm, the materials will not be

« stable » under air at « high temperature »




Not the topic of this talk, but PO2 should be taken into account for the measurement

Synthesis under air, measurement under He

→ r underestimated Synthesis under N2, measurement under N2 or air

The synthesis and measurement atmosphere must be the same

example:

Zn1-xAlxO


but how to synthesize an oxide under PO2 = 10-16

« commercial » argon: PO2 ~ 3.10-6

« good » secondary vacuum: PO2 > 10-9 + cations volatilization

1st solution: use of an electrochemical generator

typically: ZrO2-d electrochemical cell at 750°C

Pt electrode

Under a controlled applied potential difference, the system « pumps » oxygen out of the

reaction chamber

controlled PO2 = f(V)



2nd solution: use of a gaz mixture

Use of a redox couple, H2/H2O or CO/CO2

MO + H2 → M + H2O

MO + CO → M + CO2

Reducing character increases as PH2/PH2O ↑

PCO/PCO2 ↑

The controlled PH2/PH2O or PCO/PCO2 ratio is « equivalent » to a given PO2



example : PO2 = 10-16 at 1300°C

equivalent to:

PH2/PH2O ~ 2.103

PCO/PCO2 ~ 1.103


« easily » obtained


in both cases:

« easy » to create a low PO2…

… but it should correspond to the PO2 surrounding the sample

• no O2 desorbing from the pipes (electropolished stainless steel)

• no O2 desorbing close to the sample (crucibles…)

• very good sealing of the system

• preliminary purges, and flowing gas mixture before the synthesis

→ not so easy experimentally



→ consequences for « high temperature oxides » synthesis

densification: more and more use of SPS

• Graphite molds

• Argon(1-10 ppm O2) or vacuum (few Pa)

PO2 ~ 10-11

« SPS » conditions

→ strongly reducing conditions

→ non-stœchiometric samples

equilibrium

under air


If PO2 during synthesis ≠ 0.2 atm, not « stable » under air at « high temperature »


Experimentally: very quick sintering → out of equilibrium conditions

heart ≠ surface

PO2 ~ 10-11 PO2 = ??

Use of the materials at high temp → post-annealing required

as synthesized 600°C 750°C 900°C

2.0x1019

4.0x1019

6.0x1019

8.0x1019

1.0x1020

1.2x1020

heart

surface[n

] (

cm

-3)

post-synthesis

example : Zn1-xAlxO

• SPS (graphite mold, Ar)

• post-annealing under air, 24h

the temperature and duration of the post-annealing depend on the material

~temperature of application depends on oxygen diffusion coefficient (and T)



outline






nanostructuration: nanocomposites

2 possible approaches

« top-down » « bottom-up »

« thermodynamic » approach using

the phase diagrams:

• nanocrystalline second phase

precipitation in a bulk matrix

• phase separation with materials

structuration at micro or nano-scale

(spinodal decomposition, eutectic or

eutectoïd reaction, …)

densification of a nanocristallin powder

• synthesis using a solid route (mechanical

alloying) or liquid route

« hierarchical » structuration

Lorette Sicard, thursday


nanostructuration: spinodal decomposition

Gibbs free energy with an immiscibility dome

boundaries of the immiscibility dome at T2

I II III

I and III : 02

2

dX

Gd

II : 02

2

dX

Gd

Very different behaviour

between (I-III) and (II)


III I

II

binode = boundary of the

immiscibility dome

spinode

In real life, Tc ↓

(elastic stress)

• in domain II : 02

2

dX

Gd

→ any composition fluctuation: G decreases

instable situation

• in domains I and III : 02

2

dX

Gd

→ any composition fluctuation: G increases

metastable situation



Assuming an alloy with composition X’0:

• at T1: solid solution

• at T2: immiscibility, but 02

2

dX

Gd

→ large composition fluctuations are

required to have G decrease

« classical » germination and growth mechanism (similar to precipitation in a liquid)

Thermodynamical barrier to overcome



• at T2: immiscibility, but

→ small composition fluctuations are

enough to have G decrease

02

2

dX

Gd

instable alloy, and immediate decomposition, with small local composition changes

Spinodal decomposition

no thermodynamical barrier


Assuming an alloy with composition X0:

• at T1: solid solution


Grains at final

composition

directly

modulation of

composition

at low temperature (slow diffusion) and « short » time, modulation at nano-scale


same final state (equilibrium)


How to proceed experimentally?

