# 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?

Homework Helper
Gold Member
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?

Last edited:
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.

Homework Helper
Gold Member
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 $$(0.5\lambda/a)^2$$?

Last edited:
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?

#### Attachments

• xray reflection plots.xls
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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 $$(0.5\lambda/a)^2$$.