Quasi-Chemical Viscosity Model for Fully Liquid Slag
in the Al2O3-CaO-MgO-SiO2System—Part I:Revision
of the Model
MASANORI SUZUKI and EVGUENI JAK
A model has been developed that enables the viscosities of the fully liquid slag in the multi-
郑源的全部歌曲component Al2O3-CaO-FeO-Fe2O3-MgO-Na2O-SiO2system to be predicted within experi-
mental uncertainties over a wide range of compositions and temperatures.The Eyring equation
is ud to express viscosity as a function of temperature and composition.The model links the
activation and pre-exponential energy terms in the viscosity expression to the slag internal
structure through the concentrations of various Si0.5O,Me nþ
2=n O,and Me nþ微信收付款密码怎么设置
1=n
Si0:25O viscousflow
structural units(SUs).The concentrations of the SUs are derived from a quasi-chemical thermodynamic model of the liquid slag using the thermodynamic computer package FactSage. The model describes a number of slag viscosity features including the charge compensation effect specific for the Al2O3-containing systems.The predictive capability of the model is enhanced by the physical aspects of the model parameters—the correlation with other physi-cochemical properties as well as experimental viscosity data is ud to determine model parameters.The prent ries of two papers outlines(a)recent significant improvements introduced into the model formalism and(b)application of the model to the Al2O3-CaO-MgO-SiO2system,review of experimental viscosity data,and optimization of the corresponding model parameters for this system.
DOI:10.1007/s11663-013-9928-3
ÓThe Minerals,Metals&Materials Society and ASM International2013
I.INTRODUCTION
Slag viscosity is an esntial property for a number of metallurgical and power generation industrial process. Development of a structurally bad viscosity model for predictions in the multi-component slag systems valid over wide ranges of compositions and temperatures has been the focus of previous studies[1–7];the prent paper describes recent developments of the model formalism and its application for fully liquid silicate slags in the Al2O3-CaO-MgO-SiO2system.Similar to other structur-ally bad viscosity slag models,[8–12]the link of viscosities to the complex internal slag structure at the atomic level improves the predictive capability of slag viscosities.The overall description and application of the model to the Al2O3-CaO-MgO-SiO2system prented in the papers is only a part of a wider development of the viscosity model for the Al2O3-CaO-FeO-Fe2O3-MgO-Na2O-SiO2 multi-component system.The systematic trends and lf-consistency of the parameters across the whole multi-component system are esntial features of the prent development.The trend analysis was extended even further to other important slag systems,for example,to some lower-order sub-systems containing K2O and PbO. The fact of the systematic analysis of the trends across a number of key slag systems is an important feature of this work,and therefore results for some other sub-systems have been included in this manuscript.
II.MODEL
A.General Model Description
Frenkel’s kinetic theory[13–15]considers a liquid to have a solid-like structure with molecules,or more generally,structural units(SUs),oscillating in their energetic cells(potential wells)near average positions. Oscillations higher in magnitude than the potential barrier result in the movement of a SU into an adjacent vacant cell,or‘‘hole,’’provided the latter is vacant. The vacant cells,or‘‘holes,’’formed in the liquid as a result offluctuations,are distributed randomly through-out the liquid.The viscosity of liquid as a reaction to the applied shear force therefore is determined by(a)the ability of a SU to jump over the potential barrier and(b) the prence of‘‘holes’’in the liquid.The following Eyring Eq.[1]for liquid viscosity was derived[16–18]using the above principles[13]:
g¼
2RT
D E V
2p m SU kT
ðÞ1=2
v
SU
exp
E a
RT
ðg in PaÂsÞ½1
MASANORI SUZUKI,formerly Postdoctoral Rearch Fellow with PYROSEARCH,School of Chemical Engineering,The Uni-versity of Queensland,Brisbane,QLD,4072,Australia,is now Assistant Professor with Division of Materials and Manufacturing Science,Graduate School of Engineering,Osaka University,2-1 Yamadaoka,Suita,Osaka565-0871,Japan.Contact e-mail:suzuki@ saka-u.ac.jp EVGUENI JAK,Professor,is with the PYROSEARCH,School of Chemical Engineering,The University of Queensland.
