impor-The thermodynamics of dilute solutionsMany reactions encountered in extractive metallurgy involve dilute solutions of one or a number of impurities in the metal, and sometimes the
Trang 1show that CS for FeO-containing slags is somewhat higher than that of rich slags reflecting the Gibbs exchange energies
CaO-FeO C 1/2S2(g) D FeS C 1/2O2(g); G°1850D91 500 kJ mol1
1/2 2MOfMOgpS1/22
the activity coefficient ratio sulphide/oxide is very much higher in the case ofthe calcium ion than for the ferrous ion, to an extent which more than balancesthe equilibrium constant which appears to favour the calcium ion
Using the method described above, the sulphide capacity of a ponent slag may be calculated with the exchange oxide/sulphide equilibriaweighted with the metal cation fractions, thus
multicom-log CSFe2C,Mn2C,Ca2C,Mg2C
DXFe2C,Mn2C,Ca2C,Mg2C
log CSFe2C,Mn2C,Ca2C,Mg2C
Similarly the removal of phosphorus from liquid iron in a silicate slag may
be represented by the equations
2[P] C 5[O] C 3fO2g !2fPO4g; log K D ixilog Ki
(i D Ca2C, Fe2C etc which are the cationic species in the slag phase).Fellner and Krohn (1969) have shown that the removal of phosphorus fromiron–calcium silicate slags is accurately described by the Flood–Grjotheimequation with
log KCa2C D21 and log KFe2C D11
and concluded that the term in xCa2Clog KCa2Cis the only term of tance in the dephosphorizing of iron
Trang 2impor-The thermodynamics of dilute solutions
Many reactions encountered in extractive metallurgy involve dilute solutions
of one or a number of impurities in the metal, and sometimes the slag phase.Dilute solutions of less than a few atomic per cent content of the impurityusually conform to Henry’s law, according to which the activity coefficient
of the solute can be taken as constant However in the complex solutionswhich usually occur in these reactions, the interactions of the solutes with oneanother and with the solvent metal change the values of the solute activitycoefficients There are some approximate procedures to make the interactioncoefficients in multicomponent liquids calculable using data drawn from binarydata The simplest form of this procedure is the use of the equation deduced
by Darken (1950), as a solution of the ternary Gibbs–Duhem equation for aregular ternary solution, A–B–S, where A–B is the binary solvent
SACBDXA SACXB SBGxsACB/RT
Here, the solute S is in dilute solution, and the equation can be used acrossthe entire composition range of the A–B binary solvent, when XACXB isclose to one When the concentration of the dilute solute is increased, themore concentrated solution can be calculated from Toop’s equation (1965) inthe form
SACBDXB/1 XS SBCXA/1 XS SA
1 XS2GxsACB/RTThis model is appropriate for random mixtures of elements in which the pair-wise bonding energies remain constant In most solutions it is found thatthese are dependent on composition, leading to departures from regular solu-tion behaviour, and therefore the above equations must be confined in use tosolute concentrations up to about 10 mole per cent
SA SB in the equationabove, there must be significant departures from the assumption of randommixing of the solvent atoms around the solute In this case the quasi-chemicalapproach may be used as a next level of approximation This assumes that theco-ordination shell of the solute atoms is filled following a weighting factorfor each of the solute species, such that
nSA/nSBDXA/XBexp[Gexchange/RT]
where nSA and nSB are the number of S–A contacts and S–B contactsrespectively, and the Gibbs energy of the exchange reaction is for
B S C A ! A S C B
Trang 3The equation corresponding to the Darken equation quoted above is thenSACB]1/ZDXA AACB SA]1/ZCXB BACB SB]1/Z
In liquid metal solutions Z is normally of the order of 10, and so this equation
SACBwhich are close to that predicted by the random tion equation But if it is assumed that the solute atom, for example oxygen, has
solu-a significsolu-antly lower co-ordinsolu-ation number of metsolu-allic solu-atoms thsolu-an is found inthe bulk of the alloy, then Z in the ratio of the activity coefficients of the solutes
in the quasi-chemical equation above must be correspondingly decreased tothe appropriate value For example, Jacobs and Alcock (1972) showed thatmuch of the experimental data for oxygen solutions in binary liquid metalalloys could be accounted for by the assumption that the oxygen atom is fourco-ordinated in these solutions
The most important interactive effect in ironmaking is the raising of theactivity coefficient of sulphur in iron by carbon The result of this is thatthe partition of sulphur between slag and metal increases significantly as thecarbon content of iron increases, thus considerably enhancing the elimination
of sulphur from the metal Other effects, such as the raising of the activitycoefficient of carbon in solution in iron by silicon, due to the strong Fe–Siinteraction, have less effect on the usefulness of operations at low oxygenpotentials such as those at carbon-saturation in the blast furnace The effect ofone solute on the activity coefficient of another is referred to as the ‘interactioncoefficient’, defined by
to the base 10, together with the weight per cent of the components is usedrather than the more formal expressions quoted above, and so the interactioncoefficient, e, is given by the corresponding equation
Trang 4Table 14.1 Interaction coefficients of solutes (ð102) in
Numbers rounded to the nearest 0.5.
