**2.1 TiO2 addition as sintering aid**

The use of sintering aids – small additions of various compounds that enhance densification, or allow it to occur at a lower temperature during sintering – is quite common in the

Effect of TiO2 Addition on the Sintering Process of Magnesium Oxide from Seawater 313

transfer, as in the case with pure magnesium oxide to be determined by diffusion of O2 ions through the MgO lattice as the slower diffusion species. Higher temperatures improve mobility in elements forming the crystal lattice, due to which an interface is formed between particles of compact powder, porosity is eliminated and the whole system shrinks. The densities amount to 94-97% of the theoretical densities at 1600 oC, and 96-98% at 1700 oC, for duration of isothermal heating 1-5 h, and with 1, 2 and 5 wt.-% TiO2 added. Data on apparent porosity in sintered samples point to a very low presence of open pores in the system. The pores present are mainly the closed ones. Accordingly, total porosity is almost indentical to closed porosity. An apparent porosity ranges from 0.15- 0.10% at 1600 oC and 0.05-0.03% at 1700 oC, for soaking time 1-5 h for sintered magnesium oxide samples (80% precipitation) and 0.16-0.11% at 1600 oC and 0.04-0.01% at 1700 oC for sintering magnesium oxide samples (120% precipitation) under the same operating conditions (Petric et al., 1999). The low values obtained for the densification during isothermal heating in the samples examined indicate that a great part of densification process takes place during heating, i.e. before the maximum sintering temperature is

The addition of TiO2 also greatly affects the removal of boron from the sample into air, i.e., TiO2 reduces the B2O3 content during isothermal sintering of magnesium oxide obtained from seawater (Martinac, 1994). The boron content of seawater presents a problem because the hot-strength properties of certain specialized magnesia refractory products are markedly affected by their boron content. Boron is present in seawater in part as the non-dissociated orthoborate acid H3BO3 and partly as the borate ion H2BO3-. The concentration of the higher oxidation level ions HBO32- and BO33- is very low. The orthoborate acid is a weak acid with

H3BO3 = H+ + H2BO3- K1 = 5.8·10-10 (4)

H2BO3- = H+ + HBO32- K2 = 1.8·10-13 (5)

 HBO32- = H+ + BO33- K3 = 1.6·10-14 (6) By calculating the dissociation rate, one can establish the molal concentration of H2BO3-,

the orthoborate acid. For 80 % precipitation of magnesium hydroxide from seawater by dolomite lime, the pH value is 9.6 during reaction precipitation and settling of the precipitate formed. In that case the orthoborate acid dissociation in the first degree is 69.78 %, which contributes to a significant increase of the B2O3 content in the product, i.e. in magnesium oxide obtained from seawater (0.193 wt.-%). Under the conditions more favorable to coprecipitation, the boron contamination of the magnesium hydroxide can be as high as the equivalent of 0.5 parts B2O3 per 100 parts of magnesia. However, using specific reaction conditions as well as addition TiO2, the boron contamination can be virtually eliminated. The addition of TiO2 proved rather interesting since the content of B2O3 is reduced in a sintered samples by means of TiO2. Mixtures of magnesium oxide were prepared in the above composition (Tab. 1), with 1, 2 and 5 wt.-% TiO2, respectively. The dopant oxide used was an analytical reagent grade titania (TiO2 p.a.), in rutile form,

produced by Merck. The chemical analysis of TiO2 p.a. is given in Tab.2.

3-, as well as the molal dissociation rate for every degree of dissociation of

reached.

HBO3

2-, and BO3

the following dissociation constants:

production of ceramic bodies. The most commonly used additives are oxides (Li2O, Al2O3, Cr2O3, Fe2O3, SiO2, TiO2, ZrO2 and V2O5) and some halides, such as LiF and LiCl. The effect of small additions of this compaunds on the sintering of magnesium oxide has been studied in detail (Chaudhuri, 1990, 1992, 1999; Ćosić et al., 1987; Lee, 1998; Lucion, 2004; Martinac et al., 1996; Petric et al., 1987, 1989, 1994, 1999) and has received wide attention. Additions of tetravalent Si, Ti and Zr enhance sintering. There is a general consensus regarding the way in which many of these additives operate, based on a mechanism where intergranular liquid phase are formed which can restrict grain growth, assist the grain-boundary sliding and accelerate mass transport during sintering. It has been established that the addition of TiO2 greatly affect properties of magnesium oxide obtained from seawater; even a small addition of 0.5 wt.-% TiO2 significantly increases product density at 1300 oC (Petric et.al., 1989). The densities amount to 94% of the theoretical density (ρt = 3.576 g cm-3) for durationof isothermal heating 5 h. The addition of TiO2 promotes low-temperature densification of magnesium oxide, proportional to the extend of solid solution formation and vacancy formation. In that case the sintering was intensified in the presence of the liquid phase in the MgO-TiO2 system. It is evident that TiO2 addition is more efficient at lower temperatures than at the higher ones. The effect of ultravalent ions (such as Ti4+) in the periclase crystal structure creates lattice defects in the form of cation vacancies (Fig. 1) which promote material transport and sintering at relatively low temperatures. At higher temperatures, such as 1600 oC and 1700 oC, the effect of this aid is less prominent. We can assume the mass

