What Is the Angle Between the (111) and (1̅10) Planes in a Cubic Lattice?

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SUMMARY

The angle between the (111) and (1̅10) planes in a cubic lattice can be calculated using the normals to these planes. The normal vector for the (111) plane is (1, 1, 1) and for the (1̅10) plane is (1, -1, 0). By applying the dot product formula, the angle is determined to be approximately 109.47 degrees. This calculation is essential for understanding crystal structures and their properties in materials science.

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Homework Statement


Indicate the (111) and ([11]0) ([11] has an over line, so is negative, don't know how to do on forums!) planes in a cubic lattice in a diagram, then calculate the angle between them.


The Attempt at a Solution


I think I have drawn this right (see attatchment), but I am not sure what angle it is referring to.

I would guess it is 90 degrees (in red), but I doubt I would be asked this, maybe the other angle (purple), could someone give any thoughts?

Also if my drawing is wrong, let me know! I wasn't 100% sure about the negative (110)
 

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Take the angle between the normals to the planes. It will eliminate ambiguity and it will be much easier. You should know what vector is normal to the plan (h k l) if you studied reciprocal lattice.
 

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