Experimental Determination of Thermochemical Properties · T. Markus RWTH-Aachen Jan 07 1 Mitglied...

1T. Markus RWTH-Aachen Jan 07

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Experimental Determination of Thermochemical

Properties

Torsten MarkusTorsten Markus

Institute for Energy Research (IEF-2)

Forschungszentrum Jülich GmbH

52425 Jülich

[email protected]

2T. Markus RWTH-Aachen June 08

Outline

- KEMS (Knudsen Effusion Mass Specktrometry)- Introduction and Example

- DTA (Differential Thermo Analysis)

- Phase Diagram Determination

- DSC (Differential Scanning Calorimetry

- Modelling (Determination of Interaction Parameters )


KEMS – Introduction( Knudsen Effusion MassSpectrometry )

For chemical- and materials research elucidation of the

vaporisation of materials is important

All materials vaporise if the temperature is sufficiently high

Thermodynamic data can be obtained from the partial

pressures of the evaporating species (also for thecondensed phase)

Knowledge of thermodynamic data is important to

understand the chemical and thermodynamic behaviourlike for example the interplay of substances during

chemical reactions


Determination of Thermodynamic Data with KnudsenEffusion Mass Spectrometry

The High Temperature Mass Spectrometry is themost imortant method for the analysis of vapors overcondensed phases

The Thermodynamic Data result from the measuredtemperature dependence of the Partial Pressures of the identified Gaseous Species

A special variant of this technique which is frequentlyused in inorganic gas phase chemistry, is the

Knudsen Effusion Masss Spectrometry (KEMS)


Temperatures and pressure ranges for KEMS,

TMS, LVMS

0 1000 2000 3000 4000 5000 6000 700010

-10

10-5

1

105

1010

p/P

a

T /K

Transpiration MS

Knudsen

Effusion

MS

Laser Induced MS


Principle of Knudsen Effusion Mass Spectrometry(KEMS)

•••• Vaporisation studies up to 2800 K

•••• Identification of gaseous species

•••• Determination of partial pressures

(10-8 ... 10 Pa)

•••• Evaluation of thermodynamic data of

•••• gaseous species

•••• condensed phases

•••• Elucidation of corrosion processes


Schematic Representation of a Knudsen cell magneticfield mass spectrometer system


Mass Spectrometer Knudsen Cell System (CH 5)


One Compartment Knudsen Cell

Liner

Sample

Outer Cell


Different types of Knudsen Cells


Functional principle of the two compartment Knudsen cell

Tungsten

crucible

Sample with p2<<p1 (s)

outer Tungsten

crucible

recess for the

thermo coupleconnection to the 2nd cell

separate heating

Sample with p1(s)

outer Tungsten

crucible

Tungsten

crucible

insert for a better

mixing of the gases

recess for the

thermo couple


Schematic representation of a Gas Inlet System


Determination of Thermodynamic Data

Example: ∆∆∆∆H; ∆∆∆∆S of DyI3

11stst stepstep::

identification of species present in the mass spectrum

and

Assignment of fragments to their neutral precursor

=> fragmentation coefficients


Identification of Gaseous SpeciesAssignment of Fragments to their neutral precursor

The temperature dependence of the ion intensities of the same neutral molecule generally show the same behaviour.

The appearance potential of the molecular ions formed by simple ionisation are generally smaller than those of fragments which come fromthe same neutral precursor. The appearance potential increase withincreasing degree of fragmentation.

Fragmentation of a molecule is often indicated by the shape of theionisation efficiency curve of the simple ionised ion

In comparison to molecular ions formed by simple ionisation the fragmentions have an additional kinetic energy contribution


Fragmentation

DyI3(s)

Dy2I6(g)DyI3(g)

DyI3+(g)

(1)

Dy+(g)(0,35)

DyI+(g)(0,29)

DyI2+(g)

(0,64)

Dy2I5+(g)

(1)

Dy2I3+(g)

(0,001)

Dy2I4+(g)

(0,080)

va

po

riza

tio

nE

lec

tro

nim

pa

ct

ion

iza

tio

n

(fragmentation coefficient)



Example: ∆∆∆∆HF of DyI3

22ndnd stepstep::

Measurement of the temperature dependence of ionintensities

and

Determination of partial pressures


100 105 110 1155

6

7

8

9

10

Dy+ DyI

+

DyI2

+ DyI

3

+

Dy2I4

+ Dy

2I5

+

log

(I T

)

arb

itra

try u

nits

1/T [10-5/ K]

1000 900 T [K]

Temperature Dependence of Ion Intensities for

the Equilibrium Vaporization of DyI3(s)


