md2011-05-note_Part_7

# md2011-05-note_Part_7 - Then, absolute internal energy A...

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I Then, absolute internal energy A can be calculated for any λ with A ( λ ) - A ( λ 0 ) = Z λ λ 0 ± U ∂λ ² d λ . (40) I The real potential function, for which we want to calculate A is U 0 . I So, constructed U interpolates between U 0 and a harmonic lattice U ( r , λ ) = U 0 ( r ) + λ i ( r i - r 0 ) 2 A ( λ = 0 ) = A ( λ ) - R λ 0 ³ U ∂λ ´ d λ 0 . (41) I Because at large λ we now have harmonic lattice, for which we know the solution, we can integrate the real solution A ( λ = 0 ) from h U /∂λ i . Notes

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R±²³´µ²± F¶µ·¸¹´µ² I Response functions describe how the system reacts to a change in some thermodynamic variables. I Some of the most important response functions are: Constant volume heat capacity: C V = ( E T ) V Constant pressure heat capacity: C P = ( H T ) P Thermal expansion coeﬃcient: α P = V - 1 ( V T ) P Isothermal compressivity: β T = - V - 1 ( V P ) T Bulk modulus: B = 1 T Thermal pressure coeﬃcient: γ V = ( P T ) V I Many of them can be directly calculated with an MD simulation.
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## This note was uploaded on 02/14/2012 for the course CSE 6590 taught by Professor Kotakoski during the Winter '12 term at York University.

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md2011-05-note_Part_7 - Then, absolute internal energy A...

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