Calculate the distance between two cleaved crystals

In summary, Jay found that the distance "d" between two atoms is the distance between the two black lines in the diagram and that the angle between those lines is 45 degrees.
  • #1
Jay Macarus
7
0
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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  • #2
It's all in diagram a. What is the relationship between L and d?
 
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  • #3
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
 
  • #4
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?
 
  • #5
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" ?
 
  • #6
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.
 
  • #7
Ahhh that makes sense, it's nice to know that kind of thinking is legitimate. Thanks for the help!
 

1. How do you calculate the distance between two cleaved crystals?

The distance between two cleaved crystals can be calculated using the Pythagorean theorem, which states that the square of the length of the hypotenuse (the longest side) of a right triangle is equal to the sum of the squares of the lengths of the other two sides. In this case, the two sides represent the distances between the atoms in the two crystals.

2. What is the significance of calculating the distance between two cleaved crystals?

Calculating the distance between two cleaved crystals can provide valuable information about the structural properties of the crystals, such as their lattice parameters and the nature of the crystal bonding. This information can be used to understand the physical and chemical properties of the crystals, as well as their potential applications.

3. Is there a specific formula for calculating the distance between two cleaved crystals?

While there is no specific formula for calculating the distance between two cleaved crystals, the Pythagorean theorem is commonly used in this calculation. However, other mathematical methods and techniques may also be used depending on the specific properties and characteristics of the crystals.

4. Can the distance between two cleaved crystals be measured experimentally?

Yes, the distance between two cleaved crystals can be measured experimentally using techniques such as X-ray diffraction, electron microscopy, and atomic force microscopy. These methods allow for precise measurement of the distance between atoms in the crystals, providing valuable data for further analysis.

5. Are there any challenges or limitations to calculating the distance between two cleaved crystals?

One of the main challenges in calculating the distance between two cleaved crystals is the potential for error due to the complexity of the crystal structure and the presence of defects or impurities. Additionally, the precision of the measurement techniques used can also affect the accuracy of the calculated distance. It is important to carefully consider these factors when interpreting the results of the calculation.

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