QUANTITATIVE EQUILIBRIUM CALCULATIONS ON SYSTEMS WITH RELEVANCE TO

COPPER SMELTING AND CONVERTING

by

BO BJÖRKMAN

AKADEMISK AVHANDLING

som med t i l ls tå n d av rektorsämbetet v id Umeå U n ive rs ite t fö r erhållande av f i lo s o f ie doktorsexamen framlägges t i l l o f fe n t l ig granskning vid Kemiska In s titu tio n e n , sal B, LuO, onsdagen den 30 maj 1984, kl 10.00

Umeå 1984

Fakultetsopponent: Dr. P h ilip J. Spencer, Aachen

T i t le :

Author:

Address:

Abstract:

Key words:

Q uantita tive equ ilib rium ca lcu la tions on systems w ith relevance to copper smelting and converting

Bo Björkman

Department o f Inorganic Chemistry, U n ivers ity o f Umeå, S-901 87 Umeå, Sweden

The present thesis gives a summary o f resu lts obtained through theo re tica l and experimental studies o f systems w ith relevance to copper smelting and converting.

Many chemical elements are involved in the copper production pro­cesses and a deta iled experimental study would be very time- consuming and expensive. A complicating fa c t is also the co rro s i- v i ty of the liq u id phases towards container m ateria l. A powerful a lte rn a tive is equ ilib rium ca lcu la tions , in which models fo r the liq u id phases as well as re lia b le basic thermodynamic data are needed.

In the present thes is , a generalized s tructu re based model fo r liq u id s ilic a te s was developed and used in assessments o f the sys­tems PbO-SiC^, Fe-O-SiOo, CUO0 . 5 -SÌO2 and Cu-Fe-O-SiOo. In the model, the non-ideal s i l ic a te melt is treated as an ideal solu­tio n but containing a few complexes. The PbO-Si02 melt could be described by introducing the complexes Pb3 Si?0 y, Pb4 Si^0 -jQ and Pbi3 S i12O37 in addition to the components PbO and Pb2Si0 4 . The species considered in the Fe-O-SiC^ melt were FeO, FeO ]^,Fe?Si0 4 , Fe3 Sio0 7 , Fe3SigO| 5 and in the CUO0 . 5 -SÌO2 melt CuOo. 5 ana CU4 SÌO4 . Trie calculated phase diagrams, the a c t iv it ie s o f me­ta l oxides and the oxygen p a rtia l pressures were a l l in good agreement w ith the published data.

Two o f the papers in th is thesis concern the determination o f Gibbs free energies fo r Cu2S (s ,l) and Ca2 Fe2Û5 (s) through emf measurements u t i l iz in g a so lid e le c tro ly te . A c t iv it ie s and term i­nal s o lu b il i t ie s in the so lid so lu tion [Fe^,Ca]0 were also deter­mined.

The resu lts obtained from the quan tita tive equ ilib rium ca lcu la ­tions fo r conventional copper smelting and converting were used to o u tlin e the overa ll reactions taking place and the outcome o f changes in process parameters. Comparison w ith observed values, however, showed tha t the copper and magnetite contents in slag were calculated too low. These discrepancies could be completely explained by using a non-equilibrium approach in which the con­ve rte r was assumed to consist of several segments w ith concentra­tio n gradients between the segments.

Assessment o f s i l ic a te systems, model fo r l iq u id s i l ic a te s , lead s i l ic a te s , iron s i l ic a te s , cuprous s il ic a te s , q uan tita tive equi­lib rium ca lcu la tion s , emf measurements, Gibbs free energy, cup­rous sulphide, dicalcium fe r r i t e , w üs tite -ca lc ia so lid so lu tion , copper smelting and converting.

ISBN 91-7174-167-4 67 pages + 5 appendices

To Tuija

Tina & Matti

QUANTITATIVE EQUILIBRIUM CALCULATIONS ON SYSTEMS WITH RELEVANCE TO

COPPER SMELTING AND CONVERTING

BO BJÖRKMAN

Department o f Inorganic Chemistry, U n ivers ity o f Umeå,

S-901 87 Umeå, Sweden

This thesis is a summary o f the fo llow ing papers, in the te x t re fe r­

red to by th e ir Roman numerals I-V .

I. Q uantita tive Equilibrium Calculations on Conventional Copper

Smelting and Converting.

Björkman, B. and Eriksson, G., Can. M e ta ll. Q. 1982, 21, 329-

37.

I I . A Generalized Approach to the Flood-Knapp Structure Based Mo­

del fo r Binary Liquid S ilic a te s : Application and Update fo r

the PbO-SiO^ System.

Björkman, B ., Eriksson, G. and Rosén, E., Met a l l . Trans. B.

In p r in t.

I I I . An Assessment o f the System Fe-O-SiO^ Using a S tructure Based

Model fo r the Liquid S ilic a te Phase.

Björkman, B ., To be published.

i i

IV. Determination o f the S ta b il i ty o f Cu S in the Temperature

Range 1000 K-1450 K by Solid State EMF Measurements.

Björkman, B. and Fredriksson, M., Scand. J. M e ta ll. 1982, 11,

281-86.

V. A Solid State EMF Study o f the System Ca0 -Ca2 Fe2 0 5 -Fet 0 -Fe.

Björkman, B ., Scand. J. M e ta ll. Submitted fo r pub lica tion .

i i i

TABLE OF CONTENTS

INTRODUCTION 1Aim of the present study 2

Outline o f the work 3

MODEL FOR LIQUID SILICATES 5S ilic a te structures 5

Solid s ilic a te s 5Liquid s ilic a te s 7

Present models 10Proposed model fo r liq u id s ilic a te s 18

Application o f the model 21Pb0-Si02 21Fe-0-Si02 25

Cu0 0 .5 -Si02 27Cu-Fe-0-Si02 31

Discussion o f the present s truc tu re based model 35

EXPERIMENTAL STUDIES 36Method 36

Comments to resu lts 39

Af G° fo r Cu2S (s ,l) 39The system CaO-Ca^e^g-Fe^O-Fe 40

APPLICATION TO COPPER SMELTING AND CONVERTING 41Non-equilibrium conditions 47

Calculation procedure 49Results 51

FUTURE IMPROVEMENTS OF THE THERMODYNAMIC DESCRIPTION 55

ACKNOWLEDGEMENTS 57

REFERENCES 59

1

Introduction

The chemical reactions taking place in technical and geological pro­

cesses, e.g. the formation o f minerals and ores in the ea rth 's crust

and the extraction o f valuable metals from these ores, have been the

subject o f extensive studies during the la s t decades. Nevertheless’,

due to th e ir complexity, many o f these processes are not ye t fu l ly

understood. This is especia lly the case fo r the influence o f minor

elements. As an example, a survey o f the main chemical reactions ta ­

king place in conventional copper production through smelting and

converting can be obtained by studying the system Cu-Fe-S-O-SiC^.

However, to a rr ive a t a more complete descrip tion , the elements Ca,

Mg, A l, N i, Pb, As, Sb and Bi should also be incorporated. Such

multicomponent systems are usually d i f f i c u l t to handle experimental­

ly due to th e ir complexity and because a t high temperatures the cor­

ro s iv i ty o f the liq u id phases towards container material may cause

severe problems. Furthermore, a systematical study o f the influence

o f a l l components on the outcome o f a process would be very time-

consuming and expensive, especia lly i f the study is performed on a

f u l l scale process. Therefore most o f the experimental data presen­

ted h ith e rto have been determined in binary systems and very ra re ly

in systems higher than ternary.

An a lte rn a tive way to study multicomponent systems is to use quanti­

ta t iv e equ ilib rium ca lcu la tions , since in most cases re lia b le th e r­

modynamic descriptions fo r the constituen t binary and ternary sys­

tems are the only needed. Equilibrium ca lcu la tions can therefore

serve as an e ffe c tiv e tool to simulate multicomponent processes and

2

to p red ic t the outcome o f a change in process parameters.

Today, e f f ic ie n t computer programs e x is t fo r the ca lcu la tion o f equi­

lib rium compositions in multicomponent systems, e.g. the free energy

m inim ization program SOLGASMIX (1 ). This computer program has success­

fu l ly been applied to a number of systems, e.g. roasting o f chalcopy-

r i t e , CuFe$2 ( 2 ) , phase e q u ilib r ia in multicomponent a llo y systems

(3 ), mineral assemblages in p y ro lite and lh e rz o lite (4) and phase

e q u ilib r ia in a gas o f so lar composition (5 ,6 ). A p rerequ is ite fo r

these ca lcu la tions is tha t the Gibbs free energies are known fo r a l l

species which might appear in nonneglig ible amounts and tha t models

are given which describe the composition dependence o f the excess

Gibbs free energies o f the so lu tions.

Aim o f the present study

The aim o f th is study has been to ca lcu la te q uan tita tive equ ilib rium

compositions in systems w ith relevance to the conventional copper

smelting and converting and to study the extent to which equ ilib rium

ca lcu la tions may be used to simulate these processes. To accomplish

th is , a considerable part o f th is work has been directed towards ob­

ta in ing a generalized s tructu re based model fo r s i l ic a te systems.

This model was then used in an assessment o f the most important bina­

ry and ternary copper-iron slag systems.

Although a large body o f experimental data exis ts today, thermodyna­

mic data fo r many important phases in systems w ith relevance to cop­

per pyrometallurgy are e ith e r lacking or o f low accuracy. Part o f the

3

work has therefore been concerned w ith determination o f improved

thermodynamic data fo r C i^ S ts J ), Ca2 Fe2 0 ^(s) and the so lid so lu tion

[Fet ,Ca]0.

Putì ine o f t he work

This study commenced w ith a quan tita tive ca lcu la tion o f the e q u ilib ­

rium compositions in conventional copper smelting and converting ( I ) .

The composition dependence o f the a c t iv i ty co e ffic ie n ts fo r liq u id

species was described by using as simple mathematical expressions as

possible.

There have been many recent reports o f measurements by spectroscopy

and w ith ana ly tica l and high temperature X-ray d if fra c t io n techniques

on both glassy and liq u id s il ic a te s . These measurements have shown

tha t some complexation occurs between the mixed oxides, a fa c t tha t

ju s t i f ie s the use o f a s tructu re based model to describe the non­

id e a lity o f s i l ic a te melts. Information on the composition o f the

complexes present in s i l ic a te melts may thereby also be gained.

A generalized s tructu re based model fo r liq u id s ilic a te s was presen­

ted in paper ( I I ) and used in an assessment o f the systems PbO-SiO^

( I I ) and Fe-O-SiC^ ( I I I ) . The system PbO-SiC^ was chosen to te s t the

model because very accurate a c t iv it ie s o f PbO(l) are ava ilab le (7)

and because Raman spectroscopic measurements on PbO-Si0^ glasses (8 )

have shown tha t these glasses and presumably also the melt consist o f

a few s il ic a te complexes. The s tructu re based model has also been ap­

p lied to the system CuOQ g-SiO^ and to s i l ic a saturated melts in the

4

system Cu-Fe-O-SiO^. The resu lts obtained fo r these la t te r systems

w i l l be discussed in th is summary paper. The system Cu-Fe-O-SiO^ con­

ta ins the main elements fo r a descrip tion o f the slag phase in conven­

tio n a l copper pyrometallurgy.

The sulphide phase (matte phase) in conventional copper pyrometal­

lurgy consists mainly o f the elements Cu, Fe and S. Improved values

o f the Gibbs free energy o f formation fo r Cu2S (s , l) , obtained through

emf measurements u t i l iz in g ca lc ia s ta b ilize d z ircon ia as so lid e lec­

t ro ly te , are given in paper (IV ).

