An X-ray diffraction laboratory is analyzing the mineral andalusite (Al₂SiO₅). Powder diffraction of andalusite is being done while using a heating stage to heat the sample. Powder patterns are collected for andalusite at room temperature (25^oC), as well as at 400, 600, and 800 ^oC.

1) It is observed that the XRD powder pattern for andalusite changes as temperature increases. Using the Bragg equation (assuming n = 1) and that Cu K_α radiation was used (where λ = 1.541 Å): What is the room temperature d-spacing for the (200) peak at 2θ = 22.810^o ?

Please find out to 3 decimal places.
 
2) Using the same experimental conditions as above, find out the d-spacing for the (200) peak at 400 ^oC, where 2θ = 22.710^o; at 600 ^oC, where 2θ = 22.640^o; and at 800 ^oC, where 2θ = 22.580^o. Please find out to 3 decimal places.
 
3) What is happening to the a₀ dimension of the unit cell of the andalusite crystal structure, when it is being heated? Plot the a₀ (a-axis) unit cell dimension  (to 3 decimal places)  versus temperature (^oC).
a₀ = 2 * d₍₂₀₀₎

Figure: C-axis projection of the unit cell of the andalusite structure. The unit cell boundary is drawn as thick lines.