Physical Chem Question - Xrays & Crystals

[jbowers9]

[Xray reflection
1. Homework Statement

X-rays of 1.54 angstroms are reflected off copper powder
@
21.65º
25.21º
37.06º
44.96º
47.58º

Find the cubic lattice and the length of an edge of the unit cell.

2. Homework Equations

nλ = 2d sin(Θ) ; the Bragg equation

3. The Attempt at a Solution

The cubic latice is face centered at d110? Because it has 5 planes of reflection?
I tried plotting sin(Θ) vs. n to get the slope and calculate a, but it doesn't seem right?
How do I find the length of an edge of the unit cell and what is the cubic lattice?

 

[chemisttree]

Why don't you use sin\theta_{hkl} = (0.5\lambda/a)(h^2+k^2+l^2)^{0.5}

or
sin^2\theta_{hkl} = (0.5\lambda/a)^2(h^2+k^2+l^2)


I believe that is another form of the Bragg condition.

Is that any help?

 

[jbowers9]

h,k,l

Using this other Bragg equation, what would the representative indices be then for each reflected plane. I'm not sure of the geometry of the lattice in the first place.

 

[jbowers9]

h,k,l

Is it {1,1,0},{1,2,0},{1,3,0},{1,4,0},{1,5,0}?
Or {1,1,0},{1,1,1},{1,1,2},{1,1,3},{1,1,4}?
This is using the "assumption" that the lattice is in fact a face centered cubic, 'cause the xray pics in the text show 5 planes of reflection for d110, and that's a face centered cubic.
Neither of the plots are particularly linear either.

 

[chemisttree]

Your OP referred to a "cubic lattice", yes? h,k,l refers to the Miller indices.

The allowed values of h²+k²+l² are:

hkl h²+k²+l²
100 1
110 2
111 3
200 4
210 5
211 6
220 8
300 9
221 9
310 10

These are multiples of ((0.5\lambda/a)^2)

For your plot, are you using sin^2\theta? Are you also using (0.5\lambda/a)^2?

 

[jbowers9]

Miller Indices

So then the Miller Indices would be {1,1,0},{2,2,0}, etc?
How, given only the five angle measurements, are you supposed to infer - discern - the lattice structure? I am ASSUMING that if I "guess" the structure or indices of the first angle measurement, the remainder are just increments along the appropriate axis?

 

[chemisttree]

You have a list of \theta. Convert them to something like 100sin^2\theta. Examine the list again and look for the common difference (a multiple of (0.5\lambda/a)^2.