Constitutional and Structural slag models.

The interpretation and prediction of slag-metal dis­ tribution equilibria requires detailed knowledge of

activities and chemical compositions of slags to determine equilibrium constants. In multicomponent slags, activity data is often sparse or non-existent so that numerous slag models have been proposed to calculate activities of slag components from chemical analysis. A number of slag model theories have been reviewed by Ward who discusses early molecular theories and the.later ionic slag models of Temkin and Flood. The Temlcin model is an example of the constitutional theory where structural aspects of the molten slag are ignored. Temkin1s model proposed that slags consist only of ions exhibiting ideal behaviour, existing as separately charged entities and that like-charged ions were of equivalent interaction with their nearest neighbours. The activity of an oxide could be represented as follows;

- aFeO = Npe2+ nq2^ (2.15)

where N represented the ionic fraction derived from; NFe2+ = nPe2+ > Nq2- = n02~ (2.16)

£ n cations ■ ^n anions

The Temkin model takes no account of the polymerised

species which are known to occur from evidence in sections 2.5.2 and 2.5.3 (pages 38 and 40 ) and assumes silicon

4—

exists only as Sio^ ions. At compositions above the orthosilicate (>30%, SiOp), activities deviated from the

(l°) ideal line. The slag model proposed by Flood et al v "7 used the concept of electrically equivalent ion fractions which, unlike the Temkin approach, takes into account

variation of interaction between different ions. In basic slags all silicon (Si), phosphorus (?) and aluminium (Al)

4—

were present only as S1O4 , P 04 an<3 AlOo whilst all

cations existed as Ca^+ , Mn21", Mg2+ and Fe^+ ,

Liquid silicates are now widely accepted as being 2—

polyionic melts with cations, free oxygen ions ( 0 ~), and / gn \

varying sized silicate ions. Toop and Samis v have used a general form of equilibrium reaction proposed -by Richardson (^) by which equilibrium polymerisation takes place instead of a specific form of silicate anion re­ action. Three forms of oxygen were considered to exist in silicate melts;

Singly bonded Si atoms doubly bonded 2Si atoms free ions

I i 1 9_ Si — 0“ — Si — 0 Si — 0 i i i ^ • Q • A £ Q 2SiO^ Si20 7 + CT~ (2.17) 20“ 0° + 02~ _ (2.18) k = (0 ° ) ( 0

CO")

A high value of k indicated a high degree of poly­ merisation. The values of 0°, 0~ and 02*” refer to moles per mole of slag, k is not a true equilibrium constant but assumptions are made that;

(i) It is constant at constant temperature.

(ii) It is a characteristic of cations present in any binary or ternary silicate melt.

(iii) It is independent of composition.

From charge and material balances the following equation was derived:

2-

For various valiies of k obtained by curve fitting,

values of x0“ were derived as a function of xs^q where x represents the mole fraction of the particular species. Curves were produced which resembled free energy of mixing curves for binary silicates(AGM ). On this basis the model was extended to an ionic ternary Gibbs-Duhem relationship which correlated qualitatively "ionic activities” ape2+, aCa2+ and aQ„ with known activity data for ape0 and acaO* From reviews of slag models 9 it is suggested that the drawbacks suffered in the Toop and Samis model were as follows. The contribution to the entropy of mix­ ing of the three reaction parameters was not considered in the expression for free energy of mixing; there were difficulties in assigning physical significance to act­ ivities of electrically charged particles i.e. Temkin fractions; an unusual standard state for the ternary,

aQM = 1 along the CaO-’FeO1 pseudo binary which can only .. .. be true if Ca^*", Fe^+ and form ideal solutions.

Masson and Masson et al * 88 ^ have proposed two models for the calculations of the activities of basic oxide in a binary silicate melt using a predominantly

constitutional slag model approach based on polymer theory. Three main assumptions are made:

(a) The approach is limited to consideration^of

i O f y ] 4 - l

linear and branched chains of the form ■ which from stoichiometric reasons restricts the treatment to melts more basic than the metasilicate composition

(b) All 0“ groups are chemically equivalent regard­ less of the size of the polyanion to which they are

attached.

(c) The observed activities may be related to cal­ culated ion fractions by’the Temkin equation. For example for MO

aM0 = NM2+ x N02~ = ionic faction) (2.21) With these assumptions, the following expressions have been derived for the activity of MO as a function of com­ position in binary melts MO-SiO^. For linear chains;

1 1 T

— ± = 2 + — - ^

NSi02 1 ~ aM0 1 + 'Sl0^1c11” (2.22)

k n is the equilibrium ratio when n = 1 i.e.

Si044" + Si044" = Si2076- + o2- (2.23)' For all chain configurations (linear or branched):

i ._ g + ^ _ .. . 3'

NSi02 1 aM0 1 + aM0 (2.24)

From the results, S i O ^ “ was by far the most abun­ dant species in CaO-SiO^ melts at all compositions and almost the only one present when xSj.Q <0.3. At silica

6—