The refining of lead and zinc
The metals that are produced either separately or together, as in the lead–zincblast furnace, contain some valuable impurities In lead, there is a signifi-cant amount of arsenic and antimony, as well as a small but economicallyimportant quantity of silver The non-metals cause the metal to be hard, andtherefore the refining stage which removes them is referred to as lead ‘soft-ening’ This is achieved by an oxidation process in which PbO is formed toabsorb the oxides of arsenic and antimony, or, alternatively, these oxides arerecovered in a sodium oxide/chloride slag, thus avoiding the need to oxidizelead unnecessarily The thermodynamics of the reactions involved in either
of these processes can be analysed by the use of data for the followingreactions
4/3As C 2PbO D 2/3As2O3C2Pb; G°D25 580 82.6T Jand
4/3Sb C 2PbO D 2/3Sb2O3C2Pb; G°D 27 113 41.7T J
In the case of the direct oxidation, the oxygen partial pressure must be greaterthan that at the Pb/PbO equilibrium, while in the process involving sodium-based salts, the oxygen pressure is less than this The two equilibrium constantsfor the refining reactions
KAsDa2/3fAs2O3g/a4/3[As] and KSb Da2/3fSb2O3g/a4/3[Sb]
(since aPbDaPbOD1 show that the relative success of these alternativeprocesses depends on the activity coefficients of the As and Sb oxides inthe slag phase The lower these, the more non-metal is removed from themetal There is no quantitative information at the present time, but the fact
Trang 5that the sodium salts of oxy-acids are usually more stable than those of lead,would suggest that the refining is better carried out with the sodium salts thanwith PbO as the separate phase.
Another metal which accompanies silver in blast furnace lead is copper,which must also be removed during refining This is accomplished by stir-ring elementary sulphur into the liquid, when copper is eliminated as coppersulphide(s) The mechanism of this reaction is difficult to understand on ther-modynamic grounds alone, since Cu2S and PbS have about the same stability.However, a suggestion which has been advanced, based on the fact that theaddition of a small amount of silver (0.094 wt %) reduced substantially theamount of lead sulphide which was formed under a sulphur vapour-containingatmosphere, is that silver is adsorbed on the surface of lead, allowing for thepreferential sulphidation of copper
The removal of silver from lead is accomplished by the addition of zinc tothe molten lead, and slowly cooling to a temperature just above the meltingpoint of lead (600 K) A crust of zinc containing the silver can be separatedfrom the liquid, and the zinc can be removed from this product by distillation.The residual zinc in the lead can be removed either by distillation of the zinc,
or by pumping chlorine through the metal to form a zinc–lead chloride slag
The separation of zinc and cadmium by distillation
An important element that must be recovered from zinc is cadmium, which isseparated by distillation The alloys of zinc with cadmium are regular solutionswith a heat of mixing of 8300 XCdXZnJ gram-atom1, and the vapour pressures
of the elements close to the boiling point of zinc (1180 K) are
pZnD0.92 and pCdD3.90 atmos
The metals can be separated by simple evaporation until the partial pressure
of cadmium equals that of pure zinc, i.e
p°Cd CdXCdDp° ZnXZn
and using these data the zinc mole fraction would be 0.89 at 1180 K
It follows that the separation of cadmium must be carried out in a lation column, where zinc can be condensed at the lower temperature ofeach stage, and cadmium is preferentially evaporated Because of the factthat cadmium–zinc alloys show a positive departure from Raoult’s law, theactivity coefficient of cadmium increases in dilute solution as the temperaturedecreases in the upper levels of the still The separation is thus more complete
distil-as the temperature decredistil-ases
A distillation column is composed of two types of stages Those above theinlet of fresh material terminate in a condenser, and are called the ‘rectifying’
Trang 6stages Those below the inlet terminate in a boiler and are called the ‘stripping’stages When a still is run in a steady state a material balance at one stageapplies to all stages, because there is no net accumulation of material at anyone stage If the stages of the rectifying set are numbered successively fromthe top of the column downwards, the material balance at the nth stage isgiven by
VnC1DLnCD
where VnC1 moles of vapour approach the stage from the n C 1th stagebelow, Ln moles of liquid reflux towards the boiler and D (distillate) moles
