hydrides for energy storage: modelling approaches and ... · hydrides for energy storage: modelling...
TRANSCRIPT
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Hydrides for Energy Storage:modelling approaches and
translation realization
Marcello Baricco
Department of Chemistry and NISUniversity of Turin, Torino, Italy
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The trip of production
Final destination(thermodynamics
)Means of
transportation (T,P,x variations)
Itinerary (mechanism)
Time of travel (kinetics)
Picture and movies(exp. techniques)
Planning (modelling)
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Modelling and length scale
macroscale
microstructure
atomistic
electronic
Ab-initio
CalphadMD
Phase field
FEM
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Phasediagrams
0.0 0.2 0.4 0.6 0.8 1.0400
600
800
1000
1200
1400 Liang et al. CALPHAD 22 (1998) 527-544
Te
mp
era
ture
/ K
Mole fraction Mg
Available information:
- number and type of phases (Gibbs phase rule)
- composition of phases (tie lines)
- relative amount of phases (lever rule)
Cu-Mg
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Experimental determination of phase diagrams
Estimation of data
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Phase diagrams
•A phase diagram is a 2D plot of the relative stability of various
phases.
•The stability of a phase is ruled by its free energy (G).
•The free energy of a phase is a function of temperature,
pressure and composition.
),,( ixPTGGϕ=
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Phase diagrams and free energy
A.H.Cottrell, Theoretical Structural Metallurgy, Edward Arnold, London, 1955)
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Real systems
•Several invariant points
•Multicomponent
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The CALPHAD approach
* Calculated
phase diagram
* Calculated
thermodynamic
functions
CALCULATION
PROGRAM
Parameters for
description of
free energy
of all phases
G(x,T)
OPTIMIZATION
PROGRAM
Experimental
data
CALPHAD APPROACH
Developer
Translator
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Thermodynamic models•Regular solutions
• Sublattice model
•Stoichiometric compounds
•Magnetic contributions
•Lattice stabilities
Ab initio
calculations
Parametric
description
of G
Assessment(least square method)
Experimental techniques•Calorimetry, DSC
• Electromotive forces
•XRD, SEM, PCT, etc.
Experimental data:
•Thermodynamic properties
•Phase diagrams
),,(),(),,(),,( 0
i
ex
i
id
ii xPTGxTGxPTGxPTG ++=ϕDatabase
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Thermodynamic databases
A thermodynamic database is a collection of functions
describing the Gibbs free energy of each individual phase of
a system as a function of temperature, pressure and
composition
Databases for unary, binary, ternary and even higher order systems are
available!
Databases are produced by critical assessment of experimental data and
optimization of model parameters (the CALPHAD method)
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Ab-initio methods
DFTAtomic
number
Valence
electrons
Crystal
geometry
Ground
state
energy
ZPE
DOS
Phonons
Plane waves
Pseudopotentials
Gaussian
Cp, ΔH, ΔS then ΔG
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The assessment procedure
selection of
data
weight
selection of
models
thermod.
parameters
TDB file
calc.
condit.
INPUT OUTPUTMIN. OF
ERRORS
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The calculation procedure
TDB file
T,P,X
values
thermod.
quatities
vs
T,P,X
comp.
equil.
INPUT OUTPUTCALC.
TECHN.
