metals Article
Crystallization Behaviors of Anosovite and Silicate Crystals in High CaO and MgO Titanium Slag Helin Fan 1,2 , Dengfu Chen 1,2, *, Tao Liu 1,2 , Huamei Duan 1,2, *, Yunwei Huang 1,2 , Mujun Long 1,2 and Wenjie He 1,2 1
2
*
College of Materials Science and Engineering, Chongqing University, Chongqing 400044, China;
[email protected] (H.F.);
[email protected] (T.L.);
[email protected] (Y.H.);
[email protected] (M.L.);
[email protected] (W.H.) Chongqing Key Laboratory of Vanadium-Titanium Metallurgy and Advanced Materials, Chongqing University, Chongqing 400044, China Correspondence:
[email protected] (D.C.);
[email protected] (H.D.); Tel.: +86-23-6510-2467 (D.C. & H.D.)
Received: 31 August 2018; Accepted: 21 September 2018; Published: 24 September 2018
Abstract: Electric-furnace smelting has become the dominant process for the production of the titanium slag from ilmenite in China. The crystallization behaviors of anosovite and silicate crystals in the high CaO and MgO titanium slag were studied to insure smooth operation of the smelting process and the efficient separation of titanium slag and metallic iron. The crystallization behaviors were studied by a mathematical model established in this work. Results show that the crystallization order of anosovite and silicate crystals in high CaO and MgO titanium slag during cooling is: Al2 TiO5 > Ti3 O5 > MgTi2 O5 > MgSiO3 > CaSiO3 > FeTi2 O5 > Mn2 SiO4 > Fe2 SiO4 . Al2 TiO5 and Ti3 O5 have higher crystallization priority and should be responsible for the sharp increase in viscosity of titanium slag during cooling. The total crystallization rates of anosovite and silicate crystals are mainly controlled by Al2 TiO5 and MgSiO3 , respectively. The mass ratio of Ti2 O3 /ΣTiO2 has a prominent influence on the total crystallization rate of anosovite crystals while the mass ratio of MgO/FeO has a slight influence on the total crystallization rate of anosovite crystals. Keywords: crystallization behaviors; crystallization rate; anosovite crystals; silicate crystals; titanium slag
1. Introduction Titanium dioxide and metallic titanium are the main products of titanium metallurgy. Titanium dioxide is widely employed in the fields of coating, painting, paper, plastics, rubber, and ceramic because of its non-toxicity, opacity, whiteness and brightness [1–3]. Metallic titanium has various applications such as aviation, aerospace, biomedical, marine, and nuclear waste storage due to its high corrosion resistance, high specific strength, light weight, high melting point, and high chemical/heat stability [3–5]. A large amount of high-quality titanium-rich materials are increasing required due to the wider and wider application of titanium dioxide and metallic titanium. Titanium-rich materials mainly include two types: Rutile and titanium slag. With the depletion of rutile resource, titanium slag has become the main titanium-rich material to produce the metallic titanium and titanium white in China. The electric-furnace smelting has become the dominant process to produce titanium slag from ilmenite in China. During the process of the electric-furnace smelting, iron oxide in ilmenite concentrate is reduced to metallic iron and titanium oxide in ilmenite is left in the slag (called titanium slag). The flow behavior of titanium slag at high temperature is a crucially significant factor, influencing, for example, the ability to tap the titanium slag from the electric furnace, the efficiency of separation of titanium slag from metal
Metals 2018, 8, 754; doi:10.3390/met8100754
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iron, the foaming extent of titanium slag, and the kinetics of titanium smelting reactions [6]. There is some research about the flow behavior of titanium slag at high temperature in recent decades [7–10]. It has been concluded from the aforementioned research that the titanium slag crystallizes much more easily during tapping from the electric furnace and separation is more difficult from liquid iron than other metallurgical slags. Therefore, the investigation on crystallization behavior of titanium slag at a high temperature will contribute to insuring the smooth operation of the smelting and the efficient separation of titanium slag and metallic iron. The crystallization of melts consists of two steps: Nucleation and growth [11,12]. The crystallization behavior of melts can be studied by three kinds of methods: Experimental techniques, molecular dynamic simulation, and classical crystallization theory. For example, the crystallization behaviors of mold flux and Ti-bearing blast furnace slag were intensively investigated by the differential scanning calorimeter [13,14], the single hot thermocouple technique/double hot thermocouple technique [15–17], the confocal laser scanning microscope [18–20], and the viscosity-temperature curve method. Watson et al. [21] studied the crystal nucleation and growth in Pd-Ni alloys by the molecular dynamic