The d-spacings can be calculated using Bragg's law. For a cubic crystal, all cell dimensions are equal. The reflection indices can be determined by comparing d-spacings to lattice parameters.
When X-rays diffract off crystal planes, the spacing between the planes can be determined using Bragg's law:
d = λ / (2sinθ)
where d is the spacing, λ is the wavelength of the X-ray, and θ is the Bragg angle.
To calculate the d-spacings, we can plug in the given values:
a) For the first reflection, λ = 1.541 nm and θ = 15.55°:
- d = 1.541 nm / (2sin(15.55°)) = 2.847 nm
b) Since the crystal is cubic, all the cell dimensions are equal. Therefore, the cell dimensions are 2.847 nm, 2.847 nm, and 2.847 nm.
c) The reflection indices can be determined by comparing the d-spacings to the lattice parameters. For example, the first reflection corresponds to the (1 1 1) plane, the second reflection corresponds to the (2 0 0) plane, and so on.
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