MTDATA Demonstration : Oxide Systems

Contents

Introduction

A knowledge of phase equilibria in multicomponent oxide systems is important in a great many fields. These include pyro-metallurgy, energy conversion, the prevention of corrosion, pollution control and the formulation, manufacture and use of cements and refractories.

This demonstration shows how MTDATA can be used to predict phase equilibria in complex oxide systems using critically assessed thermodynamic data. Compositions, temperatures, pressures and other conditions have been chosen to relate as closely as possible to industrial practice. Of course these can be varied easily from within MTDATA to suit any particular application.

The data used were developed as part of an ongoing project sponsored through MIRO. Its aim is to cover the CaO-MgO-Fe-O-Al₂O₃-SiO₂ system and then add other important sub-systems such as those involving as copper, zinc and sulphur.

The CaO-SiO₂ system

Data for multicomponent oxide systems are built up from those for much simpler sub-systems. The CaO-SiO₂ system is a particularly important building block because lime and silica are almost universal components of pyrometallurgical slags.

Predicted invariant temperatures are superimposed on the calculated CaO-SiO₂ phase diagram along with accepted experimental values. The REPLOT command is used to do this.

Note that in defining the system to be studied charge (O/-2) is included as a component. This enables charged species to be retrieved from the database.

WHICH MODULE ? BINARY
BINARY OPTION ? DEFINE SYSTEM 'CaO,SiO2,O/-2' SOURCE OXIDE !
SEARCHING FOR SYSTEM CaO,SiO2,O/-2
oxide - NPL oxide database. Vers. 2.0. 1997.
BINARY OPTION ? CLASSIFY MISCIBILITY(LIQUID) 1 !
BINARY OPTION ? STEP TEMPERATURE 1200 3200 20 ! COMPUTE !
BINARY OPTION ? REPLOT EXPERIMENTAL_FILE 'CS.EXP' GO

The Al₂O₃-SiO₂ system

It is difficult to study the Al₂O₃-SiO₂ system experimentally because of its high liquidus temperatures and the viscosity of the melts involved. The variation in the experimental data points superimposed on the silica rich end of the calculated phase diagram reflects this fact. Fortunately good data relating to the extent of the mullite phase field are available. These have been taken into account in modelling mullite crystalline solutions and their relationships with other phases.

It is interesting to note that by classifying certain phases absent (ie not to be considered in calculations) MTDATA can be used to investigate metastable phase equilibria. The region of metastable liquid immiscibility shown just below the silica rich liquidus was mapped in this way. Experimental evidence for metastable immiscibility in silica rich liquids has been reported in the scientific literature.

BINARY OPTION ? DEFINE SYSTEM 'Al2O3,SiO2,O/-2' SOURCE OXIDE OUTPUT 'AS.MPI' !
SEARCHING FOR SYSTEM Al2O3,SiO2,O/-2
oxide - NPL oxide database. Vers. 2.0. 1997.
BINARY OPTION ? CLASSIFY MISCIBILITY(LIQUID) 1 !
BINARY OPTION ? STEP TEMPERATURE 1600 2400 20 ! COMPUTE !
BINARY OPTION ? REPLOT EXPERIMENTAL_FILE 'AS.EXP' GO

The CaO-Al₂O₃-SiO₂ system

Data for ternary oxide systems such as CaO-Al₂O₃-SiO₂ are based upon those for the component binaries (CaO-SiO₂, CaO-Al₂O₃, Al₂O₃-SiO₂) with ternary parameters added where necessary to reproduce experimental observations. Phase equilibria are usually calculated at a single temperature and plotted on a triangular grid. (Note that the SET W=1 command is used to request a diagram plotted in weight fractions rather than mole fractions).

The chosen temperature of 1800 K (1527 C) is just below the melting points of both pseudowollastonite and anorthite. Consequently rather small phase fields are associated with each of these compounds. At this temperature melts exhibit silica contents ranging between zero and about 95 weight percent silica. Silica rich and silica poor liquids are separated by a region of coexistence with the compound melilite (gehlenite).