simulation, which was only suitable for a relatively simple system. Turnbull [22] interpreted convincingly the nucleation phenomena on the basis of the classical crystallization theory. In contrast, there is almost no effective experimental technique to investigate the crystallization behaviors of many different crystals in the relatively complex system of titanium slag. Furthermore, based on the fact that the titanium slag can corrode all refractory oxide containers [9], studies of the crystallization behavior of titanium slag using experiment techniques are extremely difficult and dangerous to carry out. Therefore, few research is focused on the crystallization behavior of titanium slag at a high temperature. Panzhihua, located in southwestern China, holds ilmenite reserves of 870 million tons, accounting for 35% of total ilmenite reserves in the world [23]. The composition of mineral phases in titanium slag produced from Panzhihua ilmenite is complex due to its high content of CaO and MgO. According to the previous study by Dong et al. [24], the mineral phases in the high CaO and MgO titanium slag consisted of anosovite (FeTi2 O5 , MgTi2 O5 , Ti3 O5 , and Al2 TiO5 ), olivine (Fe2 SiO4 and Mn2 SiO4 ), and augite (CaSiO3 and MgSiO3 ) as determined by X-ray diffraction and Energy Dispersive Spectrometer. Fan et al. [25] also confirmed the complex composition of mineral phases in the high CaO and MgO titanium slag. Therefore, the crystallization behaviors of crystals in the high CaO and MgO titanium slag would become more complex. In this work, a mathematical model was established to describe the crystallization behaviors of anosovite and silicate crystals in the high CaO and MgO titanium slag. Specifically, two main issues will be addressed. First, the crystallization behaviors of anosovite and silicate crystals in the high CaO and MgO titanium slag will be determined. The crystallization ability, crystallization order, and optimum temperature ranges of different crystals in the high CaO and MgO titanium slag will be analyzed and discussed in detail. Second, the effect of the composition of titanium slag on the crystallization behaviors of anosovite crystals will be investigated. Based on the results, the smelting parameters of titanium slag will be adjusted in industrial production in further works to enhance the smooth operation of the electric furnace and to improve the separation of titanium slag and metallic iron. 2. Mathematical Model According to the classical crystallization kinetics from D. Turnbull et al. [26], the nucleation rate I of a crystal and the formation energy of a crystal nucleus could be expressed as Equations (1) and (2) respectively. nD ∆G ∗ I = 2 exp(− ) (1) kT a0 ∆G ∗ =
16πσ3 3(∆gV )2
(2)
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n=
1 a30
(3)
where I is the nucleation rate of a crystal in m−3 ·s−1 , n is the atom number per unit volume, D is the self-diffusion coefficient of atoms in the melt in m2 ·s−1 , a0 is the lattice parameter in m, ∆G* is the formation energy of crystal nucleus in J·mol−1 , k is the Boltzmann constant, T is the temperature of the melt in K, π is the pi constant, σ is the interfacial energy between the melt and crystal in J·m−2 , and ∆gV is the change of Gibbs free energy per unit volume in J·mol−1 ·m−3 . The relationship between the self-diffusion coefficient D and the viscosity η could be expressed as Equation (4) [27,28]. kT (4) D= 3πa0 η g
∆gV =
∆Hm ∆Tr V
(5)
g
where η is the viscosity of the melt in Pa·s, ∆Hm is the fusion heat per mole melt in J·mol−1 , V is the mole volume of the crystal in m3 ·mole−1 , and ∆Tr = 1 − Tr (Tr = T/Tm , Tm is the melting temperature of a crystal in K). The viscosity involves the physicochemical property of the melt and can be estimated by the National Physical Laboratory model [29]. The optical basicity of the slag component for the calculation of titanium slag is from references [29–31]. The relationship between the viscosity and temperature was expressed as Equation (6). ln η = ln A + B/T (6) The relationship between optical basicity and constants A and B could be expressed as Equations (7) and (8) [29]. B 2.88 ln = −1.77 + (7) 1000 Λ ln A = −232.69(Λ)2 + 357.32Λ − 144.17
(8)
The optical basicity of the titanium slag could be calculated by the following Equation (9). Λ=
∑ χi ni Λi ∑ χi ni
(9)
where χi and ni is the mole fraction and the number of oxygen atoms of an independent component respectively and Λi is the optical basicity of the corresponding independent component. Taking Equations (2)–(5) into Equation (1), the nucleation rate I of a crystal can be deduced as Equation (10). " #3 g 2 1/3 σ N V kT 16π ∆Hm 0 I= exp − ( ) (10) g 3Tr (∆Tr )2 RTm 3πa60 η ∆Hm where α and β are the two dimensionless parameters which have the important influence on the crystal melting process. α and β could be expressed as following Equations (11) and (12) [32]. α=
N0 V 2
1/3
g ∆Hm
σ
(11)
g
β= where N0 is the Avogadro constant.
