For first-order (111) and (200) diffraction at the stated wavelength, calculate the scattering angle 2theta for the supplied MgO structure. Which reflection is at the higher angle and what is the angular difference? Explain the direction of the shift using the structural spacing.

Use the supplied periodic conventional cubic cell, not an isolated XYZ cluster. Cartesian XYZ coordinates are in angstrom; 1 nm=10 angstrom. XYZ atom rows start at one after the two header lines. Fractional positions below are exact; each listed basis atom has occupancy 1. Cell vectors are (a,0,0),(0,a,0),(0,0,a); all angles 90 degrees. Crystal images are r_j+a*(n_x,n_y,n_z) for integer n. No relaxation, defects, thermal motion or finite crystallite envelope is supplied. 
MgO S0010: a=4.21700 angstrom. Row / element / fractional x,y,z:
1 Mg 0 0 0
2 Mg 0 1/2 1/2
3 Mg 1/2 0 1/2
4 Mg 1/2 1/2 0
5 O 0 0 1/2
6 O 0 1/2 0
7 O 1/2 0 0
8 O 1/2 1/2 1/2

Assume ideal kinematic diffraction, lambda=0.15406 nm, n=1 and a nonzero (111) and (200) structure factor for this basis (not asked to be shown here). Use 2 d sin(theta)=n lambda and obtain d from d_hkl=a/sqrt(h^2+k^2+l^2). Theta is the incident-beam/plane angle; the requested detector scattering angle is 2theta. Report degrees to two decimals. Do not predict intensities, line widths, refractive or instrumental corrections.

Attachments:
S0010: item-0003-asset-1.xyz