THERMODYNAMIC PROPERTIES AND BEHAVIOR OF
POTASSIUM OXIDE IN POTASSIUM OXIDE-ALUMINA
AND POTASSIUM OXIDE-CALCIUM OXIDE SILICATES
by
DAWID DE WET SMITH
'I
B. Sc. (Eng.) (Met.), University of Pretoria
(1980)
SUBMITTED IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS OF THE
DEGREE OF
MASTER OF SCIENCE
IN METALLURGY
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
September 1984
Massachusetts Institute of Technology
Signature of Author..
DepZ)tent of
aterial Science and Engineering
A
-
Certified by.......
,E, ey.
Accepted by-----------.
August 10, 1984
tott
John F
Thesis Supervisor
B. J. Wuensch
Chairman, Dep Jmental Committee on Graduate Students
MASSACHUSEUS
INSTITUTE
OF TECHNOLOGY
AUG 129 1984
LIBRARIES
THERMODYNAMIC PROPERTIES AND BEHAVIOR OF
POTASSIUM OXIDE IN POTASSIUM OXIDE-ALUMINA
AND POTASSIUM OXIDE-CALCIUM OXIDE SILICATES
by
DAWID DE WET SMITH
Submitted to the Department of Material Science
and Engineering on August 10, 1984 in partial
fulfillment of the requirements for the
Degree of Master of Science in Metallurgy.
ABSTRACT
measured in
was
oxide
potassium
of
The activity
K2O-SiO 2 -Al2 O2 and K 2 0-SiO 2 -CaO melts over a temperature range
of 950 to 1100 0 C. The following electrochemical cell was used:
Pt,
02 (g), K120
(K2 0-nSiO 2 )
Binary
I
K+
beta - alumina
|
z02(g), K2 0, Pt
(K2 0-nSiO 2 -XX)
Ternary
II
where XX designates A1 2 03 or CaO. The ratio of X,2 c3/Xin1om was
the same in the binary and the ternary melts.
In the K2 0-SiO 2 -A1 2 0. system, up to 8 weight % alumina was
added to 70, 65, 56, 47, and 39 weight % SiO2 binary melts. It
was found that along pseudo-binary lines of constant Xv2 0 /X0.1 2
the addition of A1 2 03 to potassium silicates decreased the
activity of K2O up to approximately log a=C2o = 0.12. The
results are compared with the published data of the same
system.
Activities of K20 in the K 2 0-SiO 2 -CaO system were measured
for the 65, 56 and 47 weight % SiO 2 binary compositions with up
to 12 weight % CaO added. The addition of CaO caused an
increase in the activity of K2 0 at constant XKmo/Xwjo2. The
- 2 -
The
0.22.
is up to approximately log a.ao =
increase
similar
of
results
the
experimental data is compared well with
The experimental data are also compared with the
systems.
The
values predicted by the Richardson's ternary mixing model.
nature
polymeric
the
activity data were Interpreted in terms of
of silicate melts
Thesis supervisor: John F. Elliott.
Title: Professor of Metallurgy.
- 3 -
TABLE OF CONTENTS.
Page
Number.
Chapter.
TITLE PAGE
1
ABSTRACT
2
TABLE OF CONTENTS
4
LIST OF FIGURES
7
LIST OF TABLES
11
ACKNOWLEDGEMENTS
12
I
INTRODUCTION.
13
2
LITERATURE SURVEY.
16
2.1
2.2
16
Solid electrolytes.
2.1.1
Introduction to solid electrolytes.
16
2.1.2
The beta-aluminas.
18
Activities
in Alkali Silicates.
25
2.2.1
The K2O-SiO 2 system.
25
2.2.2
Ternary and higher order silicates
containing potassium oxide.
29
2.2.3
Sodium and lithium silicate systems.
3
3
OUTLINE OF RESEARCH.
5
4
EXPERIMENTAL.
9
4.1
4.2
Theoretical considerations.
9
4.1.1
KO-SiOm-AlO
system.
239
4.1.2
K2O-SiO2-CaO system.
42
42
Cell Design.
- 4 -
E19i.
Chapter.
4.3
5
6
7
8
Measurement and control of the experiment.
46
4.3.1
Computer hardware.
48
4.3.2
Computer software.
51
4.4
Procedure.
51
4.5
Galvanostatic polarization test of the
electrochemical cell.
54
58
RESULTS.
5.1
K20-SiO 2 -Al20.
5.2
K20-SiO2-Ca0 system.
system.
58
70
78
DISCUSSION.
6.1
Error analysis.
78
6.2
K2-SiO2-Al203 system.
80
6.3
K2O-SiO2-CaO
system.
85
6.3.1 Comparison with other work.
85
6.3.2 Richardsons mixing model.
86
91
SUMMARY AND CONCLUSION.
RECOMMENDATION FOR FURTHER WORK.
93
APPENDIX.
A
95
K-BETA-ALUMINA.
A.1
Fabrication of K-beta-alumina.
95
A.2
Quality of product.
96
B
Electronic circuit used for control of
experiment.
104
C
Program for data acquisition and control of
the EMF experiment.
105
- 5 -
MIN
EAgt.
Chapte r .
D
Silicate melt preparation.
108
E
Sources and purities of materials.
109
F
Experimental results for
K2 0-SiO 2 -A12 03 system.
111
G
Experimental results for
K 2 0-SiO 2 -CaO system.
130
H
Quantitative error analysis.
138
141
BIBLIOGRAPHY
- 6 -
LIST OF FIGURES.
FIGURE.
Fig.
2.1
Phase diagram of NaO.
20
A120m-A12e0m.
Fig.
2.2
Oxide ion packing arrangement in
beta-alumina and beta"-alumina.
Fig. 2.3
Summary of measurements of SiO2
activity in the K2O-SiO2
system at 1100 0 C.
Fig.
2.4
Summary of measurements of K2 0
activity in the K 2 0-SiO 2
system at 1100 aC.
Fig.
3.1
Portion of
KO-S iO2-A1 20:3
ternary phase diagram. Compositions
studied are denoted by symbol x.
Fig.
3.2
Portion of K 2 0-SiO 2 -CaO
ternary phase diagram. Compositions
studied are denoted by symbol x.
Fig. 4.1
Absolute activity of K20 in binary
silicate melts. (Shigematsu and Elliott)
Fig. 4.2
Schematic diagram of experimental system
for measurement of cell EMF in oxygen.
Fig.
4.3
Temperature profile of SiC furnace used
for taking measurements.
Fig.
4.4
Computer peripherals used for measurement
and control of the experiment.
- 7 -
30
37
44
49
Fig.
4.5
Example of the response of cell potential
to temperature changes.
55
Fig.
4.6
Galvanostatic polarization test of emf cell.
57
Fig.
5.1
Experimental results for log aano
the K=0-SIO2-Al 2 0=
system for melts for which
= 0.273.
X.c~
2 /Xmw.o
Fig.
5.2
in
Experimental results for log as<=
the K20-SiO 2 -Al20a
system for melts for which
Xxm~o/X=,2
=
in
62
0.344.
5.3
Experimental results for log atco in
the K20-Si0a-Al20
system for melts for which
X.<o/X. 1 o 2 = 0.490.
63
Fig. 5.4
Experimental results for log at<o in
the K2 0-SiO2-Al2O
system for melts for which
64
Fig.
Xs<23/Xwa2
Fig. 5.5
=
0.719.
Experimental results for log asmo in
the K2 O-SiO2-Al20=
system for melts for which
Xv<==/XWa
2
=
1.000.
Fig 5.6-
The activity.of K2 0 in the
K20-SiO=-Al20,
system along pseudo-binary lines of
constant ratios of Xx=o/X=co=
at 1100 C.
Fig 5.7
Interpolated iso-activity lines for
K=O in the
K2 0-SiO2-Al2zO=
system at 11000C.
Fig 5.8
65
Experimental results for log ascax in
the K2 0-SiO-CaO system for
melts for which X~am/Xwnaz =
0.3435.
- 8 -
66
E
FIgure.
Fig 5.9
Experimental results for log a.mo in
the K2 0-SiO-CaO system for
melts for which Xx~a/Xinic
.
72
=
0.490.
Fig 5.10
Experimental results for log atcaa
in
73
the K 2 O-SiO2-CaO system for
melts for which XK=23/Xaic2 = 0.719.
Fig 5.11
The activity of K2 0 in the
K2 0-SiO2-CaO system along
pseudo-binary lines of constant ratios
of Xucc3/Xwajc3
74
at 11006C.
Fig 5.12
Interpolated iso-activity lines for
K2 0 in the K2 0-SiO=-CaO
system at 1100*C.
75
Fig 6.1
Interpolated isoactivity lines for
Na.0 in the
Na=0-Al=O-SiO=
system in air at 10500C.
82
Fig 6.2
Iso-log amma lines for
Na20-CaO-SiO2 imelts. Lines
drawn at 0.1 intervals of log
83
ammmo, from -10.3 to -8.8.
Temperature = 1070 0 C.
Sections of beta-alumina solid
electrolyte crucible analyzed with the
Electron Probe Micro Analyser.
99
Fig. A.2
and K=O
Wt% of AlO2
along section A-B of Fig A.1, after ion
exchange.
100
Fig.
Wt% of Al 2 03 and K20
along section C-D of Fig A.1, after ion
exchange.
101
Fig.
A.1
A.3
- 9 -
Fliure.
Fig. A.4
Wt% of residual Na20 in solid
electrolyte along section A-B of Fig
A.1, after ion exchange.
102
Fig. A.5
Wt% of residual Na=O in solid
electrolyte along section C-D of Fig
A.1, after ion exchange.
103
-
10
-
LIST OF TABLES
2.1
Comparison of conductivity and diffusivity in
beta-alumina single crystals.
22
2.2
Systems studied using Na-beta-alumina.
23
2.3
Li 2 O-SiQ0, Na2O-SiO2
solutions studied.
34
3.1
Scope of experimental measurements.
36
4.1
Compositions studied in the
K2O-SiO2-AlOO system.
52
5.1
Least square coefficients for
log asco = A/T + B with standard
deviations for melts in 'the
K2O-SiO 2 -AlO system.
68
5.2
Partial molar Enthalpy and Entropy of mixing
of K=O in the
K 2 O-SiO 2 -A120 system.
69
5.3
Least square coefficients for
log aKxo = A/T + B with standard
deviations for melts in the
K2 0-SiO2 -CaO system.
76
5.4
Partial molar Enthalpy and Entropy of mixing
of KO in the K=O-SiO=-CaO
system.
77
6.1
obtained in
Comparison between Log axo
this study and published values for the
K2O-SiO=-A120 system.
84
6.2
Comparison between calculated activities of
K2 0 and experimental values in the
K2 0-SiO 2 -CaO system.
90
-
11
-
I
ACKNOWLEDGEMENTS
I would like to express my sincere thanks to Professor John
F.
Elliott
guidance
advice,
his
for
encouragement
and
throughout the course of this work.
I would also like to
of the project.
Chamber
of
Thanks
also
is
and
Mines
the AISI for their sponsorship
thank
and
Iron
South-African
the
South-African
the
to
due
Steel
Corporation for the scholarships they provided to me.
A special thanks is due to Professor Shigematsu, a visiting
scientist from Japan, who introduced
with
me
helped
Richard Stanton who
me
the
to
this
work.
equipment
is
Mr.
also
thanked.
To my fellow
Research
graduate
group,
a
students in the Chemical Metallurgy
special
thanks
for
the
many
helpfull
discussions we had.
Finally, a special thanks is due to my
her encouragement and support.
-
12
-
wife, Christel, for
CHAPTERI.
INTRODUCTION.
Alkali containing
knowledge of the properties of these melts is
also
This knowledge can
other
in
useful
be
our
present
At
processes.
metallurgical
extractive
some
silicate melts play an important role in
limited.
rather
fields such as
ceramics.
An
example
of
a
which
for
process
metallurgical
is
thermodynamic data on alkali silicate melts would be useful
the
iron
blast
process,
countercurrent
this
In
furnace.
alkalis enter as constituents In the burden materials and while
the
descending the burden is heated by
conditions
necessary
metals
are
of
high
reducing
temperature
enough
gas
ascending
potential,
At
with
the
combined
a portion of
reduced and are immediately
gases.
alkali
the
volatilized
as
this
temperature is above the boiling point of the alkali metals.
travel
The alkali metal vapors then
ascending gases, and experience
-
13
up the shaft with the
progressively
-
more
oxidizing
and
for
When conditions become favourable
cooler conditions.
the formation and condensation of compounds such as carbonates,
these
of
portion
oxides and cyanides, a
vented
through
causes
the
to
alkalis
furnace.
blast
the
in
accumulate
is
phenomena
recirculation
This
off-gas.
the
rest
the
burden materials and furnace ceramic lining, and
the
onto
condense
Accumulation leads to scaffold formation causing erratic burden
of
burden
affected.
especially
material,
The only means
coke
venting
of
properties
Mechanical
movement and increased refractory wear.
is
adversely
also
of
furnace
the
these
alkalis is through fine particles in the top gas or through the
slag.
in
The slag forming materials
mainly silica and
silicates,
lime.
Because
of
the
blast
stable
the
alkali silicates are probably the most
alkali specie
in
the
furnace
nature
are
of
predominant
To predict the behavior of these
slag.
furnace
alkali silicates in the blast
slag a knowledge of the
thermodynamics of alkali silicate solutions is needed.
The purpose of this thesis is to obtain thermodynamic
on some alkali silicate
related
systems
to
the
alkalis through the slag in the blast furnace.
calcia
was
of
The activity of
silicate melts containing alumina
potassium oxide in potassium
and
removal
data
experimentally
determined
electrochemical cell.
-
14
-
using
an
mom
specially
was
used
electrolyte
The
was:
cell
the
and
potassium-beta-alumina
Pt, Oa (g), K=O
(K2 0-nSIO2)
Binary
I
potassium -
:
prepared
02(g), K20, Pt
beta - alumina : (K2 0-nSIO=-XX)
Ternary
*
where the ratio of K=0 to SiO2 is the
S
same
ternary melts and XX designates A1 2 0. or CaO.
-
15 -
II
for the binary and
CHAPTER 2.
LITERATURE SURVEY.
present the reader with some
The aim of this chapter is to
background
study.
particular.
The
in
involved
this
The first part
The chapter is divided into two parts.
gives an introduction to
in
rationale
the
about
material
solid electrolytes, the beta-aluminas
previous
the
covers
part
second
measurements of the activities of alkalis in silicate systems.
2.1 Solid electrolytes.
The first part gives
This section is divided into 2 parts.
solid
an introduction to
The second
electrolytes in general.
part covers beta-aluminas in particular.
2.1.1 Introduction to solid electrolytes.
Solid
materials
transports.
electrolytes
with
a
structure
crystal
as
solid
allowing
fast
ceramic
ionic
In these structures it can be shown that there are
pathways for the carriers
structurea.
defined
be
can
that
are
built
into
the
crystal
Calcium stabilized zirconia (CSZ) was the first of
these materials to be used extensively.
-
16
-
Information
different
disciplines3 .
intensive
the
are
Examples
in
applications
through the past decade due to their possible
many
increasing
been
has
electrolytes
solid
on
research done following the launching of the Sputnik
using
on
the renewed interest in using
CSZ for fuel cells in space, and
the
sodium-beta-alumina in sodium-sulphur batteries because of
seventies 4 .
result
of
this
increased activity in the field of solid electrolytes
is
that
energy
situation
in
the
presently a few dozen compounds
are
The
known that can reach high
These materials can be
ionic conductivity while
being
solid.
to
their
structure
classified according
ion".
The
main
the conducting
oxides,
fluorite-type
'include
classes
and
silver-iodide type materials, fluorides and the beta-aluminas.
The conducting species include F-, Cl-, Br-, 1-,
Ag*, Cu*,
Li*, Na*,
NH4 +, Tl*,
K*, Rb*,
02-, S2-, H*,
Mga* and Al"*.
The main technological applications of
solid
electrolytes
fall into the following categories*:
1.
ODen-circuit
ADDlications.
This
mainly
involves
equilibrium measurements with an emf cell, e.
g.
oxygen
sensors.
2.
Closed-circuit
ADolications. This involves supplying
an
external voltage to induce mass transfer.
3.
Energy Conversion. Electrochemical oxidization of a
fuel
to give direct rise to electric energy as in fuel cells.
-
17
-
4.
transport
Ionic
Batteries.
State
Solid
for
used
electrical energy storage.
5.
devices
of
e.g.
solids,
of
conductivity
ionic
the
utilizing
range
Ionics. This includes a
State
Solid
memoro ides'.
The
solid
of
3
in
extensively
reviewed
been
have
electrolytes
applications
and
properties,
structure,
monographsa.w,* and 2 conference proceedings*-*.
2.1.2 The Beta-aluminas.
The beta-aluminas were originally thought to be polymorphic
forms of Alumina1 *. Since monovalent ions are always present in
the
misnomer.
structures
known
is
name
that
structure,
beta-alumina
electrolytes
The beta-alumina solid
are
to
is
a
Tl*, Ag*, and Li*. Related phases also occur
X=O.5A120
having an extremely high conductivity".
