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Question: 1 the mineral garnet belongs to the isometric crystal system...

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1. 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 Å. (25,000 stacked unit cells of garnet are about as thick as a strand of hair.) (a) What are the lengths of the b and c axes of garnet? (b) Interplanar spacings or d-spacings (denoted as d) 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. i) What is the interplanar spacing for the (100) plane of garnet? ii) What are the values of: doro? doo1? do2o? d110? (c) From your answers above, calculate the values of 20 for the (100) and the (110) planes of garnet using Braggs Law for Cu Ka X-rays (As 1.54A).2. Determine the density of the garnet endmember pyrope (Mg Al,Si,O12) using the unit cell dimensions given above. (a) Determine the unit cell volume in Å. (b) Each unit cell of pyrope contains 8 formula units of Mg,Al,Si,012. Remembering that 1 mole contains Avogadros number of formula units, how many unit cells make up one mole of pyrope? (c) Calculate the volume, in Å3, of 1 mole of pyrope (d) Convert the answer from Å to cm. Be careful with your unit conversions! As, of 1 mole of pyrope (e) Calculate the mass in grams of 1 mole of pyrope by summing the atomic masses of its elemental components. You will need to use a periodic table in order to do this. (f) Calculate the density (in g/cm2) of pyrope from the volume you calculated in (d) and the mass you calculated in (e). Once you have done this, perform a reality check on your answer. Does it make sense if you compare it to the range of Specific Gravity known for garnet? If not, then you have done something wrong. Go back and check your unit conversions.

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