Fig. 1. Schematic representation of a small section of a periclase crystal (MgO), a) at low temperatures (intrinsic) and b) Schottky defect (anionic and cationic vacancies). The ions originally at the vacant lattice sites have been removed to the surface, c) The crystal has a Ti4+ ion that induces a cation vacancy, d) This crystalstal has a F ion inducing a cation vacancies.

production of ceramic bodies. The most commonly used additives are oxides (Li2O, Al2O3, Cr2O3, Fe2O3, SiO2, TiO2, ZrO2 and V2O5) and some halides, such as LiF and LiCl. The effect of small additions of this compaunds on the sintering of magnesium oxide has been studied in detail (Chaudhuri, 1990, 1992, 1999; Ćosić et al., 1987; Lee, 1998; Lucion, 2004; Martinac et al., 1996; Petric et al., 1987, 1989, 1994, 1999) and has received wide attention. Additions of tetravalent Si, Ti and Zr enhance sintering. There is a general consensus regarding the way in which many of these additives operate, based on a mechanism where intergranular liquid phase are formed which can restrict grain growth, assist the grain-boundary sliding and accelerate mass transport during sintering. It has been established that the addition of TiO2 greatly affect properties of magnesium oxide obtained from seawater; even a small addition of 0.5 wt.-% TiO2 significantly increases product density at 1300 oC (Petric et.al., 1989). The densities amount to 94% of the theoretical density (ρt = 3.576 g cm-3) for durationof isothermal heating 5 h. The addition of TiO2 promotes low-temperature densification of magnesium oxide, proportional to the extend of solid solution formation and vacancy formation. In that case the sintering was intensified in the presence of the liquid phase in the MgO-TiO2 system. It is evident that TiO2 addition is more efficient at lower temperatures than at the higher ones. The effect of ultravalent ions (such as Ti4+) in the periclase crystal structure creates lattice defects in the form of cation vacancies (Fig. 1) which promote material transport and sintering at relatively low temperatures. At higher temperatures, such as 1600 oC and 1700 oC, the effect of this aid is less prominent. We can assume the mass

Fig. 1. Schematic representation of a small section of a periclase crystal (MgO), a) at low temperatures (intrinsic) and b) Schottky defect (anionic and cationic vacancies). The ions originally at the vacant lattice sites have been removed to the surface, c) The crystal has a

ion inducing a cation

Ti4+ ion that induces a cation vacancy, d) This crystalstal has a F-

vacancies.

transfer, as in the case with pure magnesium oxide to be determined by diffusion of O2 ions through the MgO lattice as the slower diffusion species. Higher temperatures improve mobility in elements forming the crystal lattice, due to which an interface is formed between particles of compact powder, porosity is eliminated and the whole system shrinks. The densities amount to 94-97% of the theoretical densities at 1600 oC, and 96-98% at 1700 oC, for duration of isothermal heating 1-5 h, and with 1, 2 and 5 wt.-% TiO2 added. Data on apparent porosity in sintered samples point to a very low presence of open pores in the system. The pores present are mainly the closed ones. Accordingly, total porosity is almost indentical to closed porosity. An apparent porosity ranges from 0.15- 0.10% at 1600 oC and 0.05-0.03% at 1700 oC, for soaking time 1-5 h for sintered magnesium oxide samples (80% precipitation) and 0.16-0.11% at 1600 oC and 0.04-0.01% at 1700 oC for sintering magnesium oxide samples (120% precipitation) under the same operating conditions (Petric et al., 1999). The low values obtained for the densification during isothermal heating in the samples examined indicate that a great part of densification process takes place during heating, i.e. before the maximum sintering temperature is reached.

The addition of TiO2 also greatly affects the removal of boron from the sample into air, i.e., TiO2 reduces the B2O3 content during isothermal sintering of magnesium oxide obtained from seawater (Martinac, 1994). The boron content of seawater presents a problem because the hot-strength properties of certain specialized magnesia refractory products are markedly affected by their boron content. Boron is present in seawater in part as the non-dissociated orthoborate acid H3BO3 and partly as the borate ion H2BO3 -. The concentration of the higher oxidation level ions HBO32- and BO33- is very low. The orthoborate acid is a weak acid with the following dissociation constants:

$$\mathrm{H\_3BO\_3} = \mathrm{H^\*} + \mathrm{H\_2BO\_3} \qquad \qquad \mathrm{K\_1} = \mathrm{5.8} \cdot 10^{10} \tag{4}$$

$$\rm H\_2BO\_3^{\cdot \cdot} = H^\cdot + HBO\_3^{\cdot \cdot} \qquad K\_2 = 1.8 \cdot 10^{\cdot \cdot 13} \tag{5}$$

$$\mathrm{HBO} \circ 2^{\circ} = \mathrm{H^{\circ}} + \mathrm{BO} \circ 3^{\circ} \qquad \qquad \mathrm{K}\_{\heartsuit} = 1.6 \cdot 10^{\circ 14} \tag{6}$$

By calculating the dissociation rate, one can establish the molal concentration of H2BO3-, HBO3 2-, and BO3 3-, as well as the molal dissociation rate for every degree of dissociation of the orthoborate acid. For 80 % precipitation of magnesium hydroxide from seawater by dolomite lime, the pH value is 9.6 during reaction precipitation and settling of the precipitate formed. In that case the orthoborate acid dissociation in the first degree is 69.78 %, which contributes to a significant increase of the B2O3 content in the product, i.e. in magnesium oxide obtained from seawater (0.193 wt.-%). Under the conditions more favorable to coprecipitation, the boron contamination of the magnesium hydroxide can be as high as the equivalent of 0.5 parts B2O3 per 100 parts of magnesia. However, using specific reaction conditions as well as addition TiO2, the boron contamination can be virtually eliminated. The addition of TiO2 proved rather interesting since the content of B2O3 is reduced in a sintered samples by means of TiO2. Mixtures of magnesium oxide were prepared in the above composition (Tab. 1), with 1, 2 and 5 wt.-% TiO2, respectively. The dopant oxide used was an analytical reagent grade titania (TiO2 p.a.), in rutile form, produced by Merck. The chemical analysis of TiO2 p.a. is given in Tab.2.