The copper concentrates used in copper pyrometallurgy contain, in

many cases, rather large amounts o f CaO and/or MgO, e ith e r derived

from the copper ore or purposely added to bene fit the process. In the

M itsubishi process (9) CaO is added instead o f SiO^ to give an oxide

phase w ith the desired properties. The systems Ca-Fe-0 and Ca-Fe-0-

SÌO2 are therefore o f as great in te re s t fo r copper m e ta llu rg is ts as

fo r iron m e ta llu rg is ts .

In an assessment o f the systems Ca-Fe- 0 and C a-Fe-O -S^* a knowledge

o f the subsolidus phase re la tions is most important. However, fo r

some parts o f these systems the published data are con trad ic to ry .

Subsolidus phase re la tions in the system Ca0 -Ca2Fe2 0 ^-Fet 0 -Fe, a c t i ­

v it ie s o f Fe O in the so lid solu tions and the s ta b i l i t y o f Ca2 Fe2 0 ^(s)

were therefore determined from emf measurements using ca lc ia s t a b i l i ­

zed z ircon ia as so lid e le c tro ly te . The resu lts obtained are given in

paper (V).

Model fo r l iq u id s ilic a te s

Models fo r liq u id s ilic a te s have occurred qu ite frequently in the l i ­

te ra tu re . These are e ithe r based on parameterized expressions fo r the

a c t iv i ty co e ffic ie n ts o f the mixed components or on d if fe re n t assump­

tions o f the melt s truc tu re . To compare these models and to develop a

generalized model fo r liq u id s ilic a te s based on sound s tru c tu ra l as­

sumptions, a b r ie f review o f the lite ra tu re on the structures o f so­

l id and liq u id s ilic a te s is necessary.

S i l ica te structures

Sol id s i 1ica te s . In most cases s ilic o n is in fo u rfo ld coordination

w ith oxygen, resu lting in s l ig h t ly d is to rted [SiO^] tetrahedra, but

in a very few cases the oxygen coordination has been found to be s ix ­

fo ld in the shape o f a s l ig h t ly d is to rted octahedron, e.g. in thauma-

s ite Ca^ISi(OH)^][COg][SO^]•1 2 ^0 , in the high pressure m odifica tion

of S i0 2 * s tis h o v ite , and in the high pressure phase

K [(S i0 7 5 ’ AIq 25^4^8-* ^ most s ilic a te s contain iso la ted or

corner shared [SiO^] groups, the only exception being fib rous S i0^

which is b u i l t up from edge shared [S iO ^ tetrahedra. With very few

exceptions the s il ic a te anions w ith iso la ted and corner shared [S i0^]

groups can be c la s s ifie d according to Table 1.

S ilic a is a strong ly ac id ic oxide and in the presence o f a more basic

oxide w i l l react according to the reaction scheme

Table 1. Broad c la s s if ic a tio n o f s ilic a te s w ith fo u rfo ld coordinated

s il ic o n atoms. From Liebau (10).

S i ng 1 e Double T rip le Quad­ruple

Quin­tup le Hexuple

Tetrahedra + + + - - -

Chains + + + + + -

Layers + + - - - -

Frameworks +

Rings + + - - - -

7

Consider the three-dimensional array o f [SiO^] tetrahedra in the 3-

c r is to b a lite s tructu re il lu s tra te d in Fig. la . 3 -c r is to b a li te is the

stable m odifica tion o f SiO^ from 1743 K and up to the melting po in t.

I f a more basic oxide MO is added, some o f the Si-O-Si bonds w i l l be

broken according to reaction ( I ) , resu lting in a formation o f new so­

l id phases containing s i l ic a te anions w ith the s truc tu re o f e ith e r

in f in i te layers or chains or small d iscre te rings or chains (see Fig.

lb - f and Table 1).

The ra t io o f SiO^ to basic oxide is the most important fa c to r deter­

mining the degree o f condensation o f the [SiO^l tetrahedra, but not

the only important one. The size and charge o f the cations w i l l de­

termine whether a ce rta in anion is stable or not and also the perio ­

d ic ity o f e.g. the chain anions ( 1 0 ).

L iquid s i l ic a te s . The s truc tu ra l properties o f l iq u id s ilic a te s can

be assumed to be s im ila r to so lid s il ic a te s . The anions present in

s i l ic a te melts would thus be d iscre te o rth o s ilic a te anions, chain

anions, rings , layer anions and three-dimensional framework anions.

I t is not reasonable, however, to assume tha t the chains, layers and

three-dimensional framework anions in the melts are very la rge, but

tha t they are merely fragments o f the in f in i te anions present in so­

l id s il ic a te s . These assumptions on the s tructu re o f the s i l ic a te

melts are also in agreement w ith most o f the ava ilab le experimental

resu lts concerning s i l ic a te melt s tructu res.

High temperature X-ray d if fra c t io n measurements on several s i l ic a te

melt systems have been performed by Waseda et a l. (13 through 17).

8

Fig. 1. The id e a l iz e d structures o f a) c r i s toh a l i t e , b) layers o f

SiOq te trahedra, c) id e a l iz e d s ing le pyroxene chain seen in perspective

d) d i f f e r e n t configurations o f s ing le and double chains3 e) t r i p l e rings

in b e n i to i te , BaTiSi^Og, f ) d iscre te o r th o s i l ic a te anions in Mg^SiO^;

shaded c irc le s represent Mg. Throughout th is f igu re small black c irc le s

represent Si atoms and open c irc le s represent 0 atoms. F ig . la s b> d - f

fi*om V e ils ( ! ! ) and F ia . 1c from Deer e t a l . (12).

Bild borttagen – se tryckt versionImage removed – see printed version

9

The systems investigated comprise L i20-S i025 Na20-S i02 and I<2 0 -S i0 2

(13,14), Ca0-Si02 and Mg0-Si02 (15), Fe0-Si02 (16) and F eO -F e^-

Si02 (17). These measurements have confirmed th a t the fundamental

local ordering u n it in liq u id s ilic a te s is the [SiO^] tetrahedron.

The S i-S i coordination number was shown to gradually increase by the

add ition o f Si02, ind ica ting a polymerization o f [SiO^] tetrahedra.

At the m etas ilica te composition, MSiO^, the S i-S i coordination num­

ber is about three in several o f the systems.

The glasses formed on rapid cooling o f most s i l ic a te melts co n s titu ­

te a lin k between the melt and the so lid phases and i t is reasonable

to expect s im ila r structures in the glass and the melt. This has a l­

so been shown by Waseda and Toguri (15) through high temperature X-

ray d if f ra c t io n measurements and by Kashio et a l. (18) and Sweet and

White (19) through Raman and IR spectroscopy. The q u a n tita tive d is t ­

r ib u tio n can, however, d i f fe r in the glassy and the liq u id s ta te , as

was emphasized by Waseda (20). Comparison o f Raman spectra fo r both

glassy and so lid s ilic a te s (21 through 24) shows tha t the same s truc ­

tu ra l un its are to be expected in both so lid and glassy s il ic a te s .

A large number o f experimental measurements w ith Raman and IR spec­

troscopy on glasses in s i l ic a te systems have been reported: Na2 0 -

Si02 (21,25,26), L i20-S i02 ( 2 1 ) , K2 0 -S i0 2 ( 2 1 , 2 2 ) , Ca0 -S i0 2 (18,26),

PbO-Si02 (8,22,24), K20-Pb0-Si02 (22), Mg0-Ca0-Si02 (26), N a ^ - A l^ -

Si02 (26), Na20-Fe203 -S i02 (27), Ca0-Mg0-Fe0-Fe203 -S i0 2 (27), CaO-

A l203 -S i0 2 and MgO-Al203 -S i0 2 (28). The measurements showed th a t these

glasses can be in terpre ted as consisting o f only a few s tru c tu ra l

un its w ith 4, 3, 2, 1 and 0 nonbridging oxygens per s il ic o n , corres-

10

4- 6 -ponding to d iscrete o rth o s ilic a te anions, SiO^ , dimers, Si^Oy ,

chains or rings , layers or three-dimensional fragments and in f in i te

three-dimensional frameworks, respective ly . D is tin c t compositional

domains invo lv ing only some o f these s tru c tu ra l un its could be found.

The measurements w ith Raman and IR spectroscopy can, however, not

give an exact answer on the size and configura tion o f the s i l ic a te

anions present in the glasses, but, merely the types o f anions. Ex­

perimental measurements o f the exact s i l ic a te structures in these

glasses are so fa r lacking.

Present models

Models fo r liq u id sa lts can roughly be divided in to three types:

1) Models based on interm olecular forces and derived from f i r s t

p r in c ip le s , e.g. computer simulations using Monte Carlo techn i­

ques.

2) Models based on a polynomial descrip tion fo r the non -idea lity

o f the melt.

3) Models based on what is known about the real structures in the

m elt.

The exact theore tica l models, group 1) above, are today c h ie fly o f

academic in te re s t, as they can only p red ic t the properties o f a few

pure molten sa lts and very few s a lt m ixtures.

11

The only app lica tion o f a model belonging to group 1) above to s i l i ­

cate melts is the Monte Carlo ca lcu la tions by Borgianni and Granati

(29,30). Their ca lcu la tions were based on a descrip tion in which the

anion d is tr ib u tio n was given by the arrangement o f Si and vacancies

on the Si la t t ic e . However, the in te ra c tio n energies needed £5 ^ .5 ^«

evac-vac and eSi-vac could only be estimated-

Models based on d if fe re n t polynomial descriptions fo r the free energy

o f mixing or the dependence o f the a c t iv i ty c o e ffic ie n t on composi­

t io n , have been applied to liq u id and so lid so lu tions in numerous

systems. The Margules polynomial (31) fo r binary regular so lu tions

was formulated by Hildenbrand (32) as

RT,nTi ■ i j kj (1‘Xi)d (')

For an explanation o f a l l symbols not explained in the te x t, see

Table 2.

With one parameter the well-known symmetrical Margules equation is

obtained

RTlrrt^ = k2X22 (2)

where k2 is an in te ra c tio n parameter. Eq. (2) can be derived from a

symmetrical shape o f the = f(X 2) curve, where = k2Xl X2*

A number o f other polynomial descriptions fo r the n o n -id e a lity have

also been suggested. The symmetrical regular so lu tion model is fo r a

multicomponent system w ritte n :

12

Table 2. L is t o f symbols.

X bulk mole fra c tio n

X equ ilib rium mole fra c tio n

a ( i) a c t iv i ty o f i

y ( i ) a c t iv i ty c o e ffic ie n t fo r i

k- . binary in te ra c tio n parameter in the system i - j • »J

equilib rium constant fo r equ ilib rium ( I I )

equ ilib rium constant fo r equ ilib rium ( I I I )

K (i) equ ilib rium constant fo r equ ilib rium ( i )

A H enthalpy o f mixing

AH(i) enthalpy change in reaction ( i )

A^G Gibbs free energy o f mixing

AG( i ) Gibbs free energy change in reaction ( i )

A fG °(i) Gibbs free energy o f formation fo r i

GE excess Gibbs free energy

p ( i) p a rtia l pressure o f ( i )

gn equ ilib rium amount o f gas species in segment n

cn same as gp, but fo r condensed species

13

RTlnrk = i x i ( l - x k ) k i k - I a 1XJ k 1J ( 3 )

i . j ^ k

where k^k and k ^ are the in te ra c tio n co e ffic ie n ts in the binary

systems. This model was used by Lumsden ( 3 3 ) to describe the non­

ideal a c t iv it ie s in the ternary system FeO-FeO g -S it^ . The system

Fe-O-SiOg has la te r been described by Goel e t a l. ( 3 4 ) as a non­

ideal m ixture o f Fe, FeO, FeO g and SiO^. using a three s u ff ix

Margules equation w ith zero ternary in te rac tions

,nn ■ '^ (kij*kji)xr ' /2skjpx)V i(kfrkóf)xj(xj/2-xi)J O JP J

♦ ^ V W V j <4>

with k..j = k .. = 0' * J J

Models fo r liq u id s il ic a te s , more or less based on s tru c tu ra l consi­

derations, have been reviewed by Gaskell (35) and Bottinga e t a l.

