How Do I Calculate Experimental Error in X-ray Diffraction?

[Lemenks]

Homework Statement

I am writing a lab report for an X-ray diffraction. I have been attempting to come up with an equation for the error using formulas some people from college gave me and also some I found on wikipedia but I am quite sure I am doing it wrong. The only variable is the angle where the maximum intensities are found. I am using Bragg's law to calculate the spacing between the atoms.

Homework Equations

D = (N*wavelength)/(2*sin(x))

As there is no error in N, wavelength, or "2", we can let that equal A.

D = A/sin(x)

Some equations I was given:

Z = aX
dZ = adX

Z = X^a
dZ/z = |a|dx/x

Z = SinX
dZ = dX CosX

The Attempt at a Solution

D = Z = A/sin(x) = A (sin(x))^-1 = A f(y)^-1

I have tried loads of ways of calculating this but I keep getting silly answers. Any help, ideas or links would be really appreciated.

 

[vela]

Take it one step at a time. You might find it helpful to introduce new variables. For example, let w=1/sin(x). Then you have $D = Aw$, so applying your first rule, you have $\delta D = A \delta w$. (I'm using deltas instead of d because dD looks weird.) Now your job is to find $\delta w$. If you let $v=\sin x$, then $w=1/v = v^{-1}$. Using the second rule, you can find $\delta w$ in terms of $\delta v$. Then you need to find $\delta v$ in terms of $\delta x$, and then put it all together.

 

[Lemenks]

Hey thanks for the reply, it is very concise and logical, I actually tried that but assumed I must have made a mistake as the value I was getting for the error seemed to large ~80%.

The final equation I have is:

dD = A (dx cosx)/(sinx)^2

This equation seems to give a value for error of about 80%. x ranges from 3 to 35 and dx was 0.1. ie the beam angle ranged from 3 to 35 degree in 0.1 degree steps.

 

[vela]

You need to use radians, not degrees. That's probably where the issue lies.