(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Using the powder XRD data below, show that the substance has a face centred cubic structure. (xray lamda = 0.154056 nm)

Peak No.------2(theta)

1 -------------38.06

2 -------------44.24

3 -------------64.34

4 -------------68.77

5 -------------73.07

2. Relevant equations

[tex] 2dsin\theta = n\lambda[/tex]

[tex] d = \frac{a}{\sqrt{N}}[/tex]

[tex] \Delta sin\theta = \left(\frac{\lambda}{4a^{2}}\right)N_{2} - N_{1}[/tex]

[tex] N= h^{2}+k^{2}+l^{2} [/tex]

3. The attempt at a solution

I've worked out sin theta for each sin theta squared and delta sin theta:

Peak------2(theta)------sin theta----sin squared theta---delta sin squared theta

1-----------38.06-------0.32606-------0.10632------------

2-----------44.24-------0.37655-------0.14179------------0.03547

3-----------64.34-------0.53243-------0.28349------------0.1417

4-----------68.77-------0.56475-------0.31894------------0.03545

5-----------73.07-------0.59531-------0.35440------------0.03549

The only example we've covered is with a primitive cubic structure which I almost knew what I was doing(!) and the only advice that the lecturer gave was to "look for the highest common factor of values in the list delta sin squared theta to find [tex]\frac{\lambda}{4a^{2}}[/tex]

I obviously noted that the difference between peak 2 and 3 was the same value as Peak 2 but what I'm meant to do with that information I'm not so sure about!!?

I know that a fcc structure only has N values of 3,4,8,11 etc but really could do with some advice as where to go from here!!?

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# Determine crystal lattice structure from powder XRD

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