667f05hw3rev - condition(T-Θ/C − |g 4 |P s 2 g 6 P s 4 =...

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ELEG 667–016; MSEG-667-016 - Solid State Nanoelectronics – Fall 2005 Homework #3 (revised) - 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
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Unformatted text preview: condition: (T-Θ )/C − |g 4 |P s 2 + g 6 P s 4 = 0 (note: the previous version incorrectly had the term g 6 P s 6 in the above equation) 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 s 2 (Tc) = 3|g 4 | / 4g 6 . (b) Using this result, show that T c = Θ + 3 C g 4 2 / 16g 6 ....
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