Na=O.A12 0-AlO
system is
the
specie such as Na*, K*, Rb*,
monovalent
formulas X=0.7A1 2 0. (beta') and
a
hexagonal
with approximate composition X=O.11Al=O=. X is
mobile ion and
be
included
with
approximate
(beta"), the latter
A phase diagram of the
in Fig. 2.1.10 Reviews of
1
these materials has been presented by Kennedy" , and Collongues
et al.**
The crystal structure of beta-alumina consists of planes of
atoms parallel to the basal plane.
-
18
-
Four planes of oxygens in a
cubic
by rather
The
of the monovalent ion and oxygen.
layers
open
together
The spinel blocks are bound
the structure of spinel.
which
sites as in
tetrahedral
and
aluminum atoms occupy octahedral
within
slab
a
comprise
sequence
close-packed
the
between
exist
structure
Fig 2.211. Slight variations in
in
represented
structure for Na-beta-alumina is schematically
different beta-aluminas, espesially in the configuration of the
is extremely anisotropic but
conductivity over single crystals
polycrystalline materials
a
The
motion.
atom
increased
for
path
two-dimensional
provide
layer
open
bound
loosely
The
layers.
open
show less than an order of magnitude
the
to
parallel
decrease over single crystals measured
high
conductivity planes, indicating high-conductivity paths through
grain
Na-beta-alumina
is
indicating that
the
the
all
of
highest
in
sodium
of
conductivity
The
boundaries.
beta-aluminas
the
size of the sodium ion is the best suited
for the transport in the open layers.
Larger ions like Ag* and
Li*
K* have lower conductivities while smaller ions like
also
decrease the conductivity as shown in Table 2.1"1
Virtually
completely
conductivity
ionic
open-circuit thermodynamic measurements.
is
conductivity
for
beta-aluminas
different
Whittingham and Huggins*" as well as
-
19
-
that
the
secondary
no
The
measurements.
the
for
This means
electronic conduction should be very low so that
reactions interferes with
needed
as
1
Sammells *,
electronic
measured
is
four
by
to
2000
1800
-)
OP
E
1600
1400
1200
1000
'
N020-AI 2 0 3
60
70
Mole
Fig.
2.1
Phase diagram
reference 10.
-
20
-
80
90
A12 03
Al 2 0 3
0/o
of
NamO.
AlaOw-AlO =
from
Mirror
Plane
0
Mirror
Plane
C
Ax is
C
0O
0
Oxide Na+
Ion
-- I
3 "-
2-A lumina
O Oxide ion on
Sodium ion on
conduction plane
conduction plane
Fig. 2.2
Alumina
Oxide ion packing arrangement in beta-alumina
and beta"-alumina (Note:
letters refer to
stacking arrangement where
ABC
represents
face-centered cubic packing while ABAB would
represent hexagonal packing)
-
21
-
the
ionic specie, so that
the
for
than
lower
orders
five
transference number for the ionic specie is essentially unity.
with the refractory nature of beta-alumina makes
This combined
thermodynamic
high temperature
for
choice
it a very good
measurements.
TABLE 2.1.
COMPARISON OF CONDUCTIVITY AND DIFFUSIVITY IN
BETA-ALUMINA SINGLE CRYSTALS
~~~-------------
and
larger
by
similar
in
Na-beta-alumina
a(0.01
increase
in
A**.
The
large
as
(Alcoa)
was
in
-
22
-
this
study
is
change
of
replacement
for
and
cause
can
a
cause
fracture
available
Commercially
used
change
slight
plane
materials.
polycrystalline
a
Ag*,
Rb*,
K*,
c-parameter
This
is
exchange
Li*,
A
by
replaced
be
causes
the
in
ions
The
0.40
c-parameter.
the
easily
conducting
the
enter
may
Water
Tl*.
as
be
can
can
This
Cu*.
and
H=0'
NO*,
parameter
cell
the
much
Na*
Ga*,
NH.+,
Tl*,
sodium
ions:
monovalent
following
the
for
complete
of
to
fabricate
-
-
-
-
-
-
-
reaction.
exchange
an
by
ions
other
many
ions
sodium
structure,
beta-alumina
in
mobility
great
the
of
-
-
-
-
--
.10-7
.10.10-*
4.0
1.7
9.6
.10-+
.10.10-+
.10-
140
64
0.65
-1.3
Na*
Ag*
K*
Li*
Because
Diffusivity(25aC)
(cma/s]
Conductivity(25"C)
( cm)- 1]
Ion
the
K-beta-alumina by an ion exchange method.
exchanged for potassium ions.
The sodium ions were
Care was taken in
this study to
prevent hydration of the solid electrolyte by storing
them
in
dessicators.
Table 2.2
Some systems studied using Na-beta-alumina.
System
Reference
Alloy systems ( Na activity )
Na-Pb
Na-Hg
Na-S
Na-Sn
Na-Al
D.J. Fray and B. Savory*'
L.H. Such and N.D. Bennionsa
J. Balej, F. P. Dousek, and J. Jansta**
N. K. Gupta and R. P. Tischer 2 O
B. V. Joglekar, P. S. Nicholson and
W. W. Smeltzer 2 l
M. Rivier and A. D. Peltonm2
D. J. Fray 2
Oxide systems ( Na2 O activity )
NaaOCrO4-Na=SO4
Na=O-WO.
NaAO-WO=-SO
Na 2 0-MoO=
Liang and Elliott 2 ' 2
Lin and Elliotta-
7'
NaO-VOS
Na=O-SiO
Na2 O-CaO-SiOm
NazO-Fe2Oa-SiO=
NaaO-AlaO-S IO=
Na=O-Fe=O=-A120-SiO=:
Na=O-FeO-S 10a
Na=O-FeO-Al=O-SiO:
Sodium-beta-alumina
measurements in molten
Neudorf and Elliott 2
DeYoung and Ell iott
been
has
metals,
used
thermodynamic
salts, and silicates.
these applications are listed in Table 2.2.
-
for
23 -
Some of
potassium
of
properties
Dudley, Steele and Howe to study the
by
used
was
KIS./K-beta-alumina/K..FeiIOi,
cell
The
ferriteO*.
The K-beta-alumina was used to change the potassium
content in
the
potassium-ferrite
value
was
current
titration.
of about 10
composition was
new
After
the charge passed during the titration.
calculated from
current
turning the
The
times.
measured
micro-amperes for
constant
a
supplying
by
This was done
coulometric
by
off,
done
was
This
obtained.
decreasing potassium
the emf was measured until a steady
and
significant hysteresis,
without
content
increasing
for
showing that equilibrium had been obtained and that the process
'
was completely reversible.
More
to
pertinent
study
this
Shigematsu
and
Elliott
recently measured the properties of potassium oxide in K2 0-0SiO
binary melts with
through
solid
K-beta-alumina
electrolyte and found
temperature fluctuation that the cell potentials
were
They used Na=SO4 and Na2CO= as a reference
melt
reversible-*.
to determine the activity of potassium oxide in the more stable
0.214 mole% K=O melt.
the other binary
The
activity
of potassium oxide in all
was measured in a concentration
compositions
cell using the 0.214 mole% melt as a secondary reference.
The
validity
electrochemical
of
cells
K-beta-alumina
using
high
for
electrolytes
temperature
thermodynamic
measurements is therefore shown by the following facts:
-
24
-
In
transference
The
1.
potassium
of
number
in
ions
K-beta-alumina is essentially unity.
Platinum-sulfate
melts,
platinum-silicate
melt
2.
platinum-carbonate
electrodes
and
melt,
K-beta-alumina
with
electrolytes are reversible.
K-beta-alumina electrolytes have
3.
been
used
over a wide
0
range of K=O activities at temperatures up to 1100 C
the
compares
obtained
results
favorably
and
that
with
published in literature.
2.2 Activities in Alkali Silicates.
the
In this section
measurements of the alkali activities
The section is divided into 3
in silicate melts are discussed.
The
parts.
first part covers the
activity
potassium in binary silicate melts, while in
the the activity
measurements
the
second
of
part
in ternary melts are presented.
measurements
binary
The last part covers sodium activities in
and
ternary
melts.
2.2.1 The K 2 O-SiO
system.
This system has been studied by many different techniques.
Some
of
these
vaporization
rate
indirect
are
techniques
In
measurements.
this
like
those
section
techniques and their results will be discussed shortly.
-
25
-
using
these
K=O-SiO=
melts
of
in
lost
when
compositions,
initial
differing
K=O
of
Preston and Turner** measured the weight
maintained at a constant temperature between 11001C and 16000C.
As
They obtained the rate of vaporization from these results.
proportional to the
directly
was
these rates of vaporization
Callow 3 3 used Preston and Turner's results to
vapor pressures,
used
Charles*
in these melts.
calculate the activity of SIO
these vaporization rates and the phase diagram to calculate the
activity of K=O and SiO 2
Both of these
20-8102 system.
in the
appreciable
sets of calculations did not take into account the
amount of PtOm vaporization, created by containing the melts in
platinum boats.
et
Eliezer
potassium
in
contained in a
the
furnace
constant temperature graphite
The vapor was allowed to
the
tube
heating
determined
of
The
cell.
molybdenum
cell
pressure
melt
sample
was
of
was
fitted to a
with a 90 degree angle.
through a small orifice into
diffuse
furnace
the
The
system.
K20-8102
vapor
the
determined
al.0-2H*
and
the
vapor
relative to that of potassium aluminate
pressure
standards,
It was assumed that because
by an atomic absorption technique.
furnace the reaction:
graphite
the
in
conditions
reducing
of
C(graphite) + (KzO) = 2K(g) + CO(g)
took place.
2.1
This caused a concentration of CO of a few percent
which could effect
Eliezer et al.
the
sample
and
lead to a loss of SiO(g).
assumed that this high concentration
-
26
-
of CO had
no effect on these slag samples.
3 7 a0
Plantea
used
The equilibrium
was contained in a platinum cell.
spectrometer.
The
pressure
vapor
the
and
enclosure
mass
Plante et al.
process was:
assumed
the
that
potassium
oxide
2.2
the
takes place by reaction 2.2. If
of
measurements
is
assumption that vaporization
the
to
activities
of
by potassium vapor pressure
susceptible to error due
silicate
capacity to dissolve monatomic oxygen, the
take place according to the reaction:
melt
may
2.3
potential would be lower than
oxygen
the
and
calculated from equation 2.2
some
has
vaporization
K 2 O(soln) = 2K(g) + O(soln)
This would mean that the
with a
vaporization
predominant
determination
the
mass
a
negligible.
was
K=O(soln) = 2K(g) + 1/202(g)
It should be noted that
vacuum
calibrated
a vacuum the vapor pressure of PtO 2
in
a
Because the measurements were
gravimetric Knudsen measurement.
made
was
inside
with
determined
spectrometer
gas
into
orifice
small
to
melt
The
system.
measure the potassium vapor in the K 2 0-0SiO
the cell was sampled through a
spectrometer
mass
cell
Knudsen
a
activity. of
K 20
thus
calculated would be on the high side.
activity
Steiler*-**' measured the
system
by
using
a
thermogravimetric
-
27
-
of K2 0 in the K20-SIOa
method.
The
method
flow of CO-CO-Ar at a
a
involved equilibrating the slag with
of
fixed Oxygen potential and determining the rate
the sample weight at a given gas flow
rate
In
change
the oxidation
and
degree of the gas.
Frohberg et al.4
used the concentration cell:
Pt, 0=(1 atm):xK2O,ySiO2::0.214K0-0.786SiOa:Oa(1 atm), Pt
to measure the activity of SiOm in the K2O-SiO2 system relative
to
the
in
activity
the
mole
0.786
%
KaO melt.
In
measurement it was assumed that the transference number of
the
is
assumption
This
unity.
is
potassium ion in these melts
this
reasonable for acidic melts.
As mentioned in Section 2.1.2 Shigematsu
recently used the electrochemical cells:
and
Elliott*b
Pt,SO 2 (g)+0 2 (g)(lata):K-beta-alumina :0.214K 2 0-0.786SiO 2 (1),air,Pt
K=SO4*
and
Pt, CO(g)+COa(g)(I atm): K-beta-alumina :0.214K20 0.786SiO 2 ,airPt
K=CO=
to measure the activity of K20 in the 0.214
with respect
to
pure
K=CO=
and
KSO..
K20
mole
They
melt
measured
the
activity in the rest of the system between compositions 0.214
and 0.50 mole% K=O with the following concentration cell:
: K-beta-alumina :xK20-(1-x)SiO,
Pt, air(i atm)
0.214K20-0.7865102:
Determinations
was
a
over
made
-
28
-
temperature
air, Pt
range
of
950(T(1100C. They found a non-linear variation in log anao
with composition. Chou and Elliottal" used a similar cell:
Pt, air(i atm)
K2 0.SIO 2
K-beta-alumina :zK=o-(1-x)SiO=, air, Pt
the
to determine
They
system.
:
activity
of
the
in
calculated the activity in
reference melt using the Free
JANAF
K20
their
K=O-SiO=
metasilicate
of Formation data of the
Energy
experienced
They
Tables*.
Thermochemical
binary
some
difficulties in using this reference melt for reasons that will
be discussed in chapter 6.
Fig 2.3 gives results of some of
was discussed,
for
the
the activity of SiO
2
investigations
that
at 1100 0 C. In Fig 2.4
some results are given for the activity of K20. The activity of
K2 0 in the binary K20-SIO 2 system as measured
about one
order
of
by Shigematsu is
magnitude higher than that of Charles and
about three orders of magnitude higher than the values reported
by Steller and Chou.
2.2.2
Ternary
and
higher
order
silicates
containing
notassium oxide.
Activities in higher order
many people
systems
using different techniques.
determinations will be presented.
-
29
-
have
been measured by
In this section these
I-M
MMMMWM
0.6
0.5
0.O
0
N
0.3
0.2
0.5
0.8
0,7
05
0.9
XSi02
----
CHARLES
SHIGEMATSU
--
Fig.
2.3
+
ELLIOTT
FROHBERG
Summary of measurements of SIO= activity In the
K=O-SiO= system at 1100 C. The standard state
of SiOm is pure solid cristobalite.
-
30
-
-7
-7-
I
,
-8
-9
/
Charles
-10
Shigematsu
+
Elliott
-
-1l
Steiler
-12
0
7-,
z7
0
- PIante
-14
Chou +
Elliott
-15
-17
-18
20
40
30
50
XK2 O x100
Fig.
2.4
Summary of measurements of KaO activity in the
KIO-S iO= system at 1100 C. The standard state
of K=O is pure liquid K=O.
-
31
-
He
K=O-CaO-SiO=-AlO.-MgO systems.
CaO-MgO-Al2O=-SiO=
was
2.1.1.
section
in
described
as
method
Langmuir
same
the
used
in
oxide
potassium
of
activity
the
determined
also
Steiler=O
system
KO-SIO=
In addition to his work on the
Melts
of
of
K=O
studied with variable amounts
added.
The activity of K=O was found to be proportional to the
square
of
constant
at
the weight fraction of K=O added, and
basiscity (Wt % CaO + Wt % MgOJ/ Wt % SiO= and concentration of
K=O, the activity of K=O decreases as CaO is replaced by MgO.
Eliezer et
al. 4 2 used the same atomic absorption technique
vapor
as described in section 2.1.1 to determine the potassium
pressure
over
coexisting solid phases in
3
of
sets
3
diagram.
alumina rich region of the ternary phase
in
reported
information
this data as well as
the
used
They
literature
on
compounds in the system and the phase diagram, to represent the
activity coefficients of all components in the liquid phase
by
empirical equations.
Belton et al.
technique
to
43
-4
the
study
Knudsen-cell mass spectrometer
a
used
thermodynamics of mixing
silicates in the NaaO-K=O-SiO= system at the tetra-,
meta-
silicate
K=O.xSiOz
Mixtures
compositions.
of
binary
of
di-,
and
Na=O.xSiOm
had slight positive deviations from ideality
and
(where
ideality means that the free energy of mixing of the two binary
due
to
silicates
is
cations).
It was found
the entropy of
that
-
mixing
of
the
addition of 15 mole % CaO to
an
32
random
-
the metasilicate reduced the positive deviation from ideality.
Gaskell
and
the
of
depressions
the
measured
Suito'*
freezing temperatures of NaF and KF by additions of 3M=0.2SiOm,
They
of NaF and KF with
activities
calculated the variation of the
solutions studied were limited
The
the liquidus compositions.
M = Li, Na and K ).
(where
M2O.SiO 2 , MIaO.2SiO= and SiO 2
to the fluoride rich corner of the ternary system.
2.2.3 Sodium and lithium silicate systems.
in
this
section,
in these systems are summarized
studies
The most relevant
in
rest of the studies listed
the
and
a
table.
Charles* 4 used the
4
made by Preston and Turner* *-*
to calculate
the
rates of vaporization
of
measurements
and the binary
activities of Na=O and LiMO, and SiO
respective Na&O-SiOm and Li=O-SiOm binary
to Charles the activity of the
negative
deviation
from
same
for
component
an
an
in the
According
systems.
shows
alkali
ideality
cationic radius of the basic
Callow== used the
diagrams
phase
increase
increase
in
in
the
[r(K+)>r(Na+)>r(Li+)J.
measurements to calculate the activity
of SiO= in these systems.
in
Table 2.3 lists other studies
methods used.
-
33
-
these
systems
and
the
TABLE 2.3
LimO-. Na=0-SiOm Solutions Studied.