Manuscript submitted April22,2013.
Article published online August22,2013.
where R(J/K/mol)and k(J/K)are the gas and the Boltzmann constants,respectively;p%3.1416;T is the absolute temperature(K);and m SU(kg)and v SU(m3) are the average mass and volume of viscousflow SUs, respectively.The activation energy E a is determined by the strength of interactions between different SUs composing the liquid.According to Eyring,[16]the energy term D E V(a product of vaporization energy and transition probability)is related to the free volume of the ,to the concentration of the holes in the liquid.It may be argued that D E V includes the negative of the energy of the hole formation:A higher concen-tration of the holes in the liquid corresponds to the higher D E V value and to the lower viscosity.
Four parameters in Eq.[1]—the average mass and volume of SUs,and the E a and D E V energies—are related to the internal structure of liquids,types, concentrations,and interactions between SUs at the atomic/cation/anion level,and require the definition of a viscousflow SU in a particular model.
A silicate slag structure is conventionally described as
the silicate network of SiO4À
4tetrahedra broken by
different metal cations distributed to keep the total electroneutrality.[19]A silicate slag may also be consid-ered as a nearly clo-packed arrangement of larger oxygen anions with smaller metal cations that occupy the interstices and interact with each other.[20]Fincham and Richardson[21]related properties of a silicate slag to the internal slag structure through concentrations of three different types of oxygens:‘‘bridging’’(O0—con-nected to two silicon cations),‘‘non-bridging’’(OÀ—connected to only one silicon),and‘‘free’’(O2À—associated with non-silicon cations).A simplified two-dimensional schematic picture of the internal struc-ture of the slag illustrating the concepts is prented in Figure1.Bad on the above background,the viscous flow of the silicate slag in the prent model is considered to be a movement of oxygens partly associ-ated with metal cations under the applied shear force,so that the viscousflow SUs are defined as oxygen anions with metal cations partly associated with them(e ovals in Figure1),including Si0.5O(=Si-O-Si=Si-Si),
Me nþ
2=n O(=Me-O-Me=Me-Me),and Me nþ
1=n
Si0:25O
(=Si-O-Me=Si-Me),where n denotes the oxidation state of a metal cation Me n+.For example,for the binary MeO-SiO2silicate slag(e Figure1),three types of SUs can be identified,(Si-O-Si)(shaded with dark gray),(Si-O-Me)(shaded with light gray),and(Me-O-Me)(white,not shaded).Their molar fractions are indicated as X Si-Si,X Si-Me,and X Me-Me,respectively. Viscousflow SUs are specific to the prent viscosity model formulation;they differ from the conventional SUs.[19–21]The viscousflow SUs in this work are the units that are assumed to move under the shear stress and include the‘‘moving’’oxygen anions with associ-ated metal cations.For brevity,they are referred to just as‘‘SUs.’’Other models introduce SUs to describe other properties,for example,‘‘bridging,’’‘‘non-bridging’’and‘‘free’’oxygen,[21]or cond-nearest-neighbor bonds.[22]
The values of the E a and D E V energy terms,and the average mass and volume of SUs m SU and v SU in the prent model,are expresd through the respective molar fractions of the various SUs X pq with Eq.[2]: m SU¼
X
p;q
m pq X pq;
v SU¼
X
p;q
v pq X pq;E a¼
X
p;q
"E
a;pq
X pq;
D E V¼D"E V;0exp
X
p;q
e V;pq X pq
!
