Phase separation in (Hf,Ti,Zr)NiSn

by DFT/Calphad coupling

A. Berche, J.C. Tédenac and P. Jund

2

ICGM, CNRS, UMR 5253

Université de Montpellier

Half-Heusler phases (Hf,Ti,Zr)NiSn

� Among the studied materials for TE applications: the half-Heusler phase XNiSn (X=Hf, Ti, Zr)

� Experimentally, ZT ≅ 1 measured by Populoh et al.1

� Phase separation in the pseudo-quinary system2

� Continuous solid solution (Hf,Zr)NiSn

� Phase separation in (Hf,Ti)NiSn and (Ti,Zr)NiSn

� Several possible materials containing 1 or 2 phases

Ni

Sn

Ti� Several possible materials containing 1 or 2 phases

1 S. Populoh et al. Scripta Mater. 66 (2012) 1073-1076

2 K. Kurosaki et al. J. Alloys Compds. 397 (2005) 296-2993

Need the description of the pseudo-

quinary and of the constitutive binary

and ternary:

• Hf-Ni-Sn

• Ni-Sn-Ti

• Ni-Sn-Zr

Thèse Shmitt, Johannes Gutenberg-Universität Mainz, Frankfurt (2014)

Ti

Calphad method

Experimental data

Math. model of the

G of the phases

Crystallography

Assessments of the

Ab-initio calc.

Enthalpy of formation phases

Energies of defects

Mixing enthalpy…

Phase diagram

Enthalpy of formation

Mixing enthalpies

Partial pressure

IN

4

Assessments of the

parameters

Database

Chemical

compatibility

Solidification Theory of

the diffusion

Alloy

synthesis

Partial pressure

Electromotive forces…

OUT

Binary system Hf-Ni - ΔfH of the phases

Liquid

2500

� Hf-Ni binary system

� 9 intermediate phases, calculation of the △fH at 0K for each phase

� Correct agreement between DFT and calorimetric measurements

• Allows to calculate never measured thermodynamic data

-10

0 Calphad [13]DFT [18]DFT - This workDirect Calo. [15]Direct Calo. [16]

ato

m)

5

Hf Ni

C1

5b

Hcp_A3

Bcc

_A2

Fcc

_A

1

Ni 7

Hf 2

A_

HfN

i 3Ni21Hf8

Hf3Ni7

Ni 1

0H

f 7

B3

3

C1

6

B_

HfN

i

HfNi3

Ni 1

1H

f 9

0

500

1000

1500

2000

Tem

per

atu

re(K

)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

xNi

G(B33,Hf:Ni) = -52118 + 1.35*T + 0.5*GHSERHF + 0.5*GHSERNI

-60

-50

-40

-30

-20

-10

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Direct Calo. [16]KEMS - [17]

NiHf xNi

En

thal

py

of

form

atio

n (

kJ/m

ol o

f at

om

Gibbs energy of B33-HfNi:

Ternary system: example of Ni-Sn-Ti

� Global assessment of the ternary system Ni-Sn-Ti

� Isotherm and isopleth sections

� Based on available data

Sn

0.9

1.0

(K) 1800

1900

2000

2100isopleth section 25 at% Sn

ATD – Fartushna et al.6

6

T = 1223K

Ti B2-NiTi D024-Ni3TiNiTi2

Ti6Sn5

D88-Ti5Sn3

Ti2Sn

Bcc_A2 Fcc_A1

D03-Ni3Sn

Ni3Sn2_HT

Ni

Liquid

liquid

D019-Ti3Sn

0

0.1

0.2

0.5

0.6

0.7

0.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

NiTiSn

Ni2Ti2Sn

Ni2TiSnT

emp

erat

ure

(K)

x(Ni)Ti0.75Sn0.25 Ni0.75Sn0.25

1100

1200

1300

1400

1500

1600

1700

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

6 V. Fartushna et al. To be published

Projection of the liquidus

� Projection of the regions of primary-solidification of each phase

� HfNiSn and ZrNiSn can be obtained by direct solidification;

