Unformatted text preview: lattice constant from a to a (1δ ) with δ ± 1. d) Using the thermodynamic relation dW =pdV , determine how much the lattice constant of the argon crystal changes in 100 atm of pressure (1 atm =10 5 N/m 2 ). Problem 2: Phonon dispersion with alternating spring (Marder problem 13.1, 20 points) Consider a onedimensional chain of identical atoms. The springs between them alternate in strength between values K 1 and K 2 . a) Find the vibrational frequencies as a function of wave number q . Study the low q limit and ﬁnd the sound velocity. b) Discuss the physical meaning of the two branches. Sketch the way the atoms move in both cases! c) Discuss the dispersion and the normal modes for K 1 ² K 2 . d) Discuss the limit K 1 ≈ K 2 and compare with the homogeneous chain where all springs are identical (see class)....
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 Spring '11
 ThomasVojta
 Physics, Work, Fundamental physics concepts, Noble gas, Condensed matter physics, Cubic Unit Cell

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