∆Hm RTm
(12)
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Combined with Equations (11) and (12), the nucleation rate I of a crystal could be expressed as Equation (13). " # 16πα3 β kT exp − I= (13) 3πa60 η 3Tr (∆Tr )2 According to the classical kinetics of crystallization, the growth rate IL of a crystal could be expressed as Equation (14). ∆Gg fs D ) (14) IL = 1 − exp( a0 RT where fs is the proportionality coefficient of the position benefiting the atomic adsorption on the crystal at interface between melt and crystal and ∆Gg is the change of Gibbs free energy per mole between the melt and crystal. fs and ∆Gg could be expressed as Equations (15) and (16) [33]. ( fs =
1 T 0.2 TmT− m g
∆Gg = ∆Hm
∆Hm 2RTm ∆Hm 4RTm
(15)
Tm − T Tm
(16)
Combined with Equations (14)–(16), the growth rate of a crystal could be expressed as Equation (17). ( " #) g f s kT ∆Hm ∆Tr IL = 1 − exp ( ) RTm Tr 3πa20 η
(17)
Combined with Equations (11), (12) and (17), the growth rate of a crystal could be expressed as Equation (18) [34]. f s kT ∆T IL = 1 − exp − β (18) Tr 3πa20 η According to a previous research by Uhlmann et al. [33], the volume fraction (x) of a crystal could be expressed as a function with the nucleation rate (I), growth rate (IL ) and time t. x=
1 π I IL3 t4 3
(19)
1 π I IL3 3
(20)
ri =
The total crystallization rate of a crystal rtotal could be expressed as a function with mole fraction (ω i ) and crystallization rate (ri ) of a given crystal as Equation (21). rtotal =
∑ ωi r i
(21)
i
The chemical composition of titanium slag is as follows (wt. %): TiO2 = 55.20, FeO = 12.21, SiO2 = 5.89, MnO = 1.53, MgO = 2.51, Al2 O3 = 2.83, CaO = 1.00, and Ti2 O3 = 18.92. The structural parameters and melting temperatures of these crystals in titanium slag are listed in Table 1 [35–37]. a0 = (a × b × c)1/3 , in which a, b and c are lattice parameters of crystals in the titanium slag. Because the content of Mn-anosovite is small, Mn-anosovite is neglected in this work.
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Table 1. Structural parameters and melting temperature of crystals in titanium slag. Mineral Phase
Chemical Formula
a0 (Å)
Tm (K)
Anosovite
FeTi2 O5 MgTi2 O5 Ti3 O5 Al2 TiO5
7.192 [35] 7.145 [35] 7.186 [35] 6.858 [35]
1767 [36] 1930 [37] 1991 [37] 2133 [36]
Olivine
Fe2 SiO4 Mn2 SiO4
6.752 [35] 6.878 [35]
1478 [36] 1618 [36]
Augite
CaSiO3 MgSiO3
7.351 [35] 7.464 [35]
1817 [36] 1830 [36]
3. Results and Discussion 3.1. Nucleation and Growth of Crystals in Titanium Slag 3.1.1. Nucleation and Growth of Anosovite Crystals From the viewpoint of the classical crystallization theory, the crystallization process includes two stages: Nucleation and growth. The nucleation refers to the generation of a crystal nucleus from a mother phase. The growth of the crystal is realized by the growth of the crystal nucleus. Although the nucleation process is transitory compared with the subsequent growth process, the nucleation is completely different from the growth process. Figure 1 displays the nucleation and growth rates of different anosovite crystals in the titanium slag. It can be observed from Figure 1 that the nucleation rates first increase from zero to the maximum value and then decrease to zero with the degree of undercooling increasing from zero. The profiles of nucleation rates should be attributed to the interaction of two contradictory factors related to the crystallization process: The degree of undercooling and diffusion ability of atoms. With a too high or too low degree of undercooling, the small nucleation rates of crystals are formed. With a reasonable degree of undercooling, the maximum nucleation rates of crystals are formed. The profiles of growth rates have the similar characteristics to the profiles of nucleation rates. The maximum nucleation rates and maximum growth rates of anosovite crystals follow the same order: Al2 TiO5 > Ti3 O5 > MgTi2 O5 > FeTi2 O5 . The maximum nucleation rates (maximum growth rates) of different anosovite crystals are very different, indicating that the crystallization abilities of different anosovite crystals may differ remarkably.
