Q-spacing, Bragg-spacing, D-spacing & Repeat Distances Explained

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Q-spacing, Bragg-spacing, D-spacing, and repeat distance are related concepts in crystallography but are not identical. D-spacing refers to the interplanar distance within a crystal structure. Q-spacing is associated with the length of a reciprocal lattice vector, which is crucial for identifying Bragg peaks when the wave vector of incident radiation aligns with these vectors. Bragg-spacing denotes any distance that maintains translational invariance in a material, leading to the formation of Bragg peaks. In crystalline materials, the Bragg-spacing typically corresponds to the D-spacing. In more complex materials like superalloys, additional Bragg peaks can arise, indicating larger Bragg spacings. The relationship between reciprocal and real lattice vectors varies based on the specific Bravais lattice type involved.
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Could anyone tell me what the difference between Q-spacing Bragg-spacing D-spacing and repeat distance is? I've always thought that they were same, but seemingly not? What is the realtionship, what is Q?

Its keeping me up at night!
 
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d-spacing is simply the interplanar distance in a crystal. In this context, the Q-spacing is the length of a reciprocal lattice vector (you have a Bragg peak when the wave vector of the radiation used matches a reciprocal lattice vector). The Bragg-spacing is any distance over which a system is translationally invariant in some direction, and will hence produce a Bragg peak. So, in a crystal, the bragg spacing will be the d-spacing itself. In an superalloy, you will see an adiitional larger (but weaker) Bragg peak giving rise to an additional Bragg spacing. Likewise, you can have a Bragg spacing for a polymer and even a liquid crystal.

The relationship between reciprocal lattice vectors and real lattice vectors depends on the type of Bravais lattice involved.
 
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