MatSE 405: Microstructure Determination Problem set #2; due Thursday, January 31.
1. Consider a right triangle where one of the angles is very small q << 1. Let the length of the hypotenuse be L. To first order in q, derive an expression for the length of the shortest leg. To second order in q, derive an expression for the length of the other leg.
2. Use MatLab to do the same as above. Define real symbolic variables by syms L theta real and then use the taylor function to do expansions for small theta. Turn in a print out of your MatLab script and output. (Probably the fastest way to do this is to print the command window.)
3. Define N as the atomic density, i.e., the number of atoms per unit volume, of a solid. (a) What is the lattice constant a of bcc and fcc crystals in terms of N? (b) What is areal density (number of atoms per unit area) s of the closest-packed planes in fcc and bcc crystals in terms of N? (c) What are the largest and smallest values of N for the 1st row transition metals Ti to Cu? (The simplest way to do this last part of the problem is to look up the atomic weights and mass densities at, for example, www.webelements.com
4. Exercises 1.1 and 1.6 in the textbook.

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On 24 Jan 2008, 10:17.