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COMPUTERS AND CHEMICAL ENGINEERING
MINERALS ENGINEERING
CANADIAN METALLURGICAL QUARTERLY
ACTA METALLURGICA
SCRIPTA METALLURGICA
Proceedings of the International Symposium on
COMPUTER SOFTWARE
IN CHEMICAL AND
EXTRACTIVE METALLURGY
Montréal, Canada
August 28-31, 1988
Vol. 11 Proceedings of the Metallurgical Society
of the Canadian Institute of Mining and Metallurgy
Edited by
W.T. THOMPSON
Royal Military College, Kingston, Ontario, CANADA
F. AJERSCH
Ecole Polytechnique, Montréal, Quebec, CANADA
G. ERIKSSON
Ecole Polytechnique, Montréal, Quebec, CANADA
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Copyright © 1989 by The Canadian Institute of Mining and Metallurgy
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First printing 1989
Library of Congress Cataloging in Publication Data
International Symposium on Computer Software in Chemical and
Extractive Metallurgy (1988 : Montréal, Québec)
Proceedings of the International Symposium on Computer Software in
Chemical and Extractive Metallurgy, Montréal, Canada, August 28-31,
1988 / edited by W.T. Thompson, F. Ajersch, G. Eriksson.
p. cm. - (Proceedings of the Metallurgical Society of the
Canadian Institute of Mining and Metallurgy ; vol. 11)
Includes index.
ISBN 0-08-036087-4
1. Chemistry, Metallurgical-Computer programs-Congresses.
2. Metallurgy-Computer programs-Congresses. I. Thompson, W.T.
(William T.) II. Ajersch, F. III. Eriksson, G. IV. Title.
V. Series.
QD132.I58 1988
669' .0028'553-dc19 88-38661
CIP
In order to make this volume available as economically and
as rapidly as possible, the authors' typescripts have been
reproduced in their original forms. This method
unfortunately has its typographical limitations but it is
hoped that they in no way distract the reader.
Printed in the United States of America
PREFACE
This proceedings volume consists of a series of papers
presented at the International Symposium on Computer Software in
Chemical and Extractive Metallurgy held in Montreal, August
30-31, as part of the 27th Annual Conference of Metallurgists of
the Canadian Institute of Mining and Metallurgy.
The program, consisting of presentations from North
America as well as overseas, was intended to provide an overview
of software development activities including data bases in chemi-
cal thermodynamics, applications of thermochemical and transport
properties in metallurgical processes, model Iing of mineral pro-
cessing systems, expert systems and training packages for plant
operations. Some of the papers deal with stand a lone programs
for use with personal computers while others refer to on-line
systems available through data packet switching networks. The
range of activities covered, in the editors' opinion, is not
exhaustive, but is a reasonably good reflection of present prog-
ress in this rapidly developi ng specia Ity.
The symposium was organized jointly by the Basic
Sciences and Non-Ferrous Pyromet a 11urgy sections of the Metal-
lurgical Society of Cl M. The editors wish to express their
thanks to these groups and in particular Ralph Harris and George
Kachan iwsky who helped in soliciting represent at i ve cont r i bu-
tions. The editors are also grateful to the authors, session
chairmen, institutes, universities and companies who through
their co-operation and enthusiasm made this symposium possible.
F. AJERSCH
Ecole Polytechnique
W.T. THOMPSON
Royal Military College
G. ERIKSSON
Ecole Polytechnique
October 1988
ν
PROCEEDINGS OP THE INTERNATIONAL SYMPOSIUM ON
COMPUTER SOFTWARE IN CHEMICAL AND EXTRACTIVE METALLURGY
Conference Technical Program Chairman:
A.D. Pelton
Ecole Polytechnique
Montreal, Quebec
Symposium Organizing Committee:
F. Ajersch W.T. Thompson G. Eriksson
Ecole Polytechnique Royal Military College Ecole Polytechnique
Montreal, Quebec Kingston, Ontario Montreal, Quebec
Session Chairmen:
I Thermochemical Computation and Data Banks
G. ERIKSSON, Ecole Polytechnique, Montreal, Quebec
M. BLANDER, Argonne National Laboratory, Argonne,
Illinois, U.S.A.
II Pyrometallurgical and Process Applications
F. AJERSCH, Ecole Polytechnique, Montreal, Quebec
G. KAIURA, Falconbridge Ltd., Sudbury, Ontario
III Heat and Mass Transfer
F. MUCCIARDI, McGill University, Montreal, Quebec
R. BERGMAN, University of Toronto, Toronto, Ontario
IV Expert Systems and Artificial Intelligence
W.T. THOMPSON, Royal Military College, Kingston, Ontario
A. VAHED, Inco Ltd, Sudbury, Ontario
vi
SESSION I
Thermochemical Computation and Data Banks
Co-Chairmen: GUNNAR ERIKSSON
Ecole Polytechnique
Montreal, Quebec
MILTON BLANDER
Argonne National Laboratory
Argonne, Illinois, U.S.A.
