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Processes 2019, 7, 248 9 of 16 3.1.3. Identification of Crystal Growth Mechanism The growth-mechanism of Li2CO3 crystals was identified by fitting the experimental induction times from reactive crystallization over a range of temperatures and supersaturations to the expressions of different growth mechanisms. According to a previous study [26], Li2CO3 crystals are rod-like, meaning the value of m is 1. Hence n (mν + 1) can take values of either 3/2 or 2 depending on the value of ν (1/2 or 1). The expressions Fu(S) for different growth mechanisms of Li2CO3 are shown in Table 3. Table 3. The expressions Fu(S) for different growth mechanisms of Li2CO3. F1 F2 F3 F4 Growth Mechanisms Normalgrowth Spiralgrowth Volume diffusion-controlled growth 2D nucleation-mediated growth v n 1 2 1 2 1/2 3/2 1 2 Fu(S) 11 ln tind(S−1)2 S2 1 ln tind(S−1)S2 12 ln tind (S − 1) 3 S 3 . 12 ln tind (S − 1) 3 S 3 For mechanisms F1, F2, and F3, Fu(S) and 1/ln2S are in a linear relationship, while for mechanism F4, Fu(S) and 1/lnS are in a quadratic polynomial relationship. The calculated values of Fu(S) were plotted against either 1/lnS or 1/ln2S, with the results shown in Figure 5. Depending on the goodness Processes 2018, 6, x FOR PEER REVIEW 10 of 17 of fitting quality shown in Table 4, the growth mechanism can be identified. (a) (b) (d) Figure 5. Plot of 𝐹 (S) versus 1/lnS or 12/𝑙𝑛𝑆 for Li2CO3 crystals. Data are fitted using (a) normal (c) Figure 5. Plot of Fu(S) versus 1/lnS or 1/ln S for Li2CO3 crystals. Data are fitted using (a) normal growth, growth, (b) spiral growth, (c) volume diffusion-controlled growth, and (d) 2D nucleation-mediated (b) spiral growth, (c) volume diffusion-controlled growth, and (d) 2D nucleation-mediated growth. growth. Table 4. The coefficients of determination R2 for different growth mechanisms of Li2CO3 under different temperatures. T (K) R2 F1 F2 F3 F4 318.15 0.9530 0.9505 0.9539 0.9949PDF Image | Reactive Crystallization Process of Lithium Carbonate
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