(36). These models can be divided in to two groups:

1) Models based on the d is tr ib u tio n o f three d if fe re n t kinds o f2 -

oxygen in s i l ic a te s , free oxygen - 0 , oxygen bound to one

s ilic o n - 0~ and doubly bonded oxygen - 0°. The models presen­

ted by Toop and Samis (37), Yokokawa and Niwa (38) and Lin and

Pel ton (39) belong to th is group.

2) Models based on a gradual condensation o f S i0^~ tetrahedra on

add ition o f SiO^ to MO through the equ ilib rium

sio.^~ + sì 02(p+1)~ si n2 p+2 ~ + o2~ n n^ iu 4 + p 3p+l * b1 p+l 3 p+4 + U

14

Models belonging to th is group have been presented by Masson et

a l. (40 through 42), Esin (43), Kapoor e t a l. (44) and Gaskell

(45).

In the model presented by Toop and Samis (37) the equ ilib rium con­

stant Kyç. fo r the equ ilib rium

2 0 ' ♦» 0 ° + 0 2' ( I I I )

was assumed to be independent o f composition. The free amount o f

oxygen was calculated through the re la tio n

a(M0) = x (M2+) • x(02' ) (5)

derived by Temkin (46). Using the mass balances an equation was de­

rived by which kts could be calculated from measured data, a(M0) =

f(X (S i0 2) ) .

By considering the s ta t is t ic a l d is tr ib u tio n o f S i-S i and vacant-

vacant pairs on the s ilic o n la t t ic e and assuming AH( I I I ) to be inde­

pendent o f composition, Yokokawa and Niwa (38) derived an expression

re la tin g ^ G , 1 n[a(MO) ] and ln t a f S ^ ] to composition and the number

o f s ing ly bonded oxygens. A s im ila r approach was used by Lin and

Pelton (39).

In the models derived by Masson et a l. (40 through 42) conventional

polymer theory was applied to s i l ic a te melts. The equ ilib rium con­

s tan t, Kj , fo r the formation o f chain s i l ic a te anions according to

equ ilib rium ( I I ) was assumed to be independent o f chain length (40).

15

Using mass balance constra in ts and the Temkin equation (45), an exp-2 -

ression re la tin g the bulk mole fra c tio n o f SiO^, X(Si0 2 > to x(0 )

and K was derived. In the ca lcu la tions the ten simplest chain anions

were considered. This theory was la te r extended to account fo r the

formation o f branched chains (41,42).

In p r in c ip le , the same model was also considered by Kapoor e t a l.

(44) and Gaskell (45). In these models 0^~ and the d if fe re n t S iO ^

segments o f the s i l ic a te chains, instead o f 0 and the s i l ic a te

anions as in Masson's approach, are assumed to mix id e a lly . Using an

expression by Guggenheim fo r the configura tiona l entropy, they de­

rive an expression fo r ^G = f(X (S i02)) containing fo r e q u ilib ­

rium ( I I ) as a parameter. The models given by Kapoor e t a l. (44) and

Gaskell (45) d i f fe r in using d iffe re n t approximations fo r the c o n fi­

gurational entropy.

In the model ca lcu la tions by Flood and Knapp (47) on the system PbO-

SiC^j they assumed tha t oxide rich melts consist o f PbO and Pb2SiO^.

These species describe measured a c t iv it ie s o f PbO (48) very well a t

X(SiÛ2 ) < 0.2. In the composition range 0.2 < X(SiÛ2 ) < 0.4 a good

agreement w ith measured a c t iv it ie s could be obtained by adding a

complex Pb3S i30g, while in the composition range 0.4 < X(SiÛ2 ) <

0 . 6 a complex pb3SigO^ has also to be considered.

Figs. 2 and 3 show measured and calculated a c t iv it ie s o f PbO and FeO

in the binary s i l ic a te systems PbO-Si^ and F e O -S ^ , respective ly.

Measured a c t iv it ie s o f Pb0(l) can only be described accurately by

using the models o f Flood and Knapp (47), Yokokawa and Niwa (38) and

a(Pb

O)

a(Pb

O)

a(Pb

O)

16

1.0

0.8

0.6

0.4

0.2

0 Q2 0.4 0.6 08 1.0X(Si02)

y1.0

08 0.6 04 0 2

0.0

1.0

0.8

0.6

0.4

0.2

0 0.1 0.2 03 0.4 0.5X t S i q )

'fzy - c t.... r - T

_ I 4 9 ) \-

(4 8 )-^-

"Pb0-Si07 i__L . , ,r .

01 02 03 Q4 Q5X(Si02)

V

<y

O 0.6_QCL- r 0.4

O Q2 04 06 08 1.0X(Si02)

<V

o 0.6-Q

% 0.4

0 Q1 0.2 03 04 0.5XlSiO^)

oontd

a(Pb

O)

17

vIO

y

PbO 0.2X(Si02)

0 0.1 0.2 0.3 0.4 0.5X(Si02)

F ig . 2. Calculated (dashed curves) and measured (48 ) , (s o l id curves)

a c t i v i t i e s o f PbO in melts o f the system PbO-SiO^ a t 1373 K. a) Toop and

Samis (37). The la b e l l in g A, B and C o f the curves corresponds to values

o f LG° ( I I D / R T equal to 0, - 1.88 and -3 , respective ly , b) Yokokawa and

Niwa (38). c) L in and Pelton (39). Experimental values from three d i f f e ­

ren t studies (7 ,4 8 ,4 9 ) . d) Masson (40), l in e a r chains. The la b e l l in g A,

B and C corresponds to a value o f L G ° ( I I ) /R T equal to 0, -1 .8 8 and -3 ,

respective ly , e) Masson (42 ) , branched chains, f ) Gaskell (45). g) Flood

and Knapp (47). F igs . a, b and d through f are from Gaskell (34) .

18

Lin and Pelton (39). The fa ilu re of the other models can be ascribed

to two reasons. As only chain s ilic a te s are assumed to form (40-42,

44,45) the models are lim ited to mole fra c tio n s of s i l ic a less than

0.5. The differences between calculated and measured a c t iv it ie s usu­

a lly occur at mole frac tions X(Si02) = 0 .3 -0 .4 , i .e . the composition

range where more polymerized s il ic a te anions may form in appreciable

amounts. The second reason might be tha t the equ ilib rium constant

fo r the condensation o f a [SiO^] tetrahedron to a small chain is de­

pendent on chain size. This is known to be the case in conventional

polymerization chemistry and is contrad ictory to what was assumed in

the models o f e.g. Toop and Samis (37) and Masson (40).

For the system FeO-SiO^ the models presented by Masson et a l. (40

through 42) give the best f i t to measured a c t iv it ie s o f FeO(l), c f.

Fig. 3. The composition range covered by experiment in th is system

is X(S i0 2 ) < ~ 0 . 6 , which is la rge ly w ith in the range where small

chain s i l ic a te anions can be expected to predominate in the m elt.

Proposed model fo r liq u id s ilic a te s

In the model presented by Flood and Knapp (47) they assumed tha t a

s i l ic a te melt MO-SiO rich in basic oxide MO consists predominating­

ly o f free MO and d iscre te o rth o s ilic a te complexes M^SiO^. On addi­

tio n o f S i02 à lim ite d number o f more polymerized complexes are fo r ­

med. These assumptions are in good agreement w ith ava ilab le informa­

tio n on the s tructu re o f so lid and liq u id s ilic a te s .

To fa c i l i t a te the app lica tion o f the Flood and Knapp model to any

a(Fe

O)

a(Fe

O)

19

XlSiC^) XISiO,)

1360 c

(19.60 C)

KUUS2H

K(ID= 0.835_ K U)=2.86

XISiO,)0 0.1 0.2 0.3 04 0.5

X (S iC X j)

Fig. 3, Calculated and measured a c t i v i t i e s o f FeO in melts o f the sys­

tem FeO-SiO2 in equil ib rium with iron , s o l id lines correspond to measu­

red values while dashed and dashed-dotted lines correspond to ca lcu la ted

values: a) Yokokawa and Niwa (38) , w ith two d i f f e r e n t values o f the

equil ib r ium constant, b) L in and Felton (39 ) , c) Masson, dashed l in e is

ca lcu la ted w ith the model assuming only l in e a r chains (40 ) , while in the

ca lcu la t io n o f the dashed-dotted l in e also branched chains are conside­

red (42) , d) Gaskell (45) , with d i f f e r e n t values fo r K ( I I ) .

20

binary s i l ic a te system and to fa c i l i t a te a systematic search o f the

complexes which best describe measured a c t iv i t ie s , a more genera li­

zed form ulation o f the model is needed. Furthermore, to simulate

real m e ta llu rg ica l and geological processes, more complex systems

than b inaries have to be considered.

Adopting the Flood-Knapp model, a ternary s i l ic a te melt is most con­

ven ien tly described as a mixture o f the components M0,M0-j ^ and

I^SiO^ or Mj0 ,M jj0 and M^SiO^, and a number o f complexes formed from

th e ir components. The formation o f complexes in a melt o f a ternary

s i l ic a te system, e.g. M0-M0 ^-SiC^» can then be w ritte n

P » * 1 "2 S’ °4 * rn0).5 * W ^ V A q t l . S r <IV>

where p, q and r are integers and q is always non-negative. The only

type o f s i l ic a te complexes assumed are those formed by polymeriza­

tio n o f the o rth o s ilic a te anion, i .e . only negative values o f p are

considered in connection w ith reactions invo lv ing I^SiO^.

Using mass balance constra in ts , the fo llow ing equations re la tin g the

bulk mole fra c tio n s , X, to the equ ilib rium mole fra c tio n s , x, are

derived

x(M0)+2x(M2Si04)+I(p+2q)x(Mp+2q+rSiq0p+4q+1_5r)X(MO) " X(Mû)+3X(M2Siû4 )+X(M0l i 5 )+l( p +3q+r ) X(Mp+2q+rS iq0p+4q+1/ 5 r) ^

x (M0 1.5)+ Irx (Mp+2q+rS lq°p+4q+1.5r)X(M01.5)7(M0>3x(M2SiÛ4)+x(MÔ1-5)+l(p+3q+r)"X(Mp+2q+rSiq0p+4q+1_5rr ^

The l iq u id is treated as ideal and the mole frac tions are re la ted to

the aG°(IV) values as

21

X(Mp+2q+rS iq°p+4q+l.5r )=x(M0)Px(M2Si04 )qx(M01 5 ) r exp(-AG°(IV)/RT) (8 )

The mole fra c tio n s are in te rre la te d according to the expression

As the liq u id is considered as id e a l, x(M0) in Eqs. (6 ) through (9)

is equivalent to measured a c t iv it ie s o f MO.

Extensive descriptions o f the computational procedure have been given

in papers ( I I ) and ( I I I ) .

Application o f the model

The model fo r s i l ic a te and oxide melts presented in th is study has

been used in an assessment o f the systems PbO-SiO^ (paper I I ) , Fe-0-

Si02 (paper I I I ) and C u O q ^-S iO ^ Using the descriptions fo r the sys­

tems Fe-0-Si02 and C u O q ^-S i02, the properties o f C u O q ^ in s i l ic a

saturated iron s i l ic a te slags have been calculated. The resu lts from

the two la t te r systems w il l be presented in th is summary paper.