of vapour pass to the condenser If yA is the fraction of the component A in
an A–B vapour mixture, and xAis the mole fraction in the co-existing liquid,
In this equation, all of the terms except ynC1 and xn but including xA
D, areconstant Hence the relationship between ynC1A and xA
n is linear with a slope of
Ln/LnCDand a line representing the relationship on a graph of y vs x mustpass through yDDxDwhen xnDxD, since the vapour and the liquid have thesame composition in the product This is called the rectifying operating line
in a graphical representation of the distillation process
A similar material balance for the stripping stages which are labelled 1 to
Trang 7by constructing intercepts in this fashion, dropping vertically at each calculatedvapour composition The slope of the rectifying stage operating line is calledthe ‘reflux ratio’, since it defines the fraction of the liquid which is returned
to the stripping stage, the remainder passing on to the rectifying stage Theextent of refluxing is partly determined by the ability of the descending liquid
to extract heat from the ascending vapour phase In liquid metal systems,where the thermal conductivity is high, this extraction of heat is much moreefficient than in the corresponding organic systems which are convention-ally separated by distillation The separation of metals by distillation can beexpected to operate under the theoretically deduced conditions because of this(Figure 14.1)
y = x
2 1 Collector of less volatile component
Figure 14.1 The McCabe–Thiele diagram for the calculation of the number
of theoretical stages required to separate two liquids to yield relatively pure products
The New Jersey refining procedure for zinc refining is carried out in twostages of distillation In the first stage, at the higher temperature, the zincand cadmium are volatilized together, leaving a liquid phase which containsthe lead impurity together with other minor impurities such as iron In thesecond distillation column cadmium is removed at the top of the still andzinc is collected at the bottom at better than 99.99% purity The activity
Trang 8coefficient of cadmium in solution in zinc, which is a regular solution, depends
on temperature according to
CdD437.2 X2Zn/T
the average value of the coefficient being 3.3 as XZn!1 in this temperaturerange, and thus it is preferable to operate the still at the lowest feasible temper-ature, as near to the melting point of zinc (693 K) as possible The vapourpressures of pure cadmium and zinc can be related through the equationZn(g) C Cd(l) D Zn(l) C Cd(g)
K D pCdaZn/pZnaCd where G°D17 530 3.55 T J mol1
It follows that the ratio of these vapour pressures for the pure componentschanges from 13 at 700 K to 4.5 at 1100 K, again indicating the lowest feasibleoperating temperature as the preferred distillation temperature Because theingoing material contains cadmium at a low concentration (ca 1 atom percent), the relative vapour pressures will be pCd'0.03pZn
De-oxidation of steels
The removal of carbon in the BOF process leaves the metal with an oxygencontent which, if not removed, can lead to mechanical failure in the metalingot The removal of the unwanted oxygen can be achieved by the addition
of de-oxidizing agents which are metals, such as aluminium, which have amuch higher affinity for oxygen than does iron The product of aluminiumde-oxidation is the oxide Al2O3, which floats to the surface of the liquid steel
as a finely dispersed phase, leaving a very dilute solution of the metal and
a residual amount of oxygen The equilibrium constant for the de-oxidationreaction
2[Al] C 3[O] D Al2O3
where [ ] represents an element in solution in liquid iron, is given by
K D aAl2O3
X2[Al]X3[O] [Al]2 [O]3
and the final oxygen content after de-oxidation is not only determined bythe stability of the oxide which is formed, but also by the mutual effects ofaluminium and oxygen on their activity coefficients Experimental data forthis process at 1900 K show that the interaction coefficients of these elements
e0 DeAlD 1300
Trang 9hence there is a strong mutual effect It was also found that when the aluminiumcontent of iron is above 1 wt %, this relation no longer applies, and the de-oxidation product is hercynite, FeOÐAl2O3, and the oxygen content of themetal rises significantly above the values indicated by the iron–alumina equi-librium There is therefore a practical limit to the extent to which iron may bede-oxidized by this method Fine particles of alumina are found in the finalsolid iron product, indicating that not enough time is normally available inindustrial practice to allow the alumina particles to float to the surface.
