Powder X-ray Diffraction

Welcome!

X-Ray Diffraction Lab:

ERRATA: The particle-in-a-box formula has been changed from pre-lab and spreadsheet (now updated) --- orginally it was En=h_bar^2pi^2 / 2*3me*a^2 BUT it is more accurate to use En=(h_bar^2pi^2 / 2*me*a^2 )*3 -- a factor of 9 difference -- from nx=ny=nz=1.
On Tues. Apr. 17 I will be in Lab from 1:30 -2:15 to give make-up x-ray prelab -- if you need extra help please show up around 2pm and will stay to answer questions.

Hints on KCl -- I will accept analysis of KCl as either FCC, simple cubic or both -- providing you can back it up -- to agree with most literature values you'll need to show how KCl can be FCC. KCl is tricky because it is really a FCC that masks itself as a simple cubic because K+ and Cl- are isoelectronic. Also remember to consider all possible peak differences, not just adjacent ones.

NEW! Here are some quick reference websites you may find useful.

About x-ray production: X-ray 1, X-ray 2

Some short simple sites about PXRD: PXRD 1, PXRD 2

For estimating your crystallite size you are welcome to look up and use the Scherrer equation (you don't have to use the Scherrer equation as it is not really very accurate for our crystallite size). Otherwise just come up with a ballpark estimate from literature about the size of cystallites needed for powder x-ray diffraction.
NEW! To guide you in your analysis I have a .pdf of an Excel spreadsheet I made to analyze the structure of NaCl. It also should guide you on which parameters I am expecting you to find. NaCl example

Urea has tetragonal structure and is challenging (rec. you do it last). Here are a few notes to help you:

There is an error in lab manual formula 4.6 for tetragonal structures. The factor of a^2 in the denominator out-front SHOULD NOT be there.

You really only need to analyze the first 5-6 peaks of your urea data.

"a" and "c" for urea are found by trial and error:

Set l=0 to start, assume h=k=1 for the first peak and use the correct form of equation 4.6 to solve for "a". Then use the theta values for the first 5-6 peaks to make a table of possible "a" values (you will need to assign h and k values to the other peaks based on the rules you used for KCl/KBr).
If you calculate similar "a" values from different peaks, you can correctly assume this must be your true "a" value. Calculate your error in "a".
To find "c" use the correct form of equation 4.6 again, subbing in your newly found "a" value. For each of the first three theta values find possible "c's" for simple Miller indices (e.g. (001), (011), (111), etc). You should find you get a similar "c" value calculated from different theta/Miller indice values. It is safe to assume that this is the correct "c" value.
Calculate your tetragonal cell volume using V= a^2 * c. Finding Miller indices for urea peaks is not required (just find info about the unit cell from knowledge of a and c).

This is a reminder from pre-lab of a modification to the procedure (also now in instructions by diffractometer). For KCl only you need to do an additional scan from about 55 to 90 to degrees, you will later need this scan to differentiate your KBr and KCl crystal structures.

Here I will post suggestions to help you sucessfully navigate the x-ray diffraction lab. Like most Group III experiments we will introduce new concepts and theory you might not have covered in previous courses. As such you may have to rely heavily on outside resources and the GSI to understand some the key concepts of this lab. Prof. Shank will survey some the basics of x-ray diffraction during the second week of April.

In order to gain a better understanding of Miller indices the following handout may be helpful: Notes

The following are some helpful background documents:

Introduction to X-Ray Powder Diffraction

Some background info on our diffractometer

Crystallography - theoretical introduction

Short intro to crystal structures

Lots of random links and help concerning x-ray induced color or F-centers in halide salts:

Some articles about urea structure: