Prog. Theor. Phys. Vol. 60 No. 2 (1978) pp. 327-337
Note on Frequency Spectrum of Crystalline Fine Particles
Department of Physics, Kyoto University, Kyoto 606
(Received April 10, 1978)
Frequency distribution function of lattice vibration in crystalline fine particles is calculated as functions of fine particle radius by means of the moment-trace method. An FCC lattice with nearest neighbour central interaction is considered as an example and the 2n-th moment of frequency distribution is expressed as a sum over paths on the lattice connected by the dynamical matrix elements. The presence of surface gives a restriction on the sum over paths. It is shown that the frequency distribution functions constructed with the first five even moments show remarkable tendency for the phonon softening as fine particle radius becomes small.
DOI : 10.1143/PTP.60.327
- T. Matsubara, Y. Iwase and A. Momokita, Prog. Theor. Phys. 58 (1977), 1102[PTP].
- E. Matsushita and T. Matsubara, Prog. Theor. Phys. 59 (1978), 15[PTP].
E. W. Montroll, J. Chem. Phys. 10 (1942), 218[CrossRef].
J. M. Dickey and A. Paskin, Phys. Rev. B 1 (1970), 851[APS].
W. D. Kristensen, E. J. Jensen and R. M. J. Cotterill, J. Chem. Phys. 60 (1974), 4161[CrossRef].
A. A. Maradudin, R. F. Wallis, D. L. Mills and R. L. Ballard, Phys. Rev. B 6 (1972), 1106[APS].
E. W. Montroll, J. Chem. Phys. 11 (1943), 481[CrossRef].
E. W. Montroll and D. C. Peaslee, J. Chem. Phys. 12 (1944), 98[CrossRef].
C. Isenberg, Phys. Rev. 132 (1963), 2427[APS].
- T. Hama and T. Matsubara, Prog. Theor. Phys. 59 (1978), 1407[PTP].