Lindemann indices as a function of temperature for Ag NPs, Au@Ag CSNPs and Au NPs in different sizes. (a)–(d) Lindemann indices as a function of temperature for NPs with four, five, six and seven atomic layers, respectively. The black and pink curves show the Lindemann indices of Ag NPs and Au NPs, respectively. The Lindemann indices of Au@Ag CSNPs with two, three, four and five layers of Au core are plotted by red, green, blue, olive and orange curves, respectively.