(Solution) - Consider a two dimensional square crystal structure such as one -(2025 Original AI-Free Solution)

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Consider a two-dimensional square crystal structure, such as one side of the structure shown in Figure a. The largest inter planar spacing of reflecting planes are the unit cell size as. Calculate and sketch the
(a) Second largest,
(b) Third largest,
(c) Fourth largest,
(d) Fifth largest, and
(e) Sixth largest inter planar spacing.
(f) Show that your results in (a) through (e) Are consistent with the general formula d= a0/ ?h2 + k2 where h and k are relatively prime integers (they have no common factor other than unity).