First principles characterization of thermoelectric zinc antimony

UM

R 5

253

-Ins

titut

de

Chi

mie

Mol

écul

aire

et d

es M

atér

iaux

de

Mon

tpel

lier

1

K.Niedziółka, P. Jund, R. Viennois and

J.C. Tédenac

Institut Charles Gerhardt MontpellierUniversité

Montpellier II, France

The demand will double by 2050

Enormous pressure  on the energy resources

2

We

need

to save

energy!!!

Motivations

GDR Thermoélectricté, 05 Décembre 2012, Lyon

36%Used

Energy

64%Wasted Energy

Thermal Power

Plant

Nuclear

Power

Plant

Waste

Incinerator

AutomobileFactory

Thermoelectricity: recovering work from waste heat

3GDR Thermoélectricté, 05 Décembre 2012, Lyon

Figure of Merit:

where:S

–

is

the

Seebeck coeffiecient

σ

–

is

the

electrical

conductivityκ –

is

the

thermal conductivity

Our goal is

to increase

ZT⇓

Best materials:semi‐metals

doped

semiconductorsS ↑ σ ↑ κ ↓

Performance of a thermoelectric material

4GDR Thermoélectricté, 05 Décembre 2012, Lyon

availability low cost

thallium, chalcogen or/and pnictogen

based alloys

tellurium based alloys

germanium or rare-earth based

alloys

Compounds based on

ZnSb

Optimal attributes for thermoelectric materials

stability

Zn4 Sb3

Target temperature range:300 – 600°C

GDR Thermoélectricté, 05 Décembre 2012, Lyon5

VASPVASP

Bader Charge 

Analysis

Bader Charge 

Analysis

BoltzTraPBoltzTraP

Applications being used at each step

The calculations were performed within the projector augmented-wave (PAW) method using the PBE generalized gradient approximation (GGA) and HSE hybrid functional recently implemented in the VASP code

6

P. Jund

et al, Phys. Rev. B. 85, 22 4105 (2012)GDR Thermoélectricté, 05 Décembre 2012, Lyon

ZnSb

single cell (16 atoms)ZnSb

2x2x2 super cell  (128 atoms)

‐0.04eV/atom

‐

Mikhaylushkin

et al.Chem. Eur. J. 2005, 11, 4912-4920

(exp: -0.06 → -0.09 eV/atom)

‐0.04eV/atom

‐

Mikhaylushkin

et al.Chem. Eur. J. 2005, 11, 4912-4920

(exp: -0.06 → -0.09 eV/atom)7

Crystal system: orthorhombicSpace group: Pbca

(61)

(a= 6.28Å, b= 7.82Å, c= 8.23Åa= 6.22Å, b= 7.74Å, c= 8.12Å

: exp)

GDR Thermoélectricté, 05 Décembre 2012, Lyon

Band Structure calculations for ZnSb

EE

gg

=0.03eV=0.03eVEE

gg

expexp0.5 0.5 ‐‐

0.6eV0.6eV11

1M. Zavetova, Phys. Stat. Sol. 

5, K19 (1964)

EE

gg

=0.56eV=0.56eV

8

hybrid functionnal

GDR Thermoélectricté, 05 Décembre 2012, Lyon

‐

‐

Deformation charge densityBader Charge Analysis

Charge transfer:Charge transfer:0.2620.262

Charge transfer:0.2651

1Benson et al.

Phys. Rev. B

84, 125211 (2011)

9

PBE

HSE

Charge transfer:Charge transfer:0.3650.365

GDR Thermoélectricté, 05 Décembre 2012, Lyon

Seebeck

coefficient – super cell calculationsBoltzTraPBoltzTraP

(Madsen, Singh, Comp. Phys. Comm. 175, (2006), 67-71)

The code is based on the Fourier expansion of the band energies.

GGA : problem

with

theunderestimation

of

the

gap

HSE : not

realistic

(670 daysof

CPU time

for the

single cell)

⇒ shift of

the

GGA bandsaccording

to the

HSE calculation

for the

single cellEc

-Ef

= HSE resultEf

-Eb

= HSE result

Pure ZnSb10GDR Thermoélectricté, 05 Décembre 2012, Lyon

Seebeck

coefficient 300K –

super cell calculationsPure Pure ZnSbZnSb

S=-950 µV/Kn-type

Exp.:

+196 µV/KShaver, Blair, Phys. Rev. 1966, 141, 649

11

Nb:

non shiftedbands

⇒

S = -114 μV/K

GDR Thermoélectricté, 05 Décembre 2012, Lyon

Formation energy of intrinsic defects – super cell calculations

HD the enthalpy of formation of the defect DxD its atomic concentration.

Defect

type VZn VSb

SbZn

ZnSb

ISb

IZn

Formation energy

(eV/def.) 0.8 1.8 1.4 1.5 2.3 1.4

The Zn vacancy is the most probable defect

-

coherent with theZnSb

binary phase diagram

-

coherent with recent VASPcalculations (Bjerg

et al,

Chem. Mat.(2012))but no interstitial defects !

12GDR Thermoélectricté, 05 Décembre 2012, Lyon

Formation energy of intrinsic defects – super cell calculations

HD the enthalpy of formation of the defect DxD its atomic concentration.

Defect

type VZn VSb

SbZn

ZnSb

ISb

IZn

Formation energy

(eV/def.) 0.8 1.8 1.4 1.5 2.3 1.4

The Zn vacancy is the mostprobable defect

-

coherent

with

theZnSb

binary

phase diagram

-

coherent

with

recent

VASPcalculations

(Bjerg

et al,

Chem. Mat.(2012))but no

interstitial

defects

!

13

Frenkel Defect0.5

GDR Thermoélectricté, 05 Décembre 2012, Lyon

Zn vacancy in the ZnSb

super cell

14GDR Thermoélectricté, 05 Décembre 2012, Lyon

Seebeck

coefficient 300K–

super cell calculationsZnSbZnSb

+ Zn vacancy+ Zn vacancy

S= +81µV/Kp-type

15

⇒ the

p type conductivity

of

ZnSb

found

experimentally

is

due to the

Zn

vacancies

GDR Thermoélectricté, 05 Décembre 2012, Lyon

Conclusion

16

With appropriate exchange-correlation functionals it is possible to obtain correct band structures but the CPU time cost is high

The deformation charge analysis shows the covalent character of the bonds

The formation energy of Zn vacancies is small in agreement with experiments

Our calculations show that Frenkel type defects are probably present in ZnSb

The intrinsic p-type conductivity of ZnSb is due to the Zn vacancies (« pure » ZnSbis n-type) ⇒ to obtain n-type ZnSb, undesirable compensation effects should be takeninto account

ZnSb has « good » physical properties (not shown) ⇒ it is a very promising material for thermoelectric applications

GDR Thermoélectricté, 05 Décembre 2012, Lyon

17

Thank you for your attentionThank you for your attentionGDR Thermoélectricté, 05 Décembre 2012, Lyon