Bragg Diffraction: Axes Length for FeO, CoO, NiO

In summary, the conversation discusses the NaCl-structure of FeO, CoO, and NiO in their solid forms. The three compounds have reflexes from the (111), (200), and (220)-planes with corresponding \theta-values. The conversation also mentions using Bragg's law to solve for the d values and the relationship between lattice spacing and lattice parameter in a cubic structure. The formula for this relationship is d = \frac{a}{\sqrt{h^2+k^2+l^2}}, as stated in the text "Descriptive Inorganic Chemistry" by Canham and Overton.
  • #1
broegger
257
0
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 ([tex]\lambda = 0.15406~\text{nm}[/tex]) one found reflexes from the (111), (200) and (220)-planes with the following [tex]\theta[/tex]-values ([tex]\theta[/tex] is the angle in Bragg's law, [tex]2d\sin\theta=\lambda[/tex]):

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?
 
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  • #2
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.
 
  • #3
What is the general formula relating the interplanar spacing (of some hkl family) to the lattice parameter in a cubic structure ?
 
  • #4
Gokul43201 said:
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.
 
  • #5
I'm sure it's in the text : [tex]d = \frac{a}{\sqrt{h^2+k^2+l^2}} [/tex]
 
  • #6
Thank you very much. My book is Descriptive Inorganic Chemistry by Canham and Overton and I can't find that formula in it.
 

What is Bragg Diffraction?

Bragg Diffraction is a phenomenon in which x-rays or other electromagnetic radiation are diffracted by the regular atomic structure of a crystal, resulting in a distinct pattern of diffraction spots.

How is Bragg Diffraction used in the study of crystal structures?

Bragg Diffraction is used to determine the spacing between atoms in a crystal lattice, which can provide valuable information about the structure and composition of a material.

What are the axes lengths for FeO, CoO, and NiO?

The axes lengths for FeO, CoO, and NiO are dependent on the crystal system and lattice parameters of each material. The axes lengths can be calculated using the Bragg equation and the diffraction angles obtained from experiments.

What is the significance of the axes lengths in Bragg Diffraction?

The axes lengths in Bragg Diffraction provide important information about the arrangement of atoms within a crystal structure. By analyzing the diffraction pattern and calculating the axes lengths, scientists can determine the crystal system, lattice parameters, and composition of a material.

How does the axes length for FeO, CoO, and NiO differ?

The axes lengths for FeO, CoO, and NiO may differ due to variations in the crystal system, lattice parameters, and composition of each material. For example, FeO and CoO have a similar crystal structure (rock salt) but different lattice parameters, resulting in slightly different axes lengths.

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