PbO-SiOp. In the ca lcu la tions fo r the system PbO-Si02 the a c t iv it ie s

o f PbO(l) determined by Charette and Flengas (7) were used. The expe­

rimental data were divided in to a basic, X(PbO, 1 ) > 0 . 6 6 , and an a c i­

d ic range, X(PbO, 1) < 0.66. The very best f i t to experimental data

w ith in the basic range was obtained by introducing a complex Pb^Si2 0 y

in add ition to the components PbO and Pb2SiO^.

x(M0)+x(M2Si04 )+x(M01 5 )+lx(Mlp+2q+rS lq°p+4q+1.5r^ = 1 (9)

54

F ig . 4. Calculated e r r o r mean square values d ivided by 10~ , obtained in

the systematic search fo r a second complex ( -p ,q 30) in addit ion to

( - 1 ,2 ,0 ) in the PbO-SiO^ m e lt . The composition range covered is x (PbO ,l)

< 0.664. As only com er shared [SiO^\ te trahedra are considered, the p

and q values must be w ith in the area r e s t r ic te d by the s o l id l in es , ex­

cept f o r the values in d ica ted by the s o l id dots which also are impossible.

23

In the ac id ic range more polymerized s i l ic a te complexes have to be2

present. Fig. 4 shows calculated e rro r mean square values, S^, ob­

tained in a systematic search to f in d the complex which best repro­

duces measured a c t iv it ie s o f PbO(l). The e rro r mean square values

were calculated according to the re la tio n

s2 , HX(PbO)exp-X(PbO)ca)c]2 (10)f ~TFn

where N and n correspond to the number of experimental values and

parameters, respective ly . The best f i t to experimental data is ob­

tained by introducing a complex Pb^Si^O-jQ (p = - 6 , q = 4, r = 0) or

a complex P b ^ S i ^ (p = -7 , q = 5, r = 0). The model containing the

smaller complex, Pb2Si^0 ^Q, is preferred.

Fig. 5a shows the residuals A = X(PbO)exp“ x(pt>0) ca^c calculated w ith

th is set o f complexes at T = 1023 K. The measured a c t iv it ie s o f

PbO(l) are well reproduced, except in the composition range 0.48 <

X(PbO) < 0.6. To obtain an even be tte r f i t , a th ird complex o f app­

roximate composition Pb^^Si^2 ° 3 7 * corresPond'in9 to a chain u n it , has

to be introduced. However, the assumption o f chain complexes w ith

between ten and f if te e n s ilic o n tetrahedra give about the same f i t

to experimental values. Fig. 5b shows the residuals obtained w ith

the model containing the complexes Pb^Si^Oy, Pb2Si^0 iQ and

Pbi3S i12O3 7 - The residuals are now a l l about as large as or less

than the estimated experimental uncerta in ties and th is model is ac­

cepted.

Using th is descrip tion fo r the liq u id phase, an assessment o f the

24

100

10

CO

a /b

CO

20 10

b / o 0

<•-10-20

T

• ”HT t* t T 1

- )

fX I| I I|1

Pici. 5 .

0.4 0.6 0.8 X(PbO).'exp.

a) The residuals A = X(PbO) -X(PbO) 7 } p lo t te d against X(PbO)ex p Ca LC eocp

w ith the model ( - 1 ,2 ,0 ) + ( - 6 ,4 ,0 ) a t 1023 K. J Uncertainty in each expe­

r im enta l p o in t . This is estimated as twice the standard dev ia tion o f the

f i t , S p to the experimental emf values (7 ) .

h) The same as a) w ith the f i n a l l y accepted model ( - 1 ,2 ,0 ) + ( - 6 ,4 ,0 )

+ ( - 1 1 ,1 2 ,0 ) , corresponding to the complexes Pb^Si^O^, Pb^Si^O^ and

Pb13S i 12°37•

25

complete system PbO-SiC^ was performed. The resu lting phase diagram

is in good agreement w ith the experimental one (50). The thermodyna­

mic data assessed fo r the so lid phases d if fe r from corresponding va­

lues in the lite ra tu re w ith amounts equal to or less than the e s t i­

mated unce rta in tie s .

From th e ir measurements w ith Raman spectroscopy on PbO-SiO^ glasses,

Furukawa et a l. (8 ) concluded tha t glass o f o r th o s ilic a te composi-4- 2-tio n consists o f a small part o f S i0^ anions together w ith 0 ,

and probably some other la rger anion. Spectra o f lead meta­

s il ic a te glass gave about the same pattern as tha t obtained from

alam osit, PbSiO^, which is known to consist o f p a ra lle l chains w ith

a repeating u n it o f 12 tetrahedra (51). Measurements w ith Raman and

IR spectroscopy can, however, not give an exact answer regarding the

size and amounts o f the complexes but the q u a lita tiv e agreement be­

tween these measurements and the model calculated in th is study is

very good.

Fe-O-SiOp. In the system Fe^O-SiO^ the experimental data, a c t iv it ie s

o f FeO(l) and In p(O^) values, could be reproduced w ith in estimated

uncerta in ties w ith a model containing the species FeO, FeO

Fe^SiO^, Fe^Si^Oy and The melt in the system Fe-0 could

be described w ith reasonable accuracy w ithout in troducing any addi­

tiona l complex. Using these descriptions fo r the melts an assessment

o f the systems Fe-0 , Fe^O-SiC^ and Fe-O-SiC^ was made. The ca lcu la ­

ted phase diagrams as well as calculated a c t iv it ie s o f FeO(l) and

In p(O^) values were a ll in good agreement w ith lite ra tu re values.

26

in

09 - CUcSLO,

CU/SiQ

0.8 0.9 1.0X(CuOQ5)

F ig . 6. Measured and ca lcu la ted a c t i v i t i e s o f CuOq I ) a t 1653 K p lo t ­

ted against the bulk mole f r a c t io n o f CuO X(CuO^ . Thin l in e

represents the id e a l curve .

I I N ik i t in e t a l . (53)

27

The models obtained fo r the lead and iron s il ic a te systems d i f fe r in

some aspects. In the model fo r the system PbO-SiO^ (paper I I ) the

o r th o s ilic a te complex, Pb2SiO^, is the dominating s il ic a te species

in the composition range X(PbO) > 0.6, while in the iron s il ic a te

model, Fe^SÌ207 is the dominating complex in th is basic range and

Fe^SiO^ is formed in minor amounts at a l l compositions. The so lid

o r th o s ilic a te Fe2Si0 ^ (s ) , fa y a lite , is known to consist o f d iscre te

o rth o s ilic a te anions and i t would be reasonable to assume th a t the

melt in equ ilib rium w ith so lid fa y a lite contains an appreciable

amount o f the o r th o s ilic a te complex. This may suggest tha t the c a l­

culated complex Fe^Si^Oy in re a lity re fle c ts a mean composition be­

tween Fe2Si0 4 and a complex w ith composition corresponding to a ring

or a large chain s tructu re and perhaps Fe^Si2O7 • Introducing a comp­

lex w ith composition corresponding to e.g. a large chain s truc tu re

would most c e rta in ly lead to the complex Fe^Si^O^ being destab ilized

and Fe2Si0 ^ increasing in the basic range.

To resolve these types o f problems, resu lts from measurements w ith

Raman and IR spectroscopy on glasses would be h e lp fu l, but such mea­

surements have not been performed on pure iron s i l ic a te glasses to

the author's knowledge. Another technique which may give in te re s tin g

resu lts in the fu tu re is the Si-NMR technique applied to so lid samp­

les, e.g. s i l ic a te glasses.

CuOq ç-SiOp. Phase re la tions in the system CuOq 5 -SÌO2 have been re­

ported by Berezhnoi e t a l. (52). The eu tectic temperature and compo­

s it io n were given as 1333 K and about 8 wt % ( ^ 0 corresponding to

X(Cu00 5 ) = 0.906. From these values an estimation o f the liqu idus

Table 3. Thermodynamic descrip tion o f the CuOq g-Si02 system.

Standard states are Cu(s), 02 (g, 1 atm) and S i(s ) .

Species A^G°/J *mol a

1=a+b(T/K)+c(T/b

K)1n(T/K)+d*1 c

0_3 (T/K ) 2

d

CuOo.gd)

Cu4Si04 ( l )

Cu(l )

Cu20(s)

Si02 (s)

-130032

-939205

13263

-165453

-925570

399.108

108.679

-9.777

70.383

400.380

-45.4376

-30.468 7.398

29

phase boundaries was made. According to the phase diagram (52) the

terminal liq u id s o lu b il i ty o f SiO^ in melts o f the system C u O q

SÌO2 is between X ( C u O q 5 ) = 0.1 and 0.2 in the temperature range

1333 K through 1600 K. At these compositions, re s tr ic te d to the more

basic region, is i t reasonable to assume tha t the only species in

the m elt, in add ition to C u O q 5 , is the o rth o s ilic a te Cu^SiO^.

Fig. 6 shows measured ( 5 3 ) and calculated a c t iv it ie s o f C u O q ^

p lo tted against the bulk mole fra c tio n o f C u O q 5 . The calculated

values were obtained by assuming the melt to consist o f one species

in add ition to C u O q The model considering the formation o f an

o r th o s ilic a te species, Cu^SiO^, is the only one which can reproduce

the measured a c t iv i t ie s , and was used in an assessment o f the comp­

le te phase diagram. The resu lting thermodynamic data are given in

Table 3 and the calculated phase diagram is given in Fig. 7 .

The equ ilib rium oxygen p a rtia l pressures fo r the reaction between

m e ta llic Cu and Cu20(s) have been determined in numerous investiga ­

tions . The Af G°(Cu20,s) re la tionsh ip given in Table 3 was calculated

from the resu lts obtained by Fredriksson and Rosén (54), Charette

and Flengas (55) and Taskinen (56). The smoothed values agree to

w ith in 500 J w ith these experimental resu lts . The thermodynamic data

used fo r Cu(1) are the same as in paper (IV) while thermodynamic

data fo r C u O q ^(1) and Cu^SiO^(l) were calculated from the phase

diagram. The calculated A^G° values fo r C u O q ^ ( 1 ) agree to w ith in

1500 J w ith the values used in paper ( I ) and the values compiled by

E l l io t t and G leiser (57) and Schmid (58).

30

CuOqç 0.1 0.2 0.3 OåX (S i02)

Fig, 7, Calculated phase diagram f o r the binary system CuOn r-SiO^ inU * b O

equilib rite li with m e ta l l ic copper, Dashed, l ines in d ica te the liquidas

curves estimated by Berezhnoi (52),

31

Oxide melts in the system Cu-0 can contain a considerable excess o f

oxygen or copper compared to the s to ich iom etric composition C u O q

and liq u id copper in equ ilib rium w ith an oxide phase can also d is ­

solve a considerable amount o f oxygen ( 5 8 ) . The system C u O q ^-S i0^

was calculated w ith the aim o f obtaining a model which can be used to

ca lcu la te the properties o f C u O q ^ ( 1 ) in iron s i l ic a te slags. There­

fo re , as a f i r s t approximation, i t is qu ite s u ff ic ie n t to tre a t the

liq u id metal and oxide phase as pure Cu(l) and C u O q ^ ( l)» respec ti­

ve ly.

Cu-Fe-Q-SiQg. As models fo r the systems C u O q ^-SiO^ and Fe-O-SiO^

(paper I I I ) are ava ilab le , the study was extended to the quaternary

system Cu-Fe-O-SiO^. This system has been studied through the gas

e q u ilib ra tio n technique by Altman and Kellogg (59), Ruddle et a l.

(60) and Taylor and Jeffes (61). Due to the complexity o f the system

and the c o rro s iv ity o f the slag towards container m a te ria l, these

experiments were performed a t s i l ic a sa tu ra tion .