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Figure 1. rates of different anosovite crystals: (a) FeTi Ti53, O 1. Nucleation Nucleationand andgrowth growth rates of different anosovite crystals: (a)2 O FeTi 2OMgTi 5, (b)2 O MgTi (c) 5 , (b) 5 , (c)2O 5, and Al2(d) TiOAl . Ti3O(d) 5, and 2 TiO 5 . 5
3.1.2. Nucleation and and Growth Growth of 3.1.2. Nucleation of Silicate Silicate Crystals Crystals Figure displays the thenucleation nucleationand andgrowth growthrates ratesofofdifferent differentsilicate silicate crystals titanium slag. Figure 22 displays crystals inin titanium slag. It It can be observed from Figure 2 that the profiles of nucleation rates of silicate crystals have the similar can be observed from Figure 2 that the profiles of nucleation rates of silicate crystals have the similar characteristics to the the profiles profiles of The profiles profiles of of growth growth rates rates of of characteristics to of nucleation nucleation rates rates of of anosovite anosovite crystals. crystals. The silicate crystals have the similar characteristics to the profiles of growth rates of anosovite crystals. silicate crystals have the similar characteristics to the profiles of growth rates of anosovite crystals. Both and thethe maximum growth ratesrates of silicate crystals follow the same Both the the maximum maximumnucleation nucleationrates rates and maximum growth of silicate crystals follow the order: MgSiO > CaSiO > Mn SiO > Fe SiO . The maximum nucleation rates (maximum 3 3 4 4 > Fe 2 2SiO 4 4. The maximum nucleation rates (maximum growth same order: MgSiO 3 > CaSiO 3>2 Mn2SiO growth rates) of different different silicate are similar similar in in value, value, indicating indicating that that silicate silicate crystals crystals have have the the similar similar rates) of silicate crystals crystals are crystallization ability. The maximum nucleation rates (maximum growth rates) of silicate crystals are crystallization ability. The maximum nucleation rates (maximum growth rates) of silicate crystals are much smaller than those of anosovite crystals, demonstrating that silicate crystals may have much much smaller than those of anosovite crystals, demonstrating that silicate crystals may have much aa weaker weaker crystallization crystallization ability ability than than the the anosovite anosovite crystals. crystals. The driving force of the crystallization anddiffusion diffusion ability atoms is large enough when The driving force of the crystallization and ability of of atoms is large enough when the the temperature is between that of the maximum nucleation rate and the maximum growth rate. temperature is between that of the maximum nucleation rate and the maximum growth rate. Therefore, from the the temperature of maximum nucleation rate to the of maximum Therefore, the therange range from temperature of maximum nucleation ratetemperature to the temperature of growth rate is specified as the characteristic temperature range of crystallization in this work. It in is easy maximum growth rate is specified as the characteristic temperature range of crystallization this to nucleate, grow obtaingrow coarse grain within the grain characteristic temperature range. Figure 3 displays work. It is easy toand nucleate, and obtain coarse within the characteristic temperature range. the characteristic temperature ranges of crystallization of anosovite and silicate crystals in titanium Figure 3 displays the characteristic temperature ranges of crystallization of anosovite and silicate slag. It can be observed 3 that from the characteristic ranges of crystallization crystals in titanium slag. from It canFigure be observed Figure 3 that temperature the characteristic temperature ranges of crystals in titanium slag follow the sequence of Al TiO > Ti O > MgTi O > MgSiO > CaSiO 2 5 3 5 2 5 3 of crystallization of crystals in titanium slag follow the sequence of Al2TiO5 > Ti3O5 > MgTi2O5 >3 > FeTi23O5> >CaSiO Mn2 SiO > Fe SiO4 . Mn The2SiO characteristic temperature ranges of crystallization of these MgSiO 3 >4 FeTi22O5 > 4 > Fe2SiO4. The characteristic temperature ranges of crystals are in sequence as follows: K, 1620–1712 1573–1666K,K,1620–1712 1497–1589K, K,1573–1666 1487–1579 K, K, crystallization of these crystals are1728–1819 in sequence as follows:K, 1728–1819 1448–1540 K, 1333–1424 K, 1225–1312 K. The characteristic temperature ranges are consistent with the 1497–1589 K, 1487–1579 K, 1448–1540 K, 1333–1424 K, 1225–1312 K. The characteristic temperature tapping temperature smelting ilmenite to titanium in anilmenite electric furnace. ranges are consistent of with the tapping temperature of slag smelting to titanium slag in an electric furnace.
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Figure rates of different silicate crystals: (a) Fe (b) Mn SiO Figure 2. 2. Nucleation Nucleation and and growth growthrates ratesof ofdifferent differentsilicate silicatecrystals: crystals:(a) (a)Fe Fe 2SiO SiO44,4,,(b) (b)Mn Mn222SiO SiO444,, (c) (c) CaSiO CaSiO333 2 2SiO and (d) MgSiO 3 . . and (d) MgSiO33
Figure Characteristic temperature temperature ranges crystallization anosovite and silicate crystals crystals in in Figure 3. 3. Characteristic temperature ranges for for crystallization crystallization of of anosovite and silicate titanium titanium slag. slag.
