{'fraction_non_alphanumeric': 0.02127659574468085, 'fraction_numerical': 0.02127659574468085, 'mean_word_length': 5.0594059405940595, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Size- and temperature-induced phase transformations of titanium nanoparticles

The size-temperature phase diagram of titanium nanoparticles has been obtained by calculating the corresponding Gibbs free energies of the FCC, BCC and HCP structures. It is found that these structures can transform from one into the other at specific sizes and temperature ranges, which is consistent with the available data reported in the literatures. Most importantly, we firstly predict that titanium particles with BCC structure can change to the FCC one in the size range 8.1–27.3 nm and in the temperature range 1156–1715 K.