What Does d Represent in Interatomic Spacing Diagrams?

Idan9988 · May 21, 2023

Figure P1.7 showing a cubic lattice of spheres with edge length L, a face diagonal cut through it, and the two halves separated into parts a and b, with the spacing d marked between the planes.

according to the figure, it's look like d is the distance between the center of two adjacent atoms, and so it should be simply L. I don't understand what d represents in the figure.
that's the solution:

Printed solution text, problem P1.7: the diagonal plane spacing is half the diagonal distance between atoms, giving (1/2)sqrt(L^2 + L^2) = 0.141 nm for L = 0.200 nm.

Even if d is half the distance between two adjacent atoms that positioned diagonally (I don't see why), is came out to me completely different expression:

Handwritten sketch on grid paper: a square array of circles becomes a shifted arrangement, with a diagonal arrow marked d, a spacing L and the expression d = L√2 − 2·L/2 = L√2 − L.

kuruman · May 21, 2023

If the interatomic separation is ##L## (see figure below) what is the separation between the planes indicated by the solid black lines? That is how you identify what you are being asked. Note that the figure shows a different cleavage plane from the one given to you but the idea is the same.

Grid of blue circles arranged in columns and rows representing atoms, with two parallel black lines slanting through them and a horizontal arrow below labelled L marking the spacing between adjacent atoms in a row.

Idan9988 · May 21, 2023

but if the interatomic separation is L, and what I'm being asked about is the distance between those parallel lines, isn't d should be equal simply to L?

Idan9988 · May 21, 2023

Hand-annotated grid of blue circles in rows and columns, with two black lines running down through columns, a red loop around the top-left group, a red arrow pointing diagonally up-right, and red handwritten word 'point' at lower right.

according to the answer, d is half the distance between two diagonally positioned atoms, which in the figure is the line segment between one atom to the red arrow. I don't see why this segment is the answer to what I'm being asked about?

Lnewqban · May 21, 2023

Idan9988 said:

according to the answer, d is half the distance between two diagonally positioned atoms, which in the figure is the line segment between one atom to the red arrow. I don't see why this segment is the answer to what I'm being asked about?

$Diagram of a square grid of green circles on black, marked as atoms, with spacing L=0.20 nm. A dashed diagonal line is labelled atomic plane of fracture, and the perpendicular spacing between diagonal rows is d=0.14 nm. A diagonal distance of 0.28 nm is also marked.$

kuruman · May 21, 2023

Idan9988 said:

but if the interatomic separation is L, and what I'm being asked about is the distance between those parallel lines, isn't d should be equal simply to L?

Draw a line that is perpendicular to the two parallel lines. The distance ##d## between them is the segment of the perpendicular contained between the two.

What Does d Represent in Interatomic Spacing Diagrams?

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