O38-PREDICTION OF THERMODYNAMIC STABILITY OF …tofa2010/Apresentacoes...PREDICTION OF THERMODYNAMIC...
Transcript of O38-PREDICTION OF THERMODYNAMIC STABILITY OF …tofa2010/Apresentacoes...PREDICTION OF THERMODYNAMIC...
PREDICTION OF THERMODYNAMIC STABILITY OF METAL/OXIDE INTERFACE
14 Sept 2010
Hong Mei Jin Ping Wu
Institute of High
Performance
Computing
Singapore
Computational Materials Science Department
Michael SullivanDeputy Program Manager
Gan Chee KwanMTS Team Leader
Marco KlähnMM Team Leader
Daniel CheongCC Team Leader
Yu ZhigenEN Team Leader
Oct2008
Materials
Method
sProperti
esProducts
Approaches for materials research
Bulk
Interface
Hybrid
Nanostructures
Electronic
Classical
Continuum
Experiment
Chemical
Physical
Structural
Electronics
Energy
Bio-medical
interdisciplinary and multiscale nature ...
Leading research …..
Semiconductor
Physics
Solution
Chemistry
Materials
Informatics
Theory
ElectronicsEnergy Bio-medical
Devices
Zinc Alloys &
Zinc Oxides
Ti/Zr Alloys &
Ti/Zr Oxides
Delafossite
& Perovskite
Applications
Materials
ETPLCominco
IME, DSI, NTUNUS
Ontario-Singapore
Zinc alloy and Zinc oxideMetal-oxide
interface
Minor additives for Zn galvanizing
Materials ……
1998 20102005
ZnO based LED
P-type ZnO
Patent and licensing
IME, DSI, NTU
2001 2008
IMREIMENUS
Rolls RoyceNTUNYP
ICES NTU
Simtech
Ti/Zr alloy and Ti/Zr oxideMetal-oxide
interface
Bio-Ti alloys design
Materials ……
2004 20102006
SOFC
Bio-Zr alloys
Nuclear energy
Water splitting
High K ZrO2
NYPU of Montreal
2005 2008
• Introduction
• Density Functional Theory(DFT) calculation of Ni/ZrO2, Cu/ZrO2
• Empirical model for thermodynamic stability of Ni/ZrO2, Cu/ZrO2• Empirical model for thermodynamic stability of Ni/ZrO2, Cu/ZrO2
• Model prediction for Au/TiO2
• DFT verification of empirical prediction for Au/TiO2
• Summary
� Important in engineering applications:� microelectronics packaging, optoelectronics
� structure composites and coatings of nuclear reactors� heterogeneous catalysis, fuel cells
� A challenge to develop a fundamental understanding of theSchottky Barrier formation mechanism
� Well reported in TOFA2010: O1, O47, O53, O72, P31, P38
Crystal structure of Ni (Cu, Au) and c-ZrO2
Ni (Cu, Au) ZrO2
Fm-3mCubic
Fm-3mCubic
Calculation model (Calculation model (supercell approach))
dark blue color: Ni(Cu), light blue color is
Zr, red color is O atom, respectively
Calculation detailsCalculation details
DFT, planewave, pseudopotential method (vasp)Ultrasoft pseudopotential & GGACut off energy: 500 eVK points: 8x8x1Since metal is less rigid, the lattice mismatch induced Since metal is less rigid, the lattice mismatch induced small in-plane strain was assigned to the metalElectronic energy was minimized using a mixture of the blocked Davidson and RMM-DIIS algorithm. Conjugate gradient method for ionic relaxation.
Work of adhesion energyWork of adhesion energy
22
22
,
, 2/)(
ZrOmZrOm
ZrOmtottot
ZrOtotmad AEEEE
γσσ −+=
−+=
where σ is the surface energy, A is interface area, γ is interfacial energy, it can be obtained from Gibbs free energy of the system:
ATSPVNNNE OOZrZrmmtot
ZrOmZrOm 2/)(22 ,, −+−−−= µµµγ
where µ is the chemical potential, N is the number of the atoms in the interface where µ is the chemical potential, N is the number of the atoms in the interface system, V is volume and S is entropy. For typical working temperature and pressure, term PV and TS can be neglected. Further, µZrO2= µZr+2µo.