3.2. Crystallization Crystallization Behavior of of Anosovite and and Silicate Crystals Crystals 3.2. 3.2. Crystallization Behavior Behavior of Anosovite Anosovite and Silicate Silicate Crystals The crystallization rate of crystals is the main and direct indicator for evaluating theevaluating crystallization The The crystallization crystallization rate rate of of crystals crystals is is the the main main and and direct direct indicator indicator for for evaluating the the behavior. Therefore, the optimum temperature range of crystallization can be determined by the crystallization behavior. Therefore, the optimum temperature range of crystallization can crystallization behavior. Therefore, the optimum temperature range of crystallization can be be crystallization ratecrystallization of crystals. Figureof4crystals. shows the crystallization rates of different anosovite and determined determined by by the the crystallization rate rate of crystals. Figure Figure 44 shows shows the the crystallization crystallization rates rates of of different different silicate crystals in titanium slag. It can be seen from Figure 4a thatfrom the maximum crystallization rate of anosovite anosovite and and silicate silicate crystals crystals in in titanium titanium slag. slag. It It can can be be seen seen from Figure Figure 4a 4a that that the the maximum maximum Al TiO has two higher orders of magnitude than Ti O . The maximum crystallization rate of MgTi 2 5 3 5 2 O5 crystallization rate of crystallization rate of of Al Al22TiO TiO55 has has two two higher higher orders orders of magnitude magnitude than than Ti Ti33O O55.. The The maximum maximum has five higherrate ordersMgTi of magnitude than FeTi is notable that the total crystallization rate of 2 O5 . It crystallization of crystallization rate of of MgTi22O O55 has has five five higher higher orders orders of magnitude magnitude than than FeTi FeTi22O O55.. It It is is notable notable that that the the anosovite crystals is mainly controlled by Al TiO . The optimum temperature ranges of anosovite 2 5 total crystallization rate of anosovite crystals is mainly controlled by Al 2 TiO 5 . The optimum total crystallization rate of anosovite crystals is mainly controlled by Al2TiO5. The optimum crystals are asranges the following: Al2 TiO K) > Ti3 O5 (1636–1696 K) > MgTi O5 >(1589–1649 K) 5 (1744–1804 temperature crystals are temperature ranges of of anosovite anosovite crystals are as as the the following: following: Al Al22TiO TiO55 (1744–1804 (1744–18042K) K) > Ti Ti33O O55 (1636– (1636– > FeTi O (1346–1406 K). It can be seen from Figure 4b that the maximum crystallization rates of 2 5 1696 1696 K) K) >> MgTi MgTi22O O55 (1589–1649 (1589–1649 K) K) >> FeTi FeTi22O O55 (1346–1406 (1346–1406 K). K). It It can can be be seen seen from from Figure Figure 4b 4b that that the the maximum maximum crystallization crystallization rates rates of of MgSiO MgSiO33 and and CaSiO CaSiO33 have have three three higher higher orders orders of of magnitude magnitude than than Mn Mn22SiO SiO44 and and five five higher higher orders orders of of magnitude magnitude Fe Fe22SiO SiO44.. The The total total crystallization crystallization rate rate of of silicate silicate crystals crystals
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MgSiO3 and CaSiO3 have three higher orders of magnitude than Mn2 SiO4 and five higher orders of is mainly controlled by MgSiO 3. The optimum ranges of silicate crystalsby are as the magnitude Fe2 SiO4 . The total crystallization rate temperature of silicate crystals is mainly controlled MgSiO 3. following: MgSiO 3 (1512–1572K) > of CaSiO 3 (1502–1562 K) as > Mn 4 (1346–1406 K)3>(1512–1572K) Fe2SiO4 (1236– The optimum temperature ranges silicate crystals are the2SiO following: MgSiO > 1296 K). CaSiO (1502–1562 K) > Mn SiO (1346–1406 K) > Fe SiO (1236–1296 K). 3 2 4 2 4
Figure 4. Crystallization rate of different crystals in titanium slag: (a) anosovite and (b) silicate.
Notably, Notably, both both the the maximum maximum crystallization crystallizationrate rate and and the the optimum optimum temperature temperatureranges rangesof ofAl Al22TiO TiO55 and Ti O are much higher than other crystals in high CaO and MgO titanium slag. The crystallization 3 5 and Ti3O5 are much higher than other crystals in high CaO and MgO titanium slag. The crystallization priority TiO55 and and Ti Ti33O O55 isisconsistent consistent with with the the report report from from Zhao Zhao et et al. al. [7] [7] that that the the sharp sharp increase priority of of Al Al22TiO increase in viscosity of of titanium titaniumslag slagmay maybebecaused causedbybythe the high Ti32content O3 content in titanium 3 and in viscosity high AlAl 2O23O and Ti2O in titanium slag.slag. The The accuracy of the mathematical model can be preliminarily demonstrated by the consistency between accuracy of the mathematical model can be preliminarily demonstrated by the consistency between the O55 in in titanium