Fig. 8 and 9 show measured (59) and calculated a c t iv it ie s o f

C u O q ^ ( l ) and In p(O^) values in the system Cu-Fe-O-Si^ in e q u ilib ­

rium w ith m e ta llic copper and so lid s i l ic a p lo tted against the bulk

mole fra c tio n o f C u O q 5 , X ( C u O q ^). The calculated values were ob­

tained by using the compositions determined by Altman and Kellogg

(59). The standard deviation o f the f i t to a l l 46 experimental va­

lues measured by Altman and Kellogg (59) is 0.0102 and 0.55 in

a(CuOQ 5 ,1) and In p ^ ) , respective ly , which is about the same as

in the system Fe-O-SiO^. The main con tribu tion to these standard de­

v ia tions is from measured values at mole fra c tio n s X(CuOQ 5 ,1) above

32

0.200.18 0.16 O . U

' s 0 - 1 2? 0.10^ 0.08

0.06 0.04 0.02

F ig . 8. Measured and ca lcu la ted a c t i v i t i e s o f CuO ^ ( l ) in the

Cu-Fe-0~Si02 melt in equ il ib r iu m with copper and s o l id s i l i c a , p lo t te d

against the bulk mole f r a c t io n o f CuOq X(CuOq . S olid and dashed

l ines in d ica te ca lcu la ted values a t 1536 and 1560 K, res p e c t iv e ly , while

the th in liyie represents the id e a l curve .

Altman and Kellogg (59), 1536 K

Altman and Kellogg (59), 1560 K

0.02 0.04 0.06 0.08X(CuOqc)

33

0.02 0.04 0.06 0.08 X(CuO05)

Fig. 9. Measured and ca lcu la ted In p(O^) values in the Cu-Fe-O-SiO^

melt in equ il ib r ium w ith copper and s o l id s i l i c a . Legends have the same

meaning as in Fig. 7.

34

about 0.06.

The d ifferences between calculated and measured values a t la rger

X ( C u 0 q £,1) can p a rtly be due to a too s im p lifie d descrip tion fo r

the system Cu-0, but i f re a l, they can also re f le c t th a t there is

some complexation w ith FeOj in the m elt. I t could therefore be

tempting to assume tha t complexes such as CuFe^O occur in the melt

since there exists a so lid so lu tion between Fe3Û and the fe r r i t e ,

CuFe^O^, a t subsolidus temperatures. However, a complex CuFe2Û w i l l

imply lower calculated a c t iv it ie s o f C u O q ^ and lower In p ^ ) va­

lues. This leaves as the only a lte rn a tive a complexation between

FeO ^ and SiO^, which also could explain the d ifferences between

calculated and measured liqu idus boundaries a t high F e (III) contents

in the system Fe-O-SiC^. However, as the experimental inform ation at

very high F e ( II I) contents is ra ther lim ite d , i t is not reasonable

to account fo r such a complexation in the models. Nevertheless, the

models fo r the systems C u O q ^-S i0^ and Fe-O-SiC^ give a s u ff ic ie n t ly

good descrip tion o f the quaternary Cu-Fe-O-SiC^ melts a t the condi­

tions normally p reva iling in conventional copper smelting and con­

ve rtin g , i.e . X ( C u O q 5) < 0.10.

Compared to the descrip tion given in paper ( I ) fo r the slag system

Cu-Fe-O-Si^, the model presented in th is thesis is a considerable

improvement. Measured p ^ ) values and a c t iv it ie s and phase re la ­

tions in the systems Fe^O-SiO^» C u O q ^-SiO^» Fe-0, Fe-O-SiO^ and

Cu-Fe-0 -SiÛ2 are reproduced very well and more accurate p red ic tions ,

when applied outside the range where experimental data e x is t, w i l l

most c e rta in ly be obtained.

35

Discussion o f the present s truc tu re based model

In th is study a s tructu re based model fo r l iq u id s i l ic a te systems

has been presented and applied to the systems PbO-SiC^, Fe^O-SiC^,

CuOq ^-SiO^j Fe-0 , Fe-O-SiO^ and Cu-Fe-O-SiC^. The present model has

several advantages over other ex is ting s tructu re based models (37

through 45). I t involves no assumption in advance o f the arrangement

o f the s ilic o n tetrahedra in the complexes present and is not re ­

s tr ic te d to a ce rta in composition range. Furthermore, contrary to

the models given in re fs . (37 through 45) the presented model can

eas ily be applied to systems more complex than b ina ries .

The model ca lcu la tions give also some inform ation on the real compo­

s it io n of the complexes present in s i l ic a te melts. Support fo r th is

statement is gained in the good agreement between the calculated re­

su lts fo r the system PbO-Si02 and those obtained through Raman and

IR measurements (8 ).

Further support fo r the v a lid ity o f the model is obtained from i ts

a b i l i t y to reproduce phase diagrams, w ith values o f A^G° fo r the so­

l id phases which are in good agreement w ith the published values.

In s i l ic a te systems, where comprehensive experimental studies have

revealed tha t a complexation occurs in the m elt, models based on the

ava ilab le melt s tructu re information should be used. In systems

where th is inform ation is lim ite d , parameterized expressions fo r the

dependence o f the a c t iv ity co e ffic ie n ts on composition are, in most

cases, qu ite s u ff ic ie n t. An exception is the sulphide systems, where

36

ordinary polynomial models have fa ile d to describe the rapid change

o f sulphur a c t iv ity . For these systems an add itional in troduction o f

associates (62) or sub la ttices (63) have been necessary.

Many oxide and sulphide systems contain a closing m is c ib i l i ty gap in

the liq u id phase. These mi s c ib i l i ty gaps are most eas ily described

by polynomial models. A fu rth e r advantage w ith these la t te r models

is th a t extrapolations w ith in the same system are eas ily obtained.

Extending these models, e.g. the one used by Goel e t a l. fo r the

system Fe-O-SiC^ (c f. Eq. (4 ) ) , to a multicomponent system w i l l re­

s u lt in a very large number o f parameters which have to be determi­

ned.

In comparison w ith the model used by Goel et a l. the present model

is simple to use in e.g. phase diagram ca lcu la tions as only a few

complexes are considered to form in the ideal melt. The good a b i l i t y

o f the present model to reproduce measured data fo r a multicomponent

system, using data obtained in lower order systems, has been demon­

stra ted in the ca lcu la tions on the system Cu-Fe-O-SiC^.

Experimental studies

Method

The emf technique u t i l iz in g ca lc ia , magnesia or y t t r ia s ta b ilize d

z ircon ia as so lid e le c tro ly te has been used to determine the oxygen

p a r t ia l pressures o f numerous e q u ilib r ia since the pioneering work

by Kiukkola and Wagner (64). The measured quantity is an oxygen po-

37

te n ti al d iffe rence between the oxide mixtures in the two c e ll com­

partments. In the e a r lie s t measurements the e le c tro ly te consisted o f

pressed pe lle ts o f s ta b ilize d z ircon ia w ith sample and reference

m ixture on each side o f the p e lle t , both mixtures in contact w ith

the same gas phase. With th is c e ll arrangement oxygen can eas ily

d iffu se from one side o f the e le c tro ly te to the other, g iv ing r is e

to erroneous emf values. This is especia lly the case i f the d i f fe ­

rence in oxygen p a rtia l pressure between sample and reference mix­

ture is large. To avoid these problems Charette and Flengas (55) de­

veloped a "double tube" arrangement in which the e le c tro ly te con­

s is ts o f a tube, acting as a diaphragm, which completely separates

the two ce ll compartments. This technique has successfu lly been used

a t our department to measure the oxygen p a rtia l pressures above a

number o f phase assemblages, e.g. (Cu0,CuFe02 ,[Cu,Fe]Fe2 04) (65),

( [N i,Mn]0 ,N i) ( 6 6 ) , (Co0,Co304) (67), (Fe,Fet 0 ), (Ni,NiO) and (Co,

CoO) ( 6 8 ) and (Cu20 ,T i0 2 ,Cu3Ti04) (69).

The double tube arrangement was used in the measurements on the sys­

tem Ca0 -Ca2 Fe2 0 3“ Fet 0 -Fe and an extensive descrip tion o f th is tech­

nique is given in paper (V).

Id e a lly a so lid e le c tro ly te working as an oxygen sensor should exhi­

b i t good oxygen anion conductiv ity and no e lec tron ic conduc tiv ity .

However, using so lid e lec tro ly tes based on z irco n ia , the e lec tron ic

conduc tiv ity , although small w ith in an oxygen p a rtia l pressure range -20of 10 atm through 1 atm a t 12 00 K, can d is tu rb the measurements

by causing an oxygen permeation through the e le c tro ly te . As the oxy­

gen permeation rate is proportional to the d iffe rence in oxygen par-

38

t i a1 pressure between the two ce ll compartments i t can be minimized

by choosing a proper reference system. In the study o f the system

Ca0 -Ca2 Fe2 0 ^“ Fet 0 -Fe(V) a d iffe rence in oxygen p a rtia l pressure be­

tween reference and sample mixture o f less than 1.7 In p ^ ) un its

could be achieved by using Fe-Fe^O as the reference m ixture.

Another app lica tion o f the emf technique is to measure the oxygen

p a rtia l pressure of e q u ilib r ia invo lv ing also sulphur, e.g.

The technique fo r these measurements has a t our department been app­

lie d to e q u ilib r ia invo lv ing su lfides and su lfa tes in a number o f

systems, e.g. Cu-S-0 (70), Pb-S-0 (71), Ca-S-0 and Mn-S-0 (72) and

Zn-S-0 (73). Paper (IV) deals w ith the resu lts obtained in measure­

ments o f the equ ilib rium

In these measurements the sample m ixture, Cu and C^S, is e q u ilib ra ­

ted w ith a continuous flow o f SO in argon, w ith a known p a rtia l

pressure o f S0 2 » while measuring the equ ilib rium oxygen p a rtia l

pressures. Application o f the law o f mass action to equ ilib rium

(V II) gives

Cu2Û(s) + S02 (g) + 0 2 (g) <=> CuO’ CuSO^s) (V)

CaS(s) + 2 0 2 (g) ♦* CaSO^(s) (VI)

2Cu(s,l) + S02 (g) »C u 2S (s ,l) + 02 (g) (V II)

In K(V II) = In p(02) - In p(S02) (11)

A ll sulphur-containing gas species, except SÛ2 (g ), are formed in

39

neg lig ib le amounts w ith in the temperature and oxygen p a rtia l pressu­

re range studied, - In p ^ ) ~ 18-27, and the equ ilib rium p^C^) in

the c e ll can be considered the same as in the flow ing gas stream. An

extensive descrip tion o f the c e ll arrangement and c e ll operation is

given in paper (IV ).

Comments to resu lts

AfG° fo r C U g S (s ,l) . Reliable thermodynamic data fo r the sulphide

CU2S cons titu te a base fo r a l l equlibrium ca lcu la tions on conventio­

nal pyrom etallurgical copper production. This includes simulations

o f both the conventional copper smelting and converting as discussed

in paper ( I ) and the roasting process as described in the study by

Eriksson (2). The A^G° values fo r C^S given in the lite ra tu re d i f ­

fe r by as much as 12 kJ. Most o f these data have been determined

using gas e q u ilib ra tio n , which generally gives data o f much lower

accuracy than the emf technique u t i l iz in g s ta b ilize d z ircon ia as so­

l id e le c tro ly te . The values o f A^G°(Cu2S,s) determined in paper (IV)

are considered ce rta in to w ith in + 650 J.

Values o f A^G°(Cu2S ,1 ) were calculated using the AfG° values fo r so­

l id CU2S together w ith data from the lite ra tu re on the enthalpy o f

fusion fo r Cu and Cu2S and a c t iv it ie s o f Cu(l) and Cu2S (l) in the

liq u id sulphide in equ ilib rium w ith liq u id m e ta llic copper. These

AfG0 values were considered ce rta in to w ith in 2500 J. The good

agreement between calculated and measured values at 1 i qui dus tempe­

ratures is taken as an evidence fo r the r e l ia b i l i t y o f the Af G° va­

lues fo r CU2S( 1 ).

