For first-order (111) diffraction at the stated wavelength, calculate the scattering angle 2theta for each supplied material. Which has the higher-angle reflection 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 angles90 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.
silicon S0006: a=5.43070 angstrom. Row / element / fractional x,y,z:
1 Si 0 0 0
2 Si 0 1/2 1/2
3 Si 1/4 1/4 1/4
4 Si 1/4 3/4 3/4
5 Si 1/2 0 1/2
6 Si 1/2 1/2 0
7 Si 3/4 1/4 3/4
8 Si 3/4 3/4 1/4

diamond S0007: a=3.56679 angstrom. Row / element / fractional x,y,z:
1 C 0 0 0
2 C 0 1/2 1/2
3 C 1/4 1/4 1/4
4 C 1/4 3/4 3/4
5 C 1/2 0 1/2
6 C 1/2 1/2 0
7 C 3/4 1/4 3/4
8 C 3/4 3/4 1/4

Assume ideal kinematic diffraction, lambda=0.15406 nm, n=1 and a nonzero (111) structure factor for each supplied basis. Use 2 d sin(theta)=n lambda and obtain d111 from the cubic geometry. 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.

Attachment S0006:
8
Coordinates in angstrom; atoms numbered from 1.
Si 0.00000000 0.00000000 0.00000000
Si 0.00000000 2.71535000 2.71535000
Si 1.35767500 1.35767500 1.35767500
Si 1.35767500 4.07302500 4.07302500
Si 2.71535000 0.00000000 2.71535000
Si 2.71535000 2.71535000 0.00000000
Si 4.07302500 1.35767500 4.07302500
Si 4.07302500 4.07302500 1.35767500


Attachment S0007:
8
Coordinates in angstrom; atoms numbered from 1.
C 0.00000000 0.00000000 0.00000000
C 0.00000000 1.78339500 1.78339500
C 0.89169750 0.89169750 0.89169750
C 0.89169750 2.67509250 2.67509250
C 1.78339500 0.00000000 1.78339500
C 1.78339500 1.78339500 0.00000000
C 2.67509250 0.89169750 2.67509250
C 2.67509250 2.67509250 0.89169750