## 3 Results and Discussion
### Spectral Characteristics Overview for Samples Measured with XRD
In order to maintain the quality of the chocolate, a lot of efforts have been made either to optimize the structure and presence of the \(\beta\)-type polymorph [4], to modify the crystallization of cocoa butter [47; 48], or to postpone the state phase transition from \(\beta\) (V) to \(\beta\) (VI) [7; 49]. All these studies accentuate an unyielding interest in obtaining \(\beta\) (V) crystal form to improve the quality of the chocolate and potentially extend the shelf life of chocolate. According to the thermal trajectory and polymorphic forms of crystallized cocoa butter constructed by [PERSON] et al. (2015) [42] (Figure 4), \(\beta\) (V) type in the current study was generated in the processing of holding at 20 \({}^{\circ}\)C for 60 min, which is consistent with the previous finding where \(\beta\) (V) type was formed at the temperature range of 15-25 \({}^{\circ}\)C [40; 42]. Numerous authors believed that \(\beta\) (V) type is transited from \(\beta^{\prime}\) (type III and IV), which probably transited from the \(\alpha\) phase when the temperature increased [40; 42]. \(\beta\)-crystallization will be generated directly when the liquid is not memory-free, and \(\beta\)-crystallization is induced by  
Figure 3: Average X-ray diffraction patterns of Sample A (**a**), B (**b**), C (**c**), and original untreated control sample (**d**). the memory effect [45]. However, the \(\beta\) (V) phase was always formed via the \(\beta^{\prime}\) phase (type III and IV) in the study of [PERSON] and [PERSON] (2003) [39]. The authors pointed out that \(\beta\) polymorph was obtained after 4-5 weeks at crystallization temperatures of 20 and 22 \({}^{\circ}\)C [39]. Although the storage temperature in the current study was set at 10 \({}^{\circ}\)C rather than 20 \({}^{\circ}\)C, the \(\beta\) polymorph generated at 20 \({}^{\circ}\)C during processing was stable enough to store at 10 \({}^{\circ}\)C.  
As for Sample C, the XRD spectra (Figure 3c) were similar to type III (\(\beta^{\prime}\) type) observed by [PERSON] and [PERSON] (1966) [8], who obtained type III by solidification of melt at 5 to 10 \({}^{\circ}\)C or by transformation of type II by storing at 5 to 10 \({}^{\circ}\)C. According to the procedure made for Sample C, the generated \(\beta^{\prime}\) crystallization may probably follow the pathway from \(\gamma\) to \(\alpha\) and eventually reach the \(\beta^{\prime}\) phase. As stated above, the rapid freezing promotes the generation of \(\alpha\) type [8], and transient metastable \(\gamma\) and \(\alpha\) phases occurred when the temperature was below \(-15\)\({}^{\circ}\)C. This is in agreement with the procedure for producing Sample C: rapidly cooled to 10 \({}^{\circ}\)C at 40 \({}^{\circ}\)C/min and finally froze to \(-20\)\({}^{\circ}\)C. Approximately 50-75% of the \(\gamma\) phase was reported to considerably transferred into the \(\alpha\) phase in at most 10 min and completed the transition in one or more days when the preset temperature was low [40]. When the temperature increases over around 5 \({}^{\circ}\)C, the \(\alpha\) phase is no longer stable and will transform into the \(\beta^{\prime}\) formation [40], which is coincident with the procedure of Sample C, where the sample was finally stored at 4 \({}^{\circ}\)C.