Effect of TiO2 Addition on the Sintering Process of Magnesium Oxide from Seawater 315

1300 1 0.0512 0.0428 0.0293 0.0165

1500 1 0.0453 0.0431 0.0116 0.0062

Table 4. Effect of TiO2 on the B2O3 content in the sintered magnesium oxide samples (120 %

The experimental dana indicate that the TiO2 addition together with the temperature and duration of isothermal heating significantly reduces the B2O3 content during sintering. Different behaviour patterns relative to the B2O3 content were noticed in magnesium oxide obtained by 80 % or by 120 % precipitation of magnesium hydroxide in seawater; this is due to different contents of CaO in those samples. It was noted that the presence of calcium oxide caused the retention of boron in the samples during sintering. With the magnesium oxide (120 % precipitation) the content of CaO = 1.32 wt.-% is significantly higher than with the magnesium oxide (80 % precipitation) where CaO = 0.59 wt.-%, i.e. there is a significantly larger quantity of CaO than in case of 80 % precipitation which favors the Ca2B2O5 formation reaction. Namely, based on a previous paper (Petric et al., 1987) the presence of dicalcium borate (Ca2B2O5) was proved in sintered samples by the method of Xray diffraction, that is, it was established that B2O3 transforms into Ca2B2O5 through the reaction with CaO. Also the studies (Chaudhuri et al., 1992, 1999; Ćosić et al., 1989; Čeh & Kolar, 1994) show that the method of X-ray diffraction and EDAX analysis indicate that in the sintering process the TiO2 added reacts with CaO from the MgO-CaO solid solution and transforms into calcium titanate CaTiO3. Therefore, TiO2 binds a part of CaO in CaTiO3 and thus reduces the CaO content which reacts with B2O5. So a smaller quantity of Ca2B2O5 is formed which remains in the sintered samples while a greater part of B2O3 evaporates. This is the way in which the TiO2 reduces the quantity of B2O3 in a sample. The higher the CaO content, the more B2O3 is retained in the sintered samples. With MgO (80% precipitation) already a small amount of TiO2 (wt. = 1%) binds almost all of CaO present. With MgO (120 % precipitation) CaO is in excess and favors Ca2B2O5 formation; in MgO (80 % precipitation) a greater part of B2O3 evaporates from the sample into the atmosphere. In the magnesium oxide (120 % precipitation) it can be seen that a higher quantity of TiO2 (2 – 5 wt.-%) binds almost all of CaO and effects boron removal significantly. Therefore, the final content of B2O3 in the sintered samples depends both on the CaO and TiO2 content. These two mutually dependent reactions of formation of Ca2B2O5 and CaTiO3 which cause B2O3 content

B2O3 (wt.-%) in MgO + 1 wt.-% TiO2

3 0.0459 0.0109 0.0086 5 0.0376 0.0384 0.0096 0.0053

3 0.0400 0.0331 0.0100 0.0060 5 0.0318 0.0204 0.0050 0.0035

B2O3 (wt.-%) in MgO + 2 wt.-% TiO2

B2O3 (wt.-%) in MgO + 5 wt.-% TiO2

B2O3 (wt.-%) in MgO without addition

precipitation) at t = 1300 oC, 1500 oC, τ = 1, 3, 5 h, p = 625 MPa.

t / oC τ /h

reduction during sintering, are:


Table 2. Chemical analysis (wt.-%) of TiO2 p.a. (Merck).

Samples were homogenized by manual stirring in ethanol absolute (C2H6O p.a.) for 30 min. After drying (at 80 oC) the mixture was crushed into fine powder and the powders were mixed well again. The mixtures were compacted by a cold-pressing process. The process was carried out in a hydraulic press at pressure of 625 MPa. The compacts were sintered at temperatures of 1300 oC and 1500 oC, with an isothermal heating duration of τ = 1, 3 and 5 h. The sintering at 1300 oC was carried out in an electric furnace. A gas furnace, made by a French firm, Mecker, (Type 553) with zirconium(IV) oxide lining, was used for sintering at 1500 oC. The furnace was heated by burning a mixture of propane-butane in the air, with oxygen added to achieve high temperature. It took approximately 2 h to reach the maximum temperature in the furnaces. In both cases, after sintering, the samples were left to cool in the furnace. Tabs. 3 and 4 show the results obtained for the effect of TiO2 on the content of B2O3 in magnesium oxide samples after sintering at 1300 oC and 1500 oC, taking into account the method of obtaining magnesium hydroxide from seawater as well as the operating conditions listed. The results shown represent an average of a number of measurements. The standard deviation, σ, for MgO (80 % precipitation) was: σmax = 9.8·10-3 and σmin = 4.4·10-3. The standard deviation for MgO (120 % precipitation) was: σmax = 5.0·10-3 and σmin = 1.5·10-3.


