Determination of thermodynamic properties of liquid AgIn, AgSb, AgSn, InSb, SbSn, AgInSb, CuInSn and

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Determination of thermodynamic properties of
liquid Ag-In, Ag-Sb, Ag-Sn, In-Sb, Sb-Sn,
Ag-In-Sb, Cu-In-Sn and Ag-In-Sn systems by
Knudsen effusion Mass Spectrometry A. Popovic
and L. Bencze
Jozef Stefan Institute, Jamova 39, SLO-1000
Ljubljana, Slovenia.Eötvös Loránd University,
Dept. of Physical Chemistry, H-1117 Budapest,
Pázmány Péter sétány 1/A, Hungary
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The scheme of a Knudsen cell - mass spectrometer
system (FZ Jülich, Germany)
lt 20 KEMS laboratories over the world
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The scheme of single and double the Knudsen cells.
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Determination of equilibrium vapour pressure by
KEMS
Inghram, Chupka, 1955
where K is the (general) instrumental
sensitivity constant Iij is the
intensity of ion i originating from neutral
species j hi is the isotopic
abundance of ion i gi is the
multiplier gain factor of ion i (sensitivity
constant of the detector for
ion i) - in multiplier current
measurement mode only ai is the
(spectral) abundance of ion i in the mass
spectrum si is the total ionisation
cross section of species j at the actual
electron energy (si depends on j and the
ionising electron energy)
K can be determined by calibration using e.g. a
reference substance (e.g.pure component) in the
next or previous experiment, using internal
standard inside the same cell, using isothermal
long-term evaporation etc).
pj pressure over the pure component
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Determination of activities by
KEMS 1/ by direct pressure calibration (DPC)
using pure metals as reference substances in
subsequent experiments (the uncertainty can reach
as high as 20 due to a the change of
sensitivity constant day-by-day), 2/ using a
proper internal standard (ISM) being in the same
cell, 3/ using twin or multiple Knudsen cell
technique (MKC) (some of the compartments are
filled with the pure components), 4/ from the
change of the oligomer (monomer, dimer, trimer
etc.) composition in the vapour (this latter
method can be applied in the only case if the
metals vaporise in the form of oligomers,
such as Sb(g), Sb2 (g), Sb3(g), Sb4 (g)), 5/
applying the mass spectrometric Gibbs-Duhem Ion
Intensity Ratio Method (GD- IIRM) that is a
modification of the well-known Gibbs-Duhem
relationship with MS quantities (i.e. ion
intensities), 6/ applying the isothermal
evaporation method (IEM) /long-term or
total/, ------------------------------------------
--------------------------------------------------
------------------------- 7/ for ternary alloys,
by applying Miki s or Tomiska s new KEMS
methods for the determination of the
constants in the power series expression of GE.
(Miki Redlich-Kister expression, Tomiska TAP
expression)
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THERMODYNAMIC PROPERTIES OF MIXING Activities
and the activity coefficients ---gt chemical
potential change of mixing, excess chemical
potential ----gtGibbs energy change of mixing,
excess Gibbs energy The uncertainty of m Ei /d(m
Ei)/ is usually lower than -1 kJ/mol (at 1400 K,
assuming an error as factor 1.1 in the values of
activities, d1.11 kJ/mol is obtained). ----------
--------------------------------------------------
-------------------------- Temperature dependence
of activities---gt partial and integral enthalpy
changes of mixing. Uncertainties d(HEi )1-2
kJ/mol for partial quantities but in case of
wrong identification of the composition the
uncertainty of the integral quantity (HE) can
reach as high as 10 kJ/mol if the partial
quantities depend on composition very sharply.
The Gibbs-Duhem integration helps against this
problem.
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Al-Fe-Ni
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BINARY SYSTEMS
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Mikis method supplemented by us for the
calculation of all the 3 ternary Ls
Redlich-Kister-Muggianu
where GE is the excess Gibbs free energy,
expressed in terms of binary and ternary
interaction parameters.
where
where ICu / ISn is the measured ion intensity
ratio of Cu to Sn and C is a constant
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By rearranging and putting similar terms together
we finally get that
The three ternary parameters can finally be found
by solving the set of linear equations
where n is the number of the measured
compositions. If ngt4 the solution of the linear
equation system should be replaced with a
multiple regression problem. The method
provides the three ternary parameters, and, as
input parameters it needs the binary parameters
(either from own experiments or from literature)
and the measured ion intensity ratio at various
compositions for the given temperature. Any ion
intensity ratio can be used from the total 3
variations of a ternary systems.
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The result for Cu-In-Sn, obtained from ICu / ISn
of 23 compositions, is as follows

Fig1. Measured compositions.
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Fig.3. Ternary parameters as a function of
temperature by Liu et al..
Fig.2. Ternary parameters as a function of
temperature, obtained in this work.
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Fig. 4. Comparison of indium activity data
obtained from our own and Liu s ternary
parameters, from our measured mass loss data and
from the measured EMF data of Yamaguchi.
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Fig.5. Comparison of the partial excess enthalpy
of indium obtained from our own and Liu s
ternary parameters, from the ion intensity of In
vs. temperature directly and by assuming binary
parameters only.
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GE of Cu-In-Sn
Fig.6a. Iso-curves of the integral excess Gibbs
energy at 1173 K, evaluated using our own
ternary parameters.
Fig.6b. Iso-curves of the integral excess Gibbs
energy at 1173 K, evaluated Liu s ternary
parameters.
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Fig.7a. Iso-curves of the integral excess
enthalpy at 1400 K, evaluated using our own
ternary parameters.
HE of Cu-In-Sn
Fig.7b. Iso-curves of the integral excess
enthalpy at 1400 K, evaluated using Liu s
ternary parameters
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Two possibilities for getting ternary Ls
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2
1

X
2
X

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GE of Ag-In-Sn
Dataset I, Ag/In
Dataset I, Ag/Sn
our evaluation with Mikis Ag/In data
Dataset II, Ag/Sn
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Activities in Ag-In-Sn
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CONCLUSIONS 1. The uncertainties of the
ternary Redlich-Kister L-parameters obtained from
our Knudsen effusion mass spectrometric
data depend on the number of compositions
studied. 23 compositions seemed to be sufficient
to reach rather low relative uncertainty (the
case of Cu-In-Sn). Lower number of compositions
(the case of Ag-In-Sn) increases the
uncertainties of Ls but the uncertainties of GE
and of the activities remain still low. 2. There
is a complete mismatch (both in absolute values
and temperature trends) between the ternary
L-parameters of Cu-In-Sn obtained in this work
and those assessed by Liu. This mismatch results
in large difference between the values obtained
in this work and by Liu in all thermodynamic
quantities, in particular in the partial and
integral excess enthalpies and excess Gibbs
energies. 3. The GE and activity values of
Ag-In-Sn obtained from our and Miki s KEMS data
agree very well but the ternary L-values obtained
from this two sources are different. The
difference in Ls probably also could be
decreased by increasing the compositions
studied. 4. Any ion pair variation (e.g. Ag/Sn
or Ag /In in Ag-In-Sn) in the mass spectrum can
be chosen in principle for obtaining the
thermodynamic properties. The different choices
must provide the same values in case of good
consistency.
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ACKNOWLEDGEMENTS
Many thanks to the COST 531 leadership for the
support of my STSMs.
Thank You for Your attention!