½2
where p and q are metal cations,m pq and v pq are the mass and volumes of the respective SUs,"E a;pq are partial molar activation energies,D"E V;0is a unit con-stant,and e V;pq are the dimensionless partial energy coefficients of the integral energy term D E V of each SU.In the binary MeO-SiO2system,partial molar activation energies are"E a;SiÀSi,"E a;SiÀMe,and E a;MeÀMe and the integral molar activation energy is expresd as follows:
E a¼E a;SiÀSi X SiÀSiþE a;SiÀMe X SiÀMeþE a;MeÀMe X MeÀMe
½20
The m pq values are the weights of the corresponding molecules,such as Si1=2O,Me nþ
2=n
O,and Me nþ
1=n
Si1=4O.The v pq values are calculated using the effective diameters of SUs estimated from the ionic radii of various ions(O,Si, Me)composing a particular SU.The ionic radii are taken from Shannon[23];the three-dimensional arrangements of the SUs are not taken into account in the prent model at this stage.This uncertainty is‘‘absorbed’’by the model parameters later,during optimization.
In addition to one oxygen,a given SU also involves two metal cations,both of them having other neighbors and both involved in other SU(s).The partial properties E a;pq and e V;pq of a given SU(Me p-O-Me q)therefore depend on the type of cond nearest neighbors.For example,if a Si-Si SU has Si4+cations with other Me n+cations as ,a SU marked as‘‘B’’in Figure1),they will have a different partial activation molar energy compared to the ca when some or all other neighbors
are also Si4+,a SU marked as‘‘A’’in Figure1).The effect of neighboring SUs on a given partial activation energy is expresd as a function of the concentrations of other types of SUs.The partial molar activation energy of each type of SU was previously[1–6] expresd using the following Eqs.[3]to[5]:
E a;SiÀSi¼E0a;SiÀSiþE SiÀSi;1
a;SiÀSi
X SiÀSi
þE SiÀSi;2
a;SiÀSi X2
SiÀSi
þE SiÀMe
a;SiÀSi
X SiÀMe
½3
E a;SiÀMe¼E0a;SiÀMeþE SiÀMe
a;SiÀMe
X SiÀMe
þE SiÀSi
a;SiÀMe X SiÀSiþE MeÀMe
a;SiÀMe
X MeÀMe
½4
E a;MeÀMe¼E0a;MeÀMeþE MeÀMe
a;MeÀMe
X MeÀMe
þE SiÀMe
a;MeÀMe X SiÀMe
½5
Note that only the effect of the cond nearest neighbors was taken into account in the model.For example,E a;SiÀSi does not depend on X Me-Me and vice versa,becau(Me-O-Me)SU cannot be the clost neighbor of the(Si-O-Si)SU.
A higher power term E SiÀSi;2
a;SiÀSi was previously ud[1–6]
in the expression of E a;SiÀSi to describe experimental data in the SiO2-containing systems.More complex terms in the expression of E a;SiÀSi were later intro-duced[7]for the Na-and K-containing silicate slags.The composition dependencies of most of the other partial activation energies except E a;SiÀSi on the concentrations of other nearest neighbors were not taken into account due to the weak dependency on compositions and the lack or uncertainties of experimental data.The partial activation energies E a;Me1ÀMe2for the slag systems with limited experimental data ,Al2O3-‘‘FeO’’and CaO-‘‘FeO’’)were taken to be equal to1/2 (E a;Me1ÀMe1+E a;Me2ÀMe2).The dimensionless partial energy coefficients e v,Si-Si,e v,Me-Si,and e v,Me-Me were described in a similar way.
The so-called‘‘charge compensation effect’’(e.g., increa of viscosity and maximum at the Al2O3/Ca
O ratio clo to1in the Al2O3-CaO-SiO2system)was described with a specially introduced term.[1–6]
The prent as well as other structurally bad models[8–11]have advantages over phenomenological models that express viscosity as a function of just composition.The model parameters of the structurally bad models bear physical meaning;the values of the parameters obtained from the lower-order systems can be extrapolated into multi-component and higher-order systems where no experimental data are available, enabling predictions to be performed and,in some cas,discrepancies between experimental data to be identified.Certain restrictions on the model parameters can be introduced and the trends in the values of the model parameters can be identified and ud for interpolations and extrapolations in other systems in which experimental data are lacking.Such structural models areflexible enough to reflect major changes,but ‘‘rigid’’for composition ranges with similar SU distri-butions.The models expressing viscosities as polynomial functions of compositions do not have the predictive advantages.