Table 3. Effect of TiO2 on the B2O3 content in the sintered magnesium oxide samples (80 % precipitation) at t = 1300 oC, 1500 oC, τ = 1, 3, 5 h, p = 625 MPa.

Samples were homogenized by manual stirring in ethanol absolute (C2H6O p.a.) for 30 min. After drying (at 80 oC) the mixture was crushed into fine powder and the powders were mixed well again. The mixtures were compacted by a cold-pressing process. The process was carried out in a hydraulic press at pressure of 625 MPa. The compacts were sintered at temperatures of 1300 oC and 1500 oC, with an isothermal heating duration of τ = 1, 3 and 5 h. The sintering at 1300 oC was carried out in an electric furnace. A gas furnace, made by a French firm, Mecker, (Type 553) with zirconium(IV) oxide lining, was used for sintering at 1500 oC. The furnace was heated by burning a mixture of propane-butane in the air, with oxygen added to achieve high temperature. It took approximately 2 h to reach the maximum temperature in the furnaces. In both cases, after sintering, the samples were left to cool in the furnace. Tabs. 3 and 4 show the results obtained for the effect of TiO2 on the content of B2O3 in magnesium oxide samples after sintering at 1300 oC and 1500 oC, taking into account the method of obtaining magnesium hydroxide from seawater as well as the operating conditions listed. The results shown represent an average of a number of measurements. The standard deviation, σ, for MgO (80 % precipitation) was: σmax = 9.8·10-3 and σmin = 4.4·10-3. The standard deviation for MgO (120 %

> B2O3 (wt.-%) in MgO + 1 wt.-% TiO2

3 0.1655 0.1363 0.0752 0.0638 5 0.1192 0.0852 0.0645 0.0587

5 0.0689 0.0173 0.0159 0.0131

1300 1 0.1934 0.1395 0.0789 0.0652

1500 1 0.1265 0.0434 0.0396 0.0264 3 0.0756 0.0184 0.0170

Table 3. Effect of TiO2 on the B2O3 content in the sintered magnesium oxide samples (80 %

B2O3 (wt.-%) in MgO + 2 wt.-% TiO2

B2O3 (wt.-%) in MgO + 5 wt.-% TiO2

TiO2 (99 %)

Water soluble matter 0.3 % Chloride (Cl) 0.01 % Sulphate (SO4) 0.05 % Heavy metals (such as Pb) 0.001 % Iron (Fe) 0.005 % Arsenic (As) 0.0002 %

Table 2. Chemical analysis (wt.-%) of TiO2 p.a. (Merck).

precipitation) was: σmax = 5.0·10-3 and σmin = 1.5·10-3.

B2O3 (wt.-%) in MgO without addition

precipitation) at t = 1300 oC, 1500 oC, τ = 1, 3, 5 h, p = 625 MPa.

t / oC τ /h


Table 4. Effect of TiO2 on the B2O3 content in the sintered magnesium oxide samples (120 % precipitation) at t = 1300 oC, 1500 oC, τ = 1, 3, 5 h, p = 625 MPa.

The experimental dana indicate that the TiO2 addition together with the temperature and duration of isothermal heating significantly reduces the B2O3 content during sintering. Different behaviour patterns relative to the B2O3 content were noticed in magnesium oxide obtained by 80 % or by 120 % precipitation of magnesium hydroxide in seawater; this is due to different contents of CaO in those samples. It was noted that the presence of calcium oxide caused the retention of boron in the samples during sintering. With the magnesium oxide (120 % precipitation) the content of CaO = 1.32 wt.-% is significantly higher than with the magnesium oxide (80 % precipitation) where CaO = 0.59 wt.-%, i.e. there is a significantly larger quantity of CaO than in case of 80 % precipitation which favors the Ca2B2O5 formation reaction. Namely, based on a previous paper (Petric et al., 1987) the presence of dicalcium borate (Ca2B2O5) was proved in sintered samples by the method of Xray diffraction, that is, it was established that B2O3 transforms into Ca2B2O5 through the reaction with CaO. Also the studies (Chaudhuri et al., 1992, 1999; Ćosić et al., 1989; Čeh & Kolar, 1994) show that the method of X-ray diffraction and EDAX analysis indicate that in the sintering process the TiO2 added reacts with CaO from the MgO-CaO solid solution and transforms into calcium titanate CaTiO3. Therefore, TiO2 binds a part of CaO in CaTiO3 and thus reduces the CaO content which reacts with B2O5. So a smaller quantity of Ca2B2O5 is formed which remains in the sintered samples while a greater part of B2O3 evaporates. This is the way in which the TiO2 reduces the quantity of B2O3 in a sample. The higher the CaO content, the more B2O3 is retained in the sintered samples. With MgO (80% precipitation) already a small amount of TiO2 (wt. = 1%) binds almost all of CaO present. With MgO (120 % precipitation) CaO is in excess and favors Ca2B2O5 formation; in MgO (80 % precipitation) a greater part of B2O3 evaporates from the sample into the atmosphere. In the magnesium oxide (120 % precipitation) it can be seen that a higher quantity of TiO2 (2 – 5 wt.-%) binds almost all of CaO and effects boron removal significantly. Therefore, the final content of B2O3 in the sintered samples depends both on the CaO and TiO2 content. These two mutually dependent reactions of formation of Ca2B2O5 and CaTiO3 which cause B2O3 content reduction during sintering, are:

Effect of TiO2 Addition on the Sintering Process of Magnesium Oxide from Seawater 317

