The mineral garnet belongs to the isometric crystal system, and the shape of its

Question

The mineral garnet belongs to the isometric crystal system, and the shape of its unit cell is a cube. The length of the a crystallographic axis is 11.535 A. (25,000 stacked unit cells of garnet are about as thick as a strand of hair.) What are the lengths of the b and c axes of garnet? Interplanar spacings (denoted as d_hkl) are calculated as the shortest distance from the origin of a unit cell to the Miller plane of interest. This shortest distance is determined as the length of a perpendicular line from the origin to the Miller plane. You may find that using graph paper and a pencil to draw the outlines of the garnet unit cell will help you visualize the planes in order to answer the questions below. What is the interplanar spacing for the (100) plane of garnet? What are the values of: From your answers above, calculate the values of 20 for the (100) and the (110) planes of garnet using Bragg's Law for Cu Ka X-rays (lambda = 1.54A). Determine the density of the garnet endmember pyrope (Mg_3Al_2Si_3O_12) using the unit cell dimensions given above. Determine the unit cell volume in A^3. Each unit cell of pyrope contains 8 formula units of Mg_3Al_2Si_3O_12. Calculate the volume, in A^3, of 1 mole of pyrope, remembering that 1 mole contains Avogadro's number of formula units. Convert the answer from A^3 to cm^3. Calculate the density (wt/vol) from the volume in (iii) and the weight (in grams) of one mole of Mg_3Al_2Si_3O12.

Explanation / Answer

(a) Since garnet crystallizes in isometric system, a=b=c=11.535A

(b) (i) 11.535A

(ii) d010 = 11.535A

d001 = 11.535A

d020 = 23.07A

d110 = 11.535A

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