| Title: | LAMB-MOESSBAUER FACTORS IN NANOCRYSTALS |
| DOI No: | 10.1142/9789812701879_0044 |
| Source: | CLUSTERS AND NANO-ASSEMBLIES (pp 379-385)
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| Author(s): | KESHAV N. SHRIVASTAVA
Department of Electrical, Computer Engineering & Computer Science, University of Cincinnati, Cincinnati OH 45221-0030, USA
School of Physics, University of Hyderabad, Hyderabad 500046, India
PUNIT BOOLCHAND
Department of Electrical, Computer Engineering & Computer Science, University of Cincinnati, Cincinnati OH 45221-0030, USA
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| Abstract: | Lattice vibrations in a nanocrystalline solid, in contrast to bulk crystalline solid, will have an additional contribution from surface scattering. Mean square displacement (msd) of atoms in a nanocrystal is calculated using such an additional contribution. The zero-point vibrational correction to the msd is found to vary as the inverse square of a nanocrystal size (L). Furthermore, the temperature dependent term of the msd is found to vary as exp(-1/TLk), where k is a constant. Since a structural distortion of a nanocrystalline solid can be expected to set in, at a particular temperature, we introduce a gap in phonon dispersion. Calculations of the LM factors with a gap in dispersion show that f(T) shows a global maximum at a threshold temperature (Tth). Thermal expansion is expected to occur at T < Tth, while thermal contraction should result at T > Tth with increasing T. The gap is the result of a size dependent phonon scattering. We compare calculated f(T) and thermal expansion with measured results of these observables on nanometer-sized Au particles. |
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