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Interesting outputs
• Phase diagrams
• Thermodynamic functions
• PCT curves
• Van't Hoff plots
• Enthalpy of abs/des
• Driving forces for phase transformations
…from TD to kinetics…
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Solidification of stainless steels
8 9 10 11 12 13 14 151430
1450
1460
1470
1480
Fe-Cr-Ni
Cr=18 wt%
1440γ
δ γ+δ
L+γ+δ
L+γ
L+δL
DC
B
A
Te
mp
era
ture
/ °C
Weight percent NiMode A: L → L + δ → δ
Mode B: L → L + δ→ L + δ + γ→ δ + γ
Mode C: L → L+ γ → L + γ + δ→ γ + δ
Mode D: L → L+ γ → γ
M.Baricco, M.Palumbo, D.Baldissin, E.Bosco, L.Battezzati, La Met. It. 11-12
(2004) 49-56
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Tliquidus
(°C)
Tsolidus
(°C)Tγγγγ’ solvus
(°C)
∆∆∆∆Hmelt
(J/g)
Cp liquid
(1410-1480°C)
(J/K g)
Calc. Equil. 1381 1330 1295 271 0.67
Experimental(average of
different labs)1381.5±5 1320±5 1310
231±13 on heating
227±20 on cooling0.69±0.03
Calculated and
measured solid
fraction
1320 1340 1400 14200.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1.0
0.9
0.8
10 °C/min
5 °C/min
2 °C/min
1 °C/min
0 °C/min
Calculated
Fra
ctio
n S
olid
1360 1380
Temperature / °C
Thermodynamic calculations on CMSX-4
Alloy Al Co Cr Mo Ti Ta W Re Hf C Mn Si Fe Ni
CMSX 4 5.61 9.6 6.4 0.61 1.02 6.5 6.4 2.9 0.10 0.0037 0.1 0.4 0.042 Bal
M.Palumbo et al. Mat. Sci. For. (2006)
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Hydrides for hydrogen storage
RT
H
R
S
P
P ∆−
∆=
0
ln
∆S ≈ 120 J molH2-1 K-1
Reversible in
ambient conditions
∆H ≈ 30-40 kJ molH2-1
Van’t Hoff equation
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H2 in/out
insulator
Fluid for the heat
exchange (H2O from
the FC)
tank
Heat
exchanger
P.Rizzi .M.Baricco.. et al. / J. Alloys Compd , 645 Suppl. 1 (2015) S338-S342
Integrated FC system
The main hall of the Chemistry Department of UniTo was enlightened for 4 h by using the energy produced
by the integrated system
Metal
hydrides
1 kW
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Example of a chemical reactor
kineticsreaction
balance mass
balance thermal
Equations:
( ) ( )p e He
TC k T Q
tρ
∂− ∇ ⋅ ∇ =
∂
KP F
t
ερρ
η
∂+ ∇ ⋅ − ∇ =
∂
( ) ( )exp aHH
EdxC f P f x
dt RT
= ⋅ − ⋅ ⋅
TD
KIN
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Experimental Validation
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Experimental and Calculated comparison
Absorption Desorption
D. Baldissin, J. Urgnani, M. Palumbo, M. Baricco, MH Conference 2008
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EXPERIMENTAL
T = 103 °C
ΔHmelt = 4155 J/mol
CALCULATED
T = 101 °C
ΔHmelt = 5701 J/mol
LiBH4-NaBH4-KBH4
Dematteis, E. M.; Pinatel, E. R.; Corno, M.; Jensen, T. R.; Baricco, M. Phase Diagrams in the LiBH4-NaBH4-KBH4 System. PCCP, (2017)
2017)2017)
2017)
LIQ
LIQLIQ
LIQΩΩΩΩTER
TERTER
TER
=0 kJ/mol =0 kJ/mol =0 kJ/mol =0 kJ/mol ::::LIQ
LIQLIQ
LIQΩΩΩΩTER
TERTER
TER
====----14 kJ/mol 14 kJ/mol 14 kJ/mol 14 kJ/mol ::::
66 mol% LiBH66 mol% LiBH66 mol% LiBH66 mol% LiBH4
44
4
---- 11 mol% NaBH11 mol% NaBH11 mol% NaBH11 mol% NaBH4
44
4
---- 23 23 23 23
mol% KBHmol% KBHmol% KBHmol% KBH4
44
4
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Softwares
THERMOCALC SUITE (Thermocalc Software, Sweden,
www.thermocalc.com)
FACTSAGE SUITE (GTT Technologies, Germany/CRCT, Canada,
ww.factsage.com):
PANDAT (CompuTherm, USA, www.computherm.com)
MTDATA and JMATPRO (ThermoTech Ltd., UK, www.mtdata-
software.com, www.thermotech.com)
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Some thermodynamic commercial databases
Steels and Fe-alloys
TCFE5: TCS Steels/Fe-alloys database, v5
Nickel and Ni-alloys
TCNI1: TCS Ni-based superalloys database, v1
TTNI7: TT Ni-based superalloys database, v7
Light metal alloys
TTAL6: TT Al-based alloys database, v6
TTTI3: TT Ti-based alloys database, v3
TTTIAL: TT TiAl-based alloys database, v1