40

The system CaQ-CagFegO^-Fe^Q-Fe. To ca lcu la te the phase re la tions at

m elting temperatures in the ca lc ia rich slag systems involved in

both iron and steel m etallurgy as well as in non-ferrous m e ta llu rg i­

cal processes, a knowledge o f the subsolidus phase re la tions in the

system Ca-Fe-0 is most important. The data presented in the l i t e r a ­

ture fo r th is system is , however, contrad ictory in some aspects. The

dicalcium fe r r i t e , Ca2 Fe2Û^, ex ists in equ ilib rium w ith e ith e r o f

the s o lid solutions [Fet ,Ca]0 or [Ca,Fet ]0 , and iron up to a melting

temperature o f 1423 K according to re fs . (74 through 76), while ac­

cording to re fs . (77 through 80) the phase re la tions s h if t to co­

ex is ting so lid so lu tions [Fet ,Ca]0 and [Ca,Fet ]0 in equ ilib rium w ith

iron a t a temperature between 1308 and 1343 K. The figures fo r the

terminal so lid s o lu b i l i ty o f ca lc ia in w üstite vary from 12 to 37.5

mole per cent (74,75,77,80,81) a t 1300 K. To resolve some of these

con trad ic tions, a study o f the system Ca0 -Ca2 Fe2 0 5 -Fet 0 -Fe was ac­

complished (V).

The experimental emf values obtained were used to determine a c t iv i ­

t ie s o f Fe O in the so lid solu tions [Fet ,Ca]0 and [Ca,Fet ]0, the

compositions o f the terminal so lid solu tions and the s ta b i l i t y o f

the dicalcium f e r r i t e , Ca2 Fe2 0 5 . The fo llow ing four-parameter

Rediich -K is te r equation fo r the in teg ra l excess Gibbs energy o f the

so lid so lu tions was found to be consistent w ith both measured a c t i­

v it ie s and phase re la tions

G ^ / J ’ m o l ’ 1 = X | X 2 [ A + ( x -j- X 2 ) B + ( x ^ - X 2 ) 2 C + ( x 1 - X 2 ) 3 D] ( 1 2 )

where A = 2809 + 16.6205(T/K), B = 11268, C = 5038 and D = -7575. x ]

41

and x2 correspond to X(CaO) and X(Fet 0) in the solid solutions, re­

spectively. Using the data set obtained in paper (V) the phase dia­

gram fo r the pseudobinary section Fe^O-CaO in equilibrium with iron

at subsolidus temperatures was calculated.

3+ 2+In the model i t is assumed that the quotient Fe /Fe in Fe O in

equilibrium with iron is unchanged by the formation of a solid solu­

tion with CaO. This may be a too sim plified description. However, no

determination of this quotient could be made because of the d i f f i ­

culty to prepare the solid solutions in advance. In the s im ilar solid3+ 2+solution [Fe^,Mg]0 the quotient Fe /Fe has been shown to decrease

on the addition of MgO to Fe O and reaches a value of p rac tica lly

zero at a mole fraction of Fe O equal to 0.3 (c f. Fig. 10). A decrease

of the quotient Fe^+/Fe^+ may influence the oxygen partia l pressure.

This cannot be accounted fo r without using a more elaborate method

than the one used in this study. However, th is effect of Fe3+ cannot

be quantified unless extensive measurements are performed at several

Fe^+ concentrations in the w lis tite -calc ia , [Fe-j_x ,Ca]0 solid solu­

tion. Such measurements could be part of an extension of the study

in paper (V), with the aim of obtaining a consistent thermodynamic

description for the m etallurgically important systems Ca-Fe-0 and

Ca-Fe-0-Si02.

Application to copper smelting and converting

Conventional copper production processes can be divided into three

steps, namely smelting, slag blowing and copper blowing. The smelt­

ing step, where a copper sulphide concentrate is smelted together

42

0.10

♦ 0.08

0.06o/

0 0.2 Q4 0.6 0.8 1.0X(FetO)

3+Fig. 10. The quotients n(Fe ) / [n (F e ^ ^ )+ n (M g ) ] p lo t te d against the mole

f r a c t io n o f w u s tite , X(Fe^O)^ in the s o l id so lu tion [Fe^M g]0 in e q u i l ib ­

rium w ith i r o n .

Simons (8 2 )y 1573 K

----------- Katßura and Kimora (83 )3 1433 K

O Ender (8 4 ) , 1573 K

□ Giddtngo and Gordon (85)

43

with a f lux ing agent, usually s i l i c a , is carried out in a reverbera-

to ry , e le c t r ic , f lash or b las t furnace. The matte phase formed is

t ransferred to a converter w ith in which the slag blowing and copper

blowing steps are performed. In the slag blowing step, fresh s i l i c a

is added and a i r or oxygen-enriched a i r is injected u n t i l the amount

of iron sulphide in the matte phase is about 1 wt %. The slag formed

is poured o f f and is normally e ithe r rec ircu la ted to the smelting

furnace or treated in a special furnace in order to recover part o f

the copper present in the slag. In jec t ion of a i r or oxygen-enriched

a i r is then continued, and the copper sulphide begins to form l iq u id

b l is te r copper in what is terming the copper blowing step.

The temperatures normally prevail ing during a l l three steps are

1473-1523 K.

A normal copper making process (c f. Fig. 11) is defined in paper ( I )

as taking place at 1523 K. The concentrate consists o f pure chalco-

p y r i te , CuFeS25 which contains 34.6 wt % Cu. The amount o f s i l i c a

added is 0.3 mol/mol CuFeS2 and a known amount o f a i r (p(0 2) = 0 . 2 1

atm) is in jected. The oxygen e f f ic iency is assumed to be 100 %, The

composition o f the matte phase at which the smelting step is in te r ­

rupted is an adjustable process parameter. The converting (slag b lo­

wing and copper blowing) is regarded as one step with no intermedi­

ate slag removal.

The equilibr ium composition o f the gas, matte and slag phases was

calculated as a function o f the amount o f oxygen in jected ( I ) . The

resu lts , which are given in Fig. 12, were used to deduce the overall

44 Ojlair) SiOj CuFeS2

ii ii ii

T*1523 K

Gas phase- N-, SO-, S-

Slag phase; CuO05<

FeO, FeOj 333* Si02

Matte phase- CuS05< FeS

T* 1523 K

O^lair) Si0 2 J jT"

11 -Il TGas phase: N2, S02 ,S2

Slag phase CuO05' FeO, FeOj 3 3 3 ^ ^ 2

Matte phase: CuSQ5' FeS

Copper phase

Smelting

step

Converting: Slag blowing and copper blowing

F ig . 11. P rin c ip a l sketch o f the ”normal" copper making process. For .

the gas phase3 only the predominant species are given. The copper phase

does not appear u n t i l the end o f converting.

Gas phase

„ - 2

Matte phase cuSqs10

FeS

Slag phase and solid phases

F » ( W . . ~

Fig . 12. Log(p^/atm) fo r gaseous species3 amount 3 n^/mol3 o f l iq u id and

s o lid species and wt % C ulatte VS a amoun ° f ° 2 ^ ^ supplied/m ol CuFeS2) fo r the nnormal11 copper making process. Gaseous species fo r which the

p a r t ia l pressure never exceeds 10 atm are om itted.

45

reactions taking place in pyrometallurgical copper production ( I ) .

Calculations were also performed to simulate the slag removal be­

tween the smelting step and the converting and to study the outcome

of a change in such process parameters as temperature, s i l i c a con­

tent in slag and pa r t ia l pressure o f oxygen in in jected gas. From

the results o f these la t te r calculations the fo llow ing conclusions

could be drawn:

1 ) the i n i t i a l smelting step should, i f possible, be continued to

matte grades o f at least 65 wt % Cu,

2 ) the copper losses to slag are minimized i f the s i l i c a content

in slag and the temperature are as low as possible,

3) low s i l i c a content in slag, low temperature and oxygen enrich­

ment o f injected gas w i l l increase the Fe^+ content in slag.

An increased Fe^+ content w i l l , however, increase the r is k fo r mag­

n e t i te formation, and thereby a d ra s t ic a l ly increased v iscos ity and

physical entrainment o f matte part ic les in the slag phase w i l l re­

s u l t . A compromise s i tua t ion may ex is t in practice.

Fig. 13 shows calculated and observed copper losses to slag p lotted

vs wt % Cu (wt % CuSq 5 ) in the matte phase. The discrepancies can

be explained by e ithe r of the fo llow ing reasons:

1 ) su 1 phi di c copper losses to slag,

46

8

0 *6o>î%

2

__100

Fig . j g . C alcu lated and p ra c t ic a lly observed copper losses to slag vs

matte g rad e . This study3 from the ca lcu la tio n s on the nnormal" copper

making process; to ta l copper losses (s u lf id ic and o x id ic ) according

to Sehnalek and Im ris (8 6 ) ; to ta l copper losses according to

Nagamori (8 7 ); operating furnaces (86 and 88 through 9 1 ); b la s t

furnace; A > e ve rbe ra t o vy f urn ace ; V e le c t r ic furnace; Q Outukumpu

furnace; fla s h furnace; ^ Horan da furnace; Q Pierce-Smi th con­

v e rte r.

47

2) equil ibrium conditions do not prevail in operating furnaces,

3) thermodynamic description is too s im p li f ied .

In Fig. 13 is also given a selection of experimentally obtained va­

lues (86,87) of the to ta l chemical copper losses to slag, which can

be of two kinds, oxid ic or su lph id ic . Considering the d ifference be­

tween these curves and the calculated curve, which corresponds to

the oxid ic s o lu b i l i t y , i t is evident that the su lphid ic s o lu b i l i t y

is small and cannot explain the extent o f the p ra c t ica l ly observed

copper losses, especially at matte grades greater than 60 wt % Cu.

A physical entrainment o f matte pa rt ic les into the slag in operating

furnaces is more plausible and th is may account fo r part o f the ob­

served discrepancy.

In paper ( I ) the l iq u id phases were treated as non-ideal mixtures

consisting of mononuclear compounds, e.g. CuOq ^,Fe0,Fe0-j 3 3 3 and

SÌO2 in the slag phase. The non-idea lity was described by using the

simplest mathematical expressions possible. The sulphur and oxide

s o lu b i l i t y in the slag and matte phase respective ly, as well as the

influence of a l l minor elements was neglected. This thermodynamic

description is perhaps too s im p li f ied and may account fo r part of

the discrepancy between calculated and observed copper losses.

Non-equilibrium conditions

Another explanation o f the discrepancy in Fig. 13 may be non-equ il ib­

rium conditions in operating furnaces.

48

Table 4 . Typical process analysis fo r the slag blowing step o f con­

verting at the Rönnskär Works, Sweden (92).

Analysis/wt %Phase Cu Fe 0 Zn Pb Ni S T/K

Incomingmatte 40 19.75 1.35 4.80 6.80 0.71 22.90 1343

Produced

white metal 74 1.48 - 0.64 2.26 0.59 18.59 1543

Slag 4 % Cu, 20 % Fe30 4, 24 % Si02, 0.5 % S, T = 1543 K

Gas p^O ^/a tm « 0.13, oxygen e ff ic iency 92-93 %

49

Table 4 gives a typ ica l process analysis fo r the slag blowing step

of the converting at Boliden AB, Rönnskär Works, Sweden (92). The

corresponding calculated values, assuming an equilibr ium batch pro­

cess as in paper ( I ) , are given in Table 5. Comparison of the values

in Table 4 and Table 5 shows that the slag from the operating furna­

ce is r icher in magnetite and copper than predicted by the ca lcu la­

t ions . The pa r t ia l pressure o f SC^g) is calculated too high, 0.15

atm compared to 0.13 atm in the real furnace. This la t te r difference

is easily understood because the oxygen e f f ic iency is less than 100

%. To tes t whether or not these differences between calculated and

practica l values can be eliminated using a non-equilibrium approach,

some new preliminary calculations were performed.

A non-equilibrium process can be simulated using the computer pro­

gram SOLGASMIX-REACTOR developed by Eriksson and Johansson (93). In

th is program, a reactor is conceptually divided in to a number of

segments. The equilibrium conditions are assumed to be reached w ith in

each segment and concentration and/or temperature gradients ex is t

between the segments.