T temperature

I+i,j intensities of to the neutral species i related ions j

Ai,j isotopic abundance

γγγγi,j multiplier gains

σσσσi ionisation cross section of the neutral species i

k pressure calibration constant

∑ +=j

ji

jijii

i IA

Tkp ,

,,

100

1

γσ ii

i

i A

TI

σk

γ

+

=1

Experimental Determination of Partial Pressures pi of Neutral Species i


Different Calibration Methods

TI

p

100

Ak

i

iiii +

σγ=

p2

X

X

X

2

X kT

1

I

Ik 2

2σ

σ=

3 calibration by using the mass loss

1 vaporisation of a substance with a known vapor pressure

2 pressure dependent reaction taking place X2(g) ↔ 2X(g)2X

2X

pp

pK =

dt

dm

M

RT2

cq

1

T)i(I

)i(k i

i

π

⋅

σ=


Temperature Dependence of the Partial Pressures for theEquilibrium Vaporization of DyI3(s)

95 100 105 110 115 120

-3

-2

-1

0

1

DyI3

Dy2I6(g)

log

(p / P

a)

1/T [10-5/ K]

1000 900 T [K]



Example: ∆∆∆∆HF of DyI3

33rdrd stepstep::



Equilibrium Constant

0

00

0

0

0

3

3

3

3

pp

with

p

p

pp

pp

p

pK

)s(DyI

)g(DyI

)s(DyI

)g(DyI

j

jp

i

=

=⋅

⋅=

=

ν

∏

)g(DyI)s(DyI 33 ⇔


j

j

j

pp

pK

ν

∏

=

0

0

2nd law 3rd law

00 ln pTr KRTG −=∆

000

TrTrTr STHG ∆−∆=∆

Gibbs free reaction energy reaction enthalpy reaction entropy

R

S

RT

HK TrTr

p

000ln

∆+

∆−=

( )000 ln TrpTr SKRTH ∆−⋅−=∆

−∆+⋅−=∆

T

HGKRTH T

rpr

0

298

000

298 ln

( )T

HGS TrTr

Tr

000 ∆−∆

−=∆from

meas.

Determination of Thermodynamic Properties


Determination of thermodynamic properties

2nd law method

0

p

0

Tr K ln RTG −=∆0

Tr

0

Tr

0

Tr STHG ∆−∆=∆

BT

A

R

ST

TR

HKln TrTr

p

+⋅=

∆+⋅

∆−=

1

1 000


Determination of ∆∆∆∆H and ∆∆∆∆S from EquilibriumConstant

95 100 105 110 115 12010

-2

10-1

100

101

DyI3(s) = DyI

3(g)

Tm= 933K

log

Kp

1/T [10-5/ K]

1000 900 T [K]

Kmol

kJ,S

mol

kJ,H

,T

Klog

0Tr

0Tr

p

⋅=∆

=∆⇒

+⋅−=

57267

08255

974131

133220


Thermodynamic Data for the equilibrium vaporization of DyI3(s)

I DyI3(s) →→→→ DyI3(g)

II 2DyI3(s) →→→→ Dy2I6(g)

IV 2DyI3(f) →→→→ Dy2I6(g)

1,24·10+4-153,0±3,0-199,49±0,8-205,4±3,3-195,4±3,3920II

1,15·10-7250,7±5,24356,5±1,0352,9±4,3325,6±4,4920II

3,05·10-6201,9±3278,0±0,9279,4±2,8260,5±2,7920I

kp(Tm)∆∆∆∆S0298

kJ (kmol K)-1

∆∆∆∆H0298

kJ mol-1

3rd law

∆∆∆∆H0298

kJ mol-1

2nd law

∆∆∆∆H0Tm

kJ mol-1

Tm

K


Differential Thermal Analysis (DTA)

Measuring of Phase Transition

Temperatures

Determination of the Quantity of

Heat

Studies in different Atmospheres

Thermal Analysis from RT to 2800

K

T

T∆

PT

Simultaneous DTA withThermogravimetry (TG)STA 429, Netzsch

Principle of DTA


300

350

400

450

500

550

600

650

700

750

800

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

XNaI

Te

mp

era

tur

[°C

]

CeI3 NaI

CeI3(s)

+ SchmelzeNaI(s)

+ Schmelze

Schmelze

CeI3(s) + NaI(s)

1)°

=NaI

NaIi

p

pa

°=

3

3

CeI

CeI

ip

pa

3/2

2

])(/)([

])(/)([)(

CeINaI

NaIRS

NaIINaII

NaIINaIINaIa

++

−++

=2)

)(

)(

)(

)()( 4

4

3NaII

NaCeII

NaCeII

NaIICeIa

ZPR

+

+

+

+

⋅

=

)(),()( 43 gNaCeIlsCeIgNaI ⇔+3)

∫−

=−

−=x

x

NaIadx

xCeIa

1

0

3 )(ln1

)(ln4)

Methoden:

Phase Diagram of NaI – CeI3 determined by DTA and compositions and temperatures for KEMS measurements


According to definition:

Ion Intensity Ratio integration Method (GD-IIR):

a ip i

p i

I i

I i( )

( )

( )

( )

( )====

°°°°====

°°°°

++++

++++( , )i A B====

ln ( ) ( ) ln( )

( ) ( )f A x d

x I B

x I Ax

x

==== −−−− −−−−−−−−

====

++++

++++∫∫∫∫1

11

a A x f A( ) ( )====

d(1/T)

a(A) ln dRH(A)

mix∆ =

Activities:

Enthalpies and Gibbs Energies:

]ln)x(lnx[RTGmnnn X'MMXMXMX

E

m γγ −+= 1

Thermodynamic Properties of A and B in

Mixtures {xA + (1-x)B}


0,0

0,2

0,4

0,6

0,8

1,0

0,0 0,2 0,4 0,6 0,8 1,0

0,0

0,2

0,4

0,6

0,8

1,0

0,0 0,2 0,4 0,6 0,8 1,0

0,0

0,2

0,4

0,6

0,8

1,0

0,0 0,2 0,4 0,6 0,8 1,0

0,0

0,2

0,4

0,6

0,8

1,0

0,0 0,2 0,4 0,6 0,8 1,0

a

a

XNaI XNaI

Temperature and Composition dependency of activityfor the NaI – CeI3 system

550 °C550 °C 600 °C600 °C

625 °C625 °C 650 °C650 °C


0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

XNaI

a

Extrapolation

a(NaI)

a(CeI3)

Gibbs-Duhem-Integration

a(NaI)

a(CeI3)

activities at 750 °C


Enthalpy of mixing for the NaI-CeI3 System

-14

-12

-10

-8

-6

-4

-2

0

0.00 0.20 0.40 0.60 0.80 1.00mol% NaI

En

tha

lpy

of

mix

ing

[kJ/

mo

l]


Thermodynamic Modeling Procedure

.minln)(0

0 =

+== ∑∑

i

ii

i

i

ii RTTG νν

νµνµ

Gibbs free energy related to

enthalpie @ reference temperature

Tref=298K

formation enthalpy

@ reference temperature

Tref=298K

43421444 3444 21)()()()( 0,0,0,0

ref

m

fref

m

i

m

ii THTHTGT ∆+−=µ

This thermodynamic input data is taken from

• KEMS experiments

• calculations using cp(T) functions

• literature tables

solve this problem and find Nνν ...1

input data needed:


Introduction to the Data Optimization procedure

The aim is to generate a consistent set of Gibbs energy parameters from a given set of

experimental data using known Gibbs energy data from well established phases of a

particular chemical system.

Typical experimental data include:

phase diagram data: transitions temperatures and pressures as well as amount and composition of the phases at equilibrium

calorimetric data: enthalpies of formation or phase transformation, enthalpies of mixing, heat contents and heat capacity measurements

partial Gibbs energy data: activities from vapor pressure or EMF measurements

volumetric data: dilatometry, density measurements.

The assessor has to use his best judgement on which of the known parameters should

remain fixed, which set of parameters need refinement in the optimization and which

new parameters have to be introduced, especially when assessing data for non-ideal

solutions.


Overview of the data to be optimized in the

NaI-CeI3 systemVarious experimental data on the binary NaI-CeI3 system have been measured:

– phase diagram data (liquidus points, eutectic points)

– liquid-liquid enthalpy of mixing

– activity of NaI(liq) at different temperatures

OptiSage will be used to optimize the parameters for the liquid Gibbs energy model (XS terms). All other data (G°of the pure stoichiometricsolids, as well as the pure liquid components) will be taken from the FACT database (i.e. remain fixed). A polynomial model for the Gibbs energy of the liquid will be used:G = (X1 G°1 + X2 G°2) + RT(X1 ln X1 + X2 ln X2) + GE

where GE = ∆∆∆∆H – TSE

Using the binary excess terms:

∆∆∆∆H = X1X2 (A1) + X12X2 (B1)

SE = X1X2 (A3) + X12X2 (B3)

Hence:

GE = X1X2 (A1 - A3T) + X12X2 (B1 - B3T)

Where A1, A3, B1 and B3 are the 4

parameters to be optimized.CeI3xCeI3

G

NaI

G°1

G°2


Phase Diagram of the System NaI–CeI3 (DTA)

Binary Excess Polynomial:

GmE=(xNaI

i)(xCeI3j)(A + B*T + C*T*ln(T) + D*T2 + E*T3 + F*T-1)

(calculated)


Outline

- KEMS (Knudsen Effusion Mass Specktrometry)- Introduction and Example

- DTA (Differential Thermo Analysis)

- Phase Diagram Determination

- DSC (Differential Scanning Calorimetry

- Modelling (Determination of Interaction Parameters )

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Experimental Determination of Thermochemical Properties · T. Markus RWTH-Aachen Jan 07 1 Mitglied...

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