System
:
Na=O-SiOm
:
Reference
.wW
---------------------------------------
Method
------ -----
4
3
Callow
and
Charles
Calculations
Turner-*
and
Preston
rate
Vaporization
3
4
CO
Pearce**-'
solubility
2
measurements
5
al.
et
Argent
mass
cell
Knudsen
-
Hallerm*-"*-
and
Sanders
Transpiration
*
spectrometer
of
Solubility
SEmf
Eaf
-
--
--
Holmquist""
SO
-
-
-
-
-
cell
cell
(Beta-Al
2
Oa)
Vaporization
-
--.
.
rate
34
-
.
.
.
.
.
al.**
Jokokawa
et
al."
Neudorf
and
Elliott
DeYoung
and
Elliott*
Preston
and
M--------------
Callow"
-
.
et
Charles=*
Calculations
.
Frohberg
---------
----------------------------LiO-SiOm
Soerstroem"
and
Kroeger
effusion
Knudsen
Turner*7
.
.
.
.
7
2
=
.
.
.
CHAPTER 3.
OUTLINE OF RESEARCH.
The activity
of K=O in the K=O-SiO=-Al 2 O= and K2 0-SiO-CaO
with
systems in oxygen was measured
potassium-beta-alumina
a
employing
potassium-beta-alumina
an
cell
electrolyte.
The
for
this
solid
manufactured
specially
was
electrochemical
from commercially available soduim-beta-alumina
experiment
This method for
an ion exchange of the sodium with potassium.
the
measuring
activities
it
has
recently
electrolyte
can
be
because
demonstrated
been
solid
temperature
binary
The
thermodynamic measurements in silicates.
selected
that the
high
for
used successfully
was
oxide
potassium
of
by
K=O-SIO=
in the ternary
system was used as reference for the cells
fields. The following electrochemical cell was used:
where the ratio of K2 0 to SiOm is the
ternary melts and XX
Al=O=
designates
measurements in this study
K2 0-SIO
Om(g), K=O, Pt
(KAO-nSiO=-XX)
Ternary
II
potassium beta - alumina
Pt, OM (g), K=O
(K2 0-nSiOm)
Binary
was
with
same
or
-
35
-
CaO.
respect
system as a reference, any set of
activity of K=O in the binary K=O-SiO
for the binary and
to
Because
the
the
binary
measurements of the
system,
as presented in
Fig 2.4, can be
used
to
calculate the activity of KaO in the
ternary melts.
the oxygen
and
ranges,
The composition
and
temperature
potentials at which
the
measurements were made are summarized
in table 3.1. The specific
ternary
shown on the ternary diagrams7"
K2 0-SiO=-AlO
and
in
composition
figures
systems
KO-SiO-CaO
measured
3.1
were
and
are
3.2.The
investigated
because the components of these systems are present in the iron
from
blast furnace and thus melts
these systems could form in
the furnace.
Table
3.1 : Scope of experimental measurements
Composition
range
mole%
System
Temperature
range
degreec
:
:
:
Oxygen
potential
(Pom), Atm.
--------
-------------------------
21-50
K=O-SiO-A120
K=O
K=O-SiO=-CaO
950-1100
1
950-1100
1
Al.O.
0-6
50-79
SiOm
25-42
K=O
CaO
0-12
75-75
SiOm
---------
---------------------
-
36
-
O/
80
T
v
70
v7\
50
60
V
40
\70
30
W/O SiO 2
Fig.
3.1
Port ion
diagram.
symbol x.
of
K=O-SIO=-A1=O=
ternary phase
Compositions studied are denoted by
-
37
-
0
0
0
L20O0
K20CaO-6SiO2
60
K2 0 SiO 2
W/O SiO 2
Fig.
3.2
70'\
S0
K20 -4SiO2
Portion of K=O-SiO=-CaO ternary phase diagram.
Compositions studied are denoted by symbol x.
-
38
-
CHAPTER 4.
EXPERIMENTAL.
silicate melts in
The activity of K=0 has been measured in
an oxygen
atmosphere.
In this chapter the experimental method
used in this study is presented and discussed.
divided into four parts.
The
first
part
The chapter is
covers
theoretical
aspects of the electrochemical cell used for the measurements.
The
second
part covers
part presents the design of the cell.
the
computer while,
acquisition
The
third
of data and control by the Apple
in the fourth and last part, the procedures for
electrochemical cell preparation is discussed.
4.1 Theoretical Considerations.
In this section the theoretical rationale of the experiment
is presented.
4.1.1 K2O-Si0g-Al0:. System.
Measurements of the activity of KaO in alumina-silicate
melts have been obtained with the following cell:
Pt, Oa, K=O
K=O-nSiO2
Binary
III
PotassiumBetaAlumina
-
39
-
:
:
Oa, Pt, K=O
K2 0-nSiO 2 -Al2 Om
Ternary
2
The anodic half-cell reaction is:
(KaO)x
===)
( IV-1 )
2K* + (1/20=)z + 2e-
and the cathodic half-cell reaction is :
2e- + 2K* + (1/20=)zx ===>
where (1/20a),
of
The transfer
cathode.
at the
electrolyte may be written as :
equations
Summing
reaction:
yields
(IV.2)
and
the
through
potassium
IV.3 )
(
2K+ (Beta-alumina, II)
(IV.1)
)
anode and (1/20)zz is oxygen
the
is oxygen at
2K* (Beta-alumina, I) ===)
( IV.
(KaO)zx
the
overall
( IV.4 )
(KO)
1 + (1/20)zz ===> (KaO)zz +(1/20=)x
for which the free energy change is given by the equation:
.
awma3xz
(Pom.)"
G = -nFE = -RTln[ ---------------------awan.,
The oxygen potentials
at
(
I
(Po=.zx)z-a
.
the two electrodes were established,
and were made to be equal; thus the last ratio
equation 4.1 is I and equation 4.1 becomes:
R is
the
In the term of
asa=.zx
2.303 RT
E --------2 F
4.1 )
---------aica. z
--
4.2 )
1C
gas constant and F is the faraday constant.
potential
temperature T and the reversible
measured during the experiment.
-
40
E of the cell were
If the activity of
-
The
K2 0 in the
known
binary reference melt anor.z is
ternary
melt
a<c3.zx
K=0
measurements of the activity of
system, as
Any
calculated.
be
can
the K=O activity in the
in
the
binary
of
set
K=O-SiO=
in Fig 2.4, can be used to calculate the
presented
activity of K=0 in the ternary melts.
the values for
Although
log avm= as measured by Shigematsu et al=' is higher than those
of the
other
their data for the binary reference is
studies,
used in this study because:
1.
The method Shigematsu et
al.
measuring
the
direct way of
K20-SIO 2 system.
Their
used
represents the most
activity
method
is
of
the
in
K=O
discussed in section
2.1.1.
2.
The free energy
of
formation of the meta-silicate using
their data correspond to within 12 kJ/mole (+/-4.7 %
of the value given in the JANAF Thermochemical Tables**.
The cell configuration used by Shigematsu et al.
less
This is discussed in chapter 6.
prone to systematic errors.
Shigematsu and Elliott
is
the activities in the binary
found
silicate melts relative to the pure solid silica to be:
-
41
-
Composition
Log A(KO)
70 Wt% SiO
-16890.24/T + 0.3670
65 Wt% SiO3
-16990.49/T + 1.511436
56.06 Wt% 8102
-15538.74/T + 1.59214
47 Wt% SiO
-14495.02/T + 2.251773
38.95 Wt% SiO 2
-12435.44/T + 2.25034
The least square linear
fit
these data can be seen in Fig
of
4.1.
4.1.2 KgO-SiOm-CaO System.
The cell was
the
essentially
same
that
KO-SiO-Al=Om system, except
the
as
the
cell for the
binary reference melt
and the ternary working melt were reversed
so that the sign of
equation 4.2 is positive.
4.2 Cell Design.
Figure
4.2
shows
a
experimental arrangement.
schematic
diagram
of
the
general
The potassium-beta-alumina crucibles
were prepared according to Appendix A.1.
It was shaped in the form of a long thin crucible,
I.D.
by
11 mm O.D. by 55 mm long, and attached to an
tube ( Coors AD-99), 6.4 mm O.D.
by
Autostick
cement
(
by
Carlton
England). The inner electrode was a
dia.), that was sheathed
in
-
7.5
mm
alumina
4 mm I.D. by 650 mm long,
Brown
and
platinum
Partners
wire
(
Ltd.,
0.5
mm
a
3.2 mm O.D. by 1.6 mm I.D.tube
42
-
-6
50.00 M/
-7
K2 0
0
-8k
0
43.8
41.4
-9k
0
0
0~2
-1o
25.60
-
II
-12
21.46
I
7.0
Fig.
4.1
I
7.2
7.4
7.6
104 /T
,
I
I
I
7.8
8.0
8.2
Absolute activity of K=O in binary
melts. (Shigematsu and Elliott)
-
43 -
silicate
123
6
45
7
I AIR IN LET ALUMINA TUBE
7 AIR INLET ALUMINA TUBE
2 PLATINUM ELECTRODE
8 PLATINUM HOOK
3 AIR OUTLET ALUMINA TUBE
9 AUTOSTICK CEMENT
4 THERMOCOUPLE PROTECTION
TUBE
5 PT - PT(1O96 RH) THERMOCOUPLE
10 PLATINUM CRUCIBLE
II K 2 0-SIO2 REFERENCE MELT
I2TERNARY WORKING MELT
6 PLATINUM ELECTRODE
I 3 POTASSIUM-BETA-A LUMINA
Fig.
4.2
Schematic diagram of experimental
measurement of cell EMF in oxygen.
-
44
-
system
for
inlet tube.
The platinum electrode
of
electrolyte by the combined weight
against
the
and
the
platinum
the
The external melt was contained in a platinum crucible
tubing.
shape
in the
diameter
high.
pressed
was
oxygen
an
as
served
(Coors AD-99). This alumina sheath also
at
This
the
of
of a cone, 35 mm and 25 mm in
frustrum
31
the top and the bottom, respectively, and
ma
platinum crucible served as the external electrode
and electrical contact was made at the rim of the crucible with
tube.
a 0.5 mm platinum wire held in place by an alumina
solid
electrolyte
was
bottom
the
against
pressed
The external
melt
was
by
20
through
it
columns
of
anhydrous
perchlorate and calsium sulfate and then forced down
inlet tubes.
weight.
above
mm
The oxygen (supplied by Ohio Gas Products) was
passing
the
supplied with oxygen by another 6.4 mm
I.D. alumina tube, positioned approximately
melt.
its
by
platinum crucible manually and was held there
of
The
The cell temperature was measured by a
the
purified
magnesium
both
the
sheathed,
Pt-Pt/10% Rh thermocouple, positioned just above the surface of
the melt contained by the platinum crucible.
(51 mm I.D. by 57 mm O.D. by 500 mm
water-cooled
brass
electrochemical
cell
The
assembly.
was
long),
allowing
end-cap,
The furnace
fitted with a
alignment
platinum
tube
of
crucible
the
was
positioned in an alumina crucible and lowered into the vertical
alumina furnace tube,
contained ports
bubble grain alumina.
onto
The end-cap
with Wilson seals through which the electrical
leads, a gas exhaust port, and the sheathed
-
45
-
thermocouple
were
admitted to the furnace tube.
The furnace tube was heated by 6 silicon carbide resistance
a
by
was controlled
The furnace temperature
corporation.
rods supplied by Kanthal
Leeds and Northrup SCR Power Package and
Electromax current-adjusting-type controller.
the
was
controller
a
of
emf
The input to the
thermocouple,
Pt-Pt/10%Rh
positioned with its hot junction next to the heating elements.
controlled
The furnace temperature was thus
degree
C
.
The
profile
temperature
determined with a separate Pt-Pt/10%
Rh
of
+/-
about
to
was
furnace
the
and
thermocouple
1
is
given in figure 4.3. The electrochemical cell was positioned In
the
hot
(
zone
within
mm
1 degree C, approximately 50
length) near the bottom of the furnace.
in
This was sufficient to
ensure that the entire electrochemical cell
at
was
the
same
approximate temperature.
4.3 Measurement and control of the experiment.
of
Measurement and control
computerised.
the
experiment was completely
This allowed:
-
More data to be recorded on a 24 hour basis.
-
More
consistent
repetition
of
the
same
sampling
techniques.
-
The
use
of
routines, data storage,
plotting
transfer between computers.
-
46
-
and
data
0
%-0
Li
:2
0
1
2
3
4
7
6
5
8
9
10 11
12
13
POSITION FROM BOTTOM (cm)
Fig.
4.3
Temperature profile of SIC furnace
taking measurements.
-
47
-
used
for
This section is divided into two parts.
the
hardware
computer
the
describes
part
second
the
and
first part covers
The
that was set for the
software that was used and the conditions
equilibrium to be attained.
4.3.1 Computer Hardware.
description of the computer and peripherals is
A schematic
given in Fig 4.4. An Apple
and
II+
Isaac
data
computerised
This system consists
acquisition and control system were used.
of an Isaac 41A expansion box that is installed into one of the
Apple's
expansion
slots and provides four
additional
slots.
The potential of the electrochemical cell was measured with
analog to digital Isaac
slot number
was 100
Ohms
I-100
an
module, installed in
convertor
the 41A expansion box.
The input impedance
and the resolution 0.25 mV.
The average of 1000
of
0
measurements taken over a period of 10 seconds
one reading of the potential.
regularly with both
a
was accepted as
This cell potential was
Model
Beckmann
checked
No. 071 pH meter and a
Leeds and Northrup Model 778742 potentiometer, and agreement to
within 0.5 mV was always obtained.
The
potential
of the thermocouple was
measured
Isaac 1-130 Preamp interface board installed in slot
with
number
an
2
of the 41A expansion box and an Isaac I-140A isolated low level
Preamp
System.
The
is a single
1-130
channel
differential
analog input module featuring cold junction compensation for K,
-
48
-
Fig.
4.4
Computer peripherals used for
control of the experiment.
-
49
measurement
and
J,
and
of
types
T
input
The
thermocouples.
offset
calibrated to correspond with the Beckmann pH meter reading
curve is
thermocouple
the
Since
the thermocouple potential.
was
of
response
linear in nature, a polynomial fit to relate the
not
thermocouple output to the temperature was used:
8.739*10-OV4
T = 79.484 + 103.49V - 0.7810V 2 + 0.0526V" -
( 4.3 )
+ 3.43798*10-*Vw
temperature
reading
Northrup
model
accurate
to
within
I
+/-
and
potentiometer
778742
no.
by
regularly
checked
was
C.
degree
thermocouple and the electrochemical
C.
The
a Leeds
and
degree
0.61
was
temperature
the
The resolution of
found to
Connections
conductor shielded cables to prevent external
the
made with two
were
cell
to
be
electro-magnetic
interference.
Computer control
Electromax
the
of
furnace
setting was
achieved with an Isaac I-120 binary output module installed
slot number 1
of
the
channels were used to
mechanically
connected
expansion
41A
electronics
involved
DC
volt
motor which was
setting
of
the
more detailed description of
A
included
is
Signals from two
box.
temperature
the
to
Electromax furnace controller.
the
5
a
control
in
in
Appendix
B.
The
temperature setting of the electromax controller was programmed
to within +/- 10 degree C.
-
50
-
4.3.2 Comouter Software.
The Isaac unit is provided with "Labsoft", an extension
accumulate
data
the temperature of the electrochemical cell.
This
to
was written using both of these languages
and control
program
A
the "Applesoft" language of the Apple II+ computer.
of
A short description of the
C.
program is included in Appendix
program is given here.
The program was compiled out of smaller programs written to
test the different
units described in section 4.3.2.
hardware
every 5 minutes, and the
The potential of the emf was measured
to within +/- 1 mV
and
to have been reached.
assumed
minutes, equilibrium was
over a period of 30
C
1 degree
+/-
When it stayed
minutes basis.
30
readings were compared on a
equilibrium was attained the Electromax controller
setting
was
temperature
After
temperature
The
required
setting of the Electromax, the tolerance
required
changed
for the potential, the
required within the
to
the
next
temperature,
was
tolerance
setting.
as
set
well
at
as
the
the
period
start of the
program.
4.4. Procedure.
Experimental procedures used for the
electrochemical
cell
assembly and the general behavior of the cells are described in
this section.
-
51
-
dehydrated silicious acid
as described in Appendix D.
(SiOm),
the
to
dessicators
in
stored
were
melts
Prepared
the
Appendix
in
chemicals used in preparing these melts are given
E.
of
specifications
The
composition.
reference
line
or
Ternary working melts were prepared by adding alumina
to
and
carbonate
potassium
of
quantities
weighed
carefully
fusing
by
prepared
were
melts
reference
binary
Five
prevent
hydration. The compositions of the binary reference melts and
ternary working melts are given in table IV.I.
TABLE IV.I
COMPOSITIONS STUDIED IN THE K=O-SiO=-Al=Om OR CaO SYSTEM
Working Melts (Ternary)
Wt % Added to ref. Composition
: Working Melt 1 : Working Melt 2
: Wt% CaO
: Wt% Al O.
