INFLUENCES OF DIFFERENT COMPONENTS ON VISCOSITIES OF CaO-MgO-Al2O3-SiO2 MELTS

The present study is aimed to distinguish the different influences of CaO and MgO, as well as Al2O3 and SiO2 on viscosity of CaO-MgO-Al2O3-SiO2 melts. It is found that for melt without Al2O3, viscosity increases monotonously as CaO is gradually replaced by MgO. The addition of Al2O3 leads to a complex variation of viscosity. In different composition ranges, viscosity may exhibit different variation tendencies as changing the relative contents of CaO and MgO while keeping contents of other components constant. It is also found that when replacing SiO2 by equivalent mole of Al2O3, (i) in CaOAl2O3-SiO2 system, viscosity increases when Al2O3 content is small relative to CaO content (there are enough Ca2+ ions to charge compensate Al3+ ions), but decreases when CaO content is inadequate for charge compensation; (ii) in MgO-Al2O3SiO2 system, viscosity always decreases as substituting Al2O3 for SiO2. The reason for this difference for two systems may be resulted from the weak charge compensation ability of Mg2+ ion for Al3+ ion relative to Ca2+ ion. All the viscosity variations can be interpreted well by our new proposed viscosity model.


Theoretical basis
In the following sections, when analyzing the viscosity variation behavior, our new proposed viscosity model [24][25][26][27][28][29]  where  is the viscosity, Poise; A is the preexponent factor, Poise; R is the gas constant, 8.314 J/(molK); T is the absolute temperature, K; E is the activation energy, J/mol, while is calculated as follows, [2] where are the mole numbers of different types of oxygen ions; parameter describes the deforming ability of bond around the corresponding unit, which is optimized from the viscosity data of simple system.The deforming abilities of chemical bonds around different types of oxygen ions are shown in Table I.The higher the value in Table I is, the weaker the chemical bond around this type of oxygen ion will be.In the denominator of Eq. [4], the first, second, third, fourth, fifth and sixth terms represent the contributions of bridging oxygen bonded with Si 4+ ion; oxygen bonded with Al 3+ ion not being charge compensated; free oxygen bonded with metal cation i; bridging oxygen bonded with compensated Al 3+ ion by cation i; non-bridging oxygen bonded with Si 4+ ion, and non-bridging oxygen bonded with cation j and Al 3+ ion charge balanced by cation i.The numbers of different types of oxygen ions are related to composition and can be calculated by following the following assumption [28].
Assumption I: Ca 2+ ion has a higher priority than Mg 2+ ion to charge compensate Al 3+ ion.Only when the Ca 2+ ion is exhausted, Mg 2+ ion could be used to charge compensate Al 3+ ion.
Assumption II: The equilibrium constant for the charge compensation reaction of MO with Al 2 O 3 to generate M 1/2 AlO 2 unit (oxygen ion in this unit is bridging oxygen O Al, i ) is infinite.Following this rule, in the case of , all MO act as charge balancers, whereas in the case of , all Al 3+ ions form the tetrahedrons, and any excess acts as a network modifier.Assumption III: When the free oxygen (in excess MO) react with bridging oxygen (in M 1/2 AlO 2 or SiO 2 ) to generate non-bridging oxygen, it is assumed that the bridging oxygen for and tetrahedra are equivalent, and the numbers of non-bridging oxygen bonded to Al 3+ ion and Si 4+ ion are proportional to the numbers of and tetrahedral present.Assumption IV: The equilibrium constant for the reaction of a free oxygen (in excess MO) with a bridging oxygen (in M 1/2 AlO 2 or SiO 2 ) to generate non-bridging oxygen is infinite.Therefore, for a system, when the mole fraction of the excess basic oxide MO exceeds 2/3, it is assumed that there are no bridging oxygens present in melt.Assumption V: For systems containing both excess CaO and MgO, the numbers of different types of oxygen ions can be calculated by the random mixing rule.In practice, the calculation makes use of firstly, Assumption IV by considering all the excess basic oxides to be one basic oxide; then multiply each term by the re-normalized mole fractions of the excess basic oxides , or

Different influences of CaO and MgO on viscosity
In order to distinguish the different influences of CaO and MgO on viscosity, viscosities of compositions with the same contents of Al 2 O 3 and SiO 2 should be known.The measured compositions in the literature fulfilling this condition are summarized in Table II.