L11 ≥ 0; L22 ≥ 0 (14)

(L12 + L21)2 ≤ 4 L11L22 (15)

 L11 L22 – L122 ≥ 0 (16) The conjugate coefficients (i.e. L11 and L22) must be positive. Obviously, the crossed coefficients or interference coefficients (L12 and L21) have no definite sign. They may be either positive or negative; their magnitude being limited only by equation (15). If the system of phenomenological Eqs. (10) and (11) is applied to the Ca2B2O5 and CaTiO3

J1 = L11 t' + L12 τ (17)

 J2 = L21 t' + L22 τ (18) where J1 is the percent of B2O3 removed during sintering, and calculated from experimental data on the B2O3 content in sintered samples and on the content B2O3 in calcined magnesium oxide, i.e. the sample before sintering, J2 is the percent of CaO which reacted with TiO2, τ is the duration of isothermal heating (h), and t' is the themperature at 10-2 (oC), i.e., t' = t ·10-2 (oC). From this we see that we may regard t' and τ as driving forces corresponding to the fluxes J1 and J2, respectively. Tabs. 5 and 6 present the values obtained for dependence of J1 and J2 on the temperature (t') and duratin of isothermal heating (τ) for sintered magnesium oxide samples (80 % and 120 % precipitation), with different quantities of sintering

1 wt.-% TiO2

t' / τ

t' / τ

t' / τ

1 3 5 1 3 5 13 66.29 67.01 69.70 13 81.26 81.62 83.04 15 86.35 - 93.23 15 91.10 - 94.66 Table 5. Dependence of J1 and J2 on themperature (t') and duration of isothermal heating (τ) for the sintered magnesium oxide samples (80 % precipitation) with different quantities of

1 3 5 1 3 5 13 59.20 61.12 66.65 13 77.57 78.56 81.45 15 79.52 91.21 91.78 15 87.57 93.62 93.89 5 wt.-% TiO2

1 3 5 1 3 5 13 27.87 - 55.95 13 61.19 - 76.46 15 77.56 90.49 91.05 15 85.54 93.25 93.54 2 wt.-% TiO2

J2

J2

J2

t' / τ

t' / τ

t' / τ

sintering aid.

J1

J1

J1

Using again the Onsanger relation L12 = L21, equation (15) now becomes

formation reactions, which are interdependent, we assume the linear relations:

$$\text{2CaO} + \text{B}\_2\text{O}\_5 = \text{Ca}\_2\text{B}\_2\text{O}\_5 \tag{7}$$

$$\text{CaO} + \text{TiO}\_2 = \text{CaTiO}\_3 \tag{8}$$

In order to examine the effect of TiO2 on the reduction of the B2O3 content in samples sintered, experimental results on the fraction of evaporated boron and the degree of reaction CaO with TiO2 has been examined relative to the temperature and the duration of isothermal sintering for magnesium oxide samples obtained from seawatwr by 80% and 120% precipitation, with addition of wt. = 1, 2 and 5% TiO2 respectively, according to expressions used in the open system thermodynamics (De Groot & Mazur, 1984; Haase, 1990; Lavenda, 1993; Prigogine, 1968). A system of equations dealt with the open system thermodynamics has therefore been considered, and coefficients L11, L12 and L22 that describe the mutual effect of two simultaneous irreversible processes examined, have been calculated based on an important theorem due to Onsanger. Generally, the phenomenological relationship may be written in the following form:

$$\mathbf{J}\_{\hat{\mathbf{i}}} = \Sigma \mathbf{L}\_{\hat{\mathbf{i}}\hat{\mathbf{j}}} \mathbf{X}\_{\hat{\mathbf{j}}} \tag{9}$$

For each force X, there is a corresponding conjugate primary flow J. These phenomena, and other like them, are called cross-effects. The coefficients Lij (with i ≠ j) are called phenomenological coefficients. For the system with two flows caused by two driving forces, i.e., with two simultaneous irreversible processes, phenomenological dependencies can be expressed in the following way:

$$\mathbf{J}\_1 = \mathbf{L}\_{11}\mathbf{X}\_1 + \mathbf{L}\_{12}\mathbf{X}\_2 \tag{10}$$

$$\mathbf{J}\_{2} = \mathbf{L}\_{21}\mathbf{X}\_{1} + \mathbf{L}\_{22}\mathbf{X}\_{2} \tag{11}$$

where J1 and J2 denote flows and X1 and X2 denote the forces causing these flows. Coefficients Lij (with i ≠ j) describe the interference of the two irreversible processes i and j. There exists a so-called Onsanger reciprocity ratio between cross coefficients Lij and Lji which can be expressed by following equations:

$$\mathbf{I}\_{\vec{\eta}} = \mathbf{I}\_{\vec{\mu}} \text{ (ij = 1, \dots n; i \neq j)}\tag{12}$$

or

$$\begin{aligned} \left(\frac{\partial \mathbf{J}\_{\dot{\mathbf{i}}}}{\partial \mathbf{X}\_{\dot{\mathbf{j}}}}\right)\_{\mathbf{X}\_{\dot{\mathbf{i}}=\mathbf{0}^{\prime}}, \dot{\mathbf{i}} \neq \mathbf{j}} = \left(\frac{\partial \mathbf{J}\_{\dot{\mathbf{j}}}}{\partial \mathbf{X}\_{\dot{\mathbf{i}}}}\right)\_{\mathbf{X}\_{\dot{\mathbf{j}}=\mathbf{0}^{\prime}}, \dot{\mathbf{j}} \neq \mathbf{i}} \end{aligned} \tag{13}$$

