Question

7. Interplanar spacing. Show that, for an orthogonal lattice with lattice constants $a_1$, $a_2$, $a_3$, the perpendicular distance between adjacent ($hkl$) planes is $d_{hkl} = \left[ \left( \frac{h}{a_1} \right)^2 + \left( \frac{k}{a_2} \right)^2 + \left( \frac{l}{a_3} \right)^2 \right]^{-1/2}$

          7. Interplanar spacing. Show that, for an orthogonal lattice with lattice constants $a_1$, $a_2$, $a_3$, the perpendicular distance between adjacent ($hkl$) planes is
$d_{hkl} = \left[ \left( \frac{h}{a_1} \right)^2 + \left( \frac{k}{a_2} \right)^2 + \left( \frac{l}{a_3} \right)^2 \right]^{-1/2}$

7. Interplanar spacing. Show that, for an orthogonal lattice with lattice constants a1, a2, a3, the perpendicular distance between adjacent (hkl) planes is
dhkl = [ ( (h)/(a1))^2 + ( (k)/(a2))^2 + ( (l)/(a3))^2 ]^-1/2

Added by Francisco Jose G.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Khoobchandra Agrawal

07/05/2021

Step 1

The formula for interplanar spacing in an orthogonal lattice is given by: dₙₖᵢ = 1 / √((h/a₁)² + (k/a₂)² + (l/a₃)²) where dₙₖᵢ is the interplanar spacing between adjacent (h,k) planes, and a₁, a₂, a₃ are the lattice constants along the x, y, and z directions Show more…

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7. Interplanar spacing. Show that, for an orthogonal lattice with lattice constants a₁, a₂, a₃, the perpendicular distance between adjacent (h,k) planes is 2√(dₙₖᵢ) = 2√(2₁-₁/₂ + 1² + (-1)¹/₂)