TTMG4: TT Mg-based alloys database, v4
Solder alloys
NSLD2: NPL Solder solutions database, v2
Other alloys
SNOB1: SGTE Noble metal alloys database, v1
TTZR1: TT Zr-based alloys database, v1
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∆G
Eatt
STABLE
UNSTABLE
METASTABLE
dG=0
dG=0
Gib
bs fre
e e
ne
rgy
Arrangement of atoms
THERMODINAMICS AND KINETICS OF PHASE TRANSFORMATIONS
phase 1 phase 2
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Modelling of DIffusion ControlledTRAnsformations (DICTRA)
Thermodynamic databases
(THERMOCALC)
Kinetic parameters Thermodynamic parameters
Diffusivities ∑= ∂
∂−=
n
i j
ikikj
cLD
1
µ
−=
RT
Q
RT
MM kk
k exp0
Mobilities
Kinetic databases
(DICTRA)
A.Borgenstam, A. Engström, L. Höglund, J. Ågren: J. of Phase Equilibria 21 (2000), p. 269
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One-phase problems:
• Homogenisation of alloys
• Carburizing-decarburizing
• Spinodal decomposition
Moving boundary problems:
• Precipitate dissolution
• Solidification
• Growth of crystals from an amorphous matrixComplex systems:
• cooperative growth (pearlite growth)
• diffusion in dispersed systems
DICTRA
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Assumptions:
*Assuming that equilibrium hold locally at the phase interface.
*Assumption regarding the geometry and size of the system, e.g. the
interdendritic spacing (100 µm).
* Assumption regarding the cooling rate (0.5 K/s).
However: * Full consideration of diffusion in both the liquid and solid phases.
AerMet100: Fe-13.3% Co-11.1% Ni - 3.0% Cr- 0.9% Mo-0.23% C
Scheil-Gulliver Solidification SimulationAssumptions:
*Fast diffusion in liquid,
homogenous liquid.* No diffusion in solid phases,
segregations in the solid
Solidification simulation using DICTRA
Example - Solidification
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T=900 °C
T=1475 °C
T=1500 °C
Concentration profiles at different T
T=1450 °C
Solid fraction at different T
Simulation results
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Conclusions
• Thermodynamics and kinetics for materials processing
• Scientific community
• Developers– Software
– Databeses
• Translators– Understanding the processes
– Tailoring the process
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Conclusions
• Benefit– Payback time
– Experiment avoided
– Decision driver
– Input for FEM
• Opportunity– Accuracy
– Reliability
– Cost
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Conclusions
Materials properties
Available thermodynamic and kinetic data base
Thermodynamic and kinetic modelling
Assessment of materials and processes
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CALPHAD
CALculation of PHAse Diagrams
is a method
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CALPHAD
CALculation of PHAse Diagrams
is a
community
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CALPHAD
CALculation of PHAse Diagrams
is a journal
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CALPHAD
CALculation of PHAse Diagrams
is a meeting
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References TD
•L Kaufman and H Bernstein, Computer Calculation of Phase
Diagrams, Academic Press N Y (1970) ISBN 012402050X
•N Saunders and P Miodownik, Calphad, Pergamon Materials
Series, Vol 1 Ed. R W Cahn (1998) ISBN 0080421296
•H L Lukas, S G Fries and B Sundman, Computational
Thermodynamics, the Calphad Method, Cambridge University
Press (2007) ISBN 0521868114
•www.calphad.org
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References KIN
• D.A.Porter and K.E.Easterling, Phase transformations in Metals and Alloys, Chapman & Hall, 1992
• J.W.Christian, “The theory of transformations in metals and alloys”, 2nd edition, Pergamont, Oxford (UK), 1975.
• M.J.Starink, Int. Mat. Reviews, 49 (2004) 191.
• M. E. Fine, Phase Transformations in Condensed Systems, MacMillan, New York (1964)