B.Improved Model
The previous formalism[1–7]had some limitations in the description of viscosities in complex silicate slag systems and therefore had been critically reviewed and subquently revid in the prent stu
dy.A number of further significant improvements introduced into the model are discusd in the following ctions.As a result of the revision,the partial properties E a;pq and e V;pq of a given SU(Me p-O-Me q)are described with Eqs.[6]to[8]: F SiÀSi¼F0SiÀSi
þ
X
i¼Ca;Mg;Al;...
F SiÀi
SiÀSi
X SiÀi
1ÀX SiÀSiÀX iÀi
ðÞSi=i
"#þ
X
j¼Ca;Mg;...
D F SiÀAlðch;jÞ
SiÀSi
p ch;j
AlO4
X SiÀAl
c Si=Al
h i
½6
F kÀl¼F0kÀlþF kÀl kÀl X kÀl;F kÀl kÀl%0;F0lÀm%1=2F0lÀlþF0mÀm
ÀÁ
½7
F AlÀn¼F0AlÀnþ
X
j¼Ca;Mg;...
D F ch;j
AlÀn
p ch;j
AlO4
;½8
p ch;j
AlO4
¼k ch;j
AlO4
X AlÀAlþ1
P
k
X AlÀk
a Al=j
X jÀjþ1
P
n
X jÀn
4Àa Al=j
X AlÀAlþ1
2
P
k
X AlÀk
þ
P
t
bye怎么读X tÀtþ1
2
P
s;s¼t
X tÀs
! "#
½80 where i,Ca,Mg,Al,Na,…(i¼Si);j,t,Ca,Mg,…(j;t¼Si;Al;Na);k,Si,Ca,Mg,Na,…(k¼Al);l,m Ca,Mg,Na,…(l;m¼Si;Al),n,s,Si,Ca,Mg,Al,…(n;s¼Na);the symbol F denotes partial molar activa-tion energy E a or dimensionless molar energy coeffi-cients e V;the power coefficient c Si/i in the prent
formalism is a system-dependent parameter;p ch;j
AlO4
in Eqs.(8)and(8¢)is a probability function that express the probability to have a tetrahedrally coordinated alumina among existing(Al-O-Me n)and(Me j-O-Me n) SUs;k ch;j
AlO4
is an individual constant for each cation and it determines the magnitude of the probability to form a tetrahedrally coordinated alumina structure as a result of charge compensation by Me2+cation;a Al=j is the power which determines the composition dependence of the probability function p ch;j
AlO4
and in turn the proportion of the(Al-O-Me n)SUs with the tetrahedrally coordi-nated alumina(specific for each Al2O3-MeO oxide binary aluminate system);D F SiÀAlðch;jÞ
SiÀSi
and D F ch;j
AlÀm
describe additional contributions to the partial energy coefficients E a and e V of corresponding SUs due to the prence of tetrahedrally coordinated Al-containing SUs.
The concentrations of SUs in the prent study are determined using the quasi-chemical thermodynamic model of the liquid slag[22,24,25]that takes into account short-range ordering of cond-nearest-neighbor cations in the ionic melt.For a binary MeO-SiO2slag,the quasi-chemical thermodynamic model considers the formation of two nearest-neighbor pairs(Si-Me)from(Me-Me) and(Si-Si)pairs,referred to as‘‘cond nearest neigh-bour bonds’’(SNNB).[22,24,25]The concentrations of the various viscousflow SUs are equal to the concentrations of the corresponding cond-nearest-neighbor bonds of the quasi-chemical thermodynamic model(e Figure1).The quasi-chemical thermodynamic model as part of the FactSage computer package[26]has been successfully applied to describe experimental pha equilibria,thermodynamic and other types of data in many slag systems from binary to multi-component systems,and the SNNB concentrations calculated with the quasi-chemical thermodynamic model were taken as a reasonable approximation of the slag internal struc-ture.The important point here is that valuable infor-mation on the structure of the liquid slag at the atomic level can be obtained from the quasi-chemical thermo-dynamic model of the liquid pha developed by experimental data on pha equilibria and thermody-namic properties.This information can be ud as a basis for the description of other physicochemical properties, e.g.,viscosity in this study.The SNNB concentrations were calculated using the thermody-namic computer package FactSage[26]with the latest thermodynamic databa[27–29]and a specially developed software tool.