titanium slag slag and the crystallization crystallization priority priority of of Al Al22TiO TiO55 and and Ti Ti33O and the the remarkable remarkable effect effect of ofAl Al22O O33 and Ti33O O55on onviscosity viscosity titanium slag. result implies thatvariation the variation Ti3 O5 2 OTi 3 3and and Ti ofof titanium slag. ThisThis result implies that the of Al 2of O3 Al and O5 content content in titanium slag should be paid attention to during electric-furnacesmelting smelting process. process. in titanium slag should be paid closeclose attention to during thethe electric-furnace Furthermore, Song et et al. Furthermore, Song al. [38] [38] and and Handfield Handfield et et al. al. [9] [9] reported reported that that the the melting melting temperature temperature of of the the titanium slag, whose composition was similar with the titanium slag in this work, was approximately titanium slag, whose composition was similar with the titanium slag in this work, was approximately 1873 Al22TiO TiO55 in inthis thiswork workhas hasthe thecrystallization crystallizationrate rateofof 1.03 × 2310(s23−4)(sat−4the ) attemperature the temperature of 1873 K. K. Al 1.03 × 10 of 1873 1873 K.accuracy The accuracy the mathematical be further demonstrated the crystallization K. The of theof mathematical modelmodel can becan further demonstrated by the by crystallization rate of rate of Al TiO at the melting temperature of 1873 K. Al2TiO5 at2 the 5melting temperature of 1873 K. T is the the peak peak temperature temperature of is the the melting melting point Tcc is of maximum maximum crystallization crystallization rate rate of of crystals. crystals. TTmm is point of of the )/T representsthe thecrystallization crystallizationprocess processduring duringcooling. cooling. Figure Figure 5a 5a shows shows the the crystal. crystal. (T (Tmm − − TTcc)/T mm represents the relationship process. It It can bebe seen from Figure 5a relationship between betweenmelting meltingtemperature temperatureand andthe thecrystallization crystallization process. can seen from Figure that the crystal with higher crystallizescrystallizes earlier during cooling. This crystallization 5a that the crystal with melting higher temperature melting temperature earlier during cooling. This order agrees with the work from Diao et al. [39] that the mineral phases of vanadium-chromium slag crystallization order agrees with the work from Diao et al. [39] that the mineral phases of vanadiumcrystallized in the order of their melt points during cooling. Figure 5b shows the relationship between chromium slag crystallized in the order of their melt points during cooling. Figure 5b shows the the maximum crystallization rate and the peak temperature. can temperature. be seen from ItFigure thatfrom the relationship between the maximum crystallization rate and theItpeak can be5b seen crystallization order of crystals in titanium slag is obtained during cooling as follows: Al TiO > Ti 2 cooling 5 3O Figure 5b that the crystallization order of crystals in titanium slag is obtained during as5 > MgTi O > MgSiO > CaSiO > FeTi O > Mn SiO > Fe SiO . The crystal with a higher maximum 5 2TiO5 > Ti3O5 > MgTi 3 2O5 > MgSiO 2 5 3 > CaSiO 2 43 > FeTi 2 2O45 > Mn2SiO4 > Fe2SiO4. The crystal with follows:2 Al crystallization rate has a higher peak temperature. This relationship mayThis be ascribed to themay strong a higher maximum crystallization rate has a higher peak temperature. relationship be diffusion ability of atoms with the higher temperature. Obviously, anosovite crystals crystallize overall ascribed to the strong diffusion ability of atoms with the higher temperature. Obviously, anosovite earlier silicateoverall crystals during cooling. crystallization orderThe in this work is consistent crystalsthan crystallize earlier than silicateThe crystals during cooling. crystallization order inwith this the reports from Pistorius et al. [40] and Wang et al. [41] that anosovite and silicate crystals occupied work is consistent with the reports from Pistorius et al. [40] and Wang et al. [41] that anosovite and the center and outer layer the of titanium slag outer particle, respectively. The accuracy of the mathematical silicate crystals occupied center and layer of titanium slag particle, respectively. The model can again consistencyonce between crystallization order accuracy ofbe thedemonstrated mathematicalonce model canby be the demonstrated againthe by overall the consistency between the and spatial distribution of anosovite and silicate crystals in high CaO and MgO titanium slag. overall crystallization order and spatial distribution of anosovite and silicate crystals in high CaO and MgO titanium slag.
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Relationship between and(b) (b)Relationship Relationship between between Figure 5. (a) Relationship betweenmelting meltingtemperature temperatureand and(T(T − TTcc)/T )/Tccand mm− maximum crystallization rate and peak temperature.
