9780030839931, Chapter 13, Problem 1P

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Chapter 13, Problem 1P Problem On page 250 we argued that in a metal with, cubic symmetry the conductivity tensor is a constant times the unit matrix, i.e., that j is always parallel to E construct an analouges argument for a hexagonal close-packed metal, showing that the conductivity tensor is diagonal in a rectangular coordinate system with Z taken along the c-axis, with OXX = so that the current induced by afield parallel or perpendicular to the c-axis is parallel to the field. Step-by-step solution Step 1 of 1 In a hexagonal close-packed metal where the rectangular coordinate system in Z direction is taken along the c-axis, the conductivity tensor is always diagonal. Thus, the component of the conductivity tensor is = This shows j remains parallel to E. Also, if the field in the x-direction induced any current in the y-direction, the same current could arise in the -y direction. The only possible way is having a zero current which makes to vanish. Thus, the conductivity tensor is The presence of will give a unit matrix. Thus, the conductivity tensor in hexagonal close-packed metal is conductivity which is a constant times the unit matrix. Therefore, the conductivity tensor is diagonal.