C.Key Principles in Developing Model Formalism
and Model Parameters
Key principles in developing model formalism and model parameters include(a)critical review of experi-mental data,(b)determination of andfitting into the experimental values for E a and D E V where possible, (c)application of restrictions to parameters derived from the physical basis of the model,and(d)systematic analysis of the trends of the model parameters’corre-lations with available structural,physicochemical,and thermochemical properties.
1.Critical review of experimental data
All existing experimental viscosity data werefirst carefully analyzed with particular attention to the experimental procedures.Only the viscosity data mea-sured at temperatures higher than liquidus were taken into account for viscosity modeling(FactSage was ud to predict the liquidus).The contamination of the melt by the dissolution of container or nsor materials is one of major sources of uncertainties in high-temperature viscosity measurements affecting slag composition and container or nsor geometry.In this study,experimen-tal results which include post-chemical analys were preferred and tho which contain the possibility of the contamination were given low
weights.Temperature control is also esntial—experimental results where temperature was measured by thermocouples clo to the sample were preferred rather than tho where an optical pyrometer was ud.The rotating bob/crucible method was regarded as a more accurate and reliable technique for the high-temperature viscosity measure-ments compared to other methods including vibration viscometer.
2.Derivation of the experimental E a and D E V values Experimental values of the integral E a and D E V energies were derived using Eq.[1]from the gradient and intercept,respectively,of the relationship of ln g
T3=2
vs inver temperature1/T for a given composition(e Kondratiev and Jak[1]for details).The E a and D E V values were then ud along with the viscosity experi-mental data for optimizations.
3.Physical meaning of the model parameters and(d) systematic analysis of the trends of the model parameters Prent model parameters(partial E a and D E V ener-gies)have physical basis,and they are directly related to the internal slag structure and the physics of interactions at atomic scale.Strong,mostly covalent bonds linking silicate tetrahedrons in the melt result in high activation e
nergy and high viscosities in the silica-rich slags. Addition of basic metal ,CaO,MgO,…) strongly affects the bonds between silicate tetrahedrons and therefore has a strong effect on the slag properties, e.g.,decrea viscosity of the high-silicate slags signif-icantly.Some ,Al3+)behave in a different way depending on the chemical environment.The individual effect of various metal oxides on viscosity as well as on other properties is determined by a ries of factors including atomic structure,cation size,inner and outer electronic arrangement,the‘‘ea’’to donate valent electrons to the oxygen anions in the oxide melt, etc.
The physical basis of the parameters in the prent viscosity model is a foundation(i)to introduce partic-ular ,integral E a and D E V energies should be positive over the whole composition range) and(ii)to relate the parameters to other known metal cation ,cation size,ionic potential) or other physicochemical ,heat of vaporization).The model formulation was revid to facilitate the linkage of the model parameters to other physical properties and metal cation characteristics.The optimization procedures involved active asssments and estimates of physicochemical trends and the u of correlations with other properties.The prent viscosity model parameters can also help to‘‘de-convolute’’the relative physicochemical behavior of different cations in the oxide melt.The considerations were ud in th
e revision of the model formalism and optimization of the model parameters.It is an esntial feature that the model for the Al2O3-CaO-MgO-SiO2system prented in the papers is only a part of a wider development of the viscosity model for the Al2O3-CaO-FeO-Fe2O3-MgO-Na2O-SiO2multi-component system.The
systematic analysis of the trends and lf-consistency of the parameters across the whole multi-component sys-tem extending even further to other important slag systems,for example,to some lower-order sub-systems containing K2O and PbO,is an important factor of the prent development.