1
CALCULATIONS OF THE THERMODYNAMIC PROPERTIES OF
METALLURGICAL SOLUTIONS
Milton Blander
Materials Science Program/Chemical Technology Division
Argonne National Laboratory
9700 South Cass Avenue
Argonne, Illinois 60439-4837
ABSTRACT
Predictive theories for metallurgical solutions are important precursors for computer software
in chemical and extractive metallurgy. A limited selection of concepts useful for slags and
other ionic systems will be discussed and include the quasichemical theory, the conformai
ionic solution theory, and polymer theory. We emphasize theories which usefully predict
solution properties of multicomponent ionic systems, such as silicates and molten salts, to
illustrate the range of possible uses.
KEYWORDS
Solution theories; molten salt solutions; ionic solutions; conformai ionic solutions; silicate
solutions.
INTRODUCTION
The development of computer software for thermodynamic calculations for reactions involving
multicomponent ionic metallurgical melts can benefit from the use of theoretical developments
that greatly minimize the necessary input data. The most useful theories permit one to per-
form calculations for multicomponent solutions based on data for the subsidiary binary solu-
tions. Since, for a given number of components, there are a much smaller number of possible
binary systems than there are multicomponent systems and since, in addition, there is enough
understood about the physics of binary systems to make educated guesses of properties when
data are not available, these theories permit one to calculate the thermodynamic properties
of a very large number of systems a priori.
There are two major types of solutions we will consider: (A) simple solutions for which the
excess thermodynamic properties can be represented by polynomials and (B) solutions that
are highly ordered and cannot be represented by the usual polynomial representation. In
addition, there are two classes of systems in each of the above two categories-additive systems
and reciprocal systems. Additive systems contain either one kind of cation and different kinds
+
of anions (e.g., A /X~,Y~,Z~, ...) or different kinds of cations and one kind of anion (e.g.,
3
4 COMPUTER SOFTWARE IN CHEMICAL & EXTRACTIVE METALLURGY
A+, B+, C+, ... /X ). Reciprocal systems contain at least two cations and two anions and
generally exhibit very large deviations from ideal solution behavior.
Before one can discuss deviations from ideality, one needs to define an ideal solution. For a
given salt constituent of an ionic solution, A X , one can write the chemical potential in an
m n
ideal solution, μ^,
μ? = μ° + RT In X%X$ (1)
where i is the constituent A X , μ° is the standard chemical potential of constituent i and
m n
XA nad Χχ a er cation and anion fractions, respectively; these are defined as X^ = nyi/En
c
and Χχ = ηχ/Έτία where the n's designate the number of moles of the subscript species, the
subscript c denotes cations, and a denotes anions. Eq. (1) serves to completely define an ideal
solution.
The deviations of real solutions from ideal solution behavior is expressed in terms of excess
functions and activity coefficients
μί = μ° + μ'? + μ? = μ° + RT In Χ%Χ$ν = μ? + RT In ai (2)
where μΡ( — RT In 7i) is the excess chemical potential, 7» is an activity coefficient and a; is
an activity of the component i. The molar excess free energy of mixing is
G* = £*,7.f (3)
3
where Xj is the mole fraction of component j.
In what follows, we will present a brief description of different theories that have proven to be
particularly useful. Since the subject is complex, applications require reading the references
for detail. Because of limited space, this discussion is not exhaustive and some useful theories
are not discussed.
CONFORMAL IONIC SOLUTION THEORY
The conformai ionic solution theory is a statistical mechanical perturbation theory and is
the most fundamental and successful method for predicting the properties of multicomponent
molten ionic systems. Equations up to fourth order have been deduced for the excess free
energies of mixing and partial molar excess free energies of mixing of ternary additive ionic
systems in which the three salts are of the same charge type (Saboungi and Blander, 1975a).
=Σ Σ -v^i + ΣΣ + Σ Σ
GI
i<j %Φο i<j
^AXiXX + BiXfXjX (4)
2 3 k
where Xj, Xj, and Xj. are ion fractions of either cations or anions, a^-, b^, and c^ are binary
interaction coefficients and A and the three B,'s are ternary interaction coefficients that are
given in terms of the binary coefficients by the expressions
A= ( t f ^ ) ( tf ^ ( b \? lg) (5)
+ +
COMPUTER SOFTWARE IN CHEMICAL & EXTRACTIVE METALLURGY 5
and
Β, = 2(cc)1'2 (6)
iiik
Equations (4), (5), and (6) permit one to calculate the properties of ternary systems from the
properties of the three subsidiary binaries. There has been empirical support for a theoretical
conclusion by F0rland (F0rland, 1957) that the substitution of equivalent fractions for ion
fractions into the expression for the excess free energy (not into the ideal term) leads to
better representations of data in most binary systems (and probably multicomponent systems).