Vacuum refining of steel
An alternative, though more costly, de-oxidation procedure is the vacuumrefining of liquid steel This process takes advantage of the fact that the residualcarbon content reacts with the oxygen in solution to form CO bubbles whichare removed leaving no solid product in the melt Other impurities, such asmanganese, which has a higher vapour pressure than iron are also removed inthis process The removal kinetics of manganese can be calculated using thevapour pressure of the metal at steelmaking reactions in the free evaporationequation given earlier
Xbulk/Xsurface 1 D 44.32MFe
k#Fe
Mnp°Mn
MMn/T1/2For manganese which has a vapour pressure of 4.57 ð 102atmos at 1873 K,this depletion amounts to about one half of the bulk concentration, thuslowering the rate of manganese evaporation by half These equations may
be used to derive the condition for the preferential removal of a solute, A,from liquid iron
44.32p° MFe/T1/2 k#Fe/MFeMAXbulkXsurface
Trang 10Examples of this procedure for dilute solutions of copper, silicon andaluminium shows the widely different behaviour of these elements Thevapour pressures of the pure metals are 1.14 ð 102, 8.63 ð 106 and 1.51 ð
103atmos at 1873 K, and the activity coefficients in solution in liquid iron are8.0, 7 ð 103 and 3 ð 102 respectively There are therefore two elements ofrelatively high and similar vapour pressures, Cu and Al, and two elements ofapproximately equal activity coefficients but widely differing vapour pressures,
Si and Al The right-hand side of the depletion equation has the values 1.89,1.88 ð 108, and 1.44 ð 103 respectively, and we may conclude that therewill be depletion of copper only, with insignificant evaporation of silicon andaluminium The data for the boundary layer were taken as 5 ð 105cm2s1for the diffusion coefficient, and 103cm for the boundary layer thickness inliquid iron
The elimination of hydrogen and nitrogen show different kinetic behaviourduring the vacuum refining of steel Hydrogen is evolved according tothe solubility and diffusion coefficient of the gas in liquid iron DHD1.3 ð 103cm2s1, and has an apparent activation energy of elimination of
35 kJ mol1, whereas the elimination of nitrogen showed an apparent activationenergy between 100 and 250 kJ mol1, increasing with increasing oxygencontent of the metal Oxygen is known to adsorb strongly on the surface
of liquid iron, and it is concluded that this adsorbed layer reduces the number
of surface sites at which recombination of the nitrogen atoms to form N2molecules can take place
The elimination of gaseous solutes from liquid metals by the use of an inertgas purge has also been studied in two model systems In one, the removal ofoxygen from solution in liquid silver was measured, and in the other the shapes
of bubbles which are formed when a gas was bubbled through water wereobserved Oxygen dissolves in liquid silver to a well-defined extent, and resultsfor the solubility having been obtained using an electrochemical cell The exper-imental value deduced for the transfer of oxygen to argon which was bubbledthrough the liquid was 0.042 cm s1 A water model study was made sincewater has about the same viscosity as liquid steel, and this property controlsthe shapes of bubbles in liquids, and it is easy to observe the effects, which areprobably similar to those which take place in an opaque liquid such as steel.The bubbles shapes in gas purging vary from small spherical bubbles, ofradius less than one centimetre, to larger spherical-cap bubbles The masstransfer coefficient to these larger bubbles may be calculated according tothe equation
k D g1/4D1/2d1/4cm s1
where d is the diameter of a spherical bubbles of equal volume This followsfrom the fact that the velocity of rise through the liquid of a spherical-cap
Trang 11bubble has been shown to be
u D1.02gd/21/2
and this may be used, together with the diameter of the bubble, as the teristic length, in defining the Reynolds number in the mass transfer equation
charac-NSh D1.28NReNSc1/2
which gives a value of the mass transfer coefficient of 4.7 ð 102cm s1,
in good agreement with the experimental value It should be noted that thisvalue is also obtained from the diffusion coefficient of oxygen in silver, 5 ð
105cm2s1 together with a boundary layer thickness of 103cm
The evolution of nitrogen from liquid steel is also dependent on the oxygencontent, again because of the blocking of the surface sites which are necessaryfor N2 molecule formation prior to evolution
Refining by liquid salts and the Electroslag process
Since the alkali and alkaline metals have such a high affinity for oxygen,sulphur and selenium they are potentially useful for the removal of these non-metallic elements from liquid metals with a lower affinity for these elements.Since the handling of these Group I and II elements is hazardous on the indus-trial scale, their production by molten salt electrolysis during metal refining
is an attractive alternative Ward and Hoar (1961) obtained almost completeremoval of sulphur, selenium and tellurium from liquid copper by the elec-trolysis of molten BaCl2 between the metal which functioned as the cathode,and a graphite anode
Another process which improves on the conditions for sulphur removal fromsteel is to allow the liquid metal to fall as droplets through a CaO–CaF2slag, inwhich the low oxygen potential of the blast furnace is reproduced, and a higherCaO activity can be achieved, as high as 0.4, at steel melting temperatures(Duckworth and Hoyle, 1969) Because of this higher CaO activity, it followsthat the sulphur-holding properties of these fluoride-based molten phases willresult in a much higher sulphide capacity, CS as measured by the relation