The compound hatrurite (tricalcium silicate) is a major component of Portland Cement. It is stable in equilibrium with the liquid phase either alone or in conjunction with alpha dicalcium silicate or lime. (To allow lime to form crystalline solutions with other compounds of similar structure, eg wustite, it is given the generic phase name halite in MTDATA databases).

BINARY OPTION ? RETURN
WHICH MODULE ? TERNARY
TERNARY OPTION ? DEFINE SYSTEM 'CaO,SiO2,Al2O3,O/-2' SOURCE OXIDE !
SEARCHING FOR SYSTEM CaO,SiO2,Al2O3,O/-2
oxide - NPL oxide database. Vers. 2.0. 1997.
TERNARY OPTION ? CLASSIFY MISCIBILITY(LIQUID) 1 !
TERNARY OPTION ? SET TEMPERATURE 1800 W 1 ! COMPUTE !

The Fe-O-SiO₂ system

When present in slags iron always occurs in both ferrous and ferric forms. This means that FeO must always be considered together with Fe₂O₃ and Fe in calculating phase equilibria for iron containing systems.

At 1475 K (1202 C) in the FeO-SiO₂-Fe₂O₃ system a small region of single phase liquid exists. Compositions along the left hand boundary of this region, are those for which either pure iron or the compound fayalite will separate out from the slag (liquid) phase on reduction. The lines extending outside the ternary triangle to the left correspond to equilibria involving pure iron (the FCC_A1 phase). Iron itself cannot be represented within the FeO-SiO₂-Fe₂O₃ composition triangle.

Towards the right of the diagram, under more oxidising conditions, the spinel phase (magnetite) and haematite become stable. (To allow for possible crystalline solution with Al₂O₃, haematite is given the generic phase name corundum in MTDATA databases).

TERNARY OPTION ? DEFINE SYSTEM 'FeO,SiO2,Fe2O3,O/-2' SOURCE OXIDE !
SEARCHING FOR SYSTEM FeO,SiO2,Fe2O3,O/-2
oxide - NPL oxide database. Vers. 2.0. 1997.
TERNARY OPTION ? SET TEMPERATURE 1475 W 1 ! COMPUTE !

The Fe-O-Al₂O₃ system in air

Since mixtures of "iron oxide" and alumina do not constitute a true binary system (due to the presence of both ferrous and ferric iron) the BINARY module of MTDATA cannot be used to calculate a phase diagram for this system. Instead a facility within the APPLICATION module is used. This enables temperature sections (isopleths) to be plotted along a chosen line through any multicomponent system.

Phase equilibria can be calculated for any selected oxygen pressure. To do this gas phase data for O₂ are introduced and an appropriate overall pressure imposed. An oxygen pressure of about 0.21 atmospheres corresponds to that in air.

In the Fe-O-Al₂O₃ system under such conditions the compound Al₂O₃.Fe₂O₃ is stable over a limited temperature range above about 1590 K. At lower temperatures corundum crystalline solutions rich in Al₂O₃ coexist with those rich in Fe₂O₃ (haematite). At higher temperatures, until the liquid phase forms, the spinel phase becomes the main carrier of iron. The next two examples illustrate the care taken in modelling the structure and properties of this complex phase.

TERNARY OPTION ? RETURN
WHICH MODULE ? APPLICATION
APPLICATION OPTION ? DEFINE SYSTEM 'FeO,Fe2O3,Al2O3,O/-2' SOURCE OXIDE %
? OUTPUT 'WFA' !
SEARCHING FOR SYSTEM FeO,Fe2O3,Al2O3,O/-2
oxide - NPL oxide database. Vers. 2.0. 1997.
APPLICATION OPTION ? CLASSIFY MISCIBILITY(CORUNDUM) 1 MISC(SPINEL) 1 !
APPLICATION OPTION ? SET P 0.21*101325.0 !
APPLICATION OPTION ? 'ISOPLETH.MAC
Isopleth - the calculation of pseudo binary sections through
multicomponent systems
It is now necessary to define certain parameters for the calculations.
Enter composition tolerance (typically 0.0001) ?
: 0.0001
Enter number of temperature steps (perhaps 30) ?
: 50
APPLICATION OPTION ? SET W 1 "Fe2O3" 0.0 1.0 0.0 "Al2O3" 0.0 0.0 1.0 !
APPLICATION OPTION ? RANGE "Fe2O3" "Al2O3" 50 !
APPLICATION OPTION ? RANGE TEMPERATURE 1100 2500 0.1 ! COMPUTE !