3.3. Effects Effects of of Slag Slag Composition Composition on on Crystallization Crystallization Behaviors Behaviors of 3.3. of Anosovite Anosovite Crystals Crystals To investigate behaviors of of anosovite anosovite crystals, crystals, To investigate effects effects of of the the slag slag composition composition on on crystallization crystallization behaviors the mass ratio of Ti O /ΣTiO and the mass ratio of MgO/FeO are selected as two variables. 3 2 the mass ratio of Ti22O3/ΣTiO 2 and the mass ratio of MgO/FeO are selected as two variables. The The chemical compositions of slag are shown in 2. Table 2. The mass ratio of Ti22Ois3 /ΣTiO from 2 is (CS1) chemical compositions of slag are shown in Table The mass ratio of Ti 2O3/ΣTiO from 0.05 0.05 (CS1) to 0.45 (CS5) and the mass ratio of MgO/FeO is from 0.10 (CS6) to 0.90 (CS10). to 0.45 (CS5) and the mass ratio of MgO/FeO is from 0.10 (CS6) to 0.90 (CS10). Table 2. Compositions of titanium slag (wt. %). Table 2. Compositions of titanium slag (wt. %). Samples 2 2 FeO SamplesTiOTiO FeO
SiO SiO2 2
MnO MgO MgO Al Al22O O33 CaO CaO Ti2Ti Mass Ratio MnO O23O3 Mass Ratio CS1 1.53 2.51 2.83 1.00 3.78 3.78 0.05 CS1 72.46 72.46 12.21 12.21 5.89 5.89 1.53 2.51 2.83 1.00 0.05 CS2 63.62 12.21 5.89 1.53 2.51 2.83 1.00 11.35 0.15 CS2 63.62 12.21 5.89 1.53 2.51 2.83 1.00 11.35 0.15 CS3 55.20 12.21 5.89 1.53 2.51 2.83 1.00 18.92 0.25 CS3 46.79 55.20 12.21 12.21 5.89 5.89 1.53 2.51 2.83 1.00 0.25 CS4 1.53 2.51 2.83 1.00 18.92 26.49 0.35 CS4 38.37 46.79 12.21 12.21 5.89 5.89 1.53 2.51 2.83 1.00 0.35 CS5 1.53 2.51 2.83 1.00 26.49 34.06 0.45 CS6 1.53 1.34 2.83 1.00 34.06 18.92 0.10 CS5 55.20 38.37 13.38 12.21 5.89 5.89 1.53 2.51 2.83 1.00 0.45 CS7 55.20 11.32 5.89 1.53 3.40 2.83 1.00 18.92 0.30 CS6 55.20 13.38 5.89 1.53 1.34 2.83 1.00 18.92 0.10 CS8 55.20 9.81 5.89 1.53 4.91 2.83 1.00 18.92 0.50 CS7 55.20 55.20 8.66 11.32 5.89 5.89 1.53 3.40 2.83 1.00 18.92 0.30 CS9 1.53 6.06 2.83 1.00 18.92 0.70 CS8 55.20 55.20 7.75 9.81 5.89 5.89 1.53 4.91 2.83 1.00 0.50 CS10 1.53 6.97 2.83 1.00 18.92 18.92 0.90 CS9 55.20 8.66 5.89 1.53 6.06 2.83 1.00 18.92 0.70 CS10 55.20 7.75 5.89 1.53 6.97 2.83 1.00 18.92 0.90 Figure 6 shows the effects of mass ratio of Ti2 O3 /ΣTiO2 and the mass ratio of MgO/FeO on the total crystallization rates of anosovite crystals. It can be observed that the total crystallization rates of Figure 6 shows the effects of mass ratio of Ti2O3/ΣTiO2 and the mass ratio of MgO/FeO on the anosovite crystals increases one order of magnitude with the mass ratio of Ti2 O3 /ΣTiO2 increasing total crystallization rates of anosovite crystals. It can be observed that the total crystallization rates of from 0.05 to 0.45 and increases only three times with the mass ratio of MgO/FeO increasing from anosovite crystals increases one order of magnitude with the mass ratio of Ti2O3/ΣTiO2 increasing 0.10 to 0.90. It can be deduced that the mass ratio of Ti2 O3 /ΣTiO2 has a remarkable influence on the from 0.05 to 0.45 and increases only three times with the mass ratio of MgO/FeO increasing from 0.10 total crystallization rate of anosovite crystals while the mass ratio of MgO/FeO has a slight influence to 0.90. It can be deduced that the mass ratio of Ti2O3/ΣTiO2 has a remarkable influence on the total on the total crystallization rate of anosovite crystals. crystallization rate of anosovite crystals while the mass ratio of MgO/FeO has a slight influence on Figure 7 shows the effects of the mass ratio of Ti2 O3 /ΣTiO2 and the mass ratio of MgO/FeO on the total crystallization rate of anosovite crystals. the maximum total crystallization rate and peak temperature of anosovite crystals. It can be seen from Figure 7 shows the effects of the mass ratio of Ti2O3/ΣTiO2 and the mass ratio of MgO/FeO on Figure 7 that the maximum crystallization rate of anosovite crystals decreases with the mass ratio the maximum total crystallization rate and peak temperature of anosovite crystals. It can be seen from of Ti2 O3 /ΣTiO2 increasing, while the maximum crystallization rate of anosovite crystals increases Figure 7 that the maximum crystallization rate of anosovite crystals decreases with the mass ratio of with the mass ratio of MgO/FeO increasing. This phenomenon can be attributed to the variation Ti2O3/ΣTiO2 increasing, while the maximum crystallization rate of anosovite crystals increases with of the viscosity of titanium slag resulting from the composition change. The peak temperatures of the mass ratio of MgO/FeO increasing. This phenomenon can be attributed to the variation of the total crystallization rates of anosovite crystals increase with the mass ratio of Ti O3 /ΣTiO2 increasing, viscosity of titanium slag resulting from the composition change. The peak 2temperatures of total while the peak temperatures of total crystallization rates of anosovite crystals decrease with the mass crystallization rates of anosovite crystals increase with the mass ratio of Ti2O3/ΣTiO2 increasing, while ratio of MgO/FeO increasing. This phenomenon demonstrates that the increase in the viscosity of the peak temperatures of total crystallization rates of anosovite crystals decrease with the mass ratio titanium slag leads to the diffusion difficulty of atoms and the larger degree of undercooling is needed of MgO/FeO increasing. This phenomenon demonstrates that the increase in the viscosity of titanium to crystallize. slag leads to the diffusion difficulty of atoms and the larger degree of undercooling is needed to crystallize.