These Onsanger reciprocity relations state that when the flux, corresponding to the irreversible process i, is influenced by the force Xj of the irreversible process j, then the flux j is also influenced by the force Xi through the same interference coefficient Lij. Equation (12) allows a reduction in the number of phenomenological coefficients, i.e., the interaction coefficients L12 and L21 are equal. The coefficients Lij in the system of two equations, i.e., for n = 2, must satisfy the following conditions:

In order to examine the effect of TiO2 on the reduction of the B2O3 content in samples sintered, experimental results on the fraction of evaporated boron and the degree of reaction CaO with TiO2 has been examined relative to the temperature and the duration of isothermal sintering for magnesium oxide samples obtained from seawatwr by 80% and 120% precipitation, with addition of wt. = 1, 2 and 5% TiO2 respectively, according to expressions used in the open system thermodynamics (De Groot & Mazur, 1984; Haase, 1990; Lavenda, 1993; Prigogine, 1968). A system of equations dealt with the open system thermodynamics has therefore been considered, and coefficients L11, L12 and L22 that describe the mutual effect of two simultaneous irreversible processes examined, have been calculated based on an important theorem due to Onsanger. Generally, the

For each force X, there is a corresponding conjugate primary flow J. These phenomena, and other like them, are called cross-effects. The coefficients Lij (with i ≠ j) are called phenomenological coefficients. For the system with two flows caused by two driving forces, i.e., with two simultaneous irreversible processes, phenomenological dependencies can be

J1 = L11 X1 + L12 X2 (10)

 J2 = L21 X1 + L22 X2 (11) where J1 and J2 denote flows and X1 and X2 denote the forces causing these flows. Coefficients Lij (with i ≠ j) describe the interference of the two irreversible processes i and j. There exists a so-called Onsanger reciprocity ratio between cross coefficients Lij and Lji

Lij = Lji (ij = 1, … n; i ≠ j) (12)

X X j i X ,i j X ,j <sup>i</sup> i 0 j 0 <sup>∂</sup> <sup>∂</sup> <sup>=</sup> ∂ ∂ <sup>≠</sup> <sup>≠</sup> <sup>=</sup> <sup>=</sup>

These Onsanger reciprocity relations state that when the flux, corresponding to the irreversible process i, is influenced by the force Xj of the irreversible process j, then the flux j is also influenced by the force Xi through the same interference coefficient Lij. Equation (12) allows a reduction in the number of phenomenological coefficients, i.e., the interaction coefficients L12 and L21 are equal. The coefficients Lij in the system of two equations, i.e., for

<sup>J</sup> <sup>J</sup> <sup>j</sup> <sup>i</sup>

phenomenological relationship may be written in the following form:

expressed in the following way:

or

which can be expressed by following equations:

n = 2, must satisfy the following conditions:

2CaO + B2O3 = Ca2B2O5 (7)

CaO + TiO2 = CaTiO3 (8)

J LX i ij j <sup>=</sup> (9)

(13)

$$(\mathbf{L}\_{l2} + \mathbf{L}\_{21})^2 \le 4 \text{ L}\_{l1} \mathbf{L}\_{l2} \tag{15}$$

Using again the Onsanger relation L12 = L21, equation (15) now becomes

$$\mathbf{L}\_{11}\mathbf{L}\_{22} - \mathbf{L}\_{12}\mathbf{2} \ge \mathbf{0} \tag{16}$$

The conjugate coefficients (i.e. L11 and L22) must be positive. Obviously, the crossed coefficients or interference coefficients (L12 and L21) have no definite sign. They may be either positive or negative; their magnitude being limited only by equation (15). If the system of phenomenological Eqs. (10) and (11) is applied to the Ca2B2O5 and CaTiO3 formation reactions, which are interdependent, we assume the linear relations:

$$\mathbf{J}\_{1} = \mathbf{L}\_{11}\mathbf{t}' + \mathbf{L}\_{12}\mathbf{t} \tag{17}$$

$$\mathbf{J}\_{2} = \mathbf{L}\_{21}\mathbf{t}' + \mathbf{L}\_{22}\mathbf{t} \tag{18}$$

where J1 is the percent of B2O3 removed during sintering, and calculated from experimental data on the B2O3 content in sintered samples and on the content B2O3 in calcined magnesium oxide, i.e. the sample before sintering, J2 is the percent of CaO which reacted with TiO2, τ is the duration of isothermal heating (h), and t' is the themperature at 10-2 (oC), i.e., t' = t ·10-2 (oC). From this we see that we may regard t' and τ as driving forces corresponding to the fluxes J1 and J2, respectively. Tabs. 5 and 6 present the values obtained for dependence of J1 and J2 on the temperature (t') and duratin of isothermal heating (τ) for sintered magnesium oxide samples (80 % and 120 % precipitation), with different quantities of sintering


Table 5. Dependence of J1 and J2 on themperature (t') and duration of isothermal heating (τ) for the sintered magnesium oxide samples (80 % precipitation) with different quantities of sintering aid.