In the above commands Fe₂O₃ and Al₂O₃ are used as labels for the corresponding compositions.

Cation distribution in Fe-O-Al₂O₃ spinels

Two types of cation site exist within the spinel structure; tetrahedrally co-ordinated and octahedrally co-ordinated sites. For each site of the first type there are two of the second. In a "normal" spinel divalent ions (A) occupy all the tetrahedral sites and trivalent ions (B) all the octahedral sites so giving an overall formula AB₂O₄. Alternatively the tetrahedral sites may be occupied by trivalent ions and half the octahedral sites by divalent ions. The spinel is then said to be "inverse".

The calculated cation distribution along the join between Fe₃O₄ (magnetite) and FeAl₂O₄ (hercynite) at 1273 K shows hercynite to be approximately normal with Al³⁺ ions occupying octahedral sites and Fe²⁺ ions tetrahedral sites. In contrast magnetite exhibits a mixed structure with significant populations of both ferric and ferrous ions on the tetrahedral sites.

These results are in good agreement with the somewhat scattered measurements of cation distributions shown superimposed upon the calculated curves.

APPLICATION OPTION ? RETURN
WHICH MODULE ? MULTIPHASE
MULTIPHASE OPTION ? DEFINE DATA_INPUT_FILE 'WFA' !
MULTIPHASE OPTION ? CLASSIFY ABSENT PHASE(*) NORMAL PHASE(SPINEL) !
MULTIPHASE OPTION ? SET TEMPERATURE 1273 !
MULTIPHASE OPTION ? SET 'Fe3O4' 1.0 1.0 0.0 'FeAl2O4' 1.0 0.0 1.0 !
MULTIPHASE OPTION ? STEP 'Fe3O4' 'FeAl2O4' 51 !
MULTIPHASE OPTION ? COMPUTE PRINT GRAPHICS !
51 MOLE STEPS JOINING Fe3O4 TO FeAl2O4
MULTIPHASE OPTION ? ORDINATE N_(AMOUNT) SUBSTANCE(SPINEL) LIMITS 0.0 2.0 !
MULTIPHASE OPTION ? PLOT GO

Miscibility gap in the spinel phase

Below about 1130 K spinels rich in alumina (hercynite like) and spinels poor in alumina (magnetite like) separate to form two immiscible phases. MTDATA can be used to plot composition limits for this immiscibility.

The calculated solvus lies within the error bounds of all the superimposed experimental data points. Note the slight bulge in the calculated phase boundary below about 800 K close to the composition of magnetite (Fe₃O₄). This is a manifestation of magnetic contributions to the Gibbs energy of iron rich spinels becoming significant.

MULTIPHASE OPTION ? RETURN
WHICH MODULE ? APPLICATION
APPLICATION OPTION ? DEFINE DATA_INPUT_FILE 'WFA' !
APPLICATION OPTION ? CLASSIFY ABSENT PHASE(*) MISCIBILITY(SPINEL) 1 !
APPLICATION OPTION ? 'ISOPLETH.MAC
Isopleth - the calculation of pseudo binary sections through
multicomponent systems
It is now necessary to define certain parameters for the calculations.
Enter composition tolerance (typically 0.0001) ?
: 0.0001
Enter number of temperature steps (perhaps 30) ?
: 50
APPLICATION OPTION ? SET "Fe3O4" 0.5 0.5 0.0 "FeAl2O4" 0.5 0.0 0.5 !
APPLICATION OPTION ? RANGE "FeAl2O4" "Fe2O3" 50 !
APPLICATION OPTION ? RANGE TEMPERATURE 700 1300 0.1 ! COMPUTE !