(Tc, Xc)

• beginning: solid solution

• cooling down

→ first, crossing of the binode

slow cooling

transiently between

binode and spinode

→ nucleation

no spinodal decomposition

rapid cooling

no nucleation, « frozen »

solid solution

→ instable situation

Spinodal decomposition



example: PbTe-GeTe binay

PbTe-GeTe phase diagram

Yashina et al., Jalcom 413, 133 (2006)

binode

spinode

• melting of the elements

(sealed silica tube)

• homogeneization at ~ 620°C

Instable area • quenching (water or liq-N2)

• post-annealing at controlled T and t



Microstructure evolution:

Pb0.3Sn0.1Ge0.6Te - HRTEM

homogeneization followed by quenching in water

• one single phase

• « slight » composition fluctuations

after 16h at 500°C

Dado et al., J electron mat 39, 2165 (2010)



The obtained micro/nanostructure depends on the temperature and duration of the post-treatment

Pb0.36Ge0.64Te 200°C 300°C

400°C 500°C

S. Gorsse et al., Acta Materialia 59, 7425 (2011)



Large variety of possible microstructures

lamellar structure fishbone structure channel network

the micro/nano-structure depends on the grains boundaries

energy, and of the duration/temperature of the treatment

same temperature but ≠ duration



nanostructuration: in-situ précipitation

homogeneous solid → instability → precipitation → (nano)-composite

T2 < T < Tf T < T2

driving force : decrease of the

system Gibbs free energy

volume contribution:

surface contribution:

DGtot = DGS + DGV

elastic contribution (linked to elastic stress)

DGelas


DGS , DGelas

DGvol

opposite contributions with radius:

• surface free energy ↑

• elastic free energy ↑

• volume free energy ↓

→ critical radius r* for germination

r* ↓ when T ↓

→ supersaturated solid solution

radius



experimentally: almost always « heterogeneous » germination

energy gain through the formation

of a seed close to a defect

vacancies < dislocations < stalking faults <

boundaries (grains, phases) < free surfaces

possible reduction or the surface free

energy increase

Grain boundary (smaller critical size for a same given critical radius)

(decrease of the energy barrier)



The shape depends on the

« anisotropy » of gab (h,k,l

dependence)

heterogeneous germination favored



example: precipitation of Ag2Te in PbTe • melting of the elements at 1000°C

(sealed silica tubes)

• quenching

• homogeneization at 700°C

• quenching

• annealing at 500°C



• grinding + densification < 500°C

Pei et al., Adv. Func. Mat. 21, 241, 2011


depends on the phase diagram: no solubility!!


Formation of Ag2Te nano-precipitates

Pei et al., Adv. Func. Mat. 21, 241, 2011



example : nano-precipitates of Pb or Sb in PbTe

Obtained by melting at 1000°C followed by quenching, without post-annealing

→ most-probably not stable at the temperature of application

He et al., JACS 132, 8669 (2010)


(ZT>2 in « hierarchical » PbTe nanostructures


nanostructuration

top-down approaches

• can lead to various micro/nano-structures

• « in-situ » nanostructuration → no densification step required

• possible « multi-scale » micro/nano-structures

but

• require the (good) knowledge of the phase diagram

• carriers concentration not easilly controlled

alternatives : bottom-up approaches


outline






nanostructuration: aging

after the synthesis: the aging issue

nanocrystalline compounds, or nanocrystalline composites → out of equilibrium

• grains growth

• nanostructure growth

driving force: decrease of the interphase

tension / surface tension

Decrease of the surface/volume ratio

Question the stability of the nanostructure for a long term use at high temperature


nanocomposite: evolution of a nanostructure obtained by spinodal decomposition

PbxGe1-xTe

the modulated structure originating from the spinodal decomposition remains…

… but with a much larger length scale

the nanostructuration is lost… and the increase of ZT too!

S. Gorsse et al., Acta Materialia 59, 7425 (2011)



nanocomposite: evolution of a nanostructure obtained by the decomposition

of a quasi-eutectic composition (PbTe – Sb2Te3)

The lenght scale rapidly increases at 500°C…

… which corresponds to the temperature

of the application



Nanocristalline material, example: Zn1-xGaxO

densified at 200°C under 500 MPa → d = 27 nm

short annealing at different temperatures

strong crystal above 700°C…

… for applications at 800-1000°C !



possible solutions?

« nanocomposite »: pinning of the grain boundaries by the secondary phase

the grain growth energy is lowered by the presence of the secondary phase

energy barrier to overcome for the boundary migration

possible limitation of the grains growth by a few % of a nanocrystalline secondary phase


F. Iman et al., Composite Sci & Technol 70, 947 (2011)

example: pinning of the grains boundaries

in alumina by carbon nanotubes in skutterudite by Ce oxide

Al2O3

Al2O3

+

5% CNT

possible solutions?

CoSb3

CoSb3

+

CeO2


further reading:

• S-J. L. Kang, « Sintering : Densification, Grain growth and microstructure », Butterworth-Heinemann

• Kanatzidis, « The Metal Flux: A Preparative Tool for the Exploration of Intermetallic Compounds »,

Angewandte Chem Int Ed 44, 6996 (2005)

• C. Carter, « Kinetics of materials », Wiley Interscience

• D.A. Porter, « Phase transformations in metal and alloys », Chapman et Hall


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