CSD%SpO2/pS21/2
than the silicate-based slags
The melt is heated by passing a large electrical current between two trodes, one of which is the metal rod to be refined, and the other is the liquidmetal pool standing in a water-cooled copper hearth, which collects the metaldrops as they fall through the molten electrolyte This pool therefore freezes
elec-at the bottom, forming the ingot Under optimum circumstances the productbillet takes the form of a cylindrical solid separated from the molten salt by
Trang 12a thin lens of molten metal It has been found that the temperature of themelt must not be allowed to get too high, because this leads to an ingot withunsatisfactory physical properties To overcome this problem, Al2O3 is added
to lower the electrical resistance This addition is made at the cost of reducingthe sulphide capacity of the melt by a factor of 10, even though the solubility
of CaO in the melt is increased, but this still leaves a retaining, slag
Trang 13satisfactory,sulphur-Factorial analysis of metal-producing reactions
The optimization of reactions involving a large number of variables, and inthe case of metal production these might include the temperature, gas, slagand metal compositions, the state of motion of each phase, and the length ofthe refining period, could be analysed by the classical, so-called Newtonianmethod in which one variable is altered in a given series of tests while allother variables are held constant, and the results are collected in order to assessthe dependence of the productivity on that variable However, since each testwould be expensive of time and labour on the industrial scale, an alternativemay be adopted which reduces the number of plant trials required to separatethe effects of the variables
This practical alternative is called factorial analysis, and involves trials in which each variable is run at one of two values, or levels in the language
of statistical analysis, and each trial requires the level of each variable to beset at the high or low level For example, to test the effects of temperature,and slag–metal composition on the removal of sulphur during the refining
of liquid iron containing carbon as in blast-furnace operation, there could bethree variables, each at two levels, and the final content of sulphur which
is produced from a given initial concentration would be measured All othervariables, such as mixing in the gas phase and stirring of the liquids and theduration of the trial, would be held constant while the chosen variables weretested In this complex situation the factorial method reduces the number oftrials which are required in comparison to the classical procedure, but thetests are truly hybrid in that some other variables would be held constant Thecomposition-dependent variables, such as viscosities and interfacial tension
of the condensed phases are not included Of course, the analysis could beextended to include the other independent variables, but the calculation would
be lengthy, and therefore would require computer programming, which is notdifficult in this context
Labelling the variables as T, S and M, with reference symbols, a, b, crespectively in trials involving a low (l) and high (h) levels of each variable,each trial having the result xi, the factorial procedure would produce the designcode as follows:
Trang 14Variables Level Symbol Result
Once the results have been collected they may be analysed to show theeffects of each variable separately, T, S, M, the interaction of two variables,T–S, T–M, S –M, and three variable interaction, T–S –M These interactionterms measure the effect of the change in one variable on the results for theothers, and T–S –M, the ternary interaction indicates the dependence of theresults for one variable of the simultaneous change of the others
This is a novel feature of factorial design when compared with the classicallaboratory procedure which excludes indications of the interaction of the vari-able The method of analysis of the data, due to Yates, which is commonlyused to evaluate these effects, requires that the trials are conducted in thesequence shown above, and proceeds as follows
The table of results is laid out in a column, and a second column isconstructed in which in the first four rows the results would be added sequen-tially in pairs, e g x1Cx2, x3Cx4, x5Cx6 etc., and the lower four rowsare calculated by subtracting the second value from the preceding value thus,
x2x1, x4x3etc., a third column is prepared from these results by carryingout the same sequence of operations The process is continued until thereare as many columns as the number of variables Thus in the present three-variable, two level-study the process is repeated three times (Table 15.1), and
in the general n-variable, two-level case it is repeated n times (The generaldescription of trials of this kind where there are n variables and two levels, is
‘2n factorial trials’)
Each value in the final column of the table constructed above is now divided
by 4, which is the number of additions or subtractions made in each column.The results of this division show the numerical effects of each variable andthe interaction between variables The value opposite the second row showsthe effect of the temperature, the third shows the effect of the slag phasecomposition, and, the fifth the effect of the metal composition The interactionterms then follow the symbols of each row, the fourth showing the effect of
Trang 15abc x8 abc bc abc bc ac C c abc bc ac C c ab C b C a 1 ABC
T is the total of all measurements, and so