Reference Melt (Binary) :
:
Ratio*
Wt % SiOM
SiO=
K2 0/0
4, 8, 12
: 2, 4, 6
4, 8, 12
2, 3.5, 4.8, 6 :
4
: 2, 4, 6, 8
47.0
I 1, 2, 4
38.95
-~----------------------------------------65.0
57.2
0.5385
0.7838
1.1277
1.5677
*by
weight
in
1350K
in
down
cool
to
cemented
least
The
12
prefused
the
an
hours
in
an
the
and
tube
alumina
tube
evacuated
-
52
cement
-
slowly
to
allowed
to
was
crucible
was
allowed
to
dry
"Anhydrone".
containing
melt
binary
reference
and
K-beta-alumina
the
Next
furnace.
heated
melt
the
re-fuse
to
furnace
muffle
a
was
crucible
The
crucible.
K-beta-alumina
the
to
charged
and
crushed
was
melt
working
ternary
Prefused
at
2, 4, 6, 8
70.0
0.4286
a...................
--------------------
----------------
------
was
crushed,
the
powdered melt was charged to the platinum crucible and re-fused
in the muffle furnace at 1350 K. The crucible with its melt was
allowed to cool and then was connected at its rim to a sheathed
connecting
platinum
wire.
The
was
furnace
brought
to
temperature and the crucible assembly was lowered stepwise into
the furnace within the
tube
was
closed
alumina
larger
with
the
The furnace
crucible.
water-cooled
beta-alumina crucible was suspended from
brass
the
positioned near the top of the furnace tube.
head.
brass
The
head
The
and
beta-alumina
crucible was lowered into the furnace in steps at over a period
of 20 minutes, until it was 1
melt.
of
the
Next the binary electrode platinum wire and sheath,
the
oxygen supply alumina tube
into
position.
cm
and
above
the
the
thermocouple were lowered
After allowing approximately 15
thermal equilibrium to
be
reached,
was dipped into the melt and the
the
The oxygen flow rates
approximately I and
respectively.
connections
experiment were made.
was initiated
for
inner electrode was forced to
over the binary and the ternary melts were
Next
minutes
the beta-alumina crucible
the bottom of the beta-alumina crucible.
10 al/min, STP,
surface
and
the
computer
and
the
The data acquisition and control program
after
equilibrium point was
between
approximately 1 to 3 hours the first
recorded.
Then the program initiated a
change in temperature of 20 to 30 degree
reached within I to 2 hours.
To
-
53
C
and
stability was
test the reversibility of the
-
results correlated well and within
cases
In all
temperature.
cell
electrochemical
the
increasing
and
decreasing
several temperatures while
at
taken
potential, readings were
the apparent uncertainty of a measurement.
a
to
cell
a
of
response
The
temperature
illustrated in Fig. 4.5. Time to reach equilibrium
and
hour
the
as
equilibrium value to the second
the
was about 1
from
smoothly
moved
potential
is
change
temperature
the
first
changed.
Cell failure occurred after about 36 hours.
4.5 Galvanostatic reversibility test of the electrochemical
cell.
To test the reversibility of his sodium-beta-alumina cells,
cell.
between the electrodes of the
current
Neudorf"* passed a 3 mA
A similar test was done on one of the cells used in this
study.
A 3 mA current was
about
20
seconds,
The
potentiostat.
using the computer.
passed
using
a
Wenking
(model
no.
In Fig 4.6 the potential change is plotted
it can be seen that the cell had a
very large IR drop, in the order of 1100 mV compared
100 mV in the sodium-beta-alumina cells ran
corresponds
to
TSI)
70
cell potential was measured every 5 seconds
From Fig 4.6
against time.
between the cell electrodes for
by
to
-
54
-
This
Neudorf.
a cell resistance of 367 Ohms compared
Ohms for Neudorf's cells.
about
to
33
Lii
LJ
TIME (MIN)
Fig.
4.5
Example of the response of cell potential to
was
tempe rature
The
temperature changes.
to
the dashed
changed at times corresponding
lines.
-
55
the
of
Therefore the large difference in cell
potassium-beta-alumina.
have
should
resistance between this study and that of Neudorf
In Appendix A it is shown that the ion exchange
been expected.
is
215
conductivity
conductivity
the
than
higher
times
a
has
crystals
sodium-beta-alumina single
25=C
at
that
seen
be
can
it
2.1
Table
From
satisfactory
another
resistance is
cell
high
this
and
indication that the ion exchange is indeed sufficient.
A much lower current of about 0.3 mA is therefore needed to
test
the
current.
test
could
repeated
be
not
on
limit
potassium-beta-alumina.Due to a time
polarization
cells
electrochemical
of the
reversibility
As Fig. 4.6 shows, the cell
using
this study the
using this
lower
decreased
potential
to
within 20 mV of the original value in about 30 seconds and then
slowly decreased to
hours.
its
value
original
a
It is thought that using
over
lower
will significantly decrease the time needed
return to its original
potential.
cycling did result in reproducable
a
polarizing
for
Nevertheless,
results,
period of 2
the
current
cell
to
temperature
so that it can be
confidently stated that the electrochemical cells in this study
were reversible.
-
56
-
(20o
1000-
800-
600
>
400-
200-
3mA
Applied
0
20
40
60
80
100
10
140
IE
TIME (SEC)
Fig. 5.6
Polarization test of the electrochemical cell.
A constant current of 3 mA was applied across the
electrodes of the cell.
-
57
-
CHAPTER 5.
RESULTS.
part
first
The
parts.
This chapter is divided into two
contains the results for the KzO-SiO=-Al 2 .O system and the last
part the results for the K=O-SiO=-CaO system.
5.1 K=O-SiO -AlOm system.
The values of log awaa in the
calculated according
raw experimental
The
4.1.
equation
to
measurements are given in appendix G. The results
Figs. 5.1 to 5.5.
were
system
KzO-SiO-Al1O
are shown in
Each of these figures gives the results for a
each figure represents the activity
in
the
line
solid
The
particular molar ratio of X(K2 O)/X(SiO).
binary
in
reference
melt and is taken from the results of Shigematsu and Elliott='.
The
lines
state for K=O is the pure solid.
standard
are
coefficients
through
drawn
the
data
and
the
their standard deviations are
and
square
Least
square
least
tabulated
in
Table 5.1.
The partial molar enthalpies of mixing,
calculated using the van't Hoff equation:
Hl,
of
K=O
were
d(log as)
for 1000<T(11OOOC
H" = 2.303R --------- = 2.303RA&
(5.1)
d(1/T)
A, is the least
square
of the plot of log awm
slope
-
58
-
against
the reciprocal of the temperature (Table 5.1).
The partial molar entropies
using the equation:
were calculated by
mixing
of
H" - G"
S M =--------=
-
(5.2)
2.303RB*
T
intercept from the plot of log a,
where B, is the least square
against
entropies
and
The partial molar enthalpies
1/T.
of
mixing are given in Table 5.2.
The effect of AlzO= on
by plotting
the
activity of K2 0 is Illustrated
change in log auca= versus the amount of AlmO=
the
as shown in
added to each of the binary silicate compositions,
Fig 5.6 for 1100 C. There is a considerable scatter in the data
decrease in the activity of K=O
this
though
even
in a
results
clearly
shown in Fig 5.6, but addition of AlO
effect
is
small.
The solid lines in Fig. 5.6 were drawn to aid interpolation
of
interpolated
These
log aa= at intermediate compositions.
values are plotted as iso-log aua= lines, as shown in a portion
5.7. The phase diagram of
of the ternary phase diagram in Fig.
in
this ternary system is unknown
the higher KaO regions.
the part of the phase diagram that is
field
extends
measurements
field.
to
were
In the part
about
7 mole %
Al=O=
liquid phase
the
known
and
therefore
limited to compositions within
where
the
-
59
size
-
of
the
In
this
the
phase
liquid field is
unknown no crystallinity was observed in the solidified melt so
that the melts were either stable or metastable.
-
60 -
-1
I
-
-
I
-
I
-
I
0
C\J
0
0
-I
--
-
-
I
I
13.1
7.4
7.6
7.5
I/ Tc
x
Fig.
5.1
7.7
7.9
8.0
4(K 1)
Experimental results for
in the
log
K=O-S I O-A l.Om system for
melts
for
which
X.MaO/XWa1La
0.273. Solid
=
l ines
esents
repr
results for the binary potassi um si 1 icate taken
from Fig 4.1(Shigematsu and Elliot t). Standard
state is pure solid K=O at I atm. pressure.
- 61
-
-I
-I
A-
-
1.0
I 1.1
-1 1.2
-I1.
0
-1 I.E
-Il
-1 1.7
-ll8
7.4
7.5
I/T X 1O4 (K~1)
Fig.
5.2
Experimental
KJ0-SIO-Al= 0
XgC=W/XWaaj
=
results for
system for
0.344. Solid
log anca in the
melts for which
lines represents
results for the binary potassium silicate taken
from Fig 4.1(Shigematsu and Elliott). Standard
state is pure solid K=O at 1 atm. pressure.
-
62
-
-
Z.9L-
722
73
74
7.5
7.6
77
78
79
8.0
l/T x 104 (K~1 )
Fig.
5.3
Experimental
KaO-SiO=-Al=O=
results for
system for
log ao<aa in the
melts for which
=
0.490. Solid lines represents
results for the binary potassium silicate taken
from Fig 4.i(Shigematsu and Elliott). Standard
state is pure solid K=O at 1 atm. pressure.
X.<a/Xwca
-
63 -
-
a3
-8,5
-8,6
-8.7
0
-89
0
-J
-9,
-9 2
-Q 3
i /T
Fig.
5.4
X 10 4(K~ )
Experimental results for log awaa
in
the
K=O-SiO=-AlaO= system for
melts for which
Xscaa/Xmao" = 0.719. Solid lines represents
results for the binary potassium silicate taken
from Fig 4.1(Shigematsu and Elliott). Standard
state is pure solid K=O at I atm. pressure.
-
64
-
0
8
I/T x 104 (K~')
Fig.
5.5
Experimental
K=O-SiO=-AlO
Xjc=z/Xc3a=
=
results for
system for
1.000.
Solid
in the
log a4a=
melts for which
lines
represents
results for the binary potassium silicate taken
from Fig 4.1(Shigematsu and Elliott). Standard
state is pure solid K2 0 at 1 atm. pressure.
-
65
-
MOLE /o A- 0-
XK2
XK2 0
1/Xi02 0.273
S 0 2 =Q344
4
zo,
fJJZ
XK20 /XS iO2 =0.490
0
0
'2,
0
0
-I
X K2 /XSO=.
II
9
0
C!
0
0
-J
4
XK2O / XS0 =.00
0).1 0L-
0.12 r0. 4
Fig
5.6
The activity of K=O in the K=O-SiO-AlzO=
system along pseudo-binary lines of constant
ratios of X.<a/Xmtaa at
1100 C. Standard state
is pure solid K=O at 1 atm. pressure.
-
66 -
S
9
T=- 1100 C
To A12 03
9 r-N
KAISi 04
KAISi206
0
L iq
0
13.5
-6.5
0
15
2
25
30
40
45
50
55
5 5
,V-
m/o K2O
Fig. 5.7
Interpolated iso-activity lines for KaO in the
K=O-SiO=-A1 2 0. system at 11003C.
Lines drawn at 0.5 intervals of log a.<=a, from
-6.5 to -13.5. Standard state is pure solid KzO at
1 atm. pressure.
-
67
-
40
60
TABLE-5.1.
LEAST SQUARES COEFFICIENTS FOR LOG awao = A/T + B
WITH STANDARD DEVIATIONS FOR MELTS
IN THE K 2 0-A12 O0-SIO2 SYSTEM
S(log akwan)
A
B
0.0133
0.0268
0.0405
0.0544
-17031+193
0.0192
-16796+201
0.390+0.148
-0.115+0.232
0.272+0.089
0.232+0.152
0.344
0.0136
0.0273
0.0554
-17198+205
-17262+133
-17010+102
1.618+0.157
1.656+0.102
1.468+0.078
0.0211
0.0157
0.0111
0.490
0.014
0.025
0.034
0.043
-16089+78
-16363+82
-15455+196
-15656+301
1.915+0.060
2.082+0.062
1.464+0.149
1.606+0.232
0.0065
0.0082
0.0182
0.0217
0.0091
0.0137
0.0040
0.0158
0.0134
0.0199
0.0065
XwM=/Xaxaz
0.273
0.719
1.000
X4a=c=,
-16300+305
-16833+118
0.0147
0.0295
0.0445
0.0596
-14568+141
-14290+152
2.186+0.076
2.295+0.106
2.329+0.033
2.051+0.116
0.0076
0.0152
0.0306
-12468+391
-12558+185
-12606+63
2.079+0.297
2.198+0.143
2.259+0.048
-14483+100
-14689+44
0.0259
0.0109
0.0184
S(log acao) is the standard deviation for data for log acxo
about the l ine defined by A and B. Standard state for
Km0 is pure solid K=O at I atm. pressure.
-
68
-
PARTIAL MOLAR ENTHALPY AND ENTROPY OF MIXING OF K=O
IN THE K=O-SiO-A1 2 Om SYSTEM
Xeema/ XMa Ca
H"mecm
X^g mam
8"<
kJ/mole
J/mole
0.273
0.0133
0.0268
0.0405
0.0544
326+4
312+6
322+2
322+4
-7.4+2.8
2.2+4.4
-5.2+1.7
-4.4+2.9
0.344
0.0136
0.0273
0.0544
329+4
330+4
326+2
-31+3.0
-32+1.9
-28+1.5
0.490
0.014
308+1
-37+1.1
0.025
313+2
-39.8+1.1
0.034
296+4
-28.0+2.8
0.043
300+6
-30.8+4.4
0.719
1.000
0.0147
277+2
-41.9+1.4
0.0295
0.0445
279+3
281+1
-43.9+2.0
-44.6+0.6
0.0596
274+3
-39.3+2.2
0.0076
239+7
-39.8+5.7
0.0152
240+1
-39.8+5.7
0.0306
241+1
-43.3+0.9
-
69
-
5.2 Ka0-SiO -CaO
system.
l/T in Figures
system, given in appendix H, is plotted against
As
5.8 to 5.10.
KO-SiO=-Al=O=
the
in
for
figures gives the results
The
XumI/Xmaaa.
Shigematsu
and
lines
solid
molar
represents the binary
The
Elliott.
each of the
system,
particular
a
K=0-SiO=-CaO
the
in
K=O
The calculated activity data of
coefficients
and
ratio
of
data
of
standard
Figs.
deviations of the least square lines represented in
5.8
to 5.10 are given in Table 5.3.
The
thermodynamic mixing properties were calculated as
in
section 5.1 and are tabulated in Table 5.4.
of K=O is illustrated by
The effect of CaO on the activity
logarithm of the activity of
Fig 5.11, where the change in the
K=O is plotted
the
versus
amount
of CaO added to the binary
the
There is some scatter in
silicate compositions.
Fig. 5.11, but CaO additions clearly results in
data
of
an increase in
the activity of K(0.
The solid
log ane
at
lines
Fig. 5.11 was used to interpolate for
in
intermediate
values were plotted
as
compositions.
iso-log
awma
These
lines, as is shown in a
portion of the ternary phase diagram in Fig. 5.12.
- 70 -
interpolated
0-1
C\-
3-
7.3
Fig
5.8
74
75
76
7.7
4
VT x10
(K~1)
78
79
8.0
in the
Experimental results for log acc=
for which
melts
for
K=0-SiO-CaO system
XZM/XIaoM = 0.3435. Solid lines represents
results for the binary potassium silicate taken
from Fig 4.1(Shigematsu and Elliott). Standard
pressure.
state is pure solid K=O at I atm.
-
71
-
-9.8
-9(.9
0
-
I
0
-J
I/ T x1O4 (K~1)
Fig
5.9
in the
log apc<=
results for
Experimental
for which
K=O-SiOm-CaO system
f or
melts
Solid
1ines represents
0.490.
=
X,,mo/Xwjc=
results for the binary potass ium silicate taken
from Fig 4.1(Shigematsu and Elliott). Standard
pressure.
state is pure solid K=O at I atm.
-
72
-
-8.3
-8.4
-8.5
-8.6
-8.7
-8.8
-8.9
0
-9.0
0
-9,2
-9.3
7.3
74
75
76
7.7
78
79
60
I/T K 104 (K~ 1 )
Fig
5.10
Experimental
results for
log a.co
in
the
K=O-SiO=-CaO system
for
melts
for which
XPCm/
XWCM= =
719.
Solid
lines
represents
results for the binary potass ium silicate taken
from Fig 4.1(Shigematsu and Elliott). Standard
state is pure solid K=O at 1 atm. pressure.
-
73
-
<0
zj
0
0
Q3
QI
C
XK20/XSO2 =0L719
oa4~-
0.1
0
I
I
I
2
4
6
6
MOLE /
Fig 5.11
'0
12
14
it
CoO
The activity of KAO in the K=O-SiO=-CaO system
along pseudo-binary lines of constant ratios of
X~eaa/X=,am at 1100 C. Standard state is pure
solid K=O at I atm.
pressure.
-
74 -
To CcaO
20
C0
0
5
0
50
45
40
m/o
30
35
25
20
K2 0
Fig. 5.12 Interpolated isoactivity lines for K.O in the
K=O-SIO-CaO system at 1100 0 C. Lines
drawn at 0.5 intervals of log aoem=, from -8.5 to
-11.
Standard state is pure sol-id KO at I atm.
pressure.
-
75
-
15
LEAST SQUARE COEFFICIENTS FOR LOG awan = A/T + B
WITH STANDARD DEVIATIONS FOR MELTS
IN THE K 2 0-1O2 -A1 2 0=
Xgcrao /Xe
1 0:
X A3.
