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Unformatted text preview: Physics 481: Condensed Matter Physics  Midsemester test Friday, March 4, 2011 Problem 1: Structure determination (70 points) DebyeScherrer Xray diffraction is used to study a powder specimen of a monoatomic substance that is known to crystallize in a cubic Bravais lattice structure with primitive vectors ~a 1 = ( a, , 0) , ~a 2 = (0 ,a, 0) and ~a 3 = (0 , ,a ). The wavelength of the Xrays is 1.4 A. a) Find the primitive vectors of the reciprocal lattice. (15 points) b) Find the four shortest possible lengths of reciprocal vectors. (20 points) c) The first diffraction ring is at an angle of = 17 . 9 from the incident direction. Determine the lattice constant a . (20 points) d) Find the angles of the next three diffraction rings. (15 points) Problem 2: Onedimensional Morse solid (80 points points) Consider N identical atoms of mass M whose motion is restricted to the xaxis. Nearest neighbor atoms are coupled by the socalled Morse potential V M ( r ) = D 1 e ( r r )...
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This note was uploaded on 10/04/2011 for the course PHYSICS 481 taught by Professor Thomasvojta during the Spring '11 term at Missouri S&T.
 Spring '11
 ThomasVojta
 Physics, Diffraction

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