Computational Materials Science | MSE 532 j SPRING 2016 j HW 1 | DUE TBA 1 kBT i

Question

Computational Materials Science | MSE 532 j SPRING 2016 j HW 1 | DUE TBA 1 kBT in Joules and pN nm when T is (a) room temperature ~ 300 K and (b) T = 1000 K. (2) What is the energy of a typical covalent/ionic bond in a solid? Express it in terms of kBT at room temperature. (3) When is statistical averaging important? (4) When is quantum averaging important? (5) Energy scales can be converted to time scales using the energy-time uncertainty relation. What are time scales corresponding to 1 kBT at room temperature and 1 eV? (6) At what (absolute) temperature does the energy of thermal fluctuations equal 1 eV? (7) Why are the forward and backward finite difference expressions for the acceleration and velocity used in Molecular Dynamics (MD) simulations equal to each other? What property of Newton's equations leads to their equality? (8) Suppose the characteristic time scale x for a process is 10^12 s, which is the typical time scale associated with movements of the electrons in crystals. Setting tau/deltat = 100, using MD how many steps will it take to simulate a process whose characteristic time scale is 10^-6 s? (9) If one step takes 10^-7 s on a fast computer, using MD how long will it take for a computer to simulate a process with a 10 6 s time scale in a system of 100 particles? (Remember that for each particle we have to update 6 equations.)

Explanation / Answer

Solution:

The temperature at which energy of thermal fluctuations 1eV is almost equal to 450K.

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