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667f05hw3sol - ELEG 667016 MSEG-667-016 Solid State...

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ELEG 667–016; MSEG-667-016 - Solid State Nanoelectronics – Fall 2005 Solution Homework #3 - due Thursday, 22 September 2005, in class 1. Ferroelectric criterion for atoms: Consider a system of two neutral atoms separated by a fixed distance a , each atom having a polarizability α . Find the relation between a and α for such a system to be ferroelectric. Hint: The dipolar field is strongest along the axis of the dipole. 2. Saturation polarization at Curie point: In a first-order transition, the equilibrium condition: (T- Θ )/C |g 4 |P s 2 + g 6 P s 4 = 0 with T set equal T c gives one equation for the polarization P s (T c ) at the transition temperature. A further condition at the Curie point is that F(P s ,T c ) = F(0,T c ). (a) Combining these two conditions, show that P
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