# Homework Help: Debye-Scherrer method in finding atom diameter?

1. Apr 2, 2012

### Mixer

1. The problem statement, all variables and given/known data
In an examination of a certain element using the Debye-Scherrer technique the following diffraction angles (in degrees) were noted:

45.26/65.92/83.56/100.6/118.68/140.88

Radiation λ=0.1540 nm was used. Obtain two estimates of the atomic diameter of the element in question. a) that obtained assuming the atoms act as contacting hard spheres and b) that obtained from average volume per atom?

2. Relevant equations

Braggs law

2*dhklsin θ = nλ (n= 0,1,2....)

3. The attempt at a solution

I tried to use Braggs law straight away but didn't get the right result (which is for a) 0.246 nm and for b) 0.280 nm)

What am I supposed to do? I found that you are supposed to look ratios of sines squared and determine the lattice in question: http://home.hiram.edu/physics/PHYS340/Debye_Scherrer.pdf [Broken] . I couldn't find the correct lattice and therefore the correct lattice constant.

Last edited by a moderator: May 5, 2017
2. Sep 6, 2015

### Must_learn

In case someone needs the answer to Myers Question 3.5 which is this question here I'll write down the steps to follow:
First of all notice that the angles given are diffraction angles. So they are 2θ and not θ
Next step is to find sinθ and then find d from there using λ/2sinθ
from there on it's simply matching hkl values to find an a2
It will come out to be a simple cubic lattice of lattice constant about 2 angstrom
the method of using the average volume then becomes simple by equating a3 to (4/3) π r3
This will give a slightly larger value of diameter.

I hope this helps :)