The CaO-Fe-O-Al₂O₃ system at 1418 K

Under oxidising conditions (in air for example) and at temperatures low enough to exclude the spinel and liquid phases, most of the iron in the CaO-Fe-O-Al₂O₃ system occurs in the ferric form. As a result the phase equilibria appropriate to such conditions can be represented, to a good approximation, on the CaO-Fe₂O₃-Al₂O₃ ternary grid.

The ternary section calculated at 1418 K is dominated by the relationships between the calcium ferrites (C2F and CF) each of which dissolves alumina to some extent and a series of calcium aluminates (C3A, C12A7, CA, CA2 and CA6) all of which dissolve some ferric oxide. A ternary compound with the approximate formula CAF2 is also formed. (In these formulae C is used to represent CaO, A to represent Al₂O₃ and F to represent Fe₂O₃). A miscibility gap in the corundum phase (Al₂O₃ in equilibrium with haematite) is apparent along the Al₂O₃-Fe₂O₃ binary edge.

The calculated phase fields at this temperature are in excellent agreement with those observed experimentally. The experimental equilibria are identified by a series of symbols superimposed upon the calculated diagram.

APPLICATION OPTION ? RETURN
WHICH MODULE ? TERNARY
TERNARY OPTION ? DEFINE SYSTEM 'CaO,Fe2O3,Al2O3,O/-2' SOURCE OXIDE !
SEARCHING FOR SYSTEM CaO,Fe2O3,Al2O3,O/-2
oxide - NPL oxide database. Vers. 2.0. 1997.
TERNARY OPTION ? CLASSIFY MISCIBILITY(CORUNDUM) 1 !
TERNARY OPTION ? SET TEMPERATURE 1418 W 1 ! COMPUTE !

Section across the CaO-Fe-O-Al₂O₃ system between C4AF and C5A3

In studying the way phase equilibria in a multicomponent system change with temperature it is useful to be able to plot pseudo-binary sections between compositions of practical interest. An example of such a calculation is the following section across the CaO-Fe-O-Al₂O₃ system between C4AF and C5A3 at 0.21 atmospheres O₂ pressure.

The liquidus takes the form of a eutectic valley with CA as the primary phase close to C5A3 and C2F as the primary phase close to C4AF. Both CA and C2F exist as a series of crystalline solutions. The composition at the bottom of the valley (48 weight % CaO, 10 weight % Fe₂O₃ and 42 weight % Al₂O₃) agrees closely with that determined experimentally.

Since this is not a true binary diagram but a section through a multicomponent system, more than two phases may be found to coexist in some regions. The crystalline solutions CA, C12A7 and C2F at low temperatures are one example. Furthermore tie-lines in two phase fields do not necessarily lie in the plane of the diagram as would be the case for a true binary system.

TERNARY OPTION ? RETURN
WHICH MODULE ? APPLICATION
APPLICATION OPTION ? DEFINE SYSTEM 'CaO,Fe2O3,Al2O3,O2,O/-2' SOURCE OXIDE %
? OUTPUT 'CWFA.MPI' !
SEARCHING FOR SYSTEM CaO,Fe2O3,Al2O3,O2,O/-2
oxide - NPL oxide database. Vers. 2.0. 1997.
APPLICATION OPTION ? 'ISOPLETH.MAC
Isopleth - the calculation of pseudo binary sections through
multicomponent systems
It is now necessary to define certain parameters for the calculations.
Enter composition tolerance (typically 0.0001) ?
: 0.0001
Enter number of temperature steps (perhaps 30) ?
: 50
APPLICATION OPTION ? SET "C4AF" 0.46113 0.32827 0.20960 0.001 !
APPLICATION OPTION ? SET "C5A3" 0.47773 0.0001 0.52117 0.001 !
APPLICATION OPTION ? SET W 1 ! RANGE "C4AF" "C5A3" 50 !
APPLICATION OPTION ? RANGE TEMPERATURE 1400 1750 0.1 ! COMPUTE !

FeO activities in the Fe-O-SiO₂-Al₂O₃ system

Phase equilibrium calculations in a multicomponent system can be analyzed in a great many ways. MTDATA, for example, can be used to study a variety of thermodynamic functions as well as for examining the stability of phase combinations as already shown. Such functions include the activity of individual components relative to a chosen reference state.