So the above equation becomes:
ANNENENE oZrobulkZrOZr
bulkmmZrOm
totZrOm 2/)2(( 2,, 22
µγ −−−−=
for stoichiometric interface, the coefficient of µo will be zero, however, for non-stoichiometric interface, it will be a function of oxygen potential.
Calculated interfacial energy, surface energy and work of adhesion for morerelatively stable stoichiometric interface of Ni(110)/ZrO2(110) andCu(110)/ZrO2(110)surface energy (eV) interfacial energy (eV) Work of adhesion (J/m2)
Ni(110) 0.159 Ni/ZrO2 0.185 1.057
Cu(110) 0.085 Cu/ZrO2 0.139 0.6087
ZrO2(110) 0.092
Ref: D. Sotiropoulou et al., Ref: J. Mater. Sci,28(1993)356, Ceramics International, 15(1989)201.
Experiment results [ref]
Summary:
1. In the intermediate range of oxygen partial pressures, (110)Ni/Cu-(110)ZrO2 is more stable
2. At extreme high or low oxygen partial pressure, non-stoichiometricinterface could be more stable
3. The calculated adhesion energies are in agreement with experimentresults
Challenges:to replace the computing intensive DFT calculations bysimple empirical equations!
Based on MacDonald and Eberhart [1], D.Chatain et al [2] and Miedema’s model[3], we define the interfacial energy and work of adhesion as following:
)1()( 211
,><><
>< ∆+
∆−=
M
MinM
o
MinoMOm A
H
A
Hx
γ
where∆Ho in <M1> and∆H M1 in M2 are the partial enthalpy of mixing. For∆Ho in <M1>,the following equation [4] was used:
[1] Trans.Metall.Soc. AIME, 233:512-517, 1965.[2] Revue Phys. Appl. 23, 1055-1064, 1988.[3] Cohesion in metals.[4] Phys. Rev. B, V62(2000):4707[5] J. Alloys. Comp., 236(1996):236-242[6] J. Alloys. Comp., 420(2006):175[7] Appl. Phys. Lett., 69(1996):1701
For ∆H M1 in M2 , we used the literature data from [3,5-7]. A is molar interface area which is defined at the next page.
)(1012.1 15 OJmolHH fMOMino x
−><
∞>< ×+∆≅∆
For molar interface area, it can be calculated as:
234
1:}111{ NaAface =
for fcc lattice: for tetragonal lattice TiO2:
ateterTiOaNcaAface
ateterOTiaNcaAface
−+×+=
−×+=
)min2(211
:}111{
)min/(22
1:}111{
22
22
2
2
2
1:}100{
22
1:}110{
4
NaAface
NaAface
=
=
cNaAface
ateterOcNaAface
ateterTiOcNaAface
ateterTiOaNcaAface
×=
−×=
−+×=
−+×+=
:}100{
)min(22
1:}110{
)min(24
1:}110{
)min2(22
1
3
1:}111{ 22
where N is Avogradro’s number, a ,c are lattice parameters
Apply equation (1) on Ni/ZrO2(110), Cu/ZrO2(110)
Ni/ZrO2(110)
E (J/m2) γNi,ZrO2 (J/m2) Work of adhesion Ead(J/m2)Ni-O Ni-Zr total
Ni(111) 1.205 1.451 2.65 0.54
Ni(110) 1.205 0.888 2.09 1.92
Ni(100) 1.207 1.310 2.46 1.17
Cu/ZrO2(110)
E (J/m2) γCu,Zro2(J/m2) Work of adhesionEad(J/m2)Cu-O Cu-Zr total
Cu(111) 1.107 0.6758 1.78 0.81
Cu(110) 1.107 0.4132 1.52 1.31
Cu(100) 1.107 1.691 1.69 1.04
γσσ −+=2ZrOmadE
* here work of adhesion was calculated by (where σ is surface energy of metal and oxide, respectively):
