{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

EMS162-2010-Homework5_Solutions

# EMS162-2010-Homework5_Solutions - UNIVERSITY OF CALIFORNIA...

This preview shows pages 1–2. Sign up to view the full content.

EMS 162, page 1/4 Prof. Y. Takamura, 2010 UNIVERSITY OF CALIFORNIA, DAVIS Department of Chemical Engineering and Materials Science EMS 162: Structure and Characterization of Engineering Materials Homework 5 - SOLUTIONS Due Date: Tuesday, Feb. 9th, 2010, in class – NO LATE HOMEWORK Note: You must show all the steps in order to receive full credit. Be sure to include units! 1. Interference Function [23 pts] Consider the scattering of x-rays from a one dimensional periodic arrangement of electrons as shown in Figure 1: In this case, the intensity of the diffracted x-rays at a scattering angle, 2 θ , is given by the interference function: ( ) ϕ ϕ ϕ 2 2 sin sin N I where N is the number of electrons in the line, and ϕ is the phase angle given by: ( ) λ θ π λ θ π ϕ 2 sin 4 2 cos 1 2 a a = = where a is the spacing between electrons and λ is the wavelength of the x-rays. (a) Using your favorite plotting software (Excel, Origin, Matlab, Mathematica), plot the interference function as a function of phase angle (from zero to 4 π ) for the case of six, 20, and 1000 electrons in a 1D line. ( Hint : Be sure to use a small enough step size between data points as N gets large). Hand drawings will not be given ful l credit. (b) Comment on what happens to the shape of the curves as N gets large. The interference function tells us that we expect strong diffracted intensity for certain phase angles and therefore certain scattering angles, and low/no diffracted intensity for all other scattering angles.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}