Calculation procedure. Consider a copper converter, a r b i t r a r i l y d i ­

vided in to a number of segments. I n i t i a l l y the matte and SiC^ added

is assumed to be equally d is tr ibu ted between the segments. The ca l­

culation technique employed is one of re p e t i t ive subs t i tu t ion and

the i te ra t io n process proceed from top to bottom throughout the

reactor. Flows opposite to the i te ra t io n d irec t ion calculated from a

previous i te ra t io n (or i n i t i a l estimate) are used as input to the

next i te ra t io n , whereas flows in the other d irec t ion are calculated

50

Table 5, Calculated composition of white metal and slag fo r the slag

blowing step of converting (c f . Table 4) assuming an equil ibrium batch

process. The composition of the incoming matte ( in mol) corresponds to

1 kg matte o f the same composition as in Table 4, neglecting the zinc,

lead and nickel content and counting these metals as sulphides. The

composition of the white metal is obtained by assuming the same Cu/Fe

quotient as in Table 4. The amount o f S i O2 is adjusted to give a to ta l

slag content o f about 24 wt % SiO^. T = 1543 K.

Incoming matte ( in mol) 6.2946 Cu, 3.5364 Fe, 0.8465 0, 6.0065 S

Composition of

white metal 97.5 wt % CuSq 5 , 2.5 wt % FeS

Calculated slag

composition 1.0 wt % Cu, 17.2 wt % F e ^ , 23.8 wt % SiO^

Calculated gas

composition p(S02) = 0.149 atm, p(02) = 2 .9*10- 8 atm

51

as the i te ra t io n proceeds. In each i te ra t io n an increment o f a i r is

added to the bottom segment. Part of the gas is bypassing the bottom

segment and d is tr ibu ted according to Fig. 14 and leaves the furnace

at the top. The slag phase, being the least dense phase, is flowing

upwards while sulphide, metal and S iC^s) phases are flowing down­

wards and are accumulated in the top and bottom segments, respective­

ly . A princ ipa l sketch of a l l flows is given in Fig. 14. As an ex­

ample, the equilibrium amount o f sulphides in segment n, ^ ( s u lp h i ­

des), is d is tr ibu ted between segments n, n+1 and n+2 in the fo llow ing

i te ra t io n . The frac t ion o f cn(sulphides) entering segments n+1 and

n+2 is 0.08 and 0.04, respective ly , while 0 . 8 8 -cn(sulphides) remains

in segment n.

In the ca lcu la t ions, the number of segments, the f igures fo r the ga­

seous and condensed flows and the increment o f a i r injected in each

i te ra t io n are considered as parameters. These are varied u n t i l u l t i ­

mately the calculated overall composition o f slag and white metal,

the p a r t ia l pressure o f 30^(0) in the gas leaving the converter and

the oxygen e f f ic iency are a l l in agreement with the process analysis

given in Table 4. The temperature is assumed to be 1543 K in a l l seg­

ments. The thermodynamic data used are the same as in paper ( I ) .

The metal, matte and slag phases are p ra c t ic a l ly immiscible but the

reactions taking place cause a mixing and the flows of condensed spe­

cies can be thought o f as the net transport w ith in the converter.

Results. An oxygen e ff ic iency less than 100 % can be simulated in two

ways:

52

Q32gn

0.lg„T r

0.08gnTE-------

0.5gn

0.05Cn reactants Cuti) Si02(s)

0.05Cn

IGaseous reaction siag 0.08Cn-i 0.7Cn_i 0.2Cn_i products species 0.04Cn-2 û3Cn-2 0.1Cn-2

Chemical equilibrium at T=1543K

0.32gn.2 0.08gn+4 nçr' cl ilnhiHa

0-5gn>i 01gn>3 a05Cn' "products Si02(s)

T0.08Cn 0.7Cn 0.2Cn

“Släq 0.04Cn 0.3Cn ÖTÜ7reactants______________________

Gaseous reactants

Segmentnumber

n -4n - 3 n - 2 n- 1

n

n ♦ 1 n ♦ 2 n ♦ 3 n ♦ U

F ig . 14 . Sketch showing the flows w ith in the nth segment o f the conver­

te r (the other segments are in d ica ted w ith s tra ig h t lines)» An arrow

reaches the segment where the species re a c t . The eq u ilib riu m amounts o f

gaseous and condensed species in segment n are denoted by gn and c^> re ­

s p e c tiv e ly .

53

1 ) by assuming a part o f the entering gas to pass the reactor w ith ­

out reacting,

2 ) by assuming a highly oxidized segment from which a large amount

o f oxygen leaves the furnace.

Calculations according to the f i r s t a l te rna t ive above resulted in a

model where the converter consists o f three segments and with the

d is t r ib u t io n coe ff ic ien ts given in Fig. 14. The amount o f matte added

is the same as in Table 5 and the amount of SiO^ is 1.425 mol. The

a i r increment is 1.1246 mol/ i t e r a t i on.

With these conditions, a matte grade o f 97.1 wt % C u S q ^ was reached

in the 19th i te ra t io n . The calculated overall slag composition was

3.98 wt % Cu, 21.1 wt % Fe^O^ and 24.5 wt % Si0^. The calculated par­

t i a l pressure o f SC^g) in the gas leaving the converter is 0.125

atm. A l l these figures are in good agreement with those from the pro­

cess analysis (Table 4).

Fig. 15 shows the calculated p a r t ia l pressures o f gaseous species and

the amounts of condensed species in a l l three segments. Although the

flows o f condensed phases are small, the calculations give the resu lt

that a large portion o f the slag phase is accumulated in the top seg­

ment, segment no 1 , while the main part of the matte phase is accumu­

lated in the bottom segment. In segment 2 a small amount o f Cu(1) is

formed in the las t few i te ra t io n s . This metal flows to the bottom

segment where i t reacts with FeS(l) and 02 (g) to give C u S q ^ ( 1 ) and

FeO(l) or FeO 3 3 3 ( ^)• Segment 2 is also the most oxidized segment.

54

_ Gas phase

i

- Matte and metal phases

T rSlag phase

12 \F e O~o

CO

w/(! - X \SiO^

'cÛ4

F eO ,^ '

CuOi'0.5

1 2 3Segment number

Fig , 15 , C alcu lated p a r t ia l pressures o f gaseous species and amounts o f

condensed species in the three segments.

55

I f no oxygen is assumed to bypass the reactor, as in the second a l ­

te rnative above, a model where the converter is assumed to consist

of four or more segments has to be considered.

The calculations show that a real copper making process can be simu­

lated exactly by assuming concentration gradients w ith in the reac­

to r . The number o f segments and the figures fo r the d is t r ib u t io n co­

e f f ic ie n ts w i l l , however, d i f f e r in simulations of d i f fe re n t reac­

to rs , re f le c t in g the operation o f the reactor. As soon as a more

complete description o f the metal, matte and slag phases is obtained,

the influence o f a l l elements on the copper making process can be

calculated with greater precision. Then a more detailed examina­

t ion o f the p o s s ib i l i t y to simulate these processes using the com­

puter program SOLGASMIX-REACTOR could be performed.

Future improvements of the thermodynamic description

I f ternary and higher order in teractions are neg lig ib le , as in the

system Cu-Fe-0-Si02, the results presented in th is thesis can be

combined to give a model fo r the system Cu-Fe-Pb-O-SiO^. However,

there are s t i l l many more elements to take into consideration. The

main elements in pyrometallurgical copper production processes are

Cu, Fe, 0, S and S i, but to obtain a complete data base fo r ca lcu la­

tions on these processes the elements Ca, Mg, Pb, Ni, Zn, As, Sb etc

have to be considered. The behaviour o f some of these impurit ies is

very important from a practica l point o f view, because they can

cause severe problems, e.g. arsenic which has a detrimental e f fe c t

on the f in a l e le c t ro ly t ic refinement i f present in the b l is te r copper.

56

To calculate quan t ita t ive ly the e f fec t of d i f fe re n t process parame­

ters on e.g. the d is t r ib u t io n of As between metal, matte and slag

phases and to quantify the copper losses in terms o f su 1 phidi c and

oxid ic s o lu b i l i t y , more elaborate models than those in paper ( I )

have to be used fo r metal-sulphur systems. In recent years several

assessments o f complete metal-sulphur systems have been reported,

e.g. Fe-S (62 and 63), Cu-S (94), Ni-S (95), Cu-Ni-S (96 and 97)

and Cu-Fe-Ni-S (98). In these studies the l iq u id phases were descri­

bed by using e ithe r the associated model (62), in which a molecular

species is assumed to form in addition to the metal and sulphur com­

ponents, or the sub la tt ice model (63), in which metal, metal vacan­

cies, sulphur and sulphur vacancies are located on two d i f fe re n t

subla tt ices. Work is in progress at our department to obtain an

assessment of the system Cu-Fe-As-Sb-S, using the ionic sub la tt ice

model recently proposed by H i l l e r t et a l . (99). For some of the a r­

senic and antimony-containing subsystems, there is in s u f f ic ie n t

thermodynamic data published and a lack o f information on phase re­

la t ions , and additional experimental information is needed.

Thermodynamic data fo r molten slag systems have in most cases been

determined by the gas equ i l ib ra t io n technique, which usually gives

data o f much lower accuracy than the emf technique. However, the so­

l i d e lec tro ly tes available at present fo r the measurement of oxygen

a c t iv i t ie s have been found to corrode very in tens ive ly when in d i ­

rect contact with a s i l i c a te melt. To avoid these problems, new mea­

surement techniques or completely new e lec tro ly te materials have to

be developed.

57

From model calculations on s i l ic a te melts, some information on the

complexes present is obtained. Natura lly , the most stra ightforward

way to determine the true melt structures would be to use some type

o f d ire c t measurement, e.g. Raman and IR spectroscopy or high tempe­

rature X-ray d i f f ra c t io n . However, these techniques give only in fo r ­

mation on the types of complexes present and not on th e i r d e f in i te

composition and quantita t ive d is t r ib u t io n . In the fu tu re , measure­

ments with the Si-NMR technique on s i l ic a te glasses might be used to

obtain a better knowledge of the s i l ic a te melt s tructures.

Acknowledgements

I wish to express my sincere gratitude to Docents Erik Rosén and

Gunnar Eriksson fo r introducing me to the f ie ld o f high temperature

chemistry, fo r many valuable suggestions and stimulating discussions

and fo r th e i r never fa i l in g patience throughout th is work. I am also

greatly indebted to Professor N ils Ingri and Docent Erik Rosén fo r

a l l the f a c i l i t i e s placed a t my disposal.

Many thanks are also due to Ms. Margit Fredriksson fo r good collabo­

ra tion and valuable technical assistance and to Drs. Lars Pejryd,

Eva Jacobsson and Hardy Paulsson fo r many valuable and st imulating

discussions.

To Ms. Christina Broman fo r s k i l f u l typing o f the manuscript, to Mr.

Lage Bodén fo r excellent draftmanship and to Mr. Sture Pettersson

fo r valuable technical assistance I am also greatly indebted.

58

FL Robert Elston has s k i l f u l l y revised the manuscript to whom many

thanks are due. The f inanc ia l support by the Swedish Natural Science

Research Council is hereby g ra te fu l ly acknowledged.

59

References

1. Eriksson, G., Chem. Scr. 1975, 8, 100-103.

2. Eriksson, G., Thesis, University of Umeå, 1975.

3. Hack, K. and Eriksson, G., CALPHAD, In p r in t .

4. Saxena, S.K. and Eriksson, G., J. P e tro l . 1983, 24, 538-55.

5. Saxena, S.K. and Eriksson, G., Geochim. Cosmochim. Acta 1983,

47, 1865-74.

6. Saxena, S.K. and Eriksson, G., Earth Planet. Sci. L e t t . 1983,

65, 7-16.