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Figure 6. 6. Effects Effects of of slag slagcomposition compositionon ontotal totalcrystallization crystallizationrates ratesofof ofanosovite anosovitecrystals: crystals:(a) (a)TiTi Ti O /Σ Figure 6. Effects of slag composition on total crystallization rates anosovite crystals: (a) 22O 33/Σ Figure 2O 3 /Σ TiO 2 and (b) MgO/FeO. TiO 2 and (b) MgO/FeO. TiO2 MgO/FeO.
Figure 7. 7. Effects composition on maximum crystallization and peak peak temperatures temperatures of of Figure Figure 7. Effects of of slag slag composition composition on maximum maximum crystallization rates rates and and peak temperatures of anosovite crystals: Ti 2 3 /Σ TiO 2 and (b) MgO/FeO. anosovite crystals: (a) Ti O /Σ TiO and (b) MgO/FeO. 2 3 2 anosovite crystals: (a) Ti2O /Σ TiO2 and (b) MgO/FeO.
4. 4. Conclusions Conclusions A A mathematical mathematical model model was was established established to to describe describe the the crystallization crystallization behaviors behaviors of of anosovite anosovite and and silicate crystals in high CaO and MgO titanium slag. The main results are shown as follows: silicate crystals in high CaO and MgO titanium slag. The main results are shown as follows: (1) The crystallization crystallization order MgO titanium slag is (1) The order of of anosovite anosoviteand andsilicate silicatecrystals crystalsininhigh highCaO CaOand and MgO titanium slag obtained during cooling as follows: Al TiO > Ti O > MgTi O > MgSiO > CaSiO > FeTi O 5 55 > 3Ti335O55 > MgTi 2 22O 5 55 > MgSiO 3 33 > CaSiO 333 > FeTi222O555 > is obtained during cooling as follows: 2Al22TiO > Mn222SiO SiO444>>Fe Fe22SiO . 2 SiO 4 Mn 4 . 4 (2) The optimum optimumtemperature temperatureranges rangesofof crystallization of these crystals in titanium in (2) The crystallization of these crystals in titanium slag slag are inare their their crystallization order as follows: 1744–1804 K, 1636–1696 K, 1589–1649 K, 1512–1572 K, crystallization order as follows: 1744–1804 K, 1636–1696 K, 1589–1649 K, 1512–1572 K, 1502–1562 1502–1562 K, K, 1463–1523 K, 1346–1406 K, 1236–1296 K. K, 1463–1523 1346–1406 K, 1236–1296 K. (3) The total total crystallization crystallization rates (3) The rates of of anosovite anosovite and and silicate silicate crystals crystals are are mainly mainly controlled controlledby byAl Al222TiO TiO555 and MgSiO MgSiO333, ,respectively. respectively.Al Al22TiO and Ti O have a higher crystallization priority and should and 5 and Ti 3 O 5 have a higher crystallization priority and should be 2 TiO 5 3 5 5 3 5 be responsible sharp increase in viscosity of titanium slag during cooling. responsible for for thethe sharp increase in viscosity of titanium slag during cooling. (4) The mass mass ratio ratio of of Ti Ti222O O333/ΣTiO /ΣTiO a remarkable influence total crystallization rate (4) The 22 has a remarkable influence onon thethe total crystallization rate of 2 has anosovite crystals while thethe mass total of anosovite crystals while massratio ratioofofMgO/FeO MgO/FeOhas hasa aslight slight influence influence on on the total crystallization rate of anosovite crystals. Author Contributions: Contributions: H.F., H.F., D.C., D.C., T.L., T.L., and and H.D. H.D. deduce deduce and validate validate the model. model. H.F., T.L., T.L., Y.H., M.L. M.L. and W.H. W.H. Author Author Contributions: H.F., D.C., T.L., and H.D. deduce and and validate the the model. H.F., H.F., T.L., Y.H., Y.H., M.L. and and W.H. performed the calculation. All of the authors analyzed and discussed the data; H.F. wrote the paper. performed the the calculation. calculation. All All of of the the authors authors analyzed analyzed and and discussed discussed the the data; data; H.F. H.F.wrote wrotethe thepaper. paper. performed Funding: This This research research received received no no external external funding. funding. Funding: research received no external funding. Funding: Acknowledgments: Special Special appreciation appreciation is extended extended to to PhD PhD candidates Huabiao Huabiao Chen Chen and and Sheng Yu Yu at at Acknowledgments: appreciation is Acknowledgments: at Chongqing University for the help on the graphic design. Chongqing University for the help on the graphic design. Chongqing University for the help on the graphic design. Conflicts Conflictsof ofInterest: Interest: The The authors authors declare declareno noconflict conflictinterest. interest. Conflicts of Interest: The authors declare no conflict interest.
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