D.Model Parameters
Systematic optimization of the systems was carried out using the above principles in cycles from lower-order systems to the multi-component systems and back until satisfactory agreement with all accepted experimental data was achieved.Table1reports the prent model parameters.
Agreement with the experimental data using the modified model compared to the previous version[1–7] has been improved.In particular,the description of viscosities at high SiO2concentrations within experi-mental uncertainties is demonstrated in the relevant figures below.
Note that the prent parameters for the Al2O3-CaO-MgO-SiO2system are lf-consistent with
Table1.The Viscosity Model Parameters
The average mass and volume of SUs
SU Si-Si Al-Al Ca-Ca K-K Mg-Mg Na-Na NaAl-NaAl Si-Al Si-Ca Si-K Si-Mg Si-Na Si-NaAl m,SU910À26kg 4.99 5.649.3115.64 6.6910.29 6.81 5.327.1510.32 5.847.64 5.90 v,SU910À29m3 1.92 3.03 5.799.00 3.99 5.9410.38 2.43 3.50 4.58 2.83 3.56 5.01
SU Al-Ca Al-K Al-Mg Al-Na Al-NaAl Ca-K Ca-Mg Ca-Na Ca-NaAl Mg-K Mg-Na Mg-NaAl Na-K Na-NaAl m,SU910À26kg7.488.79 6.177.97 6.2312.488.009.808.0611.178.4910.1512.978.55
v,SU10À29m3 4.27 5.49 3.49 4.32 5.977.28 4.84 5.867.86 6.16 4.90 6.847.477.77
The coefficients for viscosity molar integral E a;D E V and partial E a;D E V energies(J molÀ1).(Al2O3-CaO-MgO-SiO2)
E a¼E a;SiÀSi X SiÀSiþE a;SiÀAl X SiÀAlþE a;SiÀCa X SiÀCaþE a;SiÀMg X SiÀMg
þE a;AlÀAl X AlÀAlþE a;AlÀCa X AlÀCaþE a;AlÀMg X AlÀMgþE a;CaÀCa X CaÀCaþE a;CaÀMg X CaÀMgþE a;MgÀMg X MgÀMg;
E a;SiÀSi¼570000À407000
人才培养体系X SiÀCa
1ÀX SiÀSiÀX CaÀCa
ðÞ1À0:32
À432000
芳菲的意思是什么X SiÀMg
1ÀX SiÀSiÀX MgÀMg
ÀÁ1À0:40À259000
X SiÀAl
1ÀX SiÀSiÀX AlÀAl
ðÞ1À0:58
þ66430p ch;Ca
AlO4X SiÀAl
0:58
þ48215p ch;Mg
TetraAl X SiÀAl
0:58
;
E a;CaÀCa¼78000;E a;MgÀMg¼105000;E a;SiÀCa¼157000;E a;SiÀMg¼161000;
E a;SiÀAl¼187000þ66425p ch;Ca
AlO4þ59643p ch;Mg
AlO4
;E a;AlÀAl¼169000þ67855p ch;Ca
AlO4
þ30000p ch;Mg
AlO4
职场必备
;
E a;AlÀCa¼122000þ50355p ch;Ca
AlO4þ52857p ch;Mg
地图矢量化AlO4
;E a;AlÀMg¼140000þ52857p ch;Ca
AlO4
þ28570p ch;Mg
AlO4
;
the rest,E a;iÀj¼1=2E a;iÀiþE a;jÀj
ÀÁ
D E V¼expðe V;SiÀSi X SiÀSiþe V;SiÀAl X SiÀAlþe V;SiÀCa X SiÀCaþe V;SiÀMg X SiÀMgþe V;AlÀAl X AlÀAlþe V;AlÀCa X AlÀCa
þe V;AlÀMg X AlÀMgþe V;CaÀCa X CaÀCaþe V;CaÀMg X CaÀMgþe V;MgÀMg X MgÀMgÞ;
e V;SiÀSi¼23:6À7:6
X SiÀCa
1ÀX SiÀSiÀX CaÀCa
白垩纪是什么意思ðÞ1À0:32
À8:7
X SiÀMg
1ÀX SiÀSiÀX MgÀMg
ÀÁ1À0:40
À0:0
X SiÀAl
1ÀX SiÀSiÀX AlÀAl
ðÞ1À0:58
þ2:6p ch;Ca
AlO4
X SiÀAl
0:58
þ1:6p ch;Mg
AlO4
X SiÀAl
0:58
;
e V;CaÀCa¼13:5;e V;MgÀMg¼14:1;e V;SiÀCa¼15:7;e V;SiÀMg¼15:8;
e V;SiÀAl¼16:3þ2:6p ch;Ca