S(log aocm)
0
0.049
0.096
0.143
-16745+123
-16859+49
0.490
0.719
0.3435
SYSTEMS
-15755+169
1.548+0.095
1.518+0.038
0.791+0.130
0.0113
0.0056
0.0178
0.0508
0.0982
0.1490
-14848+160
-14862+80
-14927+180
1.201+0.123
1.225+0.062
1.269+0.138
0.0163
0.0091
0.0088
0.0295
-13892+126
1.856+0.097
0.0137
S(log a(Cam)
is the standard deviation for data for log atsa
about the line defined by A and B. Standard state for KaO is
pure solid KO at I atm. pressure.
-
76
-
TABLE 5.4.
PARTIAL MOLAR ENTHALPY AND ENTROPY OF MIXING OF K 2 0
IN THE K=O-S1O=-A12Om SYSTEM
X^ IZM.
Xum/ Xa cz
---
Hm",ca
kJ/mole
S"*Co
J/mole
---------------------------------- ------------0.3435
0.049
0.096
0.143
321+2
323+1
302+3
-29.6+1.8
-29.1+0.7
-15.1+2.5
0.490
0.0508
0.0982
0.1490
284+3
285+2
286+3
-23.0+2.3
-23.5+1.2
-24.3+2.6
0.719
0.0295
265+2
-35.5+1.9
- 77 -
CUAPTER 6.
DISCUSSION.
This
three
into
divided
is
chapter
K-OSiO2 -Al2O
In the second part, the results for the
study.
first
the data obtained in this
on
section covers an error analysis
The
parts.
system is discussed and in the last section the results for the
system is discussed.
KO-SiO=-Al=mO
6.1 Error analysis.
The analytical expression for log aman is given by equation
4.2 :
2 FE
log amm.zz
= log aw=,z -- ---------
(6.1)
2.303 RT
where asn.,a
the
is
in
activity
the
the binary system and awaka.x
in
is the activity
The error in
system.
ternary
the
calculated values of log anca,zz was therefore be due to:
1.
in
Uncertainty
binary
the
both
ternary
and
melt
compositions.
2.
Random and systematic errors in measuring E and T.
3.
Systematic error in log a.<a, z
Uncertainty
in
the binary and ternary
preparation
melt
arose from random errors in
-
78
melt
-
compositions
and
systematic
error due to potassium-beta-alumina and
dissolution.
platinum
be
Random errors in melt composition were considered to
different
two
for
obtained
data
since
of
runs
small
same
the
compositions showed a small scatter.
to potassium-beta-alumina dissolution
Systematic error due
will result in a continuous shift
examination of
visual
melts
these
the beta-alumina showed that some corrosion had
emf of the
The effect of alumina dissolution on the
occurred.
over
measured
emf
this except in melts with a
of
evidence
the
contents( mole % K=O > 42). In
K=O
high
cell
no
There was
time.
in
is small as will be seen in the next section.
to
difficult
of
All
estimate.
platinum
to
The systematic error due
the
dissolution is more
melts
were
prepared
transparent except some of the melts containing CaO, which
The melts with a high amount of K20 (mole% K=O )
a gray tinge.
42) had
a
had
slight
after the cell was run for 24
tinge
amber
hours, and became darker with increased time and K=O contents.
Two
sample
melts, one in a platinum crucible and
24
alumina crucible were heated for
inside
the
platinum
inside
alumina
crucible
hours at 1100*C.
and
only
found at more than trace level was 0.1 to
unwanted
0.01
Liang and ElliottO* reported brown colors for
the Na=O-Na=SO4 system.
They
-
the
turned amber whereas
the
suggested
79 -
that
an
for
one
a
component
weight
their
in
The melt
The amber melt was sent
stayed clear.
semi-quantitative analysis
one
%
melts
Pt.
in
the brown color
was due to the formation of sodium platinate, Na=PtOw.
Similar
formation of potassium platinate, KzPtO=:
=
Pt(s) + K=O(soln) + Om
K=PtOs(soln or s)
is thought to be the cause for the amber
melts of this study.
This could
lead
(6.1)
in some of the
color
to
a
mixed
potential
being measured.
Systematic errors
These
estimate.
in
emf of the cell is difficult to
the
errors
systematic
junction or contact potentials.
could
result
The emf of the
cell was shown
to be reversible and reproducible, and the cell
well defined.
small.
This
because of
potential
was
that random errors in the eaf were
means
Uncertainty in cell temperature(+/- 20 C) was also small
in comparison to the other uncertainties.
Appendix H gives a detailed calculation of
this study.
The values thus
calculated
calculated data in Tables 5.1 to 5.4.
The
are
the
errors
shown
with
largest
in
the
systematic
error in the binary reference data is due to the uncertainty in
the electrochemical cell.
the products and reactants in
of
the free energy of formation
This error amounts to about 0.19
in
the log anno, fs,y.
6.2 K.O-SiO=-AlmO. system.
In this section the results obtained in this
system
K=0-SiO-Al=O=
is
discussed
-
80
-
and
study for the
some
of
the
characteristics of the system are presented.
activity
of
to
KO
constant Xcmo/Xwno=. This
pseudo-binary lines
along
decrease
of
is illustrated in Fig. 5.6
behavior
concentration
At constant
where data at 1100C are shown.
the
caused
The addition of Al=O. to binary K=O-SiO= melts
of
K20, the activity of K=O increases as Al=O= replaces 81=. This
is shown by the isoactivity lines for K=O given in Fig. 5.7. At
constant concentration of
as A1 2 0.
replaces
the activity of K=O decreases
SiO 2 ,
K2O. Clearly, Al2 Oa acts as an acid in this
system.
K=O
This behavior of the isoadtivity lines for
differs slightly from the isoactivity
Na=O-SiO=-Al1O= system at 1050 *C,
6.1.
DeYounga* and are shown in Fig.
along pseudo-binary lines
acts as a base.
when
increases
system, the activity of Na=O
of
The acidic behavior of
alumina
AlaO= + (00-) = (Al0 2 -. )
of
to
system
added
in
acidic in
amphoteric nature of
K=0-SiO=-Al0m=
the
system may be explained by alumina reacting to
anions, for example:
one
is
Since K=O is more basic than Na=O, this change
the K=O system is easily explained by the
Al=0*-. is
Al=O=
Xm.wa/Xmia=, and Al=Ow
constant
of A120. behavior from basic in the Na=O
Al2mO.
by
NaO-SiO=-A1mO=
the
In
the
determined
were
which
1100*C
in
NaO
of
lines
at
form
aluminate
(6.2)
many possible types of aluminate ions.
-
81
-
At
T=1050 C
A Albite
Na2 0Al203 6Si0 2
N Nepheline
C Carnegieitej Na2 0 Alz0 3 2Si0 2
+++++e-
Solid Solution
10
20
30
m/o A10?
Fig. 6.1
Interpolated isoactivity lines for Na=O in the
NazO-Al=O=-SiO= system in air at 1050C.
(Reference 29) Standard state is pure liquid Na=O
at I atm. pressure.
-
82
-
higher concentrations of AlmOm the behavior of
concentrations.
acidic than at lower
decreasing slopes of the lines in
contents.
This
the
into
Al=Om = 2(Al=+)
+ 3(O-)
Even though an
alumina
is
seen
5.6
at
higher
silicates
potassium
the
AlsOm
a
have
rich side
the difference between
and Elliott***, and
in the melts
dissolution
on potassium
effect
small
activities
potassium
and
Shigematsu
activity
In chapter 2,
silicate system.
potassium
measurements in the
the
addition decreases the activity of
Beta-alumina
of the phase diagram.
by
(6.3)
K=O this effect is very small, especially at the SiO
therefore
by
This
Fig.
less
be explained by at least a portion of the
may
dissolving
alumina
reaction:
will
is
AlmOm
measured by Chou
ElliottaO*
was mentioned.
Chou used a 50 mole% K=0 binary reference melt and Shigematsu a
21.4 mole% K=0 reference melt which was standardized against
sulphate cell.
done
The measurements
due
have a larger systematic error,
than the measurements
dissolution,
alumina
Shigematsu. Nevertheless, this
by
done
Chou will therefore
by
to
a
effect is not large enough to account for
the large difference
between the two sets of measurements.
The data obtained in this
study
is compared
with
those
reported by Eliezer et a1m*in Table 5.1. Eliezer used activity
data
obtained
by
Bowen 7 *,
and
Shairer
for
a
liquid
in
equilibrium with three solids, to calculate the activity of K=0
-
83
-
in the K=O-SiO-AlIOm system.
Table 6.1 tabulates the activity
and Bowen, Eliezer
of K=O at three points according to Shairer
The values of the present study
et al., and the present study.
is extrapolated to the
equilibrium
Shairer
and
results
of
orders
of
5
and
is between 3
Bowen
The
study.
temperature dependence found in this
Eliezer,
by using the
temperatures
magnitude higher than those obtained in the present study.
the results
of
If
Chou and Elliott*** or Steiler** is used, as a
difference
is
This large
orders of magnitude.
7
increased to between 5 and
this
system,
reference in the binary K=O-SiO=
difference in the activity of K=O between the present study and
when only 3.5 to 5.7 mole % of ternary
the values reported,
melt, is difficult to explain.
binary
a
to
Al=O is added
TABLE 6.1.
COMPARISON BETWEEN LOG aeca OBTAINED IN THIS STUDY
AND PUBLISHED VALUES FOR THE
K=O-SiO=-Al=O= SYSTEM.
Temp.
OC
Xcam/Xwnc=
log awan
Xuoca
968
0.5840
0.03460
-13.82
983
0.3958
0.04078
-15.84
0.6542
0.05689
-11.65
1083
~~-
-----
--
-
-
84
-9.79
-9.57
-10.51
-10.09
-8.33
-8.47
-
-
-
Shairer~v
Eliezer*
This study
-
-
-
-
-
-
-
-
6.3 KZO-SiO-CaO system.
study for the
In this section the results obtained in this
K2 0-SiO-CaO system, is compared with the results in some other
systems,
and
with
Richardson "ideal
results
the
from
obtained
using
the
mixing model.
6.3.1 Comparison with other work.
There
properties
are
of
no
known
measurements
K=O-SiO=-CaO
melts.
of
the
thermodynamic
consistency
The
ternary activity data may be checked by comparison
of
with
the
other
similar systems.
The main features of the ternary activity data shown in Fig
5.12 are:
1. The activity of K=O increases as XC.a increases
along
a
pseudo binary line of constant ratio of X~an/X=&aa.
of
KXO
decreases
as
X=.o increases
at
of
KaO
increases
as
Xmc3c
increases
at
The behavior of Na=O in the Na=O-SiOa-CaO system should
be
2.
The
activity
constant Xmaaa.
3.
The
activity
constant Xsa.
K=O-SiO=-CaO system as both Na=O
similar to that of K2 0 in the
and K2 O are much stronger bases
than
85
CaO.
The
iso-as.o
are shown in Fig. 6.2. It can
lines from the work of NeudorfO*
-
is
-
be seen from his work that:
is
The activity of Na=O increases when CaO
1.
added
along
lines of constant Xaman/Xwjo=.
The activity of Na=O
2.
decreases
when
Xamo increases and
when
Xa.a increases and
Xesom is held constant.
The activity of Na=O
3.
increases
Xaa is held constant.
This behavior of Na=O is similar
to the behavior of KaO in the
K=O-SiO=-CaO system, as expected.
The
data
of
Belton
et.
for
al-*'*
system
the
K2 O-Na2O-SiO= at the di-silicate composition, are shown in Fig.
6.3. It is
increases.
seen
that
Therefore
activity of K=O decreases as Xm.mo
the
for
data
the
this
system
Na=O-SiO.-CaO system both show that the activity
basic metal
oxide
decreases
of
and
the
the
more
as the less basic metal oxide is
added to the melt at constant Xmaoa.
6.3.2 Richardson mixing model.
The simplest model for calculation
of
the
activities
in
ternary melts was proposed by Richardson**. It was assumed that
when
two
binary
silicates,
of
compositions
zMIO.SiO=
zM4O.SiO=, were mixed, the free energy of mixing was
due to random mixing of
the
entirely
two cations (ideal mixing).
- 86 -
and
This
to CaO
65
15
10-
d 70
00
N
T=1070*C
/
-10.3
20
Fig. 6.2
5
25
30
35
mn/o Na 2 0
40
45
Iso-log ap..=a lines for Na=O-CaO-SIO=
intervals
melts at 10700C. Lines drawn at 0.1
of log am.wma,
from
-10.3
to -8.8. (Reference
Standard state is pure liquid Na=0 at 1 atm.
pressure.
- 87 -
59)
implied
assumption
remained
constant
the
and
that
data
ternary
MgO-MnO-SiO=.**,
"FeO'-MnO-SiO=.**-**-**,
systems
CaO-MgO-SiO=.&O and CaO-Na=O-SIO."
The
were
effects
polarization
The Richardson model has been applied with success
negligible.
in
the
distribution
anion
silicate
that
.
the
for
study
this
in
obtained
CaO-K=O-SiO= system can be compared with the Richardson *Ideal"
If
model.
mixing
following equation
ternary melts:
the
Richardson
applies
model
then
the
in
the
must hold for the activity of K=O
XW=oMa.Wusna
~e nry
au-mo~b[---------------ama2, c. amnr
------
ama om.ec
= X...
an.,
.
applies
equation
This
ternary systems.
melt
the zKO.SiO=
on
compositions
to
(6.11)
-
The subscripts t and b refer to the binary and
zCaO.SiO= join.
ternary
z
is
given
by Xw.. and
is
Xncmo.m.a
in
K*
the
of
The Temkin ion fraction
the
mole
the
fraction based on the pseudo-binary system.
Equation 6.11 was applied to the ternary
data
for
i100*C
activity
of
to
be
roughly 1.53. This estimation was based on an extrapolation
of
(Fig.
SiO=(s)
5.12),
at Xwan
in the CaO-SiO=
= 0.65 (z = 0.5384).
binary
system
was
the activity data of Rein and Chipman*". This
The
estimated
value is greater
than unity because liquid solutions are not stable at 1100*C in
-
88
-
the CaO-SiOm system.
= 0.65
in
The activity of SiO
1100*C and Xeacm
at
binary system is 0.054, from Fig. 2.3.
the K=O-Si0
With this information, the values for the activity
calculated, and these are compared
in
with
the
of K=O were
experimental
values in Table 6.1.
Table 6.1 shows that there is a small negative deviation of
the experimental
values.
model
from
values
the
calculated
"ideal" mixing
This means that the assumptions made in the Richardson
is
not
completely valid in this system at Xmaam = 0.65.
This is to be expected as:
1.
K=0 is a much stronger base than CaO.
2.
Potassium
ions
is
mono-valent
and
calcium
ions
is
divalent.
3.
The oxygen
coordination number for K* In molten K2 0-SiO
melts is 8.0 + 0.3** and the oxygen
coordination
number
for CaO in CaO-SiO= melts is a much lower 5.6 + 0.3*w.
This means that there is a change in the anion structure of
the melt to accommodate
binary K2 0-SiO
melt.
the
Ca=*
Therefore
ions when CaO is added to a
ideal
mixing,
as defined by
Richardson, does not appear to hold for the CaO-SiO-K=O system
at 1100*C.
-
89
-
Table 6.2.
COMPARISON BETWEEN CALCULATED
ACTIVITIES OF K=0 AND
EXPERIMENTAL VALUES IN THE K=O-SIO=-CaO SYSTEM
1100*C ; Xmamn
T
Xa
:
= 0.65
Log aocza
XX...
(by eq'n 6.11) : (exp't'l)
---------- -------- ---------------------------- ------
---
---
-9.50
0.939 :
-9.86
-9.96
0.871 :
-10.24
0.12
0.793 :
-10.63
-11.05
0.16
0.704
-11.05
-11.61
0.35
:
0
0.31
:
0.04
0.27
:
0.08
0.23
:
0.19
:
*
*
1.0
:
*
-10.49
s----------------------------s - e--------------r
S
Standard state is pure solid K2 0&
- 90 -
CHiPTER 7.
SUMMARY AND CONCLUSION.
A
galvanic
potassium-beta-alumina
the
measure
activity
to
as solid electrolyte, has been used
of
K=O-SiO=-CaO melts between
the KaO-SiO=-AlmOm
prepared
specially
employing
cell,
system
950 0 C
11000C. Compositions in
and
ranged
and
K=O-SiO=-Al=O.
K=0 in ternary
between 21 to 50 sole % KzO
and up to 6 mole % Al=O= was added.
In the KXO-SiO=-CaO system
the compositions ranged between 25 to
42 mole % K.O with up to
15 mole % CaO added.
Addition of Al&Om
binary
the
to
system
K=O-SiO=
at
a
constant XK==/Xwaaa ratio of decreased the value of log a=ao by
up to
The small
for the temperature range of the study.
0.12
change in the activity of K=0 due to addition of AlOi
explained
by
the
silicate
structure of the
anionic
could be
melts.
Partial molar mixing properties were calculated.
addition
The
system were obtained.
the
in
Limited data for the activity of K=O
CaO
of
to
K=O-SiOm-CaO
the
binary
K=O-SiOz system at a constant ratio of Xsc==/Xwaam increased the
value
of
studied.
log a.oa by up to 0.22 over
The experimental activity data
the
did
temperature
not
agree
range
well
with the values calculated by the Richardson ideal mixing model
at Xnan= = 0.65 and T
=
11000C. This behavior was explained in
-
91
-
terms of the
difference
in basiscity and coordination numbers
of K.O and CaO in their respective binary silicates.