Effect of TiO2 Addition on the Sintering Process of Magnesium Oxide from Seawater 319

The coefficient values L11, L12 and L22 calculated depend on the quantity of TiO2 added. Therefore, the dependence of the coefficients value L11, L12 and L22 on percent TiO2 was calculated. The relationship between the phenomenological coefficients and the percent of

where Y is the phenomenological coefficients L11, L12 and L22, x is the percent of TiO2 added and A, B and C are constants. The coefficients were calculated by the least squares method and are shown by the equations: For the sintered magnesium oxide samples (80 %

L11 = - 0.0833 x2 + 0.6659 x + 3.3635 (20)

L12 = - 0.0614 x2 + 0.4697 x + 4.2106 (21)

L22 = 0.0310 x2 – 0.3003 x + 5.0833 (22)

L11 = - 0.7692 x2 + 5.4010 x – 2.8164 (23)

L12 = - 0.3293 x2 + 2.4333 x + 1.6803 (24)

 L22 = 0.1354 x2 – 1.6347 x + 7.4791 (25) where x is the percent of TiO2. These equations describing dependence of L to x make it possible to calculate the coefficients L11, L12 and L22 for other percentages of x in the range from 1 wt.-% to 5 wt.-% TiO2. As CaO simultaneously reacts with both B2O3 and TiO2 two described reactions of formation of dicalcium borate and calcium titanate are related, and it was of interest to calculate the coefficients for Eqs. (17) and (18), as well as their dependence on the percentage of TiO2 added. The analysis provides the opportunity to determine which percentage of TiO2 should be added to the sample once to CaO and B2O3 contents are known. Thermodynamical analysis of the magnesium oxide sintering process with varying quantities of added TiO2 has made possible to predict mathematically, without experiments, the B2O3 content in samples sintered relative to the temperature and the duration of isothermal sintering, as well as on the properties of initial magnesium oxide samples. The method of describing a system by application of equations studied in the open system thermodynamics can be used in some other cases when similar laws are involved, i.e. when

The effect of TiO2 addition on the B2O3 content of sintered samples, i.e. on product properties, has been examined. The addition of TiO2 reduces the B2O3 content in the isothermal sintering process, as it binds a part of CaO in calcium titanate, CaTiO3, so that a greater part of B2O3 evaporates from the system during sintering. Depending on the CaO content of the sample, i.e, the method of obtaining magnesium hydroxide from seawater, it has been found that in magnesium oxide (80 % precipitation) a lower quantity of TiO2 (1

Y = A x2 + B x +C (19)

TiO2 added can be expressed by the following equation:

For the sintered magnesium oxide samples (120 % precipitation):

due to a motive force in a system, a flow of mass or energy occurs.

precipitation):

**3. Conclusion** 

aid, respecitvely. The coefficients L11, L12 and L22 in eqs. (17) and (18) were calculated by a computer using combination of the mean values method with the least squares method. After calculating the coefficients, the equations for J1 and J2 for each percent of TiO2 added, for the magnesium oxide (80 % precipitation) and the magnesium oxide (120 % precipitation) are shown in Tab. 7. Thus, the experimental data J1, i.e. the percent of B2O3 «removed» during sintering process, and J2, i.e. the percent of CaO which reacted with TiO2, which also indirectly affects the content of B2O3 were used to calculate the coefficients L11, L12 and L22. The calculated phenomenological coefficients L11, L12 and L22 describe simultaneneous irreversible processes (reactions) and provide an insight into the interdependence of both reactions.


Table 6. Dependence of J1 and J2 on themperature (t') and duration of isothermal heating (τ) for the sintered magnesium oxide samples (120 % precipitation) with different quantities of sintering aid.


Table 7. Equations for J1 and J2 with the calculated coefficients L11, L12 and L22 for each percent of TiO2 added, for the sintered magnesium oxide samples MgO (80 % precipitation) and MgO (120 % precipitation), respectively.

The coefficient values L11, L12 and L22 calculated depend on the quantity of TiO2 added. Therefore, the dependence of the coefficients value L11, L12 and L22 on percent TiO2 was calculated. The relationship between the phenomenological coefficients and the percent of TiO2 added can be expressed by the following equation:

$$\mathbf{Y} = \mathbf{A} \times \mathbf{z}^2 + \mathbf{B} \times \mathbf{+C} \tag{19}$$

where Y is the phenomenological coefficients L11, L12 and L22, x is the percent of TiO2 added and A, B and C are constants. The coefficients were calculated by the least squares method and are shown by the equations: For the sintered magnesium oxide samples (80 % precipitation):

$$\mathbf{L}\_{11} = \text{- } 0.0833 \text{ x}^2 + 0.6659 \text{ x} + 3.3635 \tag{20}$$

$$\mathbf{L}\_{12} = \mathbf{-0.0614} \,\mathbf{x}^2 + \mathbf{0.4697} \,\mathbf{x} + \mathbf{4.2106} \,\tag{21}$$

$$\mathbf{L}\_{22} = 0.0310 \,\mathrm{x}^2 - 0.3003 \,\mathrm{x} + 5.0833 \,\tag{22}$$