AlO4þ2:8p ch;Mg
AlO4
;e V;AlÀAl¼15:5þ3:2p ch;Ca
AlO4
þ1:6p ch;Mg
AlO4
;
e V;AlÀCa¼14:0þ2:6p ch;Ca
AlO4þ0:0p ch;Mg
AlO4
;e V;AlÀMg¼14:8þ0:0p ch;Ca
AlO4
þ1:4p ch;Mg
AlO4
;
the rest,e V;iÀj¼1=2e V;iÀiþe V;jÀj
ÀÁ
p ch;j AlO4¼14
X AlÀAlþ1
2
P
k
X AlÀk
2:5
X jÀjþ1
2
P
n
X jÀn
4À2:5
X AlÀAlþ1
2
P
k
X AlÀk
þ
P
t
X tÀtþ1
2
P
s;s¼t
X tÀs
!4j¼Ca;Mg
ðÞ
and derived using trends of the broader range of important slag systems;therefore,some results for other sub-systems containing Fe,Na,K,and Pb oxides are also prented below.
III.DETAILS OF MODEL DEVELOPMENT A.Pure Oxide Properties
The partial E a and D E V energies of pure SiO2,Al2O3, and PbO liquids have been determinedfirst using available experimental data for pure oxides.[30–40]The calculated and experimental viscosities of pure oxide melts are shown in Figure2,demonstrating good agreement.Experimental data for the SiO2melt by Bockris et al.[31]appear to be inconsistent with the others.Experimental data by Iida et al.[40]for the PbO melt were given a low weight during optimization due to a possible contamination of the melt by the dissolution of crucible material.The partial E a and D E V energies for pure CaO,MgO,Na2O,and K2O melts were derived from not only(i)the data in the clo composition ranges in the corresponding binary and ternary silicate systems but also(ii)using analysis of the E a and D E V trends as functions of available structural and other physicochemical data.Various types of data and trends were analyzed,and ionic potentials and enthalpy of vaporization were lected to assist in evaluation of the partial E a and D E V energies(e Figure3).
Figure3(a)shows the relationship between the partial molar activation energies for pure oxides and the ionic potentials of the corresponding cations(ratio of the charge to the radius of a cation)—the activation energy is higher for the cations with higher ionic potentials,indi-cating stronger bonds with oxygen anions.Figure3(b) shows the comparison between the partial energy terms D E V for pure oxides and the enthalpies of vaporizing liquid oxides in elemental gas species calculated using the la
test thermodynamic databas of the FactSage thermodynamic computation package[26–29,41]on the basis of the following reaction:
Me2=n O Liquid
ðÞ¼2=n Me Gas
ðÞþO Gas
ðÞ; where n denotes the oxidation state of a cation Me n+. Figure3(b)indicates that D E V for pure SiO2is much higher than the others,which may be attributed to the strong covalent components of the bonds involving silicon cations.The D E V values of the other pure oxide
