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# Structure.homework__5-answer - MTLE-2100 Structure of...

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MTLE-2100 Structure of Engineering Materials, Homework #5 --Answer 1. Predict the x-ray diffraction peak positions (2 θ ) for the first four (smallest angle) peaks corresponding to (001), (100), (101) and (110) for a tetragonal crystal with a = 2.300A, c= 2.500A, λ = 1.54A. d hkl = a/ h 2 + k 2 +l 2 (a/c) 2 d hkl = a/ h 2 + k 2 +l 2 (a/c) 2 sin θ 2 θ ( ° ) (001) 2.300/(a/c) =2.500 Å 0.308 35.9 (100) 2.300/ 1 2 =2.300 Å 0.3348 39.1 (101) 2.300/ 1 2 + 1 2 (a/c) 2 =1.693 Å 0.4549 54.1 (110) 2.300/ 1 2 + 1 2 = 1.626 Å 0.474 56.5 2. Transmitted intensity of x-ray is given by I = I 0 exp (- μ t) and transmittance is given by I/I 0 = exp (- μ t), where t is thickness of the specimen and μ is the linear absorption coefficient. Scattered intensity, I s , by small inclusions in a solid is proportional to both thickness and transmission, i.e. I s = I 0 k t exp (- μ t) where k is a proportionality constant. Obtain the scattered intensity normalized by the maximum

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