Size dependent Debye temperature and mean square displacements of nanocrystalline Au, Ag and Al

Effects of grain size and thermodynamic energy on the lattice parameters of metallic nanomaterials

“…The data used for the calculation are listed in Table 1 [25][26][27]. The reported experimental data for Ag [28,29], Al [29,30], Au [29,31], Cu [32], Pt [32], and Pd [33,34] are represented by the corresponding symbols. We found that the lattice parameters of the metallic Au, Cu, Al, Pt, Pd, and Ag nanocrystals are size dependent.…”

Debye temperature of nanocrystalline Fe–Cr alloys obtained by mechanical alloying

“…5 Cr 45.5 sample with <d>=10.5 nm can be seen in Fig. 5 together with the best fits to the experimental data in terms of eq.…”

“…Spectral parameters as found from the analysis of the Mӧssbauer spectra of the n-Fe 55. 5 Cr 45.5 samples in terms of the HFD method (M subspectrum) and in terms of the QSD method (P subspectrum). The average values of the hyperfine field, <B>, and those of the quadrupole splitting, <QS>, were calculated by integrating the HFD and QSD histograms, respectively, shown in Fig.…”

“…Concerning the Debye temperature,  D , a subject of the present study, it is regarded as a very important quantity to characterize materials properties such as lattice vibrations of atoms and phase transitions. There is a great body of experimental evidence that free and loosely embedded nanometer-sized particles show a decrease of  D e. g. Fe [2][3][4] and Ag, Al and Au [5], while for the well-embedded, interacting or substrate-deposited metallic particles both increase or decrease of  D is possible depending on the matrix or substrate. If the matrix is harder than the particles, then  D of the latter is enhanced e. g. Sn in Si matrix [6], and vice versa e. g. Co in Ag matrix [7].…”

On the Debye‐Waller factor and Debye temperature of CdO nanoparticles

“…Lindemann criteria have been revised many times and subsequently the melting point is obtained for various systems. For example, recently Sadaiyandi [14] had theoretically calculated the melting point of nano Au, Ag and Al and observed that Lindemann's criterion would give only an approximate estimate of the melting point. Buffat and Borel [15] have studied the size dependent melting point for nanomaterials by a phenomenological model and compared with experiment.…”