Hydrides for Energy Storage:modelling approaches and

translation realization

Marcello Baricco

Department of Chemistry and NISUniversity of Turin, Torino, Italy

marcello.baricco@unito.it

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)

Modelling and length scale

macroscale

microstructure

atomistic

electronic

Ab-initio

CalphadMD

Phase field

FEM

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

Experimental determination of phase diagrams

Estimation of data

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=

Phase diagrams and free energy

A.H.Cottrell, Theoretical Structural Metallurgy, Edward Arnold, London, 1955)

Real systems

•Several invariant points

•Multicomponent

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

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

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)

Ab-initio methods

DFTAtomic

number

Valence

electrons

Crystal

geometry

Ground

state

energy

ZPE

DOS

Phonons

Plane waves

Pseudopotentials

Gaussian

Cp, ΔH, ΔS then ΔG

The assessment procedure

selection of

data

weight

selection of

models

thermod.

parameters

TDB file

calc.

condit.

INPUT OUTPUTMIN. OF

ERRORS

The calculation procedure

TDB file

T,P,X

values

thermod.

quatities

vs

T,P,X

comp.

equil.

INPUT OUTPUTCALC.

TECHN.

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…

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

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)

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

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

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

Experimental Validation

Experimental and Calculated comparison

Absorption Desorption

D. Baldissin, J. Urgnani, M. Palumbo, M. Baricco, MH Conference 2008

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

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)

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

∆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

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

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

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

T=900 °C

T=1475 °C

T=1500 °C

Concentration profiles at different T

T=1450 °C

Solid fraction at different T

Simulation results

Conclusions

• Thermodynamics and kinetics for materials processing

• Scientific community

• Developers– Software

– Databeses

• Translators– Understanding the processes

– Tailoring the process

Conclusions

• Benefit– Payback time

– Experiment avoided

– Decision driver

– Input for FEM

• Opportunity– Accuracy

– Reliability

– Cost

Conclusions

Materials properties

Available thermodynamic and kinetic data base

Thermodynamic and kinetic modelling

Assessment of materials and processes

CALPHAD

CALculation of PHAse Diagrams

is a method

CALPHAD

CALculation of PHAse Diagrams

is a

community

CALPHAD

CALculation of PHAse Diagrams

is a journal

CALPHAD

CALculation of PHAse Diagrams

is a meeting

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

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)