Predicted interfacial energy and work of adhesion of Au/TiO2 between different crystal orientation
Au/TiO2(110)O-terminate
E (J/m2) γAu,TiO2 (J/m2) Work of adhesion (J/m2)
Au-O Au-Ti total
Au(111) 0.333 0.5419 0.875 1.81
Au(110) 0.333 0.3318 0.664 2.34
Au(100) 0.333 0.4691 0.802 2.08
Au/TiO2(110)O+Ti-terminate
E (J/m2) γ Au/TiO2(J/m2) Work of adhesion (J/m2)
Au-O Au-Ti total
Au(111) 0.669 0.5419 1.209 1.48
Au(110) 0.669 0.3318 0.999 2.01
Au(100) 0.669 0.4691 1.136 1.75
Au/TiO2(111)O-terminate
E (J/m2) γAu/TiO2 (J/m2) Work of adhesion (J/m2)
Au-O Au-Ti total
Au(111) 0.112 0.5419 0.654 1.00
Au(110) 0.112 0.3318 0.443 1.52
Au(100) 0.112 0.4691 0.581 1.03
Au/TiO2(111) E (J/m2) γAu/TiO2 (J/m2) Work of Au/TiO2(111)O+Ti-terminate
E (J/m2) γAu/TiO2 (J/m2) Work of adhesion (J/m2)
Au-O Au-Ti total
Au(111) 0.336 0.5419 0.878 0.78
Au(110) 0.336 0.3318 0.668 1.29
Au(100) 0.336 0.4691 0.805 1.04
Au/TiO2(001)O-terminate
E (J/m2) γ Au/TiO2(J/m2) Work of adhesion (J/m2)
Au-O Au-Ti total
Au(111) 0.455 0.5419 0.9972 0.58
Au(110) 0.455 0.3318 0.7871 1.10
Au(100) 0.455 0.4691 0.8592 0.92
The order of work of adhesion:
110-Au-110-TiO2 (O-ter)
100-Au-110-TiO2(O-ter)
110-Au-110-TiO2 (O+Ti-ter)
111-Au-110-TiO2(O-ter)
100-Au-(O+Ti)-110-TiO2
Different termination of Rutile-TiO2(110) surface
(a) Stoichiometric slab
(b) non-Stoichiometric slab
O deficient Ti deficient
Interface structure
110-Au/110-TiO2 110-Au/110-TiO2 100-Au/110-TiO2
Calculated surface, interfacial energy and work of adhesion(J/m2)
Au on (O- terminate 110-TiO2 surface
σσσσm σσσσTiO2 γγγγAu/TiO2 Ead
Au(100) 0.572 2.319 1.64 1.24
Au(110) 0.690 2.319 1.62 1.27
Au(111) 0.383 2.319 1.67 1.03
Au on (O+Ti)- terminate 110-TiO2 surface
σσσσm σσσσTiO2 γγγγAu/TiO2 Ead
Au(100) 0.5719 2.319 2.717 0.17
Au(110) 0.690 2.319 2.67 0.33
ATSPVNNNE OOTiTiAuAutot
TiOAuTiOAu 2/)( 2,, 2−+−−−= µµµγ
22 ,
2,2 2/)(
TiOAuTiOAu
TiOAutottot
TiOtotmad AEEEE
γσσ −+=−+=
1. DFT calculations were carried out to investigate the interface stability andwork of adhesion between Ni(Cu)/ZrO2. The calculated work of adhesionare comparable with experiment.
2. An empirical equation was proposed to estimate the interfacial energybetween metal and oxide. It was applied on Ni(Cu)/ZrO2 and reasonableagreement with experiment were obtained by comparing to the work ofadhesion.adhesion.
3. The empirical equation was extended to Au/TiO2. The interfacial energyand the work of adhesion were estimated for different surface orientationbetween Au and TiO2.
4. DFT calculation were further performed on Au/TiO2 to verify theempirical estimation results. Good agreement were obtained in terms ofrelative interface stability. The predicted and calculated resultsare also inagreement with experimental observations.
Thank you
谢谢!