NiTiSn has to be annealed

7Ti: A. Berche et al. Calphad 54 (2016) 67-75

Hf: A. Berche et al. Comput. Mater. Sci. 125 (2016) 271-277

Zr: A. Berche et al. J. Phys. Chem. Solids 103 (2017) 40-48

Synthesis of NiTiSn by melting

XRD difractogram of an as-cast sample1600

� Simulation of the solidification of an alloy Ni1/3Ti1/3Sn1/3 using the Scheil-Gulliver model

(Thermocalc software)

� Scheil-Gulliver model: ∞ diffusion in the liquids, no diffusion in the solids

� Solidification path: Ni2TiSn, Ti6Sn5, NiTiSn and finally Sn in agreement with experiments

8

200

400

600

800

1000

1200

1400

1600

TE

MP

ER

AT

UR

E_

CE

LSIU

S

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

TABLE TSCH

Liq + Ni2SnTi

Liq + Ni2SnTi + Ti6Sn5

Liq + Ni2SnTi + NiTiSn

Liq + NiTiSn + Sn

NiTiSn

Ni2TiSn

Sn

Ti6Sn5

Pseudo-quaternary systems: mixing enthalpy

0 1000 1800

� DFT calculation of△mixH in the quasi-quaternary sections

� Supercells built with the Special Quasirandom Structures (SQS) method

� Calculations reproduce experimental observations:

• Ideal mixing between ZrNiSn and HfNiSn → continuous solid solution

• TiNiSn: phase separation with ZrNiSn of HfNiSn

9

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

Mix

ing

enth

alpy

in X

NiS

n(J

/mo

l)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Fraction of HfNiSn (%)

DFT 12 atomsSQS 24 atomsSQS 81 atoms

ZrNiSn HfNiSn

Calphad

0

100

200

300

400

500

600

700

800

900

1000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

DFT 12 atomsSQS 24 atomsSQS 81 atoms

Mix

ing

enth

alpy

in X

NiS

n(J

/mo

l)

Fraction of TiNiSn (%)HfNiSn TiNiSn

Calphad

0

200

400

600

800

1000

1200

1400

1600

1800

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

DFT 12 atomsSQS 24 atomsSQS 81 atoms

Mix

ing

enth

alpy

in X

NiS

n(J

/mo

l)

Fraction of TiNiSn (%)ZrNiSn TiNiSn

Calphad

A. Berche et al. Scripta Mater. 139 (2017) 122-125

Pseudo-quinary (Hf,Ti,Zr)NiSn

� Calphad assessment of the system

� Globally good agreement between experiments and the Calphad assessment

0.7

0.8

0.9

1.0

T = 1000K

TiNiSn

1 phase

10

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Fraction of HfNiSn (%)ZrNiSn HfNiSn

1 phase

2 phases

THERMODYNAMIC EQUILIBRIUM

5 S. Populoh et al. Scripta Mater. 66 (2012) 1073–1076.

28 J. Krez et al. Phys. Chem. Chem. Phys. 17 (2015) 29854–29858.

29 M. Schwall, PhD Thesis (2012) Mainz.

� DFT / Calphad are complementary to give a consistent view of the phase relations

� Even though the (Hf,Ti,Zr)NiSn half-Heusler phase can achieve high ZTs, great caution has to

be taken during the synthesis and during the characterization of the samples prior to

thermoelectric measurements, especially for Ti-rich alloys

11

� More details about this study:

� A. Berche, J C. Tédenac, I. Fartushna and P. Jund, Calphad 54 (2016) 67-75

� A. Berche , J C. Tédenac and P. Jund, Comput. Mater. Sci. 125 (2016) 271-277

� A. Berche , J C. Tédenac and P. Jund, J. Phys. Chem. Solids 103 (2017) 40-48

� A. Berche, J C. Tédenac and P. Jund , Scripta Mater. 139 (2017) 122-125

� Perspectives : calculation of thermoelectric properties (Seebeck, electric conductivity) using

the Boltzman transport equations (BoltzTraP software)

Thank you for

your attention

12