In the following diagram FeO activities at 1673 K are plotted along a line through the Fe-O-SiO₂-Al₂O₃ system joining a 92:8 mixture of SiO₂ and Al₂O₃ with pure iron oxide in contact with iron. At high iron oxide concentrations the only stable oxide phase is the liquid. For such compositions the variation in FeO activity with the mole fraction of FeO is markedly non-linear and a pronounced hump is evident in the calculated activity curve. This is in good agreement with the superimposed experimental data points.

At higher SiO₂ and Al₂O₃ concentrations, of less importance practically, first tridymite, then tridymite and mullite are formed along with the liquid phase. Agreement between calculation and experiment is not as good for these compositions. Note however that some variation is apparent in the experimental data points.

APPLICATION OPTION ? RETURN MULTIPHASE
MULTIPHASE OPTION ? DEFINE SYSTEM 'FeO,SiO2,Al2O3,Fe,O/-2' SOU OXIDE !
SEARCHING FOR SYSTEM FeO,SiO2,Al2O3,Fe,O/-2
oxide - NPL oxide database. Vers. 2.0. 1997.
MULTIPHASE OPTION ? CLASSIFY REFERENCE(2) 1 ! SET TEMPERATURE 1673 !
MULTIPHASE OPTION ? SET 'S92A8' 0.0 0.92 0.08 0.001 'FeO' 1.0 0.0 0.0 0.001 !
MULTIPHASE OPTION ? STEP 'S92A8' 'FeO' 51 ! COMPUTE PRINT GRAPHICS !
51 MOLE STEPS JOINING S92A8 TO FeO
MULTIPHASE OPTION ? ORDINATE COMPONENT_ACTIVITY COMPONENT(FeO) ! PLOT GO
            

The iron cordierite primary phase field

Liquidus contours and primary phase maps are a convenient way of picturing high temperature phase equilibria in systems with three or more components. A relatively new feature of MTDATA allows these sorts of diagram to be drawn for any composition triangle within a multicomponent system. Liquidus temperatures are calculated and primary phases identified at all points on a grid spanning three chosen compositions. Contours are then constructed based upon these results.

In the Fe-O-SiO₂-Al₂O₃ system in contact with iron, the compound iron cordierite (Fe₂Al₄Si₅O₁₈) appears as the primary crystalline phase over a rather limited range of composition. This is sandwiched between two much more extensive primary phase fields corresponding to spinel (hercynite) crystalline solutions and cristobalite. The ends of the iron cordierite field, less then 1 weight % SiO₂ wide, are capped by fields corresponding to fayalite and mullite.

The liquidus contours superimposed on the primary phase map suggest that iron cordierite occurs as a primary phase over a temperature range of less than 150 K.

MULTIPHASE OPTION ? RETURN
WHICH MODULE ? APPLICATION
APPLICATION OPTION ? DEFINE SYSTEM 'FeO,SiO2,Al2O3,Fe,O/-2' SOURCE OXIDE !
SEARCHING FOR SYSTEM FeO,SiO2,Al2O3,Fe,O/-2
oxide - NPL oxide database. Vers. 2.0. 1997.
APPLICATION OPTION ? SET P 0.21*101325.0 W 1 !
APPLICATION OPTION ? SET 'W5S4A1' 0.5 0.4 0.1 0.0001 !
APPLICATION OPTION ? SET 'W3S6A1' 0.3 0.6 0.1 0.0001 !
APPLICATION OPTION ? SET 'W3S4A3' 0.3 0.4 0.3 0.0001 !
APPLICATION OPTION ? RANGE T 2500 1300 0.1 !
APPLICATION OPTION ? 'LIQUIDUS
Liquidus - liquidus contours and primary phase fields for ternary
slices through multicomponent systems
It is now necessary to define certain parameters for the calculations.
Enter name of composition to be plotted lower left ?
: 'W5S4A1'
Enter name of composition to be plotted at the top ?
: 'W3S6A1'
Enter name of composition to be plotted lower right ?
: 'W3S4A3'
Enter number of steps between each composition ?
: 50
Enter contour interval required ?
: 50
APPLICATION OPTION ? COMPUTE !