Interplanar Distance: Obtain Expression w/ Lattice Parameter

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In summary, the conversation discusses obtaining an expression for interplanar distance in terms of lattice parameter, specifically for orthogonal lattices such as a cubic lattice. The formula for calculating interplanar distance in this case involves using the angles made by a line through the origin to each of the axes and expanding the cosines in terms of the intercepts on the axes. The conversation also mentions the ease of sketching [110] and [222] planes in a cube.
  • #1
imran
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please help me in solving this q

obtain an expression for interplanar distance in terms of lattice parameter?
 
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  • #2
This is easy to derive for orthogonal lattices such as a cubic lattice, but harder for other geometries. In the case of an orthogonal geometry, you just have to use the fact that :

[tex]cos^2 \alpha + cos ^2 \beta + cos ^2 \gamma = 1 [/tex]

where [itex]\alpha,~\beta,~\gamma [/itex] are the angles made by a line through the origin to each of the axes. In this case, you make this line be the normal to the plane of interest (ie : its length is the interplanar spacing), and expand each of the cosines in terms of the intercepts on the axes, which in turn come from the Miller Indices of the plane.
 
  • #3
sketch the [110],[222] planes in a cube?
 
  • #4
What's the problem there ? It's pretty straightforward.
 

FAQ: Interplanar Distance: Obtain Expression w/ Lattice Parameter

1. What is Interplanar Distance?

Interplanar distance refers to the distance between two parallel planes of atoms or molecules in a crystal lattice. It is an important parameter in materials science as it affects the properties and behavior of materials.

2. How is Interplanar Distance calculated?

Interplanar distance can be calculated using the Bragg Equation, which states that the distance between two planes is equal to the wavelength of the incident X-ray or electron beam divided by twice the sine of the angle of diffraction.

3. What is the relationship between Interplanar Distance and Lattice Parameter?

The lattice parameter is the distance between the lattice points in a crystal structure. The interplanar distance is directly related to the lattice parameter and can be calculated by dividing the lattice parameter by the square root of the sum of the squares of the Miller indices of the planes.

4. How can Interplanar Distance be obtained experimentally?

Interplanar distance can be obtained experimentally through techniques such as X-ray diffraction or electron diffraction. These methods involve shining a beam of X-rays or electrons onto a sample, and the resulting diffraction pattern can be used to calculate the interplanar distance.

5. What factors can affect the Interplanar Distance?

The interplanar distance can be affected by various factors, including temperature, pressure, and the presence of impurities. Changes in these factors can cause the lattice to expand or contract, resulting in a change in the interplanar distance.

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