1. The problem statement, all variables and given/known data A two-dimensional rectangular crystal has a unit cell with sides a 6.28Å and b 3.14Å. A beam of monochromatic neutrons of wavelength 5.0 Å is used to examine the crystal. Using either the Laue condition for diffraction or Bragg's Law, determine whether it would be possible to observe the following reflections: (11), (20) and (02). 2. Relevant equations Laue conditions: K[itex]\cdot[/itex]a=2πh K[itex]\cdot[/itex]b=2πk K[itex]\cdot[/itex]c=2πl for wavevector K, lattice vectors a,b,c and integers h,k,l. Bragg's law: 2dsinθ=nλ for lattice plane spacing d, Bragg angle θ, scattering order n and wavelength λ. 3. The attempt at a solution Reciprocal space lattice is rectangular with lengths a* = 2π/a, b*=2π/b. Incoming wavevector k has magnitude 2π/5 = 1.26Å-1. Laue conditions: Direction (11) → K=a*+b* K[itex]\cdot[/itex]a=a*[itex]\cdot[/itex]a=2π K[itex]\cdot[/itex]b=b*[itex]\cdot[/itex]b=2π both are integer multiples of 2π and so (11) reflections are allowed. Direction (20) → K=2a* K[itex]\cdot[/itex]a=4π K[itex]\cdot[/itex]b=0 allowed again for same reasons. Direction (02) → K=2b* K[itex]\cdot[/itex]a=0 K[itex]\cdot[/itex]b=4π allowed. Bragg's law: (11) → d = ((h/a)2+(k/b)2)-1/2 = ((1/6.28)2+(1/3.14)2)-1/2 ≈ 2π/√5 (assuming a = 2π and b = π) (11) reflection has highest common factor 1 so it is an n=1 reflection: Bragg's law gives 1*5=2*(2π/√5)sinθ rearrangement gives sinθ = 0.88970... which is certainly an allowed value for sinθ so I conclude that it is an allowed reflection. (20) is an n=2 reflection, d = a/h = a/2 ≈ π Bragg's law gives sinθ = 5/π > 1 which is not valid so the reflection cannot happen. (02) is also n=2, d = b/k ≈ π/2 Bragg's law gives sinθ=3.18 and so it is not an allowed reflection. I'm not too confident in the way I've gone about solving this problem by either method and the contradictory conclusions definitely show that at least one of them is wrong. Could anyone give some hints as to where I'm going wrong? Thanks!