Bragg Diffraction: Axes Length for FeO, CoO, NiO

[broegger]

Hi,

In the solid form FeO, CoO and NiO all has the NaCl-structure (simple cubic). In a series of diffraction experiments with x-rays ($$\lambda = 0.15406~\text{nm}$$) one found reflexes from the (111), (200) and (220)-planes with the following $$\theta$$-values ($$\theta$$ is the angle in Bragg's law, $$2d\sin\theta=\lambda$$):

FeO: 18.04 20.95 30.28
CoO: 18.26 21.20 30.77
NiO: 18.63 21.64 31.45

The first number is the angle corresponding to the reflection from the (111)-plane, the second number corresponds to reflection from the (200)-plane and the third from the (220)-plane.

Question: What are the axis length for the three unit cells? Any hints?

 

[StatusX]

Well, you can use Bragg's law to solve for the d for each angle. Now you need to know how the spacing between certain lattice planes, d, is related to the lattice constant (length of a side of the cubic cell). For example, for the (100) planes, the spacing is just a, for (110), it is a*sqrt(2), and so on.

 

[Gokul43201]

What is the general formula relating the interplanar spacing (of some hkl family) to the lattice parameter in a cubic structure ?

 

[broegger]

What is the general formula relating the interplanar spacing (of some hkl family) to the lattice parameter in a cubic structure ?

I don't know, but man, I'd like to know that formula :!) I'm having some trouble visualizing this, to say the least.

 

[Gokul43201]

I'm sure it's in the text : $$d = \frac{a}{\sqrt{h^2+k^2+l^2}}$$

 

[broegger]

Thank you very much. My book is Descriptive Inorganic Chemistry by Canham and Overton and I can't find that formula in it.