Problem Set #4

1. Examine the color three-dimensional representation of a crystal structure (attached). Cations are represented as follows:

Si-polyhedra=dark blue Al-polyhedra=light blue Ca=blue-gray H=pink

Some anions are also shown. All (OH)- groups are represented as yellow spheres. Some oxygens are represented as red spheres.

a) Identify the coordination number of the Si and Al cations. The Ca coordination polyhedra are not represented because they are irregular. Approximately what coordination number or range of coordination numbers would you expect the Ca ion to have?

b) What molecular groups are present?

c) Identify all shared elements among the Si- and Al-polyhedra.

d) To what class of silicates does this mineral belong? What mineral is depicted?

e) Show that the chemical composition of this mineral is identical to anorthite + water. How do you account for the greater density of this mineral as compared with anorthite?

2. The gray-scale image below is a two-dimensional projection onto the a-b plane of the structure of kaolinite. The bases of the Si-tetrahedra are seen as white and light gray triangles; the Al-octahedra are seen beneath in darker gray. Such projections, viewed as two-dimensional patterns, are useful for analyzing the symmetry of crystals.

a) Identify the lattice by drawing lattice points on the image.

b) Identify the unit cell by drawing on the image. Hint: for this mineral, g is very close to 90˚.

c) An analysis of the full three-dimensional symmetry shows that a≠b≠c. To what crystal system does this structure belong?

3. The contents of the unit cell are commonly reported in terms of Z, the number of formula units. Find in your text and write down for each mineral below: the chemical formula, crystal system, lattice parameters, and Z (be careful with compositionally variable minerals)

a) Forsterite

b) Pyrope

c) Enstatite (Note error in text: Z=16, not 8 as written)

d) Beryl

Calculate the density of each mineral from this information (be careful with the hexagonal mineral). Compare your results to the values of specific gravity reported in the text (again, be careful in the case of compositionally variable minerals), discuss the comparison and comment on any differences. In order to compare effectively, you will have to convert your calculated values into useful units!