- 92 -
CHAPTER 8.
RECOMMENDATIONS FOR FURTIER WORK.
extensive
more
Regarding the present study,
data for the
K=O-SiO=-CaO ternary system are needed, as a time limit on this
study prevented the complete coverage of this system.
the
on
same reason no Gibbs-Duhem integrations
the
For
ternary
data
were performed and calculating the activity of SiO 2 , AlmO=
and
CaO in both systems using this technique is recommended.
of K2 O
ternary melts,
in
the
like "FeO" on the activity
bxides
effect of other basic metal
determine
to
be undertaken
should
studies
Further
similar to the work DeYoung 2 * did on
the Na=O containing system.
From a practical point of view, the galvanic cell technique
activity of KO in a wide variety
could be used to measure the
of
design
beta-alumina
may
with
to
necessary
be
the
factors which influence
slags.
liquid
the absorption of alkalis by
cell
the
determine
should be measured, to
More
slag.
Improvements
In
reactions
of
prevent
high
temperature
thermodynamic properties of potassium containing compounds
solutions
needed.
suitable
If these,
for use as reference
and
the
in actual blast furnace slags
K=O
thermodynamic properties of
example,
For
slags.
metallurgical
extractive
electrodes
and
is also
other experimental difficulties can be
-
93
-
overcome, the galvanic cell technique may
studies of these complex slag systems.
-
94 -
be
very
useful
in
APPENDIX A.
K-BETA-ALUMINA.
The
fabrication
of
the
K-beta-alumina
crucibles
are
described, and the quality of the crucibles is discussed.
A.1 Fabrication of K-beta-alumina.
List of chemicals used:
-
Na-beta-alumina (Alcoa)
-
Alpha-alumina (Alcoa XB superground)
-
Potassium chloride
-
Potassium carbonate
-
Magnesium oxide
The
crucibles
were
prepared by
Na-beta-alumina powder at 300
mold.
isostatically
Megapascals
in
pressing
the
a sealed rubber
The internal cavity was obtained by centering a slightly
tapered brass mandrel of the correct diameter and length in the
compact before pressing.
After pressing, the brass mandrel was
withdrawn and the green crucible cut
to
the
correct
length.
The crucibles was then subjected to an ion
exchange to replace
the Na+ ions
K*
K-beta-alumina
in
the
Na-beta-alumina
This
crucibles.
-
95
was
-
by
done
ions to produce
by
keeping
the
1000 C on
top
muffle furnace at
a
in
hours
a platinum crucible containing KCl which in
of
within
was
turn
24
for
crucibles upside down
a
alumina crucible.
enclosed
larger
procedure was repeated for another 24 hours at 1100
0C
The
with the
crucibles not inverted.
A packing material was then prepared from 213g K=CO.,
in an alumina
alpha-A=Om and 1Og MgO. The mixture was tumbled
ball mill overnight, and then
calcined
The green crucible was packed
in
dia.
at 1100 0 C for 2 hours.
this material within a 4.6cm
by 10 cm high alumina crucible
Three of the
for firing.
K-beta-alumina crucibles were packed together at a charge.
was
slowly
room temperature to 1700 0 C over a period of
17000C
for
one-half
then
hour,
2
graphite
heated
hours,
cooled
slowly
The
1700 0 C
at
susceptor in an induction furnace and sintered
The alumina crucible
a
inside
alumina crucible and its charge was placed
one-half hour.
787g
for
from
held at
to
room
temperature over a period of 3 hours.
A.2 Quality of Droduct.
The
most
crucibles are
important
that
the
demands made
on
density of the crucibles should be as
near as possible to the theoretical and that
the
transference
be as high as possible.
number of the K+ ion should
the high density, proper sintering is needed.
high temperature.
K-beta-alumina
the
To obtain
This requires
a
Too high a temperature can cause melting and
-
96
-
The best temperature
therefore loss of shape of the crucibles.
Slow heating and cooling are needed to
was found to be 1700 C.
the
and
shock
thermal
prevent
The density of the beta-alumina
crucibles.
found
was
For a high transference number for K* ions in
is
important to
possible.
the
complete
exchange
ion
to
the
be
1
higher than 95 % of the theoretical (3.25 g/cmaO)
it
of
cracking
resulting
beta-alumina
as
far
as
The Biot number can be used to determine if the mass
transfer between the gas and the beta- alumina is adsorption or
diffusion controlled. The Biot number is given by :
a L
Bi
--
(A.1)
----------------------
M.W.
where a is the sticking factor, L is the width of the crucible,
M.W.
is
constant,
the
T
coefficient.
molecular
is
the
weight of potassium,
temperature
and
D
The value of the Biot number
1/2, L =
0.275
that the
mass
cm,
and
D = 10-*cnm/sec,
is
R
the
is
the
gas
diffusion
at 1100 3 C, with a =
is 21600 indicating
transfer of K* from the gas to the beta-alumina
was diffusion controlled.
-
97
-
The series solution for diffusion'* is given by:
C
--------
Ce
-------------
L
x
0
x
4C*
C(*)
=C*
+
(2j
-
--------
(2j + 1)
J=O
1)
(2j
+
1)
Sin(--------)(Exp(
1
1
(A.2)
with:
L = 0.55 cm (thickest part of crucible)
*
*
*
*
D = 10-* cam/Sec
C* = 9.68 Wt%
x = 1/2L = 0.275 cm
The following values for C(t) at x = 0.275 cm can be calculated :
1
Time (Hours)
C(t) (Wt%)
4
9.243
:
:
9.464
12
24
9.597
9.660
The 24 hours at 1000sC and 24 hours at 1100 C to accomplish the
ion exchange is therefore more than needed.
ion
The extent to which the
exchange is completed is also
showed by
Scanning Electron Microscope analysis of sections of
the solid
electrolyte crucibles.
The sections analyzed can be
be
seen in Fig A.I. The results can
A.III.
The
seen
in
Figs
A.II
and
by
Figs
residual Na in the beta-alumina is given
A.IV and A.V. Since
there
is
no Na ions in the reference and
working melts to partake in the reactions
at
this small residual amount of Na2 O is thought
small effect on the potential reading.
-
98
-
both
to
electrodes
have
a very
Fig.
A.I
Sections of beta-alumina solid electrolyte
crucible analyzed with the Electron Probe Micro
Analyser.
-
99
-
100
re)
C%J
C\J
0-
I
4
3
2
5
6
7
Distance (mm)
Fig. A.II
Wt% of A120. and K=O along section A-B of Fig
A.I, after ion exchange.
-100
-
100
-
90
0
W-0 77-O
O-C
-00--
0
o
Al203
0___
86.10:* 1.2
80 70X60--
C*
20
30
10 0
C
Fig. A.III
9.68*0.5
3
2
1
K20
-o -- -
-tr-
-
Distance (mm)
4
5
D
Wt% of Al=Om and KaO along section C-D of Fig
A.I, after ion exchange.
-
101
-
0.101
I
I
0
I
I
I
I
0
-
0.08 -
C0
0
0.060
0-
0
0.046---------------
0
-- o-
0.04* 0.013
1
0
0.02-
I
i
0
1~
3
2
.
-
4
.
5
6
7
Distance (mm)
Fig. A.IV
Wt% of residual Na=O in solid electrolyte along
section A-B of Fig A.I, after ion exchange.
-
102
-
0.10
008 0
0.060
0,
)
0.04*
0
0
00
00.039*
S-0
S
0 0000 0
-
0
0
002
0
0
C
Fig. A.V
I
I
2
I -
3
0.012
I ---- I J
4
5
Distance (mm)
Wt% of residual NamO in solid electrolyte along
section C-D of Fig A.I, after ion exchange.
- 103 -
APPENDIX B.
Electronic circuits used for control of experiment.
- 104 -
APPENDIX C
PROGRAM FOR DATA ACQUISITION AND CONTROL OF THE EMF EXPERIMENT
Lin..
Remarks.
Reads data
unit.
30
from
Isaac
90 to 120
Read temperatures where
EMF should be taken.
32
33
142 to 160
Test if temperature is
within limits (300 C).
Sums analog value of
at rate of
1000 sweeps
target
into
10 msec.
R.
variable
210
Calculates voltage.
230
12
DIM TZ (30) .VZ (30) .CZ (30)
13 IZ=2
D$ EQUAL CTRL--D
15 D$ = " ": REM
20
& SLOT# = 2
3 DAY TO Di.D2.D3.)4
PRIN~T
3
"D2" /"D3" /"D
PRINT ")DATE
PR INT
4
INPU T
TO0LERANCE ON TEMP ( CEL
SIUS) =": T TEMP
INPUT "TOLERNCE 0N EMF IS (M
5)
V) =:TEMF
INUEES W1THIN TOLERAIN
INPUT
%00
=":EQT
CE (MULTIPLE OF
TO
I NPUT "TTAL AMOUNT OF TEMPER
3E T
ATURES WHERE EMF S:HOULDI
. TS 200
80.,)
v WS (30) .
D IMi'
100
[NPUT " TE:RA TURE 4HERE EAMF
(J)
SHOULD 0B. FAIKEN=
J = J + I
GOTO 100
I THEN
IF J
S(2
)":
110
280 to 300
Test if temperature
within tolerance.
310 to 330
Test if cell EMF
within tolerance.
is
0
S= 0
is
GOTO 41 C)
1200 THEN
GJTO 4 10
C5 THEN
GOTO
15) >WS (J) THEN
IF TE >
L
IF TE
T
I
142
144
150
3000
THEN
IF (TE + 15) K WS (J)
4000C)C
1 70 K = 0
150 L = 0
190 M = ECT / 5
200)
PRINT "TEPERATURE", "EMF
160
C = T'()
290
IF
IF
30 C
1)
D =
IF
320
IF
<
-
TS(B)
C =
C
GOro 9e
THEN
C> TTEP
- VS(B)
VS(
D
0 'THEN D
GOTO 980
D >TEMF THEN
C
GOTO
THEN
205 R =
ASUM.
20&
220 P = R
S (K)
203
/ 1000
= (P -
10. (S
R. (RT)
(TV)
W) = 1000., (D#)
=0, (C#)
2050)
*
(2500 /
2048)
S40 GOJSUB '20004)
TS(K)=
IF
260
2. 7
-
105 -
B
=
M
K
TE
>
--
THEN
M
=0
(3OTJO 990
340
350
355
.360
=
L
1
+
L
GOTO 990
IF L < M THEN
& TIME TO C1,C2.C3
PRINT "THE EQUILIBRIUM TEMPE
RATURE AND EMF IS"
.361
36-2 TF
363
65
0
=
=
VF
N
N =
1
G =
B + N
TF +
TF
3659 VF
VF +
366
368 N =N + 1
I F (3 *: K
TF /
3 1 TFE
3571 VF =VF /
PR INT TF.
Ldn..
TZ
(IZ)
VZ
(IZ-)
Rearks.
361 to 371
Calculates average o f
last temperatures an d
cell EMF.
373 to 402
Store data in file.
980 to 1030
Print cell
EMF
temperature
if
within tolerance
wait 5 minutes.
and
no
an d
2000 to 2170
Measures and calculate
tempera ture.
S+
76
.74
=
"C 1
VF
*
I
10
J
J
IF
0 SEK
2"C':)4
2063
20 *
19
+
1.
1
+-
I
:
GOYTO
THEN
140
D$: "OPEN EMF DATA"
D$: "WRITE EMF DATA"
1 TO 50
CZ(
TZ (I) , Z (I)
D$: "CLOS5E
EtiF DAT"
TS (K) , VS (K)
4:: 1
=280
B
=1C3).
49
C
=
. 78 17
E
=
. 739E
F
='3 438E -
X
3
0)
& WRDEV.
0
-
4
=i)
Q=
0
(DV)
D#)
2
& ASUM, (TV) =
1000, (C#)
SW)
2140 X =Q
=3
(W#)
=2
, (RT)
=10 (
0., (D#) = 2
1000
(X - 20413) /
*
1E
267.4 * 2048)
A + V * (D + V * (C + V
2160 TE
* (D + V * (E + V * F))))
RETURN
2170
2150 V
106 -
10
&PAUSE = SEK.
i OTcj 2105
SUBROUTI NE TO DETERMIN
REM
E TEMPERATURE
394
-
*
C2
+Ku)4
0
C3
PRINT
PRINT
FOR I
PRIN'
374
NEX T I
NT'
P I1:
4
END
L =0
37
PR INT
9 C)
F::. =
133
32
M
MH
V'F"
=. C.1
=* 12
J=
"97
TO55
THEN
TF
CZ ( IZ)
IZ
TS (G)
VS (G)
=
5
*
3000 X=2
PRINT "DECREASE
305
UIRED"
3010
BCDOUT,
R
(DV)
3030
Lirn.
Remarks.
3000 to 3120
Decreases
one step.
temperature
& PAUSE
OF
TEM'
X, (D#)
REQ=
4
340 X=0
X (D#)
& BCDOUT, (DV)
3050
3070
& PAUSE = 60
V) = ROL,
= 0,
300 & AIN, iD)
(C#) = 1
GO0TO
309 IF TPOL < 2048 T HEN
0 70
TEST IF EUIL IBRIUM TE
REM
PIA
REACHED
3110
GOTO
4000 to 4120
Increases
one step.
temperature
400
14
X := 1
FI NT INCREAE
QUIIRED"
=
&: B3CDOIUT 'Y . (DV))
4020
&PAtUSE=5
4030
Q
1
X. (D#)
& BCDOUT. (DV)
60
& PAJSE
= TROL.
. (TV)
=
AN, (D#)
(C#)
GOTO 4
IF TROIL >,:.2052 THEN
4090
070
TEST IF EQUILIBRIUM TE
REM
4100
MP IS REACHED
& PAUSE= :300
4 11 )
GOT0 140
4120
4060
4070
4080
-
107
-
Silicate melt oreparation.
The K2 O-SiO
batches by
in 30 to 40 g
reference melts were prepared
chemically
pre-weighed
mixing
potassium
pure
carbonate (CaCO=), silica (SiOm) and acetone in a mortar and
pestle
for
obtained by calcining silicic acid
1000 0 C
for
12
After
hours.
(SiOz.xH=O)
the
mixing
SiO
The
half-hour.
one
approximately
in
was
air
acetone
at
was
evaporated in a furnace at 150 0 C. The mixture was then fused
and calcined in a platinum crucible by adding small
periodically
quickly
to
prevent spilling.
The melts
were
into a clean, water-cooled stainless steel
The resulting glassy
material
amounts
poured
bucket.
was crushed and remelted for
immediate use or stored in an evacuated dessicator for later
use.
The ternary K=O-SiO=-Al2O= and K2 O-SiO=-CaO
melts
were
prepared in the same manner described above, except that the
ternary component (chemically
to
the
pure
Al=O= or CaO) was added
These melts
mixture initially.
were
smaller batches of approximately 10 g each.
-
108 -
in
The sources and
purities of materials that were used are given
E.
prepared
in Appendix
SOURCES AND PURITIES OF MATERIALS.
(AlmOm
Alumina
).
Baker and Adamson reagent code 1236
>98.5
0.005
0.05
0.005
0.001
AImOm.
C1
S 102
SO4
heavy metals
0.03
( CaO ).
Lime
MCB Manufacturing Chemists code cx0265-1
Maximum limit of impurities:
Heavy metals (as Pb)
0.005
0.01
Insoluble in HC=H0a
and NH4 OH
Fe
NO=
0.01
0.01
SO..
0.1
Zn
0.015
Cla
Potassium Carbonate
Mallinckrodt
1.0
(KmCOm ).
6814
Maximum limits of impurities
Ammonium Hydroxide Ppt.
Arsenic (As)
Calcium and Magnesium Ppt
Chloride (C)
Heavy Metals (as Pb)
Insoluble matter
Iron (Fe)
Nitrogen compounds (as N)
-
109 -
0.002
< 0.0001
0.002
0.003
0.00003
0.002
0.00002
0.001
0. 001
0. 005
0. 004
0. 002
Phosphate (PO.)
Silica (5102)
Sodium (Na)
Sulphur Compounds (as SO0)
Potassium Chloride (KCL ).
MCB Manufacturing Chemists:
Maximum Impurities and Specifications
Barium
0. 001
Bromide
0. 01
Ca, Mg and R2O Ppt
Chlorate and Nitrate (NO=)
Heavy metals (as Pb)
Insoluble matter
Iodide
Iron
Nitrogen compounds (as N)
0. 005
0. 003
5 ppm
0. 005
0. 002
3 ppm
0. 001
5 ppm
0. 005
0. 001
Phosphate
Sodium
Sulfate
Silicic Acid, n-Hydrate.
J. T. Baker
1-0324
98.1
Assay (as 8102)
Nonvolatile with HF
Chloride (Cl)
Sulfate (SO.*)
Heavy metals (as Pb)
Iron (Fe)
-
<
110 -
0.06
0.01
0.001
0.0005
0.002
EXPERIMENTAL MEASUREMENTS FOR
KmO-SiO=-Al=O= SYSTEM
computer
pages
include
measurements
made
with
temperatures.
