Interplanar Distance: Obtain Expression w/ Lattice Parameter

[imran]

please help me in solving this q

obtain an expression for interplanar distance in terms of lattice parameter?

 

[Gokul43201]

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 :

cos^2 \alpha + cos ^2 \beta + cos ^2 \gamma = 1

where \alpha,~\beta,~\gamma 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.

 

[imran]

sketch the [110],[222] planes in a cube?

 

[Gokul43201]

What's the problem there ? It's pretty straightforward.