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Bragg equation-room temperature d-spacing

An X-ray diffraction laboratory is analyzing the mineral andalusite (Al_{2}SiO_{5}). 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^{o}C), as well as at 400, 600, and 800 ^{o}C.

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 calculate to 3 decimal places.

2) Using the same experimental conditions as above, calculate the d-spacing for the (200) peak at 400 ^{o}C, where 2θ = 22.710^{o}; at 600 ^{o}C, where 2θ = 22.640^{o}; and at 800 ^{o}C, where 2θ = 22.580^{o}. Please calculate to 3 decimal places.

3) What is happening to the a_{0} dimension of the unit cell of the andalusite crystal structure, when it is being heated? Plot the a_{0} (a-axis) unit cell dimension (to 3 decimal places) versus temperature (^{o}C).

a_{0} = 2 * d_{(200)}

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

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