Phonon scattering cross section of polydispersed spherical nanoparticles

Abstract

An approximate analytical solution is proposed to estimate the phonon scattering cross section of polydispersed spherical nanoparticles. Using perturbation of the Hamiltonian due to differences in mass and bond stiffness between a host medium and a spherical nanoparticle, an analytical solution is obtained for the scattering cross section in the Rayleigh limit when the size parameter approaches zero. In the geometrical scattering limit, when the size parameter approaches infinity, the van de Hulst approximation for anomalous diffraction is used to estimate the scattering cross section as a function of acoustic impedance mismatch between the host medium and the spherical nanoparticle. Finally, these two limiting cases are bridged by a simple expression to estimate the scattering cross section for intermediate values of the size parameter. Using this, the scattering cross section for a polydispersed distribution of spherical nanoparticles was also estimated as a function of the parameters defining the statistical size distribution.

Thermal conductivity of argon-SiO2 cryocrystal nanocomposite

“…When the size parameter is small (χ 1) << , the scattering rule obeys Rayleigh law, i.e., the scattering probability varies as frequency to the fourth power. At the other limit, where the size parameter reaches big numbers ( 1) χ >> the scattering probability is independent of frequency of the phonon and the phonon scattering cross section depends on the path length through which the phonon travels across the nanoparticle and the associated phase lag [5]. Thus, the size of the nanoparticle becomes a very important factor for scattering cross section in this regime.…”

“…In the Rayleigh scattering regime, the scattering cross section depends both on the difference of masses of the nanoparticle and the host crystal and on the difference of the force constancies acting in the two constituencies [5]. In the case of polydispersion of nanoparticles, when the size of nanoparticles deviates from its mean value, the scattering cross section based on mean diameter increases with increasing standard deviation of the linear dimension of the nanoparticles [5]. The considerations sketched above do not exhaust the complexity of problems related to the thermal energy transfer in the discussed nanostructured objects.…”

Reducing the thermal conductivity of carbon nanotubes below the random isotope limit

“…Recent experimental and theoretical works have shown that introducing lattice matched nanocrystals into an alloy can further reduce its thermal conductivity, in what has been termed "beating the alloy limit" 1,2,3 . This has a very important practical application in the field of thermoelectric materials, in which a major goal is to obtain low thermal conductivities without affecting electronic properties.…”

Optimizing phonon scattering by nanoprecipitates in lead chalcogenides

“…[10][11][12][13][14] The physical basis of phonon scattering by nano-particles is well documented in the literature. 8,[15][16][17][18][19][20][21] When interpreting experimentally measured thermal conductivity data, researchers most often resort to a Matthiessen approach based on the phonon relaxationtime approximation 16,17,[22][23][24][25][26] assuming a single average (or effective) nanoparticle size. [10][11][12][13][14] However, recent measurements have found that in general the size of nanoprecipitates is distributed across a certain length scale ranging from ∼ 0.5 to ∼ 20 nm.…”

“…The precipitate scattering term τ np is computed by incorporating experimentally measured precipitate size data into the empirical model proposed by Kim and Majumdar,15 based on an expression for the scattering cross-section σ as an interpolation between a ∝ ω 4…”