phase separation in...
TRANSCRIPT
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)