The data taken,
The
next
calculated from
as
at
cells
eaf
the
printouts
well
as
the
these results are tabulated.
followed by the least-square linear
equation:
fit
of
the
various
log
acan
The tables is
of the data to the
(F.1)
Log asmn = A/T + B
The standard deviations of log
aumm,
A and B is calculated
according to the equations given in Appendix H.
-
111
-
CALCULATION OF ABSOLUTE ACTIVITY
OF K20
EXPERIMENT # A21
W% K20 30
W% SIO2 70
ADDED W% AL203 2
TEMP
E.M.F.
LOG A
9. 56E-03
1 1,j
-12. 3y9070)51
9. E7E-03
1297
12783
.0107
-12.
5579452
-12.
74331 24
-12.
9385432
1259
-13.. 13934A63
124 1
-13.
3348508
-1.tU.
0933944
12 6
9. 810E-)31
9. 81E-0'3
-1
9. 86E-03
:
-1.2. 6968937
2-.8900462
-747
1 298
.. 1042
1 4 25
1 279
-12.
.. 1087
1259
9278288
-13.. 140627
-12. 9156:349
. 1028 ~
-12.
1 318
0 1 046
-12. 5:30494
1337
.01037
12. 3491203
71 02005
-12. 1713863
-("042
-12. 0 151746
1 :390
=
SLOPE
7031. 1783
=
-1 1. 8661921
. O) 1 061
.390':04 4176
INTERCEPT
STD DE' OF Y =.019215382
STD DEV OF CONSTANT = .148183627
STD DEV OF SLOPE = 192.963212
CORRELArION
COEFFICIENT
=
-
-. 99997961
112 -
IN TERNARY MELTS
CALCULATION OF ABSOLUTE
ACTIVITY
OF K20
EXFERIMENr # A9
W% K20) 30:,U
W% SIO2 70
ADDED W% ALtL203 4
TEMP
E. M. F.
LOG A
4. 91E-03
-12.
2232392
-12.
:3935517
-12.
5541657
-12.
7268567
-13.
1.179424
-13.
92634
13.";28
2.97E-03
1256
8. 71 E-04
1274
1
1 29~";
1 64E-3
1
...
1
.
-12. 90 74:3 4
49E-.03::
4. 14DE-03
T
1329
5. 29E-03
-12.
3871063
1347
5. 69E-03
-12.
2197329
1364
6. (5E-03
1400
-1 1 . 7540083
7. 16E-03
INTERCEPT
SLOPE
-12.0655828
=
=
-. 114984466
-- 163C36). -
7
STD DEV OF Y =. 0259098764
STD DEV OF CONSTANT = .231794525
STD DEV OF SLOPE =304.510983
CORRELATION COEFFICIENT = -. 999936486
INTERPOLATION
TEMP, K
Y
12223
1273
1:373
-13.
441'257
-12. 9196323
-1 1. 9870287
-
113 -
IN
TERNARY
MELTS
CALCULATION OF ABSOLUTE ACTIVITY OF
K20
EXPERIMENT # A10
W% 120 30
SIO2 7W1,%
ADDED W% AL2O3 6
LOG A
E. 11. F.
TEMP
12. 0418
E -0)3
6. *72
1365
16
6. 76E-03
-12.0617214
6.2 16E-03
-12.
2988655
1 53,1.4
6.
25E--03
-12.
5400083
1314
6 . 1 9E-0 3
-12.
5395481
12. 7780923
1294.)
1266
5. 74E--037
-13. 0251234
1242
4. 97 E--03
-1~..
2775626
-15. 0 13 7459
1267
-12 .7668282
1701
5,, 8 6 1.E -
1 .5 14
5. 859E-03
-12.5370089
6. 129E-03
-12.
3171468
6c3E-3
-12.
1136054
1.359
7:
-12. 1 5055:14
1:57
1.381.
INTERCEPT =
SLOPE =
- 11. 91054 347 2
6.17 -3
.272081294
-16832.6907
3TD DEV OF Y =.0103981252
68966 123 74
ID DEV OF CONSTANT =.
304
20
118.
STD DEV OF SLOPE =
-. 999991031
CORRELA T ION COEFFI CENT
IN TERPOLAf1T I ON
Y
TEMP. K
1223,
12737
1 373
-13.4913617
-12. 9507708
-11. 987708
-
114 -
IN TERNARY MELTS
CALCULATION OF ABSOLUTE ACTIVITY
EXPERIMENT
W
K20
OF K20 IN
# A1l
)
W% SIC2 70
ADDED W. AL203 8
TEMP
E.M.F.
LOG A
1358
7. 67E-03
-12. 1325157
1354
7. 56E-03
-12.
1:352
7, 77E-03
-12. 1887103
1 334
7. 62E-03
-12.
7. 8E-03
-12. 5322726
7., 32E-03
-12,, 387981
1281
1686082
3569268
-1 3. 0458258
1265
6,, u4E-03
1247
-13. 02776:38
[ 267
7
1L284
E
-12. 6806284
1301
1334
a. 15SE-03
-12. 3609315
1349
8. 39E-03
-12.
1365
8. 66E--03
-12. 07575195
8. 7E-03
-1 1. 9319425
1381
INTERCEPT
SLOPE =
=
.2
2212541
9
-16796.3226
STD DEV OF Y =.0184128004
STD DEV OF CONSTANT = . 152388319
STD DEV OF SLOF'E = 20.73898
CORRELATION COEFFICIENT = -. 999974957
IN TERPOLA T ION
TEiMP.
Y
1'223
1.273
1 373
-13. 50 17052
-12. 9622823
12.0013003"
-
115 -
TERNARY MELTS
CALCULATION OF ABSOLUTE ACTIVITY OF K20
EXPERIMENT # A19
W% K20 35
W% S102 65
ADDED W% AL203 = 4
TEMP
E. M. F.
LOG A
1340
8. 23E-03
-11.
8. 5E-3
-11. 4054847
8. 53E-03
-11.
13.04
1285
2299424
5840 172
-11.7795291.
970 7377
1267
9. 07E-03
-11
1220
(9.4E-03
-12. 4928594
9. 27E-03j
-12.
1271
1290
8. 84E-0.
.5
155703
11 . 9264835
-11.
E-
7266072
1:309
3. 703E-0.3
-11. 530 1462
1289
8. 42E-03
-1 1. 7:355479
1269
8. 6E-03.
-11. 94575359
-12.1626154
1 249
1270
3. 52E-03.
1 290
8. 0)2E-)3
-1 1. 72215:34
1309
7.. 95E-03
-11-
5295301
1346
7. 4E-03
-11.
1669301
1365
6. 92E-03
-10.
9869101
1400
11 . 9345248
6.99E-03
-10.324752
~7. 04E-03
-10.6753155
1.65613588
INTERCEPT
-17262. 4034
SLOPE
STD DEV OF Y =.0157465972
STD DEV OF CONSTANT = . 1024422"34
S2TD DEV OF SLOPE = 133.079699
CORRELATION
COEFFICIENT
-
= -. 999989816
116
-
IN TERNARY MELTS
CALCULATION
OF ABSOLUTE
ACTIVITY OF K20 IN TERNARY MELTS
EXPERIMENT # A18
W/% K20 35
W% S102 65
ADDED W% AL203 = 2
TEMP
E. N. F.
LOG A
1334
8. 67E-03
-11.
13 17
B. 65E--03
-11.4556715
1298
8.23E-03
-11.6422212
1280
8. 11999999E-03
-11.8263283
1262
7.9 1E-03
-1[2.
1244
7.96E-03
-12.-2110121
6 . 99E-03
-1 1. 9648263
6. 61E-
-11.
75222636
1::;os
-11.
5592295
1325
-11.
36 148
S304
-11.5670114
1286
.
6.
12 84
2905746
0148885
-1 1.770961
-1 1 . 9700(()6 1
1265
1306
6. 5E-0
-11 . 74419
5. 31E-3..
-11.5395737
-11.3547855
1325
1344
6. 06E-03
-11.1757469
1363
5. 95E-03
-10.
9980761
1382
5. 85E-03
-10.
8253636
1400
5.46E--03-
-10.6639396
INTERCEPT = 1.61835145
SLOPE = -17198.6115
STD DEV
OF Y =.0210842284
STD DEV OF CONSTANT = .157243511
STD DEV OF SLOPE = 205.519717
CORRELATION
COEFFICIENT
-
=
-.
117 -
999818738
EXPERIMENT # A20
W% K20 35
W% S102 65
ADDED W% AL203 = 8
TEMF
E.M.F.
LOG A
1:338
8. 19E-03
-11.22486864
1320
8. 26E-03
- 11 . 4 2*3 x2221-)7
1.3
7. 71E-03
-11.
1284
7. 56E-03
-1 1. 7803814
1266
7 5E-03
-11.9668964
1247
-7
1L260
7. 19E-03
1269
7. 17E-03
1290
7. 19E-13
4E
-12.
17298 74
-[2.
0305989
-1 1. 7156679
-1 1 32365 :13
1329
1288
587724
-1 1 . ~739503
7. 63-03
1288
-1 1. 7338677
1249
-12. 1526082
1270
7. 44E-03
-11.
9259529
1289
7. 95E-03
-1 1 . 7318725
1308
7. 95E-3
-1 1. 5-3 95003!
1326
7. 94E-03
-11 . 3622623
1366
R. 02E.-03
-10.
1384
'7. 72E-03
-10.8211553
1402
~7. 67 E--03
-10. 662.4601
9858775
INTERCEPT = 1.46761953
SLOPE = -17010.2635
STD DEV OF Y =-. 0110569322
STD DEV OF CONSrANT = .0780784018
STD DEV OF SLOPE = 101.643099
CORRELATION COEFFICIENT =
-
118
-
-. 999987006
CALCULATION OF ABSOLUTE ACTIVITY OF K20
EXPERIMENT # A1
W% K2O 44
W% S102 56
ADDED W% AL203 = 2
TEMP
E. M. F.
LOG A
1381
.0108
-9.73849158
1:363
.011
-9. 88960481
1:327
.01212
-10. 2095989
13286
0
1221
-10.
1
1291
. 01343
12*73
01396
1255
. 0(.), 1:663
201.3952
-10.54892'29
-10.
72479:2
-10. 9129346
-1
. 5242964
1293
-10.
521412
1:31 1
-10.
352325:3
134~7
-01147
-10. 0295049
1361
. 0 11
-9. 90647732
1379
.01062
-9. 75360897
INTERCEPT
SLOPE =
=
1.91520591
-16089.4632
STD DEV OF Y =6.51282064E-03
STD DEV OF CONSTANT = .0604332965
STD DEV OF SLOPE = 79.8601994
CORRELATION
COEFFICIENT
-.
999951536
I NTERPOLATION
TEMP '.
Y
1223
1273
1373
-11.2405285
-10. 7238068
-9.80326695
-
119
-
IN
TERNARY MELTS
CALCULATION OF ABSOLUTE ACTIVITY OF K2O IN TERNARY MELTS
EXPERIMENT # A3
20 44
W%
W% SI02 56
ADDED W% AL203 = 3.5
TEMP
LOG A
E. M. F.
.0163
-10. 36752.59
1351
. 154
-10.
1:.*s i.,5
()14q
-10.0199411
1
13
1369
1901.193"
-9.86431698
.0144
13T.87
0142:
-9.71418562
1368
0153
-9. 87932305
1348
- i C. 05-47571
161
. 172
-10 . 230363
13 1
0194
-10. 4187675
1271
019 4
-10.
7873162
1273
1.234
.0217
-11.
1772866
1275
0201
-10.
7540127
1295
. 1
-10.5555548
-10. 3837388
1314
.0182
1352
1372
-10.
1936118
-10.
0284999
-9. 8510o)2133
.C16
INTERCEPT = 2.08226076
SLOPE = -16363.3154
STID DEV OF Y =8. 17506624E-03
STD DEV OF CONSTANT = .0618762727
STD DEV OF SLOPE = 81.7890743
CORRELATION
COEFFICIENT
-
= -.
999822599
120 -
CALCULATION OF ABSOLUTE ACTIVITY OF K20
EXPERIMENT # A2
WX K20 44
W/% SI2 56
ADDED W% AL2O3 = 4.8
TEMP
E. M. F.
LOG A
1375
9. 31E--.3
-9.77701146
1373
9. 4E-03
-9.
79423323
-9.
96811037
1352
1316
-10. 2804419
1316
8. 76E-03
-10.28251
1280
8. 39E-03
-10. 6135708
7. 54E-03
-10.
7710761
7.57E-03
-10.
9500643
7. 43E-03
-10.
76041 79
1.245
1284
. 55E--03
1340
1376
-10 . 57680 28
8. 53E-3
-10.
8. 67E-0 3
-10 . 069 1527
8. 91E-0.3
-10.
8. a3E-03
-9. 76523277
4084138
0796683
INTERCEPT = 1.46371233
SLOPE = -15455.6811
STD DEV OF Y =. 0182357958
STD
=
DEV OF CONSTANT
STD DEV OF SLOPE =
CORRELATION
.149076423
195.881199
COEFFICIENT
=
-. 999986909
INTERPOLATION
Y
TEMP.K
1223
1273
1:373
-11.1738029
-10.6774354
-9.79315665
-
121
-
IN TERNARY MELTS
CALCULATION OF ABSOLUTE ACTIVITY OF K<'20 IN TERNARY MELTS
EXPERIMENT # A4
W%. K20 44
W% S102 56
ADDED W% AL2O3 = 6
TEMP
E. M. F.
LOG A
9. 58E-03
-10.
2259286
-10. 3888592
1305
9. 57E-03
1288
9. 68E-.3
-10.5478544
1271
9. 89E-C3
-- 10. 7118958
1235
9. 96E.-03
-11.071 1273
9. 91 E-03
-10. 7120545
1287
9.83E-3.
-10. 5584.2
1320
9. 71 E--03
-10
1319
9. 98E-03
)
-10.2648249
1 352
9.8 E-03
253)7806
-9
97407477
-9
.3044756
I NTERCEPT = 1.60636291
SLOPE = -15656.0023
STD DEV OF Y =.0216728192
S'TD DEV OF CONSTANT =231588161
STD DEV OF SLOPE = 301.546544
CORRELATION
COEFFICIENT
= -.
INTERPOLATION
Y
TEMP. K
1223
1273
1373
-11.1949472
-10.6921463
-9.7964064
-
122 -
999997558
CALCULATION OF ABSOLUTE ACTIVITY
EXPERIMENT
#
OF K20 IN TERNARY MELTS
A12
W% K'20 53
W% S102 47
ADDED W% AiL2O3 = 2
E. M. F.
LOG A
6. 68E-03
-8. 2970 1577
1362
6. 6E-3
-8. 43952429
1345
6. 86 E-0-3
-8. 57660444
TEMP
-8. 714f3941
13C28
-8. 866*75863
6.
6. 94E- 03
91E -0(3
9.
12"76
162:54648
-9.
1259
7. 2E-03
1 260
7.. 97E-'.
1 97
04E-03.
~7.
-8. 978745 14
131 4
7. 83E-0 3
-8.
13-' I
7. 67E-.3
-8. 69663596
1348
8. 25E-03
--8. 56289958
1363
8. 7E-03
-8.
44721053
1'397
9. 65E-03
-8.
19367467
INTERCEPT
SLOPE
3
-9. 31597008
83950942
= 2. 18599562
= -14483.2003
STD DEV OF Y =9. 10826523lE-03
.0759269043
STD DEV OF CONSTANT
)T D DEV OF SLOPE = 10. 40799
CORRELA~TION
COEFFICIENT
-
-.
123 -
999850705
CALCULATION OF ABSOLUTE ACTIVITY OF K 20 IN TERNARY MELTS
EXPERIMENT # A13
W% K2
53
W% SIO2 47
ADDED W% A
'L2O3
= 4
TEMP
E. M. F.
LOG A
13 86
1.13E--03
-8. 21461244
139
-8. 34583385f
1 . 32lE-03
-. 4863592
1316
1 . 34E -03
--8. 6323432~7
1.46-3
-8.e77386268
--8. 92769244
11.58E-3
. 1 E-3
1280
-9.08584865
1.79E-0.3
42511621
;-9.
1-.81E-03
1 . 71E-0:3
14E -03
1 .64tE--03
-3. 89381143
138
1.. 45 E-3
.-8. 59295038
1.352
1. 44E-03
-8.48013156
1371
1. 45E-03
-8.33147701
1389
1.45E-u3
-8.19432906
1
-9. 05060747
-3*
a
INTERCEPT = 2. 29525502
SLOPE = -14567.8678
STD DEV OF Y =.01:37287675
STD DEV OF CONSTANT = . 10623724
STD DEV OF SLOPE = 140.544669
.CRRELA[
TION
COEFFICIENT
= -.
-
999998598
124 -
CALCULATION
OF ABSOLUTE ACTIVITY
OF K20
EXPERIMENT # A14
W% K'20 53
W% S102 47
ADDED W% AL2O3 = 6
E. M. F.
LOG A
5. 28E-03
-8.24479376
1367
7. 23E-03
-8. 405064 75
1:349
7.7E-*-03
1.331
7. 92E -03
TEMP
-7
-8.55077312
3. 1-5E*-03'
-8. 85887536
-9. 0251812
1 5
1293
-9.