Equivalent fractions are defined by
ziXi
(7)
Σ>=1 JX3Z
where z- and zj are the charge on the i th and j th ions, respectively; the ions considered are
t
all cations or all anions. With this modification, one can usually make accurate predictions
for mixtures of salts of different charge type. Since the ternary interaction terms (i.e., the
terms with A and Bj as coefficients) are relatively small, these equations do not have a clear
advantage over empirical methods; however, since these equations are fundamental, their use
should be preferred over empirical rules.
The equations deduced from the CIS theory for reciprocal systems (Blander and Yosim, 1963)
have proven to be particularly useful (Blander and Topol, 1966). Constituents of reciprocal
systems often exhibit very large deviations from ideal solution behavior. In ternary recipro-
cal systems, two constituents exhibit negative deviations and the other two exhibit positive
deviations from ideal behavior. This leads to chemical behavior that is a complex function of
composition and to phase diagrams with complex topologies.
Conformai ionic solution theory for ternary reciprocal molten salt systems up to second order
terms leads to an expression for the total excess free energy of mixing of the three component
salts, AX, BX, and BY,
E E
AG7 = X X A G° 4 X A G$ 4 X A G 4
MM A Y Y X X
ι
Xll 4 XAGf - XAXBXXXY^Qt (8)
A 2ZRT
0
where A G is the standard free energy change for the metathetical reaction
AX (I) + ΒΥ(1)τ±ΑΥ{1) + BX(l) (9)
The Xi are anion or cation fractions, A Gf is the excess free energy of mixing of the binary
mixture in which the two salts have the common ion i, and Ζ is a parameter that can be taken
as 6. The activity coefficients of a component, e.g., BY, are given by the expression
RT In = XXAG° + ΧΧχ (Χχ - Χγ) X
Ί Β ΥAX Α A
+X (ΧΧγ + XBXX)*B + ΧΑ (ΧΑΧΥ + ΧβΧχ)λγ
X Α
02
(AG)
+ΧΧχ (ΧΑ - Χ) λχ - ΧΧχ (ΧΑΧΥ + ΧΧχ ~ ΧβΧγ) (V 1 0)
Α Β Α Β
where the binary excess free energies, such as AG χ, are given by a quadratic expression
(11)
6 COMPUTER SOFTWARE IN CHEMICAL & EXTRACTIVE METALLURGY
where Χ χ is an energy parameter for the AX-BX system. The empirical substitution of higher
order expressions for AGf in Eq. (8), when available, appears to be a useful extension of Eq.
(10). In Fig. 1, we compare the results of the first use of Eqs. 8-11 for the calculation of the
complex topology of the phase diagram for the Li +, K+/C1~,F~ reciprocal ternary system
with measurements (Blander and Topol, 1966). The substitution of equivalent fractions in
these equations has been shown to lead to good predictions of the phase diagrams of systems
with anions and or cations having different charges (Saboungi and Blander, 1975b). One of
the best examples of the use of these equations was for deducing the phase diagrams and
gas-liquid reactions of fuel cell carbonate electrolytes (Pelton, Bale, and Lin, 1981). In Fig. 2,
we exhibit results of calculations for the Li +, K+/C03~,OH~ system and a measured phase
diagram for comparison. These equations have been extended to higher order multicomponent
systems (Saboungi, 1980).
ORDERED SOLUTIONS
The most difficult class of solutions to describe are the ordered solutions, which includes, e.g.,
silicates and chloroaluminates. This difficulty arises from the fact that the enthalpies of mixing
tend to be "V" shaped and the entropies of mixing tend to be "m" shaped. These shapes are
poorly represented by the usual polynomial representation of deviations from ideal behavior.
We have deduced a set of equations with such properties based on empirical modifications of
the quasichemical theory (Blander and Pelton, 1983, 1984, 1987; Pelton and Blander, 1984,
1986; Pelton, Eriksson, and Blander, 1988)). For binary systems, the excess free energy of
mixing is given by the expression
GE = RT(aX+bX) K -l + 2 yi , Κ l + 2y2\ (12)
l 2 Vi(K + l) V2(K + 1)
where Xj is the mole fraction of component i, and the values of a and b are equal to 0.34435
times the cationic charge of components 1 and 2, respectively. The quantities y, are equivalent
fractions and Κ is given by the equation
12/
Κ = [1 + 4yiy [exp(W /RT) - 1]] (13)
2 12
where W12 is an energy that is taken to be dependent on temperature and composition and
is written as a polynomial in concentration
Wu = Y,(h-TS)y* (14)
k k
ifc=o
where no more than four values of k chosen between 1 and 7 were found to be needed and
where the component 2 is taken to be more acid than component 1.
All these quantities define the number of the 1-1, 2-2, and 1-2 bonds in the quasichemical
model, nn, n22, and ni2. The total number of bonds to each component 1 cation is 2a and to
component 2, 2b so that if n - is the number of moles of component i, then
t
an\= nn + IU2/2
bn = n 2 + 7112/2 (15)
2 2
and if the fraction of ij bonds, Xij — η^/Ση^, then
Xn=yi-Xn/2
X22- 2/2 - ΑΊ2/2 (16)
