Lecture 23 - Landaus Phenomenological Theory 2 First order...

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Landau’s Phenomenological Theory 2. First order phase transition (i) Symmetry   survives (Ferroelectric crystals like Potassium dihydrogen phosphate or KH 2 PO 4 ) 2 2 0 ( ) ( ) a T A T T  4 a is negative. We need 6 a term (positive) in the expansion to “produce” a first-order phase transition.   2 4 6 0 2 0 4 6 1 1 1 ( ) ( ) ( ) ( ) 2 4 6 L G a T A T T a T a T First Order Phase Transition: Discontinuous jump in the order parameter which is related to Latent Heat (via the discontinuity in entropy). Conditions: 1) 0 L G minimum 2) At , ( 0, ) ( , ) c L c L s c T G T T G T T The “weak” secondary minimum seen above T c becomes equal strength at T c and then becomes deeper i.e. global minimum below T c .
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From 0 L G 35 2 0 4 6 ( ) 0 s s s A T T a a 24 2 0 4 6 0 or ( ) 0 (1) s s s A T T a a 2 2 4 4 6 2 0 6 4 ( ) 2 s a a a A T T a  2 4 6 2 0 4 ( ) a a A T T  for the second minimum to develop.
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Lecture 23 - Landaus Phenomenological Theory 2 First order...

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