## 3 Results and Discussion
### Spectral Characteristics Overview for Samples after 23 Days of Storage Measured with FT-FIR  
There was much noise after 8 THz, so the spectra before 8 THz were used for analysis. To clearly describe the characteristics of each sample, the average spectra were calculated by representative spectra in each group (Figure 5). The average thickness for Sample A, B, C, and the control group were 1.72 \(\pm\) 0.05, 1.81 \(\pm\) 0.07, 1.75 \(\pm\) 0.10, and 1.70 \(\pm\) 0.05 mm, respectively. Four different patterns could be identified according to different crystallization types, which indicates that terahertz spectroscopy can, therefore, be an emerging and innovative method to control tempering in chocolate factories. There was a valley at 2.16 THz (an asterisk) for each terahertz spectrum, which may be due to the absorbance of polyethylene that was used for making the dip window. A significant change in the  
Figure 4: Time-temperature state diagram for the specific polymorphism of crystallized cocoa butter (cited from [PERSON] et al., 2015 [42]). THz spectral pattern of Sample B when the CB temperature was maintained at 20 \({}^{\circ}\)C from 30 min to 45 min. [PERSON] stated that recrystallization to the \(\beta\) (V) type that occurs within 45 min is referred to as a short-term (\(\beta\)-) memory effect, while that takes after 45 min belongs to a long-term (\(\beta\)-) memory effect [45]. Accordingly, it seems the CB may probably be a short-term (\(\beta\)-) memory effect in the current study. There was a very broad peak at 2.55 THz for Sample A (\(\alpha\) type), and the peak was shifted to 2.72 THz for Sample C [\(\beta^{\prime}\) type (III)] whilst an evident sharp peak at 2.60 THz and 2.63 THz could be observed from Sample B [\(\beta\) (V) type] and control sample, respectively. No sharp peak at 1.85 THz can be obtained from Samples A, B, and C except for the original control group. [PERSON] et al. (2018) monitored cocoa butter in chocolate from different factories and observed peaks at 2.35 THz, 2.51 THz, 2.73 THz, and 2.97 THz from the Factory L sample, which contained one visible fat bloom [50]. For samples with 6 clear spots of fat bloom (Factory H sample), peaks at 2.41 THz and 2.65 THz can be discovered [50]. The authors claimed that the difference between the THz spectra of L and H may be due to the formation and migration of \(\beta\) (VI) associated with fatty acids [50]. The peaks at 2.55 THz from Sample A may probably be relevant to sucrose, as sucrose presents a peak at approximately 2.59 THz in the study of [PERSON] et al. (2003) [51]. According to Figure 5a,b,d, a peak at 6.80 THz can be detected from Sample A (\(\alpha\) type), B [\(\beta\) (V)], and the original control group. However, the peak at 6.80 THz for the \(\alpha\) type sample was much broader than that of the \(\beta\) type and original control type. [PERSON] et al. (2011) found palmitic acid possesses a distinct sharp peak at 235 cm\({}^{-1}\) (7.05 THz) [52], which indicates that palmitic acid--which occupies 26% of the main fatty acids of cocoa butter--may gently change in the \(\alpha\) types of crystallisations. Likewise, a comparably broad peak at 4.25 THz and 5.21 THz was observed in Sample B [\(\beta\) (V)] (Figure 5b), which may be related to the stearic acid and oleic acid that possess distinct peaks at 154 cm\({}^{-1}\) (4.62 THz) and 166 cm\({}^{-1}\) (4.98 THz), respectively [52]. In contrast, no noticeable peaks were observed from Samples A (\(\alpha\) type) and C [\(\beta^{\prime}\) type (III)]. This implies that changes in stearic acid and oleic acid may occur at \(\alpha\) and \(\beta^{\prime}\) type (III). The terahertz spectra shapes for \(\alpha\) and \(\beta^{\prime}\) type (III) were quite similar, but the peak was shifted to the higher THz range, which may indirectly validate the pathway from \(\alpha\) to \(\beta\) type (III). [PERSON] (2003) mentioned several different crystal packing configurations that can be formed from a TAG molecule [53].