ps8_sol - MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING 2.370/2.37 Molecular Mechanics Fall 2007 PROBLEM SET 8 Solution 1. Problem 1 (a) You should be able to match the values given exactly (except for statistical un- certainty). (b) i. From class we have R = 6 q 2 × 12 . 13 14 . 45 =1 . 0902 σ =3 . 7067 × 10 10 m is the nearest- neighbour distance in the low-temperature limit and a = 2 R =5 . 24 × 10 10 m is the corresponding lattice spacing. ii. There are 4 atoms per unit cell, and the volume of a unit cell is a 3 ,sothe number density is: ρ =4 /a 3 =2 . 7769 × 10 28 / m 3 . The Lennard-Jones number density is thus: ρ = ρσ 3 = 4 ( 21 . 09) 3 . 0914 iii. Again from class, U = 1 2 4 ± 12 . 13 σ 12 R 12 14 . 45 σ 6 R 6 ² To nondimensionalize, U = U/± iv. U /N = 1 2 4 ± 12 . 13 σ 12 R 12 14 . 45 σ 6 R 6 ² = 8 . 6069; you should be able to match this very closely with the code by using a small T < 0 . 001 and the value of ρ found above.
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ps8_sol - MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT...

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