1275
1256
1276
1880219
-'9,.377317
9. 83E-03
)L9. 98E-O3
-9.18679811
1 296
-9C
1:314
9.836E-03
1 333
9. 8E-03
1351
01044
- 066992
-8.85508177
-8.55522438
1369
.01067
-8.414824:39
1387
01124
-8. 28053943
INTERCEPT =- 2. 32972566
SLOPE = -14689.2322
STD DEV OF Y =3.96912662E-03
. 0335975.327
STD DEV OF CONSTANT
STD DEV OF SLOPE = 44.4994687
CORRELATION COEFFICIENT = -. 99948608
-
125
-
IN TERNARY MELTS
CALCULATION OF ABSOLUTE ACTIVITY OF K20 IN TERNARY MELTS
EXPERIMENT #
W% K20 53
W% S102 47
ADDED
W%
A15
AL203
= 8
E.M.F.
TEMP
LOS1 A
1334
-8.66838743
1315
4. 69E-03
-8..830700603
1296
4.19E-03
4.-39E-03
-8.96679989
1276
5. 2E-03
-9.14903824
1257
4..9E-03
-9.31326638
1.238
4.61E-03:
-9.49417856
1260
1 '261)
4. 8l6E-C03
-9. 28949051
4. 42E---03
-9. 0984C098
1302
4.7
7.,21.
4E-03
-8. 91781 1t
-3.. 76028691
5. 15J:E-0,)3
1299
-8. 94919381
1279
5. 5E-0o3
-9.
1259
5. 79E-3
-9. 30770456
1 280
5. 81E-03
-9.
1299
6.1'7E -0:3
-8. 95470319
6. 68,E-0o3
-3.. 78031282
1 338
6. 99E-0*'3
-8.6342345
1357
6. 43E-03
-8.47765466
1376
6. 9E- 03
-8.33294419
1394
7.8e6E-03
*)--
-8. 20321086
124661
11821437
INTERCEPT = 2.05103199
SLOPE =-142.90. 1136
STD
DEV
OF Y
=.0157562676
STD DEV OF CONSTANT = .116647328
STD DEV OF SLOPE = 151.903768
CORRELATION
COEFFICIENT
-. 999876198
-
126 -
CALCULATION OF ABSOLUTE ACTIVITY OF K2O
EXPERIMENT # AA
W% K<20 62
W% SIO2 ,38
ADDED W% AL2O3 =
TEMP
1
LOG A
E. M. F.
7,48675581
.-
.025-*' =
-7. 28919463
1347
0287
.
1 287
. 29
-7.
19637954
-7.
63913565
-7. 42949813
12
-7. 18275411
4
-7. 5:365628
12~94
INTERCEPT = 2.07929362
SLOPE = -1246c7.7381
STD DEV OF Y =. 013618768
STD DEV OF CONSTANT = .297271296
STD DEV OF SLOPE = 391. 166742
CORRELATION
COEFFICIENT
= -.
99032354
INTERPOLATION
TEMP, K
Y
1223
1273
1373
-8. 11509568
-7. 71468761
-7. 00 13605
-
127
-
IN TERNARY MELTS
CALCULATION OF ABSOLUTE ACTIVITY
A16
EXPERIMENT #
W% K20 61.1
W% 5102 38.9
ADDED
OF K20
W% AL203
=
2
LOG A
TEMF
E. M. F.
13 17
013 12
-7.29232318
1315
01422
-7. 31526854
1288
0 158
-7.52815485
1271
.01728
-7.67068244
1253
.o1816
-7.
82028233
-7.
9681-7261
1236
-7. 81249268
L274
--7. 635563
-0 1 779
50
-7
129 1
-7. 416220 18
.0178
-755 16 13696
1289
1271
91 17
02128
49
7. 7024'
02274
-7.85712641
1272
-7.
696561 58
-7.
55667367
1290
-0,21 39
1 323
01 902
1340
.02018
-7.
18163839
1358
02065
-7.
06C108 13
- 7. 29399744
. 2101l
-6.94095164
-6. 85686195
INTERCEPT = 2. 19757227
SLOE =-12558 - 0319
STD DEV OF Y =.01990440'78
STD DEV OF CONS~TANT = . 142872975
STD DEV OF SLOPE
CORRELAT ION
185. 21837
=-.
COEFFICIENT
-
128
997952125
-
IN TERNARY
MELTS
CALCULA TION OF ABSOLUTE ACTIVITY
OF K20
EXPERIMENT # A17
W% K20 61.1
W% SIO2 38.9
ADDED W% AL203 = 0
LOG A
TEMP
E. M. F.
1340
01516
-7. 14387662
1322
) 1366
-7. 260348-75
1304
1~O
1285
.() 169
-'7.
41667624
.C 133
-7.
5313-7345
1266
.1403
-7. 68398864
1246
015:3
-7.
65436934
-7.
75673455
1 260
1287
-7.54577776
.0170)8
. 01588
1325
.0147'7
-7.
24725935
-7. 4099512
--7.57000044
1284
-7.
.,1754
71981042
-7. 55143574
1286
.) 1545
-7.38330455
.) 1562
-7.
253~7256
1 345
0149 1
-7.
10708031
1365
.01437
-6. 96598762
1.30)7
1383
.0158
-6.85645781
140 1
. 0 1857
-6 . 75933342
INTERCEPT = 2. 25940709
SLOPE = -12606.4521
STD DEV OF Y =6. 49564976E-03
STD DEV OF CONSTANT = . 048026:3498
STD DEV OF SLOPE = 62.8417052
CORRELATION
COEFFICIENT
-
= -. 999355206
129
-
IN
TERNARY MELTS
EXPERIMENTAL MEASUREMENTS FOR
Ka0-SiOz-CaO SYSTEM
The
next
pages
include
measurements
made
with
temperatures.
The data taken,
calculated from
computer
the
emf
as
printouts
cells
well
as
at
the
these results are tabulated.
followed by the least-square linear
equation:
fit
of
the
various
log
awaa
The tables is
of the data to the
Log ascza = A/T + B
(G.1)
The standard deviations of log
asca,
A and B Is calculated
according to the equations given in Appendix H.
-
130
-
CALCULATION OF ABSOLUTE
ACTIVITY OF K20
EXPERIMENT # A22
WX% K2
:35
W% S102 65
ADDED W% CAO = 4
E. M. F.
TEMP
1:325
-0019
LOG
A
-11.
0819073
-11 . 04 150 12
S03052
1290
-11.
1271
431401
S1. 6277366
-. 0288
1252
-11.8156201
-12. C0152.,-6 118
794126
02897
-11.
1257
1274
.02682
-11.,6126997
1293
.02707
-- 1 1. 417898
---
-11.
1 31 1
1290
-.
-11 . 4475 124
02764
-11
--.028'5
1 27 1
2454531
.
6303537
-- 11. 8 147984
1274
-. 02827
1295
0264
1:314
-02-7283
-11.
-11 . 403145
-11.
-11 .
02741
1352
-. 030483
1371
03176
1289
. 3
INTERCEP F
SLP.-E
60 12274
2096539
2735
-10 .9 2e2509
-10.6478306
-- 11. 4061743;
7
1. 54765875
= -16745.
2174
STD DEV OF Y =. 0113238447
SD DEV OF CONSTANT = .0949232355
STD DEV OF SLOPE = 122.675033
-. 999112763
CORRELATION COEFFICIENT
-
131
-
IN TERNARY MELTS
CALCULATION OF ABSOLUTE
ACTIVITY OF K20
EXPERIMENT #
W% K20 35
W% S102 65
ADDED W% CAO = 8
TEMP
E. M.F.
LOG A
1:*' 4 3
--9. 47E-03
-11.068634
1 325
-- 01194
-11. 2207427
1287
-.
-11.5899378
0c128
1289
01283
11. 5693753
1250
-. 01355
-11.9716906
1 230
01472
-12.
01434
-1 1 . 9330534
0 1403
-11. 7242827
1273
18 13403
1292
1311
1
1
-11. 3394085
-01428
-- 11. 5479051
014 18
-1 1. 74:39204
-.
01458
-- 11.9418596
-.
0 1 408
-1 1. 7447135
1271
125
-01419
- 0 1.425
-
-11.
5380236
-11.3C481411
13 1 0
1328
-.
01468
-11.171183
1.363
-.
01499
-10.8432179
1382
-01537
1398
-.
-10.6705922
01569
-10. 5288626
INTERCEPT = 1.51771786
=LPE
-16858. 4651
STD DEV OF Y =5.64288276E-03
STD DEV OF CONSTANT = .0380584495
STD DEV OF SLOPE = 49.4104872
CORRELATION
COEFFICIENT
-
=
-. 999732321
132
-
IN TERNARY MELTS
CALCULATION OF ABSOLUTE ACTIVITY OF K20
EXPERIMENT # A 24
W% .20 35
W% S102 65
ADDED W% CAO = 12
E. H. F.
LOG A
-. 02903
-- 11. 0245043
TEMP
1:3 15
-11.
1298
-1 1 . 34370f)9
12131
-. 3 103
1264
- . -3-. 7
-11.
-12.
1248
-1.1
1281
-11.
1297
-
- '2E3
7
5078558
- 11. 6694003
1228
1"314
179130b
1
022729?
. 8254625
5041575
.'3500455
-1 1, 198C706
9
1294
-1. 1.-"3934954
1277
-II.
558 1876
1261
-.
-.03104
-- 11. 7142674
1273
-
- 0297 1
-11.
1:295
-.
02875
-11 .3848534
-. 02736
-11.238 1489
.027~03
1 1. C 774436
02651
1 0. 7700665
1328
1362
1:*91
INTERCEPT =
SLOPE =15755.
-.
5488286
-02384
-10.6616649
-02365
-10. 531~77:17
.791240589
33
STD DEV OF Y =.0173124155
129997005
STD DEV OF CONSTANT =.
STD DEV OF SLOPE = 168.957196
CORRELATION
COEFFICIENT
-
= -.
133 -
999732537
IN
TERNARY MELTS
CALCULATION OF ABSOLUTE ACTIVITY OF K20 IN TERNARY MELTS
EXPERIMENT # A25
W. K20 43.94
W% S102 56.06
ADDED W% CAO = 4
TEMP
E.M.F.
LOG A
1347
-.
01652
-9.16041791
1312
-.
01779
-9. 45510182
-. 01737
1295
1278
1 245
-
-9.61205194
-)1865
-9. 75976934
01951
-9.90518616
-1 -.
- 0213:5
0562877
-9.9041473
1262
1278
-.
0 1868
--9. 75953273
-9. 64342314
1291
-.
--9. 48225996
01775
-. 018314
.0186
-9. 8073 4334
--
0o1941L
-9.94464229
-.
01895
--9.76680739
-
0179
-9. 57140713
-.
01751
-9.47512938
-.
01585
-9.20796965
-.
0 1587
--9. ()72302 15
-.
01551
-8.95172429
-.
01472
-8.82043193
1273
1 '2277
13092
1277
1299
1342
1390
-9.56045148
INTERCEPT = 1.86015396
SLOPE = -14848. 1803
STD DEV OF Y =.0156076123
STD
DEV OF CONSTANT
.117864269
=
STD DEV OF SLOPE = 153.366738
CORRELATION
COEFFICIENT
-
=
134
-. 999956489
-
CALCULATION
OF ABSOLUTE ACTIVITY OF K20
EXPERIMENT # A26
W% K20 43.94
W% S102 56.06
ADDED W% CAO = e
TEMP
E. M. F.
1326
-.
LOG A
01797
-9. 33013152
1328
-- 01763
-9. 31526958
1289
02003
1270
-. 01945
1251
-. 02147
1232
-.
02414
-10.
1253
-.
02074
-9.
1273
-6945
1292
--. 0199
1309
-.
-9.64647444
-9.8290831
99628934
'-9.
1633348
98261188
-9.61986115
o 1(907
4720'7542
-9.
1290
--. 02129
-9.62740558
1271
-.
02-74
-9.. 80934758
1252
-.
02121
-9.98859979
1271
-.
02032
-- 9. 81267845
1286
-. 02068
-9.66913606
1306
-.
01989
-9.49267732
1343
-.
01788
-9.
18420063
1362
-.
01783
-9.
02503799
13780
-.
01715
-8.88291603
1397
-.
017
-8.
74850105
1.88435375
INTERCEPT
-14862. 3747
SLOPE
STD
DEV OF Y =. 012318824
STD DEV OF CONSTANT = .0834332973
STD DEV OF SLOPE =108.204332
CORRELATION
COEFFICIENT
-
=
-. 999880402
135 -
IN
TERNARY MELTS
CALCULATION OF ABSOLUTE ACTIVITY OF K20 IN
EXPERIMENT # A27
W% K:20 43.94
W% S10'2 56.06
ADDED W% CAO = 12
E. M. F.
TEMP
LOG A
-9- 13819307
-.
1268
-9.51156.363
01861
9. 83995021
02048
-.
1 253
-9 . 98357'723
1294
-.
-018865
--9.60961367
0@1725
-9.24887286
INTERCEPT = 1.92865149
SLOPE = -14926.64()'7
STD DEV OF Y =.0138666717
STD DEV OF CONSTANT = 217362272
282.428149
STD DEV OF SLOPE
-. 999917372
CORRELATION COEFFICIENT
INTERPOLATION
Y
TEMP. K
1223
1273
13737
-- 10. 2762878
-9.79691075
-8.94290039
-
136
-
TERNARY MELTS
CALCULATION OF ABSOLUTE ACTIVITY OF K20 IN TERNARY MELTS
EXPERIMENT # A28
W% K20 53
W% SIO2 47
ADDED W% CAO = 4
TEMP
E. M1.F.
LOG A
1326
-8. 95E-03
-8.61157956
1:326
-8.
76E-03
-8.61302388
1288
-9. 375E-03
-8.92875617
1272
-9. 969E-03-"
-9.06468467
1259
-. 01(529
--9. 17705102
9.41313492
-. 01113
--.
-9. 2305633
0 1068
1233
-9. 0534117
.01027
-8.89254217
-8. 72699103
1273
1313
1294
-9.36E-
-8. 8'770313
1272
-9. 376E--03
-9. 06542163
1 252
-.
1275
-9.52E-03
-9. 24045909
O 1059
9. C)416)7 *39
-8.82528818
1 301
1317
-7.
205E-03
--8. 69917218
1337
-6.
80C17E-03
--8.53835907
1358
-5. 89E-03
--8. 37630784
1376
-5.
:37E-03
-8. 24306079
1394
-5.
638E-03
-8.
1056(:)857
INTERCEPT = 1.8564047
-13892.32
SLOPE
STD DEV OF Y =.013707191
STD DEV OF CONSTANT = .0968977465
STD DEV OF SLOPE = 125.829169
CORRELATION
COEFFICIENT
-
=-.999933105
137
-
QUANTITATIVE ERROR ANALYSIS.
The scatter in the data, shown in Fig 5.1 to 5.5 and 5.8
to 5.10, was analyzed by applying statistical theory*
the least squares coefficients of the equation:
log anaa - A/T + B
to
(H.1)
The standard deviations of the log acao values about
least-square line were calculated using equation H.2:
the
&[(log aonao))O 1/2
S
=
-
-
(H.2)
n - 2
where A(log.aa) is the deviation of
from the least-squares line and n
an
is
actual
the
data
number
of
point
data
points. The standard deviations of A and B are then given
by equations H.3 and H.4, respectively:
n
1/2
=---.-------------------------I
(H.3)
a (1/TO=
Sa
f(
-
(1/T.))=
(1/Tr,)=
= Sa..------------------------1
ni(1/T.,)a -
1/2
W((1TO)a
The standard deviation of a computed log awao
given by equation H.4:
((1/T")= -
2(1/T 0 )t(1/To)
+ n(1/To)m
S= aS...-------------------------------------I
-
138
-
value, S=, is
1/2
(H.5)
the temperature at which the log aanc
is
where To
value is
calculated.
the
The values of
least squares coefficients and their
5.3.
The
multiplying
the
and
5.1
standard deviations were given in Table
error in H"waa and S",an was calculated by
standard deviations of the least-square slopes and constants
in Table 5.1 and 5.2 by 2.303R.
.
The systematic error in log aa
from
of
data
the
of
examination
an
can be estimated
section
Elliottaa-. The sulphate cell they used is given in
2.2.
H.6:
where E is
log
standard
free
was
K=O,
due to the
SO.
equation
+ &G.<a-*
- ----------------------2.3RT
(H.6)
The
formation of
compounds
log ---------P*na
2
the reversible cell potential.
apan
by
&Gecao + AGeo.
pa2
P'a".
1
2
------2.3RT
log a.oa.b
in
in th'is cell was given
atno, as",
Log
error
major
energies
SO.
was taken from the JANAF Thermochemical
and
respectively.
of error :
S W [ SMM +
K.SO.
of
and K2 SO4 . The data for these three
Tables**
and the uncertainties in the free energies of formation
K=O,
and
Shigematsu
826
2060,
are
Using a standard
and
2080
J/mole,
formula for the propagation
(H.7)
fSa
+ .. J'/
-
for
139 -
the systematic error in log a
or
about
0.19 over the temperature range of the present study.
There
is 250/T,
cell
values
of
the
measured in the binary system
by
Shigematsu
was a scatter in the
potential E as
and
Elliott.
This resulted in a standard deviation for log avca of 0.035.
The largest systematic error in log aoa= is therefore due to
the uncertainties in the standard free energies of formation
of K=0, SO= and K=SO..
-
140 -
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