Multiscale heat conduction near a disclinationS. Fumeron and D. Lacroix
Laboratoire d'Énergétique et de Mécanique Théorique et Appliquée, CNRS UMR 7563, Nancy Université 54506 Vandoeuvre Cedex, France, EU
received 11 October 2007; accepted in final form 29 April 2008; published June 2008
published online 4 June 2008
Microscopic defects in crystalline structure affect phonons transport and, at a macroscopic scale, heat propagation. Among them, disclinations defects change the topology by breaking the rotational symmetry in the material. Considering the Katanaev-Volovich metric for such defect description, the new phonon motion equation is derived near a disclination. Then, using the Boltzmann formalism to model phonon transport, a modified radiative transfer equation involving an effective refraction index that takes into account the disclination is introduced. The variations of the disclination index are discussed. Then, the corrections on heat flux that should be brought in such defected medium are exposed.
61.72.Bb - Theories and models of crystal defects.
61.72.Lk - Linear defects: dislocations, disclinations.
65.40.-b - Thermal properties of crystalline solids.
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