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Physical Chem Question - Xrays & Crystals

  • Thread starter jbowers9
  • Start date
  • #1
89
1
[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?
 

Answers and Replies

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

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


I believe that is another form of the Bragg condition.

Is that any help?
 
Last edited:
  • #3
89
1
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.
 
  • #4
89
1
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.
 
  • #5
chemisttree
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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 [tex]((0.5\lambda/a)^2)[/tex]

For your plot, are you using [tex]sin^2\theta[/tex]? Are you also using [tex](0.5\lambda/a)^2[/tex]?
 
Last edited:
  • #6
89
1
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?
 

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  • #7
chemisttree
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You have a list of [tex]\theta[/tex]. Convert them to something like [tex]100sin^2\theta[/tex]. Examine the list again and look for the common difference (a multiple of [tex](0.5\lambda/a)^2[/tex].
 

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