How Do You Calculate Atomic Plane Spacing in a Cleaved Crystal?

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To calculate atomic plane spacing in a cleaved crystal, one can use the Pythagorean theorem, especially when analyzing the geometry of the crystal structure. The problem involves a crystalline solid with atoms arranged in a cubic lattice with a side length of 0.200 nm. When the crystal cleaves along a face diagonal, the spacing between adjacent atomic planes can be determined. The calculated spacing, or distance d, between these planes is found to be 0.141 nm. Understanding the application of the Pythagorean theorem simplifies the problem significantly.
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I just had my first college physics class today, and already I'm stuck on the first problem. I already had physics in HS and I expected I wouldn't have that much trouble in college. So here is a question that I have no clue how to answer.

A crystalline solid consists of atoms stacked up in a repeating lattice structure. Consider a crystal as shown in figure p1. The atoms reside at the corners of the cubes of side L = 0.200 nm. One piece of evidence for the regular arrangement of atoms comes from the flat surfaces along which a crystal separates, or cleaves, when it is broken. Suppose this crystal cleaves along a face diagonal as in p2. Calculate the spacing d between two adjacent atomic planes that separate when the crystal cleaves.

(the pictures are in 3d)

OOOOOOOO
OOOOOOOO
OOOOOOOO
l<-L->l \d\



OO OOOOOO
OOO OOOOO
OOOO OOOO



the answer is .141 nm

so if anyone would help me out with this i would greatly appreciate it
 
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bang911 said:
A crystalline solid consists of atoms stacked up in a repeating lattice structure. Consider a crystal as shown in figure p1. The atoms reside at the corners of the cubes of side L = 0.200 nm. One piece of evidence for the regular arrangement of atoms comes from the flat surfaces along which a crystal separates, or cleaves, when it is broken. Suppose this crystal cleaves along a face diagonal as in p2. Calculate the spacing d between two adjacent atomic planes that separate when the crystal cleaves.

(the pictures are in 3d)

Well, maybe my picture helps.

ehild
 
Last edited:
Yeah, that picture is helpful.
 
Just use the Pythagorean theorem :cool:
 
Ya I had no clue how the pythagorean theorm was to be used when i read the problem. Thanks for the post and that nice diagram though. Doesn't seem tough any more. :cool:
 
bang911 said:
Ya I had no clue how the pythagorean theorm was to be used when i read the problem. Thanks for the post and that nice diagram though. Doesn't seem tough any more. :cool:

It's a pleasure ... :smile:

ehild
 
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