CS-MS group
The comparisons of viscosities for CaO-SiO 2 and MgO-SiO 2 melts with the same content of SiO 2 are shown in Figure 1, from which it can be seen that MgO-SiO 2 melt possesses a higher viscosity value than CaO-SiO 2 melt.This phenomenon is also found by many researchers [22,23,25].
Viscosity is related to the bond strength.Melt with a strong bond strength means a large resistance to viscous flow under the external force, so a high viscosity will be.For a ionic bond, the bond strength can be approximately evaluated by the coloumbic force I between cation M and O ( , where Q is the covalence of M ion; and are the radii of M z+ and oxygen ions, respectively).According to the Pauling's method [30], the ionic bond percentage for Ca-O and Mg-O bonds are 77.4% and 67.8% [25].Thereby, Ca-O and Mg-O bonds are mainly composed of ionic bond.From the magnitude of I Mg-O =1.956 and I Ca-O =0.907, it could be concluded that the Mg-O bond is stronger than Ca-O bond.From Table I, the deforming ability of chemical bond around is weaker than that around , so, a stronger non-bridging bond is formed in MgO-SiO 2 melt relative to CaO-SiO 2 melt, which means a higher viscosity. 158

CS-MS-CMS group
The viscosity of CaO-SiO AlO  Furthermore, the larger the is, the larger the viscosity increment will be for MgO-Al 2 O 3 -SiO 2 melt relative to CaO-Al 2 O 3 -SiO 2 melt.The value is higher for compositions CAS-MAS-7 and CAS-MAS-8 than compositions CAS-MAS-9 and CAS-MAS-10, so in Figure 3, the viscosity increment is higher for the former group.

MAS-CMAS group
Figure 4 shows that viscosity decreases when partly replacing MgO in MgO-Al 2 O 3 -SiO 2 ternary system by CaO to form a quaternary system CaO-MgO-Al 2 O 3 -SiO 2 ( ).The reason for the phenomenon is that CaO content is higher than Al 2 O 3 content, so after substitution, all Al 3+ ions originally compensated by Mg 2+ ions will be compensated by Ca 2+ ions for the higher priority of Ca 2+ ion relative to Mg 2+ ion [24].This leads to the form of more stable tetrahedron which increases the viscosity.But, according to the above analysis, the non-bridging oxygen bonded with Ca 2+ ion is weaker than that bonded with Mg 2+ ion.
CaO content is higher than Al 2 O 3 content, so nonbridging oxygen bonded with Ca 2+ ion will be formed.This factor will decrease viscosity.Furthermore, the larger the value of is, the more non-bridging oxygen bonded with Ca 2+ ion will be formed, and the larger the viscosity decrease will be.In Figure 3, from composition MAS-CMAS-1 to MAS-CMAS-2, there is only a little decrease of viscosity for the small value of .But from composition MAS-CMAS-3 to MAS-CMAS-4, viscosity decreases dramatically for its large value.

CAS-CMAS group
All the six compositions in this group fulfill >0.So, all Al 3+ ions in this group are compensated by Ca 2+ ions.It can be seen from Figure 5 that viscosity increases when substituting part of MgO for CaO (from CAS-CMAS-1 to CAS-CMAS-2, from CAS-CMAS-3 to CAS-CMAS-4, and from CAS-CMAS-5 to CAS-CMAS-6).

Replacing part of CaO by MgO but keeping
>0 can leads to two changes: part of transform to bond; part of transform to .The two changes coexist during the substitution process.The viscosity variation of the melt is determined by the deforming abilities differences (between and , as well as and) , as well as the relative concentration of and .From Table I, it can be seen that bond is stronger than bond, while bond is weaker than bond.Furthermore, the bond strength increment from to is smaller the bond strength decrement from to .Meanwhile, the concentration ratio of to is decided by the content ratio of SiO 2 to Al 2 O 3 [24] , so, when there is enough Al 2 O 3 in melt, enough will be formed to decrease viscosity.But if the content of Al 2 O 3 is smaller relative to SiO 2 , more will be formed than .Therefore, in this case, the viscosity increasing tendency resulted from transforming of to will be dominated, which leads to the increase of viscosity.In this group, the content of Al 2 O 3 for every composition is very small relative to SiO 2 , so viscosity increases when replacing part of CaO by MgO.

CMAS_1 group
It can be seen from Figure 6 that viscosity decreases as replacing part of CaO in composition CMAS_1-1 by MgO to form composition CMAS_1-2 (while keeping the mole fraction of remaining CaO higher than that of Al 2 O 3 ).According to the analyses in CAS-CMAS group, it can be concluded that more will be formed when there is a higher value of (1mol Al 2 O 3 is equivalent to 2mol SiO 2 after being charge compensated).The ratio of in this group is approximately to be 1, so AlO  AlO  the concentrations of and are almost the same [24].However, the bond strength increment from to is smaller the bond strength decrement from to , so the viscosity decrement will be dominated.Therefore, there is a decrease for viscosity from CMAS_1-1 to CMAS_1-2.

