scholarly journals Effective scattering cross-section in lattice thermal conductivity calculation with differential effective medium method

AIP Advances ◽  
2013 ◽  
Vol 3 (8) ◽  
pp. 082116 ◽  
Author(s):  
Di Wu ◽  
A. S. Petersen ◽  
S. J. Poon
Keyword(s):  
Thermal Conductivity ◽  
Cross Section ◽  
Lattice Thermal Conductivity ◽  
Effective Medium ◽  
Scattering Cross Section ◽  
Effective Medium Method ◽  
Scattering Cross ◽  
Effective Scattering Cross Section ◽  
Thermal Conductivity Calculation ◽  
Medium Method

Mode Resolved Continuum Mechanics Model of Phonon Scattering From Embedded Cylinders

2016 ◽  
Author(s):  
Vineet Unni ◽  
Joseph P. Feser
Keyword(s):  
Thermal Conductivity ◽  
Elastic Wave ◽  
Cross Section ◽  
Continuum Mechanics ◽  
Phonon Scattering ◽  
Conductivity Tensor ◽  
Scattering Cross Section ◽  
Continuum Approximation ◽  
Scattering Cross ◽  
Thermal Conductivity Tensor

Phonon scattering from media with embedded spherical nanoparticles has been studied extensively over the last decade due to its application to reducing the thermal conductivity of thermoelectric materials. However, similar studies of thermal transport in fiber-embedded media have received little attention. Calculating the thermal conductivity tensor from microscopic principles requires knowledge of the scattering cross section spanning all possible incident elastic wave orientations, polarizations and wavelengths including the transition from Rayleigh to geometric scattering regimes. In this paper, we use continuum mechanics to develop an analytic treatment of elastic wave scattering for an embedded cylinder and show that a classic treatise on the subject contains important errors for oblique angles of incidence, which we correct. We also develop missing equations for the scattering cross section at oblique angles and study the sensitivity of the scattering cross section as a function of elas-todynamic contrast mechanisms. In particular, we find that for oblique angles of incidence, both elastic and density contrast are important mechanisms by which scattering can be controlled, but that their effects can offset one another, similar to the theory of reflection at flat interfaces. The solution developed captures the scattering physics for all possible incident elastic wave orientations, polarizations and wavelengths including the transition from Rayleigh to geometric scattering regimes, so long as the continuum approximation holds. The method thus enables incorporation of coherent scattering models into calculations of the thermal conductivity tensor for media with nanofibers.

Mass Determination by Direct Measurement of Electron Scattering

1975 ◽  
Vol 33 ◽  
pp. 240-241
Author(s):  
M. K. Lamvik ◽  
A. V. Crewe
Keyword(s):  
Cross Section ◽  
Electron Scattering ◽  
Mass Density ◽  
Variable Mass ◽  
Scattering Cross Section ◽  
Mass Determination ◽  
Number Density ◽  
Cross Sectional ◽  
Thin Slice ◽  
Scattering Cross

If a molecule or atom of material has molecular weight A, the number density of such units is given by n=Nρ/A, where N is Avogadro's number and ρ is the mass density of the material. The amount of scattering from each unit can be written by assigning an imaginary cross-sectional area σ to each unit. If the current I0 is incident on a thin slice of material of thickness z and the current I remains unscattered, then the scattering cross-section σ is defined by I=IOnσz. For a specimen that is not thin, the definition must be applied to each imaginary thin slice and the result I/I0 =exp(-nσz) is obtained by integrating over the whole thickness. It is useful to separate the variable mass-thickness w=ρz from the other factors to yield I/I0 =exp(-sw), where s=Nσ/A is the scattering cross-section per unit mass.

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