Interplanar Distance: Obtain Expression w/ Lattice Parameter

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Discussion Overview

The discussion revolves around deriving an expression for interplanar distance in terms of lattice parameters, focusing on different lattice geometries, particularly orthogonal lattices like cubic lattices.

Discussion Character

  • Exploratory, Technical explanation, Homework-related

Main Points Raised

  • One participant requests assistance in deriving an expression for interplanar distance related to lattice parameters.
  • Another participant suggests that deriving this expression is straightforward for orthogonal lattices, specifically cubic lattices, and mentions a mathematical relationship involving the angles made by a line through the origin to the axes.
  • A different participant asks for a sketch of the [110] and [222] planes in a cubic lattice.
  • Another participant questions the complexity of the task, implying that it should be easy to address.

Areas of Agreement / Disagreement

There is no consensus on the difficulty of the task; some participants find it straightforward while others seek clarification and assistance.

Contextual Notes

The discussion does not clarify the specific mathematical steps required for non-orthogonal lattices or the implications of the Miller Indices on the interplanar distance.

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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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.
 
sketch the [110],[222] planes in a cube?
 
What's the problem there ? It's pretty straightforward.
 

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