For the sintered magnesium oxide samples (120 % precipitation):

$$\mathbf{L}\_{11} = \text{- } 0.7692 \,\mathrm{x}^2 + \text{5.4010} \,\mathrm{x} - \text{2.8164} \tag{23}$$

$$\mathbf{L}\_{12} = \mathbf{-0.3293} \times \mathbf{2} + \mathbf{2.4333} \times \mathbf{+1.6803} \tag{24}$$

$$\mathbf{L}\_{22} = 0.1354 \times \mathbf{\hat{z}} - 1.6347 \times + 7.4791 \tag{25}$$

where x is the percent of TiO2. These equations describing dependence of L to x make it possible to calculate the coefficients L11, L12 and L22 for other percentages of x in the range from 1 wt.-% to 5 wt.-% TiO2. As CaO simultaneously reacts with both B2O3 and TiO2 two described reactions of formation of dicalcium borate and calcium titanate are related, and it was of interest to calculate the coefficients for Eqs. (17) and (18), as well as their dependence on the percentage of TiO2 added. The analysis provides the opportunity to determine which percentage of TiO2 should be added to the sample once to CaO and B2O3 contents are known. Thermodynamical analysis of the magnesium oxide sintering process with varying quantities of added TiO2 has made possible to predict mathematically, without experiments, the B2O3 content in samples sintered relative to the temperature and the duration of isothermal sintering, as well as on the properties of initial magnesium oxide samples. The method of describing a system by application of equations studied in the open system thermodynamics can be used in some other cases when similar laws are involved, i.e. when due to a motive force in a system, a flow of mass or energy occurs.

#### **3. Conclusion**

318 Sintering of Ceramics – New Emerging Techniques

aid, respecitvely. The coefficients L11, L12 and L22 in eqs. (17) and (18) were calculated by a computer using combination of the mean values method with the least squares method. After calculating the coefficients, the equations for J1 and J2 for each percent of TiO2 added, for the magnesium oxide (80 % precipitation) and the magnesium oxide (120 % precipitation) are shown in Tab. 7. Thus, the experimental data J1, i.e. the percent of B2O3 «removed» during sintering process, and J2, i.e. the percent of CaO which reacted with TiO2, which also indirectly affects the content of B2O3 were used to calculate the coefficients L11, L12 and L22. The calculated phenomenological coefficients L11, L12 and L22 describe simultaneneous irreversible processes (reactions) and provide an insight into the

1 wt.-% TiO2

t' / τ

t' / τ

t' / τ

1 3 5 1 3 5 13 70.64 84.75 90.50 13 96.89 97.85 98.24 15 89.02 89.23 93.75 15 97.47 97.50 97.81 Table 6. Dependence of J1 and J2 on themperature (t') and duration of isothermal heating (τ) for the sintered magnesium oxide samples (120 % precipitation) with different quantities of

For 1 wt.-% TiO2

For 2 wt.-% TiO2

For 5 wt.-% TiO2

Table 7. Equations for J1 and J2 with the calculated coefficients L11, L12 and L22 for each percent of TiO2 added, for the sintered magnesium oxide samples MgO (80 % precipitation)

For MgO (80 % precipitation) For MgO (120 % precipitation)

J1 = 3.9411 t' + 4.6189 τ J1 = 1.8155 t' + 3.7793 τ J2 = 4.6189 t' + 4.8140 τ J2 = 3.7793 t' + 5.9798 τ

J1 = 4.3421 t' + 4.9044 τ J1 = 4.9090 t' + 5.2364 τ J2 = 4.9044 t' + 4.6067 τ J2 = 5.2364 t' + 4.7514 τ

J1 = 4.4856 t' + 5.0239 τ J1 = 4.9594 t' + 5.6129 τ J2 = 5.0239 t' + 4.3569 τ J2 = 5.6129 t' + 2.6914 τ

and MgO (120 % precipitation), respectively.

1 3 5 1 3 5 13 47.85 80.64 83.02 13 95.32 95.57 97.73 15 96.84 97.01 97.64 15 79.36 82.21 91.10 5 wt.-% TiO2

1 3 5 1 3 5 13 23.81 - 31.69 13 52.52 - 52.52 15 23.31 41.16 63.70 15 93.06 94.26 95.76 2 wt.-% TiO2

J2

J2

J2

interdependence of both reactions.

J1

J1

J1

t' / τ

t' / τ

t' / τ

sintering aid.

The effect of TiO2 addition on the B2O3 content of sintered samples, i.e. on product properties, has been examined. The addition of TiO2 reduces the B2O3 content in the isothermal sintering process, as it binds a part of CaO in calcium titanate, CaTiO3, so that a greater part of B2O3 evaporates from the system during sintering. Depending on the CaO content of the sample, i.e, the method of obtaining magnesium hydroxide from seawater, it has been found that in magnesium oxide (80 % precipitation) a lower quantity of TiO2 (1

Effect of TiO2 Addition on the Sintering Process of Magnesium Oxide from Seawater 321

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wt.-%) binds almost all the CaO present (which has not reacted with B2O3). In the magnesium oxide (120 % precipitation) it takes 2 wt.-% TiO2 to bind all the CaO present (which has not reacted), so that only a greater quantity (5 wt.-%) TiO2 affects boron removal during sintering to a greater degree. The higher the CaO content, the more B2O3 is retained in the sintered samples. Two mutually dependent reactions of formation of Ca2B2O5 and CaTiO3 were analysed, and phenomenological coefficients calculated according to expresions used in the open system thermodynamics. Calculated phenomenological coefficients L11, L12 and L22 describe the mutual interdependence of two simultaneous irreversible processes, based on an important theorem due to Onsanger. It is thus possible to calculate the quantity of boron (B2O3) removed during the sintering process, i.e. the quantity of B2O3 which remains in the sample sintered, for the area examined. Analogous consideration can be carried out for all the other cases when similar laws are involved, i.e. when mass or energy flows occur in the system due to a motive force.
