Calculate the distance between two cleaved crystals

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SUMMARY

The discussion centers on calculating the distance between two cleaved atomic planes in a crystalline solid, specifically when cleaving along a face diagonal. The side length of the cube, denoted as L, is 0.200 nm. The distance d between the atomic planes is not equal to L; instead, it is determined using trigonometric relationships due to the 45-degree angle formed by the cleaving lines. Understanding the geometry of the crystal structure is essential for solving this problem.

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Jay Macarus
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Hey guys, can't seem to make sense of this question from phys. It goes..

"A crystalline solid consists of atoms stacked up in a repeating lattice structure. Consider a crystal as shown in Figure a. The atoms reside at the corners of 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 shown in Figure b. Calculate the spacing d between two adjacent atomic planes that separate when the crystal cleaves."

1-p-007.gif


I considered using the visual representation from the figure, but I'm sure I'm just overlooking a simple solution. I'm not honestly sure what its looking for me to do here.
Thanks for the help!
-Jay
 

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It's all in diagram a. What is the relationship between L and d?
 
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haruspex said:
It's all in diagram a. What is the relationship between L and d?
I took another look at it and realized I was interpreting the diagram completely wrong after you said that haha. I missed that length "d" was denoted as the distance between the two atoms, not the width of the diagonal like figure b vaguely suggests. Regardless, are "d" and "L" the same distance? I still feel bit foggy..
Thanks for the time, and help!
-Jay
 
Jay Macarus said:
are "d" and "L" the same distance?
No.
d is the distance between two black lines in the diagram. What angle do those lines make to the vertical?
 
haruspex said:
No.
d is the distance between two black lines in the diagram. What angle do those lines make to the vertical?
It looks like that may be a 45 degree angle to the vertical. Is this involving a trig ratio to find the distance "d" using "L" ?
 
Jay Macarus said:
It looks like that may be a 45 degree angle to the vertical. Is this involving a trig ratio to find the distance "d" using "L" ?
Yes and yes. It does not merely look like 45 degrees. You can see that the sloping black lines are supposed to pass through the centres of spheres. Four such centres in a cluster would form a square, and the black lines run down diagonals.
 
Ahhh that makes sense, it's nice to know that kind of thinking is legitimate. Thanks for the help!
 

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