Different influences of Al 2 O 3 and SiO 2 on viscosity
The influence of Al

CAS group
Figure 7 shows that viscosity decreases from CAS-1 to CAS-2, CAS-3 to CAS-4, but increases from CAS-5 to CAS-6.Combining with the composition in Table III, it can be seen the Al 2 O 3 content is higher than CaO content for compositions CAS-1, CAS-2, CAS-3 and CAS-4, but lower than CaO content for compositions CAS-5 and CAS-6.Therefore, it can be concluded that when there is enough CaO to charge compensate Al 3+ ion, the substitution of Al 2 O 3 for SiO 2 will increase viscosity, while when CaO content is not adequate, the substitution will decrease viscosity.The reason for this is that when content of CaO is higher than Al 2 O 3 , the new added Al 2 O 3 can lead to two aspects of influences on viscosity.First, it consumes equivalent mole of CaO (which originally acts as the network modifier) to charge compensate Al 3+ ion.The compensated Al 3+ ion incorporates into the network of SiO 2 .This aspect increases viscosity.However, as substituting Al 2 O 3 for SiO 2 , strong Si-O bond is replaced by weak Al-O bond.This factor decreases viscosity.As the content of Al 2 O 3 is small relative to CaO, all the Al 3+ ions will be charge compensated and the viscosity increment will be larger than the viscosity decrement, so viscosity increases from CAS-5 to CAS-6.But when Al 2 O 3 content is higher than CaO content, part of Al 2 O 3 (= ) can not be incorporated into the SiO 2 network.This part of Al 2 O 3 can dramatically decrease viscosity for the weak Al-O bond relative to Si-O.Therefore, viscosities decrease from CAS-1 to CAS-2, CAS-3 to CAS-4.In our previous paper [31], it is also found from experiments that in CaO-Al 2 O 3 -SiO 2 melt, viscosity first increases and then decreases as gradually replacing SiO 2 by Al 2 O 3 , which agrees with the conclusion of the present study.SiO 2 regardless of or .In CaO-Al 2 O 3 -SiO 2 system, when the Al 2 O 3 content is small, the substitution will increase viscosity.Why the opposed variation tendency of viscosity is present in MgO-Al 2 O 3 -SiO 2 system.It has been pointed out above that the main factor for viscosity increase in CaO-Al 2 O 3 -SiO 2 melt are that all Al 3+ ions enter into stable tetrahedron after being charge compensated by Ca 2+ ions and part of CaO (= ) originally acting as network modifier now charge compensate Al 3+ ion.But the charge compensation ability of Mg 2+ is weak (it can be seen from Table I that bond has larger deforming ability than bond) which means a large deforming ability under external force.Therefore, in this case, during the substitution of Al 2 O 3 for SiO 2 , the viscosity increment will be smaller than the viscosity decrement resulted from the substitution of weak Al-O bond for strong Si-O bond, so viscosity decreases.

CMAS_2 group
From Figure 9, it can be seen that from CMAS_2-1 to CMAS_2-2, viscosity decreases; while from CMAS_2-5 to CMAS_2-6, viscosity increases.The reason for this may be that composition CMAS_2-1 and CMAS_2-2 only contain small content of CaO which is not enough to charge compensate all the Al 3+ ions.This case is similar to the case of MAS group.
Therefore, the viscosity variation law is the same as MAS group.CMAS_2-3 and CMAS_2-4 only contain small content of MgO, and CaO content is enough to charge compensate all Al 3+ ions, so viscosity increases when substituting Al 2 O 3 for SiO 2 as the case of CAS group.

Summary
The present study focuses on the influences of different components on CaO-MgO-Al 2 O 3 -SiO 2 melt by combining the experimental data in the literature and our theoretical viscosity model.From the above examples, it can be seen that the complex variation behavior of viscosity is resulted from the existence of Al 2 O 3 .When substituting CaO for MgO, viscosity changes monotonously for melt without Al 2 O 3 .However, the viscosity variation becomes very complicated when Al 2 O 3 is added.The present study also found that as substituting Al 2 O 3 for SiO 2 in CaO-Al 2 O 3 -SiO 2 melt, viscosity increases when the content of Al 2 O 3 is small relative to that of CaO, but decreases when there is a large substitution.However, the viscosity always decreases for MgO-Al 2 O 3 -SiO 2 melt as substituting Al 2 O 3 for SiO 2 .The weak charge compensation ability of Mg 2+ ion for Al 3+ ion may be the reason for this phenomenon.

GFigure 4 .Figure 5 .
Figure 4. Variation of viscosity for MAS-CMAS group 2 O 3 and SiO 2 on viscosity is discussed in CaO-Al 2 O 3 -SiO 2 , MgO-Al 2 O 3 -SiO 2 and CaO-MgO-Al 2 O 3 -SiO 2 system by replacing part of SiO 2 by Al 2 O 3 while keeping the contents of CaO and MgO unchanged.

Figure 8 Figure 6 .
Figure 8 shows that viscosity always decreases in MgO-Al 2 O 3 -SiO 2 system when substituting Al 2 O 3 for

Table 1 .
2 , MgO-SiO 2 and CaO-MgO-SiO 2 melts with the same content of SiO 2 are shown in Figure 2.With the gradual increase of MgO content, viscosity increases, which agrees with the conclusion obtained in CS-MS group.Therefore, in melt without Al 2 O 3 , viscosity increases monotonously as substituting MgO for CaO.Deforming abilities of chemical bonds around different type of oxygen ions

Table 2 .
Compositions for studying different influences of CaO and MgO on viscosity

Table 3 .
Compositions for studying different influences of Al 2 O 3 and SiO 2 on viscosity