Experimental Determination of Thermochemical Properties · T. Markus RWTH-Aachen Jan 07 1 Mitglied...
Transcript of 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
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 )
3T. Markus RWTH-Aachen June 08
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
4T. Markus RWTH-Aachen June 08
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)
5T. Markus RWTH-Aachen June 08
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
6T. Markus RWTH-Aachen June 08
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
7T. Markus RWTH-Aachen June 08
Schematic Representation of a Knudsen cell magneticfield mass spectrometer system
8T. Markus RWTH-Aachen June 08
Mass Spectrometer Knudsen Cell System (CH 5)
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One Compartment Knudsen Cell
Liner
Sample
Outer Cell
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Different types of Knudsen Cells
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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
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Schematic representation of a Gas Inlet System
13T. Markus RWTH-Aachen June 08
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
14T. Markus RWTH-Aachen June 08
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
15T. Markus RWTH-Aachen June 08
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)
16T. Markus RWTH-Aachen June 08
Determination of Thermodynamic Data
Example: ∆∆∆∆HF of DyI3
22ndnd stepstep::
Measurement of the temperature dependence of ionintensities
and
Determination of partial pressures
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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)
18T. Markus RWTH-Aachen June 08
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
19T. Markus RWTH-Aachen June 08
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=
20T. Markus RWTH-Aachen June 08
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]
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Determination of Thermodynamic Data
Example: ∆∆∆∆HF of DyI3
33rdrd stepstep::
Determination of Thermodynamic Data
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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 ⇔
23T. Markus RWTH-Aachen June 08
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
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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
25T. Markus RWTH-Aachen June 08
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
26T. Markus RWTH-Aachen June 08
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
27T. Markus RWTH-Aachen June 08
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
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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
29T. Markus RWTH-Aachen June 08
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}
30T. Markus RWTH-Aachen June 08
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
31T. Markus RWTH-Aachen June 08
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
32T. Markus RWTH-Aachen June 08
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]
33T. Markus RWTH-Aachen June 08
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:
34T. Markus RWTH-Aachen June 08
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.
35T. Markus RWTH-Aachen June 08
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
36T. Markus RWTH-Aachen June 08
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)
37T. 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 )