7. Charette, G.G. and Flengas, S.N., Can. Metal 1. Q. 1970, 7, 191-

200.

8. Furukawa, T., Brawer, S.A. and White, W.B., J. Mater. S c i .

1978, 13, 268-82.

9. Goto, M. and Kanamori, K., In Copper and Nickel Converters.

(R.E. Johnson, ed.) pp. 210-23. The Metallurg ical Society of

A .I.M .E., New York, 1979.

10. Liebau, F., Handbook of Geochemistry, Vol. 11/3, Springer-Verlag,

1972.

11. Wells, A.F., Structural Inorganic Chemistry, 4th ed., Clarendon

Press, Oxford, 1975.

60

12. Deer, W.A., Howie, R.A. and Zussman, J . , Rock Forming Minerals,

Vol. 2A, Single-Chain S i l ica te s , 2nd ed., Longman, London,

1978.

13. Waseda* Y. and Suito, H., Trans. Iron Steel In s t . , Jpn. 1977,

17, 82-91.

14. Waseda, Y. and Toguri, Ü.M., Trans. Iron Steel Inst . , Jpn .,

1977, 17, 601-03.

15. Waseda, Y. and Toguri, J.M., Metall. Trans. B 1977, 8B, 563-68.

16. Waseda, Y. and Toguri, J.M., Metall. Trans. B 1978, 9B, 595-

601.

17. Waseda, Y., S h ira ish i, Y. and Toguri, J.M., Trans. Jpn. In s t .

Met. 1980, 21, 51-62.

18. Kashio, S., Iguchi, Y., Goto, T ., Nishina, Y. and Fuwa, T .,

Trans. Iron Steel In s t . , Jpn. 1980, 20, 251-53.

19. Sweet, J.R. and White, W.B., Phys. Chem. Glasses 1969, 10, 246-

51.

20. Waseda, Y., Can. Metall. Q. 1981 , 20, 57-67.

21. Brawer, S.A. and White, W.B., J. Chem. Phys. 1975, 63, 2421-32.

22. Verweij, H. and Konijnendijk, W.L., Çeram_._Soc. 1976,

59, 517-21.

23. Furukawa, T ., Brawer, S.A. and White, W.B., J. Am. Ceram. Soc.

1979, 62, 351-56.

61

24. Iwamoto, N., Tsunawaki, Y. and Miyago, M., Nippon Kinzoku

Gakkaishi 1979, 43, 1138-44.

25. Furukawa, T ., Fox, K.E. and White, W.B., J. Chem. Phys. 1981,

75, 3226-37.

26. Mysen, B.O., Virgo, D. and Scarfe, C.M., Am. M ineral. 1980, 65,

690-710.

27. Mysen, B.O., S e ife r t , F. and Virgo, D., Am. M ineral. 1980, 65,

867-84.

28. S e ife r t , F., Mysen, B.O. and Virgo, D., Am. M ineral. 1982, 67,

696-717.

29. Borgianni, C. and Granati, P., M etall. Trans. B 1977, 8B, 147-

51.

30. Borgianni, C. and Granati, P., Metall. Trans. B 1979, 10B, 21-

25.

31. Margules, M., Akad. Wiss. Wien, Sitzungs. , Math.-Naturwiss.

Classe 104, Abt. I l a , 1895, 1243.

32. Hildenbrand, J .H ., J. Am. Chem. Soc. 1929, 51, 66-80.

33. Lumsden, J . , In Physical Chemistry o f Process Metallurgy.

(G.R. S t.P ie rre , ed.) pp. 165-205, Interscience, New York,

1961.

34. Goel, R.P., Kellogg, H.H. and Larra in, J . , Metall. T r ini - J*

1980, 11B, 107-17.

62

35. Gaskel 1, D.R., Can. M eta ll. Q. 1980, 20, 3-19.

36. Bottinga, Y., W e il l , D.F. and Richet, P., In Thermodynamics of

Minerals and Melts, Vol. 1 (S.K. Saxena, ed.) pp. 207-46,

Springer-Verlag, New York, 1981.

37. Toop, G.W. and Samis, C.S., Trans. A.I.M.E. 1962, 878-87.

38. Yokokawa, T. and Niwa, K., Trans. Jpn. Ins t. Met. 1969, 10, 3-7.

39. L in, P.L. and Pelton, A.D., Metall. Trans. B 1979, 10B, 667-75.

40. Masson, C.R., Proc. Roy. Soc. 1965, A287, 201-21.

41. Whiteway, S.G., Smith, I.B. and Masson, C.R., Can. J. Chem. 1970,

48, 33-45

42. Masson, C.R., Smith, I.B. and Whiteway, S.G., Can. J. Chem. 1970,

48, 1456-64.

43. Esin, O.A., Russ. J. Phys. Chem. 1973, 47, 1306-08.

44. Kapoor, M.L., Mehrotra, G.M. and Frohberg, M.G., Arch. Eisen-

hüttenw. 1974, 45, 663-69.

45. Gaskell, D.R., Metall. Trans. B 1977, 8B, 131-45.

46. Temkin, M., Acta Physicochim. U.R.S.S. 1945, 20, 411-20.

47. Flood, H. and Knapp, W.J., J. Am. Ceram. Soc. 1963, 46, 61-65.

48. Richardson, F.D. and Webb, L.E., Inst. Min. M e ta l l . , Trans.

1954-55, 64, 529-64.

49. Kozuka, Z. and Samis, C.S., Metall. Trans. 1970, 1, 871-76.

63

50. Geller, R.F., Creamer, A.S. and Bunting, E.N., J. Research

Natl. Bur. Standards 1934, 13, 237-44.

51. Boucher, M.L. and Peacor, D.R., Z. K r is t . 1967, 126, 98-111.

52. Berezhnoi, A.S., Karyakin, L . I . and Dudavskii, I . F . , Doklady

Akad. Nauk S.S.S.R. 1952, 83, 401.

53. N ik i t in , Yu.P., Taranukhina, L.V., Seredina, L.R., Pushkareva,

S.A., Popova, I.A. and Vershinina, N.V., Izv. Vysh. Uchebn.

Zavadenii, Tsvetn. Met. 1962, 5, 74-76.

54. Fredriksson, M. and Rosén, E., Scand. J. M e ta l l . 1980, 9, 173-

76.

55. Charette, G.G. and Flengas, S.N., J. Electrochem. Soc. 1968,

115, 796-803.

56. Taskinen, P., Scand. J. M e ta l l . 1981, 10, 189-91.

57. E l l i o t t , J.F. and Gleiser, M., Thermochemistry fo r Steelmaking,

Addison-Wesley, Reading, Mass. 1960.

58. Schmid, R., Metall. Trans. B 1983, 14B, 473-81.

59. Altman, R. and Kellogg, H.H., Trans. Instn. Min. M e ta l l . 1972,

C81, C163-75.

60. Ruddle, R.W., Taylor, B. and Bates, A.P., Trans. Instn. Min.

M e ta l l . 1966, C75, C I -12.

61. Taylor, J.R. and Jeffes, J.H.E., Trans. Instn. Min. M e ta l l .

1975, C84, C18-24.

64

62. Sharma, R.C. and Chang, Y.A., Metall. Trans. B 1979, 10B, 103-

08.

63. Fernandez Guillermet, A., H i l l e r t , M., Jansson, B. and Sundman,

B., Metall. Trans. B 1981, 12B, 745-54.

64. Kiukkola, K. and Wagner, C., J. Electrochem. Soc. 1957, 104,

379-83.

65. Eriksson, G. and Tegman, R., Chem. Scr. 1976, 10, 145-48.

66. Paulsson, H. and Rosén, E., Chem. Scr. 1977, 11, 204-07.

67. Björkman, B. and Rosen, E., Chem. Scr. 1978/79, 13, 139-42.

68. Jacobsson, E. and Rosén, E., Scand. J. M e ta l l . 1981, 10, 39-43.

69. Pejryd, L. and Rosén, E., High Temp. -High Press. 1982, 14, 599-

606.

70. Wittung, L . , Chem. Scr. 1976, 10, 21-26.

71. Fredriksson, M., Rosén, E. and Wittung, L . , Chem. Scr. 1977,

11, 32-36.

72. Fredriksson, M. and Rosén, E., Chem. Scr. 1977, 12, 68-71.

73. Eriksson, G., Fredriksson, M. and Rosén, E., Scand. J. M e ta l l .

1979, 8, 216-20.

74. Perrot, P., Rev. Chim. Miner. 1967, 4, 465-93.

75. Schürmann, E. and Kraume, G., Arch. EisenhLittenw. 1976, 47,

327-31.

65

76. Schürmann, E. and Kraume, G., Arch. Eisenhüttenw. 1976, 47,

471-76.

77. Abbatista, F., Burdese, A. and Maja, M., Rev. In t . Hautes Temp.

Refract. 1975, 12, 337-42.

78. Reeve, D.A. and Gregory, A.G., Ins t. Min. M e ta l l . , Trans.

Sect. C 1967, 76, 273-77.

79. Lykasov, A.A. and Kozheurova, N.V., Izv. Akad. Nauk S.S.S.R.,

Neorg. Mater. 1980, 16, 1079-82.

80. A llen , W.C. and Snow, R.B., J. Am. Ceram. Soc. 1955, 38, 264-80.

81. Aubry, J . , Berthet, A., Duchène, R., Etienne, H., Evrard, 0 . ,

Jeannot, F., G le itzer, C., Offroy, C. and Perrot, P., Ann. Chim.

1970, 5, 299-308.

82. Simons, B., Carnegie Ins t. Wash. Year Book 1980, 79, 376-80.

83. Katsura, T. and Kimura, S., Bu l l . Chem. Soc. Japan 1965, 38,

1664-70.

84. Ender, A., Thesis, I n s t i t u t fü r Kris ta llograph ie an der RWTH,

Aachen, 1977.

85. Giddings, R.A. and Gordon, R.S., J. Am. Ceram. Soc. 1973, 56,

111-15.

86. Sehnälek, F. and Imris, I . , In Advances in Extractive Metal­

lurgy and Refining (M.J. Jones, ed.) p. 1. The In s t i tu t io n of

Mining and Metallurgy, London, 1971.

66

87. Nagamori, M., Meta l l . Trans. 1974, 5, 531-38.

88. Biswas, A.K. and Davenport, W.G., Extractive Metallurgy of

Copper. In In t . Series on Materia ls, Science and Technology,

Vol. 20, Pergamon Press, Oxford, 1976.

89. Bailey, J.B.W. and Storey, A.G., The Noranda process a f te r six

years operation. Paper presented to 18th Annual CIM Conference

of M eta llu rg is ts , Sudbury, Ontario, 1979.

90. Yannapoulos, J.C. and Agarwal, J.C. (eds.), Extractive Metal­

lurgy o f Copper, New York, 1976.

91. Johnson, R.E. (ed .) , Copper and Nickel Converters, The Metal­

lu rg ica l Society of A .I.M .E., New York, 1979.

92. Johansson, L ., Boliden AB, Rönnskär Works, Sweden, Private

communication.

93. Eriksson, G. and Johansson, T ., Scand. J. Metall. 1978, 7, 264-

70.

94. Sharma, R.C. and Chang, Y.A., Meta ll. Trans. B 1980, 11B, 575-

83.

95. Sharma, R.C. and Chang, Y.A., Metall. Trans. B 1980, 1 IB, 139-

46.

96. Lee, S .L., Larrain, J.M. and Kellogg, H.H., Metall. Trans. B

1980, 1 IB, 251-55.

97. Chuang, Y. and Chang, Y.A., Metall. Trans. B 1982, 13B, 379-85.

67

98. Dinsdale, A., National Physical Laboratory, England, Private

communication.

99. H i l l e r t , M., Jansson, B., Sunénan, B. and Agren, J . , TRITA-MAC-

0218, Materials Center, Royal Ins t. Technology, Stockholm, Feb.

1984.